Center for Molecular Modeling - P.W. Ayers

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

wim — Wed, 28 Mar 2012 09:27:46 +0000

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

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.

DOI

http://dx.doi.org/10.1021/ct2007742

Private attachment

12 j. chem. theory comput 8(2)554 Burger.pdf

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

seba — Thu, 22 Mar 2012 14:20:39 +0000

S. Wouters, P.A. Limacher, D. Van Neck, P.W. Ayers

Journal of Chemical Physics

136, 134110

2012

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.

DOI

http://dx.doi.org/10.1063/1.3700087

Private attachment

12 J. Chem Phys 136,134110 Wouters.pdf

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

wim — Fri, 20 Jan 2012 15:01:32 +0000

P. Bultinck, D. Van Neck, G. Acke, P.W. Ayers

Physical Chemistry Chemical Physics (PCCP)

14, 2408-2416

2012

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.

DOI

http://dx.doi.org/10.1039/c2cp22543

Private attachment

12 pccp xxx,xxxx bultinck.pdf

Considerations on describing non-singlet spin states in variational second order density matrix methods

wim — Wed, 18 Jan 2012 15:16:17 +0000

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

Journal of Chemical Physics

136, 014110

2012

Abstract

Despite the importance of non-singlet molecules in chemistry, most variational second order density matrix calculations have focused on singlet states. Ensuring that a second order density matrix is derivable from a proper N-electron spin state is a difficult problem because the second order density matrix only describes one- and two-particle interactions. In pursuit of a consistent description of spin in second order density matrix theory, we propose and evaluate two main approaches: we consider constraints derived from a pure spin state and from an ensemble of spin states. This paper makes a comparative assessment of the different approaches by applying them to potential energy surfaces for different spin states of the oxygen and carbon dimer. We observe two major shortcomings of the applied spin constraints: they are not size consistent and they do not reproduce the degeneracy of the different states in a spin multiplet. First of all, the spin constraints are less strong when applied to a dissociated molecule than when they are applied to the dissociation products separately. Although they impose correct spin expectation values on the dissociated molecule, the dissociation products do not have correct spin expectation values. Secondly, both under “pure spin state conditions” and under “ensemble spin state” conditions is the energy a convex function of the spin projection. Potential energy surfaces for different spin projections of the same spin state may give a completely different picture of the molecule's bonding. The maximal spin projection always gives the most strongly constrained energy, but is also significantly more expensive to compute than a spin-averaged ensemble. In the dissociation limit, both the problem of nondegeneracy of equivalent spin projections, size-inconsistency and unphysical dissociation can be corrected by means of subspace energy constraints.

DOI

http://dx.doi.org/10.1063/1.3672087

Private attachment

12 J. Chem. Phys. 136 014110 VanAggelen.pdf

Fast density matrix-based partitioning of the energy over the atoms in a molecule consistent with the hirshfeld-I partitioning of the electron density

wim — Wed, 19 Oct 2011 10:03:48 +0000

D. Vanfleteren, D. Ghillemijn, D. Van Neck, P. Bultinck, M. Waroquier, P.W. Ayers

Journal of Computational Chemistry

32 (16), 3485–3496

2011

Abstract

For the Hirshfeld-I atom in the molecule (AIM) model, associated single-atom energies and interaction energies at the Hartree–Fock level are efficiently determined in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix (1DM). Starting from the Hirshfeld-I AIM model for the electron density, the molecular 1DM is partitioned with a previously introduced double-atom scheme (Vanfleteren et al., J Chem Phys 2010, 132, 164111). Single-atom density matrices are constructed from the atomic and bond contributions of the double-atom scheme. As the Hartree–Fock energy can be expressed solely in terms of the 1DM, the partitioning of the latter over the AIM naturally leads to a corresponding partitioning of the Hartree–Fock energy. When the size of the molecule or the molecular basis set does not grow too large, the method shows considerable computational advantages compared with other approaches that require cumbersome numerical integration of the molecular energy integrals weighted by atomic weight functions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011

DOI

http://dx.doi.org/10.1002/jcc.21933

Private attachment

11 j comp chem 32(16), 3485 vanfleteren.pdf

Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon, and silicon

wim — Mon, 03 Oct 2011 12:16:21 +0000

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

Physical Review A

80 (3), 032508

2009

Abstract

The isoelectronic series of Be, Ne and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We find that the method is capable of describing the strong static electron correlations due to the incipient degeneracy in the hydrogenic spectrum for increasing central charge. Apart from the ground-state energy various other properties are extracted from the variationally determined second-order density matrix. The ionization energy is constructed using the extended Koopmans' theorem. The natural occupations are also studied, as well as the correlated Hartree-Fock-like single particle energies. The exploitation of symmetry allows to study the basis set dependence and results are presented for correlation-consistent polarized valence double, triple and quadruple zeta basis sets.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1103/PhysRevA.80.032508

