B. Verstichel

Chemical verification of variational second-order density matrix based potential energy surfaces for the N2 isoelectronic series

H. van Aggelen, B. Verstichel, P. Bultinck, D. Van Neck, P.W. Ayers, D.L. Cooper
Journal of Chemical Physics
132, 114112
2010
A1

Abstract 

A variational optimization of the second-order density matrix under the P-, Q-, and G-conditions was carried out for a set of diatomic 14-electron molecules, including N2, O22+, NO+, CO, and CN−. The dissociation of these molecules is studied by analyzing several chemical properties (dipole moments, population analysis, and bond indices) up to the dissociation limit (10 and 20 Å). Serious chemical flaws are observed for the heteronuclear diatomics in the dissociation limit. A careful examination of the chemical properties reveals that the origin of the dissociation problem lies in the flawed description of fractionally occupied species under the P-, Q-, and G-conditions. A novel constraint is introduced that imposes the correct dissociation and enforces size consistency. The effect of this constraint is illustrated with calculations on NO+, CO, CN−, N2, and O22+.

Open Access version available at UGent repository

Subsystem constraints in variational second order density matrix optimization: Curing the dissociative behavior

B. Verstichel, H. van Aggelen, D. Van Neck, P.W. Ayers, P. Bultinck
Journal of Chemical Physics
132, 114113
2010
A1

Abstract 

A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P,Q,G) or even three-index (T1,T2) conditions [ H. Van Aggelen et al., Phys. Chem. Chem. Phys. 11, 5558 (2009) ]. Heteronuclear molecules tend to dissociate into fractionally charged atoms. In this paper we introduce a general class of N-representability conditions, called subsystem constraints, and show that they cure the dissociation problem at little additional computational cost. As a numerical example the singlet potential energy surface of Be B+ is studied. The extension to polyatomic molecules, where more subsystem choices can be identified, is also discussed.

Open Access version available at UGent repository

Variational density matrix optimization using semidefinite programming

B. Verstichel, H. van Aggelen, D. Van Neck, P.W. Ayers, P. Bultinck
Computer Physics Communications
182 (9), 2025-2028
2011
A1

Abstract 

We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N-representable density matrix leads to matrix-positivity constraints on the density matrix. We then formulate this in a standard semidefinite programming form, after which two interior point methods are discussed to solve the SDP. As an example we show the results of an application of the method on the isoelectronic series of Beryllium.

Open Access version available at UGent repository

Variational second order density matrix study of F3−: Importance of subspace constraints for size-consistency

H. van Aggelen, B. Verstichel, P. Bultinck, D. Van Neck, P.W. Ayers, D.L. Cooper
Journal of Chemical Physics
134, 054115
2011
A1

Abstract 

Variational second order density matrix theory under “two-positivity” constraints tends to dissociate molecules into unphysical fractionally charged products with too low energies. We aim to construct a qualitatively correct potential energy surface for F3− by applying subspace energy constraints on mono- and diatomic subspaces of the molecular basis space. Monoatomic subspace constraints do not guarantee correct dissociation: the constraints are thus geometry dependent. Furthermore, the number of subspace constraints needed for correct dissociation does not grow linearly with the number of atoms. The subspace constraints do impose correct chemical properties in the dissociation limit and size-consistency, but the structure of the resulting second order density matrix method does not exactly correspond to a system of noninteracting units. © 2011 American Institute of Physics

Open Access version available at UGent repository

A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix

B. Verstichel, H. van Aggelen, D. Van Neck, P. Bultinck, S. De Baerdemacker
Computer Physics Communications
182 (6), 1235-1244
2011
A1

Abstract 

The quantum many-body problem can be rephrased as a variational determination of the two-body reduced density matrix, subject to a set of N-representability constraints. The mathematical problem has the form of a semidefinite program. We adapt a standard primal–dual interior point algorithm in order to exploit the specific structure of the physical problem. In particular the matrix-vector product can be calculated very efficiently. We have applied the proposed algorithm to a pairing-type Hamiltonian and studied the computational aspects of the method. The standard N-representability conditions perform very well for this problem.
Keywords: Density matrix; Variational; Semidefinite programming

Open Access version available at UGent repository

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