Linear scaling calculation of excited-state properties of polyacetylene

Abstract

A new method based on the equation of motion (EOM) for the reduced single-electron-density matrix is developed to calculate the excited-state properties of very large electronic systems. When the distance between two local Orbitals is larger than a critical length, the corresponding off-diagonal density-matrix element is negligible and may be set to zero. This reduces the dimension of the EOM and the number of required matrix elements. The computational cost scales thus linearly with the system size. As an illustration, the new method is implemented to evaluate the absorption spectra of polyacetylene oligomers containing 30-500 carbon atoms. The resulting spectra agree well with those of the full calculation, and more importantly, the linear scaling of the computational time versus the size is clearly demonstrated. ©1999 The American Physical Society.