Implementation, benchmarking, and representative applications of the new FDE-ADC(3) method for describing environmental effects on excited states as a combination of frozen density embedding (FDE) and the algebraic-diagrammatic construction scheme for the polarization propagator of third order (ADC(3)) are presented. Results of FDE-ADC(3) calculations are validated with respect to supersystem calculations on test systems with varying molecule–environment interaction strengths from dispersion up to multiple hydrogen bonds. The overall deviation compared to the supersystem calculations is as small as 0.029 eV for excitation energies, which is even smaller than the intrinsic error of ADC(3). The dependence of the accuracy on the choice of method and functional for the calculation of the environment and the nonelectrostatic part of the system–environment interaction is evaluated. In three representative examples, the FDE-ADC method is applied to investigate larger systems and to analyze excited state properties using visualization of embedded densities and orbitals.

Terpyridine derivatives are of great interest due to their unique photophysical properties when used as antennas in metallic complexes. Several experimental and theoretical studies indicate strong charge-transfer character of the lowest electronic excited state, which could be exploited for predicting fluorescence quantum yields from the magnitude of the charge separation induced by electronic transitions. Focusing on substituted 4′-phenyl-2,2′:6′2′′-terpyridyl, we report on two measures of the charge separation obtained from high-level calculations in ground and excited states (length of the change of the dipole moment and the electron–hole distance). Our refined model confirms that the fluorescence quantum yield shows a global S-shape dependence on the magnitude of the charge separation, which can be quantified either by the change in dipole moments between the ground and excited states or by the associated charge–hole distances. This approach provides a remarkable tool for the molecular design of a fluorescent polyaromatic antenna.

The combination of Frozen Density Embedding Theory (FDET) and the Algebraic Diagrammatic Construction (ADC) scheme for the polarization propagator for describing environmental effects on electronically excited states is presented. Two different ways of interfacing and expressing the so-called embedding operator are introduced. The resulting excited states are compared with supermolecular calculations of the total system at the ADC(2) level of theory. Molecular test systems were chosen to investigate molecule–environment interactions of varying strength from dispersion interaction up to multiple hydrogen bonds. The overall difference between the supermolecular and the FDE-ADC calculations in excitation energies is lower than 0.09 eV (max) and 0.032 eV in average, which is well below the intrinsic error of the ADC(2) method itself.

The cooperativity index in a metallopolymer can be thought of as an estimation of the level of available water in nature. In a river, the water molecules can only feed immediate surroundings. Those in an aqueduct possess sufficient potential energy to extend this beneficial effect to wider areas. Twenty centuries ago, the Romans exploited this concept for extending their settlement in Western Europe. A reliable access to allosteric cooperativity indexes might push host–guest chemistry toward unexplored areas. More information can be found in the Full Paper by C. Piguet et al. (DOI: 10.1002/chem.201600857).

 

The basic concept of allosteric cooperativity used in biology, chemistry and physics states that any change in the intermolecular host–guest interactions operating in multisite receptors can be assigned to intersite interactions. Using lanthanide metals as guests and linear multi-tridentate linear oligomers of variable lengths and geometries as hosts, this work shows that the quantitative modeling of metal loadings requires the consideration of a novel phenomenon originating from solvation processes. It stepwise modulates the intrinsic affinity of each isolated site in multisite receptors, and this without resorting to allosteric cooperativity. An easy-to-handle additive model predicts a negative power law dependence of the intrinsic affinity on the length of the linear metallopolymer. Applied to lanthanidopolymers, the latter common analysis overestimates cooperativity factors by more than two orders of magnitude.

Besides molecular electron densities obtained within the Born–Oppenheimer approximation (�_B(r)) to represent the environment, the ensemble averaged density (〈�_B〉(r)) is also admissible in frozen-density embedding theory (FDET) [Wesolowski, Phys. Rev. A, 2008, 77, 12054]. This makes it possible to introduce an approximation in the evaluation of the solvent effect on quantum mechanical observables consisting of replacing the ensemble averaged observable by the observable evaluated at ensemble averaged �_B(r). This approximation is shown to affect negligibly the solvatochromic shift in the absorption of hydrated acetone. The proposed model provides a continuum type of representation of the solvent, which reflects nevertheless its local structure, and it is to be applied as a post-simulation analysis tool in atomistic level simulations

In numerical simulations, based on frozen-density embedding theory, the independent variables describing the total system are the embedded wave function (Ψ_A) and the density  �_B(r)  representing the environment. Due to inhomogeneity of the non-electrostatic component of the total energy:  E^nad_xcT[�_A,�_B] ≠ ∫ �_A(r)  (δE^nad_xcT[�_A,�_B] / δ�A(r))  dr   , the expectation value of the embedding potential is not equal to the corresponding component of the total energy. The differences  Δ^nad_xcT  = E^nad_xcT[�_A,�_B] –  ∫ �_A(r)  (δE^nad_xcT[�_A,�_B] / δ�_A(r))  dr are evaluated using local and semi-local approximations for the functional  E^nad_xcT[�_A, �_B] in two model systems representing embedded species weakly interacting with the environment. It is found that Δ^nad_xcT is typically one order of magnitude smaller than E^nad_xcT[�_A, �_B] and decreases with the overlap between �_A(r) and �_B(r) . The kinetic- and exchange-correlation contributions to Δ^nad_xcT cancel partially reducing its magnitude to mHartrees. Compared to local approximation for E^nad_xcT[�_A, �_B], the inhomogeneity is more pronounced in semi-local functionals.

Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles — embedded wave functions are only auxiliary objects used to obtain stationary densities — working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.

We report that anion−π and cation−π interactions can occur on the same aromatic surface. Interactions of this type are referred to as ion pair−π interactions. Their existence, nature, and significance are elaborated in the context of spectral tuning, ion binding in solution, and activation of cell-penetrating peptides. The origin of spectral tuning by ion pair−π interactions is unraveled with energy-minimized excited-state structures: The solvent- and pH-independent red shift of absorption and emission of push–pull fluorophores originates from antiparallel ion pair−π attraction to their polarized excited state. In contrast, the complementary parallel ion pair−π repulsion is spectroscopically irrelevant, in part because of charge neutralization by intriguing proton and electron transfers on excited push–pull surfaces. With time-resolved fluorescence measurements, very important differences between antiparallel and parallel ion pair−π interactions are identified and quantitatively dissected from interference by aggregation and ion pair dissociation. Contributions from hydrogen bonding, proton transfer, π–π interactions, chromophore twisting, ion pairing, and self-assembly are systematically addressed and eliminated by concise structural modifications. Ion-exchange studies in solution, activation of cell-penetrating peptides in vesicles, and computational analysis all imply that the situation in the ground state is complementary to spectral tuning in the excited state; i.e., parallel rather than antiparallel ion pair−π interactions are preferred, despite repulsion from the push–pull dipole. The overall quite complete picture of ion pair−π interactions provided by these remarkably coherent yet complex results is expected to attract attention throughout the multiple disciplines of chemistry involved.

1. Introduction  2. Frozen-Density Embedding Theory  3. Extensions and Formalisms Related to FDET  4. Approximations in FDET for Multilevel Simulations  5. Numerical Simulations Using Approximated FDET Embedding Potentials  6. Concluding Remarks

A series of long-tail alkyl ethanolamine analogs containing amide-, urea-, and thiourea moieties was synthesized and the behavior of the corresponding monolayers was assessed on the Langmuir–Pockels trough combined with grazing incidence X-ray diffraction experiments and complemented by computer simulations. All compounds form stable monolayers at the soft air/water interface. The phase behavior is dominated by strong intermolecular headgroup hydrogen bond networks. While the amide analog forms well-defined monolayer structures, the stronger hydrogen bonds in the urea analogs lead to the formation of small three-dimensional crystallites already during spreading due to concentration fluctuations. The hydrogen bonds in the thiourea case form a two-dimensional network, which ruptures temporarily during compression and is recovered in a self-healing process, while in the urea clusters the hydrogen bonds form a more planar framework with gliding planes keeping the structure intact during compression. Because the thiourea analogs are able to self-heal after rupture, such compounds could have interesting properties as tight, ordered, and self-healing monolayers.

Recent application of the Frozen-Density Embedding Theory based continuum model of the solvent, which is used for calculating solvatochromic shifts in the UV/Vis range, are reviewed. In this model, the solvent is represented as a non-uniform continuum taking into account both the statistical nature of the solvent and specific solute–solvent interactions. It offers, therefore, a computationally attractive alternative to methods in which the solvent is described at atomistic level. The evaluation of the solvatochromic shift involves only two calculations of excitation energy instead of at least hundreds needed to account for inhomogeneous broadening. The present review provides a detailed graphical analysis of the key quantities of this model: the average charge density of the solvent (<�_B>) and the corresponding Frozen-Density Embedding Theory derived embedding potential for coumarin 153.

Frozen-density embedding theory (FDET) provides the formal framework for multilevel numerical simulations, such that a selected subsystem is described at the quantum mechanical level, whereas its environment is described by means of the electron density (frozen density; �_B( r →) ) The frozen density �B( r →) is usually obtained from some lower-level quantum mechanical methods applied to the environment, but FDET is not limited to such choices for �B( r →). The present work concerns the application of FDET, in which �B( r →) is the statistically averaged electron density of the solvent <�B( r →)> . The specific solute–solvent interactions are represented in a statistical manner in <�B( r →)>. A full self-consistent treatment of solvated chromophore, thus involves a single geometry of the chromophore in a given state and the corresponding <�B( r →)>. We show that the coupling between the two descriptors might be made in an approximate manner that is applicable for both absorption and emission. The proposed protocol leads to accurate (error in the range of 0.05 eV) descriptions of the solvatochromic shifts in both absorption and emission.

Herein, we address the question whether anion–π and cation–π interactions can take place simultaneously on the same aromatic surface. Covalently positioned carboxylate–guanidinium pairs on the surface of 4-amino-1,8-naphthalimides are used as an example to explore push–pull chromophores as privileged platforms for such “ion pair–π� interactions. In antiparallel orientation with respect to the push–pull dipole, a bathochromic effect is observed. A red shift of 41 nm found in the least polar solvent is in good agreement with the 70 nm expected from theoretical calculations of ground and excited states. Decreasing shifts with solvent polarity, protonation, aggregation, and parallel carboxylate–guanidinium pairs imply that the intramolecular Stark effect from antiparallel ion pair–π interactions exceeds solvatochromic effects by far. Theoretical studies indicate that carboxylate–guanidinium pairs can also interact with the surfaces of π-acidic naphthalenediimides and π-basic pyrenes.

The density of atomic systems is analysed via the Single-Exponential Decay Detector (SEDD). SEDD is a scalar field designed to explore mathematical, rather than physical, properties of electron density. Nevertheless, it has been shown that SEDD can serve as a descriptor of bonding patterns in molecules as well as an indicator of atomic shells [P. de Silva, J. Korchowiec, and T. A. Wesolowski, ChemPhysChem13, 3462 (2012)]. In this work, a more detailed analysis of atomic shells is done for atoms in the Li–Xe series. Shell populations based on SEDD agree with the Aufbau principle even better than those obtained from the Electron Localization Function, which is a popular indicator of electron localization. A link between SEDD and the local wave vector is given, which provides a physical interpretation of SEDD.

