F. Heidar-Zadeh

An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions

A. Tehrani, J. S. M. Anderson, D. Chakraborty, J. I. Rodriguez-Hernandez, D. C. Thompson, T. Verstraelen, P. W. Ayers, F. Heidar-Zadeh
Journal of Computational Chemistry
2023
A1

Abstract 

The numerical ill-conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater-type functions is overcome by using the (extended) Kullback–Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non-negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non-negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non-negative basis functions. We present a fixed-point iteration method for optimizing the Kullback–Leibler divergence and compare it to conventional gradient-based optimization methods. These algorithms are released through the free and open-source BFit package, which also includes a L2-norm squared optimization routine applicable to any square-integrable scalar function.

Green Open Access

Constrained iterative Hirshfeld charges: A variational approach

L. Pujal, M. Van Zyl, E. Vohringer-Martinez, T. Verstraelen, P. Bultinck, P.W. Ayers, F. Heidar-Zadeh
Journal of Chemical Physics
Volume 156, Issue 19
2022
A1

Abstract 

We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties.

Published under an exclusive license by AIP Publishing.

Fanpy: A Python Library for Prototyping Multideterminant Methods in Ab Initio Quantum Chemistry

T. D. Kim, M. Richer, G. Sánchez-Díaz, F. Heidar-Zadeh, T. Verstraelen, R.A. Miranda-Quintana, P.W. Ayers
Journal of Computational Chemistry
44, 5, 697-709
2022
A1

Abstract 

Fanpy is a free and open-source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it easier to transfer the mathematical conception of a new wavefunction ans¨atze to a working implementation. Fanpy uses the framework of our recently introduced Flexible Ansatz for N-electron Configuration Interaction (FANCI), where multideterminant wavefunctions are represented by their overlaps with Slater determinants of orthonormal spin-orbitals. In the simplest case, a new wavefunction ansatz can be implemented by simply writing a function for evaluating its overlap with an arbitrary Slater determinant. Fanpy is modular in both implementation and theory: the wavefunction model, the system’s Hamiltonian, and the choice of objective function are all independent modules. This modular structure makes it easy for users to mix and match different methods and for developers to quickly try new ideas. Fanpy is written purely in Python with standard dependencies, making it accessible for most operating systems; it adheres to principles of modern software development, including comprehensive documentation, extensive testing, and continuous integration and delivery protocols. This article is considered to be the official release notes for the Fanpy library.

IOData: A python library for reading, writing, and converting computational chemistry file formats and generating input files

T. Verstraelen, W. Adams, L. Pujal, A. Tehrani, B. D. Kelly, L. Macaya, F. Meng, M. Richer, R. Hernández-Esparza, X. D. Yang, M. Chan, T. D. Kim, M. Cools-Ceuppens, V. Chuiko, E. Vohringer-Martinez, P.W. Ayers, F. Heidar-Zadeh
Journal of Computational Chemistry
45, 6, 458--464
2021
A1

Abstract 

IOData is a free and open‐source Python library for parsing, storing, and converting various file formats commonly used by quantum chemistry, molecular dynamics, and plane‐wave density‐functional‐theory software programs. In addition, IOData supports a flexible framework for generating input files for various software packages. While designed and released for stand‐alone use, its original purpose was to facilitate the interoperability of various modules in the HORTON and ChemTools software packages with external (third‐party) molecular quantum chemistry and solid‐state density‐functional‐theory packages. IOData is designed to be easy to use, maintain, and extend; this is why we wrote IOData in Python and adopted many principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. This article is the official release note of the IOData library.

Information-Theoretic Approaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes

F. Heidar-Zadeh, P.W. Ayers, T. Verstraelen, I. Vinogradov, E. Vohringer-Martinez, P. Bultinck
Journal of Physical Chemistry A
112 (17) 4219-4245
2018
A1

Abstract 

Many population analysis methods are based on the precept that molecules should be built from fragments (typically atoms) that maximally resemble the isolated fragment. The resulting molecular building blocks are intuitive (because they maximally resemble well-understood systems) and transferable (because if two molecular fragments both resemble an isolated fragment, they necessarily resemble each other). Information theory is one way to measure the deviation between molecular fragments and their isolated counterparts, and it is a way that lends itself to interpretation. For example, one can analyze the relative importance of electron transfer and polarization of the fragments. We present key features, advantages, and disadvantages of the information-theoretic approach. We also codify existing information-theoretic partitioning methods in a way, that clarifies the enormous freedom one has within the information-theoretic ansatz.

