P.W. Ayers

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.

Extended random phase approximation method for atomic excitation energies from correlated and variationally optimized second-order density matrices

H. van Aggelen, B. Verstichel, G. Acke, M. Degroote, P. Bultinck, P.W. Ayers, D. Van Neck
Computational and Theoretical Chemistry
1003 (2013), 50-54
2013
A1

The sharp-G N-representability condition

P.A. Johnson, P.W. Ayers, B. Verstichel, D. Van Neck, H. van Aggelen
Computational and Theoretical Chemistry
1003 (2013), 32-36
2013
A1

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.

Hirshfeld-E partitioning: AIM charges with an improved trade-off between robustness and accurate electrostatics

T. Verstraelen, P.W. Ayers, V. Van Speybroeck, M. Waroquier
Journal of Chemical Theory and Computation (JCTC)
9 (5), 2221–2225
2013
A1

Abstract 

For the development of ab-initio derived force fields, atomic charges must be computed from electronic structure computations, such that (i) they accurately describe the molecular electrostatic potential (ESP) and (ii) they are transferable to the force-field application of interest. The Iterative Hirshfeld (Hirshfeld-I or HI) scheme meets both requirements for organic molecules. For inorganic oxide clusters, however, Hirshfeld-I becomes ambiguous because electron densities of nonexistent isolated anions are needed as input. Herein, we propose a simple Extended Hirshfeld (Hirshfeld-E or HE) scheme to overcome this limitation. The performance of the new HE scheme is compared to four popular atoms-in-molecules schemes, using two tests involving a set of 248 silica clusters. These tests show that the new HE scheme provides an improved trade-off between the ESP accuracy and the transferability of the charges. The new scheme is a generalization of the Hirshfeld-I scheme and it is expected that its improvements are to a large extent applicable to molecular systems containing elements from the entire periodic table.

ACKS2: Atom-Condensed Kohn-Sham DFT approximated to second order

T. Verstraelen, P.W. Ayers, V. Van Speybroeck, M. Waroquier
Journal of Chemical Physics
138, 7, 07408
2013
A1

Abstract 

A new polarizable force field (PFF), namely atom-condensed Kohn-Sham density functional theory approximated to second order (ACKS2), is proposed for the efficient computation of atomic charges and linear response properties of extended molecular systems. It is derived from Kohn-Sham density functional theory (KS-DFT), making use of two novel ingredients in the context of PFFs: (i) constrained atomic populations and (ii) the Legendre transform of the Kohn-Sham kinetic energy. ACKS2 is essentially an extension of the Electronegativity Equalization Method (EEM) [W. J. Mortier, S. K. Ghosh, and S. Shankar, J. Am. Chem. Soc. 108, 4315 (1986)]10.1021/ja00275a013 in which two major EEM shortcomings are fixed: ACKS2 predicts a linear size-dependence of the dipole polarizability in the macroscopic limit and correctly describes the charge distribution when a molecule dissociates. All ACKS2 parameters are defined as atoms-in-molecules expectation values. The implementation of ACKS2 is very similar to that of EEM, with only a small increase in computational cost.

Open Access version available at UGent repository

Automated Parametrization of AMBER Force Field Terms from Vibrational Analysis with a Focus on Functionalizing Dinuclear Zinc(II) Scaffolds

S.K. Burger, M. Lacasse, T. Verstraelen, J.A. Drewry, P.T. Gunning, P.W. Ayers
Journal of Chemical Theory and Computation (JCTC)
8 (2), 554-562
2012
A1

Abstract 

A procedure for determining force constants that is independent of the internal redundant coordinate choice is presented. The procedure is based on solving each bond and angle term separately, using the Wilson B matrix. The method only requires a single ab initio frequency calculation at the minimum energy structure and is made available in the software "parafreq". The methodology is validated with a set of small molecules, by showing it can reproduce ab initio frequencies better than other methods such as taking the diagonal terms of the Hessian in internal coordinates or by using standard AMBER force fields. Finally, the utility of the method is demonstrated by parametrizing the dizinc scaffold of bis-dipicolylamine (BDPA) bound to phosphotyrosine, which is then functionalized into promising antitumor drug proteomimetics.

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.

Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods

P. Bultinck, D. Van Neck, G. Acke, P.W. Ayers
Physical Chemistry Chemical Physics (PCCP)
14, 2408-2416
2012
A1

Abstract 

The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.

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