Enhanced Method for Determining Rovibrational Eigenstates of van der Waals Molecules

A complex guided spectral transform Lanczos method for studying quantum resonance states

A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths, and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore, the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO2, and compared to previous calculations.

CALCULATION OF TRANSITION AMPLITUDES WITH A SINGLE LANCZOS PROPAGATION

We review in this article a recently proposed energy-global method that is capable of calculating the entire transition amplitude matrix with a single Lanczos propagation. This method requires neither explicit computation nor storage of the eigenfunctions, rendering it extremely memory efficient. Procedures are proposed to handle situations where "spurious" eigenvalues aggregate around true eigenvalues due to round-off errors. This method is amenable to both real-symmetric and complex-symmetric Hamiltonians. Applications to molecular spectra and reactive scattering are presented. Its relationships with other methods are also discussed.

Spectroscopy of Ar–SH and Ar–SD. II. Determination of the three-dimensional intermolecular potential-energy surface

All the pure rotational transitions reported in the previous studies [J. Chem. Phys. 113, 10121 (2000); J. Mol. Spectrosc. 222, 22 (2003)] and newly observed rotation-vibration transitions, P = 1/2 <-- 3/2, for Ar-SH and Ar-SD [J. Chem. Phys. (2005), the preceding paper] have been simultaneously analyzed to determine a new intermolecular potential-energy surface of Ar-SH in the ground state. A Schrodinger equation considering the three-dimensional freedom of motion for an atom-diatom complex in the Jacobi coordinate, R, theta, and r, was numerically solved to obtain energies of the rovibrational levels using the discrete variable representation method. A three-dimensional potential-energy surface is determined by a least-squares fitting with initial values of the parameters for the potential obtained by ab initio calculations at the RCCSD(T)/aug-cc-pVTZ level of theory. The potential well reproduces all the observed data in the microwave and millimeter wave regions with parity doublings and hyperfine splittings. Several low-lying rovibrational energies are calculated using the new potential-energy surface. The dependence of the interaction energy between Ar and SH(2pi(i)) on the bond length of the SH monomer is discussed.

Iterative solutions with energy selected bases for highly excited vibrations of tetra-atomic molecules

The use of energy selected bases (ESB) with iterative diagonalization of the Hamiltonian matrix is described for vibrations of tetra-atomic systems. The performance of the method is tested by computing vibrational states of HOOH below 10,000 cm(-1) (1296 A+ symmetry states) and H(2)CO below 13,500 cm(-1) (729 A(1) symmetry states). For iterative solutions, we tested both the implicitly restarted Lanczos method (IRLM) and the standard (nonreorthogonalizing) Lanczos approach. Comparison with other contracted basis approach as well as direct product grid representation shows superior performance of the ESB/IRLM approach. Of the two systems, H(2)CO is found to be more challenging than HOOH since it has much stronger couplings among vibrational modes, which leads to a drastically larger primitive basis set. For H(2)CO we also discuss some interesting behavior of the molecule in the high internal energy regime.