F. Heidar-Zadeh

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


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


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


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


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


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


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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