Photochemical quantum dynamics

Another problem that awaits solution is photochemical quantum dynamics, in particular, tunneling dynamics in excited electronic states. From a theorist s point of view, this implies solving the curve crossing tunneling problem for a multidimensional case. 

Warshel A, Chu ZT (2001) Nature of the surface crossing process in bacteriorhodopsin computer simulations of the quantum dynamics of the primary photochemical event. J Phys Chem B 105 9857... 

In many chemical and even biological systems the use of an ab initio quantum dynamics method is either advantageous or mandatory. In particular, photochemical reactions may be most amenable to these methods because the dynamics of interest is often completed on a short (subpicosecond) timescale. The AIMS method has been developed to enable a realistic modeling of photochemical reactions, and in this review we have tried to provide a concise description of the method. We have highlighted (a) the obstacles that should be overcome whenever an ab initio quantum chemistry method is coupled to a quantum propagation method, (b) the wavefunction ansatz and fundamental... 

In addition to the analysis of the topology of a conical intersection, the quadratic expansion of the Hamiltonian matrix can be used as a new practical method to generate a subspace of active coordinates for quantum dynamics calculations. The cost of quantum dynamics simulations grows quickly with the number of nuclear degrees of freedom, and quantum dynamics simulations are often performed within a subspace of active coordinates (see, e.g., [46-50]). In this section we describe a method which enables the a priori selection of these important coordinates for a photochemical reaction. Directions that reduce the adiabatic energy difference are expected to lead faster to the conical intersection seam and will be called photoactive modes . The efficiency of quantum dynamics run in the subspace of these reduced coordinates will be illustrated with the photochemistry of benzene [31,51-53]. 

Two papers have been presented on the photochemistry of 5-methylphena-zinium salts in aqueous solution. Fluorescence, optical flash photolysis, and electron paramagnetic resonance (e.p.r.) techniques have been used to elucidate various aspects of product formation and quantum yield. Two products have been identified, namely the 5-methyl-10-hydrophenazinium cation radical (MPH ) and the pyocyanine (l-hydroxy-5-methyl-phenozinium) cation (PyH ) in a stoicheiometric ratio of 2 1. The quantum yield of formation of (MPH ) was found to be 0.29 0.03 at pH 7.0 and 1.1 0.1 at pH 3.0. The triplet state of MP (Ti) has also been detected by triplet-triplet absorption and is found to have a lifetime of 0.5 ns. Flash photolysis and e.p.r. have also been used to study a geminate triplet radical pair obtained from hydrogen abstraction by excited triplet acetone from propan-2-ol. The authors demonstrate that the geminate pairs contribute most of the polarization in photochemically-induced dynamic electron polarization (CIDEP) as compared with free random-phase pairs. 

This makes first-principles quantum dynamical studies of ultrafast electronic decay processes possible and thus opens the perspective of unraveling in detail the most elementary steps of photochemical d3mamics in polyatomic molecules. 

It should be stressed that the wave-packet picture of photophysical relaxation and photochemical reaction dynamics described in this chapter is substantially different from the traditional concepts in this area. In contrast to the established picture of radiationless transitions in terms of interacting tiers of zero-order molecular eigenstates, the dynamics is rationalized in terms of local properties of PE surfaces such as slopes, barriers and surface intersections, a view which now becomes widely accepted in photochemistry. This picture is firmly based on ah initio electronic-structure theory, and the molecular relaxation d3mamics is described on the basis of quantum mechanics, replacing previously prevaUing kinetic models of electronic decay processes. Such a more detailed and rigorous description of elementary photochemical processes appears timely in view of the rich and specific information on ultrafast chemical processes which is provided by modern time-resolved spectroscopy. " ... 

Process in Bacteriorhodopsin Computer Simulations of the Quantum Dynamics of the Primary Photochemical Event. 

A further model Hamiltonian that is tailored for the treatment of non-adiabatic systems is the vibronic coupling (VC) model of Koppel et al. [65]. This provides an analytic expression for PES coupled by non-adiabatic effects, which can be fitted to ab initio calculations using only a few data points. As a result, it is a useful tool in the description of photochemical systems. It is also very useful in the development of dynamics methods, as it provides realistic global surfaces that can be used both for exact quantum wavepacket dynamics and more approximate methods. 

Full quantum wavepacket studies on large molecules are impossible. This is not only due to the scaling of the method (exponential with the number of degrees of freedom), but also due to the difficulties of obtaining accurate functions of the coupled PES, which are required as analytic functions. Direct dynamics studies of photochemical systems bypass this latter problem by calculating the PES on-the-fly as it is required, and only where it is required. This is an exciting new field, which requires a synthesis of two existing branches of theoretical chemistry—electronic structure theory (quantum chemistiy) and mixed nuclear dynamics methods (quantum-semiclassical). 

Most of the AIMD simulations described in the literature have assumed that Newtonian dynamics was sufficient for the nuclei. While this is often justified, there are important cases where the quantum mechanical nature of the nuclei is crucial for even a qualitative understanding. For example, tunneling is intrinsically quantum mechanical and can be important in chemistry involving proton transfer. A second area where nuclei must be described quantum mechanically is when the BOA breaks down, as is always the case when multiple coupled electronic states participate in chemistry. In particular, photochemical processes are often dominated by conical intersections [14,15], where two electronic states are exactly degenerate and the BOA fails. In this chapter, we discuss our recent development of the ab initio multiple spawning (AIMS) method which solves the elecronic and nuclear Schrodinger equations simultaneously this makes AIMD approaches applicable for problems where quantum mechanical effects of both electrons and nuclei are important. We present an overview of what has been achieved, and make a special effort to point out areas where further improvements can be made. Theoretical aspects of the AIMS method are... 

The development of an ab initio quantum molecular dynamics method is guided by the need to overcome two main obstacles. First, one needs to develop an efficient, yet accurate, method for solving the electronic Schrodinger equation for both ground and excited electronic states. Second, the quantum mechanical character of the nuclear dynamics must be addressed. (This is necessary for the description of photochemical and tunneling processes.) This section provides a detailed discussion of the approaches we have taken to solve these two problems. 

We emphasize that the critical ion pair stilbene+, CA in the two photoactivation methodologies (i.e., charge-transfer activation as well as chloranil activation) is the same, and the different multiplicities of the ion pairs control only the timescale of reaction sequences.14 Moreover, based on the detailed kinetic analysis of the time-resolved absorption spectra and the effect of solvent polarity (and added salt) on photochemical efficiencies for the oxetane formation, it is readily concluded that the initially formed ion pair undergoes a slow coupling (kc - 108 s-1). Thus competition to form solvent-separated ion pairs as well as back electron transfer limits the quantum yields of oxetane production. Such ion-pair dynamics are readily modulated by choosing a solvent of low polarity for the efficient production of oxetane. Also note that a similar electron-transfer mechanism was demonstrated for the cycloaddition of a variety of diarylacetylenes with a quinone via the [D, A] complex56 (Scheme 12). 

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