Simple and accurate method to evaluate tunneling splitting in polyatomic molecules

Abstract

A practical and accurate semiclassical method for calculating the tunneling splitting of the ground state in polyatomic molecules is presented based on a recent version of the instanton theory [J. Chem. Phys. 115, 6881 (2001)]. The method uses ab initio quantum chemical data for the potential energy surface without any concomitant extrapolation and requires only a small number of ab initio data points to get convergence even for large molecules. This enables one to use an advanced level of electronic structure theory and achieve a high accuracy of the result. The method is applied to the 9-atomic malonaldehyde molecule by making use of the potential energy surface at the level of CCSD(T) with the hybrid basis set of aug-cc-pVTZ (for oxygen atoms and the transferred hydrogen atom) and cc-pVTZ (for other atoms).

The ground state tunneling splitting of malonaldehyde: Accurate full dimensional quantum dynamics calculations

“…Such approximate methods might have a wider range of applicability by, e.g., allowing the use of on the fly techniques. As an example of such a comparison, the accurate tunneling splitting of 25.7Ϯ0.3 cm Ϫ1 obtained in the present work can be compared to the value of 30.7 cm Ϫ1 computed by MilЈnikov et al 17 using the instanton approach. The instanton approach overestimates the tunneling splitting by about 20%.…”

“…18 -24 However, due to the numerical effort for constructing a full-dimensional PES, the ab initio level has been restricted to the second-order Møller-Plesset perturbation theory. Thus the potential barrier height for hydrogen transfer of 3.2 kcal/mol is slightly low compared to higher level electronic structure methods ͑3.8 kcal/mol for CCSD͑T͒/͑aug-͒cc-PVTZ 17 28 -31 and allows the determination of excited states of high-dimensionality system. 32 The MCTDH 33,34 method has successfully been applied to study wave-packet dynamics in systems with a large number of degrees of freedom ͑see for example Refs.…”

“…Since then the determination of the ground state tunneling splitting of MA has been the focus of several studies ranging from reduced dimensionality quantum calculations 7,8 to elaborate full-dimensional semiclassical treatments. [9][10][11][12][13][14][15][16][17] Most of these studies employed MA as a test case for method development measuring the accuracy of the calculation by comparing the computed value of the ground state splitting with the experimental one.…”

Symmetric Double Proton Tunneling in Formic Acid Dimer: A Diabatic Basis Approach

“…Moreover these trends persist even when coupling is allowed between the surface modes and the other remaining modes of the model. Semi-classical instanton and WKB-like 9,10,[12][13][14][15]28 techniques have been applied to a wide range of double proton tunneling processes. Particularly noteworthy is the theory of Mil'nikov and Nakamura 29 that has been applied to FAD 12 to calculate tunneling splittings of the fundamentals in addition to the ground state.…”

Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Malonaldehyde and Tropolone

“…These results establish an independent benchmark comparison for the various semiclassical results. Mil'nikov and Nakamura [77] reformulated instanton theory to allow "practical" computations of multidimensional tunneling splittings which, with some refinements, was applied [78] to the 21D PES to obtain D 0 = 30.7 cm -1 .…”