Center for Molecular Modeling - P.A. Johnson

Probing pairing correlations in Sn isotopes using Richardson-Gaudin integrability

wim — Thu, 08 Jan 2015 13:07:12 +0000

S. De Baerdemacker, V. Hellemans, R. van den Berg, J.-S. Caux, K. Heyde, M. Van Raemdonck, D. Van Neck, P.A. Johnson, A. Buekenhoudt

Journal of Physics: Conference series

533, 012058

2014

Abstract

Pairing correlations in the even-even A = 102 − 130 Sn isotopes are discussed, based on the Richardson-Gaudin variables in an exact Woods-Saxon plus reduced BCS pairing framework. The integrability of the model sheds light on the pairing correlations, in particular on the previously reported sub-shell structure.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1088/1742-6596/533/1/012058

Private attachment

14_JPhys_533,012058_DeBaerdemacker.pdf

Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal

Bernadette — Tue, 29 Jul 2014 13:33:13 +0000

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

Journal of Chemical Physics

140 (21), 214114

2014

Abstract

We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys. 135, 044119 (2011)]. A numerical analysis is performed for the C-2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases. (C) 2014 AIP Publishing LLC.

DOI

http://dx.doi.org/10.1063/1.4880820

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

Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals

wim — Fri, 02 May 2014 09:11:47 +0000

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

Physical Chemistry Chemical Physics (PCCP)

16 (11), 5061-5065

2014

Abstract

A new multireference perturbation approach has been developed for the recently proposed AP1roG scheme, a computationally facile parametrization of an antisymmetric product of nonorthogonal geminals. This perturbation theory of second-order closely follows the biorthogonal treatment from multiconfiguration perturbation theory as introduced by Surjan et al., but makes use of the additional feature of AP1roG that the expansion coefficients within the space of closed-shell determinants are essentially correct already, which further increases the predictive power of the method. Building upon the ability of AP1roG to model static correlation, the perturbation correction accounts for dynamical electron correlation, leading to absolute energies close to full configuration interaction results. Potential surfaces for multiple bond dissociation in H2O and N-2 are predicted with high accuracy up to bond breaking. The computational cost of the method is the same as that of conventional single-reference MP2.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1039/c3cp53301h

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14_PCCP_16(11)5061_Limacher.pdf

Assessing The Accuracy Of New Geminal-Based Approaches

toon — Tue, 22 Apr 2014 08:47:18 +0000

P. Tecmer, K. Boguslawski, P.A. Johnson, P.A. Limacher, M. Chan, T. Verstraelen, P.W. Ayers

Journal of Physical Chemistry A

118 (39), 9058–9068

2014

Abstract

We present a systematic theoretical study on the dissociation of diatomic molecules and their spectroscopic constants using our recently presented geminal-based wave function ansätze. Specifically, the performance of the antisymmetric product of rank two geminals (APr2G), the antisymmetric product of 1-reference-orbital geminals (AP1roG) and its orbital-optimized variant (OO-AP1roG) are assessed against standard quantum chemistry methods. Our study indicates that these new geminal-based approaches provide a cheap, robust, and accurate alternative for the description of bond-breaking processes in closed-shell systems requiring only mean-field-like computational cost. In particular, the spectroscopic constants obtained from OO-AP1roG are in very good agreement with reference theoretical and experimental data.

DOI

http://dx.doi.org/10.1021/jp502127v

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14_JPhysChemA_xx(x)xxx_Tecmer.pdf

14_JPhysChemA_118(39)9058_Tecmer.pdf

A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals

wim — Wed, 13 Feb 2013 08:35:29 +0000

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

Computational and Theoretical Chemistry

1003 (2013), 101-113

2013

Abstract

Inspired by the wavefunction forms of exactly solvable algebraic Hamiltonians, we present several wavefunction ansatze. These wavefunction forms are exact for two-electron systems; they are size consistent; they include the (generalized) antisymmetrized geminal power, the antisymmetrized product of strongly orthogonal geminals, and a Slater determinant wavefunctions as special cases. The number of parameters in these wavefunctions grows only linearly with the size of the system. The parameters in the wavefunctions can be determined by projecting the Schrödinger equation against a test-set of Slater determinants; the resulting set of nonlinear equations is reminiscent of coupled-cluster theory, and can be solved with no greater than O (N⁵) scaling if all electrons are assumed to be paired, and with O (N⁶) scaling otherwise. Based on the analogy to coupled-cluster theory, methods for computing spectroscopic properties, molecular forces, and response properties are proposed.

DOI

http://dx.doi.org/10.1016/j.comptc.2012.09.030

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13_comp_theoretical_chem_1003_101_Johnson.pdf

The sharp-G N-representability condition

wim — Wed, 13 Feb 2013 08:30:45 +0000

P.A. Johnson, P.W. Ayers, B. Verstichel, D. Van Neck, H. van Aggelen

Computational and Theoretical Chemistry

1003 (2013), 32-36

2013

Abstract

The G-condition for the N-representability of the two-electron reduced density matrix is tightened by replacing the semidefiniteness constraint with the true upper and lower bounds of the G-type Hamiltonian operator. The lower bound is not easily computed (in contrast to the sharp P- and Q-conditions), but maps onto a well-known integer programming problem. The sharp-G, sharp-P, and sharp-Q conditions are just three members of a much broader class of conditions based on exactly solvable model Hamiltonians.

DOI

http://dx.doi.org/10.1016/j.comptc.2012.09.029

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13_comp_theoretical_chem_1003_32_Johnson.pdf

When two is better than one: the seniority scheme as a new tool to build wave functions

wim — Wed, 03 Feb 2016 11:17:26 +0000

S. De Baerdemacker, P. Claeys, W. Poelmans, D. Van Neck, P. Bultinck, M. Van Raemdonck, P.W. Ayers, P.A. Limacher, P.A. Johnson, K. Boguslawski, P. Tecmer

ISBN/ISSN:

Talk

Conference / event / venue

QCB12

Leuven, Belgium

Tuesday, 16 February, 2016

Abstract (private)

qcb12.pdf

Conference reference

Twelfth Edition of the Conference Quantum Chemistry in Belgium (QCB12)

Model Wavefunction Forms to Describe Strong Correlation in Quantum Chemistry

wim — Mon, 10 Nov 2014 11:09:14 +0000

P.A. Johnson

Sun, 28/09/2014

McMaster University, Hamilton, Ontario, Canada

http://hdl.handle.net/1854/LU-5752763

Supervisors

Prof. Dr. Paul W. Ayers, Prof. Dr. Dimitri Van Neck, Prof. Dr. Patrick Bultinck

Attachment (private)

PAJ_thesis_Aug25.pdf

Richardson-Gaudin Integrable Systems (and Beyond) for Strongly Correlated Quantum Many-Body Systems

wim — Tue, 11 Jun 2013 12:02:15 +0000

S. De Baerdemacker, P.W. Ayers, P. Bultinck, P.A. Johnson, P.A. Limacher, D. Van Neck, M. Van Raemdonck

ISBN/ISSN:

Talk

Conference / event / venue

MQM 2013

Lugano, Switzerland

Sunday, 2 June, 2013 to Friday, 7 June, 2013

Abstract (private)

MQM_debaerdemacker_stijn.pdf

Conference reference

MQM 2013