Center for Molecular Modeling - D. Van Neck

The Gradient Curves Method: An improved strategy for the derivation of molecular mechanics valence force fields from ab initio data

leen — Mon, 02 Oct 2023 10:09:51 +0000

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

LECTURE SERIES ON COMPUTER AND COMPUTATIONAL SCIENCES

Volume 7A-B, page 576 -+

2006

Abstract

A novel force-field parameterization procedure[1] is proposed that surmounts well-known difficulties of the conventional least squares parameterization. The multidimensional ab initio training data are first transformed into individual one-dimensional data sets, each associated with one term in the force-field model. In the second step conventional methods call be used to fit each energy term separately to its corresponding data set. The first step call be completed without any knowledge of the analytical expressions for the energy terms. Moreover the transformed data sets dictate the form of these expressions, which makes the method very suitable for deriving valence force fields. During the transformation in the first step, continuity and least-norm criteria are imposed. The latter facilitate the intuitive physical interpretation of the energy terms that are fitted to the transformed data sets, a prerequisite for transferable force fields. Benchmark parameterizations have been performed oil three small molecules, showing that the new method results in physically intuitive energy terms, exactly when a conventional parameterization would suffer from parameter correlations, i.e. when the number of redundant internal coordinates in the force-field model increases.

DOI

http://dx.doi.org/

Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry

kgunst — Wed, 21 Aug 2019 18:03:29 +0000

K. Gunst, F. Verstraete, D. Van Neck

Journal of Chemical Theory and Computation (JCTC)

15, 2996-3007

2019

Abstract

We extend the three-legged tree tensor network state (T3NS) [J. Chem. Theory Comput. 2018, 14, 2026-2033] by including spin and the real abelian point group symmetries. T3NS intersperses physical tensors with branching tensors. Physical tensors have one physical index and at most two virtual indices. Branching tensors have up to three virtual indices and no physical index. In this way, T3NS combines the low computational cost of matrix product states and their simplicity for implementing symmetries, with the better entanglement representation of tree tensor networks. By including spin and point group symmetries, more accurate calculations can be obtained with lower computational effort. We illustrate this by presenting calculations on the bis($\mu$-oxo) and $\mu-\eta^2:\eta^2$ peroxo isomers of $[\mathrm{Cu}_2\mathrm{O}_2]^{2+}$. The used implementation is available on github.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1021/acs.jctc.9b00071

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acs.jctc_.9b00071.pdf

T3NS: Three-Legged Tree Tensor Network States

kgunst — Thu, 15 Mar 2018 09:07:08 +0000

K. Gunst, F. Verstraete, S. Wouters, Ö. Legeza, D. Van Neck

Journal of Chemical Theory and Computation

14 (4), pp 2026–2033

2018

Abstract

We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two virtual indices, as in the matrix product state (MPS) ansatz of the density matrix renormalization group (DMRG). Branching tensors have no physical index, but up to three virtual indices. In this way, advantages of DMRG, in particular a low computational cost and a simple implementation of symmetries, are combined with advantages of TTNS, namely incorporating more entanglement. Our code is capable of simulating quantum chemical Hamiltonians, and we present several proof-of-principle calculations on LiF, N$_2$, and the bis(μ-oxo) and μ–η$^2$:η$^2$ peroxo isomers of [Cu$_2$O$_2$]$^{2+}$.

DOI

http://dx.doi.org/10.1021/acs.jctc.8b00098

Method for making 2-electron response reduced density matrices approximately N-representable

caitlin — Thu, 01 Mar 2018 08:49:44 +0000

C. Lanssens, Paul W. Ayers, D. Van Neck, S. De Baerdemacker, K. Gunst, P. Bultinck

Journal of Chemical Physics

148, 8, 084104

2018

Abstract

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not $N$-representable. That is, the response 2-RDM does not correspond to an actual physical $N$-electron wave function. We present a new algorithm for making these non-$N$-representable 2-RDMs approximately $N$-representable, i.e., it has the right symmetry and normalization and it fulfills the $P$-, $Q$-, and $G$-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-$N$-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, $Q$-matrix, and $G$-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-$N$-representable 2-RDMs which are close to being $N$-representable. Through the $N$-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important $N$-representability conditions.

