Generalized Valence Bond Research Articles

Nature of the chemical bond and origin of the inverted dipole moment in boron fluoride: a generalized valence bond approach.

The generalized product function energy partitioning (GPF-EP) method has been applied to investigate the nature of the chemical bond and the origin of the inverted dipole moment of the BF molecule. The calculations were carried out with GPF wave functions treating all of the core electrons as a single Hartree-Fock group and the valence electrons at the generalized valence bond perfect-pairing (GVB-PP) or full GVB levels, with the cc-pVTZ basis set. The results show that the chemical structure of both X (1)Σ(+) and a (3)Π states is composed of a single bond. The lower dissociation energy of the excited state is attributed to a stabilizing intraatomic singlet coupling involving the B 2sp-like lobe orbitals after bond dissociation. An increase of electron density on the B atom caused by the reorientation of the boron 2sp-like lobe orbitals is identified as the main responsible effect for the electric dipole inversion in the ground state of BF. Finally, it is shown that π back-bonding from fluorine to boron plays a minor role in the electron density displacement to the bonding region in both states. Moreover, this effect is associated with changes in the quasi-classical component of the electron density only and does not contribute to covalency in either of the states. Therefore, at least for the case of the BF molecule, the term back-bonding is misleading, since it does not contribute to the bond formation.

Restricted Hartree Fock using complex-valued orbitals: a long-known but neglected tool in electronic structure theory.

Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H2 insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O2, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.

Insights into the electronic structure of disulfur tetrafluoride isomers from generalized valence bond theory.

Sulfur and fluorine can participate in a variety of bonding motifs, lending significant diversity to their chemistry. Prior work has identified three distinct minima for disulfur tetrafluoride (S2F4) compounds: two FSSF3 isomers and one SSF4 species. We used a combination of sophisticated explicitly correlated coupled cluster calculations and generalized valence bond (GVB) theory to characterize the electronic structure of these species as well as additional stationary points on the potential energy surface with F2SSF2 connectivity. On the singlet surface, the two stationary points considered in this work with an F2SSF2 structure are first- or second-order saddle points and not minima. However, on the triplet surface, we discovered a novel C2 symmetric F2SSF2 minimum that was anticipated from the structure of an excited state ((3)B1) of SF2. Analysis using the GVB wave function in conjunction with the recoupled pair bonding model developed by our group provides a straightforward explanation of the bonding in all of the S2F4 structures considered here. In addition, the model predicted the existence of the F2SSF2((3)B) minimum.

Description of Polar Chemical Bonds from the Quantum Mechanical Interference Perspective.

The Generalized Product Function Energy Partitioning (GPF-EP) method has been applied to a set of molecules, AH (A = Li, Be, B, C, N, O, F), CO and LiF with quite different dipole moments, in order to investigate the role played by the quantum interference effect in the formation of polar chemical bonds. The calculations were carried out with GPF wave functions treating all the core electrons as a single Hartree-Fock group and the bonding electrons at the Generalized Valence Bond Perfect-Pairing (GVB-PP) level, with the cc-pVTZ basis set. The results of the energy partitioning into interference and quasi-classical contributions along the respective Potential Energy Surfaces (PES) show that the main contribution to the depth of the potential wells comes from the interference term, which is an indication that all the molecules mentioned above form typical covalent bonds. In all cases, the stabilization promoted by the interference term comes from the kinetic contribution, in agreement with previous results. The analysis of the effect of quantum interference on the electron density reveals that while polarization effects (quasi-classical) tend to displace electronic density from the most polarizable atom toward the less polarizable one, interference (quantum effects) counteracts by displacing electronic density to the bond region, giving rise to the right electronic density and dipole moment.

