A coarse-grained density functional theory, chemical potential equalization and electric response in molecular systems Swapan K. Ghosh * Theoretical Chemistry Section, Bhabha Atomic Research Centre, Mumbai 400085, India article info Article history: Received 15 September 2009 Received in revised form 16 December 2009 Accepted 16 December 2009 Available online 23 December 2009 Keywords: Density functional theory Chemical potential equalization Response properties Polarizability abstract A simple coarse grained description of the electron density changes in molecular systems due to change in external potential, which may include the effect of external electric fields in addition to the potential due to the nuclei, has been proposed in terms of the induced atom–atom charges and atomic dipoles. The density functional perturbation theory has been used for deriving the expressions for the interaction energy and the effective chemical potentials in terms of these coarse grained variables. A route to the cal- culation of these quantities and hence the dipole polarizability of the molecular system is provided. The proposed approach would also be useful for obtaining polarizable charge based force field for intermolec- ular interaction in computer simulation. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Density functional theory (DFT) [1] has proved itself to be a valuable tool for the quantum mechanical description of electronic structure and properties of atoms, molecules, clusters and solids. The central theme of DFT is the use of the single-particle electron density [2] as the basic variable to express the energy of a many- electron system as a unique functional of the density. Starting with the pioneering work of Hohenberg and Kohn [3], DFT has been elevated from its status of being a ground state theory to include excited states [4] and time-dependent phenomena [5]. Besides providing conceptual simplicity and computational economy, DFT has given birth to a number of important chemical concepts [1,6] and has also provided rigorous foundation to many of the existing concepts, important examples being the concepts of electronega- tivity [7], chemical hardness [8], Fukui function [9] and several other chemical reactivity indices [10,11]. DFT in its usual form uses the full electron density [1,2,12] func- tion in 3D space to describe the system which itself is a tremen- dous simplification. However, for describing molecule formation, intermolecular interaction or interaction with external fields, fur- ther simplification is possible through a coarse graining of the elec- tron density, viz in terms of its monopole or dipole representation, such as charges and dipoles at atomic sites. Partial atomic charges in molecules [13] have been used for describing ionic binding which was later extended to covalent binding [14] as well. Analo- gously the use of atomic dipoles has been proposed [15] for describing electric response of molecular systems and hence to predict the molecular polarizability. Application of these coarse grained variables has also been extended [16] to solids for describ- ing the phonons and the response properties. Recently, both the charge and dipole variables have been jointly used [17] to describe molecular response properties. Most of these approaches, however, employ these course grained variables directly for expansion of the relevant energy quantities. There have, however, been attempts to provide a microscopic quantum mechanical picture in terms of the physically appealing electron density variable, followed by subse- quent coarse graining to derive expressions for the energy and other quantities in terms of atomic charge and dipole variables [18]. The basic approach starts with a functional Taylor expansion of the energy of the system in terms of the electron density and the potential, which is then followed by suitable approximations to ex- press the energy in terms of the coarse grained variables such as atomic charges and dipoles, which has been discussed in details re- cently by Wadehra and Ghosh [18]. However, the use of atomic charges as the variables has met with difficulties [19] due to super- linear dependence of the polarizability on the size of long chain and large molecular systems. The so called split charge formalism [20] in terms of charge transfer between adjacent bonded atoms has been introduced by Chelli et al. and others [21,22] as a rescue. This has recently been supplemented [23] by combining the atomic dipole variables along with the split charge variables. The ap- proach, however, is based on expansion directly in terms of the coarse grained variables and not on a microscopic theory. Hence it is the purpose of the present work to provide a rigorous founda- tion of the joint split charge and dipole approach based on a func- tional Taylor expansion within the framework of microscopic density functional theory. The present work can thus be also con- 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.12.023 * Tel.: +91 22 25595092; fax: +91 22 25505151. E-mail address: skghosh@barc.gov.in Journal of Molecular Structure: THEOCHEM 943 (2010) 178–182 Contents lists available at ScienceDirect Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem