generalized valence bond (GVB)

A complete active space valence bond (CASVB) method is proposed which is particularly adapted to chemical interpretation. A CASVB wave function can be obtained simply by transforming a canonical CASSCF function and readily interpreted in terms of the well known classical VB resonance structures. The method is applied to the ground and excited states of benzene, butadiene, and the ground state of methane. The CASVB affords a clear view of the wave functions for the various states. The electronic excitation is represented in a VB picture as rearrangements of the spin couplings or as charge transfers which involve breaking covalent bonds and forming new ionic bonds. The former gives rise to covalent excited states and the latter to ionic excited states. The physical reasons why it is so difficult to describe the ionic excited states at the CASSCF level with a single active space and why the lowest 1 1B+2 state in cis-butadiene is so stabilized compared to the corresponding 1 1B+u state...

Ž . A semi-empirical valence bond VB method, called VBDFT s , is described and applied to C H conjugated hydrocarbons. The method is a Huckel-type VB scheme with energies scaled to density functional theory energies based on a single parameter; the matrix element l due to spin transposition between bonded atoms. Total energies, excitation energies, resonance and p-bond energies are presented for the various species. The insight that can be derived from the corresponding wavefunctions is discussed.

We present a new method for the analysis of spin correlation in molecular systems. The method is based on the spin-coupled theory of nlole!cuiar 4eetrunic stmctnre, the modem single-configuration gcuemliion of classical valm bond theory. The analysis consists in performing a decoupling of the (S*) expectation v&e into local centributions arising from tiectron spins in different subgmups of spia&nt@d orbitals. 'IIre method is then i&u&n&d by tbs ap@iestion to the lowest singlet and triplet statesoftHlosimpIeIr~~systems-octatemienermdb.Aspin ~is~~~~~~ with the classical valence bond concePt of resonance provi&s the key to the description of spin correlation in these and related systems.

We present a general method to construct one-dimensional translationally invariant valence-bond solid states with a built-in Lie group G and derive their matrix product representations. The general strategies to find their parent Hamiltonians are provided so that the valence-bond solid states are their unique ground states. For quantum integer-spin-S chains, we discuss two topologically distinct classes of valence-bond solid states: one consists of two virtual SU͑2͒ spin-J variables in each site and another is formed by using two SO͑2S +1͒ spinors. Among them, a spin-1 fermionic valence-bond solid state, its parent Hamiltonian, and its properties are discussed in detail. Moreover, two types of valence-bond solid states with SO͑5͒ symmetries are further generalized and their respective properties are analyzed as well.

Diradical molecules are essential species involved in many organic and inorganic chemical reactions. The computational study of their electronic structure is often challenging, because a reliable description of the correlation, and in particular of the static one, requires multireference techniques. The Jastrow correlated antisymmetrized geminal power (JAGP) is a compact and efficient wave function ansatz, based on the valence-bond representation, which can be used within quantum Monte Carlo (QMC) approaches. The AGP part can be rewritten in terms of molecular orbitals, obtaining a multideterminant expansion with zero-seniority number. In the present work we demonstrate the capability of the JAGP ansatz to correctly describe the electronic structure of two diradical prototypes: the orthogonally twisted ethylene, C 2 H 4 , and the methylene, CH 2 , representing respectively a homosymmetric and heterosymmetric system. In the orthogonally twisted ethylene, we find a degeneracy of π and π* molecular orbitals, as correctly predicted by multireference procedures, and our best estimates of the twisting barrier, using respectively the variational Monte Carlo (VMC) and the lattice regularized diffusion Monte Carlo (LRDMC) methods, are 71.9(1) and 70.2(2) kcal/mol, in very good agreement with the high-level MR-CISD+Q value, 69.2 kcal/mol. In the methylene we estimate an adiabatic triplet-singlet (X ̃3B 1 -ã1A 1 ) energy gap of 8.32(7) and 8.64(6) kcal/mol, using respectively VMC and LRDMC, consistently with the experimental-derived finding for T e , 9.363 kcal/mol. On the other hand, we show that the simple ansatz of a Jastrow correlated single determinant (JSD) wave function is unable to provide an accurate description of the electronic structure in these diradical molecules, both at variational level (VMC torsional barrier of C 2 H 4 of 99.3(2) kcal/mol, triplet-singlet energy gap of CH 2 of 13.45(10) kcal/mol) and, more remarkably, in the fixed-nodes projection schemes (LRDMC torsional barrier of 97.5(2) kcal/mol, triplet-singlet energy gap of 13.36(8) kcal/mol) showing that a poor description of the static correlation yields an inaccurate nodal surface. The suitability of JAGP to correctly describe diradicals with a computational cost comparable with that of a JSD calculation, in combination with a favorable scalability of QMC algorithms with the system size, opens new perspectives in the ab initio study of large diradical systems, like the transition states in cycloaddition reactions and the thermal isomerization of biological chromophores.