The nature of the SO bond of chlorinated sulfur–oxygen compounds

Sulfur–oxygen chemistry encompasses a rich variety of chemical species and reactions. Sulfur–oxygen bonds can be quite short and strong, and historically, there has been disagreement as to the nature of the SO bond in sulfinyl groups. Early work invoked participation by the 3d orbitals of sulfur to explain the apparent double-bond character of sulfinyl bonds, but modern calculations have clearly established that sulfur 3d atomic orbitals do not participate as valence orbitals in hypervalent sulfur compounds. In prior work, we used generalized valence bond (GVB) theory to explain the features of the SO bond in the HSO/SOH structural isomers, and we extend that work here to the chlorinated analogs (ClSO/SOCl). We also use GVB theory to elucidate the nature of the bonding in Cl2SO and its higher energy structural isomer ClSOCl. We find that recoupled pair bonding, which we first introduced in our study of sulfur fluorides, is integral to describing the SO bond in all of these species. We also connect our analysis to the use of hyperconjugation to explain the back-bonding in the π system in the sulfinyl halides.

Bonding in PF2Cl, PF3Cl, and PF4Cl: insight into isomerism and apicophilicity from ab initio calculations and the recoupled pair bonding model

Following previous work on PF n and SF n Cl compounds, we report high-level ab initio quantum chemical calculations on PF2Cl, PF3Cl, and PF4Cl. Coupled cluster (CCSD(T)) calculations were used to determine the structures and energetics of the various PF n Cl isomers, while generalized valence bond calculations were used to gain a deeper understanding of the factors influencing the structure and energetics of the isomers. Muetterties’ rule, which predicts that more electronegative elements occupy the apical positions in pentavalent phosphorus compounds, is examined in the context of the recoupled pair bonding model, which provides invaluable insights into the bonding, structure, and reactivity of hypervalent compounds. While we found more electronegative fluorine is favored in the apical position in closed-shell PF4Cl, the opposite is true for PF3Cl and two triplet excited state isomers of PF2Cl, all of which are open-shell species.

Insights into the Perplexing Nature of the Bonding in C2 from Generalized Valence Bond Calculations.

Diatomic carbon, C2, has been variously described as having a double, triple, or quadruple bond. In this article, we report full generalized valence bond (GVB) calculations on C2. The GVB wave function-more accurate than the Hartree-Fock wave function and easier to interpret than traditional multiconfiguration wave functions-is well-suited for characterizing the bonding in C2. The GVB calculations show that the electronic wave function of C2 is not well described by a product of singlet-coupled, shared electron pairs (perfect pairing), which is the theoretical basis for covalent chemical bonds. Rather, C2 is best described as having a traditional covalent σ bond with the electrons in the remaining orbitals of the two carbon atoms antiferromagnetically coupled. However, even this description is incomplete as the perfect pairing spin function also makes a significant contribution to the full GVB wave function. The complicated structure of the wave function of C2 is the source of the uncertainty about the nature of the bonding in this molecule.

Block correlated second order perturbation theory with a generalized valence bond reference function

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

Multi‐level quantum monte Carlo wave functions for complex reactions: The decomposition of α‐hydroxy‐dimethylnitrosamine

We present here several novel features of our recently proposed Jastrow linear generalized valence bond (J-LGVB) wave functions, which allow a consistently accurate description of complex potential energy surfaces (PES) of medium-large systems within quantum Monte Carlo (QMC). In particular, we develop a multilevel scheme to treat different regions of the molecule at different levels of the theory. As prototypical study case, we investigate the decomposition of α-hydroxy-dimethylnitrosamine, a carcinogenic metabolite of dimethylnitrosamine (NDMA), through a two-step mechanism of isomerization followed by a retro-ene reaction. We compute a reliable reaction path with the quadratic configuration interaction method and employ QMC for the calculation of the electronic energies. We show that the use of multideterminantal wave functions is very important to correctly describe the critical points of this PES within QMC, and that our multilevel J-LGVB approach is an effective tool to significantly reduce the cost of QMC calculations without loss of accuracy. As regards the complex PES of α-hydroxy-dimethylnitrosamine, the accurate energies computed with our approach allows us to confirm the validity of the two-step reaction mechanism of decomposition originally proposed within density functional theory, but with some important differences in the barrier heights of the individual steps.