Private attachment

09 phys. rev. A 80(3)032508 verstichel.pdf

Incorrect diatomic dissociation in variational reduced density matrix theory arises from the flawed description of fractionally charged atoms

wim — Mon, 03 Oct 2011 11:47:59 +0000

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

Physical Chemistry Chemical Physics (PCCP)

11 (27), 5558-5560

2009

Abstract

The behaviour of diatomic molecules is examined using the variational second-order density matrix method under the P, Q and G conditions. It is found that the method describes the dissociation limit incorrectly, with fractional charges on the well-separated atoms. This can be traced back to the behaviour of the energy versus the number of electrons for the isolated atoms. It is shown that the energies for fractional charges are much too low.

DOI

http://dx.doi.org/

Private attachment

09 phys. chem. chem. phys 11(27)5558 van aggelen.pdf

Exact ionization potentials from wavefunction asymptotics: The extended Koopmans’ theorem, revisited

wim — Mon, 03 Oct 2011 11:32:54 +0000

D. Vanfleteren, D. Van Neck, P.W. Ayers, R.C. Morrison, P. Bultinck

Journal of Chemical Physics

130 (19), 194104

2009

Abstract

A simple explanation is given for the exactness of the extended Koopmans’ theorem, (EKT) for computing the removal energy of any many-electron system to the lowest-energy ground state ion of a given symmetry. In particular, by removing the electron from a “removal orbital” of appropriate symmetry that is concentrated in the asymptotic region, one obtains the exact ionization potential and the exact Dyson orbital for the corresponding state of the ion. It is argued that the EKT is not restricted to many-electron systems but holds for any finite many-body system, provided that the interaction vanishes for increasing interparticle distance. A necessary and sufficient condition for the validity of the EKT for any state (not just the lowest-energy states of a given symmetry) in terms of the third-order reduced density matrix is stated and derived.

DOI

http://dx.doi.org/10.1063/1.3130044

Private attachment

09 j. chem. phys. 130(19)194104 vanfleteren.pdf

The Gradient Curves Method: An Improved Strategy for the Derivation of Molecular Mechanics Valence Force Fields from ab Initio Data

wim — Mon, 03 Oct 2011 07:50:56 +0000

T. Verstraelen, D. Van Neck, P.W. Ayers, V. Van Speybroeck, M. Waroquier

Journal of Chemical Theory and Computation (JCTC)

3 (4), 1420–1434

2007

Abstract

A novel force-field development strategy is proposed that tackles the well-known difficulty of parameter correlations arising in a conventional least-squares optimization. In the first step of the new gradient curves method (GCM), continuity criteria are imposed to transform the raw multidimensional ab initio training data to distinct sets of one-dimensional data, each associated with an individual energy term. In the second step, the transformed data suggest suitable analytical expressions, and the parameters in these expressions are fitted to the transformed data; that is, one does not have to postulate a priori analytical expressions for the force-field energy terms. This approach facilitates the derivation of valence terms. Benchmarks have been performed on a set of small molecules. The results show that the new method yields physically acceptable energy terms exactly when a conventional parametrization would suffer from parameter correlations, that is, when an increasing number of redundant internal coordinates is used in the force-field model. The generic treatment of parameter correlations in the proposed method facilitates an intuitive physical interpretation of the individual terms in the force-field expression, which is a prerequisite for the transferability of force-field models.

DOI

http://dx.doi.org/10.1021/ct6002093

Private attachment

07 j. chem. theory & comp 3(4)1420 verstraelen.pdf

Characterization of the electron propagator with a GW-like self-energy in closed-shell atoms

wim — Mon, 03 Oct 2011 07:06:34 +0000

S. Verdonck, D. Van Neck, P.W. Ayers, M. Waroquier

Physical Review A

74 (6), 062503

2006

Abstract

The electron propagator is calculated for a set of closed-shell atoms using GW-like self-energies that contain the coupling of single-particle degrees of freedom with excited states in the framework of the random phase approximation. The effect of including exchange diagrams is investigated. Calculations are performed in the Hartree-Fock (HF) basis of the neutral atom. The HF continuum is taken into account using a discretization procedure, and the basis set limit is estimated using a systematic increase of basis set size. We check the approximation of taking the self-energy diagonal in the HF basis, and to what extent the extended Koopman’s theorem is fulfilled using an approximate self-energy. Finally we try to model the information contained in the propagator in terms of a functional containing Hartree-Fock quantities and demonstrate the feasibility of simultaneously reproducing the correlation and ionization energy of an underlying ab initio model.

DOI

http://dx.doi.org/10.1103/PhysRevA.74.062503

Private attachment

06 physrev A 74 062503 verdonck.pdf