Transferable Total Energy Parametrization for Metals
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"TRANSFERABLE
TOTAL ENERGY PARAMETRIZATION FOR METALS
VI. SIGALAS* AND D.A. PAPACONSTANTOPOULOS Complex Systems Theory Branch, Naval Research Laboratory, Washington, D.C. 20375 5 "Current address: Department of Physics, Iowa State University, Ames, Iowa 50011 ABSTRACT We have investigated total energy expressions that consist of a term describing the eigenvalue sum and a pair potential term. Such expressions can be used to fit the results of first principles total energy calculations at given structures, and then obtain the total energy of another configuration of atoms avoiding the complexity of further ab initio calculations. In this work we present a method of fitting APW total energy results to a non-orthogonal tight-binding Hamiltonian from which the sum of the eigenvalues is derived and to a pair potential represented by a 5th order polynomial. We fit total energies for the fcc and bcc structures and we then obtain the elastic constants Cii in good agreement with both full potential LAPW calculations and experiment. We present results of this method for Ir. INTRODUCTION
The problem of fitting first principles total energy results of given structures to an interpolation formula that is transferable and can be used to obtain the energetics of other 1 atomic configurations has received a lot of attention in the last few years. At the outset we should state that there is no completely satisfactory solution to this problem. All models that have been proposed have a limited range of applicability. Nevertheless, these models are useful and provide satisfactory results for specific situations. In this work we developed a procedure to fit total energy results for the fcc and bcc structures and then calculated the total energy of the hcp structure and the elastic constants. METHOD
The method works in the following way. We write the total energy as a sum of two terms as follows: E(Rj.)
= E cE 1(Rj)
+ E~~R'
(1)
The first term is the sum of the eigenvalues of the occupied states of a one-electron Hamiltonian and the second is a repulsive pair potential which is a function of the bond length R- The sum of the ei envalues is determined by a tight-binding (TB) Hamiltonian that is fit, A la Slater-Koster, to the individual eigenvalues of first principles augmented plane wave (APW) calculations. 3 This TB Hamiltonian involves s, p and d orbitals, includes first nearest neighbor interactions and is non-orthogonal. So for a transition element the Hamiltonian is a 9X9 matrix that contains 20 hopping integrals and 4 on-site energies. The above TB parameters are determined by fitting the APW energy bands of the fcc structure for 6 different lattice parameters. For a typical transition metal and for each lattice constant we fit 6 valence bands at 33 k-points in the 1/48th of the Brillouin zone. The fit has an rms Mat. Res. Soc. Symp. Proc. Vol. 291. ýc)1993 Materials Research Society
28
error of approximately 5 mRy for all 6 bands. In the next step we fit each TB parameter individually to a quadratic function of the bond
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