In this paper, we proceed with our project of generating an algorithm for molecular dynamics simulations of isotope complexes of hydrogen atoms (Chem. Phys. Lett. 320 (2000) 118). The isotope selection is carried out by forces derived from adiabatic potential energy curves that are obtained within a modi®ed electron mass theory. Arguments are presented in favour of the use of the generalized valence bond electronic wavefunctions. We exemplify with simulations and geometry optimization of H 2 isotopomers and discuss the effects of long-range interactions and electron correlation on the forces.

The multi-configurational ansatz of valence-bond theory may serve as basis for calculating intermolecular interaction energies in a non-orthogonal basis. We look in the present contribution at the possibility to obtain the 1st-order electrostatic interactions from breathing-orbital valencebond densities, and the 2nd-order dispersion energy from dipole-dipole interactions. The discussion is based on numerical results for the interaction of two N 2 O molecules.

The multi-configurational ansatz of valence-bond theory may serve as basis for calculating intermolecular interaction energies in a non-orthogonal basis. We look in the present contribution at the possibility to obtain the 1st-order electrostatic interactions from breathing-orbital valencebond densities, and the 2nd-order dispersion energy from dipole-dipole interactions. The discussion is based on numerical results for the interaction of two N 2 O molecules.

The effect of orbital magnetism on the chemical bonding of lateral, two-dimensional artificial molecules is studied in the case of a 2e double quantum dot (artificial molecular hydrogen). It is found that a perpendicular magnetic field reduces the coupling (tunneling) between the individual dots and, for sufficiently high values, it leads to complete dissociation of the artificial molecule. The method used is building on Löwdin's work on Projection Operators in Quantum Chemistry; it is a spin-andspace unrestricted Hartree-Fock method in conjunction with the companion step of the restoration of spin and space symmetries via Projection Techniques (when such symmetries are broken). This method is able to describe the full range of couplings in two-dimensional double quantum dots, from the strong-coupling regime exhibiting delocalized molecular orbitals to the weak-coupling and dissociation regimes associated with a Generalized Valence Bond combination of atomic-type orbitals localized on the individual dots.

A complete active space self-consistent field (SCF) wave function is transformed into a valence bond type representation built from nonorthogonal orbitals, each strongly localized on a single atom. Nonorthogonal complete active space SCF orbitals are constructed by Ruedenberg’s projected localization procedure so that they have maximal overlaps with the corresponding minimum basis set of atomic orbitals of the free-atoms. The valence bond structures which are composed of such nonorthogonal quasiatomic orbitals constitute the wave function closest to the concept of the oldest and most simple valence bond method. The method is applied to benzene, butadiene, hydrogen, and methane molecules and compared to the previously proposed complete active space valence bond approach with orthogonal orbitals. The results demonstrate the validity of the method as a powerful tool for describing the electronic structure of various molecules.

We introduce a method for accurate quantum chemical calculations based on a simple variational wave function, defined by a single geminal that couples all the electrons into singlet pairs, combined with a real space correlation factor. The method uses a constrained variational optimization, based on an expansion of the geminal in terms of molecular orbitals. It is shown that the most relevant nondynamical correlations are correctly reproduced once an appropriate number n of molecular orbitals is considered. The value of n is determined by requiring that, in the atomization limit, the atoms are described by Hartree–Fock Slater determinants with Jastrow correlations. The energetics, as well as other physical and chemical properties, are then given by an efficient variational approach based on standard quantum Monte Carlo techniques. We test this method on a set of homonuclear (Be2, B2, C2, N2, O2, and F2) and heteronuclear (LiF and CN) dimers for which strong nondynamical correlations...

