We propose a new approach to determine a suitable zeroth-order wavefunction for multiconfigurational perturbation theory. The same ansatz as in complete active space (CAS) wavefunction optimization is used but it is split in two parts, a principal space (A) and a much larger extended space (B). Löwdin's partitioning technique is employed to map the initial eigenvalue problem to a dimensionality equal to that of (A) only. Combined with a simplified expression for the (B) portion of the wavefunction, we are able to drastically reduce the storage and computational demands of the wavefunction optimization. This scheme is used to produce reference wavefunctions and energies for subsequent second-order perturbation theory (PT2) corrections. Releasing the constraint of computing the exact CAS energy and wavefunction prior to the PT2 treatment introduces a nonstandard paradigm for multiconfigurational methods. Based on the results of test calculations, we argue that principal parts with only few percents of the total number of CAS configurations could provide final multiconfigurational PT2 energies of the same accuracy as in the standard paradigm. In the future, algorithmic improvements for this scheme will bring into reach active spaces much beyond the present limit of CAS-based methods, therefore allowing for accurate studies of systems featuring strong correlation.

The recently developed second-order perturbation theory restricted active space (RASPT2) method has been benchmarked versus the well-established complete active space (CASPT2) approach. Vertical excitation energies for valence and Rydberg excited states of different groups of organic (polyenes, acenes, heterocycles, azabenzenes, nucleobases, and free base porphin) and inorganic (nickel atom and copper tetrachloride dianion) molecules have been computed at the RASPT2 and multistate (MS) RASPT2 levels using different reference spaces and compared with CASPT2, CCSD, and experimental data in order to set the accuracy of the approach, which extends the applicability of multiconfigurational perturbation theory to much larger and complex systems than previously. Relevant aspects in multiconfigurational excited state quantum chemistry such as the valence−Rydberg mixing problem in organic molecules or the double d-shell effect for first-row transition metals have also been addressed.

The only operating mechanism in the oxidation of water to dioxygen catalyzed by the mononuclear cis-[Ru^II(bpy)₂(H₂O)₂]²⁺ complex when treated with excess Ce^IV was unambiguously established. Theoretical calculations together with ¹⁸O-labeling experiments (see plot) revealed that it is the nucleophilic attack of water on a Ru=O group.

Recent studies of organouranium chemistry have provided unusual pairs of similar polymetallic molecules containing (N)^3− and (O)^2− ligands, namely [(C₅Me₅)U(μ-I)₂]₃(μ₃-N), 1, and [(C₅Me₅)U(μ-I)₂]₃(μ₃-O), 2, and chair and boat conformations of [(C₅Me₅)₂U(μ-N)U(μ-N₃)(C₅Me₅)₂]₄, 3. These compounds were analyzed by density functional theory and multiconfigurational quantum chemical studies to differentiate nitride versus oxide in molecules for which the crystallographic data were not definitive and to provide insight into the electronic structure and unique chemical bonding of these polymetallic compounds. Calculations were also performed on [(C₅Me₅)₂UN₃(μ-N₃)]₃, 4, and [(C₆F₅)₃BNU(N[Me]Ph)₃], 5, for comparison with 1 and 3. On the basis of these results, the complex, [(C₅Me₅)U(μ₃-E)]₈, 6, for which only low-quality X-ray crystallographic data are available, was analyzed to predict if E is nitride or oxide.

The compounds Tc₂Cl₄(PMe₃)₄ and Tc₂Br₄(PMe₃)₄ were formed from the reaction between (n-Bu₄N)₂Tc₂X₈ (X = Cl, Br) and trimethylphosphine. The Tc(II) dinuclear species were characterized by single-crystal XRD, UV−visible spectroscopy, and cyclic voltammetry techniques, and the results are compared to those obtained from density functional theory and multiconfigurational (CASSCF/CASPT2) quantum chemical studies. The compound Tc₂Cl₄(PMe₃)₄ crystallizes in the monoclinic space group C2/c [a = 17.9995(9) Ã…, b = 9.1821(5) Ã…, c = 17.0090(9) Ã…, β = 115.4530(10)°] and is isostructural to M₂Cl₄(PMe₃)₄ (M = Re, Mo, W) and to Tc₂Br₄(PMe₃)₄. The metal−metal distance (2.1318(2) Ã…) is similar to the one found in Tc₂Br₄(PMe₃)₄ (2.1316(5) Ã…). The calculated molecular structures of the ground states are in excellent agreement with the structures determined experimentally. Calculations of effective bond orders for Tc₂X₈^2− and Tc₂X₄(PMe₃)₄ (X = Cl, Br) indicate stronger Ï€ bonds in the Tc₂⁴⁺ core than in Tc₂⁶⁺ core. The electronic spectra were recorded in benzene and show a series of low intensity bands in the range 10000−26000 cm−1. Assignment of the bands as well as computing their excitation energies and intensities were performed at both TD-DFT and CASSCF/CASPT2 levels of theory. Calculations predict that the lowest energy band corresponds to the δ* → σ* transition, the difference between calculated and experimental values being 228 cm^−1 for X = Cl and 866 cm^−1 for X = Br. The next bands are attributed to δ* → Ï€*, δ → σ*, and δ → Ï€* transitions. The cyclic voltammograms exhibit two reversible waves and indicate that Tc₂Br₄(PMe₃)₄ exhibits more positive oxidation potentials than Tc₂Cl₄(PMe₃)₄. This phenomenon is discussed and ascribed to stronger metal (d) to halide (d) back bonding in the bromo complex. Further analysis indicates that Tc(II) dinuclear species containing Ï€-acidic phosphines are more difficult to oxidize, and a correlation between oxidation potential and phosphine acidity was established.

Since the discovery of a formal quintuple bond in Ar′CrCrAr′ (CrCr = 1.835 Ã…) by Power and co-workers in 2005, many efforts have been dedicated to isolating dichromium species featuring quintuple-bond character. In the present study we investigate the electronic configuration of several, recently synthesized dichromium species with ligands using nitrogen to coordinate the metal centers. The bimetallic bond distances of Power’s compound and Cr₂-diazadiene (1) (CrCr = 1.803 Ã…) are compared to those found for Cr₂(μ-η²-ArNC(R)NAr)₂ (2) (CrCr = 1.746 Ã…; R = H, Ar = 2,6-Et₂C₆H₃), Cr₂(μ-η²-Ar^XylNC(H)NAr^Xyl)₃ (3) (CrCr = 1.740^reduced/1.817^neutral Ã…; Ar^Xyl= 2,6-C₆H₃-(CH₃)₂), Cr₂(μ-η²-TippPyNMes)₂ (4) (CrCr = 1.749 Ã…; TippPyNMes = 6-(2,4,6-triisopropylphenyl)pyridin-2-yl (2,4,6-trimethylphenyl)amide), and Cr₂(μ-η²-DippNC(NMe₂)N-Dipp)₂ (5) (CrCr = 1.729 Ã…, Dipp = 2,6-i-Pr₂C₆H₃). We show that the correlation between the CrCr bond length and the effective bond order (EBO) is strongly affected by the nature of the ligand, as well as by the steric hindrance due to the ligand structure (e.g., the nature of the coordinating nitrogen). A linear correlation between the EBO and CrCr bond distance is established within the same group of ligands. As a result, the CrCr species based on the amidinate, aminopyridinate, and guanidinate ligands have bond patterns similar to the Ar′CrCrAr′ compound. Unlike these latter species, the dichromium diazadiene complex is characterized by a different bonding pattern involving Cr−NÏ€ interactions, resulting in a lower bond order associated with the short metal−metal bond distance. In this case the short CrCr distance is most probably the result of the constraints imposed by the diazadiene ligand, implying a Cr₂N₄ core with a closer CrCr interaction.

Quantum chemical calculations were performed to investigate the cooperative effect of the nitrogen and silicon atoms on the singlet-triplet energy spacing and the reactivity of the singlet state in 1,2-diazacyclopentane-3,5-diyls and 1,2-diaza-4-silacyclopentane-3,5-diyls. The largest singlet-triplet energy gap (ΔE^c_ST = -36.1 kcal/mol) found so far in localized 1,3-diradicals was in the C_2v symmetry of 4,4-difluoro-1,2-diaza-4-silacyclopentane-3,5-diyl at the UB3LYP/6-31G(d) level of theory. The cooperative effect was also found in the energy differences of singlet diradicals with the corresponding ring-closing compounds, bicyclo[2.1.0]pentane derivatives. The singlet state of the 1,2-diaza-4-silacyclopentane-3,5-diyls was calculated to be energetically more stable than the ring-closing compound. The notable finding on the stability of the singlet diradicals may be attributed to the resonance structures that specifically stabilize the singlet state of diradicals. The computational studies predict that the singlet 1,2-diaza-4-silacyclopentane-3,5-diyl is a persistent molecule under conditions without intermolecular-trapping reagents.

The results of a computational study with multiconfigurational quantum chemical methods on actinide monoxides (AnO) and dioxides (AnO₂) for An = Th, Pa, U, Np, Pu, Am, and Cm, are presented. First and second ionization energies were determined and compared with experimental values, when available. The trend along the series is analyzed in terms of the electronic configurations of the various species. The agreement with experiment is excellent in most cases. Of particular interest is the first ionization of PuO₂. We applied cutting-edge theoretical methods to refine the ionization energy, but our computed data fall in the range of ~6 eV and not in the ~7 eV region as the experiment dictates. Such a system requires further computational and experimental attention.

