Oxidative Addition of Dihydrogen to Divanadium in Solid Ne: Multiple‐Bonded Triplet HVVH and Singlet V2(μ‐H)2

Dinuclear compounds of early transition metals with a high metal–metal bond order are of fundamental interest due to their intriguing bonding situation and of practical interest because of their potential involvement in catalytic processes. In this work, two isomers of V₂H₂ have been generated in solid Ne by the reaction between V₂ and H₂ and detected by infrared spectroscopy: the linear HVVH molecule (³Σ_g^? ground state), which is the product of the spin‐allowed reaction between V₂ (³Σ_g^? ground state) and H₂, and a lower‐energy, folded V₂(μ‐H)₂ isomer (¹A₁ ground state) with two bridging hydrogen atoms. Both isomers are characterized by metal–metal bonding with a high bond order; the orbital occupations point to quadruple bonding. Irradiation with ultraviolet light induces the transformation of linear HVVH to folded V₂(μ‐H)₂, whereas irradiation with visible light initiates the reverse reaction.     

Maximum Spin Polarization in Chromium Dimer Cations as Demonstrated by X‐ray Magnetic Circular Dichroism Spectroscopy

X‐ray magnetic circular dichroism spectroscopy has been used to characterize the electronic structure and magnetic moment of Cr₂⁺. Our results indicate that the removal of a single electron from the 4sσ_g bonding orbital of Cr₂ drastically changes the preferred coupling of the 3d electronic spins. While the neutral molecule has a zero‐spin ground state with a very short bond length, the molecular cation exhibits a ferromagnetically coupled ground state with the highest possible spin of S=11/2, and almost twice the bond length of the neutral molecule. This spin configuration can be interpreted as a result of indirect exchange coupling between the 3d electrons of the two atoms that is mediated by the single 4s electron through a strong intraatomic 3d‐4s exchange interaction. Our finding allows an estimate of the relative energies of two states that are often discussed as ground‐state candidates, the ferromagnetically coupled ¹²Σ and the low‐spin ²Σ state.     

Oxidative Addition of Dihydrogen to Divanadium in Solid Ne: Multiple-Bonded Triplet HVVH and Singlet V2(μ-H)2

Dinuclear compounds of early transition metals with a high metal–metal bond order are of fundamental interest due to their intriguing bonding situation and of practical interest because of their potential involvement in catalytic processes. In this work, two isomers of V₂H₂ have been generated in solid Ne by the reaction between V₂ and H₂ and detected by infrared spectroscopy: the linear HVVH molecule (³Σ_g⁻ ground state), which is the product of the spin-allowed reaction between V₂ (³Σ_g⁻ ground state) and H₂, and a lower-energy, folded V₂(μ-H)₂ isomer (¹A₁ ground state) with two bridging hydrogen atoms. Both isomers are characterized by metal–metal bonding with a high bond order; the orbital occupations point to quadruple bonding. Irradiation with ultraviolet light induces the transformation of linear HVVH to folded V₂(μ-H)₂, whereas irradiation with visible light initiates the reverse reaction.     

C2 in a Box: Determining Its Intrinsic Bond Strength for the X1Σg+ Ground State

The intrinsic bond strength of C₂ in its ¹Σ_g⁺ ground state is determined from its stretching force constant utilizing MR‐CISD+Q(8,8), MR‐AQCC(8,8), and single‐determinant coupled cluster calculations with triple and quadruple excitations. By referencing the CC stretching force constant to its local counterparts of ethane, ethylene, and acetylene, an intrinsic bond strength half way between that of a double bond and a triple bond is obtained. Diabatic MR‐CISD+Q results do not change this. Confinement of C₂ and suitable reference molecules in a noble gas cage leads to compression, polarization, and charge transfer effects, which are quantified by the local CC stretching force constants and differences of correlated electron densities. These results are in line with two π bonds and a partial σ bond. Bond orders and bond dissociation energies of small hydrocarbons do not support quadruple bonding in C₂.     

