Quantum theory of bimolecular chemical reactions

In this review we discuss quantum dynamically based theoretical methods for studying bimolecular gas phase chemical reactions. The scope is largely limited to reactions occurring on a single Born-Oppenheimer potential energy surface and mainly to time-independent Hamiltonians. An introductory overview is given, which includes a general discussion on approaches aiming to solve the time-independent and the time-dependent Schrodinger equation respectively, and how the resulting scattering matrix can be related to observables. The main topics of the review are the time-dependent wavepacket and the time-independent hyperspherical coordinate approaches to quantum dynamics. To perform such calculations it is necessary to first specify the relevant Hamiltonian operator, which has a kinetic and a potential part. The kinetic energy operator is easy to obtain in Cartesian coordinates, but more cumbersome in curvilinear coordinates. Two procedures are described. We also describe how to obtain the potential energy surfaces. The required input data are often obtained using ab initio methods, which themselves are not discussed. A very brief section on Green function methods for quantum scattering is also included. Rigorous quantum dynamic calculations quickly become expensive as the size of the problem grows. Therefore, reduced dimensionality calculations are often performed. However, only the most important degrees of freedom are treated explicitly. We discuss how the other degrees of freedom can be handled. An alternative way to reduce computational cost is to use semiclassical approaches, which have recently received renewed interest and we briefly review the main approaches. A few examples of reactions that have been studied with quantum dynamic theories are also included.