Spin-Coupled Generalized Valence Bond (SCGVB) theory provides the foundation for a comprehensive theory of the electronic structure of molecules. SCGVB theory offers a compelling orbital description of the electronic structure of molecules as well as an efficient and effective zero-order wave function for calculations striving for quantitative predictions of molecular structures, energetics and other properties. The orbitals in the SCGVB wave function are usually semi-localized and, for most molecules, can be interpreted using concepts familiar to all chemists (hybrid orbitals, localized bond pair, lone pairs, etc.). SCGVB theory also provides new perspectives on the nature of the bonds in molecules such as C2, Be2 and SF4/SF6. SCGVB theory contributes unparalleled insights into the underlying cause of the first-row anomaly in inorganic chemistry as well as the electronic structure of organic molecules and the electronic mechanisms of organic reactions. The SCGVB wave function accounts for nondynamical correlation effects and, thus, corrects the most serious deficiency in molecular orbital (RHF) wave functions. Dynamical correlation effects, which are critical for quantitative predictions, can be taken into account using the SCGVB wave function as the zero-order wave function for multireference configuration interaction or coupled cluster calculations. * In prior articles in the literature the Spin-Coupled Generalized Valence Bond wave function has usually been referred to as the Spin-Coupled Valence Bond (SCVB) wave function or the full Generalized Valence Bond (full GVB) wave function. These wave functions are identical; to prevent confusion, the authors have adopted the allencompassing SCGVB name.

The inertness of molecular nitrogen and the reactivity of acetylene suggest there are significant variations in the nature of triple bonds. To understand these differences, we performed generalized valence bond as well as more accurate electronic structure calculations on three molecules with putative triple bonds: N2, HCN and HC2H. The calculations predict that the triple bond in HC2H is quite different than the triple bond in N2, with HCN being an intermediate case but closer to N2 than HC2H. The triple bond in N2 is a traditional triple bond with the spins of the electrons in the bonding orbital pairs predominantly singlet coupled in the GVB wave function (92%). In HC2H, on the other hand, there is a substantial amount of residual CH(a4Σ-) fragment coupling in the triple bond at its equilibrium geometry with the contribution of the perfect pairing spin function dropping to 82% (77% in a full valence GVB calculation). This difference in the nature of the triple bond in N2 and HC2H...

We present spin-coupled valence bond calculations on the reaction pathway for the insertion of a methyl cation onto the aromatic system of benzene, leading to the Wheland intermediate C 6 H 6 CH 3 +. Simultaneously with the geometrical rehybridization of the two carbons forming the new substrate-electrophile bond (from sp 2 to sp 3), we observe the crossing of two spin-coupled potential energy curves; at large separations, these correspond to C 6 H 6 + CH 3 + and to C 6 H 6 + + CH 3. In the neighborhood of the crossing point, the spincoupled valence bond wave function obtained by mixing these two orbital configurations switches continuously from the former to the latter.

We present spin-coupled valence bond calculations on the reaction pathway for the insertion of a methyl cation onto the aromatic system of benzene, leading to the Wheland intermediate C 6 H 6 CH 3 +. Simultaneously with the geometrical rehybridization of the two carbons forming the new substrate-electrophile bond (from sp 2 to sp 3), we observe the crossing of two spin-coupled potential energy curves; at large separations, these correspond to C 6 H 6 + CH 3 + and to C 6 H 6 + + CH 3. In the neighborhood of the crossing point, the spincoupled valence bond wave function obtained by mixing these two orbital configurations switches continuously from the former to the latter.

An efficient algorithm for energy gradients in valence bond theory with nonorthogonal orbitals is presented. A general Hartree‐Fock‐like expression for the Hamiltonian matrix element between valence bond (VB) determinants is derived by introducing a transition density matrix. Analytical expressions for the energy gradients with respect to the orbital coefficients are obtained explicitly, whose scaling for computational cost is m4, where m is the number of basis functions, and is thus approximately the same as in HF method. Compared with other existing approaches, the present algorithm has lower scaling, and thus is much more efficient. Furthermore, the expression for the energy gradient with respect to the nuclear coordinates is also presented, and it provides an effective algorithm for the geometry optimization and the evaluation of various molecular properties in VB theory. Test applications show that our new algorithm runs faster than other methods. © 2008 Wiley Periodicals, Inc....

