Accuracy of second order perturbation theory in the polaron and variational polaron frames

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.     

State-to-state dissociation rate coefficients in electronically excited diatomic gases

In the present Letter, state dependent dissociation rate coefficients in diatomic gases with non-equilibrium vibrational and electronic excitation and chemical reactions are studied. A widely used Treanor–Marrone model is generalized to take into account state-to-state vibrational and electronic distributions. The influence of electronic excitation on the rate of dissociation from various electronic states of CO molecules is estimated.     

The Influence of Dissipation on Vibrational Dynamics in a System of Two Interacting Electronic States

The vibrational dynamics of a nonadiabatic transition between two interacting electronic states in a molecular system in a thermal environment was considered. Two models were used. In one of these, both states, and in the other, only one state interacted with the environment. The electronic states were described by one-dimensional harmonic oscillators on the assumption that the interaction amplitude with the environment (bath) linearly depended on the coordinates of the bath and system. Model parameters typical of electron transfer in photosynthesis reaction centers were selected. The numerical solutions to the Redfield equations for the reduced density matrix were used to calculate the time characteristics of the system, including the mean vibrational energy, product population, and the degree of vibrational motion coherence. The influence of temperature and intensity of interactions with the bath on the time dependence of these values was studied. The character of vibrational dynamics had features common to both models, namely, (1) the vibrational energy monotonically decreased with the time, and this dependence was close to one-exponential in the majority of cases and (2) the time dependence of reaction yield, i.e., product population, was a step function, and the probability of the electron transition decreased as the temperature increased. It was found that there was a fundamental difference between the models under consideration: if only the reaction product interacted with the bath, vibrational coherence was retained for a long time (up to 2000 fs).     

Time-resolved photoelectron spectroscopy: from wavepackets to observables

Time-resolved photoelectron spectroscopy (TRPES) is a powerful tool for the study of intramolecular dynamics, particularly excited state non-adiabatic dynamics in polyatomic molecules. Depending on the problem at hand, different levels of TRPES measurements can be performed: time-resolved photoelectron yield; time- and energy-resolved photoelectron yield; time-, energy-, and angle-resolved photoelectron yield. In this pedagogical overview, a conceptual framework for time-resolved photoionization measurements is presented, together with discussion of relevant theory for the different aspects of TRPES. Simple models are used to illustrate the theory, and key concepts are further amplified by experimental examples. These examples are chosen to show the application of TRPES to the investigation of a range of problems in the excited state dynamics of molecules: from the simplest vibrational wavepacket on a single potential energy surface; to disentangling intrinsically coupled electronic and nuclear motions; to identifying the electronic character of the intermediate states involved in non-adiabatic dynamics by angle-resolved measurements in the molecular frame, the most complete measurement.     

Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat many-body quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show the time-dependent formation of a polaron state that results in a pronounced suppression of the current corresponding to the phenomenon of phonon blockade. We show that this phenomenon cannot be explained solely by the polaron shift of the energy but requires methods that incorporate the dynamical effect of the vibrations on the transport. The accurate results obtained with the ML-MCTDH in this parameter regime are compared to results of nonequilibrium Green's function theory.     

Excited and ground state vibrational dynamics revealed by two-dimensional electronic spectroscopy

Broadband two-dimensional electronic spectroscopy (2DES) can assist in understanding complex electronic and vibrational signatures. In this paper, we use 2DES to examine the electronic structure and dynamics of a long chain cyanine dye (1,1-diethyl-4,4-dicarbocyanine iodide, or DDCI-4), a system with a vibrational progression. Using broadband pulses that span the resonant electronic transition, we measure two-dimensional spectra that show a characteristic six peak pattern from coherently excited ground and excited state vibrational modes. We model these features using a spectral density formalism and the vibronic features are assigned to Feynman pathways. We also examine the dynamics of a particular set of peaks demonstrating anticorrelated peak motion, a signature of oscillatory wavepacket dynamics on the ground and excited states. These dynamics, in concert with the general structure of vibronic two-dimensional spectra, can be used to distinguish between pure electronic and vibrational quantum coherences.     

