7 Ultrafast Laser-Induced Processes Described by Ab Initio Molecular
165
classical trajectories of the nuclei describe the most relevant features observed in
quantum dynamical calculations subjected to laser fields, also strong ones. Without
large statistical sampling the dynamics of the internuclear distance follows the average position of the wave packet. Additionally, the nuclei gain little kinetic energy
during the dynamics and, although the method is classical and cannot reproduce
the zero vibrational quantum energy, the final average vibrational energy only differs slightly from the quantum value. More importantly, SHARC can consistently
reproduce the effects of non-adiabatic processes as the duration of the laser fields
becomes smaller and the nuclei gain some extra vibrational energy.
In the presence of strong fields, the observed dynamics is equivalent to the Ehrenfest dynamics, although in the SHARC scheme, SH dynamics is included, allowing jumps between the different LIPs close to degeneration points. Moreover, the
SHARC formalism recalculates the K matrix in the LIPs, by considering that the
LIP is a combination of several “bare” potentials. In contrast, in the related FISH
methodology [71] in which, with respect to the laser couplings, a diabatic representation is employed, the constant “hops” between the states (recall Figs. 7.1d and
7.8d) cannot correct the strong deviations of the dynamics from that given by the
“bare” electronic gradients, even with high statistical sampling. The same behavior
is expected whenever large Stark effects and laser-induced potential shaping affects
the dynamics.
On the contrary, we expect that whenever the strong-field drives the dynamics
of molecules with negligible ionization, and particularly if the time-variation of the
field is slow enough that the nuclei respond to the average electronic forces, the
SHARC scheme will be able to reproduce the results of fully quantum treatments,
with the benefit of allowing for the calculation of the dynamics in many dimensions,
as it is required for polyatomic molecules. More work along these lines, including
the effects of rotation, alignment, and the influence of strong fields in systems governed by conical intersections is in prospect.
Acknowledgements This work is financed by the Deutsche Forschungsgemeinschaft (DFG)
within the project GO 1059/6-1, by the German Federal Ministry of Education and Research
within the research initiative PhoNa, the Dirección General de Investigación of Spain under Project
No. CTQ2012-36184, a Juan de la Cierva contract, and the European COST Action CM0702.
References
1. S.A. Rice, M. Zhao, Optical Control of Molecular Dynamics (Wiley, New York, 2000)
2. M. Shapiro, P. Brumer, Principles of Quantum Control of Molecular Processes (Wiley, New
York, 2003)
3. L. Wöste, J. Manz (eds.), Femtosecond Chemistry, Vols. I, II (VCH, Weinheim, 1995)
4. B. Whitaker (ed.), Femtosecond Chemistry, Vols. I, II (Cambridge University Press, Cambridge, 2003)
5. V. Sundström (ed.), Femtochemistry and Femtobiology: Ultrafast Reaction Dynamics at
Atomic-Scale Resolution (Imperial College Press, London, 1996)
6. F.C.D. Schryver, S. DeFeyter, G. Schweitzer (eds.), Femtochemistry (Wiley-VCH, Weinheim, 2001)
165
classical trajectories of the nuclei describe the most relevant features observed in
quantum dynamical calculations subjected to laser fields, also strong ones. Without
large statistical sampling the dynamics of the internuclear distance follows the average position of the wave packet. Additionally, the nuclei gain little kinetic energy
during the dynamics and, although the method is classical and cannot reproduce
the zero vibrational quantum energy, the final average vibrational energy only differs slightly from the quantum value. More importantly, SHARC can consistently
reproduce the effects of non-adiabatic processes as the duration of the laser fields
becomes smaller and the nuclei gain some extra vibrational energy.
In the presence of strong fields, the observed dynamics is equivalent to the Ehrenfest dynamics, although in the SHARC scheme, SH dynamics is included, allowing jumps between the different LIPs close to degeneration points. Moreover, the
SHARC formalism recalculates the K matrix in the LIPs, by considering that the
LIP is a combination of several “bare” potentials. In contrast, in the related FISH
methodology [71] in which, with respect to the laser couplings, a diabatic representation is employed, the constant “hops” between the states (recall Figs. 7.1d and
7.8d) cannot correct the strong deviations of the dynamics from that given by the
“bare” electronic gradients, even with high statistical sampling. The same behavior
is expected whenever large Stark effects and laser-induced potential shaping affects
the dynamics.
On the contrary, we expect that whenever the strong-field drives the dynamics
of molecules with negligible ionization, and particularly if the time-variation of the
field is slow enough that the nuclei respond to the average electronic forces, the
SHARC scheme will be able to reproduce the results of fully quantum treatments,
with the benefit of allowing for the calculation of the dynamics in many dimensions,
as it is required for polyatomic molecules. More work along these lines, including
the effects of rotation, alignment, and the influence of strong fields in systems governed by conical intersections is in prospect.
Acknowledgements This work is financed by the Deutsche Forschungsgemeinschaft (DFG)
within the project GO 1059/6-1, by the German Federal Ministry of Education and Research
within the research initiative PhoNa, the Dirección General de Investigación of Spain under Project
No. CTQ2012-36184, a Juan de la Cierva contract, and the European COST Action CM0702.
References
1. S.A. Rice, M. Zhao, Optical Control of Molecular Dynamics (Wiley, New York, 2000)
2. M. Shapiro, P. Brumer, Principles of Quantum Control of Molecular Processes (Wiley, New
York, 2003)
3. L. Wöste, J. Manz (eds.), Femtosecond Chemistry, Vols. I, II (VCH, Weinheim, 1995)
4. B. Whitaker (ed.), Femtosecond Chemistry, Vols. I, II (Cambridge University Press, Cambridge, 2003)
5. V. Sundström (ed.), Femtochemistry and Femtobiology: Ultrafast Reaction Dynamics at
Atomic-Scale Resolution (Imperial College Press, London, 1996)
6. F.C.D. Schryver, S. DeFeyter, G. Schweitzer (eds.), Femtochemistry (Wiley-VCH, Weinheim, 2001)