A block-correlated coupled cluster (BCCC) method based on the generalized valence bond (GVB) wave function (GVB-BCCC in short) is proposed and implemented at the ab initio level, which represents an attractive multireference electronic structure method for strongly correlated systems. The GVB-BCCC method is demonstrated to provide accurate descriptions for multiple bond breaking in small molecules, although the GVB reference function is qualitatively wrong for the studied processes. For a challenging prototype of strongly correlated systems, tridecane with all 12 single CC bonds at various distances, our calculations have shown that the GVB-BCCC2b method can provide highly comparable results as the density matrix renormalization group method for potential energy surfaces along simultaneous dissociation of all CC bonds.

The aim of this paper is to unravel the physical phenomena involved in the calculation of the spin density of the CuCl 2 and [CuCl 4 ] 2− systems using wave function methods. Various types of wave functions are used here, both variational and perturbative, to analyse the effects impacting the spin density. It is found that the spin density on the chlorine ligands strongly depends on the mixing between two types of valence bond structures. It is demonstrated that the main difficulties found in most of the previous studies based on wave function methods come from the fact that each valence bond structure requires a different set of molecular orbitals and that using a unique set of molecular orbitals in a variational procedure leads to the removal of one of them from the wave function. Starting from these results, a method to compute the spin density at a reasonable computational cost is proposed.

Chosen from István Mayer's very impressive canon of important work on bond orders and related quantities, we explore a paper from 2012 which introduced a "pseudo spin density matrix" for correlated singlet-state wave functions, leading to "improved" definitions of bond orders and free valence. Examining such "improved" bond orders for the singlet ground states of H 2 ,N 2 and CH + we find that all of them exhibit sensible geometry dependences. Mayer's free valence index works well for H 2 and N 2 ; the asymptotic behavior for CH + turns out to be slightly more complicated but can easily be explained. Using B 2 H 6 to examine three-center bonding, a simple generalization of Mayer's approach produces numerical results close to those based on the "pseudo spin density matrix." As expected, the various "correction" terms remain small, albeit some of them are larger for the multicenter indices of ground and excited singlet states of benzene, S 2 N 2 and square (D 4h) cyclobutadiene. KEYWORDS "improved" bond order, free valence index, multicenter index, pseudo spin density matrix 1 | INTRODUCTION As is well known, a central theme of István Mayer's distinguished scientific career was the extraction of useful chemical information from molecular wave functions. Among his principal requirements for such methodologies were that they should be well-defined and produce results that make proper chemical sense. He was of course particularly active in the development of successful measures of bond orders and related quantities. He published an interesting personal account of his work up to 2006 on the development of bond orders [1], with various subsequent studies, as well as work on energy components, being included in his 2017 book [2]. He identified, in the intervening years, a specific issue with his usual definition of bond orders for correlated singlet-state wave functions, publishing in 2012 his "improved" definitions of bond orders and free valence for correlated singlet-state wave functions [3]. The well-chosen specific example in that 2012 paper [3] and subsequently in his 2017 book (on pages 99-100) [2] is the dissociation of the singlet ground state of ethene into two triplet methylene fragments. Whereas the calculation of bond orders using the two open-shell CH 2 subsystems does of course involve the spin density associated with the unpaired electrons, the overall singlet state of H 2 C CH 2 has zero spin density and so there can be no such net contribution to the bond orders. The effect on the calculated values turned out to be marginal in this case but, characteristically, Mayer did of course note the conceptual inadequacy of being able to obtain different results for two triplets as opposed to one

We present a new coupled Hartree-Fock(HF)/Kohn-Sham DFT perturbation method that accounts for the effect of enlarging the basis set in electronic structure calculations. In contrast with previous approaches, our dual basis set treatment yields not only a correction for the total energy, but also for the orbital eigenvalues and density. The zero-th order solution is obtained from the projection of the small basis set coefficients. Diagonalization of the full Fock matrix in the large basis set is avoided. In this first paper of a series, we develop the theoretical foundations of our approach for molecules, including the coupled-perturbed equations through second order and the energy expressions through fourth order-as our method complies with Wigner's 2n + 1 rule. The first-order perturbation equation turns out to be uncoupled and odd-order terms in the energy expansion vanish. In calculations on simple molecules, our method recovers over 93% (84%) of the missing DFT(HF) energy when going from the cc-pVDZ to the aug-cc-pVDZ basis,

The quantum chemical definition of valence as a property of an atom in a molecule was generalized to functional groups in molecules. The new definition was applied to a series of functional groups in simple organic molecules. The results were found to be in agreement with expectation on the basis of classical valence rules. CH2, N2 and CO group valences in selected organic molecules are compared. Group valences for systems violating the classical valence rules are also briefly discussed with an emphasis on the role of multicenter bonding in the phenomenon of hyper-and subvalence. Finally, Si2 groups serve to probe the bulk character of small and medium silicon clusters.

