Generalized Valence Bond Wavefunctions Research Articles

An ab initio study of nitrous acid: geometries, force constants, fundamental frequencies, and potential surface for cis-trans isomerization

The geometries, quadratic force fields, and fundamental vibrational frequencies of cis- and trans-nitrous acid have been determined by using local fourth-order Moller-Plesset perturbation theory, and also two-pair generalized valence bond wave functions. The Hartree-Fock approximation is inadequate for this molecule, due to strong electron correlation. The theoretical force field for the trans isomer agrees, after scaling, very well with the experimental values of Deeley and Mills. The experimental force field of the cis isomer is less accurately known and the present results are probably the most reliable date available. The energies and force constants along the cis-trans isomerization path have been determined for future studies of the dynamics of the isomerization reaction.

Singlet–triplet energy gaps in fluorine-substituted methylenes and silylenes

We report singlet and triplet state splittings (ΔEST) for fluorine-substituted methylenes and silylenes using dissociation-consistent configuration interaction (CI) (based on generalized valence bond wave functions). These relatively simple CI calculations emphasize correlation consistency between the singlet and triplet states. Values of ΔEST for CH2, CF2, SiH2, and SiF2 are in excellent agreement with available experimental results, and we expect the predictions for the other cases CHF (14.5) and SiHF (41.3) to be equally accurate. This result strongly suggests that the correct choice among the experimental values for ΔEST of CHF is 14.7±0.2 kcal/mol.

Intraatomic exchange and the violation of Hund's rule in twisted ethylene

It is demonstrated that the reason the singlet state lies below the triplet state in twisted ethylene (in violation of Hund's rule) is because there remains a significant component of the antiferromagnetic coupling of two triplet methylenes optimal for the methylene—methylene separated limit. We find that this effect can be completely described using a simple generalized valence bond wavefunction.

Rates of molecular desoption from solid surfaces: Adsorption site dependence for CO on Ni(100)

The role of different adsorption sites on the rate of desorption of CO from Ni(100) surfaces has been studied using the classical stochastic diffusion theory (CSDT) formulation. The microscopic parameters of the system (force constants and bond energies) have been obtained form ab initio cluster calculation (Ni 14 and Ni 20 clusters) with generalized valence bond wavefunctions. In good agreement with experiment, our calculations show that desorption occurs in two temperature ranges: 400–600 K and 150–250 K. In the higher-temperature range, the one-fold and two-fold sites are primarily responsible for the desorption rate, while for the lower-temperature range, the four-fold (weakest binding site) is dominant (experimentally achieved by poisoning the surface with S).

Effect of basis set on electron populations calculated by using Bader's criterion for partitioning electron density between atoms

The effect of basis set on Bader's criterion for partitioning electron density between atoms is examined. The major effect is on the position of minimum electron density along the bond of interest. The 6-31G(**) basis leads to the more satisfactory results. The effect of including electron correlation was examined via the use of generalized valence bond wavefunctions. The change in the electron populations was small. The partitioning of electron density is useful in examining the way in which substituents interact with hydrocarbon groups.

Perturbation theory applied to potential energy surfaces. I. The choice of a suitable reference function ψ(0)

The effect of the choice of zero order wave function on the accuracy of third-order perturbation theory is examined. The restricted Hartree–Fock, unrestricted Hartree–Fock, and generalized valence bond wave functions are considered as zero order wave functions for both Epstein–Nesbet and Mo/ller–Plesset perturbation theory. In each case the third-order perturbation results are reported for the H2 X1Σ+g potential energy curve. The behavior of Epstein–Nesbet perturbation theory relative to Mo/ller–Plesset perturbation theory is found to be independent of ψ(0). However, the nature of the perturbation and hence the absolute accuracy of both perturbation theories is determined by the choice of ψ(0). A comparison with CI calculations demonstrates that of the three examples, only the GVB perturbation theory is consistently accurate over the entire potential surface. The RHF expansion as expected becomes slowly convergent at large internuclear separations as a direct result of improper dissociation. On the other hand, the third-order UHF perturbation calculations have large errors (∼0.0225 hartree) at intermediate internuclear separations (3–4 bohr) where there is a strong contribution from single excitations. In contrast, the third-order EN–GVB perturbation theory has a maximum error of only 0.0001 hartree for any H2 geometry. The errors in the MP–GVB expansion for H2 are about an order of magnitude larger but can be considerably reduced (to ∼0.0002 hartree) by using the geometric approximation.

