Direct nonadiabatic dynamics

The approximations defining minimal END, that is, direct nonadiabatic dynamics with classical nuclei and quantum electrons described by a single complex determinantal wave function constructed from nonoithogonal spin... 

Electron nuclear dynamics theory is a direct nonadiabatic dynamics approach to molecular processes and uses an electronic basis of atomic orbitals attached to dynamical centers, whose positions and momenta are dynamical variables. Although computationally intensive, this approach is general and has a systematic hierarchy of approximations when applied in an ab initio fashion. It can also be applied with semiempirical treatment of electronic degrees of freedom [4]. It is important to recognize that the reactants in this approach are not forced to follow a certain reaction path but for a given set of initial conditions the entire system evolves in time in a completely dynamical manner dictated by the interparticle interactions. 

In the case of direct nonadiabatic dynamics the rendering of dynamical events needs some rethinking. When the nuclei are treated as classical particles or by narrow wave packets movies of dynamically changing ball and stick models can be quite effective and informative. It is possible to use the rendering of such trajectories for finding errors in the dynamics and to illustrate mechanisms. 

This chapter focused on the role of photon polarization in producing ultrafast Jt-electron rotation by a single-color laser. If a two-color laser is employed, its relative optical phase can be another controlling factor for the rotation direction of Jt electrons [17, 39]. The next step is to extend the series of our studies to cover ultrafast nonadiabatic dynamics of chiral aromatic molecules in laser fields of arbitrary polarization. 

Basic questions are analyzed, as is the case for the photochemistry of formaldehyde. Contrary to previous results, direct quantum dynamics simulations showed that the H2 + CO H + HCO branching ratio in the Si/Sq nonadiabatic photodissociation of formaldehyde is controlled by the direction and size of the mean momentum of the wavepacket when it crosses the seam of conical intersection. In practice, if the wavepacket falls down from the barrier to the conical intersection with no initial momentum the system leads to H2 + CO, while an extra momentum toward products favors... 

A semiclassical description is well established when both the Hamilton operator of the system and the quantity to be calculated have a well-defined classical analog. For example, there exist several semiclassical methods for calculating the vibrational autocorrelation function on a single excited electronic surface, the Fourier transform of which yields the Franck-Condon spectrum. ° In particular, semiclassical methods based on the initial-value representation of the semiclassical propagator,which circumvent the cumbersome root-search problem in boundary-value based semiclassical methods, have been successfully applied to a variety of systems (see, for example, the reviews Refs. 85, 86 and references therein). These methods cannot directly be applied to nonadiabatic dynamics, though, because the Hamilton operator for the vibronic coupling problem [Eq. (1)] involves discrete degrees of freedom (discrete electronic states) which do not possess an obvious classical counterpart. 

Worth, G. A., Hunt, R, 8c Robb, M. A. (2003). Nonadiabatic dynamics A comparison of surface hopping direct dynamics with quantum wavepacket calculations. The Journal of Physical Chemistry A, 107(5), 621-631. 

Persico M, Granucci G (2014) An overview of nonadiabatic dynamics simulations methods, with focus on the direct approach versus the fitting of potential energy surfaces. Theor Chem Acc 133 1526... 

Abstract We present a general theoretical approach for the simulation and control of ultrafast processes in complex molecular systems. It is based on the combination of quantum chemical nonadiabatic dynamics on the fly with the Wigner distribution approach for simulation and control of laser-induced ultrafast processes. Specifically, we have developed a procedure for the nonadiabatic dynamics in the framework of time-dependent density functional theory using localized basis sets, which is applicable to a large class of molecules and clusters. This has been combined with our general approach for the simulation of time-resolved photoelectron spectra that represents a powerful tool to identify the mechanism of nonadiabatic processes, which has been illustrated on the example of ultrafast photodynamics of furan. Furthermore, we present our field-induced surface hopping (FISH) method which allows to include laser fields directly into the nonadiabatic... 

In order to establish the connection of the experimentally optimized pulse shapes with the underlying dynamical processes as well as between theoretically and experimentally optimized pulses, developments of theoretical methods are needed which allow for the design of interpretable laser pulses for complex systems. To avoid the obstacle of precalculating multidimensional PES, ab-initio adiabatic and in particular nonadiabatic MD on the fly is parlicularly suifable provided fhaf an accurate description of the electronic structure is feasible [56], In addition, this approach offers the advantages that the MD on the fly can be applied fo relatively complex systems and can be also directly connected with different procedures for optimal control [56-58]. Moreover, as recently proposed by us, it is particularly convenient to introduce the field direcfly in ihe nonadiabatic dynamics which can be then optimized as desired [59]. 

Obviously, the BO or the adiabatic states only serve as a basis, albeit a useful basis if they are determined accurately, for such evolving states, and one may ask whether another, less costly, basis could be Just as useful. The electron nuclear dynamics (END) theory [1-4] treats the simultaneous dynamics of electrons and nuclei and may be characterized as a time-dependent, fully nonadiabatic approach to direct dynamics. The END equations that approximate the time-dependent Schrddinger equation are derived by employing the time-dependent variational principle (TDVP). 

For example, the ZN theory, which overcomes all the defects of the Landau-Zener-Stueckelberg theory, can be incorporated into various simulation methods in order to clarify the mechanisms of dynamics in realistic molecular systems. Since the nonadiabatic coupling is a vector and thus we can always determine the relevant one-dimensional (ID) direction of the transition in multidimensional space, the 1D ZN theory can be usefully utilized. Furthermore, the comprehension of reaction mechanisms can be deepened, since the formulas are given in simple analytical expressions. Since it is not feasible to treat realistic large systems fully quantum mechanically, it would be appropriate to incorporate the ZN theory into some kind of semiclassical methods. The promising semiclassical methods are (1) the initial value... 

---