Playing with a full deck: Single-crystal X-ray and neutron diffraction data show that the Th center in the title complex 1 (see structure; Th orange, B beige, N purple, C black, H blue) forms bonds with 15 H atoms, thus making 1 the first crystallographically characterized example of a complex with a Werner coordination number of fifteen. DFT calculations suggest that 1 adopts the fully symmetric 16-coordinate structure in the gas phase.

Palladium carbene complexes, CX₂=PdX₂, are prepared along with the insertion products, CX₃–PdX, in reactions of laser-ablated Pd atoms with tetrahalomethanes and identified from matrix infrared spectra and density functional frequency calculations. The carbon–metal bonds of the CCl₂=PdCl₂ and CClF=PdCl₂ complexes are essentially double bonds with effective bond orders of 1.9, near those for the Pt and Ni analogues, as calculated by CASPT2 methods. On the other hand, only insertion complexes are generated from mono-, di-, and trihalomethane precursors. While the carbenes have staggered allene-type structures, many insertion complexes containing C–Cl bonds reveal distinct bridged structures, which indicate effective coordination of Cl to the metal center.

Multiconfigurational second-order perturbation theory based on either a complete active space reference wave function (CASSCF/CASPT2) or a restricted active space reference wave function (RASSCF/RASPT2) has been applied to compute one-electron ionization potentials and vertical electronic energy differences of oligomers of length n formed from ethylene (n = 1-10), acetylene (n = 1-5), and phenylene (n = 1-3) subunits. The RASSCF/RASPT2 approach offers an accuracy similar to CASSCF/CASPT2 at significantly reduced computational expense (both methods show good agreement with experimental data where available). It is shown that RASPT2 extends the range of CASPT2-like approaches by permitting the use of larger active spaces.

A thorough characterization of the Ru−Hbpp (in,in-{[Ru^II(trpy)(H₂O)]₂(μ-bpp)}³⁺ (trpy is 2,2′:6′,2′′-terpyridine, bpp is bis(2-pyridyl)-3,5-pyrazolate)) water oxidation catalyst has been carried out employing structural (single crystal X-ray), spectroscopic (UV−vis and NMR), kinetic, and electrochemical (cyclic voltammetry) analyses. The latter reveals the existence of five different oxidation states generated by sequential oxidation of an initial II,II state to an ultimate, formal IV,IV oxidation state. Each of these oxidation states has been characterized by UV−vis spectroscopy, and their relative stabilities are reported. The electron transfer kinetics for individual one-electron oxidation steps have been measured by means of stopped flow techniques at temperatures ranging from 10 to 40 °C and associated second-order rate constants and activation parameters (ΔH_‡ and ΔS_‡) have been determined. Room-temperature rate constants for substitution of aqua ligands by MeCN as a function of oxidation state have been determined using UV−vis spectroscopy. Complete kinetic analysis has been carried out for the addition of 4 equiv of oxidant (Ce^IV) to the initial Ru−Hbpp catalyst in its II,II oxidation state. Subsequent to reaching the formal oxidation state IV,IV, an intermediate species is formed prior to oxygen evolution. Intermediate formation and oxygen evolution are both much slower than the preceding ET processes, and both are first order with regard to the catalyst; rate constants and activation parameters are reported for these steps. Theoretical modeling at density functional and multireference second-order perturbation theory levels provides a microscopic mechanism for key steps in intermediate formation and oxygen evolution that are consistent with experimental kinetic data and also oxygen labeling experiments, monitored via mass spectrometry (MS), that unambiguously establish that oxygen−oxygen bond formation proceeds intramolecularly. Finally, the Ru−Hbpp complex has also been studied under catalytic conditions as a function of time by means of manometric measurements and MS, and potential deactivation pathways are discussed.

Nickel carbene complexes, CX₂ = NiX₂, are prepared along with the insertion products, CX₃ – NiX, in reactions of laser-ablated Ni atoms with tetrahalomethanes. These reaction products are identified from matrix infrared spectra and density functional frequency calculations. In agreement with the previously studied Pt cases, the carbon – nickel bonds of the Ni carbene complexes are essentially double bonds with CASPT2-computed effective bond orders of 1.8 – 1.9. On the other hand, only insertion complexes are generated from dihalomethane and trihalomethane precursors. The nickel carbenes have staggered structures, and several insertion complexes containing C – Cl bonds reveal distinct bridged structures similar to those observed in the corresponding Fe products, which indicate effective coordination of Cl to the metal center. The unique F-bridged CH₂F – NiCl structure is also observed.

Multiconfigurational second-order perturbation theory calculations based on a complete active space reference wave function (CASPT2), employing active spaces of increasing size, are well converged at the level of 12 electrons in 12 orbitals for the singlet−triplet state−energy splittings of three supported copper−dioxygen and two supported copper−oxo complexes. Corresponding calculations using the restricted active space approach (RASPT2) offer similar accuracy with a significantly reduced computational overhead provided an inner (2,2) complete active space is included in the overall RAS space in order to account for strong biradical character in most of the compounds. The effects of the different active space choices and the outer RAS space excitations are examined, and conclusions are drawn with respect to the general applicability of the RASPT2 protocol.

CoCo loco! Ligand-bridged dimers (see picture) with the shortest known Co-Co interactions are the first amidinato and guanidinato cobalt(I) complexes. The nature of the interactions has been probed by magnetic and theoretical investigations, and has been shown to be multiconfigurational. Preliminary reactivity studies of the complexes have also been carried out.

Laser-ablated late lanthanide metal atoms were condensed with pure hydrogen at 4 K, and new infraredabsorptions are assigned to binary metal hydrides on the basis of deuterium substitution and density functionaltheory frequency calculations. The dominant absorptions in the 1330-1400 cm^-1 region are identified asLnH₃ complexes with very weak ligand bands near 3900 cm^-1. With ytterbium, YbH and YbH₂ were themajor initial products, but YbH₃ increased at their expense upon sample irradiation. Evidence is also presentedfor the LuH and ErH molecules and the tetrahydride anions in solid hydrogen.

Deviations from statistical binding, that is cooperativity, in self-assembled polynuclear complexes partly result from intermetallic interactions ΔE^M,M, whose magnitudes in solution depend on a balance between electrostatic repulsion and solvation energies. These two factors have been reconciled in a simple point-charge model, which suggests severe and counter-intuitive deviations from predictions based solely on the Coulomb law when considering the variation of ΔE^M,M with metallic charge and intermetallic separation in linear polynuclear helicates. To demonstrate this intriguing behaviour, the ten microscopic interactions that define the thermodynamic formation constants of some twenty-nine homometallic and heterometallic polynuclear triple-stranded helicates obtained from the coordination of the segmental ligands L1-L11 with Zn²⁺ (a spherical d-block cation) and Lu³⁺ (a spherical 4f-block cation), have been extracted by using the site binding model. As predicted, but in contrast with the simplistic coulombic approach, the apparent intramolecular intermetallic interactions in solution are found to be i) more repulsive at long distance (ΔE^Lu,Lu_{1-4 >} ΔE^Lu,Lu_1-2), ii) of larger magnitude when Zn²⁺ replaces Lu³⁺ (ΔE^Zn,Lu_1-2 > ΔE^Lu,Lu_1-2) and iii) attractive between two triply charged cations held at some specific distance (ΔE^Lu,Lu_1-3 < 0). The consequences of these trends are discussed for the design of polynuclear complexes in solution.

A method is suggested which allows truncation of the virtual space in Cholesky decomposition-based multiconfigurational perturbation theory (CD-CASPT2) calculations with systematic improvability of the results. The method is based on a modified version of the frozen natural orbital (FNO) approach used in coupled cluster theory. The idea is to exploit the near-linear dependence among the eigenvectors of the virtual-virtual block of the second-order Møller–Plesset density matrix. It is shown that FNO-CASPT2 recovers more than 95% of the full CD-CASPT2 correlation energy while requiring only a fraction of the total virtual space, especially when large atomic orbital basis sets are in use. Tests on various properties commonly investigated with CASPT2 demonstrate the reliability of the approach and the associated reduction in computational cost and storage demand of the calculations.

The technetium(III) compound (n-Bu₄N)₂[Tc₂Br₈] was prepared by metathesis of (n-Bu₄N)₂[Tc₂Cl₈] with concentrated aqueous HBr in acetone and recrystallized from acetone–diethyl ether solution (2 : 1 v/v). The acetone solvate obtained, (n-Bu₄N)₂[Tc₂Br₈]·4[(CH₃)₂CO] ( 1), crystallizes in the monoclinic space group P2₁/n with a = 13.8959(8) Ã…, b = 15.2597(9) Ã…, c = 15.5741(9) Ã…, β = 109.107(1)°, R1 = 0.028, and Z = 4. The Tc–Tc distance (2.1625(9) Ã…) and the average Tc–Br distances (2.4734(7) Ã…) are in excellent agreement with those previously determined by EXAFS spectroscopy. These and other experimental data on quadruply metal–metal bonded group 7 [M₂X₈]^2- dimers (M = Tc, Re; X = Cl, Br) are compared to the results of a set of multi-configurational quantum chemical studies. The calculated molecular structures of the ground states are in very good agreement with the structures determined experimentally. The theory overestimates the * transition energies by some 1000 cm^-1, but mimics the trends in δ – δ* energies across the series.

Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante et al., J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.

Theoretically speaking: The mechanistic details associated with the generation and reaction of [CuO]⁺ species from Cu^I-α-ketocarboxylate complexes, especially with respect to modifications of the ligand supporting the copper center, were investigated (see scheme). Theoretical models were used to characterize the electronic structures of different [CuO]⁺ species and their reactivity in CH activation and O-atom transfer reactions.

This Letter discusses the nature of the chemical bond between two chromium atoms in different di-chromium complexes with the metal atoms in different oxidation states. Starting with the Cr diatom, with its formally sextuple bond and oxidation number zero, we proceed to analyse the bonding in some Cr(I)-Cr(I) XCrCrX complexes with X varying from F, to Phenyl, and Aryl. The bond distance in these complexes varies over a large range: 1.65-1.83 Ã… and we suggest explanations for these variations. A number of dichromium complexes with bond distances around or shorter than 1.80 Ã… have recently been synthesized and we study one of these complexes, Cr₂(diazadiene)₂ and show how the Cr-Cr bond order is related to the oxidation number and the ligand bonding, factors that are all involved in the determination of the short Cr-Cr bond length: 1.80 Ã…. The discussion is based on the use of multicon?gurational wave func- tions, which give a qualitatively correct description of the electronic structure in these multiply bonded systems.

The results of a combined spectroscopic and computational study of lanthanide hydrides with the general formula MH_x(H₂)_y, where M = La, Ce, Pr, Nd, Sm, Eu, and Gd, x = 1−4, and y = 0−6 are reported. To understand the nature of the dihydrogen complexes formed with lanthanide metal hydride molecules, we have first identified the binary MH_x species formed in the ablation/deposition process and then analyzed the dihydrogen supercomplexes, MH_x(H₂)_y. Our investigation shows that the trihydrides bind dihydrogen more weakly than the dihydrides and that the interaction between the central lanthanide and the H₂ molecules occurs via a 6s electron transfer from the lanthanide to the H₂ molecules. Evidence is also presented for the SmH and EuH diatomic molecules and the tetrahydride anions in solid hydrogen.

Multiconfigurational quantum chemical methods (CASSCF/CASPT2) have been used to study the chemiionization reactions Ce + O → CeO⁺ + e^- and Ce + O₂ → CeO₂⁺ + e^-. Selected spectroscopic constants for CeO_n and CeO_n⁺ (n = 1, 2), as well as reaction enthalpies of the chemiionization reactions of interest, have been computed and compared with experimental values. In contrast to the lanthanum case, for both Ce + O₂(X³Î£_g^-) and Ce + O₂( a¹Î”_g), the Ce + O₂ → CeO₂⁺ + e^- reaction is shown to be exothermic, and thus, contributes to the experimental chemielectron spectra. The apparent discrepancy between the computed reaction enthalpies and the high kinetic energy offset values measured in the chemielectron spectra is rationalized by arguing that chemielectrons are produced mainly via two sequential reactions (Ce + O₂ → CeO + O, followed by Ce + O → CeO⁺ + e^-) as in the case of lanthanum. For Ce + O₂ (a¹Î”_g), a chemielectron band with higher kinetic energy than that recorded for Ce + O₂( X³Î£_g^-) is obtained. This is attributed to production of O( ¹D) from the reaction Ce + O₂( a¹Î”_g) → CeO + O( ¹D), followed by chemiionization via the reaction Ce + O( ¹D) → CeO⁺ + e^-. Accurate potential energy curves for the ground and a number of excited states of CeO and CeO⁺ have been computed, and a mechanism for the chemiionization reactions investigated experimentally was proposed.

Multiconfigurational quantum chemical calculations on the R-diimines dichromium compound confirm that the Cr−Cr bond, 1.80 Å, is among the shortest Cr^I−Cr^I bonds. However, the bond between the two Cr atoms is only a quadruple bond rather than a quintuple bond. The reason why the bond is so short has to be attributed to the strain in the NCCN ligand moieties.

The ground and excited states of neutral and cationic PuO and PuO₂ have been studied with multiconfigurational quantum chemical methods followed by second order perturbation theory, the CASSCF/CASPT2 method. Scalar relativistic effects and spin–orbit coupling have been included in the treatment. As literature values for the ionization energy of PuO₂ are in the wide range of ~6.6 eV to ~10.1 eV, a central goal of the computations was to resolve these discrepancies; the theoretical results indicate that the ionization energy is near the lower end of this range. The calculated ionization energies for PuO, PuO⁺ and PuO₂⁺ are in good agreement with the experimental values.

The La + O and La + O₂ chemiionization reactions have been investigated with quantum chemical methods. For La + O₂(X³Î£_g) and La + O₂(a¹Î”_g), the chemiionization reaction La + O₂ → LaO₂⁺ + e^− has been shown to be endothermic and does not contribute to the experimental chemielectron spectra. For the La + O₂(X³Î£_g) reaction conditions, chemielectrons are produced by La + O₂ → LaO + O, followed by La + O → LaO⁺ + e^−. This is supported by the same chemielectron band, arising from La + O → LaO⁺ + e^−, being observed from both the La + O(³P) and La + O₂(X³Î£_g) reaction conditions. For La + O₂(a¹Î”_g), a chemielectron band with higher electron kinetic energy than that obtained from La + O₂(X³Î£_g) is observed. This is attributed to production of O(¹D) from the reaction La + O₂(a¹Î”_g) → LaO + O(¹D), followed by chemiionization via the reaction La + O(¹D) → LaO⁺ + e^−. Potential energy curves are computed for a number of states of LaO, LaO* and LaO⁺ to establish mechanisms for the observed La + O → LaO⁺ + e^− chemiionization reactions.

We describe the preparation of a helicate containing four closely spaced, linearly arrayed copper(I) ions. This product may be prepared either directly by mixing copper(I) with a set of precursor amine and aldehyde subcomponents, or indirectly through the dimerization of a dicopper(I) helicate upon addition of 1,2-phenylenediamine. A notable feature of this helicate is that its length is not limited by the lengths of its precursor subcomponents: each of the two ligands wrapped around the four copper(I) centers contains one diamine, two dialdehyde, and two monoamine residues. This work thus paves the way for the preparation of longer oligo- and polymeric structures. DFT calculations and electrochemical measurements indicate a high degree of electronic delocalization among the metal ions forming the cores of the structures described herein, which may therefore be described as "molecular wires".

A large set of electronic states of scandium dimer has been calculated using high-level theoretical methods such as quantum diffusion Monte Carlo (DMC), complete active space perturbation theory as implemented in GAMESS-US, coupled-cluster singles, doubles, and triples, and density functional theory (DFT). The ³Î£_u and ⁵Σ_u states are calculated to be close in energy in all cases, but whereas DFT predicts the ⁵Σ_u state to be the ground state by 0.08 eV, DMC and CASPT2 calculations predict the ³Î£_u to be more stable by 0.17 and 0.16 eV, respectively. The experimental data available are in agreement with the calculated frequencies and dissociation energies of both states, and therefore we conclude that the correct ground state of scandium dimer is the ³Î£_u state, which breaks with the assumption of a ⁵Σ_u ground state for scandium dimer, believed throughout the past decades.

A multireference second-order perturbation theory using a restricted active space self-consistent field wave function as reference (RASPT2/RASSCF) is described. This model is particularly effective for cases where a chemical system requires a balanced orbital active space that is too large to be addressed by the complete active space self-consistent field model with or without second-order perturbation theory (CASPT2 or CASSCF, respectively). Rather than permitting all possible electronic configurations of the electrons in the active space to appear in the reference wave function, certain orbitals are sequestered into two subspaces that permit a maximum number of occupations or holes, respectively, in any given configuration, thereby reducing the total number of possible configurations. Subsequent second-order perturbation theory captures additional dynamical correlation effects. Applications of the theory to the electronic structure of complexes involved in the activation of molecular oxygen by mono- and binuclear copper complexes are presented. In the mononuclear case, RASPT2 and CASPT2 provide very similar results. In the binuclear cases, however, only RASPT2 proves quantitatively useful, owing to the very large size of the necessary active space.

Some dimetal fullerenes M₂@C₆₀ (M = Cr, Mo, W) have been studied with computational quantum chemistry methods. The transition metal diatomic molecules Cr₂, Mo₂, W₂ form exohedral complexes with C₆₀, while U₂ forms a highly symmetric endohedral compound and it is placed in the center of the C₆₀ cavity. This highly symmetric structure is an artifact due to the small size of the C₆₀ cavity, which constrains U₂ at the center. If a larger cavity is used, like C₇₀ or C₈₄, U₂ preferentially binds the internal walls of the cavity and the U−U bond no longer exists.

