On-the-fly dynamics

We now briefly describe the way in which the nonadiabatic event (surface hop) can be described in on the fly dynamics methods. We can represent the time-dependent wavefunction in the Cl space as a vector ... 

On-the-fly dynamics simulations in the Si excited state were carried out for all 7AI(H20)i 5 complexes described above. The simulated trajectories were sorted into two types of reaction (1) ESPT when 7AI tautomerization is... 

Asturiol D, Lasorne B, Robb MA, Blancafoit L (2009) Photophysics of the pi.pi and n,pi states of thymine Ms-caspt2 minimum-energy paths and casscf on-the-fly dynamics. J Phys Chem A 113 10211... 

Asturiol, D., Lasorne, B., Robb, M. A., Blancafort, L. (2009). Photophysics of the tttt and n,7T states of thymine MS-CASPT2 minimum energy paths and CASSCF on-the-fly dynamics. The Journal of Physical Chemistry A, 113(38), 10211-10218. doi 10.1021/jp905303g. 

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

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). 

In the examples described above, the UltraLink is associated with the extracted concepts. To augment its flexibility and applicability, we allow for a dynamic UltraLink construction from a portion of text selected by the user. When the user selects a section of a document with the mouse, a list of UltraLinks is generated on the fly on release of the mouse button as shown in Figure 31.4A. Furthermore, the Web Interface allows for several UltraLink windows to be opened simultaneously as shown in Figure 31.4B. 

On the potential energy surfaces thus obtained 2D wavepacket dynamics calculations have been performed in the diabatic state representation. The reduced massses are regarded as those of CH2-ethylene system. The validity was examined by using on-the-fly ab initio molecular dynamics that were supplementarily performed. The dynamics calculations performed are composed of the following steps ... 

Zgierski and coworkers proposed for guanine the same biradical mechanism that was proposed for all the other bases [172], Furthermore, on the fly molecular dynamics using density functional theory have been used to study initial evolution along the Si surface of methylated guanine [167-169],... 

With the characterized mechanism, the next key question is the origin of its catalytic power. A prerequisite for this investigation is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio QM/MM approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9... 

The basic idea underlying AIMD is to compute the forces acting on the nuclei by use of quantum mechanical DFT-based calculations. In the Car-Parrinello method [10], the electronic degrees of freedom (as described by the Kohn-Sham orbitals y/i(r)) are treated as dynamic classical variables. In this way, electronic-structure calculations are performed on-the-fly as the molecular dynamics trajectory is generated. Car and Parrinello specified system dynamics by postulating a classical Lagrangian ... 

Semiclassical techniques like the instanton approach [211] can be applied to tunneling splittings. Finally, one can exploit the close correspondence between the classical and the quantum treatment of a harmonic oscillator and treat the nuclear dynamics classically. From the classical trajectories, correlation functions can be extracted and transformed into spectra. The particular charm of this method rests in the option to carry out the dynamics on the fly, using Born Oppenheimer or fictitious Car Parrinello dynamics [212]. Furthermore, multiple minima on the hypersurface can be treated together as they are accessed by thermal excitation. This makes these methods particularly useful for liquid state or other thermally excited system simulations. Nevertheless, molecular dynamics and Monte Carlo simulations can also provide insights into cold gas-phase cluster formation [213], if a reliable force field is available [189]. 

Another major, future advance in the quantum chemical computation of potential energy surfaces for reaction dynamics will be the ability to routinely compute the energies of molecular systems on the fly . The tedious and time-consuming process of fitting computed quantum chemical values to functional forms could be avoided if it were possible to compute the PES as needed during a classical trajectory or quantum dynamics calculation. For many chemical reactions, it should be practical in the near future to prudently select a sufficiently rapid and accurate electronic structure method to facilitate dynamics computations on the fly. 

In recent years, dynamic calculations of both the electronic and the molecular structure of complex molecular systems have started to become feasible. " These methods are based on the general idea that the electronic structure of the system is to be calculated on the fly as the nuclei move, while the nuclei respond to the forces determined from the dynamically calculated electronic structure. This assumes that the system moves on the lowest electronic state, and transitions between states are either ignored (because they are well separated in energy) or treated semiclassi-cally. 

The explanation of classical MD given above was meant in part to emphasize that the dynamics of atoms can be described provided that the potential energy of the atoms, U U(ru. .., r3N), is known as a function of the atomic coordinates. It has probably already occurred to you that a natural use of DFT calculations might be to perform molecular dynamics by calculating U U(r, ..., r3N) with DFT. That is, the potential energy of the system of interest can be calculated on the fly using quantum mechanics. This is the basic concept of ab initio MD. The Lagrangian for this approach can be written as... 

This relation provides a simple closure to the iGLE in which the microscopic dynamics is connected to the macroscopic behavior. Because of this closure, the microscopic dynamics are said to depend self-consistently on the macroscopic (averaged) trajectory. Formally, this construction is well-defined in the sense that if the true (R(t)) is known a priori, then the system of equations return to that of the iGLE with a known g(t). In practice, the simulations are performed either by iteration of (R(t)) in which a new trajectory is calculated at each step and (R(t)) is revised for the next step, propagation of a large number of trajectories with (R(t)) calculated on-the-fly, or some combination thereof. 

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