Multi-reference extension to virtual crystal approximation pseudo-potentials

In this study a computational method of the multi-reference VCA (virtual crystal approximation) pseudo-potential generation is presented. This is an extension of that proposed by Ramer and Rappe (2000), the scheme of which is in want of the explicit incorporation of semi-core states. To compensate this drawback, a kind of fine tuning is applied to the non-multi-reference VCA pseudo-potential; the form of the pseudo-potential is slightly modified within the cut-off radius in order that the agreements between the pseudo-potential and all-electron calculations are guaranteed both for semi-core and valence states. The improvement in the present work is validated by atomic and crystalline test calculations for the transferability and the lattice constant estimation.