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.     

XMVB: a program for ab initio nonorthogonal valence bond computations

An ab initio nonorthogonal valence bond program, called XMVB, is described in this article. The XMVB package uses Heitler-London-Slater-Pauling (HLSP) functions as state functions, and calculations can be performed with either all independent state functions for a molecule or preferably a few selected important state functions. Both our proposed paired-permanent-determinant approach and conventional Slater determinant expansion algorithm are implemented for the evaluation of the Hamiltonian and overlap matrix elements among VB functions. XMVB contains the capabilities of valence bond self-consistent field (VBSCF), breathing orbital valence bond (BOVB), and valence bond configuration interaction (VBCI) computations. The VB orbitals, used to construct VB functions, can be defined flexibly in the calculations depending on particular applications and focused problems, and they may be strictly localized, delocalized, or bonded-distorted (semidelocalized). The parallel version of XMVB based on MPI (Message Passing Interface) is also available.     

Implementation of molecular symmetry in valence bond calculation

A novel strategy for the construction of many-electron symmetry-adapted wave function is proposed for ab initio valence bond (VB) calculations and is implemented for valence bond self-consistent filed (VBSCF) and breathing orbital valence bond (BOVB) methods with various orbital optimization algorithms. Symmetry-adapted VB functions are constructed by the projection operator of symmetry group. The many-electron symmetry-adapted wave function is expressed in terms of symmetry-adapted VB functions, and thus the VB calculations can be performed with the molecular symmetry restriction. Test results show that molecular symmetry reduces the computational cost of both the iteration numbers and CPU time. Furthermore, excited states with specific symmetry can be conveniently obtained in VB calculations by using symmetry-adapted VB functions.     

Identity SN2 reactions X- + CH3X --> XCH3 + X- (X=F, Cl, Br, and I) in vacuum and in aqueous solution: a valence bond study

The recently developed (L. Song, W. Wu, Q. Zhang, S. Shaik, J. Phys. Chem. A 2004, 108, 6017) valence bond method coupled with a polarized continuum model (VBPCM) has been applied to the identity SN2 reaction of halides in the gas phase and in aqueous solution. The barriers computed at the level of the breathing orbital VB method (P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 1992, 189, 259), BOVB and VBPCM//BOVB, are comparable to CCSD(T) and CCSD(T)//PCM results and to experimentally derived barriers in solution (W. J. Albery, M. M. Kreevoy, Adv. Phys. Org. Chem. 1978, 16, 85). The reactivity parameters needed to apply the valence bond state correlation diagram (VBSCD) method (S. Shaik, J. Am. Chem. Soc. 1984, 106, 1227), were also determined by VB calculations. It has been shown that the reactivity parameters along with their semiempirical derivations provide a satisfactory qualitative and quantitative account of the barriers.     

A Valence Bond Model for Electron‐Rich Hypervalent Species: Application to SFn (n=1, 2, 4), PF5, and ClF3

Some typical hypervalent molecules, SF₄, PF₅, and ClF₃, as well as precursors SF (⁴Σ^? state) and SF₂ (³B₁ state), are studied by means of the breathing‐orbital valence bond (BOVB) method, chosen for its capability of combining compactness with accuracy of energetics. A unique feature of this study is that for the first time, the method used to gain insight into the bonding modes is the same as that used to calculate the bonding energies, so as to guarantee that the qualitative picture obtained captures the essential physics of the bonding system. The ⁴Σ^? state of SF is shown to be bonded by a three‐electron σ bond assisted by strong π back‐donation of dynamic nature. The linear ³B₁ state of SF₂, as well as the ground states of SF₄, PF₅ and ClF₃, are described in terms of four VB structures that all have significant weights in the range 0.17–0.31, with exceptionally large resonance energies arising from their mixing. It is concluded that the bonding mode of these hypervalent species and isoelectronic ones complies with Coulson’s version of the Rundle–Pimentel model, but assisted by charge‐shift bonding. The conditions for hypervalence to occur are stated.     

The Menshutkin Reaction in the Gas Phase and in Aqueous Solution: A Valence Bond Study

The recently developed (L. Song, W. Wu, Q. Zhang, S. Shaik, J. Phys. Chem. A 2004 , 108, 6017–6024) valence bond method coupled to a polarized continuum model (VBPCM) is applied to the Menshutkin reaction, NH₃+CH₃Cl→CH₃NH₃⁺+Cl^?, in the gas phase and in aqueous solution. The computed barriers and reaction energies at the level of the breathing orbital VB method (P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 1992 , 189, 259), BOVB and VBPCM//BOVB, are comparable to CCSD(T) and CCSD(T)//PCM results and to experimental values in solution. The gas‐phase reaction is endothermic and leads to an ion‐pair complex via a late transition state. By contrast, the reaction in the aqueous phase is exothermic and leads to separate solvated ions as reaction products, via an early transition state. The VB calculations provide also the reactivity parameters needed to apply the valence bond state correlation diagram method, VBSCD (S. Shaik, A. Shurki, Angew. Chem. Int. Ed. 1999 , 38, 586). It is shown that the reactivity parameters along with their semiempirical derivations provide together a satisfactory qualitative and quantitative account of the barriers.     

