Functional Theory for Open-Shell Molecules

Density Functional Theory for Open-Shell Molecules 

A different - and the most popular - approach to describe open-shell electronic structures is the density functional theory (DFT) [106, 107], where the system and its properties are completely determined by the electron density p(r). The most widespread implementation of DFT is the Kohn-Sham formalism [108] in which an artificial reference system of noninteracting electrons is introduced to yield exactly the same electron density as the fully interacting system. In Kohn-Sham DFT, the electronic energy is a functional of p(r) and can be partitioned into several contributions. 

In this equation, T [p] is the kinetic energy of the noninteracting reference system, Vg ([p] the interaction energy with some external potential, J[p] the Coulomb interaction of the electrons, and represents the exchange-correlation functional 

We can incorporate more physics into the approximate exchange-correlation potentials by introducing additional variables such as the individual spin components of p(r), p (r) and //(r), which sum up to the total electron density [109], 

In particular, for any nonsinglet state with total spin S (and in the absence of a magnetic field), the eigenstates of are 2(S -i- l)-fold degenerate and the total electron density and spin density for each spin projection are connected through a 

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Casida, M. E., Ipatov, A., and Cordova, F. (eds) (2006) Linear-response time-dependent density-functional theory for open-shell molecules in Time-Dependent Density-Functional Theory (ed. Marques, M. A. L., Ullrich, C., Nogueira, F., Rubio, A., and Gross, E. K. U.) Springer, Berlin, pp, 243-257. 

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