The equilibrium geometries and chemical reactivities of the novel coumarine derivative, 3-[1-(3hydroxypropylamino)ethylidene]chroman-2,4-dione, in water and benzene were investigated. The Fukui parameters, calculated by the Natural and Atoms in Molecules charges, were determined for all atoms in both phases. The most potent sites for the electrophilic, nucleophilic, and radical attack are discussed. Molecular docking analysis was carried out to identify the potency of inhibition of the title molecule against human cartilage proteins. The inhibition activity was obtained for ten conformations of ligand inside protein. This study proved that the Fukui indices can be used as the reactivity descriptors for the novel substances with inhibitory activity.

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In the same way that the valence of an atom issues from the definition of bond index, we show here that the three-center bond index lends itself to the definition of a bond valence. Within the charge of a bond, we show that its self-charge (i.e., the amount of electrons kept by the atoms involved in the bond) is split in such a way that the more electronegative atom tends to hold more electronic charge than the other atom. We give examples of these quantities and discuss the results for different kinds of chemical systems. We also give some results for four-center indices and report six-center indices for hexagonal rings.

The first and second bond dissociation energies for H20 have been calculated in an ab initio manner using a multistructure valence-bond scheme. The basis set consisted of a minimal number of non-orthogonal atomic orbitals expressed in terms of gaussian-lobe functions. The valence-bond structures considered properly described the change in the molecular system as the hydrogen atoms were individually removed to infinity. The calculated equilibrium geometry for the H20 molecule has an O-H bond length of 1.83 Bohrs and an HOH bond angle of 106.5 ~ With 49 valence-bond structures the energy of H20 at this geometry was-76.0202 Hartrees. The calculated equilibrium bond length for the OH radical was 1.86 Bohrs and the energy, using the same basis set, was-75.3875 Hartrees. After correction for zero point energies the calculated bond dissociation energies are: H20 ~ OH + H, D 1 = 75.38 kcal/mole and OH-~O + H, D 2 = 54.79 kcal/mole. Die ersten und zweiten Dissoziatiousenergien der Bindungen von HzO wurden mit einem ab initio Verfahren nach der Valenzstrukturmethode berechnet. Die Basis bestand aus einer minimalen Anzahl von nicht-orthogonalen Atomorbitalen, die durch Gaul3funktionen ausgedrfickt wurden. Die beteiligten Valenzstrukturen beschrieben in geeigneter Weise den Wechsel in der Molekfilstruktur bei Abspaltung der einzelnen Wasserstoffatome. Die berechnete Gleichgewichtsgeometrie des H20-Molekfils hat eine O-H-Bindungslfinge von 1,83 Bohr und einen HOH-Winkel yon 106,5 ~ Mit 49 Valenzstrukturen betrug die Energie des H20 bei dieser Geometrie-76,0202 Hartree. Die berechnete Bindungsliinge des OH-Radikals ffir das Gleichgewicht betrug 1,86 Bohr und die Energie wurde mit derselben Basis zu-75,3875 Hartree berechnet. Nach Korrekturen ffir die Nullpunktenergien betrugen die berechneten Dissoziationsenergien der Bindungen: H20-.OH + H, D 1 = 75,38 kcal/Mol und OHiO + H, D 2 = 54,79 kcal/Mol.

The effect of orbital magnetism on the chemical bonding of lateral, two‐dimensional artificial molecules is studied in the case of a 2e double quantum dot (artificial molecular hydrogen). It is found that a perpendicular magnetic field reduces the coupling (tunneling) between the individual dots and, for sufficiently high values, it leads to complete dissociation of the artificial molecule. The method used is building on Löwdin's work on projection operators in quantum chemistry; it is a spin‐and‐space unrestricted Hartree–Fock method in conjunction with the companion step of the restoration of spin and space symmetries via projection techniques (when such symmetries are broken). This method is able to describe the full range of couplings in two‐dimensional double quantum dots, from the strong‐coupling regime exhibiting delocalized molecular orbitals to the weak‐coupling and dissociation regimes associated with a generalized valence bond combination of atomic‐type orbitals local...

