Center for Molecular Modeling - FWO D. Van Neck / P. Bultinck (3G057510) B/10895/*

Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods

wim — Mon, 01 Aug 2016 10:10:59 +0000

D.R. Alcoba, A. Torre, L. Lain, G. Massaccesi, O.B. Ona, P.W. Ayers, M. Van Raemdonck, P. Bultinck, D. Van Neck

Theoretical Chemistry Accounts

135 (6), 153

2016

Abstract

The coefficients of full configuration interaction wave functions (FCI) for N-electron systems expanded in N-electron Slater determinants depend on the orthonormal one-particle basis chosen although the total energy remains invariant. Some bases result in more compact wave functions, i.e. result in fewer determinants with significant expansion coefficients. In this work, the Shannon entropy, as a measure of information content, is evaluated for such wave functions to examine whether there is a relationship between the FCI Shannon entropy of a given basis and the performance of that basis in truncated CI approaches. The results obtained for a set of randomly picked bases are compared to those obtained using the traditional canonical molecular orbitals, natural orbitals, seniority minimising orbitals and a basis that derives from direct minimisation of the Shannon entropy. FCI calculations for selected atomic and molecular systems clearly reflect the influence of the chosen basis. However, it is found that there is no direct relationship between the entropy computed for each basis and truncated CI energies.

DOI

http://dx.doi.org/10.1007/s00214-016-1905-x

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16-TheorChemAcc-135-153-Alcoba.pdf

Eigenvalue-based determinants for scalar products and form factors in Richardson–Gaudin integrable models coupled to a bosonic mode

wim — Mon, 07 Dec 2015 10:18:18 +0000

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck

Journal of Physics A: Mathematical and Theoretical

48 (42), 425201

2015

Abstract

Starting from integrable su(2) (quasi-)spin Richardson–Gaudin (RG) XXZ models we derive several properties of integrable spin models coupled to a bosonic mode. We focus on the Dicke–Jaynes–Cummings–Gaudin models and the two-channel (p + ip)-wave pairing Hamiltonian. The pseudo-deformation of the underlying su(2) algebra is here introduced as a way to obtain these models in the contraction limit of different RG models. This allows for the construction of the full set of conserved charges, the Bethe ansatz state, and the resulting RG equations. For these models an alternative and simpler set of quadratic equations can be found in terms of the eigenvalues of the conserved charges. Furthermore, the recently proposed eigenvalue-based determinant expressions for the overlaps and form factors of local operators are extended to these models, linking the results previously presented for the Dicke–Jaynes–Cummings–Gaudin models with the general results for RG XXZ models.

This paper has been selected as editor's pick

DOI

http://dx.doi.org/10.1088/1751-8113/48/42/425201

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15-JPhysA-48-425201-Claeys.pdf

Latest article by Pieter Claeys selected as publisher's pick by Journal of Physics A: Mathematical and Theoretical

wim — Mon, 07 Dec 2015 10:09:37 +0000

"Eigenvalue-based determinants for scalar products and form factors in Richardson–Gaudin integrable models coupled to a bosonic mode" has been selected as editor's pick by the Journal of Physics A: Mathematical and Theoretical. Read the interview with Pieter Claeys, Stijn de Baerdemacker, Mario van Raemdonck and Dimitri van Neck here.

Polynomial scaling approximations and Dynamic Correlation Corrections to Doubly Occupied Configuration Interaction wave functions

Ward — Thu, 09 Jul 2015 15:26:35 +0000

M. Van Raemdonck, D. Alcoba, W. Poelmans, S. De Baerdemacker, A. Torre, L. Lain, G. Massaccesi, D. Van Neck, P. Bultinck

Journal of Chemical Physics

143 (10), 104106

2015

Abstract

A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1063/1.4930260

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1.4930260.pdf

Variational optimization of the second order density matrix corresponding to a seniority-zero configuration interaction wave function

Ward — Thu, 09 Jul 2015 15:20:53 +0000

W. Poelmans, M. Van Raemdonck, B. Verstichel, S. De Baerdemacker, A. Torre, L. Lain, G. Massaccesi, D. Alcoba, P. Bultinck, D. Van Neck

Journal of Chemical Theory and Computation (JCTC)

11 (9), 4064–4076

2015

Abstract

We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index $N$-representability $\mathcal{P}$-, $\mathcal{Q}$-, and $\mathcal{G}$-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly-occupied many-electron wave function, i.e.\ a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index $N$-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, $\text{N}_2$ and $\text{CN}^-$). This work is motivated by the fact that a doubly-occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly-occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as $L^3$, where $L$ is the number of spatial orbitals. Since the doubly-occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly-occupied framework.

