Quantum-Mechanical Definition of Atoms and Chemical Bonds in Molecules

Langhoff, P. W.; Mills, J. D.; Boatz, Jerry A.; Gallup, Gordon A

doi:10.21236/ada626631

Cited by 2 publications

(15 citation statements)

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“…The individual hydrogen state populations in both Panels of Figure 10 also indicate rather small continuum contributions in molecular hydrogen, reflecting only modest charge transfer contributions to the two lowest-lying molecular states in this homopolar compound [83]. The relatively larger discrete atomic state contributions are quite different for the two molecular states in the 1 to 6 Bohr region, associated with the different bonding characteristics of the states, whereas the population curves exhibit considerable qualitative similarity in the larger R region associated with weak van der Waals attraction [91].…”

Section: Atomic State Promotion Probabilities In Diatomic Hydrogenmentioning

confidence: 88%

“…Additional calculation of atomic promotion and interaction energies in low-lying triatomic hydrogen states not reported here, which include three-body dissociation pathways relevant to Dalitz plot geometries conveniently accessible to experimental observations [117][118][119][120][121], have been reported separately elsewhere [91]. These calculations include in particular symmetric C 3v triatomic dissociations particularly well-suited for experimental observation in view of the corresponding equilibrium stucture of the precursor H + 3 ion.…”

Section: Atomic State Promotion Probabilities In Diatomic Hydrogenmentioning

confidence: 95%

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Quantum-mechanical definition of atoms and their mutual interactions in Born-Oppenheimer molecules

2018

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The apparent absence of meaningful assignments of electrons and indistinguishable nuclei to particular atoms in a chemical aggregate would seem to preclude quantum-mechanical definition of atomic Hamiltonian operators within molecules and matter. The electronic energies of individual constituent atoms, as well as the interactions between them, are accordingly widely perceived as objectively undefined in molecular quantum theory, requiring additional auxiliary conditions to achieve quantitative specificity, giving rise to a plethora of individual preferences. Here we address the issue of assignments of electrons to atoms within molecules at the Born-Oppenheimer classical "fixednuclei" level of theory, and provide thereby quantum-mechanical definitions of atomic operators and of the interactions between them. In the spirit of early work of Longuet-Higgins, a "van-der-Waals" subgroup of the full molecular electronic symmetric group is shown to facilitate assignments of electrons to particular atomic nuclei in a molecule. The orthonormal (Eisenschitz-London) outerproducts of atomic eigenstates that provide separable Hilbert space representations of this symmetric subgroup furthermore support totally antisymmetric solutions of the molecular Schrödinger equation. Self-adjoint atomic and atomic-interaction operators within a molecule defined in this way are seen to have universal Hermitian matrix representatives and physically significant expectation values in totally antisymmetric molecular eigenstates. Adiabatic Born-Oppenheimer molecular energies emerge naturally from the development in the form of sums of the energies of individual atomic constituents, and of their atomic pairwise interactions, in the absence of additional auxiliary conditions. A detailed and nuanced quantitative description of electronic structure and bonding is provided thereby which includes the interplay between atomic promotion and intereaction energies, common representations of atomic-state hybridization and inter-atomic charge apportionment, potentially measurable multi-atom entanglements upon coherent dissociations of molecules, and other attributes of the development revealed by selected illustrative calculations. These include applications to the ground and electronically excited states of diatomic and triatomic hydrogen molecules, which exhibit significant accommodation among the atomic promotion and interaction energies, as well as entanglements among atomic states, over the entire range of molecular geometries transversed in the course of two-and three-atom dissociations.

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Section: Atomic State Promotion Probabilities In Diatomic Hydrogenmentioning

confidence: 88%

Section: Atomic State Promotion Probabilities In Diatomic Hydrogenmentioning

confidence: 95%

Quantum-mechanical definition of atoms and their mutual interactions in Born-Oppenheimer molecules

2018

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“…The subscript O indicates adoption of an odometer ordering convention for the sequence of N-term atomic spectral products in the row vector Φ ( r : R ), in which the enumeration of the atomic eigenstates appearing later in eq is advanced prior to those appearing earlier. This convention has a number of consequences, including particularly the specific forms of matrix representatives of Hamiltonian operators in the spectral-product basis, with additional aspects of notational conventions described in the sequel and reported in great detail elsewhere. − …”

Section: Atomic Spectral-product Formulationmentioning

confidence: 99%

“…In the second line, the diagonal elements of the first terms on the right are atomic-pair energies within the molecular environment, with the second terms there required to correct for overcountings of atomic energies in the sum over the atomic-pair terms. These fragment energies are seen to depend upon the positions R = ( R 1 , R 2 , ..., R N ) of all the atoms in the aggregate, consequent of the matrix Ũ H ( R ) which diagonalizes the complete Hamiltonian matrix, thereby including the “nonlocality” that arises in molecular quantum-mechanical calculations conventionally due to the spatially dispersed nature of constituent atomic electrons and associated multicentered electronic integrals, and also providing the indicated individual energy terms …”

Section: Atomic Spectral-product Formulationmentioning

confidence: 99%

“…An attractive alternative approach, potentially capable of overcoming the aforementioned limitations, is based on enforcing the antisymmetry requirements of Pauli’s principle “ex-post-facto” by unitary transformation of a Hamiltonian matrix which is considerably simpler to evaluate than those of conventional developments, also offering additional flexibility in choice of forms of product representations employed for this purpose. − In the case of simple atomic- or molecular-orbital representations in Hartree-product forms, for example, it has been shown that results identical with conventional use of Slater determinants are obtained, employing either finite or arbitrarily large orbital basis sets, and adding confidence to the approach, but not providing any particular computational advantage in orbital-product cases. By contrast, use of Hartree-like products of universal many-electron atomic eigenstates as an orthonormal representation for purposes of analysis and for support suitable for molecular computations, as described in the original formulation of the method, , has led to a continuing series of investigations in clarification of aspects of the theory, ,,− , and for purposes of implementation. ,,,, These developments also incorporate in a unified ab initio formalism earlier attempts to employ atomic-based representations in combined descriptions of van der Waals and chemical forces, semiempirical “atoms-in-molecules” calculations of chemical bond strengths, adoption of atomic-pair energies in semiempirical “diatomics-in-molecules” approximations to potential energy surfaces, and clarification of the role of electron permutation symmetry in long-range atomic interactions. , …”

Section: Introductionmentioning

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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Quantum-Mechanical Definition of Atoms and Chemical Bonds in Molecules

Cited by 2 publications

References 76 publications

Quantum-mechanical definition of atoms and their mutual interactions in Born-Oppenheimer molecules

Quantum-mechanical definition of atoms and their mutual interactions in Born-Oppenheimer molecules

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

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