Large-scale normal coordinate analysis for molecular structures

We apply truncated RQ-iteration (TRQ) and the Jacobi Davidson (JD) method t o perform vibrational ( eigenvalue) analysis for large-scale molecular syst ems. Both algorithms employ a preconditioned iterative solver to construct a low-dimensional subspace that contains desired vibrational modes. We disc uss several strategies for speeding up the eigenvalue calculation. In parti cular, we illustrate how to construct effective preconditioners and analyze the quality of these preconditioners. We show that convergence can be impr oved by choosing appropriate shifts and deflating the translational and rot ational modes. Numerical examples are provided to demonstrate the efficienc y of our computation.