Parallel filter diagonalization: A novel method to resolve quantum states in dense spectral regions

A parallel version of D. Neuhauser's filter diagonalization algorithm is pr esented. In contrast to the usual procedure of acting with a set of narrow filter operators on a single or just a few initial vectors, parallelizabili ty is achieved by working with a single, broad filter operator and a corres pondingly large number of initial vectors. Apart from the obvious speedup i n computation time, there is no need for communication between the processo rs involved in the computation. Furthermore, because a significantly reduce d number of matrix vector multiplications is needed per initial vector, par allel filter diagonalization is numerically more stable than the single pro cessor approach. It is argued that this method is particularly attractive f or calculating eigenvectors of the large-scale secular matrices arising in quantum chemistry, especially in dense spectral regions. An application to dense state distributions of a cationic molecular cluster serves as an illu strative example. This is the first time filter diagonalization is used as a tool for ab initio electronic structure calculations. (C) 2000 American I nstitute of Physics. [S0021-9606(00)01321-0].