A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions

Abstract

Articles you may be interested inUsing a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrödinger equation for C2H4 J. Chem. Phys. 135, 064101 (2011); 10.1063/1.3617249Using nonproduct quadrature grids to solve the vibrational Schrödinger equation in 12DA finite basis representation Lanczos calculation of the bend energy levels of methaneWe present a contracted basis-iterative method for calculating numerically exact vibrational energy levels of methane ͑a 9D calculation͒. The basis functions we use are products of eigenfunctions of bend and stretch Hamiltonians obtained by freezing coordinates at equilibrium. The basis functions represent the desired wavefunctions well, yet are simple enough that matrix-vector products may be evaluated efficiently. We use Radau polyspherical coordinates. The bend functions are computed in a nondirect product finite basis representation ͓J. Chem. Phys. 118, 6956 ͑2003͔͒ and the stretch functions are computed in a product potential optimized discrete variable ͑PODVR͒ basis. The memory required to store the bend basis is reduced by a factor of ten by storing it on a compacted grid. The stretch basis is optimized by discarding PODVR functions with high potential energies. The size of the primitive basis is 33 billion. The size of the product contracted basis is six orders of magnitude smaller. Parity symmetry and exchange symmetry between two of the H atoms are employed in the final product contracted basis. A large number of vibrational levels are well converged. These include almost all states up to 8000 cm Ϫ1 and some higher local mode stretch bands.

Global Analytical Potential Energy Surfaces for High‐resolution Molecular Spectroscopy and Reaction Dynamics

“…In a previous paper (Bentley et al 1992), a DVR method was used on a potential energy surface for the HCN/HNC system of similar quality as that developed by Bowman et al (1993), and deviations from experimental vibrational term values were as large as 150 cm −1 . With improved computer power and the development of refined algorithms to solve equation (1), the numerical precision of calculations of vibrational eigenvalues given a PES has increased, in the last years, to better than 1 cm −1 for to up to penta-atomic molecules, typically (Wang and Carrington 2003a,b, Luckhaus 2003, Shirin et al 2003, Richter et al 2007, Iung and Pasin 2007). The largest uncertainties as compared to experiment thus arise from the underlying potential hypersurface.…”

Rovibronic analysis of the Jahn–Teller effect in CH2D2+ at low energies

“…Studies of the nine-dimensional nuclear motion on the three electronic potential surfaces arising from the triply degenerate ground state still represent a challenge, but recent progress in vibrational calculations in molecular systems of similar complexity suggests that an adequate treatment may become available soon. 7,8 Photoelectron spectroscopy of CH 4 and its deuterated isotopomers in the gas phase [9][10][11][12][13][14][15][16][17] and electron paramagnetic resonance ͑EPR͒ spectroscopy of CH 4 + and its deuterated isotopomers in rare gas matrices [18][19][20] have been the main spectroscopic methods with which information on the methane cation has been obtained experimentally.…”

Survey of the high resolution infrared spectrum of methane (12CH4 and 13CH4): Partial vibrational assignment extended towards 12 000 cm−1

“…[1][2][3][4][5][6][7] Its current interest ranges from quantum dynamics and chemical reactions on potential hypersurfaces on the one hand [8][9][10][11][12][13][14][15][16][17][18][19][20] to atmospheric and astrophysical spectroscopy including its effects as a greenhouse gas on the other hand. [21][22][23][24][25][26][27][28][29][30][31][32][33][34] Methane combustion with a reaction enthalpy R H 0 0 −800 kJ mol −1 is also among the largest chemical processes of mankind at a technical scale for energy production in the TJ range per year.…”