Theoretical and computational chemistry

Excited-state dynamics

Follow the evolution of molecular wavepackets after photoexcitation, from ultrafast relaxation and conical intersections to measurable spectra and reaction outcomes.

1 Lower secondary 2 Upper secondary 3 Undergraduate 4 Advanced 5 Research

IntuitionA photon launches nuclear motion

Light can place a molecule on an excited electronic surface. Because nuclei are initially still at the ground-state geometry, excitation is approximately vertical; the resulting wavepacket then moves, spreads, and may reach regions where electronic states strongly mix.

The schematic excited-state surface funnels a wavepacket toward a conical intersection with the ground state, enabling rapid radiationless decay.

SchoolRadiative and radiationless pathways

Definition: Lifetime

The excited-state lifetime characterizes the decay of the population. For a single first-order channel, $N(t)=N_0e^{-t/\tau}$ and the rate is $k=1/\tau$ .

k_{\mathrm{tot}}=k_{\mathrm{rad}}+k_{\mathrm{IC}}+k_{\mathrm{ISC}}+k_{\mathrm{rxn}}

Example: Infer a decay rate

A state has a measured single-exponential lifetime of 200 fs. What total first-order rate does this imply?

Solution

$k=1/(200\times10^{-15}\,\mathrm{s})=5.0\times10^{12}\,\mathrm{s}^{-1}$ , under the single-exponential assumption.

UndergraduatePotential-energy surfaces and nonadiabatic coupling

On a single Born–Oppenheimer surface, nuclei evolve under one electronic state. Near an avoided crossing or conical intersection, derivative couplings transfer amplitude between states; population dynamics may no longer be represented by independent surface motion.

i\hbar\frac{\partial}{\partial t}\boldsymbol\chi=\left[\mathbf T_N\mathbf I+\mathbf V(\mathbf R)\right]\boldsymbol\chi

Method	Representation	Strength / limitation
Surface hopping	Ensemble of classical trajectories	Scales to many atoms; decoherence treatment matters

AdvancedConnecting dynamics to experiments

Time-resolved absorption, photoelectron spectra, and diffraction probe different projections of the evolving nuclear-electronic wavepacket. A calculated trajectory is not itself an observable: simulate the measurement, average over initial conditions, and compare instrument-broadened signals.

ResearchFrontier: predictive nonadiabatic dynamics

References

Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers · Ahmed H. Zewail, 2000
Role of Conical Intersections in the Photophysics and Photochemistry of Organic Molecules · Wolfgang Domcke and David R. Yarkony, 2012