Solid-state density functional methods

Chapter 2 we worked through the two most commonly used quantum mechanical models r performing calculations on ground-state organic -like molecules, the ab initio and semi-ipirical approaches. We also considered some of the properties that can be calculated ing these techniques. In this chapter we will consider various advanced features of the ab Itio approach and also examine the use of density functional methods. Finally, we will amine the important topic of how quantum mechanics can be used to study the solid state. 

Density Functional Methods for Studying the Solid State ... 

Callaway, J. and March, N.H. (1985). Density functional methods theory and applications, Solid State Phys. 38, 135-221. 

Applications of density functional theory in solid state chemistry, Recent advances in Density Functional Methods, Vol. 1, Part 3, V. Barone A. Bencini, P. Fantucci (eds.). World Scientific Publishing Company,... 

The vibrational modes of the ground-state phenol were examined by a number of spectroscopic techniques including UV-VIS - , IR for the vapour ", and the IR and Raman spectra in the solid and liquid phases - and microwave spectroscopy ", see also References 164-166. They are collected in Table 8, where both nomenclatures by Wilson and coworkers and VarsanJ i are used. Recently, the vibrational modes of phenol have become a benchmark for testing ab initio and density functional methods " . The Hartree-Fock calculations of the vibrational spectrum of phenol were first performed using the 6-31G(d,p) basis set. An MP2 study with the same basis set was later carried out. A combination" of three methods, viz. HF, MP2 and density functional BLYP, in conjunction with the 6-31G(d,p) basis was used to study the phenol spectrum and to make the complete and clear assignment of its vibrational modes (see Table 9). 

Figure 15. The potential energy surfaces for the excess electron bubble states in C He) clusters portraying the total energy EtiRi, R, N) versus the bubble radius Rf, for fixed values of N marked on the curves. The open and full points represent the results of the computations for the clusters using the density functional method for Ej Ri, R, N) and the quantum mechanical treatment for Ee(Ri, R, N), while for the bulk we took Ed Rb, R — oo, iV oo) = AttyR. The black point ( ) on each configurational diagram represents the equilibrium bubble radius. The Rj-dependence of the energy of the quasi-free electron state Vo(Rt, R, N) in the cluster of the smallest size of N = 6.5 X 10 (dashed line) and the bulk value of To (solid line) are also presented. The To values for each Rj, for iV = 8.1 x 10 to 1.88 x 10 fall between these two nearly straight fines.

A more recent introduction to quantum chemistry is density-functional methods (DFT). These in fact pre-date the other methods but were for a long time used primarily by physicists and were applied to solids. The electron density is given by the square of the wavefunction, and is a measure of how much electron there is at any point. Working from the realization that all properties of a molecule in its lowest energy state can be calculated from the electron density, Walter Kohn and his co-workers re-wrote the wave equation in terms of electron density to show that... 

DFT-Based Pseudopotentials. - The model potentials and shape-consistent pseudopotentials as introduced in the previous two sections can be characterized by a Hartree-Fock/Dirac-Hartree-Fock modelling of core-valence interactions and relativistic effects. Now, Hartree-Fock has never been popular in solid-state theory - the method of choice always was density-functional theory (DFT). With the advent of gradient-corrected exchange-correlation functionals, DFT has found a wide application also in molecular physics and quantum chemistry. The question seems natural, therefore Why not base pseudopotentials on DFT rather than HF theory ... 

This Chapter has been designed to provide an overview over recent understanding of and investigations on relativistic effects in solids. The focus is on the electronic ground state treated with density functional methods. The idea was to go the whole way from fundamentals via the tedious subtleties of code implementation to examples of physical properties that are influenced or even determined by relativity. All of these three areas have experienced a vivid development lately. The selection of the presented specific problems is mainly based on the authors interests and thus necessarily incomplete. 

Density functional (DF) [201] methods (for reviews see [202, 203, 204, 205]) were very popular in solid state physics since about 1965, but were hardly applied in chemistry for quite a while (among the applications to structural chemistry see e.g. ref. [206]), before suddenly around 1988 they really conquered chemistry. Even before this the rather good performance in solid theory did not remain unobserved by quantum chemists, but the reluctance to consider density functional methods more seriously had various reasons. 

Plane waves used historically in the theory of the solid state, these functions are being used increasingly in molecular theories in conjunction with the density functional method discussed in Chapter 32. These functions are not dependent on the positions of the nuclei and offer considerable simplifications in gradient calculations. 

Fig. 6. The optical absorption spectrum and the electronic structure of Mn2". (a) Experimental data, where a photodissociation action spectrum of Mn2 was measured by observing Mn" " photofragment, (b) The spectrum calculated by a hybrid-type density-functional method. The bars show oscillator strengths the solid line a spectral profile, (c) Density-of-states profiles of the majority and the minority spin electrons obtained by the same theoretical calculation. The shadows indicate occupied electronic levels. The manganese dimer ion, Mn2 ", was shown to have a spin multiplicity of twelve with a bond length of 3.01 A. ...

Abstract. This paper provides an overview of the title paper by Yin and Cohen. I will briefly review some of the background for this work, provide some details of the calculations and discuss how this paper has influenced the field. In particular, this paper led to the development of the first realistic calculations for the structural energies of solids. It was the origin of the pseudopotential density functional method applied to the solid state. 

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