Exact quantum dynamics background of dispersion interactions: case study for CH₄·Ar in full (12) dimensions

Abstract

A full-dimensional ab initio potential energy surface of spectroscopic quality is developed for the van-der-Waals complex of a methane molecule and an argon atom. Variational vibrational states are computed on this surface including all twelve (12) vibrational degrees of freedom of the methaneargon complex using the GENIUSH computer program and the Smolyak sparse grid method.The full-dimensional computations make it possible to study fine details of the interaction and distortion effects and to make a direct assessment of the reduced-dimensionality models often used in the quantum dynamics study of weakly bound complexes. A 12-dimensional (12D) vibrational computation including only a single harmonic oscillator basis function (9D) to describe the methane fragment (for which we use the ground-state effective structure as the reference structure) has a 0.40 cm −1 root-mean-square error (rms) with respect to the converged 12D bound-state excitation energies, which is less than half of the rms of the 3D model set up with the r 0 methane structure.Allowing 10 basis functions for the methane fragment, the rms of the bound state vibrational energies is reduced to 0.07 cm −1 , which is much better than the 3D models. The full-dimensional potential energy surface correctly describes the dissociation of the system, which together with further development of the variational (ro)vibrational methodology opens the route for the study of the role of dispersion forces on the excited methane vibrations and the energy transfer from the intra-to the intermolecular vibrational modes. * Gustavo Avila@telefonica.net †

Using nondirect product Wigner D basis functions and the symmetry-adapted Lanczos algorithm to compute the ro-vibrational spectrum of CH4–H2O

“…[28,30,58] If the amplitude of wavefunctions at singularities is not large, then it is possible to compute converged wavefunctions by using a large direct product basis. [59][60][61][62] This is true for the same reason that the expansion of an associated Legendre function Θ ,m=1 in a very large Θ ,m=0 basis can be made accurate almost everywhere. The price one pays for using a direct product basis is that it must be large.…”

CH4·F− revisited: full-dimensional ab initio potential energy surface and variational vibrational states

“…where n = 6, in Ref. [32]. The PES is determined using 9355 coefficients in a weighted leastsquares fit on the energy points, with a weight of (E0/(E0 + E))×(E1/(E1 + E)) with E0 = 0.05 hartree and E1 = 0.5 hartree applied on a given energy E relative to the global minimum of the data set.…”

“…Over the past decade, development is observed in several important directions, (a) coordinate representation and the kinetic energy operator [10,11,12,13,14,15,16,17]; (b) contraction techniques [3,4,5,6,7], (c) gridpruning techniques [1,18,19,20,21,22]; (d) collocation [23,24,25]; and (e) PES representation for high-dimensional quantum dynamics [26,27,28]; and (f) highly parallel computation of millions of states [29,30,31]. Methodological progress makes it possible to attenuate the exponential scale-up, including systems with large-amplitude motions [1,21,32].…”

“…The fluoridemethane complex is an excellent work horse for these developments. In comparison with methane-argon [1,32], the strong and anisotropic interaction with the fluoride introduces substantial distortions of the methane fragment and the interaction couples several methane rovibrational states.…”

A Smolyak algorithm adapted to a system-bath separation: application to an encapsulated molecule with large amplitude motions

“…The Smolyak method [13][14][15] has been used as an accurate and efficient tensor compression method for highdimensional grids and applied successfully to obtain the vibrational spectra of molecules up to 12 degrees of freedom [16][17][18][19][20][21][22][23][24][25]. At present, the approach is capable of treating a few tens of degrees of freedom, opening up a new direction for the improvement of quantum dynamics simulation [16, 18-20, 22, 23].…”