Spin-dependent polaron recombination in conjugated polymers

We simulate the interchain polaron recombination process in conjugated polymer systems using a nonadiabatic molecular dynamics method, which allows for the coupled evolution of the nuclear degrees of freedom and multiconfigurational electronic wavefunctions. Within the method, the appropriate spin symmetry of the electronic wavefunction is taken into account, thus allowing us to distinguish between singlet and triplet excited states. It is found that the incident polarons can form an exciton, form a bound interchain polaron pair, or pass each other, depending on the interchain interaction strength and the strength of an external electric field. Most importantly, we found that the formation of singlet excitons is considerably easier than triplet excitons. This shows that in real organic light emitting devices, the electroluminescence quantum efficiency can exceed the statistical limitation value of 25%, in agreement with experiments.     

Femtosecond primary events in bacteriorhodopsin and its retinal modified analogs: revision of commonly accepted interpretation of electronic spectra of transient intermediates in the bacteriorhodopsin photocycle

Femtosecond primary events in bacteriorhodopsin (BR) and its retinal modified analogs are discussed. Ultrafast time resolved electronic spectra of the primary intermediates induced in the BR photocycle are discussed along with spectral and kinetic inconsistencies of the previous models proposed in the literature. The theoretical model proposed in this paper based on vibrational coupling between the electronic transition of the chromophore and intramolecular vibrational modes allows us to calculate the equilibrium electronic absorption band shape and the hole burning profiles. The model is able to rationalize the complex pattern of behavior for the primary events in BR and explain the origin of the apparent inconsistencies between the experiment and the previous theoretical models. The model presented in the paper is based on the anharmonic coupling assumption in the adiabatic approximation using the canonical transformation method for diagonalization of the vibrational Hamiltonian instead of the commonly used perturbation theory. The electronic transition occurs between the Born-Oppenheimer potential energy surfaces with the electron involved in the transition being coupled to the intramolecular vibrational modes of the molecule (chromophore). The relaxation of the excited state occurs by indirect damping (dephasing) mechanisms. The indirect dephasing is governed by the time evolution of the anharmonic coupling constant driven by the resonance energy exchange between the intramolecular vibrational mode and the bath. The coupling with the intramolecular vibrational modes results in the Franck-Condon progression of bands that are broadened due to the vibrational dephasing mechanisms. The electronic absorption line shape has been calculated based on the linear response theory whereas the third order nonlinear response functions have been used to analyze the hole burning profiles obtained from the pump-probe time-resolved measurements. The theoretical treatment proposed in this paper provides a basis for a substantial revision of the commonly accepted interpretation of the primary events in the BR photocycle that exists in the literature.     

A quantum-classical approach to the photoabsorption spectrum of pyrazine

We have used the time-dependent discrete variable representation (TDDVR) method to simulate the photoabsorption spectrum of pyrazine. The time-dependent molecular dynamics of pyrazine after excitation to the S2 electronic state is considered as a benchmark to investigate the S2 absorption spectrum. We have carried out the dynamics on a basic four-mode model of pyrazine with the inclusion of five major modes as well as the rest of the vibrational modes as bath modes. Investigations reveal the effect of bath modes such as energy and population transfer from the subsystem to the bath. Calculated results demonstrate excellent agreement with traditional quantum-mechanical findings during the entire propagation and converge to the exact quantum results when enough gridpoints are used. It appears that TDDVR, as a numerical quantum dynamics methodology, is a good compromise between accuracy and speed.     

Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment

The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.     

Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: application to formaldehyde

We have demonstrated the use of ab initio molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.     

Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath

Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.     

