Multiphoton tea CO2 laser excitation of the triplet state of propynal

Multiple infrared photon excitation of propynal triplet molecules gives rise to a strongly perturbed phosphorescence. Following absorption of a few IR photons per molecule the phosphorescence spectrum extends to higher energy, the intensity increases, the decay — deviating from the original exponential decay — accelerates and the emission quantum yield drops dramatically. These findings are explained in terms of temperature sensitive radiative (T₁ → S₀) and radiationless (T₁ → S₀) processes with the vibrational temperature as the determining factor. During the perturbed triplet decay, the IR excitation initially confined to the vibrational degrees of freedom becomes distributed among all degrees of freedom which results in a decrease in the vibrational temperature and thus a complex phosphorescence decay.     

Effect of bending on the predissociation dynamics of N2O+

In this paper we introduce a modified version of the infinite-order sudden approximation (IOSA) for rotational and bending degrees of freedom, together     

An adiabatic linearized path integral approach for quantum time correlation functions: electronic transport in metal-molten salt solutions

We generalize the linearized path integral approach to evaluate quantum time correlation functions for systems best described by a set of nuclear and electronic degrees of freedom, restricting ourselves to the adiabatic approximation. If the operators in the correlation function are nondiagonal in the electronic states, then this adiabatic linearized path integral approximation for the thermal averaged quantum dynamics presents interesting and distinctive features, which we derive and explore in this paper. The capability of these approximations to accurately reproduce the behavior of physical systems is demonstrated by calculating the diffusion constant for an excess electron in a metal-molten salt solution.     

Quantum dynamical simulation of electron-transfer reactions in an anharmonic environment

The multilayer multiconfiguration time-dependent Hartree theory is applied to study the quantum dynamics of ultrafast electron-transfer reactions in a condensed-phase environment with anharmonic potential functions. Effects of anharmonicity for both the nuclear degrees of freedom of the environment and the intramolecular vibrational degrees of freedom are investigated. Whereas the former can in principle be mapped to a fictitious harmonic bath, the latter cannot be represented in this way and, thus, go beyond the commonly employed linear response approximation. Numerical examples are presented to illustrate these findings.     

A coherent state approach to semiclassical nonadiabatic dynamics

A semiclassical (SC) approximation to the quantum mechanical propagator for nonadiabatic systems is derived. Our derivation starts with an exact path integral expression that uses canonical coherent states for the nuclear degrees of freedom and spin coherent states for the electronic degrees of freedom. A stationary path approximation (SPA) is then applied to the path integral to obtain the SC approximation. The SPA results in complex classical trajectories of both nuclear and electronic degrees of freedom and a double ended boundary condition. The root search problem is solved using the previously proposed "real trajectory local search" algorithm. The SC approximation is tested on three simple one dimensional two-state systems proposed by Tully [J. Chem. Phys. 93, 1061 (1990)], and the SC results are compared to Ehrenfest and surface hopping predictions. Excellent agreement with quantum results is reached when the SC trajectory is far away from caustics. We discuss the origin of caustics in this SC formalism and the strengths and weaknesses of this approach.     

Homogeneity and Markovity of electronic dephasing in liquid solutions

The electronic dephasing dynamics of a solvated chromophore is formulated in terms of a non-Markovian master equation. Within this formulation, one describes the effect of the nuclear degrees of freedom on the electronic degrees of freedom in terms of a memory kernel function, which is explicitly dependent on the initial solvent configuration. In the case of homogeneous dynamics, this memory kernel becomes independent of the initial configuration. The Markovity of the dephasing process is also the most conveniently explored by comparing the results obtained via the non-Markovian master equation to these obtained via its Markovian counterpart. The homogeneous memory kernel is calculated for a two-state chromophore in liquid solution, and used to explore the sensitivity of photon echo signals to the heterogeneity and non-Markovity of the underlying solvation dynamics.     

