The performance of the Hartree–Fock–Wigner correlation model for light diatomic molecules

Fondermann, Rebecca; Hanrath, Michael; Dolg, Michael

doi:10.1007/s00214-007-0360-0

Cited by 7 publications

(7 citation statements)

References 29 publications

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“…has been the most popular to date and has been studied numerically in several papers. 15,[17][18][19][20][21][22] In sections IV and V of the present paper, however, the Dot intracule ansatz…”

Section: Introductionmentioning

confidence: 99%

Intracule functional models : Part III. The dot intracule and its Fourier transform

Bernard

Crittenden

Gill

2008

Phys. Chem. Chem. Phys.

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The dot intracule D(x) of a system gives the Wigner quasi-probability of finding two of its electrons with u.v = x, where u and v are the interelectronic distance vectors in position and momentum space, respectively. In this paper, we discuss D(x) and show that its Fourier transform d(k) can be obtained in closed form for any system whose wavefunction is expanded in a Gaussian basis set. We then invoke Parseval's theorem to transform our intracule-based correlation energy method into a d(k)-based model that requires, at most, a one-dimensional quadrature.

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Section: Introductionmentioning

confidence: 99%

Intracule functional models : Part III. The dot intracule and its Fourier transform

Bernard

Crittenden

Gill

2008

Phys. Chem. Chem. Phys.

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“…Gadea and coworkers calculated potential energy curves 2,6,7,8 , radial couplings 9 , nonaa Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Naru-diabatic energy shifts 10 as well as the LiH formation by radiative association in ion collisions 11 . Results of several other calculations, including semiempirical and ab initio approaches to describe important physical and chemical properties of LiH are available 12,13,14,15,16,17,18,19,20,21,22 . Calculations related to LiH are also used in the description of ultracold polar molecules formation in a single quantum state (e.g.…”

Section: In 2006mentioning

confidence: 99%

Electronic structure and time-dependent description of rotational predissociation of LiH

Jasik

Sienkiewicz

Domsta

et al. 2017

Phys. Chem. Chem. Phys.

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Adiabatic potential energy curves of the 1 Σ + and 1 Π states of the LiH molecule have been calculated. They correlate asymptotically to atomic states, like 2s+1s, 2p+1s, 3s+1s, 3p+1s, 3d+1s, 4s+1s, 4p+1s and 4d+1s. Very good agreement is found between our calculated spectroscopic parameters and experimental ones. The dynamics of the rotational predissociation process of the 1 1 Π state has been studied by solving the time-dependent Schrödinger equation. The classical experiment of Velasco [Can. J. Phys. 35, 1204(1957] on dissociation in the 1 1 Π state is explained in detail.

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“…Gill has suggested several forms of intracule functionals, 33 among them is the Wigner intracule which was subsequently tested on a set of light atom diatomics. 37 Investigations continue into various intracule forms and their applicability. 39 An approach that resembles IFT and DFT but differs in the basic construction of the correlation functional , is orbital functional theory.…”

Section: ( ) _ Jexc[p(r)]mentioning

confidence: 99%

Properties and applications of the average interparticle distance

Hollett

Poirier

2008

J Mol Model

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ewfoundland AbstractThe first and second moment operators are used to define the origin invariant shape and size of a molecule or functional group, as well as expressions for the distance between two electrons and the distance between an electron and a nucleus.The measure of molecular size correlates quite well with an existing theoretical measure of molecular volume calculated from isodensity contours. Also, the measure of size is effective in predicting steric effects of substituents which have been measured experimentally. The electron-electron and electron-nuclear distances are related to components of the Hartree-Fock energy. The average distance between two electrons models the Coulomb energy quite well, especially in the case of localized molecular orbitals. The average distance between an electron and a nucleus is closely related to the electron-nuclear attraction energy of a molecule.The relationships discovered between the average interparticle distances and molecular energy components have led to the development of a new empirical approach to modelling the electronic structure of molecules. The general energy expression for a simulated electronic structure theory is defined, along with the functional form of t he interatomic distance dependent energy functions. The theory is used to model the hydrogen molecule, the first-row hydrides, and ethane. The models, which have the correct RHF/6-31G(d) optimized geometries, also fit the RHF/6-31G(d) energy at equilibrium and the UHF /6-31G( d) energy at the bond dissociation limit, as well as some vibrational frequencies.Also directly related to the interelectronic distance, is the issue of electron correlation. Several new approaches to the electron correlation problem have emerged 11 in recent years. Among the new methods is orbital functional theory, in which the correlation energy is a functional of the molecular orbitals. The correlation energy of different isoelectronic series as a function of nuclear charge is investigated in an effort to design a correlation operator. Insight is also gained by examining the explicit CISD energy expression.Ill

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The performance of the Hartree–Fock–Wigner correlation model for light diatomic molecules

Cited by 7 publications

References 29 publications

Intracule functional models : Part III. The dot intracule and its Fourier transform

Intracule functional models : Part III. The dot intracule and its Fourier transform

Electronic structure and time-dependent description of rotational predissociation of LiH

Properties and applications of the average interparticle distance

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