LMTO-ASA Methods Part II Total Energy

IMPROVED LMTO-ASA METHODS PART II TOTAL ENERGY 

In this paper we will present a way to improve the evaluation of total energies in LMTO calculations. The Kohn Sham energy functional [1] can be written in the form 

Consider the electrostatic terms. These are hard to evaluate because the output charge density is a complicated non spherical function in space. In traditional LMTO calculations the charge density is first spheridised before Ees is calculated. In this method p(r) is reduced to a sum of spherically symmetric balls of charge inside each ASA sphere [2]. 

The electrostatic energy is then calculated for this system of charge [2], giving 

The consequences of this approximation are well known. While E s is good enough for calculating bulk moduli it will fail for deformations of the crystal that do not preserve symmetry. So it cannot be used to calculate, for example, shear elastic constants or phonons. The reason is simple. changes little if you rotate one atomic sphere 

We therefore require a new way to evaluate es and we will need to retain the full, non spherical, charge density p(r). 

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