Computation of Interior Eigenstates of Large Matrices Using the Quasiadiabatic Evolution of Instantaneous Eigenvectors

A two-stage iterative scheme is proposed to handle a central problem of molecular dynamics, the computation of interior eigenvalues of large Hamiltonian matrices. The proposed method involves an initial propagation process for a time-dependent wave operator which is then inserted in an iterative process (R.D.W.A. or S.C.M.) to yield the exact stationary wave operator. The merits of the wave operator formalism for quasi-adiabatic propagation are analysed, and possible improvements such as the use of partial adiabatic representations and spectral lters, are outlined. The proposed algorithm is applied to the test case of two coupled oscillators with variable coupling strength, and yields accurate results even with small switching times.