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.     

An efficient algorithm for complete active space valence bond self‐consistent field calculation

This article describes a novel algorithm for the optimization of valence bond self‐consistent field (VBSCF) wave function for a complete active space (CAS), so‐called VBSCF(CAS). This was achieved by applying the strategies adopted in the optimization of CASSCF wave functions to VBSCF(CAS) wave functions, using an auxiliary orthogonal orbital set that generates the same configuration space as the original nonorthogonal orbital set. Theoretical analyses and test calculations show that the VBSCF(CAS) method shares the same computational scaling as CASSCF. The test calculations show the current capability of VBSCF method, which involves millions of VB structures. © 2012 Wiley Periodicals, Inc.     

An Accurate Barrier for the Hydrogen Exchange Reaction from Valence Bond Theory: Is this Theory Coming of Age?

One of the landmark achievements of quantum chemistry, specifically of MO-based methods that include electron correlation, was the precise calculation of the barrier for the hydrogen-exchange reaction (B. Liu, J. Chem. Phys. 1973, 58, 1925; P. Siegbahn, B. Liu, J. Chem. Phys. 1978, 68, 2457). This paper reports an accurate calculation of this barrier by two recently developed VB methods that use only the eight classical VB structures. To our knowledge, the present work is the first accurate ab initio VB barrier that matches an experimental value. Along with the accurate barrier, the VB method provides accurate bond energies and diabatic quantities that enable the barrier height to be analyzed by the VB state correlation diagram approach, VBSCD (S. Shaik, A. Shurki, Angew. Chem. 1999, 111, 616; Angew. Chem. Int. Ed. Engl. 1999, 38, 586). This is a proof of principal that VB theory with appropriate account of dynamic electron correlation can achieve quantitative accuracy of reaction barriers, and still retain a compact and interpretable wave function. A sample of S(N)2 barriers and dihalogen bonding energies, which are close to CCSD(T) and G2(+) values, show that the H(3) problem is not an isolated case, and while it is premature to conclude that VB theory has come of age, the occurrence of this event is clearly within sight.     

Generation of Kekulé valence structures and the corresponding valence bond wave function

A new scheme, called "list of nonredundant bonds", is presented to record the number of bonds and their positions for the atoms involved in Kekulé valence structures of (poly)cyclic conjugated systems. Based on this scheme, a recursive algorithm for generating Kekulé valence structures has been developed and implemented. The method is general and applicable for all kinds of (poly)cyclic conjugated systems including fullerenes. The application of the algorithm in generating Valence Bond (VB) wave functions, in terms of Kekulé valence structures, is discussed and illustrated in actual VB calculations. Two types of VBSCF calculations, one involving Kekulé valence structures only and the second one involving all covalent VB structures, were performed for benzene, pentalene, benzocyclobutadiene, and naphthalene. Both strictly local and delocalised p-orbitals were used in these calculations. Our results show that, when the orbitals are restricted to their own atoms, other VB structures (Dewar structures) also have a significant contribution in the VB wave function. When removing this restriction, the other VB structures (Dewar and also the ionic structures) are accommodated in the Kekulé valence structures, automatically. Therefore, at VBSCF delocal level, the ground states of these systems can be described almost quantitatively by considering Kekulé valence structures only at a considerable saving of time.     

A valence bond study of three-center four-electron pi bonding: electronegativity vs electroneutrality

Three-center four-electron (3c4e) pi bonding systems analogous to that of the ozone molecule have been studied using modern valence bond theory. Molecules studied herein consist of combinations of first row atoms C, N, and O with the addition of H atoms where appropriate in order to preserve the 3c4e pi system. Breathing orbital valence bond (BOVB) calculations were preformed at the B3LYP/6-31G**-optimized geometries in order to determine structural weights, pi charge distributions, resonance energies, and pi bond energies. It is found that the most weighted VB structure depends on atomic electronegativity and charge distribution, with electronegativity as the dominant factor. By nature, these systems are delocalized, and therefore, resonance energy is the main contributor to pi bond energies. Molecules with a single dominant VB structure have low resonance energies and therefore low pi bond energies.     