Frozen-Density-Embedding Theory (FDET) is a formalism to obtain the upper bound of the ground-state energy of the total system and the corresponding embedded wavefunction by means of Euler-Lagrange equations [T. A. Wesolowski, Phys. Rev. A77(1), 012504 (2008)]. FDET provides the expression for the embedding potential as a functional of the electron density of the embedded species, electron density of the environment, and the field generated by other charges in the environment. Under certain conditions, FDET leads to the exact ground-state energy and density of the whole system. Following Perdew-Levy theorem on stationary states of the ground-state energy functional, the other-than-ground-state stationary states of the FDET energy functional correspond to excited states. In the present work, we analyze such use of other-than-ground-state embedded wavefunctions obtained in practical calculations, i.e., when the FDET embedding potential is approximated. Three computational approaches based on FDET, that assure self-consistent excitation energy and embedded wavefunction dealing with the issue of orthogonality of embedded wavefunctions for different states in a different manner, are proposed and discussed.

Retinal is the light-absorbing biochromophore responsible for the activation of vision pigments and light-driven ion-pumps. Nature has evolved molecular tuning mechanisms that significantly shift the optical properties of the retinal pigments to enable their absorption of visible light. Using large-scale quantum chemical calculations at the density functional theory level combined with the frozen density embedding theory approach, we show here how the protein environment of vision pigments tune the absorption of retinal to the 2.3-2.6 eV (480-530 nm) region by electrostatically dominated interactions between the chromophore and the surrounding protein residues. The calculations accurately reproduce the experimental absorption maxima of rhodopsin (2.49 eV/498 nm), and the red, green, and blue color pigments (2.3-2.9 eV/430-530 nm). We further identify key interactions responsible for the red- and blue-shifting effects by mutating the rhodopsin structure in silico, and find that deprotonation of the retinyl is likely to be responsible for the blue shifted absorption in the blue cone vision pigment.

According to Frozen-Density Embedding Theory, any observable evaluated for the embedded species is a functional of the frozen density (�_B —the density associated with the environment). The environment-induced shifts in the energies of local excitations in organic chromophores embedded in hydrogen-bonded environments are analyzed. The excitation energies obtained for �_B , which is derived from ground-state calculations for the whole environment applying medium quality basis sets (STO–DZP) or larger, vary in a narrow range (about 0.02 eV which is at least one order of magnitude less than the magnitude of the shift). At the same time, the ground-state dipole moment of the environment varies significantly. The lack of correlation between the calculated shift and the dipole moment of the environment reflects the fact that, in Frozen-Density Embedding Theory, the partitioning of the total density is not unique. As a consequence, such concepts as “environment polarization� are not well defined within Frozen-Density Embedding Theory. Other strategies to generate �_B (superposition of densities of atoms/molecules in the environment) are shown to be less robust for simulating excitation energy shifts for chromophores in environments comprising hydrogen-bonded molecules.

The recently introduced molecular descriptor (Single Exponential Decay Detector - SEDD) [P. de Silva, J. Korchowiec, T. A. Wesolowski, ChemPhysChem 2012, 13, 3462] is used to visualize bonding patterns in molecules. In each point of space SEDD is simply related to the electron density:

SEDD(r) = ln[1/Ï�²(∇(∇Ï�/Ï�)²)²}.

Either experimental or computed densities �(r) can be used to evaluate SEDD. Here, maps of SEDD are obtained from theoretical densities and reveal such features as core electrons, chemical bonds, lone pairs and delocalization in aromatic systems. It is shown that SEDD provides fingerprints of aromaticity, which can be separated into geometric and electronic effects.

The one-electron equation for orbitals embedded in frozen electron density (Eqs. 20-21 in [Wesolowski and Warshel, J. Phys. Chem, 97 (1993) 8050]) in its exact and approximated version is solved for an analytically solvable model system. The system is used to discuss the role of the embedding potential in preventing the collapse of a variationally obtained electron density onto the nucleus in the case when the frozen density is chosen to be that of the innermost shell. The approximated potential obtained from the second-order gradient expansion for the kinetic energy prevents such a collapse almost perfectly but this results from partial compensation of flaws of its components. It is also shown that that the quality of a semi-local approximation to the kinetic-energy functional, a quantity needed in orbital-free methods, is not related to the quality of the non-additive kinetic energy potential - a key component of the effective embedding potential in one-electron equations for embedded orbitals.

Approximations to the non-interacting kinetic energy T_s[�], which take the form of semilocal analytic expressions are collected. They are grouped according to the quantities on which they explicitly depend. Additionally, the approximations for quantities related to T_s[�] (kinetic potential and non-additive kinetic energy), for which the analytic expressions for the “parent� approximation for the functional T_s[�] are unknown, are also given.

The absorption spectrum of fluorenone in zeolite L is calculated from first-principles simulations. The broadening of each band is obtained from the explicit treatment of the interactions between the chromophore and its environment in the statistical ensemble. The comparison between the simulated and measured spectra reveals the main factors affecting the spectrum of the chromophore in hydrated zeolite L. Whereas each distinguishable band is found to originate from a single electronic transition, the bandwidth is determined by the statistical nature of the environment of the fluorenone molecule. The K+...O=C motif is retained in all conformations. Although the interactions between K+ and the fluorenone carbonyl group result in an average lengthening of the C=O bond and in a redshift of the lowest energy absorption band compared to gas phase or non-polar solvents, the magnitude of this shift is noticeably smaller than the total shift. An important factor affecting the shape of the band is fluorenone’s orientation, which is strongly affected by the presence of water. The effect of direct interactions between fluorenone and water is, however, negligible.

In methods based on frozen-density embedding theory or subsystem formulation of density functional theory, the non-additive kinetic potential (v_t^nad(r)) needs to be approximated. Since v_t^nad(r) is defined as a bifunctional, the common strategies rely on approximating v_t^nad[�_A,�_B](r). In this work, the exact potentials (not bifunctionals) are constructed for chemically relevant pairs of electron densities (�_A and �_B) representing: dissociating molecules, two parts of a molecule linked by a covalent bond, or valence and core electrons. The method used is applicable only for particular case, where �_A is a one-electron or spin-compensated two-electron density, for which the analytic relation between the density and potential exists. The sum �_A + �_B is, however, not limited to such restrictions. Kohn-Sham molecular densities are used for this purpose. The constructed potentials are analyzed to identify the properties which must be taken into account when constructing approximations to the corresponding bifunctional. It is comprehensively shown that the full von Weizsäcker component is indispensable in order to approximate adequately the non-additive kinetic potential for such pairs of densities.

We introduce a new tool (single exponential decay detector: SEDD) to extract information about bonding and localization in atoms, molecules, or molecular assemblies. The practical evaluation of SEDD does not require any explicit information about the orbitals. The only quantity needed is the electron density (calculated or experimental) and its derivatives up to the second order.

Within the linear combination of atomic orbitals (LCAO) approximation, one can distinguish two different Kohn-Sham potentials. One is the potential available numerically in calculations, and the other is the exact potential corresponding to the LCAO density. The latter is usually not available, but can be obtained from the total density by a numerical inversion procedure or, as is done here, analytically using only one LCAO Kohn-Sham orbital. In the complete basis-set limit, the lowest-lying Kohn-Sham orbital suffices to perform the analytical inversion, and the two potentials differ by no more than a constant. The relation between these two potentials is investigated here for diatomic molecules and several atomic basis sets of increasing size and quality. The differences between the two potentials are usually qualitative (wrong behavior at nuclear cusps and far from the molecule even if Slater-type orbitals are used) and δ-like features at nodal planes of the lowest-lying LCAO Kohn-Sham orbital. Such nodes occur frequently in LCAO calculations and are not physical. Whereas the behavior of the potential can be systematically improved locally by the increase of the basis sets, the occurrence of nodes is not correlated with the size of the basis set. The presence of nodes in the lowest-lying LCAO orbital can be used to monitor whether the effective potential in LCAO Kohn-Sham equations can be interpreted as the potential needed for pure-state noninteracting v-representability of the LCAO density. Squares of such node-containing lowest-lying LCAO Kohn-Sham orbitals are nontrivial examples of two-electron densities which are not pure-state noninteracting v-representable.

Shifts in the π → π^∗ excitation energy of the cis-7-hydroxyquinoline chromophore induced by hydrogen bonding with small molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the high-level equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and noniterative triples, which provide the reference ab initio data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and the available experimental data. It is demonstrated that the spectral shifts resulting from the FDET calculations employing nonrelaxed environment densities and their EOMCC counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT approach do not agree with the EOMCC reference data. Among the discussed issues are the effects of higher-order correlations on the excitation energies and complexation-induced excitation energy shifts resulting from the EOMCC calculations, and the choice of the approximants that represent the nonadditive kinetic energy contributions to the embedding potential of FDET.

This work illustrates a simple approach for optimizing the lanthanide luminescence in molecular dinuclear lanthanide complexes and identifies a particular multidentate europium complex as the best candidate for further incorporation into polymeric materials. The central phenyl ring in the bis-tridentate model ligands L3–L5, which are substituted with neutral (X = H, L3), electron-withdrawing (X = F, L4), or electron-donating (X = OCH₃, L5) groups, separates the 2,6-bis(benzimidazol-2-yl)pyridine binding units of linear oligomeric multi-tridentate ligand strands that are designed for the complexation of luminescent trivalent lanthanides, Ln(III). Reactions of L3–L5 with [Ln(hfac)₃(diglyme)] (hfac^– is the hexafluoroacetylacetonate anion) produce saturated single-stranded dumbbell-shaped complexes [Ln₂(Lk)(hfac)₆] (k = 3–5), in which the lanthanide ions of the two nine-coordinate neutral [N₃Ln(hfac)₃] units are separated by 12–14 Ã…. The thermodynamic affinities of [Ln(hfac)₃] for the tridentate binding sites in L3–L5 are average (6.6 ≤ log(β_2,1^Y,Lk) ≤ 8.4) but still result in 15–30% dissociation at millimolar concentrations in acetonitrile. In addition to the empirical solubility trend found in organic solvents (L4 > L3 >> L5), which suggests that the 1,4-difluorophenyl spacer in L4 is preferable, we have developed a novel tool for deciphering the photophysical sensitization processes operating in [Eu₂(Lk)(hfac)₆]. A simple interpretation of the complete set of rate constants characterizing the energy migration mechanisms provides straightforward objective criteria for the selection of [Eu₂(L4)(hfac)₆] as the most promising building block.

The bi-functional for the non-electrostatic part of the exact embedding potential of frozen-density embedding theory (FDET) depends on whether the embedded part is described by means of a real interacting many-electron system or the reference system of non-interacting electrons (see [Wesolowski, Phys. Rev. A. 77, 11444 (2008)]). The difference δΔF^MD[�_A] / δ�_A^(r), where ΔF^MD[�_A] is the functional bound from below by the correlation functional E_c[�_A] and from above by zero. Taking into account ΔF^MD[�_A] in both the embedding potential and in energy is indispensable for assuring that all calculated quantities are self-consistent and that FDET leads to the exact energy and density in the limit of exact functionals. Since not much is known about good approximations for ΔF^MD[�_A], we examine numerically the adequacy of neglecting ΔF^MD[�_A] entirely. To this end, we analyze the significance of δΔF^MD[�_A] / δ�_A^(r) in the case where the magnitude of ΔF^MD[�_A] is the largest, i.e., for Hartree-Fock wavefunction. In hydrogen bonded model systems, neglecting δΔF^MD[�_A] / δ�^(r) in the embedding potential marginally affects the total energy (less than 5% change in the interaction energy) but results in qualitative changes in the calculated hydrogen-bonding induced shifts of the orbital energies. Based on this estimation, we conclude that neglecting δΔF^MD[�_A] / δ�_A^(r) may represent a good approximation for multi-reference variational methods using adequate choice for the active space. Doing the same for single-reference perturbative methods is not recommended. Not only it leads to violation of self-consistency but might result in large effect on orbital energies. It is shown also that the errors in total energy due to neglecting δΔF^MD[�_A] / δ�_A^(r) do not cancel but rather add up to the errors due to approximation for the bi-functional of the non-additive kinetic potential.

