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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.