Tight-binding molecular dynamics: A primer
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Vol. 28, N. 10
2005
Tight-binding molecular dynamics: A primer L. Colombo(∗ ) Dipartimento di Fisica, Universit` a di Cagliari and SLACS (INFM-CNR) Cittadella Universitaria, I-09042 Monserrato (CA), Italy (ricevuto il 16 Maggio 2006)
Summary. — Following the seminal paper by Slater and Koster (1954) the tightbinding model has been widely and successfully applied to investigate electronic properties of materials over several decades. Eventually the advent of efficiently computable ab initio methods, as well as the ever increasing power of digital computers, has obscured its relevance as a tool for electronic structure calculations. Nevertheless, in the last 15 years or so, the tight-binding description of electronic states has been resumed as a state-of-the-art research tool since it can provide a reliable semi-empirical total energy method suitable for large-scale molecular dynamics simulations at a comparatively small numerical effort. Under this respect, tight binding represents a conceptual bridge between superior (but expensive) ab initio simulations and model-potential ones, characterized both by a reduced computational workload and reduced transferability. In addition, the tight-binding approach is optimally tailored for training materials scientists to perform atomistic simulations: in fact, it is firmly rooted into an intuitive physico-chemical description of bonding and it does not necessarily require complex numerical tools. In this paper I review the tight-binding formalism and I discuss the key issues of the method as for its practical implementation as well as its underlying physical picture. I further extend the basic theory to the realm of molecular dynamics simulations and I discuss a linear scaling formulation of the method. PACS 71.15.-m – Methods for electronic structure calculations. PACS 65.40.-b – Thermal properties of crystalline solids.
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Introduction Molecular dynamics . 2 1. The basic conceptual framework . 2 2. The generation of particle trajectories . 2 3. The control of the thermodynamical ensemble . 2 4. Constant temperature ensemble . 2 5. Constant pressure ensemble
(∗ ) E-mail: [email protected] c Societ` a Italiana di Fisica
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The tight-binding method . 3 1. Basic formalism: from atomic orbitals to Bloch sums . 3 2. The L¨ owdin orbitals . 3 3. The core of the method: the two-center approximation for energy integrals . 3 4. Another major step forward: two-center energy integrals as constants to fit . 3 5. The semi-empirical tight binding at work: silicon as a show-case . 3 6. The effective repulsive potential . 3 7. The Harrison rule The tight-binding theory of total energy . 4 1. Generating a transferable TB model for total energy calculations . 4 2. Improving the GSP method . 4 3. Beyond the GSP method . 4 4. Managing charge-transfer effects . 4 5. Non-orthogonal tight-binding total energy models Moving up and down in sophistication . 5 1
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