Quantum dynamical simulations

Often a degree of freedom moves very slowly for example, a heavy-atom coordinate. In that case, a plausible approach is to use a sudden approximation, i.e. fix that coordinate and do reduced dimensionality quantum-dynamics simulations on the remaining coordinates. A connnon application of this teclmique, in a three-dimensional case, is to fix the angle of approach to the target [120. 121] (see figure B3.4.14). 

While the classical approach to simulation of slow activated events, as described above, has received extensive attention in the literature and the methods are in general well established, the methods for quantum-dynamical simulation of reactive processes in complex systems in the condensed phase are still under development. We briefly consider electron and proton quantum dynamics. 

Drukker, K., Hammes-Schiffer, S. An analytical derivation of MC-SCF vibrational wave functions for the quantum dynamical simulation of multiple proton transfer reactions Initial application to protonated water chains. J. Chem. Phys. 107 (1997) 363-374. 

Berendsen, H.J.C., Mavri, J. Quantum dynamics simulation of a small quantum system embedded in a classical environment. In Quantum mechanical simulation methods for studying biological systems, D. Bicout and M. Field, eds. Springer, Berlin (1996) 157-179. 

Vendrell O, Gelabert R, Moreno M, Lluch M (2008) Operation of the proton wire in green fluorescent protein. A quantum dynamics simulation. J Phys Chem B 112 5500-5511... 

Following Fey nman s original work, several authors pmsued extensions of the effective potential idea to construct variational approximations for the quantum partition function (see, e g., Refs. 7,8). The importance of the path centroid variable in quantum activated rate processes was also explored and revealed, which gave rise to path integral quantum transition state theory and even more general approaches. The Centroid Molecular Dynamics (CMD) method for quantum dynamics simulation was also formulated. In the CMD method, the position centroid evolves classically on the efiective centroid potential. Various analysis and numerical tests for realistic systems have shown that CMD captures the main quantum effects for several processes in condensed matter such as transport phenomena. 

To illuminate the physical mechanism behind the efficient population of a preselected molecular target state, we employ quantum dynamics simulations and... 

Figure 6.19 Quantum dynamics simulations for the two distinct situations of selective population of the (a) upper and (b) the lower target state. The frame (iv) shows the population dynamics induced by the shaped laser field pictured in (iii). The remaining panels depict (ii) the oscillations of the laser field together with the induced dipole moment and (1) the induced energetic splitting in the X-A-subsystem along with the accessibility of the target states. Gray backgrounds highlight the relevant time windows that are discussed in the text.

M. Quack Prof. Zewail and Gerber, when you make an interpretation of your femtosecond observations (detection signal as a function of excitation), would it not be necessary to try a full quantum dynamical simulation of your experiment in order to obtain a match with your molecular, mechanistic picture of the dynamics or the detailed wavepacket evolution Agreement between experimental observation and theoretical simulation would then support the validity of the underlying interpretation (but it would not prove it). The scheme is of the following kind ... 

J. Manz The state of the art in the quantum dynamical simulations of molecular dynamics is, to the best of our knowledge, as follows ... 

The last years have witnessed tremendous progress in the theoretical description of surfaces and processes on surfaces. A variety of surface properties can now be described from first principles, i.e. without invoking any empirical parameters [1], In particular, whole potential energy surfaces (PES) can nowadays be mapped out by total energy calculations based on ab initio electronic structure theory. This development has also motivated new efforts in the dynamical treatment of adsorption/desorption processes in the last decade such as the development of efficient schemes for high-dimensional quantum dynamical simulations [2, 3]. 

Figure 7 A comparison of dissociation probabilities obtained from six-dimensional classical and quantum dynamics simulations for the H2/Cu(l 0 0) system [57]. There is good agreement between quantum and quasiclassical (for which hie molecule has initial vibrational energy equal to that of the quantum state) results.

Rego LGC, Batista VS. Quantum dynamics simulations of interfacial electron transfer in sensitized Ti02 semiconductors. J Am Chem Soc 2003 125 7989-97. 

While the accurate evaluation of electronic coupling (Tj/) among the different chromophores is also very difficult, and is undoubtedly sensitive to uncertainties in the experimental atomic coordinates, several studies (based either on ab initio electronic structure calculations [112e, 154] or a quantum dynamical simulation with parameters adjusted to reproduce experimental kinetic data ]156]) have yielded results in general accord with each other and also with earlier estimates inferred from experimental kinetic data based on a non-adiabatic model [152, 153]. The results are summarized in Table 6, and show two clear trends in coupling magnitudes ... 

Tif values obtained from phenomenological analysis of experimental kinetic data based on quantum dynamics simulation [156]. 

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]. 

In the photochemistry of benzene, the so-called channel 3 represents a well-known decay route along which fluorescence is quenched above a vibrational excess of 3000 cm [57], The decay takes place through a prefulvenic conical intersection characterized by an out of plane bending [52,58] and results in the formation of benzvalene and fulvene. The purpose of this study is to find distinct radiationless decay pathways that could be selected by exciting specific combinations of photoactive modes in the initial wavepacket created by a laser pulse. For this, we carry out quantum dynamics simulations on potential energy surfaces of reduced dimension, using the analysis outlined above for the choice of the coordinates. 

Quantum dynamics simulations were run within a nine-dimensional model subspace including the nine most important modes displayed on Fig. 10 and a fivedimensional model including only the pseudo-branching-plane modes 1 and 15, and the three out-of-plane photoactive modes 4, 16x, and 16 j [31,53]. The results were interpreted with regard to the topological features of the extended seam of conical intersection and their influence on the photoreactivity. This is illustrated with Fig. 11. 

It is interesting that both dynamical methods give the same gross mechanistic explanation (with very good matches for the coherent vibrational timescale), but crucially they differ in the precise nature of the coherent vibration observed. Both dynamics methods have their own deficiencies, and further quantum dynamical simulation with better potentials, more coupled vibrational modes, and longer simulation times are therefore desirable for this important system. Another possible fruitful method is using time-independent vibrational structure approaches, with similar potentials expanded around the unsaturated minima in the Jahn-Teller moat . Recent advances in such methodology should see this approach utilized in the near future [110, 111]. 

R J. Rossky (1998) Nonadiabatic quantum dynamics simulation using classical baths. In G. Ciccotti B. Berne, and D. Coker, editors, Classical and quantum dynamics in condensed phase simulations. World Scientific, Dordrecht, p. 515... 

The Hamiltonian in Eq. (4.1) has an almost product-like form since the majority of coordinates are treated as harmonic oscillators. This makes it rather suitable for quantum dynamics simulations, either in the time-dependent Hartree approximation [31] or using the more general multi-configuration time-dependent Hartree approach [36, 37]. 

---