Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer

Abstract

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Observation of the Low‐Frequency Spectrum of the Water Dimer as a Sensitive Test of the Water Dimer Potential and Dipole Moment Surfaces

“…Forschungsartikel predicted to be even about 7cm À1 lower in frequency, [27,50] as well as the K a = 0 ! 1(2s) transition cannot be observed here.…”

“…Thetwo AS tunneling levels are also denoted as (1s) and (2s) state.R ecent experimental [29,31,[43][44][45] and theoretical studies, [27,50] showed that the IC tunneling splitting can be dramatically increased upon vibrational excitation. Thetwo AS tunneling levels are also denoted as (1s) and (2s) state.R ecent experimental [29,31,[43][44][45] and theoretical studies, [27,50] showed that the IC tunneling splitting can be dramatically increased upon vibrational excitation.…”

“…[27,50] In the gas phase, [31,44] only the K a = 0 ! [27,50] In the gas phase, [31,44] only the K a = 0 !…”

“…Thee xperimental work has been supported by the cluster of excellence RESOLVf unded by the Deutsche Forschungsge- [a] Experimental energies are compared to theoretical predictions [27,50] of the low-frequency VRT levels and tunneling splittings for (H 2 O) 2 .V alues in parentheses denote the size of the interchange tunnelingsplitting. All values are given in cm À1 .…”

“…Given the experimental frequencyresolution of 1cm À1 in our present study,inthe ground state,only the AS tunneling splitting can be resolved. Thetwo AS tunneling levels are also denoted as (1s) and (2s) state.R ecent experimental [29,31,[43][44][45] and theoretical studies, [27,50] showed that the IC tunneling splitting can be dramatically increased upon vibrational excitation. Theselection rules in the G 16 molecular symmetry group are A 1 [47] Note that in Figure 2b the labeling of the E-states as either E 1 or E 2 is arbitrary and does not imply any further restrictions on selection rules.T ransitions between E-states are allowed as long as the selection rule + $À is fulfilled.…”