Monte Carlo algorithms for simulating systems with adiabatic separation of electronic and nuclear degrees of freedom

Two Monte Carlo algorithms for the adiabatic sampling of nuclear and electronic degrees of freedom are introduced. In these algorithms the electronic degrees of freedom are subject to a secondary low-temperature thermostat in close analogy to the extended Lagrangian formalism used in molecular dynamics simulations. Numerical tests are carried out for two model systems of coupled harmonic oscillators, and for two more realistic systems: the water dimer and bulk liquid water. A statistical-mechanical discussion of the partition function for systems with adiabatic separation of electronic and nuclear degrees of freedom, but with finite electronic temperature, is presented. The theoretical analysis shows that the algorithms satisfy the adiabatic limit using suitable choices of the electronic temperature, T _elec, the number of electronic moves, R _elec, and the maximum step sizes used for displacements of nuclear coordinates. For quadratic coupling of the nuclear and electronic degrees of freedom, the electronic phase-space volume is independent of the nuclear coordinates. In this case, the sampling of the nuclear coordinate phase-space recovers the correct Born-Oppenheimer limit independent of T _elec, but each electronic degree of freedom contributes an offset of 0.5k _B T′_elec (with T _elec ^′−1=T ⁻¹+T _elec ⁻¹) to the average total energy. For nonquadratic coupling, satisfactory sampling of the nuclear coordinate phase-space requires a low T _elec to limit the ratio of the electronic phase-space volumes at T _elec and T′_elec to be close to unity. Received: 22 December 1998 / Accepted: 5 January 1999 / Published online: 21 June 1999     

On the influence of nuclear fluctuations on calculated NMR shieldings of benzene and ethylene: a Feynman path integral–ab initio investigation*

The absolute magnetic shieldings of benzene and ethylene have been theoretically studied under the conditions of thermal equilibrium, i.e., under explicit consideration of the nuclear degrees of freedom. For this purpose we have combined the Feynman path integral quantum Monte Carlo (PIMC) formalism with the gauge‐including atomic orbital (GIAO) approach in the Hartree–Fock (HF) approximation. The HF operator has been employed to derive the NMR parameters of the two hydrocarbons via an ensemble averaging over large sets of molecular configurations that are populated in thermal equilibrium. The nuclear fluctuations are responsible for a deshielding of the nuclei relative to the shieldings at the vibrationless minimum of the potential energy surface (PES). The influence of the nuclear degrees of freedom is largest for the isotropic part of the ¹³C shielding tensor. The theoretical results can be explained on the basis of simple geometrical considerations. The bond lengths in thermal equilibrium are larger than the bond lengths at the minimum of the PES. This length enhancement is the prerequisite for a deshielding of the nuclei in thermal equilibrium. The vibrational corrections of the nuclear magnetic resonance (NMR) parameters of benzene and ethylene are quantum driven; classical thermal degrees of freedom of the nuclei are of minor importance. Conceptual problems of theoretical studies of NMR parameters on the basis of a single molecular geometry are emphasized. The influence of the spatial uncertainty of the nuclei becomes decisive in molecules with light atoms. It is pointed out that the combination of the PIMC formalism with electronic Hamiltonians of state‐of‐the‐art quality renders possible accurate determinations of NMR parameters. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem 86: 280–296, 2002     

On the role of nuclear motions in electron and excitation transfer rates: Importance of transfer-integral dependence upon nuclear coordinate

The role of nuclear degrees of freedom in modifying the electron or exciton transfer rates between molecules is investigated. In addition to the usual Franck-Condon overlap factors which arise from the overlaps of initial and final vibrational states, we discuss a dependence of the transfer integral upon nuclear motions, a dependence which has been often cited, but nearly always ignored, in the usual dynamical theories of transfer processes. We show, within a Bom-Oppenheimer treatment, that the transfer integral dependence upon librational, rotational and vibrational modes can profoundly change both the rate itself and its functional dependences (upon temperature, upon orientation, etc.). Using a simple cosine form for the dependence of the transfer integral upon the modifying nuclear mode and a simple displaced-oscillator transformation, we obtain a closed-form solution for the transfer rate, which includes a new overlap factor arising from the dependence of the transfer integral upon nuclear coordinates. Some general remarks about the role of this dependence are made, and applications to particular transfer systems are briefly discussed.     

Short-time dynamics through conical intersections in macrosystems. I. Theory: effective-mode formulation

The short-time dynamics through a conical intersection of a macrosystem comprising a large number of nuclear degrees of freedom (modes) is investigated. The macrosystem is decomposed into a "system" part carrying a limited number of modes, and an "environment" part. An orthogonal transformation in the environment's space is introduced, as a result of which a subset of three effective modes can be identified which couple directly to the electronic subsystem. Together with the system's modes, these govern the short-time dynamics of the overall macrosystem. The remaining environmental modes couple, in turn, to the effective modes and become relevant at longer times. In this paper, we present the derivation of the effective Hamiltonian, first introduced by Cederbaum et al. [Phys. Rev. Lett. 94, 113003 (2005)], and analyze its properties in some detail. Several special cases and topological aspects are discussed.     