The local response of global descriptors

F. Heidar-Zadeh, S. Fias, E. Vohringer-Martinez, T. Verstraelen, P.W. Ayers
Theoretical Chemistry Accounts
136 (1), 19
2017
A1

Abstract 

We consider the problem of defining an appropriate local descriptor corresponding to an arbitrary global descriptor. Although it does not seem easy to rigorously and uniquely define local analogues of derived global descriptors (e.g., the electrophilicity) or the fundamental global descriptors associated with the canonical ensemble (e.g., the hardness), the local response of these global descriptors can be defined unambiguously. We look at the local response of the global electrophilicity and compare it to the conventional, ad hoc, definition of the local electrophilicity. The local response of global nucleofugality and electrofugality is also discussed.

An Explicit Approach to Conceptual Density Functional Theory Descriptors of Arbitrary Order

F. Heidar-Zadeh, M. Richer, S. Fias, R.A. Miranda-Quintana, M. Chan, M. Franco-Perez, C. Gonzalez-Espinoza, T.D. Kim, C. Lanssens, A.H.G. Patel, X.D. Yang, E. Vohringer-Martinez, C. Cárdenas, T. Verstraelen, P.W. Ayers
Chemical Physics Letters
660, 307–312
2016
A1

Abstract 

We present explicit formulas for arbitrary-order derivatives of the energy, grand potential, electron density, and higher-order response functions with respect to the number of electrons, and the chemical potential for any smooth and differentiable model of the energy versus the number of electrons. The resulting expressions for global reactivity descriptors (hyperhardnesses and hypersoftnesses), local reactivity descriptors (hyperFukui functions and local hypersoftnesses), and nonlocal response functions are easy to evaluate computationally. Specifically, the explicit formulas for global/local/nonlocal hypersoftnesses of arbitrary order are derived using Bell polynomials. Explicit expressions for global and local hypersoftness indicators up to fifth order are presented.

When is the Fukui Function Not Normalized? The Danger of Inconsistent Energy Interpolation Models in Density Functional Theory

F. Heidar-Zadeh, R.A. Miranda-Quintana, T. Verstraelen, P. Bultinck, P.W. Ayers, A. Buekenhoudt
Journal of Chemical Theory and Computation (JCTC)
12 (12), 5777–5787
2016
A1

Abstract 

When one defines the energy of a molecule with a noninteger number of electrons by interpolation of the energy values for integer-charged states, the interpolated electron density, Fukui function, and higher-order derivatives of the density are generally not normalized correctly. The necessary and sufficient condition for consistent energy interpolation models is that the corresponding interpolated electron density is correctly normalized to the number of electrons. A necessary, but not sufficient, condition for correct normalization is that the energy interpolant be a linear function of the reference energies. Consistent with this general rule, polynomial interpolation models and, in particular, the quadratic E vs N model popularized by Parr and Pearson, do give normalized densities and density derivatives. Interestingly, an interpolation model based on the square root of the electron number also satisfies the normalization constraints. We also derive consistent least-norm interpolation models. In contrast to these models, the popular rational and exponential forms for E vs N do not give normalized electron densities and density derivatives.

Minimal Basis Iterative Stockholder: Atoms-in-Molecules for Force-Field Development

T. Verstraelen, S. Vandenbrande, F. Heidar-Zadeh, L. Vanduyfhuys, V. Van Speybroeck, M. Waroquier, P.W. Ayers
Journal of Chemical Theory and Computation (JCTC)
12(8), 3894-3912
2016
A1

Abstract 

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback-Leibler divergence of the pro-density from a reference electron density, e.g. obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a linear-scaling computational cost, enabling applications to supramolecular systems. The benefits of the MBIS method are demonstrated with systematic applications to molecular databases and extended models of condensed phases. A comparison to 14 other AIM methods shows its effectiveness when modeling electrostatic interactions. MBIS is also suitable for rescaling atomic polarizabilities in the Tkatchenko-Sheffler scheme for dispersion interactions.

Non-covalent force field expressed in terms of spherical density functions

ISBN/ISSN:
Talk

Conference / event / venue 

255th National Meeting and Exposition of the American-Chemical-Society (ACS) - Nexus of Food, Energy, and Water a
New Orleans, LA, USA
Sunday, 18 March, 2018 to Thursday, 22 March, 2018

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