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.

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[�].

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 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.

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 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.

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 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.

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.