In embedding methods such as those labeled commonly as QM/MM, the embedding operator is frequently approximated by the electrostatic potential generated by nuclei and electrons in the environment. Such approximation is especially useful in studies of the potential energy surface of embedded species. The effect on energy of neglecting the non-Coulombic component of the embedding operator is corrected a posteriori. The present work investigates applicability of such approximation in evaluation of electronic excitation energy, the accuracy of which depends directly on that of the embedding potential. For several model systems involving cis-7-hydroxiquinoline hydrogen-bonded to small molecules, we demonstrate that such truncation of the embedding operator leads to numerically unstable results upon increasing the size of the atomic basis sets. Approximating the non-Coulombic component of the embedding potential using the expression derived in Frozen-Density Embedding Theory ([Wesolowski and Warshel, J. Phys. Chem.1993, 97, 8050] and subsequent works) by means of even a simple bifunctional dependent on the electron density of the chromophore and its hydrogen-bonded environment, restores the numerical stability of the excitation energies that reach a physically meaningful limit for large basis sets.

Several assertions which are incorrect or might be misleadingly interpreted as well as omissions of issues concerning the non-additive kinetic energy potential made by Fux et al. are analyzed. They concern issues of great importance for any computational method based on the orbital-free embedding theory: evaluation of the total energy, approximating the non-additive kinetic potential, exact properties of non-additive kinetic energy potential. In a nutshell, the authors do not distinguish between two different quantities: the functional, i.e., the correspondence assigning the non-additive kinetic potential to a pair of electron densities and the function (the potential itself).

For nine solvents of various polarity (from cyclohexane to water), the solvatochromic shifts of the lowest absorption band of coumarin 153 are evaluated using a computational method based on frozen-density embedding theory [Wesolowski and Warshel, J. Chem Phys., 1993, 97, 9050, and subsequent articles]. In the calculations, the average electron density of the solvent 〈�_B(r→)〉 is used as the frozen density. 〈�_B(r→)〉 is evaluated using the statistical-mechanical approach introduced in Kaminski et al., J. Phys. Chem. A, 2010, 114, 6082. The small deviations between experimental and calculated solvatochromic shifts (the average deviation equals to about 0.02 eV), confirm the adequacy of the key approximations applied: (a) in the evaluation of the average effect of the solvent on the excitation energy, using the average density of the solvent instead of averaging the shifts over statistical ensemble and (b) using the approximant for the bi-functional of the non-electrostatic component of the orbital-free embedding potential, are adequate for chromophores which interact with the environment by non-covalent bonds. The qualitative analyses of the origin of the solvatochromic shifts are made using the graphical representation of the orbital-free embedding potential.

Shifts in the excitation energy of the organic chromophore, cis-7-hydroxyquinoline (cis-7HQ), corresponding to the π→π^* transition in cis-7HQ and induced by the complexation with a variety of small hydrogen-bonded molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the supermolecular equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and non-iterative triples, which provide the reference theoretical data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and experiment. Unlike in the supermolecular EOMCC and TDDFT cases, where each complexation-induced spectral shift is evaluated by performing two separate calculations, one for the complex and another one for the isolated chromophore, the FDET shifts are evaluated as the differences of the excitation energies determined for the same many-electron system, representing the chromophore fragment with two different effective potentials. By considering eight complexes of cis-7HQ with up to three small hydrogen-bonded molecules, it is shown that the spectral shifts resulting from the FDET calculations employing non-relaxed environment densities and their EOMCC reference counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT method do not agree with the EOMCC reference data. The average absolute deviation between the complexation-induced shifts, which can be as large, in absolute value, as about 2000 cm^-1, obtained using the non-relaxed FDET and supermolecular EOMCC approaches that represent two entirely different computational strategies, is only about 100 cm^-1, i.e., on the same order as the accuracy of the EOMCC calculations. This should be contrasted with the supermolecular TDDFT calculations, which produce the excitation energy shifts that differ from those resulting from the reference EOMCC calculations by about 700 cm^-1 on average. Among the discussed issues are the choice of the electronic density defining the environment with which the chromophore interacts, which is one of the key components of FDET considerations, the basis set dependence of the FDET, supermolecular TDDFT, and EOMCC results, the usefulness of the monomer vs supermolecular basis expansions in FDET considerations, and the role of approximations that are used to define the exchange-correlation potentials in FDET and supermolecular TDDFT calculations.

The importance of the nonelectrostatic component of the embedding potential is investigated by comparing the complexation induced shifts of the iso-g obtained in embedding calculations to its supermolecular counterparts. The analyses are made in view of such multilevel simulations, for which supermolecular strategy is either impractical or impossible, such as the planned simulations for the whole enzyme ferredoxin oxidoreductase. For the biliverdin radical surrounded by a few amino acids, it is shown that the embedding potential comprising only Coulomb terms fails to reproduce even qualitatively the shifts evaluated from supermolecular calculations. The nonelectrostatic component of the exact embedding potential is a bifunctional of two electron densities [Wesolowski and Warshel, J. Phys. Chem. 1993, 97, 8050; Wesolowski, Phys. Rev. A 2008, 77, 012504]. Therefore we analyze in detail both the quality of the approximant for the bifunctional and the importance of the choice of the electron densities at which it is evaluated in practical calculations.

The effective embedding potential introduced by Wesolowski and Warshel [J. Phys. Chem., 97 (1993) 8050] depends on two electron densities: that of the environment (n _B ) and that of the investigated embedded subsystem (n _A ). In this work, we analyze this potential for pairs n _A  and n _B , for which it can be obtained analytically. The obtained potentials are used to illustrate the challenges in taking into account the Pauli exclusion principle.

The mechanochemical reaction of LiBH₄ with MnCl₂ produces the neutral complex Mn(BH₄)₂. Thermal desorption studies show that the mechanochemical reaction of NaBH₄ with MnCl₂produces a different species, apparently Na₂Mn(BH₄)₄, that undergoes dehydrogenation of a much lower weight percent H at a ~20 °C higher temperature than the neutral Mn(BH₄)₂. Vibrational spectroscopy also reveals that a complex manganese borohydride(s) in addition to Mn(BH₄)₂ are formed from the mechanochemical reactions. Analysis of the vibrational spectra in conjunction with DFT calculations on a model Mn(BH₄)₄^2− complex suggest bidentate binding of the [BH₄]^− ligands to the Mn center in the anionic complex. The calculated highest frequencies of the B−H stretching modes (corresponding to the “freeâ€� B−H bonds) agree well with the experimental frequencies and support the presence of this structural feature.

The correspondence between the exact embedding potential and the pair of the electron densities—that of the embedded molecule and that of its environment [Wesolowski and Warshel, J. Phys. Chem. 1993, 97, 8050]—is used to generate the average embedding potential and to subsequently calculate the solvatochromic shifts in a number of organic chromophores in solvents of various polarities. The averaged embedding potential is evaluated at a fictitious electron density of the solvent, which is obtained by means of “dressing up� with electrons the classical site distributions derived from the statistical-mechanical, 3D molecular theory of solvation (aka 3D-RISM method) [Kovalenko In Molecular Theory of Solvation; Hirata, Ed.; Understanding Chemical Reactivity; 2003, Vol 24], self-consistently coupled with the electronic structure of the solute. The proposed approach to modeling solvatochromic shifts can be situated between the implicit and explicit type of models for the solvent. Numerical examples are given for the lowest-lying n → π* and π → π* excitations.

A brief historical overview of physical chemistry at the University of Geneva as well as a description of the present research activities at the department of physical chemistry are presented.

Laser resonant two-photon ionization UV spectra provide clear evidence that the effect of increasing the length of the hydrogen-bonded chain consisting of molecules such as NH₃, H₂O, or CH₃OH on the Ï€ → Ï€* excitations of cis-7-hydroxyquinoline (cis-7HQ) is strongly cooperative [Thut; et al. J. Phys. Chem. A 2008, 112, 5566.] A theoretical analysis of the experimental data is provided to identify the origin of this cooperativity for four chains. The computational method to determine the changes of the electronic structure of a molecule due to interactions with its environment uses the nonempirical expression for the embedding potential [Wesolowski; WarshelJ. Phys. Chem. 1993, 97, 8050.] It is concluded that the electronic coupling between the molecules at the ends of the chain, which are hydrogen-bonded to cis-7HQ, plays a crucial role in this cooperativity.

The effective embedding potential introduced by Wesolowski and Warshel [J. Phys. Chem., 97 (1993) 8050] depends on two electron densities: that of the environment (n _B ) and that of the investigated embedded subsystem (n _A ). In this work, we analyze this potential for pairs n _A and n _B , for which it can be obtained analytically. The obtained potentials are used to illustrate the challenges in taking into account the Pauli exclusion principle.

Minimization of the Hohenberg-Kohn total energy functional EHK [�] in the presence of the constraint � - �_B  ≥ 0, where �_B is some arbitrarily chosen electron density comprising integer number of electrons is considered. To access better numerical accuracy of approximations to EHK [�] in practice, the search for optimal � - �_B is performed using auxiliary quantities such as orbitals of a reference system of non-interacting electrons [Wesolowski and Warshel, J Phys Chem 1993, 97, 8050] or a wavefunction-like object corresponding to interacting electrons [Wesolowski, Phys Rev A 2008, 77, 012504]. In both cases, the condition � - �_B  ≥ 0 leads to a local potential (orbital-free effective embedding potential) of the same general form if expressed by means of universal density functionals. In this work, it is shown that the same local potential is obtained if the search for optimal � - �_B is performed among one-particle reduced density matrices.

Conventionally, solving one-electron equations for embedded orbitals[Eqs. (20) and (21) in Wesolowski and Warshel, J Phys Chem, 1993, 97, 8050] proceedsby a self-consistent procedure in which the whole effective potential, including itsembedding component, is updated in each iteration. We propose an alternative scheme(splitSCF), which uses the linearized embedding potential in the inner iterative loop andthe outer-loop is used to account for its deviations from linearity. The convergence ofthe proposed scheme is investigated for a set of weakly bound intermolecularcomplexes representing typical interactions with the environment. The outer loop isshown to converge very fast. No more than 3-4 iterations are needed. Errors due toskipping the outer loop completely and using the electron density obtained in theabsence of the environment in the linearized embedding potential are investigated indetail. It is shown that this computationally attractive simplification, used already innumerical simulations by others, is adequate not only for van der Waals and hydrogen-bondedcomplexes but even if the complex comprises charged components, i.e., wherestrong electronic polarization takes place. In charge-transfer type of complexes, largerchanges of electron of density upon complex formation occur and the abovesimplification is not recommended. Figure (a) The splitSCF scheme: In the inner loop(i-index), the embedding potential v_emb[�_A,�_B]is evaluated for A taken from the previous iteration in theouter loop (j-index) and remains constant, whereas thev_KS[�_A] component is recalculated as A changes. (b) The conventional SCF scheme: Both v_KS[�_A] andv_emb[�_A,�_B] are recalculated as A changes.

