Hermitian Kohn-Sham

The Hamiltonian being hermitian, one can recover the canonical Kohn-Sham equations from Eq.(9) by a unitary transformation on the wavefunctions, so that ... 

For variational methods, such as Hartree-Fock (HF), multi-configurational self-consistent field (MCSCF), and Kohn-Sham density functional theory (KS-DFT), the initial values of the parameters are equal to zero and 0) thus corresponds to the reference state in the absence of the perturbation. The A operators are the non-redundant state-transfer or orbital-transfer operators, and carries no time-dependence (the sole time-dependence lies in the complex A parameters). Furthermore, the operator A (t)A is anti-Hermitian, and tlie exponential operator is thus explicitly unitary so that the norm of the reference state is preserved. Perturbation theory is invoked in order to solve for the time-dependence of the parameters, and we expand the parameters in orders of the perturbation... 

Here 0) is tire unperturbed Kohn-Sham determinant, and /<( ) the anti-Hermitian operator... 

The use of the orbital concept in the Hartree-Fock (HE) and Kohn-Sham (KS) methods leads to similar variational equations a coupled set of eigenvalue equations with a hermitian operator (See for example [7, 25]). This system of integro-differential equations is transformed into a matrix problem when we use a basis set. In both methods, one has to solve a generalized eigenvalue equation ... 

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