# Nonadiabatic Dynamics

## Nonadiabatic Vibrational Dynamics in the $\mathrm{HCO}{}_{2}^{-}\cdot {\mathrm{H}}_{2}\mathrm{O}$ Complex

Based on extensive ab initio calculations and the
time-propagation of a 6-dimensional nuclear Schrödinger equation, we
study the vibrational relaxation dynamics and resulting spectral
signature of the OH stretch vibration of a hydrogen-bonded complex,
$\mathrm{HCO}{}_{2}^{-}\cdot {\mathrm{H}}_{2}\mathrm{O}$.
Despite its smallness, it has been shown
experimentally by Johnson and coworkers that the gas-phase IR spectra
of these types of complexes exhibits much of the complexity commonly
observed for hydrogen bonded systems, i.e., a significant red shift
together with an extreme broadening and a pronounced substructure of
the OH stretch vibration, reflecting its very strong
anharmonicity. Employing an adiabatic separation of timescales between
the three intramolecular high-frequency modes of the water molecule
and the three most important intermolecular low-frequency modes of the
complex, we identify a vibrational conical intersection seam that
connects the OH stretch vibration to the HOH bend overtone. The
conical intersection results in a coherent population transfer between
the two states, the first step of which being ultrafast with 60~fs and
irreversible, as one would intuitively predict based on the knowledge
accumulated for ultrafast photophysical processes between electronic
potential energy surfaces. The density of states of our model is large
enough to also realistically describe the subsequent incoherent
relaxation of vibrational energy into the HOH bend and ground
state. However, despite the fact that no conical intersection connects
to these states, that relaxation is only insignificantly slower, as
opposed to what would be expected in the electronic case. The
underlying adiabatic picture hence constituted only a rather poor
approximation of vibrational dynamics. We identify the smaller
effective mass difference as the major difference between a
vibrational and the more common electronic adiabatic approximation.

Nonadiabatic Vibrational Dynamics in the
$\mathrm{HCO}{}_{2}^{-}\cdot {\mathrm{H}}_{2}\mathrm{O}$
Complex
J. Chem. Phys. 143, 134308 (2015)

## Vibrational Conical Intersections as a Mechanism of Ultrafast Vibrational Relaxation

Presenting true crossings of adiabatic potential
energy surfaces, conical intersections are a paradigm of ultrafast
and efficient electronic relaxation dynamics. The same mechanism is
shown to apply also for vibrational conical intersections,
which may occur when two high-frequency modes (such as OH stretch
vibrations) are coupled to low-frequency modes (such as hydrogen
bonding modes). By derivation of a model Hamiltonian and its
parameterization for a concrete example, malonaldehyde, the
conditions that such intersections occur are identified and the
consequences for the vibrational dynamics and spectra are
demonstrated.

Vibrational conical intersections as mechanism of ultrafast vibrational relaxation,
Phys. Rev. Lett. 109, 173201 (2012)

# Ultrafast nonadiabatic photoreactions

## A quantum dynamical description

Modern pulsed laser techniques provide an ultrafast camera that allows us to explore
the motion of atoms at a femtosecond (10

^{-15}s) time resolution. The fascination of*femtosecond chemistry*lies in the possibility to*directly*observe elementary chemical reactions. For example, femtosecond experiments have shed light on the primary electron transfer process in the bacterial photoreaction center and have witnesses the making and braking of hydrogen bonds in biopolymers.
State-of-the-art femtosecond experiments generate an
enormous amount
of data, which require a careful theoretical analysis. However,
neither straightforward quantum mechanics nor simple classical
modeling is typically suited to describe the femtosecond dynamics and
spectroscopy of complex systems. The theory therefore is challenged to
develope new strategies. Approaches pursued in this group include the
development of multidimensional reduced quantum-models and of new
mixed quantum-classical concepts. Hereby the ultimate goal is an
truely microscopic understanding of the underlying physics and, of
course, the pleasure play
with new theoretical ideas.

As an example, the upper picture shows a recently proposed model of the photoinduced

As an example, the upper picture shows a recently proposed model of the photoinduced

*cis-trans*isomerization of retinal in rhodopsin, representing the first step in vision. Shown are two-dimensional potential-energy surfaces of the ground and excited electronic states. The photoreaction is initiated via vertical excitation by a pump laser pulse, which prepares a vibrational wave packet on the excited electronic state. The wave packet, shown in the right picture, is seen to bifurcate at a*conical intersection*of the adiabatic surfaces, whereby the*photoproduct*is formed with high efficiency and within only 200 fs such as the making and breaking of chemical bonds in real time, that is, on a femtosecond time scale.
Femtosecond time-resolved spectroscopy of the dynamics at conical intersections,
in: Conical Intersections, eds: W. Domcke, D. R. Yarkony, and H. Koppel, (World Scientific, Singapore, 2003)

## A classical description

Since the birth of quantum theory there has been a considerable
interest in the transition from quantum to classical mechanics. Because
the two formulations are given in a different
theoretical framework (nonlinear classical trajectories vs.
expectation values of linear operators), this transition is far more
involved than the naive limit

In this research project, we are concerned with various theoretical formulations that allow us to treat nonadiabatic quantum dynamics in a classical description. We are interested in fundamental aspects of semiclassical dynamics as well as in the development of practical mixed quantum-classical techniques which are capable of describing the dynamics of complex molecular systems. Considering multidimensional model problems describing photoinduced electron transfer, internal-conversion via conical intersections and nonadiabatic photoisomerization, the methods employed include mean-field, surface-hopping, and the quantum-classical Liouville formulations. In particular, we are interested in the mapping approach to nonadiabatic quantum dynamics. Going beyond the usual quasiclassical approximation, the formulation allows us to characterize the classical phase space and the periodic orbits of a nonadiabatic system and to achieve a true semiclassical treatment of nonadiabatic dynamics via an initial-value representation.

*h*→ 0 suggests. Furthermore, many quantum-mechanical systems and phenomena have no obvious classical analog. For example, it is not obvious how to extend a trajectory simulation running on a single Born-Oppenheimer potential-energy surface to a classical description of nonadiabatic processes taking place on several coupled electronic potential-energy surfaces.In this research project, we are concerned with various theoretical formulations that allow us to treat nonadiabatic quantum dynamics in a classical description. We are interested in fundamental aspects of semiclassical dynamics as well as in the development of practical mixed quantum-classical techniques which are capable of describing the dynamics of complex molecular systems. Considering multidimensional model problems describing photoinduced electron transfer, internal-conversion via conical intersections and nonadiabatic photoisomerization, the methods employed include mean-field, surface-hopping, and the quantum-classical Liouville formulations. In particular, we are interested in the mapping approach to nonadiabatic quantum dynamics. Going beyond the usual quasiclassical approximation, the formulation allows us to characterize the classical phase space and the periodic orbits of a nonadiabatic system and to achieve a true semiclassical treatment of nonadiabatic dynamics via an initial-value representation.

As an example, we consider a
two-state three-mode model of
nonadiabatic

*cis-trans*photoisomerization. The figure compares the quantum-mechanical (left) and quasiclassical mapping (right) probability densities of the time-dependent wave packet along isomerization coordinate*ϕ*, projected on the S_{1}(upper panel) and S_{0}(lower panel) adiabatic electronic state, respectively. The classical approach is seen to be in good agreement with the quantum calculation, it facilitates the interpretation of the diffuse wave function in terms of irregular vibronic periodic orbits, and allows us to extend the study to many (up to 10^{4}) vibrational degrees of freedom.
Classical
Description of Nonadiabatic Quantum Dynamics,
Adv. Chem. Phys. 131, 243-375 (2005)