New insights into the stability of alkenes and alkynes, fluoro-substituted or not: a DFT, G4, QTAIM and GVB study

Many undergraduate organic chemistry books do not agree with the order of relative stability of alkenes towards hydrogenation reactions. Although they ascribe the stability of alkenes to the number and spatial position of the alkyl groups attached to the vinyl carbon atoms, results from the quantum theory of atoms in molecules indicate that the influence of an alkyl substituent on the stability of unsaturated hydrocarbons arises from the slight removal of electron density of the π bond, not from donation of their charge density to unsaturated carbon atoms as stated in many text books. There is an inverse relation between delocalization index--the number of shared electrons between two atoms, or Wiberg bond index of C=C bond--and the number of methyl groups attached to the vinyl carbon atoms. Electron withdrawing groups (EWGs) attached to unsaturated carbon atoms of alkenes and alkynes have two different behaviors: slight EWGs (alkyl groups) stabilize unsaturated carbon atoms while the strong EWG destabilizes the unsaturated carbon atoms. Generalized valence bond theory was also used to study the ambiguous behavior of fluorine substituents bonded to vinyl carbon atoms.

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree-Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self-consistent field method, Møller-Plesset perturbation theory method, and time-dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self-consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations-All Atom (OPLS-AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented.

Bonding in Sulfur–Oxygen Compounds—HSO/SOH and SOO/OSO: An Example of Recoupled Pair π Bonding

The ground states (X(2)A″) of HSO and SOH are extremely close in energy, yet their molecular structures differ dramatically, e.g., re(SO) is 1.485 Å in HSO and 1.632 Å in SOH. The SO bond is also much stronger in HSO than in SOH: 100.3 kcal/mol versus 78.8 kcal/mol [RCCSD(T)-F12/AVTZ]. Similar differences are found in the SO2 isomers, SOO and OSO, depending on whether the second oxygen atom binds to oxygen or sulfur. We report generalized valence bond and RCCSD(T)-F12 calculations on HSO/SOH and OSO/SOO and analyze the bonding in all four species. We find that HSO has a shorter and stronger SO bond than SOH due to the presence of a recoupled pair bond in the π(a″) system of HSO. Similarly, the bonding in SOO and OSO differs greatly. SOO is like ozone and has substantial diradical character, while OSO has two recoupled pair π bonds and negligible diradical character. The ability of the sulfur atom to form recoupled pair bonds provides a natural explanation for the dramatic variation in the bonding in these and many other sulfur-oxygen compounds.

Bonding in FSSF3: Breakdown in Bond Length-Strength Correlations and Implications for SF2 Dimerization

The product of SF2 dimerization is an unusual molecule with many unexpected properties. For instance, there are four nonequivalent SF bond lengths, and they are not inversely correlated with their respective bond dissociation energies. Further, the minimum energy pathway to dissociation into two SF2 molecules does not involve breaking the longest or weakest SF bond. In this paper, we provide compelling explanations for both of these unusual observations by analyzing the generalized valence bond (GVB) wave function for FSSF3.

On the electronic structure of the diazomethane molecule

The electronic structure and chemical bonding in the diazomethane molecule are investigated using full-valence generalized valence bond (GVB) methods. We point out that an ab initio-based bonding model must correspond directly to a wave function that yields at least qualitatively corrects values for the structural parameters of a molecule, that is, molecular geometry, vibrational frequencies, and dipole moment. However, in the case of diazomethane, when trying to emulate the bonding models proposed in the literature through full-valence GVB wave functions, we found out that all of them are directly associated with optimized molecular geometries that are saddle points in the molecular potential energy surface. This spurious behavior is corrected by a multiconfiguration–self-consistent field (MCSCF) wave function that incorporates an enlarged “pi-like” active space enabling a complete active space self-consistent field (CASSCF) block, with more active orbitals than electrons, together with a “sigma-like” generalized valence bond with restricted configuration interaction (GVB-RCI) block. With this wave function, we are able to generate the best calculated set of harmonic frequencies to date for the diazomethane molecule. The physical effects that are important for the correct description of its electronic and vibrational structure are then discussed using a series of MCSCF wave functions. This result leads to a decomposition of the electronic wave function into diabatic GVB-RCI chemical structures along the CH2 wagging mode illustrating the necessity to understand the chemical bonding in this molecule as a superposition of bonding patterns. Some structural properties of diazomethane and diazocompounds are then successfully analyzed using our model.