DOI

http://dx.doi.org/10.1021/acs.jctc.5b00378

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15-JCTC-11(9)4064-Poelmans.pdf

Eigenvalue-based method and form-factor determinant representations for integrable XXZ Richardson-Gaudin models

wim — Tue, 07 Apr 2015 07:01:00 +0000

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck

Physical Review B

91 (15), 155102

2015

Abstract

We propose an extension of the numerical approach for integrable Richardson-Gaudin models based on a new set of eigenvalue-based variables [A. Faribault et al., Phys. Rev. B 83, 235124 (2011); O. El Araby et al., Phys. Rev. B 85, 115130 (2012)]. Starting solely from the Gaudin algebra, the approach is generalized towards the full class of XXZ Richardson-Gaudin models. This allows for a fast and robust numerical determination of the spectral properties of these models, avoiding the singularities usually arising at the so-called singular points. We also provide different determinant expressions for the normalization of the Bethe ansatz states and form factors of local spin operators, opening up possibilities for the study of larger systems, both integrable and nonintegrable. These expressions can be written in terms of the new set of variables and generalize the results previously obtained for rational Richardson-Gaudin models [A. Faribault and D. Schuricht, J. Phys. A 45, 485202 (2012)] and Dicke-Jaynes-Cummings-Gaudin models [H. Tschirhart and A. Faribault, J. Phys. A 47, 405204 (2014)]. Remarkably, these results are independent of the explicit parametrization of the Gaudin algebra, exposing a universality in the properties of Richardson-Gaudin integrable systems deeply linked to the underlying algebraic structure.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1103/PhysRevB.91.155102

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15_PhysRevB_91(15)155102_Claeys.pdf

A hybrid configuration interaction treatment based on seniority number and excitation schemes

wim — Mon, 16 Feb 2015 13:16:22 +0000

D.R. Alcoba, A. Torre, L. Lain, O.B. Ona, P. Capuzzi, M. Van Raemdonck, P. Bultinck, D. Van Neck

Journal of Chemical Physics

141 (24), 244118

2014

Abstract

We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method. (c) 2014 AIP Publishing LLC.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1063/1.4904755

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14_j_chem_phys_141(24)244118_Alcoba.pdf

Non-Variational Orbital Optimization Techniques for the AP1roG Wave Function

wim — Mon, 24 Nov 2014 09:53:36 +0000

K. Boguslawski, P. Tecmer, P.W. Ayers, P. Bultinck, S. De Baerdemacker, D. Van Neck

Journal of Chemical Theory and Computation (JCTC)

10 (11), 4873-4882

2014

Abstract

We introduce new nonvariational orbital optimization schemes for the antisymmetric product of one-reference orbital geminal (AP1roG) wave function (also known as pair-coupled cluster doubles) that are extensions to our recently proposed projected seniority-two (PS2-AP1roG) orbital optimization method [ J. Chem. Phys. 2014, 140, 214114)]. These approaches represent less stringent approximations to the PS2-AP1roG ansatz and prove to be more robust approximations to the variational orbital optimization scheme than PS2-AP1roG. The performance of the proposed orbital optimization techniques is illustrated for a number of well-known multireference problems: the insertion of Be into H2, the automerization process of cyclobutadiene, the stability of the monocyclic form of pyridyne, and the aromatic stability of benzene.

DOI

http://dx.doi.org/10.1021/ct500759q

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14_JCTC_10(11)4873_Boguslawski.pdf

Efficient description of strongly correlated electrons with mean-field cost

wim — Tue, 23 Sep 2014 13:56:48 +0000

K. Boguslawski, P. Tecmer, P.W. Ayers, P. Bultinck, S. De Baerdemacker, D. Van Neck

Physical Review B

89 (20), 201106

2014

Abstract

We present an efficient approach to the electron correlation problem that is well suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. The performance of our approach is illustrated for one-dimensional Hubbard rings with different numbers of sites, and for the nonrelativistic quantum-chemical Hamiltonian exploring the symmetric dissociation of the H-50 hydrogen chain.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1103/PhysRevB.89.201106

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14_phys_rev_B_89,201106_Boguslawski.pdf

The influence of orbital rotation on the energy of closed-shell wavefunctions

wim — Mon, 26 May 2014 07:41:24 +0000

P.A. Limacher, T.D. Kim, P.W. Ayers, P.A. Johnson, S. De Baerdemacker, D. Van Neck, P. Bultinck

Molecular Physics

112 (5-6), 853-862

2014

Abstract

The orbital dependence of closed-shell wavefunction energies is investigated by performing doubly-occupied configuration interaction (DOCI) calculations, representing the most general class of these wavefunctions. Different local minima are examined for planar hydrogen clusters containing two, four, and six electrons applying (spin) symmetry-broken restricted, unrestricted, and generalised orbitals with real and complex coefficients. Contrary to Hartree-Fock (HF), restricted DOCI is found to properly break bonds and thus unrestricted orbitals, while providing a quantitative improvement of the energy, are not needed to enforce a qualitatively correct bond dissociation. For the beryllium atom and the BH diatomic, the lowest possible HF energy requests symmetry-broken generalised orbitals, whereas accurate results for DOCI can be obtained within a restricted formalism. Complex orbital coefficients are shown to increase the accuracy of HF and DOCI results in certain cases. The computationally inexpensive AP1roG geminal wavefunction is proven to agree very well with all DOCI results of this study.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1080/00268976.2013.874600

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14_MolPhys_112(5-6)853_Limacher.pdf