Hindered rotor tunneling splittings: an application of the two-dimensional non-separable method to benzyl alcohol and two of its fluorine derivatives

Abstract

In this work we present a novel application of the two-dimensional non-separable (2D-NS) method to the calculation of torsional tunneling splittings in systems with two hindered internal rotors. This method could be considered an extension of one-dimensional methods for the case of compounds with two tops. The 2D-NS method includes coupling between torsions in the kinetic and potential energy. Specifically, it has been applied to benzyl alcohol (BA) and two of its fluorine derivatives: 3-fluorobenzyl alcohol (3FBA) and 4-fluorobenzyl alcohol (4FBA). These molecules present two torsions, i.e., about the -CH2OH (ϕ1) and -OH (ϕ2) groups. The electronic structure calculations to build the two-dimensional torsional potential energy surface were performed at the DF-LMP2-F12//DF-LMP2/cc-pVQZ level of theory. For BA and 4FBA the calculated ground-state vibrational level splittings are 429 and 453 MHz, respectively, in good agreement with the experimental values of 337.10 and 492.82 MHz, respectively. In these two cases there are four equivalent wells and the tunneling splitting is the result of transitions between the two closer minima along ϕ1. The analysis of the wavefunctions, as well as the previous experimental work on the system, supports this conclusion. For 3FBA the observed ground-state splitting is 0.82 MHz, whereas in this case the calculated value amounts only to 0.02 MHz. The 2D-NS method, through the analysis of the wavefunctions, shows that this tiny tunneling splitting occurs between the two most stable minima of the potential energy surface. Additionally, we predict that the first vibrationally excited tunneling splitting will also be small and exclusively due to the interconversion between the second lowest minima.

Understanding benzyl alcohol aggregation by chiral modification: the pairing step

“…The global minima of B are two mirrorimage conformers with both dihedrals synchronized in gauche arrangements with the same sign: G−g− and G+g+ (Fig. 2), in agreement with previous calculations 13, [48][49][50][51][52] and results from rotational spectroscopy 51 . They can interconvert via a shallow barrier of 2.0 kJ mol −1 (B3LYP-D3, zero-point corrected), even down to low conformational temperatures in a jet expansion.…”

“…This has attracted considerable interest in recent years for B and its derivatives. [51][52][53][54][55][56][57][58] The gas phase conformation resembles the one in the crystal structure. 31 Another conformer is predicted with an eclipsed (E) respectively trans (t) arrangement of the dihedrals, with all heavy atoms and the hydroxy hydrogen (almost) in the plane of the phenyl ring.…”

Anharmonicity of Coupled Torsions: The Extended Two-Dimensional Torsion Method and Its Use To Assess More Approximate Methods

“…The 2D-NS partition function is obtained from the direct sum of the eigenvalues E j obtained from eq 14 divided by the symmetry number due to the torsions, σ tor : Qtor2D−NS=1σtor∑je−βEj and, therefore, the method can also be used to calculate the tunneling splitting of the lowest vibrational level due to torsional motion. 18…”

“…and, therefore, the method can also be used to calculate the tunneling splitting of the lowest vibrational level due to torsional motion. 18 The 2D-NS method is usually prohibitively expensive to extend to more than two degrees of freedom because of the size of the matrix to diagonalize when using the variational method. PG proposed an approximation that avoids solving the Schrodinger equation but corrects for quantum effects with a multiplicative factor F q given by the ratio between the quantum and classical partition harmonic oscillator partition functions at the global minimum.…”

Simple models for the quick estimation of ground state hydrogen tunneling splittings in alcohols and other compounds

“…Here, a two-dimensional approach is more appropriate for the complex tunneling motion in this alcohol. 102…”