4.4.2 Non-adiabatic Excited-State Dynamics
MD in the electronically excited state is the basis for simulating time-resolved
spectroscopy, fluorescence quenching, excited-state electron or proton transfer, and
resonant energy transfer. Topological analysis of the excited-state PES in terms of
minima, transition states, and conical intersections provides a rigorous understanding of the photochemistry that supports the interpretation of time-resolved experimental data. This is, however, the most challenging area of theoretical spectroscopy
(see [121] for a recent review). The description of excited-state PES reveals many
limitations of the quantum chemical methods described in Sect. 4.2 that can be
widely ignored in ground-state simulations close to the equilibrium. The QM
method must deal with open-shell and multi-configurational wave functions, with
variable amount of CT. It must provide a balanced description of both dynamic and
static correlation, because these often have contrary effects on observables. Error
bars of a few kcal/mol, as desired for quantitative predictions of reaction rates for
competing pathways, are difficult to achieve for excited states. Therefore,
benchmarks and error discussions are much more important for excited-state
applications than for standard ground-state simulations, where established methods
like B3LYP, MP2, CCSD(T) have well-known error bars and can be used in a
black-box manner.
To describe the decay of the excited-state population due to the nonadiabatic
coupling between the electronic and vibronic degrees of freedom, the Tully surface
hopping (SH) approach [122, 123] is most widely used for larger molecules. It is
efficient and easy to implement due to the stochastic treatment of the nuclear
degrees of freedom and the separate time-propagation of electrons and nuclei on
different timescales. Approximate variants omit the electronic time-propagation
and simply use the nonadiabatic coupling vector (or even more simple criteria) to
calculate the electronic transition probability on-the-fly. Other approaches, like
multiple-spawning [124] or the variational multi-configuration Gaussian
wavepacket method (vMCG) [125] include interference effects by expressing the
nuclear wavepacket in a Gaussian basis.
Many successful simulations of nonadiabatic excited-state dynamics employed
CASSCF/CASPT2, ab initio [126] or semi-empirical MRCI [127, 128]. Illustrative
examples can be found for the photoisomerisation of the retinal chromophore [129,
130], the solvated chromophore of the green fluorescent protein [131],
photoswitching of a fluorescent protein [132], DNA bases [133–135] and other
systems [124, 136, 137].
References
1. Kochendoerfer, G., Wang, Z., Oprian, D.D., Mathies, R.A.: Examination of the wavelength
regulation mechanism in human visual pigments. Biochemistry 36, 6577–6587 (1997)
2. Fra ¨hmcke, J.S., Wanko, M., Phatak, P., Mroginski, M.A., Elstner, M.: The protonation state
of Glu181 in rhodopsin revisited: interpretation of experimental data on the basis of QM/MM
calculations. J. Phys. Chem. B 114, 11338–11352 (2010)
58
M. Wanko and A. Rubio
MD in the electronically excited state is the basis for simulating time-resolved
spectroscopy, fluorescence quenching, excited-state electron or proton transfer, and
resonant energy transfer. Topological analysis of the excited-state PES in terms of
minima, transition states, and conical intersections provides a rigorous understanding of the photochemistry that supports the interpretation of time-resolved experimental data. This is, however, the most challenging area of theoretical spectroscopy
(see [121] for a recent review). The description of excited-state PES reveals many
limitations of the quantum chemical methods described in Sect. 4.2 that can be
widely ignored in ground-state simulations close to the equilibrium. The QM
method must deal with open-shell and multi-configurational wave functions, with
variable amount of CT. It must provide a balanced description of both dynamic and
static correlation, because these often have contrary effects on observables. Error
bars of a few kcal/mol, as desired for quantitative predictions of reaction rates for
competing pathways, are difficult to achieve for excited states. Therefore,
benchmarks and error discussions are much more important for excited-state
applications than for standard ground-state simulations, where established methods
like B3LYP, MP2, CCSD(T) have well-known error bars and can be used in a
black-box manner.
To describe the decay of the excited-state population due to the nonadiabatic
coupling between the electronic and vibronic degrees of freedom, the Tully surface
hopping (SH) approach [122, 123] is most widely used for larger molecules. It is
efficient and easy to implement due to the stochastic treatment of the nuclear
degrees of freedom and the separate time-propagation of electrons and nuclei on
different timescales. Approximate variants omit the electronic time-propagation
and simply use the nonadiabatic coupling vector (or even more simple criteria) to
calculate the electronic transition probability on-the-fly. Other approaches, like
multiple-spawning [124] or the variational multi-configuration Gaussian
wavepacket method (vMCG) [125] include interference effects by expressing the
nuclear wavepacket in a Gaussian basis.
Many successful simulations of nonadiabatic excited-state dynamics employed
CASSCF/CASPT2, ab initio [126] or semi-empirical MRCI [127, 128]. Illustrative
examples can be found for the photoisomerisation of the retinal chromophore [129,
130], the solvated chromophore of the green fluorescent protein [131],
photoswitching of a fluorescent protein [132], DNA bases [133–135] and other
systems [124, 136, 137].
References
1. Kochendoerfer, G., Wang, Z., Oprian, D.D., Mathies, R.A.: Examination of the wavelength
regulation mechanism in human visual pigments. Biochemistry 36, 6577–6587 (1997)
2. Fra ¨hmcke, J.S., Wanko, M., Phatak, P., Mroginski, M.A., Elstner, M.: The protonation state
of Glu181 in rhodopsin revisited: interpretation of experimental data on the basis of QM/MM
calculations. J. Phys. Chem. B 114, 11338–11352 (2010)
58
M. Wanko and A. Rubio