Quantum mechanical calculations, using both CASPT2 and DFT methods, for the model systems (MeMMMe, PhMMPh, (MeMMMe)(C₆H₆)₂, Ar^§MMAr^§, Ar^#MMAr^#; M = Cr, Fe, Co; Ar^§ = C₆H₄-2(C₆H₅), Ar^# = C₆H₃-2,6(C₆H₃-2,6-Me₂)₂) are described. These studies were undertaken to provide a multireference description of the metal−metal bond in the simple dimers MeMMMe and PhMMPh (M = Cr, Fe, Co) and to determine the extent of secondary metal−arene interaction involving the flanking aryl rings of the terphenyl ligands in quintuply bonded Ar′CrCrAr′ (Ar′ = C₆H₃-2,6(C₆H₃-2,6-Prⁱ₂)₂). We show that in the Cr−Cr species the Cr−arene interaction is a feeble one that causes only a small weakening of the quintuple bond. In sharp contrast, in the analogous Fe and Co species strong η⁶-arene interactions that preclude significant metal−metal bonding are predicted.

The relative energies of side-on versus end-on binding of molecular oxygen to a supported Cu(I) species, and the singlet versus triplet nature of the ground electronic state, are sensitive to the nature of the supporting ligands and, in particular, depend upon their geometric arrangement relative to the O₂ binding site. Highly correlated ab initio and density functional theory electronic structure calculations demonstrate that optimal overlap (and oxidative charge transfer) occurs for the side-on geometry, and this is promoted by ligands that raise the energy, thereby enhancing resonance, of the filled Cu d_xz orbital that hybridizes with the in-plane Ï€* orbital of O₂. Conversely, ligands that raise the energy of the filled Cu d_z² orbital foster a preference for end-on binding as this is the only mode that permits good overlap with the in-plane O₂ Ï€*. Because the overlap of Cu d_z² with O₂ Ï€* is reduced as compared to the overlap of Cu d_xz with the same O₂ orbital, the resonance is also reduced, leading to generally more stable triplet states relative to singlets in the end-on geometry as compared to the side-on geometry, where singlet ground states become more easily accessible once ligands are stronger donors. Biradical Cu(II)-O₂ superoxide character in the electronic structure of the supported complexes leads to significant challenges for accurate quantum chemical calculations that are best addressed by exploiting the spin-purified M06L local density functional, single-reference completely renormalized coupled-cluster theory, or multireference second-order perturbation theory, all of which provide predictions that are qualitatively and quantitatively consistent with one another.

The new bis(pentalene) complex Cr₂(η⁵:η⁵-C₈H₄^1,4-SiiPr₃)₂ has been synthesized and characterized; it is found to exhibit paramagnetism at room temperature, and solid-state magnetic studies show that the dimer is best modeled as containing a pair of antiferromagnetically interacting S = ½ centers with the separation between the singlet ground state and triplet excited state being 2.23 kJ mol^−1. Structural data show a Cr−Cr distance of 2.2514(15) Ã…, consistent with a strong metal−metal interaction. The bonding has been further investigated by density functional, hybrid, and CASPT2 methods. The metal−metal interaction is best described by a double bond with each metal having an 18-electron count. Theory predicts the singlet and triplet states to lie close in energy but puts the triplet state at a slightly lower energy than the singlet. The energy difference predicted by CASPT2 is closest to the experimental value.

Laser-ablated Th atoms react with molecular hydrogen to give thorium hydrides and their dihydrogen complexes during condensation in excess neon and hydrogen for characterization by matrix infrared spectroscopy. The ThH₂, ThH₄, and ThH₄(H₂)_x (x = 1−4) product molecules have been identified through isotopic substitution (HD, D₂) and comparison to frequencies calculated by density functional theory and the coupled-cluster, singles, doubles (CCSD) method and those observed previously in solid argon. Theoretical calculations show that the Th−H bond in ThH₄ is the most polarized of group 4 and uranium metal tetrahydrides, and as a result, a strong attractive “dihydrogenâ€� interaction was found between the oppositely charged hydride and H₂ ligands ThH₄(H₂)_x. This bridge-bonded dihydrogen complex structure is different from that recently computed for tungsten and uranium hydride super dihydrogen complexes but is similar to that recently called the “dihydrogen bondâ€� (Crabtree, R. H. Science 1998, 282, 2000). Natural electron configurations show small charge flow from the Th center to the dihydrogen ligands.

The codeposition of laser-ablated tungsten atoms with neat hydrogen at 4 K forms a single major product with a broad 2500 cm^-1 and sharp 1860, 1830, 1782, 1008, 551, and 437 cm^-1 absorptions, which are assigned to the WH₄(H₂)₄ complex on the basis of isotopic shifts and agreement with isotopic frequencies calculated by density functional theory. This D_2d structured complex was computed earlier to form exothermically from W atoms and hydrogen molecules. Annealing the matrix allows hydrogen to evaporate and the complex to aggregate and ultimately to decompose. Comparison of the H−H stretching mode at 2500 cm^-1 and the W−H₂ stretching mode at 1782 cm^-1 with 2690 and 1570 cm^-1 values for the Kubas complex W(CO)₃(PR₃)₂(H₂) suggests that the present physically stable WH₄(H₂)₄ complex has more strongly bound dihydrogen ligands. Our CASPT2 calculations suggest a 15 kcal/mol average binding energy per dihydrogen molecule in the WH₄(H₂)₄ complex.

Americium and curium oxides AmO_n and CmO_n (n = 1, 2) were studied using state-of-the-art multiconfigurational, relativistic, quantum chemical methods. Spectroscopic properties for the ground state and several excited states of the four target compounds were determined. The computed dissociation energy of AmO (4.6 eV) agrees fairly well with estimates derived from experimental studies (5.73 ± 0.37 eV) while the computed dissociation energy of CmO (7.1 eV) agrees well with the experimental value (7.5 eV). The computed ionization energy of AmO (6.3 eV) is in good agreement with the current experimental value (5.9 ± 0.2 eV).

Values of σ and σ⁺, for use in linear free energy relationships, are determined for para hydrogen atoms having nuclear charges other than 1 (nucleomers). Hammett Ï� values for a variety of free energies of activation, reaction, and other extrathermodynamic properties (e.g., vibrational frequencies) are computed therefrom and compared to those computed using typical para functional groups. The nucleomer correlations show excellent qualitative agreement with standard correlations but the quantitative agreement is less good, typically underestimating the standard Ï�-value by 10-60%.

A series of copper(I)−α-ketocarboxylate complexes have been prepared and shown to exhibit variable coordination modes of the α-ketocarboxylate ligand. Reaction with O₂ induces decarboxylation of this ligand, and the derived copper−oxygen intermediate(s) has been intercepted, resulting in hydroxylation of an arene substituent on the supporting N-donor ligand. Theoretical calculations have provided intriguing mechanistic notions for the process, notably implicating hydroxylation pathways that involve novel [Cu^I−OOC(O)R] and [Cu^II−O^-• ↔ Cu^III = O^2-]⁺ species.

Molecular dynamics simulations of Cm(III) in water were performed at two different temperatures, namely, T = 300 K and T = 473 K. Fully ab initio intermolecular potentials were employed. At the lower temperature, T = 300 K, nine water molecules coordinate preferentially the Cm(III) ion in the first coordination sphere, while at the higher temperature, T = 473 K, the preferential coordination number is eight instead of nine. The number of water molecules in the second coordination sphere is not uniquely defined, but the most probable number is 16.

The vibrational spectra of UBz and ThBz have been measured in solid argon. Complementary quantum chemical calculations have allowed the assignments of the vibrational spectra. According to the calculations, AcBz are stable molecules, as well as other species like BzAcBz and BzAc₂Bz. Experimentally, there is no evidence for the sandwich compounds BzAcBz and BzAc₂Bz due to the limitations in the reagent concentrations.

The incorporation of enantiopure 1-amino-2,3-propanediol as a subcomponent into a dicopper double helicate resulted in perfect chiral induction of the helicate's twist. DFT calculations allowed the determination of the helicity of the complex in solution. The same helical induction, in which S amines induced a Λ helical twist, was observed in the solid state by X-ray crystallography. Electronic structure calculations also revealed that the unusual deep green color of this class of complexes was due to a metal-to-ligand charge transfer excitation, in which the excited state possesses a valence delocalized Cu₂³⁺ core. The use of a racemic amine subcomponent resulted in the formation of a dynamic library of six diastereomeric pairs of enantiomers. Surprisingly, this library converted into a single pair of enantiomers during crystallization. We were able to observe this process reverse upon redissolution, as initial ligand exchange was followed by covalent imine metathesis.

Several monouranium and diuranium polyhydride molecules were investigated using quantum chemical methods. The infrared spectra of uranium and hydrogen reaction products in condensed neon and pure hydrogen were measured and compared with previous argon matrix frequencies. The calculated molecular structures and vibrational frequencies were used to identify the species present in the matrix. Major new absorptions were observed and compared with the previous argon matrix study. Spectroscopic evidence was obtained for the novel complex, UH₄(H₂)₆, which has potential interest as a metal hydride with a large number of hydrogen atoms bound to uranium. Our calculations show that the series of complexes UH₄(H₂)_1,2,4,6 are stable.

