A symmetry-adapted Lanczos method for calculating energy levels with different symmetries from a single set of iterations

We present a symmetry-adapted Lanczos method that uses projection operators to calculate energy levels with different symmetries from a single sequence of matrix–vector products. Compared with the conventional Lanczos method, this method has the advantage that energy levels are computed more efficiently and with symmetry labels. High-lying stretching energy levels of a coupled Morse oscillator Hamiltonian describing SiH428 are calculated to demonstrate the advantage of the symmetry-adapted method.