Spherical tensor theory of molecular multipole moments and polarizabilities

Gray, C.G.; Lö, B.

doi:10.1016/0301-0104(76)80028-6

Cited by 84 publications

(22 citation statements)

References 28 publications

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“…This is clear, because generalized spherical polarizabilities of any system described in Ref. 8 are defined in terms of reduced resolvent for this system and Eq. (42) makes it possible for us to introduce reduced resolvents for A and B into general expressions for any-order interaction energy between A and B.…”

Section: Connection Of Interaction Energy With Molecular Properties Omentioning

confidence: 98%

“…Here we introduced Gray's [8] irreducible polarizability tensors into the first two terms (e.g. induction terms).…”

Section: Connection Of Interaction Energy With Molecular Properties Omentioning

confidence: 99%

“…(39) directly from Eq. (8) by applying Eq. (42) and the fact that in terms of reduced resolvent reducible spherical polarizabilities may be written in the form [8]:…”

Section: Connection Of Interaction Energy With Molecular Properties Omentioning

confidence: 99%

“…We will use the results of systematic study of molecular multipole moments and polarizabilities in the light of spherical tensor theory given in Ref. 8.…”

Section: Connection Of Interaction Energy With Molecular Properties Omentioning

confidence: 99%

“…These expressions are related to the tensors localized on interacting systems and orientational dependence, which occurs in them is simplified to the utmost. Molecular spherical multipoles and polarizabilities are more convenient, when higher-order electrostatic interactions are considered [8]. So the second aim of this work is to show how we can simplify exact formulas for interaction energy and connect them with molecular properties related to the body-fixed coordinate systems.…”

Section: Introductionmentioning

confidence: 99%

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Spherical tensor theory of long‐range interactions between two molecules

Piecuch

1984

Int J of Quantum Chemistry

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The Rayleigh-Schrodinger perturbation treatment can be applied in the quantum mechanical study of long-range interactions between molecules, when we can assume that the molecular charge distributions do not overlap. In these cases the multipole expansion is a good approximation of real interaction potential and can be treated as a perturbation. In this paper we obtain closed expressions for the anisotropic long-range interaction energy between two molecules in all orders of the perturbation, using spherical tensor formalism. Then we show how spherical multipoles and polarizabilities of the isolated molecules can be inserted into general formulas for interaction energy.

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Section: Connection Of Interaction Energy With Molecular Properties Omentioning

confidence: 98%

“…Here we introduced Gray's [8] irreducible polarizability tensors into the first two terms (e.g. induction terms).…”

Section: Connection Of Interaction Energy With Molecular Properties Omentioning

confidence: 99%

“…(39) directly from Eq. (8) by applying Eq. (42) and the fact that in terms of reduced resolvent reducible spherical polarizabilities may be written in the form [8]:…”

Section: Connection Of Interaction Energy With Molecular Properties Omentioning

confidence: 99%

“…We will use the results of systematic study of molecular multipole moments and polarizabilities in the light of spherical tensor theory given in Ref. 8.…”

Section: Connection Of Interaction Energy With Molecular Properties Omentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spherical tensor theory of long‐range interactions between two molecules

Piecuch

1984

Int J of Quantum Chemistry

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Weakly Bonded Systems

Lenthe

Rijdt

Duijneveldt

1987

Advances in Chemical Physics

242

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A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank

et al. 2011

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A finite field method for calculating spherical tensor molecular polarizability tensors αlm;l′m′ = ∂Δlm/∂ϕl′m′* by numerical derivatives of induced molecular multipole Δlm with respect to gradients of electrostatic potential ϕl′m′* is described for arbitrary multipole ranks l and l′. Inter-conversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole-hexadecapole level are calculated for water at the HF, B3LYP, MP2, and CCSD levels. In addition, inter-molecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared to ab initio reference values calculated by the Reduced Variation Space (RVS) method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields.

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Spherical tensor theory of molecular multipole moments and polarizabilities

Cited by 84 publications

References 28 publications

Spherical tensor theory of long‐range interactions between two molecules

Spherical tensor theory of long‐range interactions between two molecules

Weakly Bonded Systems

A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank

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