J. Phys. Chem. A 2010, 114, 8873–8877
8873
Second-Order Many-Body Perturbation Study of Solid Hydrogen Fluoride† Olaseni Sode and So Hirata* Quantum Theory Project and The Center for Macromolecular Science and Engineering, Departments of Chemistry and Physics, UniVersity of Florida, GainesVille, Florida 32611-8435 ReceiVed: March 25, 2010; ReVised Manuscript ReceiVed: June 15, 2010
A linear-scaling, local-basis, electron-correlation method based on a truncated many-body expansion of energies has been applied to crystalline hydrogen fluoride in three dimensions. The energies, equilibrium atomic positions, lattice constants, and dipole moments of the two structures (polar and nonpolar) have been determined, taking account of one- and two-body Coulomb (electrostatic), exchange, and correlation interactions exactly and three-body and higher-order Coulomb interactions approximately within certain truncation radii. The longer-range two-body Coulomb interactions are also included to an infinite distance by computing the Madelung constant. The second-order Møller-Plesset perturbation method has been used in conjunction with the aug-cc-pVDZ and aug-cc-pVTZ basis sets for correlation. Counterpoise corrections of the basis-set superposition errors have also been made. Predicted relative energies show that the nonpolar arrangement is considerably more stable than the polar one, establishing the precise three-dimensional structure of this crystal and finally resolving the controversy. The computed lattice constants of the nonpolar configuration agree with the observed to within 0.3 Å. I. Introduction The treatment of three-dimensional crystalline systems using ab initio electronic structure methods that go beyond the usual Hartree-Fock (HF) and density-functional theory (DFT) approximations is the subject of recent research efforts.1 The difficulty is caused by the high dimensionality of the equation of motion for large or infinite number of particles in the system and the nonscalability of ab initio electronic structure methods with system size. The vast majority of studies of such systems have been undertaken using a reciprocal space framework, namely, the crystalline orbital (CO) theory.2-10 This approach employs a delocalized description under the periodic boundary conditions, in which the orbitals extend throughout the length of the system. It is particularly useful for calculating energy bands and widely used for one-dimensional extended systems.5,11,12 Yet, applications to two- or three-dimensional systems can be quite difficult. Furthermore, while implementations based on HF and DFT have been well established, those using ab initio correlated methods are scarce and extremely tedious to develop.7,9,13,14 Crystal defects, surface reactions and adsorption, non-in-phase lattice vibrations and phonon dispersion, etc., where perfect periodic symmetry is lost, prove to be challenging to study by the CO theory.15,16 In molecular and ionic crystals, electrons can be thought of as confined around the respective atoms or molecules, such that only weak and/or classical intermolecular interactions become the primary concern in reproducing the total crystal energies accurately. In such a system, a localized description of the electronic structure, namely, treating the system as a collection of overlapping finite molecules becomes possible, breaking up the high-dimensional equation of motion into many lowdimensional ones.17-20 The finite molecules must be embedded in an electrostatic field of the infinite system. The binaryinteraction method21,22 that we have developed realizes such a †
Part of the “Klaus Ruedenberg Festschrift”. * Corresponding author. Electronic mail:
[email protected].
description and approximates the energy of a one-dimensional molecular crystal by the sum of the energies of monomers and overlapping dimers:21,22 S
Ecell )
∑ (Ei(0)j(0) - Ei(0) - Ej(0)) + 21 ∑ (1 - δn0) × i