Ab initio valence bond calculations. VII. HF,HF+, and H2F+

Ab initio valence bond calculations for the ground and excited states of HF and HF⁺ are presented. Total energies, equilibrium geometries, dissociation energies, dipole moments, and spectroscopic constants for HF and HF⁺ have been calculated. The photoelectron spectrum of HF has been examined and interpreted by means of the valence bond formalism. The ground state of the protonated species H₂F⁺ has been investigated.     

Predictions of the bond length and vibrational frequency of Ge2

We present a pseudopotential local spin density calculation of the bond length, vibrational frequency, and binding energy for the ³Σ_g^? state of the germanium dimer. Predictions for the equilibrium bond length and vibrational frequency are given. An overestimate of the binding energy is obtained; this is consistent with other local spin density calculations for sp bonded diatomic molecules.     

Analysis of chemical bonding in C2 using Dyson orbitals

Multireference configuration interaction wave functions with single and double excitations were calculated for the ¹Σ⁺_g ground state of the C₂ molecule and the excited states of C⁺₂ with symmetries ²Σ⁺_g, ²Σ^-_u, ²Π_u, and ²Π_g. The corresponding σ_g, σ_u, π_u, and π_g valence Dyson orbitals were calculated. Most of the density due to the valence electrons is accounted for by three σ_g, one σ_u, and one degenerate pair of π_u Dyson orbitals. Electron correlation plays an important role in the bond strength of C₂ by increasing the occupation of the σ_g valence orbitals and decreasing the occupation of the σ_u and π_u valence orbitals. © 1996 John Wiley & Sons, Inc.     

Insight into spin–orbital interaction using MCSCF method: A special analysis of the 1Σg+ electronic state in C2 and the linear polyacetylenic C4 and C6

The symmetry-broken wave function can transform the ¹Σ_g⁺ state of C₂ from the classic double bonding to the quadruple bonding, where the transformed wave functions of ϕ _L and ϕ _R are singly occupied by two opposite-spinning electrons. In this article, the effective bond order (EBO) contribution of the fourth bond in C₂ is assessed through the overlap integral between ϕ _L and ϕ _R , namely the value (0.60) is the EBO contribution of the fourth bond in the transformed scheme. Hence, the new EBO is 3.36, which is more equitable than the original EBO (2.15) in the traditional scheme. In addition, the singlet diradical character of the linear polyacetylenic C₄ and C₆ in the ¹Σ_g⁺ state is addressed for the first time. No spin-polarized bonding exists in other linear C_2n clusters, because the ionic interaction in the polyacetylenic ¹Σ_g⁺ state of C₄ is negligible. Moreover, the coupling energy between α and β single electrons in C₄ is only 4.0 kcal mol⁻¹ based on the electron spin-flip energy. © 2019 Wiley Periodicals, Inc.     

A Valence Bond Study of the Low‐Lying States of the NF Molecule

The electronic structures of the three lowest‐lying states of NF are investigated by means of modern valence bond (VB) methods such as the VB self‐consistent field (VBSCF), breathing orbital VB (BOVB), and VB configuration interaction (VBCI) methods. The wave functions for the three states are expressed in terms of 9–12 VB structures, which can be further condensed into three or four classical Lewis structures, whose weights are quantitatively estimated. Despite the compactness of the wave functions, the BOVB and VBCI methods reproduce the spectroscopic properties and dipole moments of the three states well, in good agreement with previous computational studies and experimental values. By analogy to the isoelectronic O₂ molecule, the ground state ³Σ^? possesses both a σ bond and 3‐electron π bonds. However, here the polar σ bond contributes the most to the overall bonding. It is augmented by a fractional (19 %) contribution of three‐electron π bonding that arises from π charge transfer from fluorine to nitrogen. In the singlet ¹Δ and ¹Σ⁺ excited states the π‐bonding component is classically covalent, and it contributes 28 % and 37 % to the overall bonding picture for the two states, respectively. The resonance energies are calculated and reveal that π bonding contributes at least 24, 35 and 42 kcal mol^?1 to the total bonding energies of the ³Σ^?, ¹Δ and ¹Σ⁺ states, respectively. Some unusual properties of the NF molecule, like the equilibrium distance shortening and bonding energy increasing upon excitation, the counterintuitive values of the dipole moments and the reversal of the dipole moments as the bond is stretched, are interpreted in the light of the simple valence bond picture. The overall polarity of the molecule is very small in the ground state, and is opposite to the relative electronegativity of N vs F in the singlet excited states. The values of the dipole moments in the three states are quantitatively accounted for by the calculated weights of the VB structures.     

