Symmetry-adapted filter diagonalization: Calculation of the vibrational spectrum of planar acetylene from correlation functions

Abstract

A Lorentzian function based spectral filter for calculating the energy of excited bound states in quantum mechanics Physical and mathematical content of coupled-cluster equations. II. On the origin of irregular solutions and their elimination via symmetry adaptation A symmetry-adapted filter-diagonalization method is used to calculate the vibrational spectrum of planar acetylene. In this method, vibrational eigenvalues in a given symmetry are obtained by solving a generalized eigenproblem in which the Hamiltonian and overlap matrices are assembled from symmetry-adapted correlation functions. Since no filtered state is explicitly needed, the calculation requires a relatively small memory. The numerical efficiency is further improved as the correlation functions belonging to various symmetry species are generated from a single wave packet. Comparison with existing data for the acetylene system confirms its accuracy and efficiency.

Quantum calculations of highly excited vibrational spectrum of sulfur dioxide. III. Emission spectra from the C̃ 1B2 state

“…[39][40][41] In particular, the eigenvalues were obtained from symmetry-adapted autocorrelation functions calculated by propagating a single wave packet. 42,43 The emission spectrum at those eigenvalues (⌺ (n) (E m )) was then calculated using Eq. ͑4͒ with the corresponding E m .…”

Quantum calculations of highly excited vibrational spectrum of sulfur dioxide. II. Normal to local mode transition and quantum stochasticity

“…The latter were calculated using a symmetry-enhanced propagation method that symmetrizes the propagation state at each time step. 45,46 This method is efficient because a single wave packet is propagated. An alternative is to symmetrize the hamiltonian to a block-diagonal form.…”

“…45,46 This approach yields 2K values for each symmetry-adapted correlation function from K propagation steps. The Chebyshev propagation was carried out for Kϭ90 000 steps with a random initial state, which took approximately 50 h on our 500 MHz DEC Alpha workstation.…”

Scattering and Bound States: A Lorentzian Function-Based Spectral Filter Approach

“…On the other hand, the iterative method has gained further popularity in recent years due to the development of a filter diagonalization (FD) scheme by Neuhauser 60-66 and others. 9,51,[67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86] A FD scheme involves an energy-dependent spectral filter, which acts on an arbitrary state to generate a basis set spanning a preselected energy window and uses it for the purpose of matrix diagonalization. Since the filter operator is usually expressed in a degenerate kernel infinite series 94 consisting of orthogonal polynomials (therefore satisfying a three-term recursion relation similar to eq 2), the FD scheme can also be visualized as yet another prescription for computing the coefficients, R k and β k , and the filtering process itself is akin to applying the "shift operator" as mentioned above.…”