Theory of Ultrafast Nonadiabatic Excited-State Processes and their Spectroscopic Detection in Real Time

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.

Slow Intramolecular Vibrational Relaxation Leads to Long-Lived Excited-State Wavepackets

Broadband optical pump and compressed white light continuum probe were used to measure the transient excited-state absorption, ground-state bleach, and stimulated emission signals of cresyl violet solution in methanol. Amplitude oscillations caused by wavepacket motion in the ground and excited electronic states were analyzed. It was found that vibrational coherences in the excited state persist for more than the experimental waiting time window of 6 ps, and the strongest mode had a dephasing time constant of 2.4 ps. We hypothesize the dephasing of the wavepacket in the excited state is predominantly caused by intramolecular vibrational relaxation (IVR). Slow IVR indicates weak mode-mode coupling and therefore weak anharmonicity of the potential of this vibration. Thus, the initially prepared vibrational wavepacket in the excited state is not significantly perturbed by nonadiabatic coupling to other electronic states, and hence the diabatic and adiabatic representations of the system are essentially identical within the Born-Oppenheimer approximation. The wavepacket therefore evolves with time in an almost harmonic potential, slowly dephased by IVR and the pure vibrational decoherence. The consistency in the position of node (phase change in the wavepacket) in the excited-state absorption and stimulated emission signals without undergoing any frequency shift until the wavepacket is completely dephased conforms to the absence of any reactive internal conversion.

Exciton dynamics in perturbed vibronic molecular aggregates

A site specific perturbation of a photo-excited molecular aggregate can lead to a localization of excitonic energy. We investigate this localization dynamics for laser-prepared excited states. Changing the parameters of the electric field significantly influences the exciton localization which offers the possibility for a selective control of this process. This is demonstrated for aggregates possessing a single vibrational degree of freedom per monomer unit. It is shown that the effects identified for the molecular dimer can be generalized to larger aggregates with a high density of vibronic states.

Alternative view of two-dimensional spectroscopy

Femtosecond two-dimensional (2D) spectroscopy has become a widely employed method for the investigation of the dynamics of complex chemical and biological systems. In 2D spectroscopy, the sample is excited with three phase-locked femtosecond pulses, and the signal is heterodyned with the local oscillator field. The 2D spectrum is obtained by double Fourier transform with respect to the time delay between the first two pulses and the time delay between the third pulse and the local oscillator field. We show that 2D optical signals can alternatively be measured and computationally simulated as four-wave-mixing signals generated by two femtosecond pulses and two one-sided continuous-wave (CW) pulses. The first femtosecond pulse and one-sided CW pulse create the doorway state, while the second femtosecond pulse and one-sided CW pulse create the window state. This picture relates 2D spectroscopy to other mixed time-frequency-domain techniques, which is useful for the interpretation of the corresponding signals. Moreover, it allows a computationally efficient evaluation of 2D spectra.

Quantum Mechanical Studies on the Photophysics and the Photochemistry of Nucleic Acids and Nucleobases

The photophysics and photochemistry of DNA is of great importance due to the potential damage of the genetic code by UV light. Quantum mechanical studies have played a key role in interpretating the results of modern time-resolved pump-probe spectroscopy, and in elucidating the main photoactivated reactive paths. This review provides a concise, complete picture of the computational studies carried out, approximately, in the past decade. We start with an overview of the photophysics of the nucleobases in the gas phase and in solution. We discuss the proposed mechanisms for ultrafast decay to the ground state, that involve conical intersections, consider the role of triplet states, and analyze how the solvent modulates the photophysics. Then we move to larger systems, from dinucleotides to single- and double-stranded oligonucleotides. We focus on the possible role of charge transfer and delocalized or excitonic states in the photophysics of these systems and discuss the main photochemical paths. We finish with an outlook on the current challenges in the field and future directions of research.

Experimental Detection of Branching at a Conical Intersection in a Highly Fluorescent Molecule

Conical intersections are molecular configurations at which adiabatic potential-energy surfaces touch. They are predicted to be ubiquitous, yet condensed-phase experiments have focused on the few systems with clear spectroscopic signatures of negligible fluorescence, high photoactivity, or femtosecond electronic kinetics. Although rare, these signatures have become diagnostic for conical intersections. Here we detect a coherent surface-crossing event nearly two picoseconds after optical excitation in a highly fluorescent molecule that has no photoactivity and nanosecond electronic kinetics. Time-frequency analysis of high-sensitivity measurements acquired using sub-8 fs pulses reveals phase shifts of the signal due to branching of the wavepacket through a conical intersection. The time-frequency analysis methodology demonstrated here on a model compound will enable studies of conical intersections in molecules that do not exhibit their diagnostic signatures. Improving the ability to detect conical intersections will enrich the understanding of their mechanistic role in molecular photochemistry.