Transition energy and potential energy curves for ionized inner-shell states of CO, O2 and N2 calculated by several inner-shell multiconfigurational approaches

Potential energy curves and inner-shell ionization energies of carbon monoxide, oxygen and nitrogen molecules were calculated using several forms of the inner-shell multiconfigurational self-consistent field (IS-MCSCF) method-a recently proposed protocol to obtain specifically converged inner-shell states at this level. The particular forms of the IS-MCSCF method designated IS-GVB-PP, IS-FVBL and IS-CASSCF stand for perfect pairing generalized valence bond, full valence bond-like MCSCF and complete active space self consistent field, respectively. A comparison of these different versions of the IS-MCSCF method was carried out for the first time. The results indicate that inner-shell states are described accurately even for the simplest version of the method (IS-GVB-PP). Dynamic correlation was recovered by multireference configuration interaction or multireference perturbation theory. For molecules not having equivalent atoms, all methods led to comparable and accurate transition energies. For molecules with equivalent atoms, the most accurate results were obtained by multireference perturbation theory. Scalar relativistic effects were accounted for using the Douglas-Kroll-Hess Hamiltonian.

Size-Extensive Wave Functions for Quantum Monte Carlo: A Linear Scaling Generalized Valence Bond Approach.

We propose a new class of multideterminantal Jastrow-Slater wave functions constructed with localized orbitals and designed to describe complex potential energy surfaces of molecular systems for use in quantum Monte Carlo (QMC). Inspired by the generalized valence bond formalism, we elaborate a coupling scheme between electron pairs which progressively includes new classes of excitations in the determinantal component of the wave function. In this scheme, we exploit the local nature of the orbitals to construct wave functions which have increasing complexity but scale linearly. The resulting wave functions are compact, can correlate all valence electrons, and are size extensive. We assess the performance of our wave functions in QMC calculations of the homolytic fragmentation of N-N, N-O, C-O, and C-N bonds, very common in molecules of biological interest. We find excellent agreement with experiments, and, even with the simplest forms of our wave functions, we satisfy chemical accuracy and obtain dissociation energies of equivalent quality to the CCSD(T) results computed with the large cc-pV5Z basis set.

Insights into the Unusual Barrierless Reaction between Two Closed Shell Molecules, (CH3)2S + F2, and Its H2S + F2 Analogue: Role of Recoupled Pair Bonding

Early flowtube studies showed that (CH(3))(2)S (DMS) reacted very rapidly with F(2); hydrogen sulfide (H(2)S), however, did not. Recent crossed molecular beam studies found no barrier to the reaction between DMS and F(2) to form CH(2)S(F)CH(3) + HF. At higher collision energies, a second product channel yielding (CH(3))(2)S-F + F was identified. Both reaction channels proceed through an intermediate with an unusual (CH(3))(2)S-F-F bond structure. Curiously, these experimental studies have found no evidence of direct F(2) addition to DMS, resulting in (CH(3))(2)SF(2), despite the fact that the isomer in which both fluorines occupy axial positions is the lowest energy product. We have characterized both reactions, H(2)S + F(2) and DMS + F(2), with high-level ab initio and generalized valence bond calculations. We found that recoupled pair bonding accounts for the structure and stability of the intermediates present in both reactions. Further, all sulfur products possess recoupled pair bonds with CH(2)S(F)CH(3) having an unusual recoupled pair bond dyad involving π bonding. In addition to explaining why DMS reacts readily with F(2) while H(2)S does not, we have studied the pathways for direct F(2) addition to both sulfide species and found that (for (CH(3))(2)S + F(2)) the CH(2)S(F)CH(3) + HF channel dominates the potential energy surface, effectively blocking access to F(2) addition. In the H(2)S + F(2) system, the energy of the transition state for formation of H(2)SF(2) lies very close to the H(2)SF + F asymptote, making the potential pathway a roaming atom mechanism.

