Impact of electron–electron cusp on configuration interaction energies

Nolan, Michael; Filippi, Claudia; Fahy, Stephen; Greer, James C.

doi:10.1063/1.1383585

Cited by 43 publications

(50 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, it is expected that cusps appear in the wavefunction at collisions if the wavefunction does not vanish; it is also possible for an exact eigenfunction to have a node at the singularity 13,14 . Whether the inclusion of such cusps by means of trial wavefunctions involving r ee ij in electronic structure calculations could improve their accuracy has been quite widely studied; an example can be found in 15 . We shall consider the matter further from a mathematical standpoint 16 when examining the proposed factorisations.…”

Section: The Coulomb Hamiltonianmentioning

confidence: 99%

On factorization of molecular wavefunctions

Jecko¹,

Sutcliffe²,

Woolley³

2015

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

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.

show abstract

Section: The Coulomb Hamiltonianmentioning

confidence: 99%

On factorization of molecular wavefunctions

Jecko¹,

Sutcliffe²,

Woolley³

2015

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…We note that Prendergast et al [86] have argued that the removal of the electron-electron cusp in a small region around the coalescence point does not significantly improve the convergence of the energy in the millihartree level of accuracy. At first sight, their conclusion might appear to be in contradiction with our observation of the exponential convergence of the long-range correlation en-TABLE II.…”

Section: B Convergence Of the Correlation Energymentioning

confidence: 99%

Basis convergence of range-separated density-functional theory

Franck

Mussard

Luppi

et al. 2015

The Journal of Chemical Physics

View full text Add to dashboard Cite

Range-separated density-functional theory is an alternative approach to Kohn-Sham densityfunctional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the oneelectron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with the cardinal number X of the Dunning basis sets cc-p(C)VXZ, and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

show abstract

“…The comparison of the CTH calculation to the ICI method and other highly accurate results can be seen in Table IV. The impact of electron-electron cusp on ground state energy was investigated in detail by Prendergast [12] and coworker using CI and QMC methods. Their study concluded that one can still expect to get mHartree level of accuracy even in situations where the exact cusp condition is not satisfied.…”

Section: Discussionmentioning

confidence: 99%

“…Currently, there are various computational techniques for efficient calculation of the expansion coefficients. [12,[46][47][48][49][50] The calculation requires matrix elements involving the operators { Φ k |O α |Φ k , α = 2, . .…”

Section: B Optimization Of the Trial Wavefunctionmentioning

confidence: 99%

“…[6][7][8] The electron-electron cusp has been the focus of intense research because of its direct relation to the electron correlation problem and accurate description of the Coulomb and Fermi hole. [9][10][11][12][13] However, unlike the electronnuclear cusp, atom-centered basis functions are not ideal for accurate description of the many-electron wavefunction near the electron-electron cusp. [14][15][16] Indeed it * corresponding author: archakra@syr.edu has been shown that the slow convergence of a full configuration interaction (FCI) calculation with respect to the one-particle basis is related to the inadequate treatment of the electron-electron cusp.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

2012

View full text Add to dashboard Cite

The congruent transformation of the electronic Hamiltonian is developed to address the electron correlation problem in many-electron systems. The central strategy presented in this method is to perform transformation on the electronic Hamiltonian for approximate removal of the Coulomb singularity. The principle difference between the present method and the transcorrelated method of Handy and Boys is that the congruent transformation preserves the Hermitian property of the Hamiltonian. The congruent transformation is carried out using explicitly correlated functions and the optimum correlated transform Hamiltonian is obtained by performing a search over a set of transformation functions. The ansatz of the transformation functions are selected to facilitate analytical evaluation of all the resulting integrals. The ground state energy is obtained variationally by performing a full configuration interaction (FCI) calculation on the congruent transformed Hamiltonian. Computed results on well-studied benchmark systems show that for the identical basis functions, the energy from the congruent transformed Hamiltonian is significantly lower than the conventional FCI calculations. Since the number of configuration state functions in the FCI calculation increases rapidly with the size of the 1-particle basis set, the results indicate that the congruent transformed Hamiltonian provides a viable alternative to obtain FCI quality energy using a smaller underlying 1-particle basis set.

show abstract

Impact of electron–electron cusp on configuration interaction energies

Cited by 43 publications

References 31 publications

On factorization of molecular wavefunctions

On factorization of molecular wavefunctions

Basis convergence of range-separated density-functional theory

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

Contact Info

Product

Resources

About