Quantum Structural Methods for the Solid State and Surfaces

Abstract

Our intention is to give a brief survey of advanced theoretical methods used to determine the electronic and geometric structure of solids and surfaces. The electronic structure encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric structure refers to the equilibrium atomic positions. Quantities that can be derived from the electronic structure calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), structural (lattice constants, equilibrium structures), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on techniques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. In his chapter on the fundamentals of quantum mechanics of condensed phases (A1.3), James R Chelikowsky introduces the plane wave pseudopotential method. Here, we will complement his chapter by introducing in some detail tight-binding methods as the simplest pedagogical illustration of how one can construct crystal wavefunctions from atomic-like orbitals. These techniques are very fast but generally not very accurate. After reviewing some of the efforts made to improve upon the local density approximation (LDA, explained in A1.3), we will discuss general features of the technically more complex all-electron band structure methods, focusing on the highly accurate but not very fast linear augmented plane wave (LAPW) technique as an example. We will introduce the idea of orbital-free electronic structure methods based directly on density functional theory (DFT), the computational effort of which scales linearly with size, allowing very large systems to be studied. The periodic Hartree–Fock (HF) method and the promising quantum Monte Carlo (QMC) techniques will be briefly sketched, representing many-particle approaches to the condensed phase electronic structure problem. In the final section, we will survey the different theoretical approaches for the treatment of adsorbed molecules on surfaces, taking the chemisorption on transition metal surfaces, a particularly difficult to treat yet extremely relevant surface problem [1], as an example. While solid state approaches such as DFT are often used, hybrid methods are also advantageous. Of particular importance in this area is the idea of embedding, where a small cluster of surface atoms around the adsorbate is treated with more care than the surrounding region. The advantages and disadvantages of the approaches are discussed.