The ground state properties and absorption spectra of N-benzylideneaniline (NBA) have been studied at the density functional (DFT) and at the time-dependent density functional (TD-DFT) level of the theory. The equilibrium geometries of the E and Z isomers in the ground state and their vibrational frequencies have been computed. Furthermore, the excitation energies of the lowest excited singlet and triplet states and the potential energy curves along the torsion and the inversion isomerization coordinates were evaluated. The results are discussed in light of the available experimental data.

The ground and excited electronic state properties of calicene (triapentafulvalene or 5-(cycloprop-2-en-1-ylidene)cyclopenta-1,3-diene) have been studied with a variety of density functional models (mPWPW91, PBE, TPSS, TPSh, B3LYP) and post-Hartree−Fock models based on single (MP2 and CCSD(T)) and multideterminantal (CASPT2) reference wave functions. All methods agree well on the properties of ground-state calicene, which is described as a conjugated double bond system with substantial zwitterionic character deriving from a charge-separated mesomer in which the three- and five-membered rings are both aromatic. Although the two rings are joined by a formal double bond, contributions from the aromatic mesomer reduce its bond order substantially. A rotational barrier of 40−41 kcal mol^-1 is predicted in the gas phase and solvation effects reduce the barrier to 37 and 33 kcal mol^-1 in benzene and water, respectively, because of increased zwitterionic character in the twisted transition-state structure. Multi-state CASPT2 (MS-CASPT2) is used to characterize the first few excited singlet and triplet states and indicates that the most important transition occurs at 4.93 eV (251 nm). A cis−trans photoisomerization about the inter-ring double bond is found to be inefficient.

Maxing out at six: The maximum bond order that can be achieved between two equal atoms in the periodic system is six. The picture shows the potential energy curves for the diatoms Cr₂, Mo₂, and W₂, where the latter two are sextuply bonded molecules (d=internuclear distance in atomic units).

Recent advances in computational actinide chemistry are reported in this tutorial review. Muticonfigurational quantum chemical methods have been employed to study the gas phase spectroscopy of small actinide molecules. Examples of actinide compounds studied in solution are also presented. Finally the multiple bond in the diuranium molecule and other diactinide compounds is described.

The endohedral fullerene CH₄@C₈₄ has been studied using density functional theory (DFT) and second-order Møller-Plesset perturbation theory (MP2). In addition to the structure with a C— bond of CH₄ in a tetrahedral pocket conformation, we find an alternative minimum, very close in energy (6.3-9.5 kJ/mol higher according to the level of theory), with the methane inverted, which we call the antipocket conformation. Computed IR spectra are reported for CH₄@C₈₄ and also for the reference system CH₄@C₆₀. The calculated vibrational levels, in a harmonic approximation, reveal close-lying translational, librational, and shell-vibrational modes. The results are also presented for the isoelectronic species NH₄⁺@C₆₀.

Multiconfigurational quantum chemical methods (CASSCF/CASPT2) have been used to study the chemical bond in the actinide diatoms Ac₂, Th₂, Pa₂, and U₂. Scalar relativistic effects and spin−orbit coupling have been included in the calculations. In the Ac₂ and Th₂ diatoms the atomic 6d, 7s, and 7p orbitals are the significant contributors to the bond, while for the two heavier diatoms, the 5f orbitals become increasingly important. Ac₂ is characterized by a double bond with a ³âˆ‘_g^-(0_g⁺) ground state, a bond distance of 3.64. Ã…, and a bond energy of 1.19 eV. Th₂ has quadruple bond character with a ³D_g(1_g) ground state. The bond distance is 2.76 Ã… and the bond energy (D₀) 3.28 eV. Pa₂ is characterized by a quintuple bond with a ³âˆ‘_g^-(0_g⁺) ground state. The bond distance is 2.37 Ã… and the bond energy 4.00 eV. The uranium diatom has also a quintuple bond with a ⁷O_g (8_g) ground state, a bond distance of 2.43 Ã…, and a bond energy of 1.15 eV. It is concluded that the strongest bound actinide diatom is Pa₂, characterized by a well-developed quintuple bond.

The binding of N-heterocyclic carbenes to Ce(III) and U(III) compounds is characterized by quantum chemical methods. Density functional methods are in qualitative agreement with experiment that binding to U(III) is more favorable than to Ce(III); after correcting for basis-set superposition error, quantitative agreement with experiment is achieved with a multireference second-order perturbation theory approach accounting for relativistic effects. The small computed (and observed) preference derives from a combination of several small effects, including differences in electronic binding energies, rovibrational partition functions, and solvation free energies. Prospects for ligand modification to improve the differentiation between lanthanides and actinides are discussed on the basis of computational predictions.

The relative energetics of μ-η¹:η¹ (trans end-on) and μ-η²:η² (side-on) peroxo isomers of Cu₂O₂ fragments supported by 0, 2, 4, and 6 ammonia ligands have been computed with various density functional, coupled-cluster, and multiconfigurational protocols. There is substantial disagreement between the different levels for most cases, although completely renormalized coupled-cluster methods appear to offer the most reliable predictions. The significant biradical character of the end-on peroxo isomer proves problematic for the density functionals, while the demands on active space size and the need to account for interactions between different states in second-order perturbation theory prove challenging for the multireference treatments. In the latter case, it proved impossible to achieve any convincing convergence.

Nice to see U₂! The [PhUUPh] molecule (see picture; U pink, C gray, H white) has been studied by multiconfigurational quantum chemical methods. It was found that a quintuple bond is formed between the two uranium atoms with a U—U bond length of 2.29 Ã…. The phenyl ligand was used to mimic a bulky terphenyl ligand, which could be a promising candidate for the stabilization of multiply bonded uranium compounds.

Quantum chemistry can today be employed to invent new molecules and explore unknown molecular bonding. An overview of novel species containing metals bound to polynitrogen clusters is presented. The prediction of metal polyhydrides is discussed. Finally, some species containing gold that behaves as a halogen are described, together with recent advances in actinide chemistry and exploration of the nature of the actinide–actinide chemical bonding.

A series of 6-styryl-2,4-diphenylpyrylium salts exhibiting dual fluorescence has been investigated by fluorescence up-conversion in conjunction with quantum chemical calculations. The short-wavelength emission is due to an excited state localized on the pyrylium fragment and the long-wavelength emission arises from a charge-transfer state delocalized over the whole molecule. The two fluorescing states do not exhibit a precursor−successor relationship. The rise time of the short-wavelength fluorescence is smaller than 200 fs, and that of the long-wavelength emission depends on the electron-donating property of the styryl group substituent. The rise is almost prompt with the weaker donors but is slower, wavelength and viscosity dependent with the strongest electron-donating group. A model involving a S₂/S₁ conical intersection is proposed to account for these observations.

Multiconfigurational quantum chemical methods show that a quintuple bond is present between the two Cr^I units in the model complex [PhCrCrPh]. The Cr—Cr (1.75 Ã…) and Cr—Ph (2.02 Ã…) bonds are shorter than those in the recently reported compound [Ar'CrCrAr'] (Ar'=2,6-(2,6-iPr₂C₆H₃)₂C₆H₃; 1.83 and 2.15 Ã…, respectively). This difference is attributed to the additional Cr—Ar' interactions.

Matrix isolation infrared (IR) studies have been carried out on the vaporisation of the alkali-metal azides MN₃ (M = Na, K, Rb and Cs). The results show that under high vacuum conditions, molecular KN₃, RbN₃ and CsN₃ are present as stable high-temperature vapour species, together with variable amounts of nitrogen gas and the corresponding metal atoms. The characterisation of these molecular azides is supported by ab initio molecular orbital calculations and density functional theory (DFT) calculations, and for CsN₃ in particular, by the detection of the isotopomers Cs(¹⁴N¹⁵N¹⁴N) and Cs(¹⁵N¹⁴N¹⁴N). The IR spectra are assigned to a "side-on" (C_2v) structure by comparison with the spectral features predicted both by vibrational analysis and calculation. The most intense IR features for KN₃, RbN₃ and CsN₃ isolated in nitrogen matrices lie at 2005, 2004.4 and 2002.2 cm^-1, respectively, and correspond to the N₃ asymmetric stretch. The N₃ bending mode in CsN₃ is identified at 629 cm^-1. An additional feature routinely observed in these experiments occurred at approximately 2323 cm^-1 and is assigned to molecular N₂, perturbed by the close proximity of an alkali-metal atom. The position of this band appeared to show very little cation dependence, but its intensity correlated with the extent of sample thermal decomposition.

Accurately describing the relative energetics of alternative bis(μ-oxo) and μ-η²:η² peroxo isomers of Cu₂O₂ cores supported by 0, 2, 4, and 6 ammonia ligands is remarkably challenging for a wide variety of theoretical models, primarily owing to the difficulty of maintaining a balanced description of rapidly changing dynamical and nondynamical electron correlation effects and a varying degree of biradical character along the isomerization coordinate. The completely renormalized coupled-cluster level of theory including triple excitations and extremely efficient pure density functional levels of theory quantitatively agree with one another and also agree qualitatively with experimental results for Cu₂O₂ cores supported by analogous but larger ligands. Standard coupled-cluster methods, such as CCSD(T), are in most cases considerably less accurate and exhibit poor convergence in predicted relative energies. Hybrid density functionals significantly underestimate the stability of the bis(μ-oxo) form, with the magnitude of the error being directly proportional to the percentage Hartree−Fock exchange in the functional. Single-root CASPT2 multireference second-order perturbation theory, by contrast, significantly overestimates the stability of bis(μ-oxo) isomers. Implications of these results for modeling the mechanism of C−H bond activation by supported Cu₂O₂ cores, like that found in the active site of oxytyrosinase, are discussed.

