P.A. Limacher

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

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
A1

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

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

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
A1

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

Assessing The Accuracy Of New Geminal-Based Approaches

P. Tecmer, K. Boguslawski, P.A. Johnson, P.A. Limacher, M. Chan, T. Verstraelen, P. W. Ayers
Journal of Physical Chemistry A
Publication Date (Web): April 18, 2014
2014
A1

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.

A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals

P.A. Limacher, P.W. Ayers, S. De Baerdemacker, D. Van Neck, P. Bultinck
Journal of Chemical Theory and Computation (JCTC)
9 (3), 1394-1401
2013
A1

Abstract 

We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrödinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.

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

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
A1

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.

Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations

S. Wouters, P.A. Limacher, D. Van Neck, P.W. Ayers
Journal of Chemical Physics
136, 134110
2012
A1

Abstract 

We have implemented the sweep algorithm for the variational optimization of SU(2) x U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab-initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are presented. This allows to assess the performance of other quantum chemical methods. For small basis sets, MPS calculations in the saturation regime of the optical response properties can be performed. These results are extrapolated to the thermodynamic limit.

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