On the valence bond diatomics‐in‐molecules method. I. A projection operator reformulation

Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches

Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and the pairwise-atomic Hamiltonian matrices required for practical applications. These matrices can be retained as functions of scalar atomic-pair separations and employed in assembling aggregate Hamiltonian matrices, with Wigner rotation matrices providing analytical representations of their angular degrees of freedom. In this way, ab initio potential energy surfaces are obtained in the complete absence of repeated evaluations and transformations of the one- and two-electron integrals at different molecular geometries required in most ab inito molecular calculations, with large Hamiltonian matrix assembly simplified and explicit diagonalizations avoided employing partitioning and Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory. Illustrative applications of the important components of the formalism, selected aspects of the scaling of the approach, and aspects of "on-the-fly" interfaces with Monte Carlo and molecular-dynamics methods are described in anticipation of subsequent applications to biomolecules and other large aggregates.

Optimizing the Performance of the Multiconfiguration Molecular Mechanics Method

Multiconfiguration molecular mechanics (MCMM) is a general algorithm for constructing potential energy surfaces for reactive systems (Kim, Y.; Corchado, J. C.; Villà, J.; Xing, J.; Truhlar, D. G. J. Chem. Phys. 2000, 112, 2718). This paper illustrates how the performance of the MCMM method can be improved by adopting improved molecular mechanics parameters. We carry out calculations of reaction rate constants using variational transition state theory with optimized multidimensional tunneling on the MCMM PESs for three hydrogen transfer reactions, and we compare the results to direct dynamics. We find that the MCMM method with as little as one electronic structure Hessian can describe the dynamically important regions of the ground-electronic state PES, including the corner-cutting-tunneling region of the reaction swath, with practical accuracy.

Combined valence bond-molecular mechanics potential-energy surface and direct dynamics study of rate constants and kinetic isotope effects for the H+C2H6 reaction

This article presents a multifaceted study of the reaction H+C(2)H(6)-->H(2)+C(2)H(5) and three of its deuterium-substituted isotopologs. First we present high-level electronic structure calculations by the W1, G3SX, MCG3-MPWB, CBS-APNO, and MC-QCISD/3 methods that lead to a best estimate of the barrier height of 11.8+/-0.5 kcal/mol. Then we obtain a specific reaction parameter for the MPW density functional in order that it reproduces the best estimate of the barrier height; this yields the MPW54 functional. The MPW54 functional, as well as the MPW60 functional that was previously parametrized for the H+CH(4) reaction, is used with canonical variational theory with small-curvature tunneling to calculate the rate constants for all four ethane reactions from 200 to 2000 K. The final MPW54 calculations are based on curvilinear-coordinate generalized-normal-mode analysis along the reaction path, and they include scaled frequencies and an anharmonic C-C bond torsion. They agree with experiment within 31% for 467-826 K except for a 38% deviation at 748 K; the results for the isotopologs are predictions since these rate constants have never been measured. The kinetic isotope effects (KIEs) are analyzed to reveal the contributions from subsets of vibrational partition functions and from tunneling, which conspire to yield a nonmonotonic temperature dependence for one of the KIEs. The stationary points and reaction-path potential of the MPW54 potential-energy surface are then used to parametrize a new kind of analytical potential-energy surface that combines a semiempirical valence bond formalism for the reactive part of the molecule with a standard molecular mechanics force field for the rest; this may be considered to be either an extension of molecular mechanics to treat a reactive potential-energy surface or a new kind of combined quantum-mechanical/molecular mechanical (QM/MM) method in which the QM part is semiempirical valence bond theory; that is, the new potential-energy surface is a combined valence bond molecular mechanics (CVBMM) surface. Rate constants calculated with the CVBMM surface agree with the MPW54 rate constants within 12% for 534-2000 K and within 23% for 200-491 K. The full CVBMM potential-energy surface is now available for use in variety of dynamics calculations, and it provides a prototype for developing CVBMM potential-energy surfaces for other reactions.