Nonadiabatic chemical dynamics in an intense laser field: electronic wave packet coupled with classical nuclear motions

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

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.

Local Control Theory in Trajectory Surface Hopping Dynamics Applied to the Excited-State Proton Transfer of 4-Hydroxyacridine

The application of local control theory combined with nonadiabatic ab initio molecular dynamics to study the photoinduced intramolecular proton transfer reaction in 4-hydroxyacridine was investigated. All calculations were performed within the framework of linear-response time-dependent density functional theory. The computed pulses revealed important information about the underlying excited-state nuclear dynamics highlighting the involvement of collective vibrational modes that would normally be neglected in a study performed on model systems constrained to a subset of the full configuration space. This study emphasizes the strengths of local control theory for the design of pulses that can trigger chemical reactions associated with the population of a given molecular excited state. In addition, analysis of the generated pulses can help to shed new light on the photophysics and photochemistry of complex molecular systems.

Interplay of radiative and nonradiative transitions in surface hopping with radiation-molecule interactions

We implemented a method for the treatment of field induced transitions in trajectory surface hopping simulations, in the framework of the local diabatization scheme, especially suited for on-the-fly dynamics. The method is applied to a simple one-dimensional model with an avoided crossing and compared with quantum wavepacket dynamics. The results show the importance of introducing a proper decoherence correction to surface hopping, in order to obtain meaningful results. Also the energy conservation policy of standard surface hopping must be revised: in fact, the quantum wavepacket energetics is well reproduced if energy absorption/emission is allowed for in the hops determined by radiation-molecule coupling. To our knowledge, this is the first time the issues of decoherence and energy conservation have been analyzed in depth to devise a mixed quantum-classical method for dynamics with molecule-field interactions.

DETERMINATION OF THE ELECTRONIC GROUND STATE OF MOLECULAR SYSTEMS WITH THE MULTI-CONFIGURATION TIME-DEPENDENT HARTREE–FOCK METHOD

In this paper, we present progress in the application of the explicitly time-dependent multi-configuration time-dependent Hartree–Fock (MCTDHF) method. The spin–orbitals and equations of motion are expressed in the basis of Gaussian Type Orbitals. MCTDHF is then applied to the calculation of the electronic ground state of various small molecules by imaginary time propagation. We were able to take between four and 12 active electrons into account. We discuss the suitability of a core guess as initial wave function, the possibility to obtain excited states, as well as the consequences of a neglect of core excitations.

Generalization of classical mechanics for nuclear motions on nonadiabatically coupled potential energy surfaces in chemical reactions

Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified.

Dynamics of Electronic States and Spin−Flip for Photodissociation of Dihalogens in Matrices: Experiment and Semiclassical Surface-Hopping and Quantum Model Simulations for F2 and ClF in Solid Ar

Three approaches are combined to study the electronic states' dynamics in the photodissociation of F(2) and ClF in solid argon. These include (a) semiclassical surface-hopping simulations of the nonadiabatic processes involved. These simulations are carried out for the F(2) molecule in a slab of 255 argon atoms with periodic boundary conditions at the ends. The full manifold of 36 electronic states relevant to the process is included. (b) The second approach involves quantum mechanical reduced-dimensionality models for the initial processes induced by a pump laser pulse, which involve wavepacket propagation for the preoriented ClF in the frozen argon lattice and incorporate the important electronic states. The focus is on the study of quantum coherence effects. (c) The final approach is femtosecond laser pump-probe experiments for ClF in Ar. The combined results for the different systems shed light on general properties of the nonadiabatic processes involved, including the singlet to triplet and intertriplet transition dynamics. The main findings are (1) that the system remains in the initially excited-state only for a very brief, subpicosecond, time period. Thereafter, most of the population is transferred by nonadiabatic transitions to other states, with different time constants depending on the systems. (2) Another finding is that the dynamics is selective with regard to the electronic quantum numbers, including the Lambda and Omega quantum numbers, and the spin of the states. (3) The semiclassical simulations show that prior to the first "collision" of the photodissociated F atom with an Ar atom, the argon atoms can be held frozen, without affecting the process. This justifies the rigid-lattice reduced-dimensionality quantum model for a brief initial time interval. (4) Finally, degeneracies between triplets and singlets are fairly localized, but intertriplet degeneracies and near degeneracies can span an extensive range. The importance of quantum effects in photochemistry of matrix-isolated molecules is discussed in light of the results.

Time-dependent approach to electronically excited states of molecules with the multiconfiguration time-dependent Hartree-Fock method

In this paper the authors show how the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method can be used for the calculation of electronic properties of molecules associated with the population of excited states. In contrast to other methods for correlated electron dynamics, such as configuration interaction, MCTDHF does not rely on a solution of the electronic Schrodinger equation prior to the propagation. The authors apply this approach to the calculation of vertical excitation energies, transition dipole moments, and oscillator strengths for two test molecules, lithium hydride and methane.

On the validity range of the Born-Oppenheimer approximation: A semiclassical study for all-particle quantization of three-body Coulomb systems

The validity range of the Born-Oppenheimer (BO) approximation is studied with respect to the variation of the mass (m) of negatively charged particle by substituting an electron (e) with muon (mu) and antiproton (p) in hydrogen molecule cation. With the use of semiclassical quantization applied to these (ppe), (ppmu), and (ppp) under a constrained geometry, we estimate the energy difference of the non-BO vibronic ground state from the BO counterpart. It is found that the error in the BO approximation scales to the power of 3/2 to the mass of negative particles, that is, m(1.5). The origin of this clear-cut relation is analyzed based on the original perturbation theory due to Born and Oppenheimer, with which we show that the fifth order term proportional to m(5/4) is zero and thereby the first correction to the BO approximation should arise from the sixth order term that is proportional to m(6/4). Therefore, the validity range of the Born-Oppenheimer approximation is wider than that often mistakenly claimed to be proportional to m(1/4).

Non-Born-Oppenheimer path in anti-Hermitian dynamics for nonadiabatic transitions

A serious difficulty in the semiclassical Ehrenfest theory for nonadiabatic transitions is that a path passing across the avoided crossing is forced to run on a potential averaged over comprising adiabatic potential surfaces that commit the avoided crossing. Therefore once a path passes through the crossing region, it immediately becomes incompatible with the standard view of "classical trajectory" running on an adiabatic surface. This casts a fundamental question to the theoretical structure of chemical dynamics. In this paper, we propose a non-Born-Oppenheimer path that is generated by an anti-Hermitian Hamiltonian, whose complex-valued eigenenergies can cross in their real parts and avoid crossing in the imaginary parts in the vicinity of the nonadiabatic transition region. We discuss the properties of this non-Born-Oppenheimer path and thereby show its compatibility with the Born-Oppenheimer classical trajectories. This theory not only allows the geometrical branching of the paths but gives the nonadiabatic transition amplitudes and quantum phases along the generated paths.