A strategy to construct approximants to the kinetic-energy-functional dependent component (v[�_A,�_B](→r)) of the effective potential in one-electron equations for orbitals embedded in a frozen-density environment [Eqs. (20) and (21) in Wesolowski and Warshel, J. Phys. Chem. 97, (1993) 8050 ] is proposed. In order to improve the local behavior of the orbital-free effective embedding potential near nuclei in the environment, the exact behavior of v_t[�_A,�_B](→r) at �_A→0 and ∫�_Bd→r = 2 is taken into account. As a result, the properties depending on the quality of this potential are invariably improved compared to the ones obtained using conventional approximants which violated the considered exact condition. The approximants obtained following the proposed strategy and especially the simplest one constructed in this work are nondecomposable, i.e., cannot be used to obtain the analytic expression for the functional of the total kinetic energy.

LiSc(BH₄)₄ has been prepared by ball milling of LiBH₄ and ScCl₃. Vibrational spectroscopy indicates the presence of discrete Sc(BH₄)₄^− ions. DFT calculations of this isolated complex ion confirm that it is a stable complex, and the calculated vibrational spectra agree well with the experimental ones. The four BH₄^− groups are oriented with a tilted plane of three hydrogen atoms directed to the central Sc ion, resulting in a global 8 + 4 coordination. The crystal structure obtained by high-resolution synchrotron powder diffraction reveals a tetragonal unit cell with a = 6.076 Ã… and c = 12.034 Ã… (space group P-42c). The local structure of the Sc(BH₄)₄^− complex is refined as a distorted form of the theoretical structure. The Li ions are found to be disordered along the z axis.

Gradient-dependent approximations to the functional of the kinetic energy of non-interacting electrons (T_s[�]), which reflect various properties of the exact functional, are considered. For specially constructed pairs of electron densities, for which the analytic expression for the differences of T_s[�] is known, it is shown that the accuracy of the quantities derivable from a given approximation to T_s[�]: energy differences and their functional derivatives, does not reflect that of T_s[�] itself. The comparisons between the exact values of the kinetic energy in such cases are proposed as an independent condition/criterion for appraisal of approximations to T_s[�].

Variational methods to treat a many-electron system embedded in the environment, which is represented by means of only its electron density, are considered. It is shown that the embedding operator is a local potential in the case where the electron-electron repulsion is treated exactly and the trial embedded wave function takes the multideterminantal form with a fixed number of determinants. The local embedding potential is constructed by imposing that it leads to the same electron density as the one which minimizes the Hohenberg-Kohn functional. For the limiting cases of single-determinant and configuration interaction forms of the embedded wave function, the expressions for the local embedding potential using commonly known density functionals are given. The relation between the derived local embedding potential and the effective embedding potential in the case of the embedded Kohn-Sham system [T. A. Wesołowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993)] is discussed in detail.

Interaction energies for a representative sample of 39 intermolecular complexes are calculated using two computational approaches based on the subsystem formulation of density functional theory introduced by Cortona (Phys. Rev. B 44:8454, 1991), adopted for studies of intermolecular complexes (Wesolowski and Weber in Chem. Phys. Lett. 248:71, 1996). The energy components (exchange-correlation and non-additive kinetic) expressed as explicit density functionals are approximated by means of gradient-free- (local density approximation) of gradient-dependent- (generalized gradient approximation) approximations. The sample of the considered intermolecular complexes was used previously by Zhao and Truhlar to compare the interaction energies derived using various methods based on the Kohn-Sham equations with high-level quantum chemistry results considered as the reference. It stretches from rare gas dimers up to strong hydrogen bonds. Our results indicate that the subsystem-based methods provide an interesting alternative to that based on the Kohn-Sham equations. Local density approximation, which is the simplest approximation for the relevant density functionals and which does not rely on any empirical data, leads to a computational approach comparing favorably with more than twenty methods based on the Kohn-Sham equations including the ones, which use extensively empirical parameterizations. For various types of non-bonding interactions, the strengths and weaknesses of gradient-free and gradient-dependent approximations to exchange-correlation and non-additive kinetic energy density functionals are discussed in detail.

The emergence of a family of computational methods, known under the label ‘density functional theory∈dex theory! density functional ’ or ‘DFT’, revolutionalized the field of computer modelling of complex molecular systems. Many computational schemes belonging to the DFT family are currently in use. Some of them are designed to be universal (nonempirical) whereas other to treat specific systems and/or properties (empirical). This review starts with the introduction of the formal elements underlying all these methods: Hohenberg-Kohn theorems∈dex theorem! Hohenberg-Kohn , reference system∈dex reference system of noninteracting electrons∈dex reference system! noninteracting electrons , exchange-correlation energy∈dex energy functional! exchange-correlation functional∈dex functional , and the Kohn-Sham equations∈dex equation! Kohn-Sham . The main roads to approximate the exchange-correlation-energy functional based on: local density approximation∈dex approximation! local density (LDA), generalized gradient approximation∈dex approximation! generalized gradient (GGA), meta-GGA∈dex energy functional! exchange-correlation! meta-GGA , and adiabatic connection∈dex adiabatic connection formula (hybrid functionals∈dex energy functional! exchange-correlation! hybrid ), are outlined. The performance of these approximations in describing molecular properties of relevance to intermolecular interaction∈dex interactions! intermolecular s and their interactions with environment in condensed phase (ionization potential∈dex potential! ionization s, electron∈dex electron affinities∈dex electron! affinity , electric moments∈dex electric moment , polarizabilities∈dex polarizability ) is reviewed. Developments concerning new methods situated within the general Hohenberg-Kohn-Sham framework or closely related to it are overviewed in the last section

The subsystem formulation of density functional theory is used to obtain equilibrium geometries and interaction energies for a representative set of noncovalently bound intermolecular complexes. The results are compared with literature benchmark data. The range of applicability of two considered approximations to the exchange-correlation- and nonadditive kinetic energy components of the total energy is determined. Local density approximation, which does not involve any empirical parameters, leads to excellent intermolecular equilibrium distances for hydrogen-bonded complexes (maximal error 0.13 Ã… for NH₃−NH₃). It is a method of choice for a wide class of weak intermolecular complexes including also dipole-bound and the ones formed by rare gas atoms or saturated hydrocarbons. The range of applicability of the chosen generalized gradient approximation, which was shown in our previous works to lead to good interaction energies in such complexes, where Ï€-electrons are involved in the interaction, remains limited to this group because it improves neither binding energies nor equilibrium geometries in the wide class of complexes for which local density approximation is adequate. An efficient energy minimization procedure, in which optimization of the geometry and the electron density of each subsystem is made simultaneously, is proposed and tested.

We argue with Kryachko's criticism [Int J Quantum Chem 2005, 103, 818] of the original proof of the second Hohenberg-Kohn theorem. The Kato cusp condition can be used to refute a "to-be-refuted" statement as an alternative to the original proof by Hohenberg and Kohn applicable for Coulombic systems. Since alternative ways to prove falseness of the "to-be-refuted" statement in a reduction ad absurdum proof do not exclude each other, Kryachko's criticism is not justified.

The bifunctional of the nonadditive kinetic energy in the reference system of noninteracting electrons ( T^nad_s [�_A, �_B] = T_s[�_A + �_B] − T_s[�_A] − T_s[�_B]) is the key quantity in orbital-free embedding calculations because they hinge on approximations to T^nad_s [�_A,�_B]. Since T^nad_s [�_A,�_B] is not linear in �_A, the associated potential (functional derivative) T^nad_s [�,�_B]/δ�|_�=�A(r^→) changes if �_A varies. In this work, for two approximations to T^nad_s [�_A,�_B], which are nonlinear in �_A (gradient-free and gradient-dependent), their linearized versions are constructed, and the resulting changes (linearization errors) in various properties of embedded systems (orbital energies, dipole moments, interaction energies, and electron densities) are analyzed. The considered model embedded systems represent typical nonbonding interactions: van der Waals contacts, hydrogen bonds, complexes involving charged species, and intermolecular complexes of the charge-transfer character. For van der Waals and hydrogen bonded complexes, the linearization of T^nad_s [�_A,�_B] affects negligibly the calculated properties. Even for complexes, for which large complexation induced changes of the electron density can be expected, such as the water molecule in the field of a cation, the linearization errors are about 2 orders of magnitude smaller than the interaction induced shifts of the corresponding properties. Linearization of T^nad_s [�_A,�_B] is shown to be inadequate for the complexes of a strong charge-transfer character. Compared to gradient-free approximation to T^nad_s [�_A,�_B], introduction of gradients increases the linearization error.

The ligand-field induced splitting energies of f-levels in lanthanide-containing elpasolites are derived using the first-principles universal orbital-free embedding formalism [Wesolowski and Warshel, J. Phys. Chem. 1993, 97, 8050]. In our previous work concerning chloroelpasolite lattice (Cs₂NaLnCl₆), embedded orbitals and their energies were obtained using an additional assumption concerning the localization of embedded orbitals on preselected atoms leading to rather good ligand-field parameters. In this work, the validity of the localization assumption is examined by lifting it. In variational calculations, each component of the total electron density (this of the cation and that of the ligands) spreads over the whole system. It is found that the corresponding electron densities remain localized around the cation and the ligands, respectively. The calculated splitting energies of f-orbitals in chloroelpasolites are not affected noticeably in the whole lanthanide series. The same computational procedure is used also for other elpasolite lattices (Cs₂NaLnX₆, where X=F, Br, and I)—materials which have not been fabricated or for which the ligand-field splitting parameters are not available.

The idea of describing a many-electron system using only its electron density, i.e. without constructing its wavefunction, was initiated in the works of Thomas and Fermi. Hohenberg-Kohn theorems of modern density functional theory transformed this idea into an exact theory. The Kohn-Sham formalism, widely used in computer simulations of polyatomic systems today, is based on these theorems but is not orbital-free. It reintroduces orbitals to minimize errors in approximating the total energy. The present review concerns an alternative formalism based also on Hohenberg-Kohn theorems, in which orthogonal orbitals are used not for the whole system but only for subsystems [Cortona, Phys. Rev. B, 44 (1991) 8454]. These orbitals are derived from Kohn-Sham-like one-electron equations, called here Kohn-Sham Equations with Constrained Electron Density (KSCED), in which all terms representing the interactions between the subsystems are expressed as universal functionals of electron density. This formulation provides the formal basis for the orbital-free embedding in first-principles based multi-level simulations of complex systems, in which the orbital-level is retained for a selected subsystem, whereas its environment is described at the orbital-free level [Wesolowski and Warshel, J. Phys. Chem., 97 (1993) 8050]. The formal aspects, development and testing of relevant approximate density functionals, and the possible use of the orbital-free embedding in multi-level modelling are covered in detail in this review. Examples of applications, especially those concerning the electronic structure of embedded systems in the condensed phase are provided.

