Molecular structure calculations without clamping the nuclei

Sutcliffe, Brian T.; Woolley, Richard

doi:10.1039/b509723c

Cited by 65 publications

(63 citation statements)

References 60 publications

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“…where r nn gh (R n ) is the internuclear separation distance expressed in terms of the {R n } and the inverse mass matrix 1/µ n gh is in standard form 11 . The electronic and nuclear motions are coupled only via a potential term,…”

Section: The Coulomb Hamiltonianmentioning

confidence: 99%

On factorization of molecular wavefunctions

Jecko¹,

Sutcliffe²,

Woolley³

2015

J. Phys. A: Math. Theor.

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Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions {Φ} of the molecular Schrödinger equation as originally proposed by Hunter in the 1970s. The idea is to represent Φ in the form ϕχ where χ is purely a function of the nuclear coordinates, while ϕ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born and Oppenheimer, the hope being that an 'exact' representation of Φ can be achieved in this form with ϕ and χ interpretable as 'electronic' and 'nuclear' wavefunctions respectively. We offer a mathematical analysis of these proposals that identifies ambiguities stemming mainly from the singularities in the Coulomb potential energy.

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Section: The Coulomb Hamiltonianmentioning

confidence: 99%

On factorization of molecular wavefunctions

Jecko¹,

Sutcliffe²,

Woolley³

2015

J. Phys. A: Math. Theor.

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“…Of course, if it is possible, the first way should be preferred, since it allows to develop a deeper insight about the terms we are neglecting and the specific details that we will miss. However, although in virtually every quantum chemistry book [18,19,[26][27][28] hand-waving derivations up to different levels of detail are performed and the Born-Oppenheimer approximation is typically presented as unproblematic, it seems that the fine mathematical details on which these 'standard' approaches are based are far from clear [29][30][31]. This state of affairs does not imply that the final equations that will need to be solved are ill-defined or that the numerical methods based on the theory are unstable; in fact, it is just the contrary (see the discussion below), because the problems are related only to the precise relation between the concepts in the whole theory and those in its simplified version.…”

Section: Unit Of Massmentioning

confidence: 99%

A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry

Echenique¹,

Alonso²

2007

Molecular Physics

104

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We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.

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“…Then, by calculating the expectation value for the distance of a nucleus picked out from the set of type X and another one from the set of type Y nuclei, a single mean value is obtained even if in the classical molecular structure one would measure several different X-Y bond lengths. 11,13,24 This problem was described in a numerical all-particle study of the H + 3 molecular ion by Cafiero and Adamowicz. 12 By calculating the expectation values of the proton-proton distance and the angle for the three protons it was not possible to decide whether the molecule has a linear or a triangular shape.…”

Section: Introductionmentioning

confidence: 99%

Extracting elements of molecular structure from the all-particle wave function

Mátyus

Hutter

Müller-Herold

et al. 2011

The Journal of Chemical Physics

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Structural information is extracted from the all-particle (non-Born-Oppenheimer) wave function by calculating radial and angular densities derived from n-particle densities. As a result, one-and two-dimensional motifs of classical molecular structure can be recognized in quantum mechanics. Numerical examples are presented for three-(H(-), Ps(-), H(2) (+)), four-(Ps(2), H(2)), and five-particle (H(2)D(+)) systems. Extracting elements of molecular structure from the all-particle wave function Structural information is extracted from the all-particle (non-Born-Oppenheimer) wave function by calculating radial and angular densities derived from n-particle densities. As a result, one-and twodimensional motifs of classical molecular structure can be recognized in quantum mechanics. Numerical examples are presented for three-(H − , Ps − , H + 2 ), four-(Ps 2 , H 2 ), and five-particle (H 2 D + ) systems.

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Molecular structure calculations without clamping the nuclei

Cited by 65 publications

References 60 publications

On factorization of molecular wavefunctions

On factorization of molecular wavefunctions

A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry

Extracting elements of molecular structure from the all-particle wave function

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