Stationary nature of the density-functional free energy: Application to accelerated multiple-scattering calculations

Locally self-consistent Green’s function approach to the electronic structure problem

“…Following Nicholson et al, 19,20 we now surround an atom at site R by M Ϫ1 neighboring atoms, forming an M -atom local interaction zone. However, instead of solving the local multiple scattering problem directly, as it is done in the LSMS method, we embed each local interaction zone in the effective medium constructed above.…”

“…As we shall show, the site-diagonal block of the Green's function matrix for a particular atom in a large system may be obtained with sufficient accuracy by considering only the electronic multiple scattering processes in a finite region of space containing M atoms and called the local interaction zone ͑LIZ͒. 19,20 This multiple scattering problem scales as O(M 3 ), but when it is applied, in turn, to each atom in the unit cell the combined computational procedure exhibits the desired linear scaling in N with a prefactor determined by M and by the number of basis functions.…”

“…14 and 18-20 this prefactor is determined either by the convergence of the truncated series of the recursion method 14,18 or by the real-space convergence of the multiple scattering processes of the locally selfconsistent multiple scattering method. 19,20 In both cases, however, the system beyond the truncated region is neglected and one needs relatively large M values to obtain an accurate total energy. Recently, Abrikosov et al 21 showed that the size of the LIZ and hence the computational effort may be considerably reduced by embedding the truncated region in an effective medium.…”

“…[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] They are all based on the assumption, tacitly assumed in most solid-state calculations, that a change in an external potential at sufficiently large distances has no effects on the property, e.g., the total energy, under consideration. One example is the neglect of surface effects in ordinary bulk calculations.…”

Multi-center electronic structure calculations for plasma equation of state

“…The thermodynamic extension to finite temperatures is easily accomplished by introducing Fermi occupation factors into the average electron per unit cell description, generalizing the band energy as determining the free energy [ 110 …”