Experimental (IR and Raman) and theoretical (Kohn-Sham calculations) methods are used in a combined analysis aimed at refining the available structural data concerning the molecular guests in channels formed by stacked dibenzo-18-crown-6 (DB18C6) crown ether. The calculations are performed for a simplified model comprising isolated DB18C6 unit and its complexes with either H₂O or H₃O⁺ guests, which are the simplest model ingredients of a one-dimensional diluted acid chain, to get structural and energetic data concerning the formation of the complex and to assign the characteristic spectroscopic bands. The oxygen centers in the previously reported crystallographic structure are assigned to either H₂O or protonated species.

Computer simulation methods using orbital level of description only for a selected part of the larger systems are prone to the artificial charge leak to the parts which are described without orbitals. The absence of orbitals in one of the subsystems makes it impossible to impose explicitly the orthogonality condition. Using the subsystem formulation of density functional theory, it is shown that the absence of explicit condition of orthogonality between orbitals belonging to different subsystems, does not cause any breakdown of this type of description for the chosen intermolecular complexes (F^−H₂O and Li⁺H₂O), for which a significant charge-leak problem could be a priori expected.

The oxidative half-reaction of oxygen atom transfer from nitrate to an Mo^IV complex has been investigated at various levels of theory. Two models have been used to simulate the enzyme active site. In the second, more advanced model, additional amino acid residues capable of significantly affecting the catalytic efficiency of the enzyme were included. B3LYP/6-31+G*, ONIOM, and orbital-free embedding approaches have been used to construct the potential energy profile and to qualitatively compare the results of a QM/MM study with those obtained by a full quantum mechanical strategy. The study has confirmed the utility of the orbital-free embedding method in the description of enzymatic processes.

The local structure and optical and vibrational properties associated with Mn²⁺-doped cubic AMF₃ (A = K, Rb; M = Mg, Zn, Cd) fluoroperovskites are studied by means of embedding calculations using Kohn–Sham equations with constrained electron density. It is shown that while an electronic parameter like 10Dq essentially depends on the Mn²⁺–F^− distance, the local vibration frequencies ω_i (i = a_1g, e_g modes) are dominated by the interaction between F^− ligands and nearest M²⁺ ions lying along bonding directions. The high ω_a values observed for KMgF₃:Mn²⁺ and KZnF₃:Mn²⁺, the huge variations of ω_e and ω_a frequencies when the host lattice is changed, as well as the increase of Huang–Rhys factors and the Stokes shift following the host lattice parameter, are shown to be related to this elastic coupling of the MnF₆^4− complex to the rest of the host lattice. The present results support the conclusion that the Stokes shift is determined by the interaction of the excited ⁴T_1g state with a_1g and e_g local modes while the coupling with the t_2g shear mode is not relevant. The variations of local vibrational frequencies and the Stokes shift induced by a hydrostatic pressure on a given system are shown to be rather different to those produced by the chemical pressure associated with distinct host lattices.

The formalism based on the total energy bifunctional (E[Ï�_I,Ï�_II]) is used to derive interaction energies for several hydrogen-bonded complexes (water dimer, HCN–HF, H₂CO–H₂O, and MeOH–H₂O). Benchmark ab initio data taken from the literature were used as a reference in the assessment of the performance of gradient-free [local density approximation (LDA)] and gradient-dependent [generalized gradient approximation (GGA)] approximations to the exchange-correlation and nonadditive kinetic-energy components of E[Ï�_I,Ï�_II]. On average, LDA performs better than GGA. The average absolute error of calculated LDA interaction energies amounts to 1.0 kJ/mol. For H₂CO–H₂O and H₂O–H₂O complexes, the potential-energy curves corresponding to the stretching of the intermolecular distance are also calculated. The positions of the minima are in a good agreement (less than 0.2 Å) with the reference ab initio data. Both variational and nonvariational calculations are performed to assess the energetic effects associated with complexation-induced deformations of molecular electron densities.

The orbital-free frozen-density embedding scheme within density-functional theory [ T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993) ] is applied to the calculation of induced dipole moments of the van der Waals complexes CO₂⋯X (X = He, Ne, Ar, Kr, Xe, Hg). The accuracy of the embedding scheme is investigated by comparing to the results of supermolecule Kohn-Sham density-functional theory calculations. The influence of the basis set and the consequences of using orbital-dependent approximations to the exchange-correlation potential in embedding calculations are examined. It is found that in supermolecular Kohn-Sham density-functional calculations, different common approximations to the exchange-correlation potential are not able to describe the induced dipole moments correctly and the reasons for this failure are analyzed. It is shown that the orbital-free embedding scheme is a useful tool for applying different approximations to the exchange-correlation potential in different subsystems and that a physically guided choice of approximations for the different subsystems improves the calculated dipole moments significantly.

In this study, we investigate the performance of the frozen-density embedding scheme within density-functional theory [ J. Phys. Chem. 97, 8050 (1993) ] to model the solvent effects on the electron-spin-resonance hyperfine coupling constants (hfcc’s) of the H₂NO molecule. The hfcc’s for this molecule depend critically on the out-of-plane bending angle of the NO bond from the molecular plane. Therefore, solvent effects can have an influence on both the electronic structure for a given configuration of solute and solvent molecules and on the probability for different solute (plus solvent) structures compared to the gas phase. For an accurate modeling of dynamic effects in solution, we employ the Car-Parrinello molecular-dynamics (CPMD) approach. A first-principles-based Monte Carlo scheme is used for the gas-phase simulation, in order to avoid problems in the thermal equilibration for this small molecule. Calculations of small H₂NO-water clusters show that microsolvation effects of water molecules due to hydrogen bonding can be reproduced by frozen-density embedding calculations. Even simple sum-of-molecular-densities approaches for the frozen density lead to good results. This allows us to include also bulk solvent effects by performing frozen-density calculations with many explicit water molecules for snapshots from the CPMD simulation. The electronic effect of the solvent at a given structure is reproduced by the frozen-density embedding. Dynamic structural effects in solution are found to be similar to the gas phase. But the small differences in the average structures still induce significant changes in the computed shifts due to the strong dependence of the hyperfine coupling constants on the out-of-plane bending angle.

Recent applications of one-electron equations for embedded electron density introduced originally for multi-level modeling of solvated molecules (T.A. Wesolowski, A. Warshel, J. Phys. Chem. 1993, 97, 8050) are reviewed. The considered applications concern properties directly related to the electronic structure of molecules (or an atom) in condensed phase such as: i) localized electronic excitations in a chromophore involved in a hydrogen-bonded intermolecular complex; ii) UV/Vis spectra of acetone in water; and iii) energy levels of f-orbitals for lanthanide cations in a crystalline environment. For each case studied, the embedding potential is represented graphically and its qualitative features are discussed.

The absorption spectra of aminocoumarin C151 in water and n-hexane solution are investigated by an explicit quantum chemical solvent model. We improved the efficiency of the frozen-density embedding scheme, as used in a former study on solvatochromism (J. Chem. Phys. 2005, 122, 094115) to describe very large solvent shells. The computer time used in this new implementation scales approximately linearly (with a low prefactor) with the number of solvent molecules. We test the ability of the frozen-density embedding to describe specific solvent effects due to hydrogen bonding for a small example system, as well as the convergence of the excitation energy with the number of solvent molecules considered in the solvation shell. Calculations with up to 500 water molecules (1500 atoms) in the solvent system are carried out. The absorption spectra are studied for C151 in aqueous or n-hexane solution for direct comparison with experimental data. To obtain snapshots of the dye molecule in solution, for which subsequent excitation energies are calculated, we use a classical molecular dynamics (MD) simulation with a force field adapted to first-principles calculations. In the calculation of solvatochromic shifts between solvents of different polarity, the vertical excitation energy obtained at the equilibrium structure of the isolated chromophore is sometimes taken as a guess for the excitation energy in a nonpolar solvent. Our results show that this is, in general, not an appropriate assumption. This is mainly due to the fact that the solute dynamics is neglected. The experimental shift between n-hexane and water as solvents is qualitatively reproduced, even by the simplest embedding approximation, and the results can be improved by a partial polarization of the frozen density. It is shown that the shift is mainly due to the electronic effect of the water molecules, and the structural effects are similar in n-hexane and water. By including water molecules, which might be directly involved in the excitation, in the embedded region, an agreement with experimental values within 0.05 eV is achieved.

Metal (4f)−ligand (Cl 3p) bonding in LnCl₆^3- (Ln = Ce to Yb) complexes has been studied on the basis of 4f→4f and Cl,3p→4f charge-transfer spectra and on the analysis of these spectra within the valence bond configuration interaction model to show that mixing of Cl 3p into the Ln 4f ligand field orbitals does not exceed 1%. Contrary to this, Kohn−Sham formalism of density functional theory using currently available approximations to the exchange-correlation functional tends to strongly overestimate 4f−3p covalency, yielding, for YbCl₆^3-, a much larger mixing of Cl 3p→4f charge transfer into the f¹³ ionic ground-state wave function. Thus, ligand field density functional theory, which was recently developed and applied with success to complexes of 3d metals in our group, yields anomalously large ligand field splittings for Ln, the discrepancy with experiment increasing from left to the right of the Ln 4f series. It is shown that eliminating artificial ligand-to-metal charge transfer in Kohn−Sham calculations by a procedure described in this work leads to energies of 4f−4f transitions in good agreement with experiment. We recall an earlier concept of Ballhausen and Dahl which describes ligand field in terms of a pseudopotential and give a thorough analysis of the contributions to the ligand field from electrostatics (crystal field) and exchange (Pauli) repulsion. The close relation of the present results with those obtained using the first-principles based and electron density dependent effective embedding potential is pointed out along with implications for applications to other systems.

It is shown that for pairs of electron densities (�_α and �_α‾) obtained from mixing orbital densities in a spin-compensated four-electron system, the kinetic energy functional of the non-interacting reference system (T_s[�]) satisfies the general inequality T_s[�_α  +�_α‾] ≥ T_s[�_α] + T_s[�_α‾]. This condition is discussed in the context of the gradient expansion approximation to T_s[�] and its possible use in variational orbital-free calculations. In particular, it is shown that the second-order term of the analytic form given by von Weizsäcker violates this inequality for the considered pairs.

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [ J. Phys. Chem. 97, 8050 (1993) ] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n→π^* excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20–0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.

Geometry and interaction energy in complexes of the Ph-L type (L = Ar, N₂, CO, H₂O, NH₃, CH₄, CH₃OH, CH₃F) involving neutral or cationic phenol were determined using the density functional theory formalism based on the minimization of the total energy bifunctional and gradient-dependent approximations for its exchange-correlation and nonadditive kinetic-energy parts. For the neutral complexes the calculated interaction energies range from 1 kcal/mol for the Ph-Ar complex to about 10 kcal/mol for Ph-NH₃. The interactions are stronger if the cationic phenol is involved (up to 25 kcal/mol). It is found, except for neutral Ph-Ar, that the hydrogen-bonded structure is more stable than the Ï€-bound one. Calculated interaction energies (D_e) correlate well with the experimental dissociation energies (D₀).

The basis set effect on the results of the minimization of the total energy bifunctional E[�_A, �_B] approximated at the local density approximation level is analyzed for several weak intermolecular complexes. The considered complexes formed by hydrocarbons at the equilibrium geometry were previously studied by means of the same formalism using large decontracted basis sets consisting of Gaussian-type atomic orbitals limited to s-, p-, and d-functions. In this work, we use our two new computer implementations of the formalism to analyze the basis set effects accompanying changing the basis sets from Gaussian-type orbitals to Slater-type orbitals and including f-functions. We show that the interaction energies, their components, and the energies of the highest occupied molecular orbital converge within a range of 0.07 kcal/mol, 0.08 kcal/mol, and 0.06 eV, respectively.