Electronic structure and bonding of HBeLi, HmgLi, and HCaLi in their bent equilibrium geometries

Compact, yet accurate, non-orthogonal multi-configuration wavefunctions have been computed for HBeLi, HMgLi, and HCaLi in their respective nonlinear equilibrium geometries. They appear to be dominated by just two configurations, "orbitally relaxed" versions of the single-configuration spin-coupled and generalized valence bond (GVB) wavefunctions, respectively, with a smaller contribution from a self-consistent field (SCF)-like configuration. Double excitations out of the main configurations, while required for quantitative accuracy, enter the wavefunction with such small weights that they do not alter the qualitative picture that emerges from the orbital structure of the two main configurations. For comparison, calculations have also been carried out with two orthogonality-free configurations as reference, and no GVB-like or SCF-like configuration. Atoms-in-molecules (AIM) topological analyses of the overall electron densities, and considerations of local energetics in the differential neighbourhood of the equilibrium geometries, have been used to provide independent assessments of the nature of bonding in these molecules. Orbital structure and AIM results together suggest the existence of three-centre two-electron M-H-M' bonds through hydrogen in all three molecules. Orbital pictures suggest these bonds are at least partially covalent, while a strict interpretation of values of the electron density Laplacian at AIM bond critical points would imply closed-shell interactions. Also for all three molecules, the orbital structures of the two main configurations suggest the presence of a one-electron two-centre bond between Li and the alkaline-earth atom. This bond may provide at least a partial explanation for the relative shortness of the inter-metallic distances, but is apparently too spread out to show up in AIM analyses of the total electron density. Considerations of local energetics support the more nuanced description of bonding that emerges, for these three molecules, from their orbital structure.

Separation of strong (bond-breaking) from weak (dynamical) correlation

A CC (coupled-cluster) ansatz based on a GVB (generalized valence bond) or an APSG (antisymmetrized product of strongly orthogonal geminals) reference function arises naturally if one tries to treat strong correlations exactly (to infinite order), and weak correlations by TCC (traditional coupled cluster) theory. This ansatz is proposed as an alternative to MC-CC (multi-configuration coupled cluster) theory. One uses especially that APSG and GVB are of CC type, but allow to combine separability with the variation principle. The energy and the stationarity conditions are formulated in terms of spinfree density cumulants. The replacement operators corresponding to the APSG ansatz generate a Lie algebra which is a subalgebra of that of all replacement operators.

Chemical Bonding and the Equilibrium Composition of Grignard Reagents in Ethereal Solutions

A thorough analysis of the electronic structure and thermodynamic aspects of Grignard reagents and its associated equilibrium composition in ethereal solutions is performed. Considering methylmagnesium halides containing fluorine, chlorine, and bromine, we studied the neutral, charged, and radical species associated with their chemical equilibrium in solution. The ethereal solvents considered, tetrahydrofuran (THF) and ethyl ether (Et(2)O), were modeled using the polarizable continuum model (PCM) and also by explicit coordination to the Mg atoms in a cluster. The chemical bonding of the species that constitute the Grignard reagent is analyzed in detail with generalized valence bond (GVB) wave functions. Equilibrium constants were calculated with the DFT/M06 functional and GVB wave functions, yielding similar results. According to our calculations and existing kinetic and electrochemical evidence, the species R(•), R(-), (•)MgX, and RMgX(2)(-) must be present in low concentration in the equilibrium. We conclude that depending on the halogen, a different route must be followed to produce the relevant equilibrium species in each case. Chloride and bromide must preferably follow a "radical-based" pathway, and fluoride must follow a "carbanionic-based" pathway. These different mechanisms are contrasted against the available experimental results and are proven to be consistent with the existing thermodynamic data on the Grignard reagent equilibria.