Valence Bond Study of Dissociation Behavior and Spectroscopic Constants for the Ground States of LiF and NaF

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Charge transfer in the electron donor-acceptor complex BH3NH3

As a simple yet strongly binding electron donor-acceptor (EDA) complex, BH(3)NH(3) serves as a good example to study the electron pair donor-acceptor complexes. We employed both the ab initio valence bond (VB) and block-localized wave function (BLW) methods to explore the electron transfer from NH(3) to BH(3). Conventionally, EDA complexes have been described by two diabatic states: one neutral state and one ionic charge-transferred state. Ab initio VB self-consistent field (VBSCF) computations generate the energy profiles of the two diabatic states together with the adiabatic (ground) state. Our calculations evidently demonstrated that the electron transfer between NH(3) and BH(3) falls in the abnormal regime where the reorganization energy is less than the exoergicity of the reaction. The nature of the NH(3)-BH(3) interaction is probed by an energy decomposition scheme based on the BLW method. We found that the variation of the charge-transfer energy with the donor-acceptor distance is insensitive to the computation levels and basis sets, but the estimation of the amount of electron transferred heavily depends on the population analysis procedures. The recent resurgence of interest in the nature of the rotation barrier in ethane prompted us to analyze the conformational change of BH(3)NH(3), which is an isoelectronic system with ethane. We found that the preference of the staggered structure over the eclipsed structure of BH(3)NH(3) is dominated by the Pauli exchange repulsion.     

X-ray absorption edge spectroscopy and computational studies on LCuO2 species: Superoxide-Cu(II) versus peroxide-Cu(III) bonding

The geometric and electronic structures of two mononuclear CuO2 complexes, [Cu(O2){HB(3-Ad-5-(i)Prpz)3}] (1) and [Cu(O2)(beta-diketiminate)] (2), have been evaluated using Cu K- and L-edge X-ray absorption spectroscopy (XAS) studies in combination with valence bond configuration interaction (VBCI) simulations and spin-unrestricted broken symmetry density functional theory (DFT) calculations. Cu K- and L-edge XAS data indicate the Cu(II) and Cu(III) nature of 1 and 2, respectively. The total integrated intensity under the L-edges shows that the 's in 1 and 2 contain 20% and 28% Cu character, respectively, indicative of very covalent ground states in both complexes, although more so in 1. Two-state VBCI simulations also indicate that the ground state in 2 has more Cu (/3d8) character. DFT calculations show that the in both complexes is dominated by O2(n-) character, although the O2(n-) character is higher in 1. It is shown that the ligand L plays an important role in modulating Cu-O2 bonding in these LCuO2 systems and tunes the ground states of 1 and 2 to have dominant Cu(II)-superoxide-like and Cu(III)-peroxide-like character, respectively. The contributions of ligand field (LF) and the charge on the absorbing atom in the molecule (Q(mol)M) to L- and K-edge energy shifts are evaluated using DFT and time-dependent DFT calculations. It is found that LF makes a dominant contribution to the edge energy shift, while the effect of Q(mol)M is minor. The charge on the Cu in the Cu(III) complex is found to be similar to that in Cu(II) complexes, which indicates a much stronger interaction with the ligand, leading to extensive charge transfer.     

Density embedded VB/MM: a hybrid ab initio VB/MM with electrostatic embedding

A hybrid QM/MM method that combines ab initio valence-bond (VB) with molecular mechanics (MM) is presented. The method utilizes the ab initio VB approach to describe the reactive fragments and MM to describe the environment thus allows VB calculations of reactions in large biological systems. The method, termed density embedded VB/MM (DE-VB/MM), is an extension of the recently developed VB/MM method. It involves calculation of the electrostatic interaction between the reactive fragments and their environment using the electrostatic embedding scheme. Namely, the electrostatic interactions are represented as one-electron integrals in the ab initio VB Hamiltonian, hence taking into account the wave function polarization of the reactive fragments due to the environment. Moreover, the assumptions that were utilized in an earlier version of the method, VB/MM, to formulate the electrostatic interactions effect on the off-diagonal matrix elements are no longer required in the DE-VB/MM methodology. Using DE-VB/MM, one can calculate, in addition to the adiabatic ground state reaction profile, the energy of the diabatic VB configurations as well as the VB state correlation diagram for the reaction. The abilities of the method are exemplified on the identity SN2 reaction of a chloride anion with methyl chloride in aqueous solution. Both the VB configurations diagram and the state correlation diagram are presented. The results are shown to be in very good agreement with both experimental and other computational data, suggesting that DE-VB/MM is a proper method for application to different reactivity problems in biological systems.     

Graphical representation of a new algorithm for nonorthogonalab initio valence bond calculations

A pictorial representation of the algorithm using successive expansion method for the nonorthogonal VB calculations is given. With the help of this representation and the graph analysis, the efficiency of this algorithm is improved and theN! problem is reduced by a factor of about (N!)^1/2. Anab initio VB program for valence bond self-consistent-field (VBSCF) calculations has been implemented based on this algorithm. Some VBSCF calculations have been performed for systems of up to 14 electrons. The statistics of the CPU time of the calculations indicate that this new group-theoretical approach is quite practical.     

Valence bond theoretical study for chemical reactivity

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