Trajectory on-the-fly molecular dynamics approach to tunneling splitting in the electronic excited state: A case of tropolone

The semiclassical tunneling method is applied to evaluate the tunneling splitting of tropolone due to the intramolecular proton transfer in the electronic excited state, first time, in a framework of the trajectory on-the-fly molecular dynamics (TOF-MD) approach. To prevent unphysical zero-point vibrational energy transfer among the normal modes of vibration, quantum zero-point vibrational energies are assigned only to the vibrational modes related to intramolecular proton transfer, whereas the remaining modes are treated as bath modes. Practical ways to determine the tunnel-initiating points and tunneling path are introduced. It is shown that the tunneling splitting decreases as the bath-mode energy increases. The experimental tunneling splitting value is well reproduced by the present TOF-MD approach based on the Wentzel-Kramers-Brillouin (WKB) approximation.     

Real time quantum propagation on a Monte Carlo trajectory guided grids of coupled coherent states: 26D simulation of pyrazine absorption spectrum

In this work we apply the coupled coherent states technique of quantum molecular dynamics to simulation of the absorption spectrum of pyrazine. All 24 vibrational modes are taken into account. The nonadiabatic coupling obetween the S(1) and S(2) electronic states is treated by a mapping approach that adds two extra degrees of freedom to the effective vibronic Hamiltonian. The results are in a good agreement with experiment and with previous calculations by quantum multiconfigurational time dependent Hartree and semiclassical Herman-Kluk methods.     

Electronic to vibrational energy transfer assisted by interacting transition dipole moments: a quantum model for the nonadiabatic I2(E) + CF4 collisions

We report a theoretical study of nonadiabatic transitions within the first-tier ion-pair states of molecular iodine induced by collisions with CF(4). We propose a model that treats the partner as a spherical particle with internal vibrational structure. Potential energy surfaces and nonadiabatic matrix elements for the I(2)-CF(4) system are evaluated using the diatomics-in-molecule perturbation theory. A special form of the intermolecular perturbation theory for quasi-degenerate electronic states is implemented to evaluate the corrections to the long-range interaction of transition dipole moments of colliding molecules. The collision dynamics is studied by using an approximate quantum scattering approach that takes into account the coupling of electronic and vibrational degrees of freedom. Comparison with available experimental data on the rate constants and product state distributions demonstrates a good performance of the model. The interaction of the transition dipole moments is shown to induce very efficient excitation of the dipole-allowed upsilon(3) and upsilon(4) modes of the CF(4) partner. These transitions proceed predominantly through the near-resonant E-V energy transfer. The resonant character of the partner's excitation and the large mismatch in vibrational frequencies allow one to deduce the partner's vibrational product state distributions from the distributions measured for the molecule. The perspectives of the proposed theoretical model for treating a broad range of molecular collisions involving the spherical top partners are discussed.     

Theoretical investigation of the mechanism and dynamics of intramolecular coherent resonance energy transfer in soft molecules: a case study of dithia-anthracenophane

A computational study is conducted on dithia-anthracenophane (DTA), for which there is experimental evidence for coherent resonance energy transfer dynamics, and on dimethylanthracene (DMA), a molecule representing the energy donor and the acceptor in DTA. Electronic excitation energies are calculated by configuration interaction singles (CIS) and time-dependent density functional theory (TD-DFT) methods and are compared to experimental ones. Electronic coupling constants are calculated between two DMAs embedded into the ground-state structure of DTA employing methods based on transition densities. The resulting values of electronic coupling provide a more consistent interpretation of experiments than those based on one-half the level spacing of DTA excitation energies. Solvation effects are studied based on the polarizable continuum model (PCM). Solvent-induced polarization and screening effects are shown to make opposite contributions, and the net electronic coupling is little different from the value in a vacuum. The likelihood of coherent population transfer is assessed on the basis of a recently developed theory of coherent resonance energy transfer. The time scale of bath is shown to have an important role in sustaining the quantum coherence. The combination of quantum chemical and dynamical data suggests that the electronic coupling in DTA is in the range of 50-100 cm(-1). The presence of oscillatory excitation population dynamics can be understood from the picture of polaronic excitation moderately dressed with dispersive vibrational modes. The effect of torsional modulation on the excitation energies of DTA and electronic coupling is examined on the basis of optimized structures with the torsional angle constrained. The result suggests that inelastic effect due to torsional motion cannot be disregarded in DTA.