On-the-fly molecular dynamics

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]. 

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],... 

On-the-fly molecular dynamics have been employed in order to simulate the photochemistry of carbonyl-containing compounds. The on-the-fly mechanism implemented in the MNDO program is the velocity-Verlet algorithm. Here an additional aspect of the usage of a computational cheap semiempirical method is visible. In order to provide realistic relative yields of different photochemical reactions, a large enough sample of trajectories is needed. For these systems, a substantial amount of trajectories (around 100) has been calculated for a relatively long timescale (up to 100 ps). 

On-the-fly molecular dynamics simulations in the first excited state of 7AI(H20)i 5 complexes were carried out at RI-ADC(2)/SVP-SV(P) level. The following conclusions concerning the excited-state proton-transfer process and the effect of the second hydration shell on it can be drawn from our results ... 

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 ... 

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... 

G. Csanyi et al Learn on the Fly A hybrid classical and quantum-mechanical molecular dynamics simulation. Phys. Rev. Lett. 93, 175503 (2004)... 

We wish to end this section by saying that now it is possible to perform molecular dynamics simulations on the fly without precomputing the potential energy surface. This idea was introduced by Carr and Parrinello344-345, and is known as the Carr-Parrinello dynamics. In this approach the nuclear motions are treated classically within the molecular dynamics method, but the energy and force are precomputed for each configuration of the nuclei with a suitable version of... 

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