Results from quantum chemical calculations that predict the existence of a series of diuranium molecules are reported. Two diuranium chlorides, U₂Cl₆ and U₂Cl₈^2-, and three different carboxylates, U₂(OCHO)₄, U₂(OCHO)₆, and U₂(OCHO)₄Cl₂ have been studied. All species have been found to be stable with a multiply bonded U₂ unit.

The tendency for mixed-isotope O₂ fragments to exhibit different stretching frequencies in asymmetric environments is examined with various levels of electronic structure theory for simple peroxides and peroxyl radicals, as well as for a variety of monocopper–O₂ complexes. The study of the monocopper species is motivated by their relevance to the active site of galactose oxidase. Extensive theoretical work with an experimental model characterized by Jazdzewski et al. (J. Biol. Inorg. Chem. 8:381–393, 2003) suggests that the failure to observe a splitting between ¹⁶O¹⁸O and ¹⁸O¹⁶O isotopomers cannot be taken as evidence against end-on O₂ coordination. Conformational analysis on an energetic basis, however, is complicated by biradical character inherent in all of the copper–O₂ singlet structures.

Quantum chemical calculations show that metal−hydride molecules are more compact when they are placed inside a fullerene cage than when they are isolated molecules. The metal−hydrogen bond distance in ZrH₄ becomes 0.15 Ã… shorter when it is placed inside a C₆₀ cage. Metal−polyhydride molecules with a large number of H atoms such as ScH₁₅ and ZrH₁₆, which are not bound as isolated molecules, are predicted to be bound inside a fullerene cage. It is also shown that two TiH₁₆ clusters are bound inside a bicapped (9,0) carbon nanotube. Possible ways to make metal−hydrides inside C₆₀ and nanotubes are suggested.

Four compounds containing metal−metal quadruple bonds, the [M₂(CH₃)₈]^n- ions (M = Cr, Mo, W, Re and n = 4, 4, 4, 2, respectively), have been studied theoretically using multiconfigurational quantum-chemical methods. The molecular structure of the ground state of these compounds has been determined and the energy of the δ → δ* transition has been calculated and compared with previous experimental measurements. The high negative charges on the Cr, Mo, and W complexes lead to difficulties in the successful modeling of the ground-state structures, a problem that has been addressed by the explicit inclusion of four Li⁺ ions in these calculations. The ground-state geometries of the complexes and the δ → δ* transition have been modeled with either excellent agreement with experiment (Re) or satisfactory agreement (Cr, Mo, and W).

Covalent bonding is commonly described by Lewis's theory, with an electron pair shared between two atoms constituting one full bond. Beginning with the valence bond description for the hydrogen molecule, quantum chemists have further explored the fundamental nature of the chemical bond for atoms throughout the periodic table, confirming that most molecules are indeed held together by one electron pair for each bond. But more complex binding may occur when large numbers of atomic orbitals can participate in bond formation. Such behaviour is common with transition metals. When involving heavy actinide elements, metal–metal bonds might prove particularly complicated. To date, evidence for actinide–actinide bonds is restricted to the matrix-isolation of uranium hydrides, including H₂U–UH₂, and the gas-phase detection and preliminary theoretical study of the uranium molecule, U₂. Here we report quantum chemical calculations on U₂, showing that, although the strength of the U₂ bond is comparable to that of other multiple bonds between transition metals, the bonding pattern is unique. We find that the molecule contains three electron-pair bonds and four one-electron bonds (that is, 10 bonding electrons, corresponding to a quintuple bond), and two ferromagnetically coupled electrons localized on one U atom each—so all known covalent bonding types are contributing.

The U+O chemi-ionization reaction has been investigated by quantum chemical methods. Potential-energy curves have been calculated for several electronic states of UO and UO⁺. Comparison with the available spectroscopic and thermodynamic values for these species is reported and a mechanism for the chemi-ionization reaction U+O→UO⁺+e^− is proposed. The U+O and Sm+O chemi-ionization reactions are the first two metal-plus-oxidant chemi-ionization reactions to be studied theoretically in this way.

Quantum chemical calculations, based on multiconfigurational wave functions and including relativistic effects, show that the U₂²⁺ system has a large number of low-lying electronic states with S of 0 to 2 and Λ ranging from zero to ten. These states share a very small bond length of about 2.30 Ã…, compared to 2.43 Ã… in neutral U₂. The Coulomb explosion to 2 U⁺ lowers the energy by only 1.6 eV and is separated by a broad barrier.

The gas-phase electronic spectra of 2-(2'-hydroxybenzoyl)pyrrole and 2-(2'-methoxybenzoyl)pyrrole have been determined using multiconfigurational perturbation theory (CASPT2). Solvatochromic spectral shifts for these molecules have been measured in cyclohexane and methanol and the electrostatic components of these shifts have been estimated using the vertical electrostatic model (VEM 4.2) developed for the configuration interaction with single excitations model implemented with the intermediate neglect of differential overlap Hamiltonian (CIS/INDO/S2). Comparison between theory and experiment and an interpretation of the main spectral differences between the two substituted pyrroles and their solvation are presented.

The electronic spectrum of the UO₂ molecule has been determined using multiconfigurational wave functions together with the inclusion spin−orbit coupling. The molecule has been found to have a (5fφ)(7s), ³Î¦_2u, ground state. The lowest state of gerade symmetry, ³H_4g, corresponding to the electronic configuration (5f)² was found 3330 cm^-1 above the ground state. The computed energy levels and oscillator strengths were used for the assignment of the experimental spectrum in the energy range 17 000−19 000 and 27 000−32 000 cm^-1.

The coordination environment of uranyl in water has been studied using a combined quantum mechanical and molecular dynamics approach. Multiconfigurational wave function calculations have been performed to generate pair potentials between uranyl and water. The quantum chemically determined energies have been used to fit parameters in a polarizable force field with an added charge transfer term. Molecular dynamics simulations have been performed for the uranyl ion and up to 400 water molecules. The results show a uranyl ion with five water molecules coordinated in the equatorial plane. The U−O(H₂O) distance is 2.40 Ã…, which is close to the experimental estimates. A second coordination shell starts at about 4.7 Ã… from the uranium atom. No hydrogen bonding is found between the uranyl oxygens and water. Exchange of waters between the first and second solvation shell is found to occur through a path intermediate between association and interchange. This is the first fully ab initio determination of the solvation of the uranyl ion in water.

Cumulated triple bonds: A new class of molecules, the isoelectronic series of NUIr, (depicted) has been postulated and theoretically studied. The bond between the actinide and the 5d-metal atom is very short and is shown to correspond to triple bonding. The N — U bond is also a triple bond.

The fragmentation behaviour of the ion MeP(O)OMe⁺ has been investigated using quantum mechanical calculations at the B3LYP and MP2 levels to support experiments made with an Ion Trap Mass Spectrometer. Two mechanisms for the loss of CH₂O are found, one involving a 1,3-H migration to phosphorus and the other a 1,2-methyl migration to give P(OMe)₂⁺ followed by a 1,3-H migration. In each case an ion-dipole complex is formed that rapidly dissociates to yield CH₂O. The relative importance of each route has been previously determined experimentally via isotopic labelling experiments, and the theoretical results are found to be consistent with these experimental results. The mechanisms suggested in the earlier work involving a 1,4 H migration to O are shown to be energetically unfavourable.

In the present paper we report the results of a multiconfigurational computational study on potential-energy curves of azobenzene along the NN twisting to clarify the role of this coordinate in the decay of the S₂(ππ*) and S₁(nÏ€*) states. We have found that there is a singlet state, S₃ at the trans geometry, on the basis of the doubly excited configuration n²Ï€*², that has a deep minimum at about 90° of twisting, where it is the lowest excited singlet state. The existence of this state provides an explanation for the short lifetime of S₂(ππ*) and for the wavelength-dependence of azobenzene photochemistry. We have characterized the S₁(nÏ€*) state by calculating its vibrational frequencies, which are found to correspond to the recently observed transient Raman spectrum. We have also computed the potential-energy curve for the triplet T₁(nÏ€*) at the density functional theory B3LYP level, which indicates that in this state the isomerization occurs along the twisting coordinate.

In this paper, we identify the most efficient decay and isomerization route of the S₁, T₁, and S₀ states of azobenzene. By use of quantum chemical methods, we have searched for the transition states (TS) on the S₁ potential energy surface and for the S₀/S₁ conical intersections (CIs) that are closer to the minimum energy path on the S₁. We found only one TS, at 60° of CNNC torsion from the E isomer, which requires an activation energy of only 2 kcal/mol. The lowest energy CIs, lying also 2 kcal/mol above the S₁ minimum, were found on the torsion pathway for CNNC angles in the range 95−90°. The lowest CI along the inversion path was found ca. 25 kcal/mol higher than the S₁ minimum and was character₁ state decay involves mainly the torsion route and that the inversion mechanism may play a role only if the molecule is excited with an excess energy of at least 25 kcal/mol with respect to the S₁ minimum of the E isomer. We have calculated the spin−orbit couplings between S₀ and T₁ at several geometries along the CNNC torsion coordinate. These spin−orbit couplings were about 20−30 cm^-1 for all the geometries considered. Since the potential energy curves of S₀ and T₁ cross in the region of twisted CNNC angle, these couplings are large enough to ensure that the T₁ lifetime is very short (~10 ps) and that thermal isomerization can proceed via the nonadiabatic torsion route involving the S₀−T₁−S₀ crossing with preexponential factor and activation energy in agreement with the values obtained from kinetic measures.

