EXTRAPOLATION OF REAL-SPACE QUANTUM-CHEMICAL CALCULATIONS FROM FINITE-SIZE SUPER CELLS TO THE IDEAL INFINITE SYSTEM .1. THEORY

A method is proposed how to calculate the correct density matrix of an infinite polymeric chain from that of a standard finite supercell cal culation. The density matrix of the finite supercell is transformed in to k-space for all k-values allowed by the periodic boundary condition s. The k-dependent matrices are then unitarily transformed, with each unitary matrix being represented by a set of complex rotation matrices . It is shown that the corresponding angles can be interpolated and ex trapolated toward the zone boundaries in a straightforward manner and that this extrapolation can be done from any finite supercell with rea sonable accuracy. This gives rise to an infinite system density matrix for which all fundamental properties are guaranteed by construction. This infinite system density matrix may be used to construct a correct ed density matrix for the finite supercell calculation. (C) 1994 John Wiley & Sons, Inc.