The packing preferences of dimers formed by nitrogen-containing planar polycyclic aromatic hydrocarbons ((C₃₀H₁₅N)₂ and (C₃₆H₁₅N)₂) were studied by means of theoretical calculations. Potential energy curves corresponding to various relative motions of the monomers (vertical displacement, rotating, slipping, and combinations of them) were derived. It was found that the monomers in such Ï€-stacked dimers are rather strongly held together (the interaction energy is about −9 kcal/mol) in an off-centered arrangement. It emerges as a general picture that the aligned structures are less stable than the ones where the nitrogen atoms, as the centers of the considered monomers, are not on top of each other but offset by 1.8−2.7 Ã…. Displacing the centers further results in a rapid reduction of the interaction energy. Within these relatively large relative motions (up to about 3 Ã…) of the monomers, however, no significant loss of stability of the dimers is noted. In the case of C₃₀H₁₅N, changing the orientation of the enantiotopic faces in the dimer formation leads to two nonequivalent minimum energy structures of similar energies but notably different geometries. The most stable structure of both dimers studied resembles that of two adjacent layers of graphite. We conclude, therefore, that the studied molecules could be considered as good building block candidates for the fabrication of columnar organic conductors.

Ligand field splitting energies of lanthanides Ln³⁺ (Ln = from Ce to Yb) in octahedral environment are calculated using the Hohenberg–Kohn theorems based orbital-free embedding formalism. The lanthanide cation is described at orbital level whereas its environment is represented by means of an additional term in the Kohn–Sham-like one-electron equations expressed as an explicit functional of two electron densities: that of the cation and that of the ligands. The calculated splitting energies, which are in good agreement with the ones derived from experiment, are attributed to two main factors: (i) polarization of the electron density of the ligands, and; (ii) ion–ligand Pauli repulsion.

The theoretically calculated dimerization-induced shifts of the lowest excitation energies in two model systems, adenine−thymine and guanine−cytosine base pairs, are analyzed. The applied formalism is based on first principles and allows one to study the influence of the microscopic environment of a given molecule on its ground- [Wesolowski, T. A.; Warshel, A. J. Phys. Chem. 1993, 97, 8050] and excited-state [Casida, M. E.; Wesolowski, T. A. Int. J. Quantum Chem. 2004, 96, 577] properties. The assessment of the relative importance of such effects as (a) Coulomb interactions, (b) orbital interactions, (c) electronic polarization of the environment, and (d) electron density overlap effects is straightforward in this formalism. In the applied formalism, electron density overlap effects can be further decomposed into the exchange−correlation component which provides a small attractive contribution and the repulsive kinetic energy-dependent component. It is shown that the shifts can be attributed to the electrostatic interactions and the repulsive overlap-dependent term in the embedding potential. The electronic polarization of the environment plays a significant role (up to 30% of the total shift) only in transitions involving the orbitals localized on hydrogen bond donor groups. For all analyzed shifts, the contribution of the intermolecular orbital interactions is negligible. The analysis of this work provides strong evidence supporting the use of the widely applied embedding-molecule strategy in computational studies of chromophores in a condensed phase even in such cases where only one end of the hydrogen bond is included in the quantum mechanical part.

By means of ¹H-NOESY- and Raman-spectroscopic analyses, we experimentally demonstrated the presence of the equatorial N — Me conformer of King's sultam 4b in solution, resulting from a rapid equilibrium. As a consequence, the value of the N lone-pair anomeric stabilization should be revised to 1.5-1.6 kcal/mol. Independently from the N tilting, natural bond orbital (NBO)-comparative analyses suggest that the S d* orbitals do not appear as primordial and stereospecific acceptors for the N lone pair. Second, the five-membered-ring sultams do not seem to be particularly well-stabilized by the S — C σ* orbital in the N-substituted pseudo-axial conformation, as opposed to an idealized anti-periplanar situation for the six-membered-ring analogues. In this latter case, the other anti-periplanar C — C σ* and C(1') — H/C(2') σ*orbitals are as important, if not more, when compared to the S — C σ* participation. In the pseudo-equatorial conformation, γ-sultams particularly benefit from the N lone-pair hyperconjugation with the anti-periplanar S — O₁ σ* and C(2) — H/C or C(1') — H/C σ* orbitals. This is also the case for δ-sultams when the steric requirement of the N-substituent exceeds 1.6 kcal/mol. When both axial and equatorial conformations are sterically too exacting, the N-atom is prone to sp² hybridization or/and conformational changes (i.e., 12c). In that case also, the mode of stereoelectronic stabilization differs from γ- to δ-sultams.

The role of one-electron functions known as orbitals in various theoretical methods used to describe molecules and complex materials at a quantum mechanical level is outlined in a historical perspective. A hierarchy consisting of three types of general formalism, ordered according to the importance of orbital-dependent expressions in the total energy, is presented. Two such formalisms, less known to the general chemistry community, are discussed in detail together with their recent applications in modelling complex systems: a) the orbital-free formulation of density functional theory, which does not use orbitals at all and which can be seen as the modern realization of the original ideas of Thomas and Fermi, and b) the density partitioning based formalism, in which the orbitals are used only for smaller parts of a larger system (subsystems). The emphasis is placed on the second type of formalism, a topic of strong interest of our Geneva group.

The uranyl salophene complex and its co-complexes with several anions (H₂PO₄^-, HSO₄^-, NO₂^-, OH^-, Cl^-, F^-) in the gas phase are investigated theoretically. Equilibrium geometries of relevant species and complexation-induced structural changes are discussed. The ¹³C NMR chemical shifts calculated at the gas-phase optimized geometry agree very well with experimental liquid-phase results. The optimized geometry agrees also very well with available crystallographic data. This indicates that the gas-phase structures derived from theoretical calculations can be considered representative also for the condensed phase. For all anions, except H₂PO₄^-, the calculated gas-phase binding energies correlate well with experimental Gibbs free energies of complexation. The possible role of the solvent in the case of H₂PO₄^- complexation is discussed.

The Kohn-Sham equations with constrained electron density (KSCED) embedding formalism of Wesolowski and coworkers was originally developed and is good for the case of two weakly interacting molecular regions with weakly overlapping densities, such as might be expected in describing solvation. A generalization is given here for the case of three molecular regions with strongly overlapping densities with the idea that this generalized theory can offer a better description of embedding in the context of situations that might be encountered in, for example, chemisorption on surfaces or active sites in enzymes. This three-partition generalization includes the original two-partition formalism as a special case. Time-dependent response theory equations are then developed for the two- and three-partition theories for application to the problem of the calculation of polarizabilities and other response properties, including excitation spectra, of embedded molecules or molecular structures.

The kinetic energy functional T_s[�] in a reference system of non-interacting electrons is a key quantity in density functional theory. Approximating it as an explicit functional of the electron density � is the object of continuous interest since the earliest days of quantum mechanics (Thomas–Fermi electron gas theory). A simple proof of the exact inequality T_s[�_A + �_B] − T_s[�_A] − T_s[�_B] ≥ 0 valid for a special class of spin-compensated pairs of electron densities �_A and �_B (v^AB-representable pairs) is provided. The derived relation is discussed to rationalize some of the results of the past attempts to approximate T_s[�]. It is also discussed as a tool for deriving approximations to the functional T_s[�] and/or the bi-functional T^nad_s[�_A, �_B] = T_s[�_A + �_B] − T_s[�_A] − T_s[�_B].

Density functional theory generalized gradient approximation calculations, which were tested in our previous detailed study of [RhCl(PF₃)₂]₂ (Seuret et al., 2003, Phys. Chem. chem. Phys., 5, 268-274), were applied for a series of homologous organometallic compounds of the [RhXL₂]₂ (X = Cl, Br, or I; L = CO, PH₃, or PF₃) type. Various properties of the studied compounds were obtained. Optimized geometries of [RhCl(PH₃)₂]₂ and [RhCl(CO)₂]₂ are in very good agreement with available experimental data. Geometries of other compounds as well as other properties (thermochemistry of selected fragmentation channels, barriers to structural changes, frontier orbitals) which are not available experimentally were predicted. All the considered compounds are not planar. Enforcing planarity of the central [RhX]₂ moiety requires only a small energetic cost ranging from 2.2 to 3.9 kcal mol^-1. The analysis of frontier orbitals indicates that the metals provide the most favourable site for the electrophilic attack in all considered compounds. The analysis of the shape of the lowest unoccupied molecular orbitals indicates that the halogens and ligands provide the most favourable site for the nucleophilic attack for [RhCl(CO)₂]₂ or [RhCl(PF₃)₂]. For [RhBr(PF₃)₂]₂, [RhI(PF₃)₂]₂ and [RhCl(PH₃)₂]₂, the nucleophilic attack on the halogen is less probable. Except for [RhCl(CO)₂]₂, the least energetically expensive decomposition channel involves initial separation of ligands. For [RhCl(CO)₂]₂, its decomposition into the RhCl(CO)₂ fragments was found to be the least energetically expensive fragmentation reaction which is probably one of the reasons for the known catalytic activity of this compound.

A [4](hetero)helicenium cation was resolved using the hexacoordinated phosphorus-containing binphat anion (see picture: N, blue; O, red; C, gray). Its absolute configuration was determined by vibrational circular dichroism spectroscopy. The barrier of interconversion of its enantiomers is higher than that of [6]helicene.

We report on the first stage of our theoretical study of the quino[2,3,4-kl]acridinium,1,13-dimethoxy-5,9-dipropyl-cation. This molecule, involved in the synthesis of novel triazaangulenium dyes of high chemical stability, is a chiral [4]-helicenium. The structure and the IR spectrum of the quino[2,3,4-kl]acridinium,1,13-dimethoxy-5,9-dimethyl-cation derived from theoretical calculations which use various density functional theory methods, are compared with the geometry derived from X-ray diffraction measurements and the experimental IR spectrum. Our study shows that the chosen variant of DFT methods (Becke88 for exchange, P86 for correlation, 3-21G** basis set) reproduces the experimental geometry within 0.004 Å and the IR frequencies within 15 cm^−1.

Experimental and theoretical techniques have been applied to study the decomposition of the [RhCl(PF₃)₂]₂ molecule which is known as a precursor in electron beam induced deposition (EBID) of Rh. Mass spectrometry (MS) has been carried out to study the electron ionisation and fragmentation of isolated molecules. Auger electron spectroscopy has been used to characterize the EBID deposit. The MS data indicate the presence of free phosphorus and rhodium ions. This is in agreement with the analysis of the composition of the EBID deposit containing: 60% Rh, 12–25% P, 2–13% Cl, no F, 3–20% O and N. Theoretical calculations (density functional theory) has been used to characterize the precursor molecule and to derive the enthalpies of several simple decomposition reactions. The calculated geometries are in a good agreement with the available X-ray crystallographic data. The [RhCl(PF₃)₂]₂ appears not to be rigid: the PF₃ groups can rotate with a relatively low barrier (0.6 kcal mol^–1) whereas the barrier for the butterfly-like motion of (RhCl)₂ moiety is only 3.5 kcal mol^–1. According to the theoretical results, the lowest energy pathway of the decomposition corresponds to a consecutive loss of PF₃ ligands, resulting in a (RhCl)₂ moiety (without phosphorus). The same conclusion is also valid for the ionised precursor. Experimental data combined with the theoretical results concerning the energetics of the considered various simple decomposition processes indicate that the electron induced dissociation of the precursor cannot be seen as a simple one-step decomposition process.

