Calculation of highly excited vibrational states of five-dimensional planar acetylene.

摘要

The 5-D vibrational states of a planar model of acetylene are obtained using pseudospectral methods. Potential matrix elements are diagonal and are evaluated on the grid points. Compact analytical expressions can be used to formulate the kinetic energy matrix elements. Fourier, Hermite and Laguerre pseudospectral basis sets are chosen and optimized with the potential energy for each degree of freedom to reduce the total number of basis in the active space. A 3-D stretch Hamiltonian is first solved and contracted to decrease the basis size. The 2-D angular Hamiltonian matrices are coupled with the radial part through potential energy terms in the off diagonal blocks to form the final 5-D matrix. Direct methods are used to solve the 5-D eigenvalue problems. Lanczos algorithm is applied on a smaller 5-D direct product basis to check the convergence of low energy states. Results are compared with the reported experimental and theoretical values.