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Register a new userSemiclassical instanton formulation of Marcus-Levich-Jortner theory
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Marcus-Levich-Jortner (MLJ) theory is one of the most commonly used methods for including nuclear quantum effects into the calculation of electron-transfer rates and for interpreting experimental data. It divides the molecular problem into a subsystem treated quantum-mechanically by Fermis golden rule and a solvent bath treated by classical Marcus theory. As an extension of this idea, we here present a reduced semiclassical instanton theory, which is a multiscale method for simulating quantum tunnelling of the subsystem in molecular detail in the presence of a harmonic bath. We demonstrate that instanton theory is typically significantly more accurate than the cumulant expansion or the semiclassical Franck-Condon sum, which can give orders-of-magnitude errors and in general do not obey detailed balance. As opposed to MLJ theory, which is based on wavefunctions, instanton theory is based on path integrals and thus does not require solutions of the Schrodinger equation, nor even global knowledge of the ground- and excited-state potentials within the subsystem. It can thus be efficiently applied to complex, anharmonic multidimensional subsystems without making further approximations. In addition to predicting accurate rates, instanton theory gives a high level of insight into the reaction mechanism by locating the dominant tunnelling pathway as well as providing information on the reactant and product vibrational states involved in the reaction and the activation energy in the bath similarly to what would be found with MLJ theory.
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Fermis golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be calculated if the wave functions of all internal states are known, which is typically not the case in molecular systems. Marcus theory provides a closed-form expression for the rate constant, which is a classical limit of the golden rule, and indicates the existence of a normal regime and an inverted regime. Semiclassical instanton theory presents a more accurate approximation to the golden-rule rate including nuclear quantum effects such as tunnelling, which has so far been applicable to complex anharmonic systems in the normal regime only. In this paper we extend the instanton method to the inverted regime and study the properties of the periodic orbit, which describes the tunnelling mechanism via two imaginary-time trajectories, one of which now travels in negative imaginary time. It is known that tunnelling is particularly prevalent in the inverted regime, even at room temperature, and thus this method is expected to be useful in studying a wide range of molecular transitions occurring in this regime.
We discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting t-NEVPT2 method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics. We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules, and outline directions for the future.
Electron transfer organic reaction rates are considered employing the classic physical picture of Marcus wherein the heats of reaction are deposited as the energy of low frequency mechanical oscillations of reconfigured molecular positions. If such electron transfer chemical reaction events occur in the neighborhood of metallic plates, then electrodynamic interface fields must also be considered in addition to mechanical oscillations. Such electrodynamic interfacial electric fields in principle strongly effect the chemical reaction rates. The thermodynamic states of the metal are unchanged by the reaction which implies that metallic plates are purely catalytic chemical agents.
In the pioneering work by R. A. Marcus, the solvation effect on electron transfer (ET) processes was investigated, giving rise to the celebrated nonadiabatic ET rate formula. In this work, on the basis of the thermodynamic solvation potentials analysis, we reexamine Marcus formula with respect to the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Interestingly, the obtained RRKM analogue, which recovers the original Marcus rate that is in a linear solvation scenario, is also applicable to the nonlinear solvation scenarios, where the multiple curve{crossing of solvation potentials exists. Parallelly, we revisit the corresponding Fermis golden rule results, with some critical comments against the RRKM analogue proposed in this work. For illustration, we consider the quadratic solvation scenarios, on the basis of physically well-supported descriptors.
We describe how the semiclassical theory of radical pair recombination reactions recently introduced by two of us [D. E. Manolopoulos and P. J. Hore, J. Chem. Phys. 139, 124106 (2013)] can be generalised to allow for different singlet and triplet recombination rates. This is a non-trivial generalisation because when the recombination rates are different the recombination process is dynamically coupled to the coherent electron spin dynamics of the radical pair. Furthermore, because the recombination operator is a two-electron operator, it is no longer sufficient simply to consider the two electrons as classical vectors: one has to consider the complete set of 16 two-electron spin operators as independent classical variables. The resulting semiclassical theory is first validated by comparison with exact quantum mechanical results for a model radical pair containing 12 nuclear spins. It is then used to shed light on the spin dynamics of a carotenoid-porphyrin-fullerene (CPF) triad containing considerably more nuclear spins which has recently been used to establish a proof of principle for the operation of a chemical compass [K. Maeda et al., Nature 453, 387 (2008)]. We find in particular that the intriguing biphasic behaviour that has been observed in the effect of an Earth-strength magnetic field on the time-dependent survival probability of the photo-excited C+PF- radical pair arises from a delicate balance between its asymmetric recombination and the relaxation of the electron spin in the carotenoid radical.
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