Constrained Search Method for Constructing Kohn-Sham Potentials

5 Constrained Search Method for Constructing Kohn-Sham Potentials 

The one-to-one correspondence between electron density and effective potential, which is proven on the basis of the constrained search formulation, suggests that the effective potential can be determined directly from the electron density. Parr and coworkers developed a procedure for determining highly accurate exchange-correlation potentials from electron densities, which are calculated by high-level ab initio correlation wavefunction theories. This procedure is called the Zhao-Morrison-Parr (ZMP) method (Zhao et al. 1994). In this method, the effective potential is given by the Lagrange undetermined multiplier method with a potential. 

This also makes a finite A available and upgrades the convergence and accuracy of the SCF method. 

calculate the terms in Eq. (4.21) using the exact electron density, po- 

If A does not reach the preset limit value, set a larger A and then return to process 2 with the given orbitals and orbital energies. If A reaches the preset limit value, the calculated orbitals and orbital energies correspond to the exact electron density. 

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