ABSTRACT
In this work we present the extended two-dimensional torsion (E2DT) method and use it to analyze the performance of several methods that incorporate torsional anharmonicity more approximately for calculating rotational-vibrational partition functions. Twenty molecules having two hindered rotors were studied for temperatures between 100 and 2500 K. These molecules present several kinds of situations; they include molecules with nearly separable rotors, molecules in which the reduced moments of inertia change substantially with the internal rotation, and molecules presenting compound rotation. Partition functions obtained by the rigid-rotor harmonic oscillator approximation, a method involving global separability of torsions and the multistructural methods without explicit potential coupling [MS-T(U)] and with explicit potential coupling [MS-T(C)] of torsions, are compared to those obtained with a quantized version - called the extended two-dimensional torsion (E2DT) method - of the extended hindered rotor approximation of Vansteenkiste et al. ( Vansteenkiste et al. J. Chem. Phys. 2006 , 124 , 044314 ). In the E2DT method, quantum effects due to the torsional modes were incorporated by the two-dimensional nonseparable method, which is a method that is based on the solution of the torsional Schrödinger equation and that includes full coupling in both the kinetic and potential energy. By comparing other methods to the E2DT method and to experimental thermochemical data, this study concludes that the harmonic approximation yields very poor results at high temperatures; the global separation of torsions from the rest of the degrees of freedom is not justified even when an accurate method to treat the torsions is employed; it is confirmed that methods based on less complete potential energy coupling of torsions, such as MS-T(U), are not accurate when dealing with rotors with different barrier heights, and more complete inclusion of torsional coupling to the method in MS-T(C) improves substantially the results in such a way that it could be used in cases where the E2DT method is unaffordable.
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 (Ï1) and -OH (Ï2) 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 Ï1. 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.
ABSTRACT
In this work we apply multipath canonical variational transition state theory with small-tunneling corrections (MP-CVT/SCT) to the hydrogen abstraction reaction from ethanol by atomic hydrogen in aqueous solution at room temperature. This reaction presents two transition states which can interconvert by internal rotations about single bonds and another two transition states that are non-interconvertible enantiomers to the former structures. The study also includes another three reactions with isotopically substituted species for which there are experimental values of thermal rate constants and kinetic isotope effects (KIEs). The agreement between the MP-CVT/SCT thermal rate constants and the experimental data is good. The KIEs obtained by the MP-CVT/SCT methodology are factorized in terms of individual transition state contributions to facilitate the analysis. It was found that the percentage contribution of each transition state to the total KIE is independent of the isotopic substitution.
ABSTRACT
We present the application of an accurate quantum treatment, called two-dimensional non-separable (2D-NS), to the calculation of internal rotation partition functions of molecules with two rotors. This methodology involves full coupling in the kinetic and potential energies; the later is written as a Fourier series type potential. The resulting Hamiltonian is introduced in the Schrödinger equation and solved by the variational method. The method was applied to the 2-propenol and to the 3-fluoro-2-propenol molecular systems. The former molecule presents weak coupling between the torsion, whereas the later is an example of strong coupling. The comparison of 2D-NS with one-dimensional accurate models that involve separation of the two torsions, indicate that a separable model is inadequate to study systems in the strong coupling regime. The results indicate that for the case of strong coupling the multi-conformer harmonic approximation gives better results than a separable anharmonic model.