Monte Carlo and event-driven dynamics of Brownian particles with orientational degrees of freedom

Recently, a simple scaling argument was introduced that allows us to map, with some precautions, Brownian and Monte Carlo dynamics for spherical particles. Here, we extend the scaling to study systems that have orientational degrees of freedom and carefully asses its validity over a wide region of temperature and density. Our work allows us to devise a Brownian Monte Carlo algorithm that produces, to a good approximation, physically meaningful trajectories with a minimum programming effort, although at the expense of some sampling efficiency.     

Structurally determined directionality identifies the boundary between mobile and immobile domains in a disordered material

The structure and available degrees of freedom of an amorphous configuration can determine the location of dynamic heterogeneities. In the same way, these features can also determine the directionality of the particle motion. In this paper we propose that directionality can be attributed to those particles that only participate in a single unconstrained motion. The consequences of this suggestion in terms of the spatial distribution of particles with high directionality are explored using a random bond model.     

Multi‐Resolution Simulation of Biomolecular Systems: A Review of Methodological Issues

Theoretical‐computational modeling with an eye to explaining experimental observations in regard to a particular chemical phenomenon or process requires choices concerning essential degrees of freedom and types of interactions and the generation of a Boltzmann ensemble or trajectories of configurations. Depending on the degrees of freedom that are essential to the process of interest, for example, electronic or nuclear versus atomic, molecular or supra‐molecular, quantum‐ or classical‐mechanical equations of motion are to be used. In multi‐resolution simulation, various levels of resolution, for example, electronic, atomic, supra‐atomic or supra‐molecular, are combined in one model. This allows an enhancement of the computational efficiency, while maintaining sufficient detail with respect to particular degrees of freedom. The basic challenges and choices with respect to multi‐resolution modeling are reviewed and as an illustration the differential catalytic properties of two enzymes with similar folds but different substrates with respect to these substrates are explored using multi‐resolution simulation at the electronic, atomic and supra‐molecular levels of resolution.     

Exact quantum statistics for electronically nonadiabatic systems using continuous path variables

We derive an exact, continuous-variable path integral (PI) representation of the canonical partition function for electronically nonadiabatic systems. Utilizing the Stock-Thoss (ST) mapping for an N-level system, matrix elements of the Boltzmann operator are expressed in Cartesian coordinates for both the nuclear and electronic degrees of freedom. The PI discretization presented here properly constrains the electronic Cartesian coordinates to the physical subspace of the mapping. We numerically demonstrate that the resulting PI-ST representation is exact for the calculation of equilibrium properties of systems with coupled electronic and nuclear degrees of freedom. We further show that the PI-ST formulation provides a natural means to initialize semiclassical trajectories for the calculation of real-time thermal correlation functions, which is numerically demonstrated in applications to a series of nonadiabatic model systems.     

Spectroscopic units in conjugated polymers: a quantum chemically founded concept?

In conjugated polymers the concept of spectroscopic units belonging to different spatial segments of the chain, which are responsible for the spectroscopic properties of the polymer, has been used to explain the spectral heterogeneity and the excitation migration by (F?rster type) hopping transfer. In the present work we study the possible mechanism of segmentation of polythiophene into spectroscopic units by using quantum-chemical methods (ZINDO). We found that static geometric defects such as kinks or torsions do not result in a significant localization of the excited states to a certain segment. Hence, we propose that a dynamic localization of excitation due to the interaction between the nuclear and electronic degrees of freedom is responsible for the formation of the spectroscopic units.     

Exciton coherence lifetimes from electronic structure

We model the coherent energy transfer of an electronic excitation within covalently linked aromatic homodimers from first-principles. Our results shed light on whether commonly used models of the bath calculated via detailed electronic structure calculations can reproduce the key dynamics. For the systems we model, the time scales of coherent transport are experimentally known from time-dependent polarization anisotropy measurements, and so we can directly assess whether current techniques are predictive for modeling coherent transport. The coupling of the electronic degrees of freedom to the nuclear degrees of freedom is calculated from first-principles rather than assumed, and the fluorescence anisotropy decay is directly reproduced. Surprisingly, we find that although time-dependent density functional theory absolute energies are routinely in error by orders of magnitude more than the coupling energy between monomers, the coherent transport properties of these dimers can be semi-quantitatively reproduced from these calculations. Future directions which must be pursued to yield predictive and reliable models of coherent transport are suggested.