Explicitly correlated electronic structure theory from R12/F12 ansätze

Ten‐no, Seiichiro; Noga, Jozef

doi:10.1002/wcms.68

Cited by 156 publications

(135 citation statements)

References 62 publications

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“…This is an expected result and is in agreement with previous work on explicitly correlated methods. [51,64,65] The negative values of geminal parameters indicate the role of the geminal function in providing a better description of the Coulomb hole. The analytical forms of the GTG functions are inherently approximate and are not capable of describing the cusp correctly because their first derivative vanishes in the limit of r ee = 0…”

Section: Discussionmentioning

confidence: 99%

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

2012

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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.

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Section: Discussionmentioning

confidence: 99%

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

2012

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“…In the intervening years this approach has matured, with important advances taking it from a promising technique to an indispensable tool for high-accuracy quantum chemical methods for large systems [30][31][32][33][34][35][36]. These advances include the introduction of a complementary auxiliary basis set in which to perform the RI [37,38], refinement of the approximations used in order to minimize the impact of the RI and maintain orbital invariance [39][40][41][42][43], a more general function of the interelectronic coordinate to approximately capture longer range effects [44,45], and the introduction of specially designed basis sets for optimal efficiency [46,47].…”

Section: Introductionmentioning

confidence: 99%

Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

Grüneis

Shepherd

Alavi

et al. 2013

The Journal of Chemical Physics

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We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order Møller-Plesset perturbation theory (MP2). The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.

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“…The resulting wavefunctions are known as explicitly-correlated wave functions (for recent reviews, see Refs. [4][5][6], and it is the purpose of the present Communication to show that the basis-set convergence of the RPA correlation energy can be improved by computing a correction from explicitly-correlated second-order manybody perturbation theory. We shall focus on the direct version of the random-phase approximation to the correlation energy (which we shall refer to as dRPA), and accordingly, this second-order correction is obtained from a direct secondorder many-body perturbation theory, which we shall refer to a) Author to whom correspondence should be addressed.…”

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confidence: 97%

Communication: Explicitly-correlated second-order correction to the correlation energy in the random-phase approximation

Hehn

Klopper

2013

The Journal of Chemical Physics

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Within the framework of density-functional theory, the basis-set convergence of energies obtained from the random-phase approximation to the correlation energy is equally slow as in wavefunction theory, as for example in coupled-cluster or many-body perturbation theory. Fortunately, the slow basis-set convergence of correlation energies obtained in the random-phase approximation can be accelerated in exactly the same manner as in wavefunction theory, namely by using explicitly correlated two-electron basis functions that are functions of the interelectronic distances. This is demonstrated in the present work.

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Explicitly correlated electronic structure theory from R12/F12 ansätze

Cited by 156 publications

References 62 publications

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

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

Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions

Communication: Explicitly-correlated second-order correction to the correlation energy in the random-phase approximation

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