A method for describing resonance between generalized valence bond wavefunctions

In a valence bond (VB) description of wavefunctions there may be several distinct but energetically similar bonding structures. Examples include aromatic molecules (e.g. benzene) and excited states of molecules with equivalent chromophores (e.g. glyoxal). The variational generalization of VB theory, the generalized valence bond (GVB) method, has limitations for such systems since it can only describe one of the bonding structures, allowing no explicit mixing or “resonance” with the other structures. We present herein a method for evaluating the matrix elements necessary to optimize the mixing between the various distinct bonding structures. Evaluation of such matrix elements has heretofore been computationally difficult since the wavefunctions in general have nonzero overlap. Applications of the method are presented for the resonance in allyl radical and the splitting of the localized core hole states of N2+.

The pairwise correlated generalized valence bond model of electronic structure. II. A simple physical model for electron correlation

AbstractWhen electron pair correlations are incorporated into generalized valence bond wave functions, the necessary and sufficient wave functions for the quantitative description of chemical reactions are achieved. The resulting electron pair correlation functions are shown to be invariant; hence the generalized valence bond orbitals contain all the information in the correlated wave functions. In the case of pair correlation energies, this information is expressed through a simple function of the orbital overlaps. The resulting overlap approximation is applied to ground states, excited states, and transition states for chemical reactions. In all cases the exact energy is reproduced to within 0.5 kcal/mol (0.001 hartree). The pairwise correlated generalized valence bond method provides an opportunity to accurately predict reaction pathways for system of chemical interest.

Orbital optimization in electronic wave functions; equations for quadratic and cubic convergence of general multiconfiguration wave functions

We derive variational equations for optimization of the orbitals of arbitrary multiconfiguration wave functions. Expressing the transformation matrix connecting the set of orthonormal trial vectors and the set of final optimal orbitals as an exponential matrix of independent rotation angles allows a simple derivation of the coupled variational equations to arbitrary order. We include the explicit results through third order which are sufficient for cubic convergence in the iterative solution of the optimum orbitals. The equations were programmed (including all terms), and applications to Hartree-Fock and generalized valence bond wave functions of the carbon atom, ${\mathrm{FeO}}_{2}$, and ${\mathrm{NiCH}}_{2}$ are reported.

The pairwise correlated generalized valence bond model of electronic structure. III. Photoionization of the helium atom

The calculation of photoionization cross sections for the helium atom provides a simple but sensitive test of the accuracy of correlated wavefunctions and has been used to evaluate the relative importance of orbital splitting and dynamic electron correlation. We find that although dynamic correlation has a greater effect on the total energy, orbital splitting has a greater effect on the transition probabilities. However, if we wish to reduce the errors in calculated transition probabilities below 10%, we must include both orbital splitting and dynamic electron correlation. The pairwise correlated generalized valence bond wavefunction, which includes both effects, gives transition probabilities with errors of about 1%.

Vibrational matrix elements of the quadrupole moment of N2(x1Σg+)

The quadrupole moment ( Theta zz) of the ground state of molecular nitrogen has been calculated with accurate Hartree-Fock and generalized valence bond wavefunctions. The dependence of Theta zz on internuclear separation differs markedly in the two approximations, reflecting the inability of the Hartree-Fock wavefunction to correctly describe dissociation. This difference has a substantial effect on the calculated vibrational matrix elements of the molecular quadrupole moment, especially for large off-diagonality.

Self-Consistent Procedures for Generalized Valence Bond Wavefunctions. Applications H3, BH, H2O, C2H6, and O2

Methods of efficiently optimizing the orbitals of generalized valence bond (GVB) wavefunctions are discussed and applied to LiH, BH, H3, H2O, C6H6, and O2. The strong orthogonality and perfect pairing restrictions are tested for the X 1Σ+ state of LiH, the X 1Σ+, a 3π, and A 1π states of BH, and the H2+D⇄H+HD exchange reaction. The orbitals of H2O and C2H6 naturally localize into OH, CH, and CC bonding pairs. The nonbonding orbitals of H2O are approximately tetrahedral but this description is only 2 kcal lower than the optimum description in terms of σ and π lone-pair functions. The calculated rotational barrier for C2H6 is 3.1 kcal, in good agreement with the experimental value (2.9 kcal). The description of the O2 molecule in the GVB approach is presented and the results of carrying out CI calculations using the GVB orbitals are discussed. The GVB orbitals are found to be a good basis set for configuration interaction calculations. The general features of GVB orbitals in other molecules are summarized.

Generalized valence bond wavefunctions for the low lying states of methylene

Generalized valence bond (GVB) calculations are reported for the 3B 1, 1A 1, and 1B 1 states of the CH 2 molecule. The GVB method is discussed and compared with other multi-configuration and separated pair methods. The lowest singlet state ( 1A 1) is found to lie 0.50 eV about the lowest triplet state ( 3B 1) and the 1B 1- 1A 1 separation is found to be 1.40 eV.