Here we test the concept that a potential energy model (force field) based on an expansion of the bondvalence model can use molecular geometry to make a reasonable prediction of the thermodynamic energy. The backbone of the model is a non-standard choice of structural descriptors for the energy decomposition, which relates the energy to particular aspects of the structure. Most force fields use a many-body decomposition to describe structures (with two-, three-, and possibly four-body terms, etc.), whereas ours employs a multipole expansion of the bond valence incident to each atom. This valence multipole model separates the energy associated with each atom into terms related to total bonding (valence monopole), bonding asymmetry (valence dipole), and ellipsoidal deformation (valence quadrupole). All of these are inherently multi-body terms that are calculated by combining two-body terms (bond valences). Provided bond valence sums are satisfied to within 0.2 v.u. of the ideal for all atoms, this model can provide accuracies of ~5 kJ/mol per unique atom in the Al-Si-H-O system, at least for the equilibrium structures tested here, comparable to most quantum mechanical calculations. More development is needed to produce a fully functional force field suitable for molecular dynamics simulations, but this work shows that the development of such a force field is likely to be feasible.

High level MRCI and RCCSD(T) calculations with correlation consistent basis sets were used to characterize SF_n species. By examining both the stable structures and the bonding processes that occur during SF_n + F --> SF_{n+1} additions, we have derived a new model for describing hypervalent behavior that we call recoupled pair bonding, in which a pair of electrons on S can be decoupled to allow formation of a bond with F. The new model accounts for the origin of hypervalency, the presence of low-lying excited states, and the structures and spectral properties of neutral and ionic SF_n species; it has more predictive capability than other models. For example, while SF and SF_2 both have covalently bonded ground states, they each have low-lying excited states with at least one recoupled pair bond. To the best of our knowledge, the SF(^4Sigma^-), SF_2(^3B_1), and SF_2(^3A_2) states have not yet been observed experimentally.

In this work, a model to explain the unusual stability of atomic lithium clusters in their highest spin multiplicity is presented and used to describe the ferromagnetic bonding of high-spin Li10 and Li8 clusters. The model associates the (lack of-)fitness of Heisenberg Hamiltonian with the degree of (de-)localization of the valence electrons in the cluster. It is shown that a regular Heisenberg Hamiltonian with four coupling constants cannot fully explain the energy of the different spin states. However, a more simple model in which electrons are located not at the position of the nuclei but at the position of the attractors of the electron localization function succeeds in explaining the energy spectrum and, at the same time, explains the ferromagnetic bond found by Shaik using arguments of valence bond theory. In this way, two different points of view, one more often used in physics, the Heisenberg model, and the other in chemistry, valence bond, come to the same answer to explain...

Ab initio classical valence bond theory in terms of localized orbitals has several advantages over electronic structure methods based on canonical delocalized Hartree-Fock molecular orbitals, with two key distinctions being greater applicability to inherently multiconfigurational systems (also called multireference systems or strongly correlated systems) and great interpretability in terms of covalent and ionic valence bond configurations (also called valence bond structures). This can be especially advantageous for applications to chemical reactions. However, until now only limited work tested the quantitative accuracy for the energetics of chemical reactions. The present study provides such tests and validations for a representative test set of six barrier heights corresponding to forward and reverse barriers of three hydrogen transfer reactions. In particular, we test the valence bond self-consistent-field theory (VBSCF) and three post-VBSCF methods that use VBSCF as a reference function for adding dynamic correlation, in particular valence bond configuration interaction (VBCI), breathing orbital valence bond (BOVB), and valence bond second-order perturbation theory (VBPT2). The VBSCF method itself is, as expected, not quantitatively accurate, with a mean unsigned error (MUE) for the six barrier heights of $17 kcal/mol. But the post-VBSCF methods are found to be quite successful. Depending on the basis set, and valence bond structure selection we obtain MUEs (in kcal/mol) as low as 3.7 for VBCI, 4.5 for BOVB, and (using a bigger basis-set) 1.3 for VBPT2. These compare well, on the same data set, with 1.6 for coupled clusters with singles and doubles (CCSD) and 1.5 for multireference second order perturbation theory based on a complete active space self-consistent field reference function (MRPT2). We discuss the results in terms of the pros and cons of each of these methods.

