Classical density-functional theory for water Sahak A. Petrosyan, David Roundy, Jean-Fran¸cois Bri` ere and Tom´ as A. Arias Department of Physics, Cornell University, Ithaca, NY 14853 (Dated: in press) We introduce a new computationally efficient and accurate classical density-functional theory for water and apply it to hydration of hard spheres and inert gas atoms. We find good agreement with molecular dynamics simulations for the hydration of hard spheres and promising agreement for the solvation of inert gas atoms in water. Finally, we explore the importance of the orientational ambiguity in state-of-the-art continuum theories of water, which are based on the molecular density only. Water is the most abundant liquid on earth and is es- sential for life. Water is a called a universal solvent for its ability to dissolve both acids and bases, as well as polar and non-polar molecules. Despite its importance to a wide range of problems in chemistry and biology, it is still an open challenge to build a first principles theory of the microscopic structure of water and its interaction with solutes[1]. The underly- ing reason for this is the complex interplay between the kinetic energy of molecules and the the orientation de- pendent potential energy of inter-molecule interactions. and work in a classical density-functional theory frame- work. There are two main advantages of working in this framework. First, the classical density-functional the- ory of liquids is a continuous theory of the liquid state which is exact in principle. Moreover, this framework gives the free energy and the density profile of the liq- uid in any external potential V ( ⃗ r ) in terms of a single density-functional[1], so that study of the hydrophobic effect (liquid in contact with either an impenetrable wall or an impenetrable hard sphere) and of the interaction of the liquid with any solute can be carried out in a single, unified framework. A number of approximate density- functionals have been developed for water and applied to the hydrophobic effect[10, 14]. Much more demanding theories which go beyond the average molecular density to consider explicitly the distribution of molecular orien- tations in water have also been developed[15, 16]. All of these density functional theories, however, prove to be either quite computationally demanding or provide an over-simplified description. For the study of liquids and their interactions with ex- ternal systems, two general classes of theoretical meth- ods have been developed. The first treats the liquid as a collection of molecules treated either ab initio within density-functional theory or with a model interatomic po- tential, such as the simple point charge (SPC) model [2] or the 4-site transferable intermolecular potential TIP4P [3], and then uses molecular dynamics (MD) or Monte Carlo numerical methods to perform statistical averag- ing over the thermal phase space[4–6]. These methods are intuitively simple to understand and also relatively straightforward to implement numerically. However, be- cause they involve statistical averaging of many molecules over an exponentially growing configuration phase space, these methods are numerically very demanding. The sec- ond class of methods treats the liquid as a continuous media[7–11]. Without the need for thermal averaging or to represent molecules individually, these latter meth- ods are much more efficient computationally. However, such models are generally built in an empirical way and, generally, there is no systematic way to improve them. We begin this work by introducing a new, compu- tationally efficient density-functional theory for water which accurately reproduces the hydrophobic effect near hard boundaries. We then present the first application of a classical density-functional theory to realistic ab ini- tio potential energy surfaces of solutes, applying our the- ory to the solvation of the inert gas sequence. This lat- ter study allows us to address directly the question of whether explicit orientation dependence, with all of the concomitant computational demands, is necessary to pro- vide an accurate description of the solvation of even the simplest solutes. Nonetheless, significant progress has been made in un- derstanding the interaction of water with external envi- ronments using this approach, such as the work of Pratt and Chandler [12] on the theory of the hydrophobic ef- fect and the Lum, Chandler, Weeks (LCW) theory of hydrophobicity[13]. Classical density-functional theory for liquids follows from a variational principle which was first established by Hohenberg and Kohn[17] for the inhomogeneous electron gas at zero temperature and later generalized to finite temperature by Mermin[18]. The theorem states that the equilibrium grand poten- tial Ω$_{0}$ of a liquid at chemical potential µ in any exter- In this work, we explore the nature of the interaction of water with external environments using a somewhat different approach than that of Chandler and coworkers arXiv:1001.2350v2 [cond-mat.stat-mech] 16 Jan 2010 CLASSICAL DENSITY-FUNCTIONAL THEORY INTRODUCTION