We analyze the performance of gradient-free local density approximation (LDA) and gradient-dependent generalized gradient approximation (GGA) functionals in a density functional theory variational calculations based on the total energy bifunctional (E[Ï�₁,Ï�₂]). These approximations are applied to the exchange-correlation energy and to the nonadditive component of the kinetic energy of the complex. Benchmark ab initio interaction energies taken from the literature for 25 intermolecular complexes for which the interaction energies fall into the 0.1–3.0 kcal/mol range are used as reference. At the GGA level, the interaction energies derived from E[Ï�₁,Ï�₂] are more accurate than the Kohn–Sham ones. LDA leads to very good interaction energies for such complexes where the Ï�₁,Ï�₂ overlap is very small (Ne-Ne, Ar-Ar, for instance) but it is not satisfactory for such cases where the overlap is larger. Introduction of gradient-dependent terms into the approximate part of E[Ï�₁,Ï�₂] improves significantly the overall accuracy of the interaction energies. Gradient-dependent functionals applied in E[Ï�₁,Ï�₂] lead to the average error and the average absolute error of the interaction energies amounting to 0.08 kcal/mol and 0.29 kcal/mol, respectively.

Recent formal developments and applications of the 'freeze-and-conquer' strategy proposed by Wesolowski and Warshel in 1993 to study large systems at quantum mechanical level are reviewed. This universal approach based on density functional theory allows one to link, via the orbital-free embedding potential, two parts of a larger system described at different levels of accuracy leading thus to significant savings in computational costs. As a result, applicability of conventional methods of quantum chemistry can be extended to even larger systems. It is shown that the 'freeze-and-thaw' approach applying the first-principles based approximation to the orbital-free embedding potential recently developed in our group provides a powerful and universal technique to study such embedded molecules (or molecular complexes), which are not linked with their microscopic environment by covalent bonds.

The repartition of molecular hydrogen in space, and its depletion on solid particles in particular, is an important question of modern astrophysics. In this paper, we report a theoretical study of the physisorption of molecular hydrogen, H₂, on a major component of the interstellar dust known as polycyclic aromatic hydrocarbons (PAHs). Two different density functional theory approaches were used:  (i) the conventional Kohn−Sham theory and (ii) the subsystem-based approach (Kohn−Sham equations with constrained electron density, KSCED) developed in our group. The approximate exchange-correlation energy functional applied in all calculations and the nonadditive kinetic-energy functional needed in KSCED have a generalized gradient approximation form and were chosen on the basis of our previous studies. The results of both approaches show similar trends:  weak dependence of the calculated interaction energies on the size of the PAH and negligible effect of the complexation of two PAH molecules on the adsorption of molecular hydrogen. The KSCED interaction energy calculated for the largest considered PAH (ovalene), amounting to 1.27 kcal/mol, is in excellent agreement with experimental estimates ranging from 1.1 to 1.2 kcal/mol, whereas the one derived from supermolecular Kohn−Sham calculations is underestimated by more than 50%. This result is in line with our previous studies, which showed that the generalized gradient approximation applied within the KSCED framework leads to interaction energies of weakly bound complexes that are superior to the corresponding results of supermolecular Kohn−Sham calculations.

An approximate kinetic-energy functional of the generalized gradient approximation form was derived following the "conjointness conjecture" of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange-energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed-shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic-energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form.

The approximate nonempirical kinetic-energy functional proposed by Tal and Bader is analyzed for polyatomic systems. The performance of this functional and the functionals derived from the gradient expansion approximation truncated to zeroth, second, and fourth order is investigated for a testing set of 68 neutral and charged molecules. It is shown that the Tal–Bader functional, despite the simplicity of the idea behind its construction, leads to significantly better total kinetic energies than the gradient expansion approximation functionals. The local behavior of the kinetic-energy density derived from the Tal–Bader functional is also discussed.

A Comment on the Letter by Thorsten Klüner et al., Phys. Rev. Lett. 86, 5954 (2001). The authors of the Letter offer a Reply.

An approach in which the total energy of interacting subsystems is expressed as a bifunctional depending explicitly on two functions: electron densities of the two molecules forming a complex (Ï�₁ and Ï�₂) was used to determine the equilibrium geometry and the binding energy of several weak intermolecular complexes involving carbazole and such atoms or molecules as Ne, Ar, CH₄, CO, and N₂. For these complexes, the experimental dissociation energies fall within the range from 0.48 to 2.06 kcal/mol. Since the effect of the intermolecular vibrations on the dissociation energy is rather small, the experimental measurements provide an excellent reference set. The obtained interaction energies are in a good agreement with experiment and are superior to the ones derived from conventional Kohn–Sham calculations. A detailed analysis of relative contribution of the terms which are expressed using approximate functionals (i.e., exchange-correlationE_xc[Ï�₁+Ï�₂] and nonadditive kinetic energy T_s^nad[Ï�₁,Ï�₂] = T_s[Ï�₁+Ï�₂]−T_s[Ï�₁]−T_s[Ï�₂]) is made. The nonvariational version of the applied formalism is also discussed.

The density-functional approach based on the partition into subsystems was applied to study the benzene dimer. For several structures, the calculated interaction energy and intermolecular distance were compared with the previous theoretical results. A good agreement with high level ab initio correlated methods was found. For instance, the interaction energies obtained in this work and the CCSD(T) method agree within 0.1 - 0.6 kcal/mol depending on the structure of the dimer. The structure with the largest interaction energy is T-shaped, in agreement with CCSD(T) results. The T-shaped structure of benzene dimer was suggested by several experimental measurements. The calculated interaction energy of 2.09 kcal/mol agrees also well with experimental estimates based on the dissociation energy which ranges from 1.6±0.2 to 2.4±0.4 kcal/mol and the estimated zero-point vibration energy of 0.3 - 0.5 kcal/mol.

The CO molecule is frequently used as a probe in studies of zeolites where it adsorbs on metal cations. Compared with the free CO molecule, the stretching frequency of CO adsorbed in a zeolite is blue-shifted. The magnitude of the shift depends on the cation. The theoretical studies by Ferrari et al. [J. Chem. Phys., 105, 4129 (1996)] show that the isolated cation does not provide a good model of the zeolite because the calculated shifts are significantly overestimated. In this work, the effects of the interactions between theMe⁺CO (Me=Li, Na, or K) complex and the zeolite framework on the properties of CO adsorbed on the cation site are investigated. The properties of the investigated complexes are studied using the embedded molecule approach applying the orbital-free effective embedding potential derived within the subsystem formulation of density functional theory. In order to identify the major microsopic effects affecting the properties of the bound probe molecule, a hierarchy of cluster models is used to represent the zeolite framework. For the largest cluster model applied, the calculated frequency shifts agree within few cm^−1 with experimental data. 

In this comment, it is pointed out that the generalized gradient approximation (GGA) functionals considered by Milet et al. [ J. Chem. Phys. 111, 7727 (1999)] share the same exchange part (B88) which violates significantly the Lieb–Oxford bound. Violation of this exact condition was shown to result in significant errors of the exchange energy in the case of weakly overlapping electron densities [Wesołowski et al., J. Phys. Chem. A 101, 7818 (1997); Zhang et al., J. Chem. Phys. 107, 7921 (1997)]. Numerical examples are given to illustrate that such exchange functionals which better satisfy the Lieb–Oxford bound lead to better interaction energies also for the complexes studied by Milet et al.

The use of hybrid ab initio QM/MM methods in studies of metalloenzymes and related systems presents a major challenge to computational chemists. Methods that include the metal ion in the quantum mechanical region should also include the ligands of the metal in this region. Such a treatment, however, should be very demanding if one is interested in performing the configurational averaging needed for proper calculations of activation free energies. In the present work we examine the ability of the frozen DFT (FDFT) and the constrained DFT (CDFT) approaches to be used in ab initio studies of metal-catalyzed reactions, while allowing for an effective QM (rather than a QM/MM) treatment of the reacting complex. These approaches allow one to treat the entire enzyme by ab initio DFT methods, while confining the SCF calculations to a relatively small subsystem and keeping the electron density of the rest of the system frozen (or constrained). It is found that the FDFT and CDFT models can reproduce the trend obtained by a full DFT calculation of a proton transfer between two water molecules in a (Im)₃Zn²⁺(H₂O)₂ system. This and related test cases indicate that our approximated models should be capable of providing a reliable representation of the energetics of metalloenzymes. The reasons for the special efficiency of the FDFT approach are clarified, and the strategies that can be used in FDFT studies of metalloenzymes are outlined.

The formalism of the Kohn–Sham equations with constrained electron density is extended to the spin-polarized case. The isotropic hyperfine coupling constants (A_iso(Mg)) of Mg⁺ embedded in a Ne or Ar matrix represented using a cluster are calculated and compared to that of free Mg⁺. For the largest basis set used, the calculated values (222.9 and 210.4 gauss for Ar and Ne, respectively) agree with experimental measurements (222.4 and 211.6). The shifts of A_iso(Mg) relative to the values for free Mg⁺ are rather basis-set-independent.

The structure and stretching frequency of the CO molecule physisorbed on the MgO(100) surface were investigated using the recently developed formalism of Kohn-Sham equations with constrained electron density (KSCED). The KSCED method makes it possible to divide a large system into two subsystems and to study one of them using Kohn-Sham-like equations in which the effective potential takes into account the interactions between subsystems. Compared to the standard Kohn-Sham formalism, the KSCED method involves an additional functional due to the non-additivity of the kinetic energy. The surface was represented using a cluster ((MgO₅)^8− or Mg₉O₉) embedded in an array of electric point-charges. The KSCED calculations led to a blue-shift of the stretching frequency of the C-down adsorbed CO molecule amounting to 47–21 cm^−1 depending on the distance from the surface. At the C–Mg distance of 2.42 Å, which corresponds to a typical minimum of the potential energy curve derived from supermolecule Kohn-Sham calculations applying gradient-corrected functionals, the KSCED frequency shift amounts to 35 cm^−1 in excellent agreement with the most recent experiments. The CO stretching frequency of the O-down adsorbed CO molecule is red-shifted. The effects of cluster size and choice of the functionals on the KSCED frequencies, geometries and energies were analyzed. For C–Mg distances varying between 2.3 and 3.0 Å, changing the cluster size affects the frequencies by less than 4 cm^−1 and the CO bond length by less than 0.0003 Å. At C–Mg distances larger than 2.4 Å, the change of the cluster size negligibly affects the KSCED interaction energies. The KSCED formalism makes it possible to study directly the effects associated with relaxation of the surface's electron density upon adsorbing CO. It is shown that these effects might contribute up to 30% of the KSCED interaction energy, but that they do not result in significant changes of either the geometries or frequencies.

