An approximate diatomics in molecules formulation of generalized valence bond theory

Cullen, John M.

doi:10.1002/jcc.20808

Cited by 1 publication

(3 citation statements)

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“…The exact atomic-pair approach provides a rigorous theoretical underpinning for earlier inventive ad hoc theoretical and semiempirical attempts to employ atomic representations ,− and diatomic information ,− in devising approximations to the electronic structures of polyatomic molecules. The early seminal work of Eisenschitz and London is extended by the introduction of the ex-post-facto method, , by demonstration of the presence of the totally antisymmetric representation therein once and only once, and by development of methods to isolate it among other representations of the symmetric groups, establishing the essential equivalence of post- and prior-antisymmetrization in calculations of total molecular electronic energies. , …”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…The early semiempirical atoms-in-molecules method of Moffitt, in which experimental atomic energies are employed in molecular electronic calculations, is placed in the context of the ab initio approach when the unfaithful metrically defined atomic-interaction matrices employed are eliminated in favor of the ex-post-facto methodology, providing unambiguous definitions of the energies of atoms and their interactions in molecules, illustated by calculations on the H 2 molecule reported here. The diatomic-based approaches are unable to deal successfully with the nonorthogonality of the antisymmetric pair and total aggregate basis sets when employed together, and must assume aggregate orthogonality as an intrinsic part of the methodology. ,− …”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…Absent from these early approaches is the recognition that totally antisymmetric states need not be expressed as sums of terms which are individually totally antisymmetric. The early approaches further do not take cognizance of the absence of faithful representations of fragment atomic operators in support provided in term-by-term totally antisymmetric form. ,− The ab initio exact-pair development offers a rigorous analytical perspective and computational basis from which to view the earlier related methods, clarifying aspects of these pioneering studies, extending them, and arguably attaining most of their stated goals, and building thereby upon the very earliest ad hoc attempts to simplify constructions of potential energy surfaces. − …”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

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

et al. 2016

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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.

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