Density-matrix Functional Theory and Its Computational Method
With the popularity of density functional theory,the inventor Kohn won the Nobel prize in chemistry in 1998.In the density functional theory,the orbital occupation numbers are restricted to be 1 or 0.In 1975,Gilbert proposed density-matrix functional theory,in which the occupation numbers can take additional fractional numbers between 0 and 1.Therefore,it can be regarded as a generalization of density functional theory.However,Gilbert found that the orbital energies were all degenerate for orbitals with fractional occupation numbers,which contradicts with the energy structure observed in experiments.Because of the degeneracy,there was no real eigenvalue equation for the orbitals in density-matrix functional theory,only a non-linear optimisation method could be used in the calculation,which was very inefficient.The nearly half-a-century problem was solved by us recently.After employing the information entropy to extract the correlation energy in density-matrix functional theory,we obtain the self-consistent field eigenvalue equation for the orbitals,so that efficient computation is realized within the density-matrix functional theory.