Heavy Atom Tunneling in Organic Reactions at Coupled Cluster Potential Accuracy with a Parallel Implementation of Anharmonic Constant Calculations and Semiclassical Transition State Theory

A Perspective on the Investigation of Spectroscopy and Kinetics of Complex Molecular Systems with Semiclassical Approaches

In this Perspective we show that semiclassical methods provide a rigorous hierarchical way to study the vibrational spectroscopy and kinetics of complex molecular systems. The time averaged approach to spectroscopy and the semiclassical transition state theory for kinetics, which have been first adopted and then further developed in our group, provide accurate quantum results on rigorous physical grounds and can be applied even when dealing with a large number of degrees of freedom. In spectroscopy, the multiple coherent, divide-and-conquer, and adiabatically switched semiclassical approaches have practically permitted overcoming issues related to the convergence of results. In this Perspective we demonstrate the possibility of studying the semiclassical vibrational spectroscopy of a molecule adsorbed on an anatase (101) surface, a system made of 51 atoms. In kinetics, the semiclassical transition state theory is able to account for anharmonicity and the coupling between the reactive and bound modes. Our group has developed this technique for practical applications involving the study of phenomena like kinetic isotope effect, heavy atom tunneling, and elusive conformer lifetimes. Here, we show that our multidimensional anharmonic quantum approach is able to tackle on-the-fly the thermal kinetic rate constant of a 135 degree-of-freedom system. Overall, semiclassical methods open up the possibility to describe at the quantum mechanical level systems characterized by hundreds of degrees of freedom leading to the accurate spectroscopic and kinetic description of biomolecules and complex molecular systems.

A note on vibrational perturbation theory for tunneling splitting in a symmetric double well potential

The modified version of second and fourth order vibrational perturbation theory, whereby the Euclidean action for tunneling is computed on the inverted potential at a shifted energy that is ℏ2 dependent, is applied to a symmetric double well quartic potential. The mean energies of the doublets in each well are also computed using vibrational perturbation theory. Results show that the modified vibrational perturbation theory significantly improves the estimates of tunneling splitting energies both for the ground state and for excited state doublets.

Unbiased Comparison between Theoretical and Experimental Molecular Structures and Properties: Toward an Accurate Reduced-Cost Evaluation of Vibrational Contributions

The tremendous development of hardware and software is constantly increasing the role of quantum chemical (QC) computations in the assignment and interpretation of experimental results. However, an unbiased comparison between theory and experiment requires the proper account of vibrational averaging effects. In particular, high-resolution spectra in the gas phase are now available for molecules containing up to about 50 atoms, which are too large for a brute-force approach with the available QC methods of sufficient accuracy. In the present paper, we introduce hybrid approaches, which allow the accurate evaluation of vibrational averaging effects for molecules of this size beyond the harmonic approximation, with special attention being devoted to rotational constants. After the validation of new tools for relatively small molecules, the β-estradiol hormone and a prototypical molecular motor have been considered to witness the feasibility of accurate computations for large molecules.

Unraveling Water Solvation Effects with Quantum Mechanics/Molecular Mechanics Semiclassical Vibrational Spectroscopy: The Case of Thymidine

We introduce a quantum mechanics/molecular mechanics semiclassical method for studying the solvation process of molecules in water at the nuclear quantum mechanical level with atomistic detail. We employ it in vibrational spectroscopy calculations because this is a tool that is very sensitive to the molecular environment. Specifically, we look at the vibrational spectroscopy of thymidine in liquid water. We find that the C═O frequency red shift and the C═C frequency blue shift, experienced by thymidyne upon solvation, are mainly due to reciprocal polarization effects, that the molecule and the water solvent exert on each other, and nuclear zero-point energy effects. In general, this work provides an accurate and practical tool to study quantum vibrational spectroscopy in solution and condensed phase, incorporating high-level and computationally affordable descriptions of both electronic and nuclear problems.

Coupled Cluster Semiclassical Estimates of Experimental Reaction Rates: The Interconversion of Glycine Conformer VIp to Ip

We apply the full-dimensional Semiclassical Transition State Theory (SCTST) to estimate the rate constant of glycine molecule interconversion between the VIp and Ip conformers. We have reached an electronic structure accuracy up to the explicitly correlated Coupled Cluster method (CCSD(T)-F12b/cc-pVDZ-F12) thanks to our parallel implementation. The reaction has been experimentally investigated in the literature and is known to proceed by quantum mechanical tunneling. The SCTST rates improve over other theoretical methods, and our results align with the experimental measurements, thus confirming the accuracy of the fully coupled anharmonic semiclassical tunneling treatment, providing that the level of electronic structure theory gives a reliable estimate of the reaction barrier height and shape. The comparison with experimental half-life times supports the validity of SCTST for glycine VIp-Ip conformer conversion in the cryogenic temperature range, where this theory is usually not considered applicable due to the onset of the deep tunneling regime.

$\hbar ^{2}$ Expansion of the transmission probability through a barrier

Ninety years ago, Wigner derived the leading order expansionterm in $\hbar ^{2}$ for the tunneling rate through a symmetric barrier. Hisderivation included two contributions, one came from the parabolic barrier,but a second term involved the fourth order derivative of the potential atthe barrier top. He left us with a challenge which is answered in thispaper, to derive the same but for an asymmetric barrier. A crucial elementof the derivation is obtaining the $\hbar^{2}$ expansion term for theprojection operator which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (SCTST) reproduces the anharmonic corrections to the leading order of $\hbar^2$. The efficacy of the resulting expression is demonstrated for an Eckartbarrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, ratherthan the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of $\hbar$ and thus provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics and ring polymer molecular dynamics methods.

Defining the temperature of an isolated molecule

The microcanonical temperature of an isolated molecule is derived in terms of Boltzmann and Gibbs volume entropies within the quantum harmonic vibrational and equivalent degenerated model approximations. The effects of the entropy functional choice and various approximations are examined. The difference between Boltzmann and Gibbs volume temperatures is negligible for molecules bigger than ten atoms. However, it is significant for smaller systems, opening a way to probe them experimentally. A simple, analytical expression of the temperature as a function of the vibrational energy is provided, allowing predictions with a ±3% margin of error compared to the exact harmonic estimate. The microcanonical temperature is discussed and exemplified with polycyclic aromatic hydrocarbon molecules and other molecules of astrophysical interest.