The Sm+O chemiionization reaction has been investigated theoretically using a method that allows for correlation and relativistic effects. Potential energy curves have been calculated for several electronic states of SmO and SmO⁺. Comparison with available spectroscopic and thermodynamic values for these species is reported and a mechanism for the chemiionization reaction Sm+O is proposed. The importance of spin–orbit coupling in the excited states of SmO, in allowing this chemiionization reaction to take place, has been revealed by these calculations. This paper shows the metal-plus-oxidant chemiionization reaction.

Quantum chemical calculations suggest that a series of molecules with the general formula MAu₆ are stable, where M is a a group 6 atom, Cr, Mo, W, respectively. These species have a structure analogous to the corresponding MH₆ compounds, while they differ from the MX₆, where X is a halogen. The further reaction MAu₆ + 3Au₂→MAu₁₂ is strongly exothermic.

A new method is presented, which makes it possible to partition molecular properties like multipole moments and polarizabilities, into atomic and interatomic contributions. The method requires a subdivision of the atomic basis set into occupied and virtual basis functions for each atom in the molecular system. The localization procedure is organized into a series of orthogonalizations of the original basis set, which will have as a final result a localized orthonormal basis set. The new localization procedure is demonstrated to be stable with various basis sets, and to provide physically meaningful localized properties. Transferability of the methyl properties for the alkane series and of the carbon and hydrogen properties for the benzene, naphtalene, and anthracene series is demonstrated.

Quantum chemical calculations predict the existence of new molecular species with general formula MH₁₂, where M is a group 6 atom. The previous MH_n species had n values up to 9. The new systems with n = 12 would be a new record for metal hydrides.

An attempt has been made to study the reaction between a uranium atom and a nitrogen molecule theoretically using multiconfigurational wave functions. The C_2v part of the reaction surface has been computed for several electronic states of various spin multiplicities. The system proceeds from a neutral uranium atom in its (5f)³(6d)(7s)², ⁵L ground state to the linear molecule NUN, which has a ¹Î£⁺_g ground state and uranium in a formal U(VI) oxidation state. The effect of spin–orbit coupling has been estimated at crucial points along the reaction. These preliminary results shows that the system proceeds from a quintet state for U + N₂, via a triplet transition state to the final closed shell molecule. An eventual energy barrier for the insertion reaction is caused by the spin–orbit coupling energy.

Results are presented from a theoretical study of the lower electronic states of the CUO molecule. Multiconfigurational wave functions have been used with dynamic correlation added using second order perturbation theory. Extended basis sets have been used, which for uranium were contracted including scalar relativistic effects. Spin–orbit interaction has been included using the state-interaction approach. The results predict that the ground state of linear CUO is Φ₂ with the closed shell Σ+0 state 0.5 eV higher in energy. This is in agreement with matrix isolation spectroscopy, which predicts Φ₂ as the ground state when the matrix contains noble gas atoms heavier than Ne. In an Ne matrix, the experiments indicate, however, that CUO is in the Σ+0 state. The change of ground state due to the change of the matrix surrounding CUO cannot be explained by the results obtained in this work and remains a mystery.

One of the prototype compounds for metal−metal multiple bonding, the Re₂Cl₈^2- ion, has been studied theoretically using multiconfigurational quantum chemical methods. The molecular structure of the ground state has been determined. It is shown that the effective bond order of the Re−Re bond is close to three, due to the weakness of, in particular, the δ bond. The electronic spectrum has been calculated with the inclusion of spin−orbit coupling. Observed spectral features have been reproduced with good accuracy, and a number of new assignments are suggested.

Quantum chemical calculations suggest that group 4 tetra-azides M(N₃)₄, where M = Ti, Zr, Hf, and Th, are stable species. They present a unique structural feature; namely, the M−N−N−N fragments are linear. These species are energetically more stable than the corresponding isomers with general formula η⁵-N₅ −M−η⁷-N₇, and the Th species, Th(N₃)₄, is the most stable of all. Possible mixed nitride azides NMN₃ were also investigated.

Quantum chemical calculations suggest that a series of molecules with the general formula MAu₄ are stable, where M = U, Th, and a group-4 atom. They correspond to Au in the formal valence state −1 and indicate that gold can act as a ligand similar to the halogen series. Of the MAu₄ species studied, UAu₄, the first predicted mixed gold uranium compound, has a short M−Au bond distance, 2.71 Ã…, which would locate Au between Br and I from the bond length point of view in the U-tetrahalide series. Energetically, the U−Au bond is weaker than the corresponding U−Br and U−I bonds.

Quantum chemical calculations suggest that inverse sandwich compounds with the general formula MN₇ M', where M is an alkali metal (K,Rb,Cs), N₇ is a ten-Ï€-electron ring, and M' is an alkaline-earth metal (Ca,Sr,Ba), are local C_7v minima. Among these systems, the CsN₇Ba molecule is the stablest of all and presents a barrier of 35 kcal/mol to dissociation towards CsNBa and three N₂ molecules. Substantial 5d character is found in the bonding. Possible ways of making these high-energy compounds are discussed.

The results of a study on the ground-state of monocarbonate, bicarbonate, and tricarbonate complexes of neptunyl using multiconfigurational second-order perturbation theory (CASSCF/CASPT2) are presented. The equilibrium geometries of the complexes corresponding to neptunium in the formal oxidation state (V) have been fully optimized at the CASPT2 level of theory in the presence of an aqueous environment modeled by a reaction field Hamiltonian with a spherical cavity. Some water molecules have been explicitly included in the calculation. This study is consistent with the hypothesis that the monocarbonate complex has a pentacoordinated structure with three water molecules in the first coordination shell and that the bicarbonate complex has a hexacoordinated structure, with two water molecules in the first coordination shell. The typical bond distances are in good agreement with experimental results. The tricarbonate complex was studied with explicit counterions, which resulted in somewhat longer Np−carbonate bond distances than experiment indicates.

Ab initio calculations at the B3LYP and MP2 levels suggest that a series of compounds with the general formula N₅MN₇ (M = Ti, Zr, Hf, Th) are locally stable. These compounds are thermodynamically at least as stable as the recently suggested ScN₇ molecule. N₅ThN₇ seems the most stable of all. It lies 21.5 kcal/mol below a transition state, corresponding to the opening of one N−N bond in the N₇ ring, and only 132 kcal/mol above Th + 6 N₂, or 22 kcal/(mol N₂).

The two-photon spectrum of the 2¹A_g â†� 1¹A_g transition in trans-stilbene has been calculated at the complete active space self-consistent field (CASSCF) level of theory. Energies were obtained at the complete active space second-order perturbation (CASPT2) level of theory, while the geometries of both the initial and final states were optimized at the CASSCF level. The energy and the geometry optimizations were performed using an active space of 14 electrons in 14 active Ï€ orbitals. The vibrational frequencies of both states and the two-photon transition (TPT) cross-section were calculated with a smaller active space where the two lowest Ï€ orbitals were kept inactive. A newly implemented algorithm, in the quantum chemical package Molcas was used to determine the two-photon transition intensity. This method requires only the linear response of the CASSCF wavefunction. Furthermore, the vibronic structure of this TPT was studied. The Franck-Condon factors were obtained by calculating the overlap between the vibrational states involved, which were determined from the force fields of both the initial and final states, at the CASSCF level of theory. The results are in agreement with experiment.

Quantum chemical calculations of vibrational frequencies of Stilbene were followed by the computation of the potential energy surface for the two rotors related to the single bonds. By the flexible model approach applied to the computed surface we have confirmed previous assignment of mode 37 and determined frequency of the elusive mode 48. The same analysis was performed not only for the ground, but also for the excited electronic state. The shape of the potential energy surface in S₀ is in agreement with that of styrene and the barrier height obtained from the fitting in S₁ is increased with respect to S₀, as expected.

The existence of a series of triatomic molecules with the general formula MNM‘, where M is an alkaline metal (K, Rb, Cs), and M‘ is an alkaline earth metal (Ca, Sr, Ba), has been predicted by quantum chemical methods. Among these, the CsNBa molecule shows a feature not found before, the presence of a multiple bond between barium and nitrogen. As a consequence of this novel bonding situation, the molecule is linear. The same holds for all Ba triatomics, MNBa, independent of the nature of the alkali M atom, and for all Sr compounds, MNSr. The presence of a multiple bond makes CsNBa, and other related Ba and Sr molecules, particularly stable and appealing experimentally. The systems with the alkaline earth metal M‘ = Ca, on the other hand, turned out to be bent. Calculations have also been performed on the negative ions BaN^- and CaN^-, which form a well-defined entity in the MNM‘ systems (M‘ = Ba, Ca). The results show that the two ions have a different electronic structure in the ground state, which is one reason for the different properties of the MNM‘ systems and explains why the molecules containing the BaN^- moiety are linear, while those containing CaN^- are bent.