The valence-bond state correlation diagram (VBSCD), which was developed by Shaik and co-workers is an excellent tool to understand reactivity patterns in chemical reactions. The strength of the model is in its ability to describe the whole spectrum of reaction types and unify them under a single general paradigm. Moreover, it allows one to understand, conceptualize, and predict chemical reactivity in a general as well as specific manner. As such, VBSCD is a valuable model. The model has been largely tested on various systems in the gas phase both qualitatively and quantitatively. However, its application to reactions in solution was given less attention because of the difficulties to represent solvent reorganization and estimate non-equilibrium solvation effects, which, on the basis of the model, are expected to be fundamental. The recently developed valence-bond molecular mechanics (VB/MM) method overcomes these difficulties because it involves explicit solvent molecules and thus allows quantitative examination of these solvent effects. This work presents a study of the identity S N 2 reaction X-+ H 3 CX f XCH 3 + X-; (X) F, Cl, Br, I) in aqueous solution. The various parameters that form the VBSCD model are calculated and compared with the corresponding model's estimated values. A relatively good agreement between the calculated and estimated values is found. It is shown that when facing quantitative considerations, the picture may not be as simplistic as in the qualitative study; yet, the fundamental nature of the description is unaffected. This indicates that combined together, the VB/MM approach and the VBSCD model offer a very powerful tool to study reactions in complex systems and understand their reactivity patterns.

We present a technique for using quantum Monte Carlo (QMC) to obtain high quality energy differences. We use generalized valence bond (GVB) wave functions, for an intuitive approach to capturing the important sources of static correlation, without needing to optimize the orbitals with QMC. Using our modifications to Walker branching and Jastrows, we can then reliably use diffusion quantum Monte Carlo to add in all the dynamic correlation. This simple approach is easily accurate to within a few tenths of a kcal/mol for a variety of problems, which we demonstrate for the adiabatic singlet-triplet splitting in methylene, the vertical and adiabatic singlet-triplet splitting in ethylene, 2+2 cycloaddition, and Be2 bond breaking.

Spin unrestriction is typically defined as a free variation of the molecular orbitals of different spins in order to lower the molecular energy. When applied to approximate active space electron correlation methods, such as generalized valence bond coupled cluster (GVB-CC) models, this approach often leads to undesirable artifacts. We therefore present an alternative unrestricted in active pairs (UAP) procedure for spin polarization in GVB-CC methods, which resembles the corresponding orbitals of unrestricted Hartree-Fock theory. The UAP procedure permits spin polarization only within the two orbital subspaces describing each electron pair (consisting of one nominally occupied and one virtual orbital). This great reduction to just a linear number of degrees of freedom associated with spin polarization eliminates many of the undesirable artifacts associated with unconstrained spin unrestriction. The UAP procedure is tested on a variety of potential curves for bond breaking and the properties of small radicals as well as larger polyenyl radicals, allyl, pentadienyl, and heptatrienyl.

The Complete Active Space Self-Consistent Field calculations offer a definition of a set of molecularly optimized valence mono-electronic functions and a basis of Orthogonal Valence Bond (OVB) configurations. However this variational description misses important dynamical correlation effects, affecting both the energy and the weights of the various OVB components. The dynamical polarization effects induce for instance an increase of the weight of the ionic VB components. The mapping of these dynamical correlation effects into an effective OVB Hamiltonian is not straightforward, but would be useful for the production of reliable model Hamiltonians, making possible the treatment of large systems. The present work takes benefit of a solution proposed to the multi-parentage problem in Multi-Reference Coupled Cluster methods to define in a rational way dressed OVB Hamiltonians. A test study on the F 2 molecule shows that the dynamical correlation not only diminishes the energy difference between the neutral and ionic configurations, but also the interaction between them. I)

We investigate the one-dimensional strongly correlated electron models which have the resonating-valence-bond state as the exact ground state. The correlation functions are evaluated exactly using the transfer matrix method for the geometric representations of the valence-bond states. In this method, we only treat matrices with small dimensions. This enables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insulating. Since the corresponding non-interacting systems may be insulating or metallic, we can say that the gap originates from strong correlation. The persistent currents of the present models are also investigated and found to be exactly vanishing.