Relativistic all electron configuration interaction calculation of ground and excited states of the gold hydride molecule

We present relativistic configuration interaction calculations with the spin-free no-pair hamiltonian on the gold hydride molecule, treating the ground state as well as the eleven lowest excited states. The calculations provide a picture of the bonding in theX ¹Σ⁺ ground state consistent with previous work on this species using four-component spinors: compared to non-relativistic calculations, the dipole moment is reduced by a factor of two, hybridization (and thus participation ofd orbitals at the bonding) is greatly enhanced, the bond length is shortened by 20 pm, and the dissociation energy is increased by 50%. Comparison of the spin-averaged potential curves of the excited states with experiment suggests a reinterpretation of theC ¹Σ⁺ as the 0⁺ fine structure component of 2³Π and the prediction of a weakly bound³Σ⁺ state with weak transitions to the ground state in the range of 2.9–3.1 eV.     

Dissociation patterns in N2O following electron impact

A number of dissociation channels in N₂0 have been observed by time-of-flight spectroscopy following electron impact excitation. The metastable atoms and molecules produced were directly detected. Excited N₂ molecules were produced in the A³Σ_u⁺, B³Π_g and B′³Σ_u^? states in conjunction with ground state oxygen atoms. A number of additional dissociation channels were monitored by observing the production of oxygen and nitrogen atoms in Rydberg states. The results indicate the existence of potential minima in some of the repulsive surfaces involved.     

Configuration-Interaction study of lower excited states of O2: Valence and rydberg characters of the two lowest 3Σu − states

Configuration-interaction calculations, with an extended basis, are carried out on the ground and lower excited states of O₂ and O₂⁺ at and near the equilibrium internuclear distance (R = 2.3 a.u.) of the ground state of O₂. Particular attention has been paid to the two lowest ³Σ_u^? states, and the mixing of the valence and Rydberg characters in these states are studied. The lowest ³Σ_u^? state is a Rydberg-type state for R < 2.3 a.u., but becomes valence-type for R ? 2.3 a.u. The second ³Σ_u^? state, which is 1.6 eV above the lowest ³Σ_u^? at R = 2.3 a.u., changes its character from Rydberg to valence, valence to Rydberg, and then to valence again when R increases from 1.9 to 3.1 a.u. Satisfactory agreement between the calculated and experimental vertical excitation energies is obtained.     

The externally contracted CI method applied to N2

An approximate multireference CI method is presented. By grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory, the number of variational parameters is drastically reduced. The loss of correlation energy is shown to be usually less than 2%, and the timing is less than one ordinary CI iteration. Examples from calculations on some states of the nitrogen atom and nitrogen molecule are given. The basis set convergence for the lowest excitation energy in the atom is very slow. Less than 50% of the correlation effect is obtained at the s, p, d limit. After the inclusion of ? functions this value is improved to 83%. The dissociation energies of the molecule also show slow basis set convergence with errors of 0.5 eV even after addition of ? functions. The bond distances are, howeever, accurately reproduced with errors of less than 0.005 Å for all the states. A qualitative discussion of predissociation in the a ¹Π_g and B ³Π_gstates caused by spin–orbit interaction with the ⁵Σ_g⁺ state, is finally presented. Rapidly oscillating lifetimes between the different vibrational states are predicted.     

Modeling of heavy-atom-ligand NMR spin-spin coupling in solution: molecular dynamics study and natural bond orbital analysis of Hg-C coupling constants

Ab initio molecular dynamics (MD) and relativistic density functional NMR methods were applied to calculate the one‐bond Hg? C NMR indirect nuclear spin–spin coupling constants (J) of [Hg(CN)₂] and [CH₃HgCl] in solution. The MD averages were obtained as J(¹⁹⁹Hg? ¹³C)=3200 and 1575 Hz, respectively. The experimental Hg? C spin–spin coupling constants of [Hg(CN)₂] in methanol and [CH₃HgCl] in DMSO are 3143 and 1674 Hz, respectively. To deal with solvent effects in the calculations, finite “droplet” models of the two systems were set up. Solvent effects in both systems lead to a strong increase of the Hg? C coupling constant. From a relativistic natural localized molecular orbital (NLMO) analysis, it was found that the degree of delocalization of the Hg 5d_σ nonbonding orbital and of the Hg? C bonding orbital between the two coupled atoms, the nature of the trans Hg? C/Cl bonding orbital, and the s character of these orbitals, exhibit trends upon solvation of the complexes that, when combined, lead to the strong increase of J(Hg? C).     

The nickel-group IV molecules NiC,NiSi, and NiGe

All electron ab initio calculations have been applied to elucidate the electronic states and the nature of the chemical bonds in the molecules NiC, NiSi, and NiGe. The calculations have revealed that the ground states of all three molecules are¹Σ⁺, but due to the open 3d shell of the Ni atom the molecules have many low-lying electronic states. The NiC molecule is strongly polar, and the low-lying electronic states have been identified as those arising when the angular momenta of the³F_g Ni⁺ ion are coupled to the angular momenta of the⁴S_uC^? anion. The chemical bond in the NiC molecule has triple bond character due to the valence bond couplings between the Ni 4s and 3dπ electrons and theC 2p electrons. The chemical bonds in the molecules NiSi and NiGe are very much alike; they are double bonds composed of oneσ and oneπ bond. Theσ bond is due to the doubly occupied delocalized molecular orbital composed of the Ni 4s orbital and the Si 3pσ or the Ge 4pσ orbital. Theπ bond originates from the valence bond coupling between the localized hole in the Ni 3dπ orbital and the valencepπ electron of Si or Ge.     

Electronic states and nature of bonding of the molecule NiSi by all electron ab initio HF-CI and CASSCF calculations

All electron ab initio Hartree-Fock (HF), configuration interaction (CI) and multiconfiguration self-consistent field (CASSCF) calculations have been applied to investigate the low-lying electronic states of the NiSi molecule. The ground state of the NiSi molecule is predicted to be¹Σ⁺. The chemical bond in the¹Σ⁺ ground state is a double bond composed of one σ and one π bond. The σ bond is due to a delocalized molecular orbital formed by combining the Ni 4s and the Si 3pσ orbitals. The π bond is a partly delocalized valence bond, originating from the coupling of the 3dπ hole on Ni with the 3pπ electron on Si. Withing the energy range 1 eV 18 electronic states have been identified. The lowest lying electronic states have been characterized as having a hole in either the 3dπ or the 3dδ orbital of Ni, and the respective final states are formed when either of these holes are coupled to the 3pπ valence electron of Si.     

CAS SCF/CI calculations of potential energy surfaces of He3+ and He2+

Complete active space MC SCF (CAS SCF) calculations followed by second-order configuration interaction (SOCI) calculations are carried out on the potential energy surfaces (bending surface, linear surfaces) of the ²Σ_g⁺ ground state of He₃⁺. The potential minimum for the ²Σ_g⁺ state occurs at a linear geometry with HeHe bond length of 1.248 Å. The binding energy of He₃⁺ with respect to He + He⁺ + He was calculated to be 2.47 eV at the SOCI level. The energy required to dissociate He₃⁺ (²Σ_g⁺) into He₂⁺ (²Σ_u⁺) and He(¹S) is calculated to be 0.14 eV. The same level of SOCI calculations of He₂⁺ yield a D_e value of 2.36 eV.     

