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Quantum dynamics at conical intersections

Final Report Summary - QDYNCI (Quantum dynamics at conical intersections)

In this project, we aimed to understand better the mechanism through which chemical reactions proceed, especially in those cases in which nuclear quantum effects (zero-point energy, tunnelling and/or non-adiabatic effects) play a major role. We have focused on simple bimolecular processes, namely: (1) H + H2; (2) OH + H2; and (3) H + CH4. The interest in the hydrogen-exchange reaction (1) lies in the fact that its small size allows high-level calculations and thus a direct comparison to experiment. On the other hand, reaction (2) poses a computational challenge since diatom-diatom reactive collisions constitutes the state-of-the-art calculations, particularly concerning the computation of state-to-state reaction probabilities. Additionally, both systems present conical intersections. Moreover, reaction (3) has been chosen as the prototypical polyatomic bimolecular reaction.

The preliminary step in our project consisted in the calculation of the non-adiabatic effects at high energies on H + H2 [J. Chem. Phys. 128, 124322 (2008)]. The most relevant conclusions can be summarised as follows:
(i) the contribution of the excited state to the state-to-state reaction probabilities resulted negligible; and
(ii) the geometric phase effects cancelled completely in the integral cross sections.
However, despite the success of quantum dynamics methods, it is recognised that the study of chemical reactions suffers from major drawbacks:
(i) the exponential growth of the calculation with dimensionality, and
(ii) the accuracy and availability of potential energy surfaces (PES).

With respect to the dimensionality aspect, we have made use of a promising approach based on the path integral formalism: the recently developed ring polymer molecular dynamics method for the computation of reaction rates. In this method, quantum results can be obtained by performing classical dynamics of a necklace of system replicas linked through temperature-dependent harmonic potentials.

Regarding the PES, the computation of gradients for the dynamical calculation constitutes a formidable bottleneck. To overcome this, we have devised a simple solution based on hybrid potential energy surfaces. These result from the combination of an accurate ab initio second-order expansion of the energy around the saddle point region with a lower quality potential. Particularly, suitable are semiempirical methods, which present an advantage over conventional electronic structure ones: their computation is much faster than the latter, although they provide, in most of the cases, a qualitative description of the electronic energies.

The link between the two surfaces is achieved by means of polynomial switching functions and the transition from one description to another is based on the concept of the trust region. Hence, the combination of both levels of calculation results in an inexpensive improvement of the quality of the description, since the second order expansion is analytical. In addition to this, the semiempirical Hamiltonian is reparametrised with a set of coefficients, which are specific to a particular reaction or family of reactions, the specific reaction parameter approach.