This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond‐molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches. © 2006 Wiley Periodicals, Inc. J Comput Chem, 2007

In this work, a model to explain the unusual stability of atomic lithium clusters in their highest spin multiplicity is presented and used to describe the ferromagnetic bonding of high-spin Li 10 and Li 8 clusters. The model associates the (lack of-)fitness of Heisenberg Hamiltonian with the degree of (de-)localization of the valence electrons in the cluster. It is shown that a regular Heisenberg Hamiltonian with four coupling constants cannot fully explain the energy of the different spin states. However, a more simple model in which electrons are located not at the position of the nuclei but at the position of the attractors of the electron localization function succeeds in explaining the energy spectrum and, at the same time, explains the ferromagnetic bond found by Shaik using arguments of valence bond theory. In this way, two different points of view, one more often used in physics, the Heisenberg model, and the other in chemistry, valence bond, come to the same answer to explain those atypical bonds.

We have investigated four different already synthesized meta-and para-connected diradicals to get their magnetic exchange coupling constants (J) through generalized valence bond (GVB) approach and also with Hartree-Fock (HF) theory with a view to establish the superiority of GVB method over HF theory for the prediction of J. In doing so, at first optimization of these molecules are done at B3LYP level of density functional theory using the 6-31++g(d) basis set. With these optimized geometries, J values are computed at GVB method along with TZV basis set and these values are compared with those of the J values obtained using HF/TZV level of theory. Nonetheless, J values found in both the theoretical processes are also compared with the experimental findings. Thus, the supremacy of the wavefunction based GVB method in predicting J is established in comparison with the HF method.

ABSTRACTBond valence sums (BVS) calculated for lone-pair cations are found increasingly higher than their formal valences as the retraction of the lone electron pair (LEP) from the nucleus is more pronounced. The increase in BVS is interpreted as a continuous increase of an effective valence of an atom that is a measure of its actual ability to bind other atoms without changing its formal valence. How the LEP of a lone-pair cation affects the effective valence of other atoms in a structure is studied by bond valence calculations for specific structures. For structures rich in alkali cations, it is found that the high effective valence of the lone-pair cations tends to be balanced by low effective valence of alkali cations. The LEP transfers bonding power or effective valence from the alkali cations to the lone-pair cations by joining the coordination sphere of the alkali cations.

We recently proposed that calculated bond-valence sums, BVS, represent a non-integer structural valence, `struct V', rather than the integer-value stoichiometric valence, stoich V. Therefore, the usual attempts to `optimize' bond-valence parameters r 0 and b by adjusting them to stoich V are based on the false assumption that numerical values of struct V and stoich V are always equal. Bond-valence calculations for several compounds with stereoactive cations SnII, SbIII and BiIII reveal the balanced distribution of the bonding power struct V between atoms of each structure.

During a reorganization of the mineralogical collection of Turin University, old samples of the so-called mohsite of Colomba were found. “Mohsite” was discredited in 1979 by Kelly et al., as a result of some analyses performed on the equivalent material coming from the French region of Hautes-Alpes, but the original samples found in similar geological setting in Italy were lost and never analysed with modern equipment. After more than a century, the rediscovered samples of Professor Colomba were analysed by means of SEM-EDS analysis, microRaman spectroscopy, and X-ray diffraction. The results have demonstrated that the historical samples studied by Colomba are Pb-free dessauite-(Y), and pointed to an idealized crystal chemical formula (Sr0.70Na0.25Ca0.09)Σ=1.04 (Y0.62U0.18Yb0.09Sc0.08)Σ=0.97  Fe22+(Ti12.66Fe4.783+V0.263+)Σ=17.70O38 and unit-cell parameters a = 10.376(3) Å, c = 20.903(6) Å, and V = 1949(1) Å3.

The quasi ab-initio PRDDO method, with and without the generalized valence bond (GVB)-type correlation of one pair of orbitals is used to examine some interesting features of the bonding in [l.l.l]propellane. It is found that the singlet, partial diradical configuration is the most stable one and that the central, interbridgehead bond is a weak one, i.e., it is characterized by a low degree of bonding. We thus integrate apparently contradictory evidence from former calculations. We also used the PRDDO approximation together with the synchronous transit method to study the rearrangement of [l.l.l]propellane to 3-methylene-cyclobutene, in theoretical detail.

Ab initio and semiempirical definitions of atomic valence, anisotropy, and degree of bonding between pairs of atoms have previously been applied to LCAO-MO RHF, UHF or GVB wavefunctions. It is shown that the same definitions can be applied to a CI wave function. Numerical examples are given as well as a comparison of the result of "opening shells" by means of CI or GVB. *Dedicated to Professor Robert S. Mulliken. **Career member of the Consejo National de Investigaciones Cientificas y Tecnicas (Conicet) Argentina, and to whom all correspondence should be addressed.