Theoretical studies on structure and stretching frequency of the CO molecule physisorbed on the MgO(100) or ZnO(1010) surfaces are reported. The properties of the adsorbed molecule were investigated by means of the recently developed formalism of Kohn-Sham equations with constrained electron density (KSCED). The KSCED method makes it possible to divide a large system into two subsystems and to study one of them using Kohn-Sham-like equations with an effective potential which takes into account the interactions between subsystems. This method (KSCED) was shown to be adequate to study the properties of the CO molecule adsorbed on the MgO(100) surface as reported in a previous paper (Wesolowski et. al.: J. Mol. Struct., THEOCHEM, in press). The effect of the interactions with the surface on the CO stretching frequency and geometry was analyzed for vertically bound (C-down) CO at the Zn-site of the ZnO(1010) surface. The ZnO(1010) surface was represented using several cluster models: Zn²⁺, (ZnO₃)^4-, or Zn₉O₉ embedded in a matrix of point charges. The KSCED frequency shift of the CO stretching vibration is blue-shifted and in good agreement with experiment.

n view of further application to the study of molecular and atomic sticking on dust particles, we investigated the capability of the “freeze-and-thawâ€� cycle of the Kohn–Sham equations with constrained electron density (KSCED) to describe potential energy surfaces of weak van der Waals complexes. We report the results obtained for C₆H₆⋯X(X=O₂, N₂, and CO) as test cases. In the KSCED formalism, the exchange-correlation functional is defined as in the Kohn–Sham approach whereas the kinetic energy of the molecular complex is expressed differently, using both the analytic expressions for the kinetic energy of individual fragments and the explicit functional of electron density to approximate nonadditive contributions. As the analytical form of the kinetic energy functional is not known, the approach relies on approximations. Therefore, the applied implementation of KSCED requires the use of an approximate kinetic energy functional in addition to the approximate exchange-correlation functional in calculations following the Kohn–Sham formalism. Several approximate kinetic energy functionals derived using a general form by Lee, Lee, and Parr [Lee et al., Phys. Rev. A. 44, 768 (1991)] were considered. The functionals of this type are related to the approximate exchange energy functionals and it is possible to derive a kinetic energy functional from an exchange energy functional without the use of any additional parameters. The KSCED interaction energies obtained using the PW91 [Perdew and Wang, in Electronic Structure of Solids ’91, edited by P. Ziesche and H. Eschrig (Academie Verlag, Berlin, 1991), p. 11] exchange-correlation functional and the kinetic energy functional derived from the PW91 exchange functional agree very well with the available experimental results. Other considered functionals lead to worse results. Compared to the supermolecule Kohn–Sham interaction energies, the ones derived from the KSCED calculations depend less on the choice of the approximate functionals used. The presented KSCED results together with the previous Kohn–Sham ones [WesoÅ‚owski et al., J. Phys. Chem. A 101, 7818 (1997)] support the use of the PW91 functional for studies of weakly bound systems of our interest.

Applicability of the approximate kinetic energy functionals to study hydrogen-bonded systems by means of the formalism of Kohn–Sham equations with constrained electron density (KSCED) [Cortona, Phys. Rev. B 44, 8454 (1991); WesoÅ‚owski and Warshel, J. Phys. Chem. 97, 8050 (1993); WesoÅ‚owski and Weber, Chem. Phys. Lett. 248, 71 (1996)] is analyzed. In the KSCED formalism, the ground-state energy of a molecular complex is obtained using a “divide-and-conquerâ€� strategy, which is applied to the Kohn–Sham-like equations to obtain the electron density of a fragment embedded in a larger system. The approximate kinetic energy functional enters into the KSCED formalism in two ways. First, the effective potential in which the electrons of each fragment move contains a component which is expressed by means of a functional derivative of an approximate kinetic energy functional (functional derivative of the non-additive kinetic energy). Second, the KSCED energy functional contains a component (non-additive kinetic energy) which is expressed using the approximate kinetic energy functional. In this work, the KSCED energies and densities of (H₂O)₂, (HF)₂, (HCl)₂, and HFNCH are compared to the ones obtained using the standard supermolecule Kohn–Sham approach. The following factors determining the agreement between the KSCED and supermolecule Kohn–Sham results are analyzed: the analytical form of the gradient-dependent terms in the approximate kinetic energy functional and the number of atom-centered orbitals used to expand electron density of fragments. The best agreement between the supermolecule Kohn–Sham and the KSCED results is obtained with the kinetic energy functional derived following the route of Lee, Lee, and Parr [Lee et al., Phys. Rev. A 44, 768 (1991)] from the exchange functional of Perdew and Wang [Perdew and Wang, in Electronic Structure of Solids ’91, edited by P. E. Ziesche and H. Eschrig (Academie Verlag, Berlin, 1991), p. 11]. The difference between the KSCED and the supermolecule Kohn–Sham energies of studied complexes amounts to less than 0.35 kcal/mol at the equilibrium geometry.

Although density functional theory (DFT) is more and more commonly used as a very efficient tool for the study of molecules and bulk materials, its applications to weakly bonded systems remain rather sparse in the literature, except studies that consider hydrogen bonding. It is, however, of essential interest to be able to correctly describe weaker van der Waals complexes. This prompted us to investigate more precisely the reliability of several widely-used functionals. The equilibrium geometries and the binding energies of C₆H₆···X (X = O₂, N₂, or CO) complexes are determined within the standard Kohn−Sham approach of DFT using different exchange−correlation functionals and at the MP2 level of theory for comparison. It is comprehensively concluded that extreme care must be taken in the choice of the functional since only those that behave properly at large and intermediate values of the reduced density gradient s give relevant results. The PW91 exchange functional, the enhancement factor of which does not diverge at increasing s, appears as the most reliable for the studied systems. It is furthermore demonstrated that the quality of the DFT results is determined by the exchange energy component of the total energy functional.

We analyze differences between ground-state electron densities of a model molecular complex obtained by solving the Kohn-Sham equations with constrained electron density (KSCED) [Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993)] and as a solution of the standard Kohn-Sham equations applied to the whole complex. The differences between KSCED and KS electron densities which result from the inaccuracy of the kinetic energy functional applied in the KSCED equations are discussed. The model molecular complex consists of collinear H₂ and HCN molecules separated by a short distance. Several kinetic energy functional approximations are applied within the KSCED framework and the differences between resulting electron densities are studied. The KSCED electron densities depend directly on the functional derivative of the kinetic energy functional applied in the KSCED equations. Among the studied functionals, the one proposed by Zhao et al. [Phys. Rev. A 47, 918 (1993)] and the gradient-dependent functional proposed by Perdew and Wang [Phys. Rev. B 33, 8800 (1986)] led to the smallest differences between KS and KSCED electron densities, thus having the most accurate functional derivative. Both functionals allow one to extend the range of applicability of the KSCED equations to system geometries where an overlap of electron densities of the partners of the complex is significant.

The recently developed frozen density functional theory (FDFT) is extended to ab initio free energy calculations of chemical reactions in solution. This method treats the solute−solvent system as a supermolecule but constrains the electron density of the solvent molecules. Unlike hybrid quantum mechanical/molecular mechanics techniques, FDFT represents the solvent quantum mechanically. The quality of the solute−solvent interaction potential is examined by generating clusters of a reacting system and several solvent molecules and comparing the supermolecule DFT energies to the corresponding FDFT energies. The FDFT potential surfaces for solute−solvent systems provide a good approximation of the supermolecule DFT surfaces and require, in some cases, several orders of magnitude less computation time (in particular if one treats many solvent molecules quantum mechanically). The ab initio free energy surface for the F^- + HF → FH + F^- proton transfer reaction in solution is calculated using the corresponding “classical� empirical valence bond (EVB) potential surface as a reference potential. The encouraging results indicate that FDFT can be used to study chemical reactions in solution, capturing the quantum mechanical aspects of the solvent, which is not possible using hybrid quantum mechanical/molecular mechanics approaches. Furthermore, the use of EVB as a reference potential is found to be an extremely effective way of obtaining ab initio free energies for chemical processes in solution or in clusters.

Ground�state properties of a linear hydrogen�bonded FH...NCH complex are studied by means of the ‘‘freeze�and�thaw’’ cycle of Kohn–Sham Equations with constrained electron density (KSCED) [T. A. Wesolowski and J. Weber, Chem. Phys. Lett. 248, 71, (1996)]. For several geometries of the complex, the electron density and the total energy are compared to the ones obtained by means of the standard Kohn–Sham calculations. The comparisons are made to assess the accuracy of several gradient dependent approximate kinetic energy functionals applied in the KSCED equations. It was found that the closest results to the Kohn–Sham ones were obtained with the functional whose analytical form was proposed by Perdew and Wang for exchange energy [J. P. Perdew and Y. Wang in Electronic Structure of Solids ’91, edited by P. Ziesche and H. Eschrig (Academie Verlag, Berlin, 1991), p. 11] and parametrized by Lembarki and Chermette for kinetic energy [A. Lembarki and H. Chermette, Phys. Rev. A 50, 5328 (1994)]. Around the interaction energy minimum as well as for larger intermolecular distances, the ‘‘freeze�and�thaw’’ cycle of KSCED leads to very similar potential energy surface as the standard supermolecule Kohn–Sham calculations. 

A new method for calculating the ground state electron density of interacting molecules is presented. The supermolecule electron density is obtained using an iterative procedure. At each step the electron density of one molecule is calculated using previously introduced Kohn-Sham equations with constrained electron density. These equations contain terms representing the coupling between constrained and non-constrained electron densities. The coupling terms also involve a new functional, namely the non-additive kinetic energy functional that is not present in the original Kohn-Sham method. Its first-principles analytical form in not yet known. We examine the analytical form of this functional derived from Thomas-Fermi theory. The electron density obtained is compared with that calculated using the original Kohn-Sham method applied to the supermolecule. Good agreement has been found for a broad range of electron density overlaps.

A practical ab initio quantum-mechanical approach for calculations of free energies of molecules in solutions is developed. This approach treats the solute molecules by an explicit ab initio self-consistent-field approach while representing the solvent molecules by a pseudopotential. The solvation energies are evaluated by a free-energy perturbation approach that uses the distribution function associated with a classical force field as a reference state for the quantum-mechanical calculations. The performance of the method is examined by evaluating the solvation energy of an Li + ion. It is found that the calculation times are not much longer than that of the corresponding classical free-energy perturbation calculations.

Massive amounts of coordinate data result from molecular dynamics calculations. The animation program MDKINO is a simple but powerful tool for previewing or reviewing the results. In recent simulations of elastase, we have examined hydrogen bonding patterns, conformational changes involving shifts in ring positions and rotations of amino acid side chains, electric fields in interatomic space, and electric forces acting on chosen nuclei. Animation is also useful for checking on the stability of calculations in progress. Simple programming techniques achieve acceptable levels of animation with readily available hardware (PS330 or PS390 display with a serial interface to a laboratory VAX). In about half an hour, it is possible to make and watch a color stereo “movie� of a selected subsystem of a simulation (up to 1 000 frames of about 100 atoms each).

Two related molecules from the acyclic nucleoside family 9-(1,3-dihydroxy-2-propoxymethyl) guanine (DHPG) and 9-(1,5-dihydro-4-hydroxymethyl-3-oxapentyl-2- [R])guanine (2′, 3′- secoG) have been compared by means of force field conformational analysis. They are respectively active and nonactive analogs of the antivirial compound 9-((2-hydroxyethoxy)methyl)guanine (ACG). As in the case of ACG many local minima are found for both molecules, indicating their great flexibility. For all three molecules conformations similar to those occurring in cyclic nucleosides have energies from 3 to 7 kcal mol^−1 above the most stable minima.