Local control theory in trajectory-based nonadiabatic dynamics

Abstract

In this paper, we extend the implementation of nonadiabatic molecular dynamics within the framework of time-dependent density-functional theory in an external field described in Tavernelli et al. [Phys. Rev. A 81, 052508 (2010)] by calculating on-the-fly pulses to control the population transfer between electronic states using local control theory. Using Tully's fewest switches trajectory surface hopping method, we perform MD to control the photoexcitation of LiF and compare the results to quantum dynamics (QD) calculations performed within the Heidelberg multiconfiguration time-dependent Hartree package. We show that this approach is able to calculate a field that controls the population transfer between electronic states. The calculated field is in good agreement with that obtained from QD, and the differences that arise are discussed in detail. CURCHOD, PENFOLD, ROTHLISBERGER, AND TAVERNELLI PHYSICAL REVIEW A 84, 042507 (2011) * J (r; R)Ĥ el I (r; R)d r, (2.4) d J I,γ (R) are the first-order nonadiabatic coupling vectors, defined as d J I,γ (R) = * J (r; R)[∇ γ I (r; R)]d r, (2.5) and D J I,γ (R) are the second-order nonadiabatic coupling elements given by D J I,γ (R) = * J (r; R) ∇ 2 γ I (r; R) d r.(2.6)

Ab Initio Nonadiabatic Quantum Molecular Dynamics

“…This approach has also been explored for other trajectorybased nonadiabatic methods. [172][173][174][175][176][177][178][179][180][181] The light/matter interaction term, in the dipole approximation, can easily be included in the Hamiltonian matrix and the spawning algorithm modified accordingly. The influence of laser pulse characteristics -such as intensity, carrier-envelope phase (CEP), or duration -on the excitation process can also be studied in detail.…”

Constraint Trajectory Surface-Hopping Molecular Dynamics Simulation of the Photoisomerization of Stilbene

“…Classical trajectory is propagated on a single adiabatic potential energy surface all the time. However, once trajectory is across the seam line, we compute effective coupling 2 and effective collision energy 2 according to the method given in Appendix C. Then, we can evaluate onepassage nonadiabatic transition probability by (12) and (13). We obtain the seam line by calculating local minima of effective coupling 2 and found that they all are located at avoided crossing points.…”

“…The other theoretical approaches such as Liouville dynamics [6], Bohmian dynamics [7], path integrals [8,9], and multiple spawning [10] have been proposed. Nonadiabatic dynamic based on Tully's FS algorithm has been widely applied for photochemistry of large molecular and biomolecular systems [11][12][13][14][15][16][17][18][19] and it has been well documented in the recent review paper [20]. Nonadiabatic transition probabilities calculated from Tully's FS method require calculation of nonadiabatic coupling vectors while the transition probabilities calculated from LZ and ZN formulas require information only from two adiabatic potential energy surfaces around the crossing International Journal of Photoenergy seam.…”

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches

“…In the absence of nonadiabatic couplings, the time evolution of the projector operator can then be written as $\frac{\mathrm{d}〈{\mathrm{script-boldP}}_i〉}{\mathrm{d}t}=-\frac{i}{\hslash }\overrightarrow{E}(t)〈\mathit{\psi }(t)|[\stackrel{true^}{\stackrel{true\to }{\mathrm{bold-italic\mu }}},{\mathrm{script-boldP}}_i]|\mathit{\psi }(t)〉.$Equation (32) is common to most of the LCT implementations irrespective of the underlying dynamical method. However, in the method developed in the framework of the NCCR MUST, LCT has been implemented within a trajectory surface hopping (TSH) ab initio molecular dynamics scheme 134 . All the required quantities, such as electronic energies, nuclear forces, nonadiabatic couplings, and transition dipole elements, have been calculated on-the-fly with LR-TDDFT as implemented in the software package CPMD.…”

“…LCT, when combined with ab initio molecular dynamics, carries more appeal as it requires a single forward propagation in time, while conventional optimal control theory typically involves several forward and backward propagations. The TSH/LCT implementation developed in the framework of the NCCR MUST targets typically state-specific electronic transitions 134,238 . Starting from a system, usually in its ground electronic state, it computes the instantaneous optimal pulse which induces electronic population transfer to the desired state, eventually leading to a trajectory hop from the initial state to the target state.…”