Simulation of femtosecond two-dimensional electronic spectra of conical intersections

We have simulated femtosecond two-dimensional (2D) electronic spectra for an excited-state conical intersection using the wave-function version of the equation-of-motion phase-matching approach. We show that 2D spectra at fixed values of the waiting time provide information on the structure of the vibronic eigenstates of the conical intersection, while the evolution of the spectra with the waiting time reveals predominantly ground-state wave-packet dynamics. The results show that 2D spectra of conical intersection systems differ significantly from those obtained for chromophores with well separated excited-state potential-energy surfaces. The spectral signatures which can be attributed to conical intersections are discussed.

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

We derive a somewhat crude, yet very efficient semiclassical approximation for computing nonadiabatic spectra. The resulting method, which is a generalization of the multiple-surface dephasing representation, includes quantum effects through interference of mixed quantum-classical trajectories and through quantum treatment of the collective electronic degree of freedom. The method requires very little computational effort beyond the fewest-switches surface hopping or Ehrenfest locally mean-field dynamics and is very easy to implement. The proposed approximation is tested by computing the absorption and time-resolved stimulated emission spectra of pyrazine using the four-dimensional three-surface model which allows for comparison with the numerically exact quantum spectra. As expected, the multiple-surface dephasing representation is not suitable for high-resolution linear spectra, yet it seems to capture all the important features of pump-probe spectra. Finally, the method is combined with on-the-fly ab initio evaluation of the electronic structure (i.e., energies, forces, electric-dipole, and nonadiabatic couplings) in order to compute fully dimensional nonadiabatic spectra of pyrazine without approximations inherent to analytical, including vibronic-coupling models. The Appendix provides derivations of perturbative expressions for linear and pump-probe spectra of arbitrary mixed states and for arbitrary laser pulse shapes.

Polaron dynamics in two-dimensional photon-echo spectroscopy of molecular rings

We have developed a new approach to the computation of third-order spectroscopic signals of molecular rings, by incorporating the Davydov soliton theory into the nonlinear response function formalism. The Davydov D1 and D Ansätze have been employed to treat the interactions between the excitons and the primary phonons, allowing for a full description of arbitrary exciton-phonon coupling strengths. As an illustration, we have simulated a series of optical 2D spectra for two models of molecular rings.

Strong-pump strong-probe spectroscopy: effects of higher excited electronic states

The present paper is devoted to the simulation of (integral and dispersed) pump-probe signals in the nonperturbative regime for a series of material systems with multiple electronic states and excited-state absorption. We show that strong-pump strong-probe spectroscopy permits the probing of vibrational wavepackets in high-lying and/or short-lived excited electronic states with a time resolution which is not limited by the pulse durations. The field strength can be regarded as an additional experimentally controllable parameter, which can be tuned to maximize the spectroscopic information for a given material system.

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 parametrization for a concrete example, malonaldehyde, the conditions that such conical intersections occur are identified and the consequences for the vibrational dynamics and spectra are demonstrated.

FIRST PRINCIPLES MOLECULAR DYNAMICS INVOLVING EXCITED STATES AND NONADIABATIC TRANSITIONS

Extensions of traditional molecular dynamics to excited electronic states and non-Born–Oppenheimer dynamics are reviewed focusing on applicability to chemical reactions of large molecules, possibly in condensed phases. The latter imposes restrictions on both the level of accuracy of the underlying electronic structure theory and the treatment of nonadiabaticity. This review, therefore, exclusively deals with ab initio "on the fly" molecular dynamics methods. For the same reason, mainly mixed quantum-classical approaches to nonadiabatic dynamics are considered.

Interference Effects in Vibronic 2D-Spectra of Diatomic Molecules

We theoretically study interference effects in two-dimensional (2D) vibronic spectra which arise from two electronically excited states taking part in the multi-photon process initiated by femtosecond laser pulses. Therefore, a model is employed which mimiques the situation encountered in many halogen and interhalogen molecules. There, upon excitation from the ground state, an excited bound state and a dissociative state exist which are close in energy. We demonstrate that the different pathways to final states which enter into the third-order polarization result in pronounced interference patterns in the 2D-spectra.