DOI

https://doi.org/10.1063/1.4994618

Variational method for integrability-breaking Richardson-Gaudin models

claeys — Mon, 30 Oct 2017 17:20:00 +0000

P. Claeys, J.-S. Caux, D. Van Neck, S. De Baerdemacker

Physical Review B

96, 155149

2017

Abstract

We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of integrability allows for an efficient evaluation and minimization of the energy functional. The method is shown to return exact results for integrable models and improve substantially on perturbation theory for models close to integrability. For large integrability-breaking interactions, it is shown how (avoided) level crossings necessitate the use of excited states of integrable Hamiltonians in order to accurately describe the ground states of general nonintegrable models.

Green Open Access

DOI

http://dx.doi.org/10.1103/PhysRevB.96.155149

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PhysRevB.96.155149.pdf

Inner products in integrable Richardson-Gaudin models

claeys — Mon, 30 Oct 2017 17:16:15 +0000

P. Claeys, D. Van Neck, S. De Baerdemacker

Scipost Physics

3, 028

2017

Abstract

We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula.
Furthermore, this framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.

Open Access version available at UGent repository

Gold Open Access

DOI

http://dx.doi.org/10.21468/SciPostPhys.3.4.028

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SciPostPhys.3.4.028.pdf

Block product density matrix embedding theory for strongly correlated spin systems

wim — Wed, 21 Jun 2017 07:14:36 +0000

K. Gunst, S. Wouters, S. De Baerdemacker, D. Van Neck

Physical Review B

95, 195127

2017

Abstract

Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic J1−J2 model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.

Open Access version available at UGent repository

Green Open Access

DOI

https://doi.org/10.1103/PhysRevB.95.195127

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CDMET.pdf

Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach

wim — Thu, 12 Jan 2017 09:31:48 +0000

O.B. Ona, O. De Clercq, D.R. Alcoba, A. Torre, L. Lain, D. Van Neck, P. Bultinck

ChemPhysChem

17 (18), 2881–2889

2016

Abstract

The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes.

DOI

http://dx.doi.org/10.1002/cphc.201600433

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O-a_et_al-2016-ChemPhysChem.pdf

Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods

wim — Mon, 01 Aug 2016 10:10:59 +0000

D.R. Alcoba, A. Torre, L. Lain, G. Massaccesi, O.B. Ona, P.W. Ayers, M. Van Raemdonck, P. Bultinck, D. Van Neck

Theoretical Chemistry Accounts

135 (6), 153

2016

Abstract

The coefficients of full configuration interaction wave functions (FCI) for N-electron systems expanded in N-electron Slater determinants depend on the orthonormal one-particle basis chosen although the total energy remains invariant. Some bases result in more compact wave functions, i.e. result in fewer determinants with significant expansion coefficients. In this work, the Shannon entropy, as a measure of information content, is evaluated for such wave functions to examine whether there is a relationship between the FCI Shannon entropy of a given basis and the performance of that basis in truncated CI approaches. The results obtained for a set of randomly picked bases are compared to those obtained using the traditional canonical molecular orbitals, natural orbitals, seniority minimising orbitals and a basis that derives from direct minimisation of the Shannon entropy. FCI calculations for selected atomic and molecular systems clearly reflect the influence of the chosen basis. However, it is found that there is no direct relationship between the entropy computed for each basis and truncated CI energies.

DOI

http://dx.doi.org/10.1007/s00214-016-1905-x

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16-TheorChemAcc-135-153-Alcoba.pdf

Read-Green resonances in a topological superconductor coupled to a bath

wim — Mon, 01 Aug 2016 10:06:08 +0000

P. Claeys, S. De Baerdemacker, D. Van Neck

Physical Review B

93 (22), 220503

2016

Abstract

We study a topological superconductor capable of exchanging particles with an environment. This additional interaction breaks particle-number symmetry and can be modeled by means of an integrable Hamiltonian, building on the class of Richardson-Gaudin pairing models. The isolated system supports zero-energy modes at a topological phase transition, which disappear when allowing for particle exchange with an environment. However, it is shown from the exact solution that these still play an important role in system-environment particle exchanges, which can be observed through resonances in low-energy and low-momentum level occupations. These fluctuations signal topologically protected Read-Green points and cannot be observed within traditional mean-field theory.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1103/PhysRevB.93.220503

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16-PhysRevB-93-220503-Claeys.pdf