A systematic procedure for extracting fragment matrices for the method of diatomics‐in‐molecules fromabinitiocalculations on diatomics

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.

Cationic Van-der-Waals Complexes: Theoretical Study of Ar2H+ Structure and Stability

The electronic and geometric structure, stability and molecular properties of the cationic van-der-Waals complex Ar2H+ in its ground electronic state are studied by means of two ab-initio quantum-chemical approaches: conventional configuration interaction (multi-reference and coupled-cluster methods) and a diatomics-in-molecules model with ab-initio input data. To ensure consistency between the two approaches, one and the same one-electron atomic basis set (aug-cc-pVTZ by Dunning) is employed in both. The topography of the ground-state potential-energy surface is examined with respect to the nature of the binding and the stability of structures corresponding to stationary points. In accordance with most earlier theoretical work, there are two local minima at linear arrangements: a strongly bound centro-symmetric moiety, (Ar–H–Ar)+, and a weakly bound van-der-Waals complex, Ar···ArH+. These are separated by a low barrier. Only the centro-symmetric molecule is significantly stable (D e = 0.68eV) against fragmentation into Ar + ArH+ and should have structural and dynamical relevance. A fairly simple diatomics-in-molecules model taking into account only the few lowest electronic fragment states yields a qualitatively correct description of the ground state but shows quantitative deviations from the more accurate configuration-interaction data in detail. Nevertheless, it should provide a good starting point for the treatment of larger complexes Ar n H+ with n > 2.