Exchange-Correlation Energy as a Function of the Orbital Occupancies

Abstract

Electronic structure methods comprise both first-principles total energy methods and many-body theory (MBT). These two approaches have taken different hamiltonians as their paradigms (the nearly-free electron hamiltonian in the case of the total energy methods and the Hubbard hamiltonian for MBT) and have developed as two separate fields. This is also reflected in the basis sets used in these calculations: typically, first-principles methods are implemented using a plane wave basis [1, 2], while MBT calculations are naturally performed using atomic-like orbitals. In an attempt to bring together these two different methodologies, a novel scheme for the description of electron exchange-correlation effects has been developed: the Orbital-Occupancy (00) approach [3, 4]. Basically, the 00-approach is a DFT-like method, suitable for highly correlated systems, in which the role that the electron density $\rho \left( {\overline r } \right)$ plays in standard DFT methods (LDA,GGA) is assumed by the set of the orbital occupation numbers,{n _µσ }:

$$\rho \left( {\overline r } \right) \Rightarrow \left\{ {{n_{\mu \sigma }}} \right\}$$

(1)

$\left( {{n_{\mu \sigma }} = < {{\widehat n}_{\mu \sigma }} > } \right)$. Then, the total energy E is obtained as a function of the orbital occupancies:

$$E\left( {\left\{ {{n_{\mu \sigma }}} \right\}} \right) = {E^H}\left( {\left\{ {{n_{\mu \sigma }}} \right\}} \right) + {E^{XC}}\left( {\left\{ {{n_{\mu \sigma }}} \right\}} \right).$$

(2)

The Hartree-like contribution E ^H, as a function of the {n _µơ },is easily obtained [5] and, as usual, the difficult part resides in determining the exchange-correlation term E^XC ({n _µσ }).