Structures,g-tensors,and hyperfine coupling constants of L-α-alanine radicals in radiation dosimetry: An ab initio molecular dynamics simulation study

Alanine is used as a transfer standard dosimeter for gamma ray and electron beam calibration. An important factor affecting its dosimetric response is humidity which can lead to errors in absorbed dose calculations. Ab initio molecular dynamics calculations were performed to determine the environmental effects on the electron paramagnetic resonance (EPR) parameters of L-α-alanine radicals in acidic and alkaline solutions. A new result, not dissimilar to the closed-shell amino acid molecule alanine, is that the non-zwitterionic form of the alanine radical is the stable form in the gas phase while the zwitterionic neutral alanine radical is not a stable structure in the gas phase. Geometric and EPR parameters of radicals in both gas and solution phases are found to be dependent on hydrogen bonding of water molecules with the polar groups and on dynamic solvation. Calculations on the optimized free radicals in the gas phase revealed that for the neutral radical, hydrogen bonding to water molecules drives a decrease in the magnitudes of g-tensor components g _xx and g _yy without affecting neither g _zz component nor the hyperfine coupling constants (HFCCs). The transfer from the gas to solution phase of the alanine radical anion is accompanied with an increase in the spin density on the carboxylic group's oxygen atoms. However, for the neutral radical, this transfer from gas to solution phase is accompanied with the decrease in the spin density on oxygen atoms. Calculated isotropic HFCCs and g-tensor of all radicals are in good agreement with experiment in both acidic and alkaline solutions.     

Theoretical study on Pd dimer and trimer interaction with the hydrogen molecule

The H₂ interaction with the Pd dimer and trimer were studied using multiconfigurational self-consistent field (MC-SCF) calculations with the relativistic effective core potential (RECP); the correlation energy correction was included in the extended multireference configuration interaction (MRCI), variational and perturbative to second order. Here, we considered the Pd₂ first six states: ³Σ⁺_u, ¹Σ⁺_g, ³Π_g, ³Δ_xy, ¹Σ⁺_u, and ³Σ⁺_g. For them, the four geometrical approaches included were the side-on H₂ toward Pd₂, for the hydrogen molecule in and out the Pd dimer plane; the perpendicular end-on H₂ toward Pd₂; and the perpendicular end-on Pd₂ to H₂. The Pd₂ ground state is ³Σ⁺_u, which only captures H₂ in the C_2v end-on approach, softly relaxing the H(SINGLE BOND)H bond. The closed-shell ¹Σ⁺_g captures the H₂ molecule in all the approaches considered: The side-on approach of this state presents deep wells and relaxes the H(SINGLE BOND)H bond, and the end-on approach captures H₂ with a relatively longer H(SINGLE BOND)H distance and also a deep well. The ³Π_g state was the only one which did not capture H₂. For the triangular Pd₃ clusters, H₂ was approached in the C_2v symmetry in and out of the Pd₃ plane. In the triangular case, H₂ was absorbed in both spin states, with deep wells and relaxing the H(SINGLE BOND)H distance. The linear Pd₃ singlet and triplet states capture outside of the Pd₃ and break the H(SINGLE BOND)H bond. © 1997 John Wiley & Sons, Inc.     

Nature of the chemical bonding in D3h [MH3M]+ cations (M = Be,Mg)

Motivated by the particularly short metal-metal distance that has been predicted for the D_3h [BeH₃Be]⁺ cation, comparable to those anticipated for triple bonds, we investigate the nature of the bonding interactions in the D_3h [MH₃M]⁺ cations (M = Be, Mg). CCSD(T)/cc-pVQZ calculations are used to determine optimized geometries for all of the various species, including those “capped” by He or Ne atoms (as proxies for an inert gas matrix). The primary tools that are then used to investigate the nature of the chemical bonding are spin-coupled generalized valence bond calculations and the analysis of localized natural orbitals and of domain-averaged Fermi holes. The various results for all of the systems considered indicate the presence of highly polar three-center two-electron M─H─M bonding character instead of any significant direct metal-metal bonding.