P.W. Ayers

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
118 (39), 9058–9068
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.

DOI 

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

CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry

S. Wouters, W. Poelmans, P.W. Ayers, D. Van Neck
Computer Physics Communications
185 (6), 1501-1514
2014
A1

Abstract 

The density matrix renormalization group (DMRG) has become an indispensable numerical tool to find exact eigenstates of finite-size quantum systems with strong correlation. In the fields of condensed matter, nuclear structure and molecular electronic structure, it has significantly extended the system sizes that can be handled compared to full configuration interaction, without losing numerical accuracy. For quantum chemistry (QC), the most efficient implementations of DMRG require the incorporation of particle number, spin and point group symmetries in the underlying matrix product state (MPS) ansatz, as well as the use of so-called complementary operators. The symmetries introduce a sparse block structure in the MPS ansatz and in the intermediary contracted tensors. If a symmetry is non-abelian, the Wigner-Eckart theorem allows to factorize a tensor into a Clebsch-Gordan coefficient and a reduced tensor. In addition, the fermion signs have to be carefully tracked. Because of these challenges, implementing DMRG efficiently for QC is not straightforward. Efficient and freely available implementations are therefore highly desired. In this work we present CheMPS2, our free open-source spin-adapted implementation of DMRG for ab initio QC. Around CheMPS2, we have implemented the augmented Hessian Newton-Raphson complete active space self-consistent field method, with exact Hessian. The bond dissociation curves of the 12 lowest states of the carbon dimer were obtained at the DMRG(28 orbitals, 12 electrons, DSU(2)=2500)/cc-pVDZ level of theory. The contribution of 1s core correlation to the X1Σ+g bond dissociation curve of the carbon dimer was estimated by comparing energies at the DMRG(36o, 12e, DSU(2)=2500)/cc-pCVDZ and DMRG-SCF(34o, 8e, DSU(2)=2500)/cc-pCVDZ levels of theory.

Open Access version available at UGent repository

DOI 

http://dx.doi.org/10.1016/j.cpc.2014.01.019

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.

DOI 

http://dx.doi.org/10.1021/ct300902c

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.

DOI 

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

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

DOI 

http://dx.doi.org/10.1016/j.comptc.2012.09.036

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.

DOI 

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

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.

DOI 

http://dx.doi.org/10.1021/ct4000923

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

DOI 

http://dx.doi.org/10.1063/1.4791569

The Conformational Sensitivity of Iterative Stockholder Partitioning Schemes

T. Verstraelen, P.W. Ayers, V. Van Speybroeck, M. Waroquier
Chemical Physics Letters
545, 138-143
2012
A1

Abstract 

Chemical interpretation and empirical modeling of partial charges requires a robust partitioning scheme to derive these charges from the molecular electronic density. The degree of undesirable conformational sensitivity is assessed for three iterative stockholder partitioning schemes: Hirshfeld-I (HI), Iterative Stockholder Analysis (ISA) and a new Gaussian ISA variant (GISA). GISA has fewer degrees of freedom than ISA and enforces monotonically decaying pro-atoms. These improvements accelerate the converge of GISA as compared to ISA. However, the conformational sensitivity of the charges does not decrease and is still large compared to HI.

Open Access version available at UGent repository

DOI 

http://dx.doi.org/10.1016/j.cplett.2012.07.028

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