The results of a theoretical study of the ground state, 1¹A_g, and of the lowest ¹B_u states oftrans-stilbene are presented. The vertical and adiabatic excitation energies of the lowest ¹B_ustates have been computed using multiconfigurational SCF theory, followed by second-order perturbation theory. It is shown that the two lowest excited states are separated by a small energy gap in the Franck−Condon region. They are the 1¹B_u, characterized by the HOMO→LUMO single excitation substantially localized on the ethylenic moiety, and the 2¹B_u, formed by a combination of one electron excitations localized mainly on the benzene rings. The most intense transition is found to be the lowest in energy when the interaction between different states is included at the level of second-order perturbation theory. The vibronic structure of emission and absorption spectra of the two lowest ¹B_u states have been determined within the Franck−Condon approximation. The spectrum calculated for the 1¹B_ustate agrees with the experimental spectrum, while the low intensity band computed for the 2¹B_u state has no experimental counterpart. It is concluded that this band is buried in the strong 1¹B_u absorption and therefore not observed.

This article presents a numerical quadrature intended primarily for evaluating integrals in quantum chemistry programs based on molecular orbital theory, in particular density functional methods. Typically, many integrals must be computed. They are divided up into different classes, on the basis of the required accuracy and spatial extent. Ideally, each batch should be integrated using the minimal set of integration points that at the same time guarantees the required precision. Currently used quadrature schemes are far from optimal in this sense, and we are now developing new algorithms. They are designed to be flexible, such that given the range of functions to be integrated, and the required precision, the integration is performed as economically as possible with error bounds within specification. A standard approach is to partition space into a set of regions, where each region is integrated using a spherically polar grid. This article presents a radial quadrature which allows error control, uniform error distribution and uniform error reduction with increased number of radial grid points. A relative error less than 10^−14 for all s-type Gaussian integrands with an exponent range of 14 orders of magnitude is achieved with about 200 grid points. Higher angular lquantum numbers, lower precision or narrower exponent ranges require fewer points. The quadrature also allows controlled pruning of the angular grid in the vicinity of the nuclei.

The results of a study on the ground states of tricarbonato complexes of dioxouranate using multiconfigurational second-order perturbation theory (CASSCF/CASPT2) are presented. The equilibrium geometries of the complexes corresponding to uranium in the formal oxidation states VI and V, [UO₂(CO₃)₃]^4- and [UO₂(CO₃)₃],^5- have been fully optimized in D_3h symmetry at second-order perturbation theory (MBPT2) level of theory in the presence of an aqueous environment modeled by a reaction field Hamiltonian with a spherical cavity. The uranyl fragment has also been optimized at CASSCF/CASPT2, to obtain an estimate of the MBPT2 error. Finally, the effect of distorting the D_3h symmetry to C₃ has been investigated. This study shows that only minor geometrical rearrangements occur in the one-electron reduction of [UO₂(CO₃)₃]^4- to [UO₂(CO₃)₃],^5- confirming the reversibility of this reduction.

The results of a theoretical study on the formation of the nitrogen cluster N₁₀ from the ionic species N₅⁺ and N₅^− are presented. The possibility to form N₈ from N₅⁺ and N₃^−has also been studied but no stable form was found. Structural and vibrational data are given for the different clusters. It is suggested that the anion N₅^− might be stable enough to be synthesized. The calculations have been carried out using multiconfigurational self-consistent-field wave functions and second-order perturbation theory.

An implementation of spin–orbit coupling within a two-component generalization of the density functional code MAGIC is described. The spin–orbit operator is represented in the effective one-electron mean-field approximation and included into the Fock matrix within an iterative self-consistent scheme. First tests have been carried out for the spin–orbit splitting of several atoms. The spin–orbit effect on the bond distance and harmonic frequency of some diatomics has also been determined. This scheme allows to include spin–orbit in a simple way and can be efficiently used to treat large systems.

Three all-nitrogen chemical species in bulk compounds are experimentally known from the three last centuries: N₂, N₃^-, and N₅⁺. The last one was predicted in 1991. Furthermore there is evidence for tetrahedral N₄ in matrixes. Could further "nitrogens" exist? In recent years, the hypothetical existence of poly-nitrogen clusters has been the object of several theoretical investigations (refs 5−16 and references therein). Besides their theoretical interest, these structures have drawn attention because of their possible use as high energy-density materials (HEDM), that is, the large ratio between the energy released in a fragmentation reaction and the specific weight.

The structure and vibrational frequencies of the UO₂ molecule have been determined using multiconfigurational wave functions (CASSCF/CASPT2), together with a newly developed method to treat spin−orbit coupling. The molecule has been found to have a (5fφ)(7s), ³Î¦_u, Ω = 2 ground state with a U−O bond distance of 1.77 Ã…. The computed antisymmetric stretching σ_u frequency is 923 cm^-1 with a 16/18 isotope ratio of 1.0525 which compares with the experimental values of 915 cm^-1 and 1.0526, respectively. Calculations of the first adiabatic ionization energy gave the value 6.17 eV, which is 0.7 eV larger than the currently accepted experimental result. Reasons for this difference are suggested.

The isomerization reaction of cubic N8 to the planar bicyclic structure analogous to pentalene has been investigated using multiconfigurational self-consistent field and second-order perturbation theory (CASPT2). Comparative calculations using density functional theory have also been performed. Five local minima on the energy surface have been found, and the transition states between each two consecutive minima have been determined. The results show that all steps in the isomerization process, except one, can proceed via a set of transition states with moderately high energy barriers (10–20kcal/mol).

The HF/3s2pld and MP2/3s2pld structures, energies and vibrational frequencies were calculated for ten N8 isomers, corresponding to ten analogous CH structures. Comparative calculations using density functional theory (DFT), with a cc-pVTZ basis set, were also performed. All ten structures were found to be local minima on the energy hypersurface at the Hartree-Fock (HF) level, whereas at the second-order Möller-Plesset (MP2) level nine structures were stable. At the DFT level, eight local minima were found. The total energies were recomputed using 4s3p2dlf basis sets at the HF and MP2 levels of theory.

An implementation of the Douglas–Kroll (DK) transformation is described within a new relativistic quantum chemistry code, MAGIC, which performs calculations on systems containing heavy atoms. This method reduces the computational cost in terms of memory requirements that are associated with completeness identities in the DK implementation by factorizing the one-electron matrices into smaller ones that depend only on two atoms at a time. Examples are presented.

A study on the UF6 monomer and dimer was carried out within the density functional method. The U−F distance in the UF6 monomer was optimized at different levels of theory, pointwise, assuming octahedral geometry, (1) by using an all-electron basis for both U and F in a nonrelativistic calculation; (2) by using a relativistic effective core potential (RECP) on U and nonrelativistic effective core potential (ECP) on the fluorines; and (3) by using RECP on the U atom and an all-electron basis on the F atoms. Atomization energies of 23.11, 33.92, and 35.66 eV were obtained at the three levels, respectively. Relativistic effects lead to about a 50% increase in the atomization energy. For the UF6 dimer, the potential energy curve, as a function of the intermolecular U−U distance, was computed at level 2, and the rotational barrier between the two monomers was determined. Similar calculations were performed on the corresponding PuF6 species. Comparisons are made with experiment and other theoretical studies, where available.

An efficient approach for evaluating effective core potential integrals which involve projection operators has been implemented in the MAGIC quantum chemistry program. The methodology is presented and its performance is examined through illustrative calculations on transition metal and actinide compounds.

A full configuration interaction study on the BH molecule is presented. The potential energy curves of 20 different electronic states have been calculated correlating the four valence electrons. On the two most important states, i.e. the X1Sigma+ and A1Pi states, a complete study has been performed. This includes the effect of core electron correlation, estimated via truncated configuration interaction techniques. The dissociation energy of the molecule in the two states and the height of the predissociative barrier in the A1Pi state have been determined with basis sets of increasing quality.

We present a method for the direct generation of the lists of strings, suited for integral-driven full-CI (FCI) algorithms. This method generates the string lists each time they are used, and hence sensibly reduces the memory requirements, compared to our previous method that precalculates the lists. It was also extended to permit a truncation of the string space, according to the level of excitation.

Complete Active-Space Self-Consistent-Field (CAS-SCF) calculations for cubic N8 are presented. We studied the N8↔4N2 reaction inD 4h symmetry and found its energy release and activation barrier with three different atomic basis sets. The energy release for this reaction is predicted to be around 526 kcal/mol, while the energy barrier to dissociation is estimated about 159 kcal/mol. These results are in substantial agreement with previousab initio estimates.

We performed CAS-CI calculations on Li2 using a set of molecular orbitals (MO) optimized with a procedure that, in the case of highly symmetric molecules, permits extraction of a small set of MO out of a large set of atomic orbitals (AO). The dimension of the CAS-CI space was of about 12 million symmetry-adapted determinants. We determined some spectroscopic constants of Li2 with three different atomic basis sets of increasing quality. The values obtained with the largest atomic basis set are very close to the experimental results.