Journal of Computational Chemistry

Reply to ‘comment on “extending hirshfeld-I to bulk and periodic materials”’

D.E.P. Vanpoucke, I. Van Driessche, P. Bultinck
Journal of Computational Chemistry
Volume 34, Issue 5, pages 422-427
2013
A1
Published while none of the authors were employed at the CMM

Abstract 

The issues raised in the comment by Manz are addressed through the presentation of calculated atomic charges for NaF, NaCl, MgO, SrTiO3 , and La2Ce2O7 , using our previously presented method for calculating Hirshfeld-I charges in solids (Vanpoucke et al., J. Comput. Chem. doi: 10.1002/jcc.23088). It is shown that the use of pseudovalence charges is sufficient to retrieve the full all-electron Hirshfeld-I charges to good accuracy. Furthermore, we present timing results of different systems, containing up to over 200 atoms, underlining the relatively low cost for large systems. A number of theoretical issues are formulated, pointing out mainly that care must be taken when deriving new atoms in molecules methods based on “expectations” for atomic charges.

Open Access version available at UGent repository

Extending Hirshfeld-I to bulk and periodic materials

D.E.P. Vanpoucke, P. Bultinck, I. Van Driessche
Journal of Computational Chemistry
Volume 34, Issue 5, pages 405-417
2013
A1
Published while none of the authors were employed at the CMM

Abstract 

In this work, a method is described to extend the iterative Hirshfeld-I method, generally used for molecules, to periodic systems. The implementation makes use of precalculated pseudopotential-based electron density distributions, and it is shown that high-quality results are obtained for both molecules and solids, such as ceria, diamond, and graphite. The use of grids containing (precalculated) electron densities makes the implementation independent of the solid state or quantum chemical code used for studying the system. The extension described here allows for easy calculation of atomic charges and charge transfer in periodic and bulk systems. The conceptual issue of obtaining reference densities for anions is discussed, and the delocalization problem for anionic reference densities originating from the use of a plane wave basis set is identified and handled.

Open Access version available at UGent repository

Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining

A. Ghysels, B.T. Miller, F.C. Pickard III, B.R. Brooks
Journal of Computational Chemistry
33(28), 2250–2275
2012
A1

Abstract 

Dimension reduction is often necessary when attempting to reach longer length and time scales in molecular simulations. It is realized by constraining degrees of freedom or by coarse-graining the system. When evaluating the accuracy of a dimensional reduction, there is a practical challenge: the models yield vectors with different lengths, making a comparison by calculating their dot product impossible. This article investigates mapping procedures for normal mode analysis. We first review a horizontal mapping procedure for the reduced Hessian techniques, which projects out degrees of freedom. We then design a vertical mapping procedure for the “implosion” of the all-atom (AA) Hessian to a coarse-grained scale that is based upon vibrational subsystem analysis. This latter method derives both effective force constants and an effective kinetic tensor. Next, a series of metrics is presented for comparison across different scales, where special attention is given to proper mass-weighting. The dimension-dependent metrics, which require prior mapping for proper evaluation, are frequencies, overlap of normal mode vectors, probability similarity, Hessian similarity, collectivity of modes, and thermal fluctuations. The dimension-independent metrics are shape derivatives, elastic modulus, vibrational free energy differences, heat capacity, and projection on a predefined basis set. The power of these metrics to distinguish between reasonable and unreasonable models is tested on a toy alpha helix system and a globular protein; both are represented at several scales: the AA scale, a Gō-like model, a canonical elastic network model, and a network model with intentionally unphysical force constants. Published 2012 Wiley Periodicals, Inc.

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

D. Vanfleteren, D. Ghillemijn, D. Van Neck, P. Bultinck, M. Waroquier, P.W. Ayers
Journal of Computational Chemistry
32 (16), 3485–3496
2011
A1

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

Comparative study of various normal mode analysis techniques based on partial Hessians

A. Ghysels, V. Van Speybroeck, E. Pauwels, S. Catak, B.R. Brooks, D. Van Neck, M. Waroquier
Journal of Computational Chemistry
31 (5), 994-1007
2010
A1

Abstract 

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine-stretch, the spectrum of quinine and a bis-cinchona derivative, and the low frequency modes of the LAO binding protein. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010

A self-consistent Hirshfeld method for the atom in the molecule based on minimization of information loss

D. Ghillemijn, P. Bultinck, D. Van Neck, P.W. Ayers
Journal of Computational Chemistry
32, 1561-1567
2011
A1

Abstract 

Based on the so-called Hirshfeld atom in the molecule scheme, a new AIM method is presented. The method is similar to the Hirshfeld-I scheme, with the AIM weight function being constructed by minimizing the information loss upon formation of the molecule, but now requiring explicitly that the promolecular densities integrate to the same number of electrons as the AIM densities. This new weight function leads to a new iterative AIM scheme, and the resulting operative scheme is examined and discussed. The final results indicate that the newly proposed method does not perform as well as the Hirshfeld-I method.

Open Access version available at UGent repository
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