Crystalline density functional theory

The present chapter is organized as follows. We focus first on a simple model of a nonuniform associating fluid with spherically symmetric associative forces between species. This model serves us to demonstrate the application of so-called first-order (singlet) and second-order (pair) integral equations for the density profile. Some examples of the solution of these equations for associating fluids in contact with structureless and crystalline solid surfaces are presented. Then we discuss one version of the density functional theory for a model of associating hard spheres. All aforementioned issues are discussed in Sec. II. 

Density functional theory was originally developed by solid-state physicists for treating crystalline solids and almost all applications were in that field until the mid-1980s. It is a current hot topic in chemistry, with many papers appearing in the primary journals. 

Density functional theory has been extensively used to calculate vibrational properties of minerals and other crystalline phases in addition to molecules and molecule-like substances. This method has recently begun to be used to calculate isotope fractionation factors (Schauble et al. in press Anbar et al. in press), and shows great potential for future research. Programs such as ABINIT (Gonze et al. 2002), pwSCF (Baroni et al. 2001)—both freely available—and the commercial package CASTEP (Accelrys, Inc.) can be used to calculate vibrational properties of crystals. 

In this paper we present preliminary results of an ab-initio study of quantum diffusion in the crystalline a-AlMnSi phase. The number of atoms in the unit cell (138) is sufficiently small to permit computation with the ab-initio Linearized Muffin Tin Orbitals (LMTO) method and provides us a good starting model. Within the Density Functional Theory (DFT) [15,16], this approach has still limitations due to the Local Density Approximation (LDA) for the exchange-correlation potential treatment of electron correlations and due to the approximation in the solution of the Schrodinger equation as explained in next section. However, we believe that this starting point is much better than simplified parametrized tight-binding like s-band models. 

We will of course be rather more focused here. We shall be concerned with the generic computational strategies needed to address the problems of phase behavior. The physical context we shall explore will not extend beyond the structural organization of the elementary phases (liquid, vapor, crystalline) of matter, although the strategies are much more widely applicable than this. We shall have nothing to say about a wide spectrum of techniques (density functional theory [1], integral equation theories [2], anharmonic perturbation... 

The density functional theory (DFT) [7,8] is now widely used in studying both infinite bulk crystalline materials and finite atoms, molecules, and clusters. In principle, the ground-state total energy as well as the electron density itself in interacting many-electron systems is accurately described in DFT. Therefore, the geometry optimization by minimizing the total energy should also be accurate in DFT as well. The electronic band structure is, on the other hand, a very useful but approximate physical concept based on the quasiparticle theory for inter-... 

A great number of studies related to thermochemical properties of QDO and PDO derivatives have been recently described by Ribeiro da Silva et al. [98-103]. These studies, which have involved experimental and theoretical determinations, have reported standard molar enthalpies of formation in the gaseous state, enthalpies of combustion of the crystalline solids, enthalpies of sublimation, and molar (N - O) bond dissociation enthalpies. Table 5 shows the most relevant determined parameters. These researchers have employed, with excellent results, calculations based in density functional theory in order to estimate gas-phase enthalpies of formation and first and second N - O dissociation enthalpies [103]. 

The difference of total energies of the two conformations 7 and 8 with symmetry Z)2 and Cu> respectively, for the dibenzotetrathiocine 6 (X = F) was calculated by density functional theory (DFT) to be only 4.6 kj mol 1 in favor of the twist boat 7 <1998CJC1093>. Indeed, 6 (X = F) undergoes a slow conformational isomerization in solution (Section 14.09.3.1) but adopts the chair conformation 8 in crystalline form (cf. Section 14.09.4). 

Ke et al. conducted a study on the structural properties of AIH3 using density functional theory (DPT) methods [45]. They reported that the a -(orthorhombic) and (3-(cubic) modifications are more stable than a-(hexagonal) at 0 K (no phonons). The finding is, however, in contrast to experimental results, which have shown that the a-crystalline phase is the most stable phase at ambient conditions. 

The electronic structure of solids and surfaces is usually described in terms of band structure. To this end, a unit cell containing a given number of atoms is periodically repeated in three dimensions to account for the infinite nature of the crystalline solid, and the Schrodinger equation is solved for the atoms in the unit cell subject to periodic boundary conditions [40]. This approach can also be extended to the study of adsorbates on surfaces or of bulk defects by means of the supercell approach in which an artificial periodic structure is created where the adsorbate is translationally reproduced in correspondence to a given superlattice of the host. This procedure allows the use of efficient computer programs designed for the treatment of periodic systems and has indeed been followed by several authors to study defects using either density functional theory (DFT) and plane waves approaches [41 3] or Hartree-Fock-based (HF) methods with localized atomic orbitals [44,45]. 

The first density-functional theory of melting to make use of the modern direct correlation function-based approach to liquid theory was formulated by Ramakrishnan and Yussouff [127], who treated crystalline order as a perturbation on liquid order. This perturbative approach to... 

M. Plazanet, N. Fukushima, M.R. Johnson, A.J. Horsewill, H.P. Trommsdorff (2001). J. Chem. Phys., 115, 3241-3248 The vibrational spectrum of crystalline benzoic acid Inelastic neutron scattering and density functional theory calculations. H.B. Burgi S.C. Capelli (2000). Acta Cryst., A56 403-412. Dynamics of molecules in crystals from multi-temperature anisotropic displacement parameters. I Theory. 

Roewer G, Herzog U, Trommer K, Muller E, Friihauf S (2002) Silicon Carbide - A Survey of Synthetic Approaches, Properties and Applications 101 59-136 Rosa A, Ricciardi G, Gritsenko O, Baerends EJ (2004) Excitation Energies of Metal Complexes with Time-dependent Density Functional Theory 112 49-116 Rosokha SV, Kochi JK (2007) X-ray Structures and Electronic Spectra of the it-Halogen Complexes between Halogen Donors and Acceptors with it-Receptors. 126 137-160 Rowan SJ, Mather PT (2008) Supramolecular Interactions in the Formation of Thermotropic Liquid Crystalline Polymers. 128 119-149... 

To describe quantitatively the effects of a crystalline environment on the structure, PES, and vibrational spectra of strong H-bonds in terms of density functional theory (DFT) calculations with periodic boundary conditions. 

Abstract We examine the performance of hybrid (HF-DFT) exchange functionals within Density Functional Theory (DFT) in describing the properties of crystalline solids. Recent applications are reviewed, and an extensive set of new results presented on transition metal compounds. 

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