Time-dependent density functional theory of open quantum systems in the linear-response regime

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Go?rling-Levy perturbation theory is calculated.     

Formation and relaxation of excited states in solution: a new time dependent polarizable continuum model based on time dependent density functional theory

In this paper a novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model. Such an approach uses the excited state relaxed density matrix to correct the time dependent density functional theory excitation energies and it introduces a state-specific solvent response, which can be further generalized within a time dependent formalism. This generalization is based on the use of a complex dielectric permittivity as a function of the frequency, epsilonomega. The approach is here presented in its theoretical formulation and applied to the various steps involved in the formation and relaxation of electronic excited states in solvated molecules. In particular, vertical excitations (and emissions), as well as time dependent Stokes shift and complete relaxation from vertical excited states back to ground state, can be obtained as different applications of the same theory. Numerical results on two molecular systems are reported to better illustrate the features of the model.     

Electronic structure contributions to electron-transfer reactivity in iron-sulfur active sites: 1. Photoelectron spectroscopic determination of electronic relaxation

Electronic relaxation, the change in molecular electronic structure as a response to oxidation, is investigated in [FeX(4)](2)(-)(,1)(-) (X = Cl, SR) model complexes. Photoelectron spectroscopy, in conjunction with density functional methods, is used to define and evaluate the core and valence electronic relaxation upon ionization of [FeX(4)](2)(-). The presence of intense yet formally forbidden charge-transfer satellite peaks in the PES data is a direct reflection of electronic relaxation. The phenomenon is evaluated as a function of charge redistribution at the metal center (Deltaq(rlx)) resulting from changes in the electronic structure. This charge redistribution is calculated from experimental core and valence PES data using a valence bond configuration interaction (VBCI) model. It is found that electronic relaxation is very large for both core (Fe 2p) and valence (Fe 3d) ionization processes and that it is greater in [Fe(SR)(4)](2)(-) than in [FeCl(4)](2)(-). Similar results are obtained from DFT calculations. The results suggest that, although the lowest-energy valence ionization (from the redox-active molecular orbital) is metal-based, electronic relaxation causes a dramatic redistribution of electron density ( approximately 0.7ē) from the ligands to the metal center corresponding to a generalized increase in covalency over all M-L bonds. The more covalent tetrathiolate achieves a larger Deltaq(rlx) because the LMCT states responsible for relaxation are significantly lower in energy than those in the tetrachloride. The large observed electronic relaxation can make significant contributions to the thermodynamics and kinetics of electron transfer in inorganic systems.     

Basis set study of classical rotor lattice dynamics

The reorientational relaxation of molecular systems is important in many phenomenon and applications. In this paper, we explore the reorientational relaxation of a model Brownian rotor lattice system with short range interactions in both the high and low temperature regimes. In this study, we use a basis set expansion to capture collective motions of the system. The single particle basis set is used in the high temperature regime, while the spin wave basis is used in the low temperature regime. The equations of motion derived in this approach are analogous to the generalized Langevin equation, but the equations render flexibility by allowing nonequilibrium initial conditions. This calculation shows that the choice of projection operators in the generalized Langevin equation (GLE) approach corresponds to defining a specific inner-product space, and this inner-product space should be chosen to reveal the important physics of the problem. The basis set approach corresponds to an inner-product and projection operator that maintain the orthogonality of the spherical harmonics and provide a convenient platform for analyzing GLE expansions. The results compare favorably with numerical simulations, and the formalism is easily extended to more complex systems.     

Polaronic quantum master equation theory of inelastic and coherent resonance energy transfer for soft systems

This work extends the theory of coherent resonance energy transfer [S. Jang, J. Chem. Phys. 131, 164101 (2009)] by including quantum mechanical inelastic effects due to modulation of donor-acceptor electronic coupling. Within the approach of the second order time local quantum master equation (QME) in the polaron picture and under the assumption that the bath degrees of freedom modulating the electronic coupling are independent of other modes, a general time evolution equation for the reduced system density operator is derived. Detailed expressions for the relaxation operators and inhomogeneous terms of the QME are then derived for three specific models of modulation in distance, axial angle, and dihedral angle, which are all approximated by harmonic oscillators. Numerical tests are conducted for a set of model parameters. Model calculation shows that the torsional modulation can make significant contribution to the relaxation and dephasing mechanisms.     

Semiclassical initial value series representation in the continuum limit: application to vibrational relaxation

A recently formulated continuum limit semiclassical initial value series representation (SCIVR) of the quantum dynamics of dissipative systems is applied to the study of vibrational relaxation of model harmonic and anharmonic oscillator systems. As is well known, the classical dynamics of dissipative systems may be described in terms of a generalized Langevin equation. The continuum limit SCIVR uses the Langevin trajectories as input, albeit with a quantum noise rather than a classical noise. Combining this development with the forward-backward form of the prefactor-free propagator leads to a tractable scheme for computing quantum thermal correlation functions. Here we present the first implementation of this continuum limit SCIVR series method to study two model problems of vibrational relaxation. Simulations of the dissipative harmonic oscillator system over a wide range of parameters demonstrate that at most only the first two terms in the SCIVR series are needed for convergence of the correlation function. The methodology is then applied to the vibrational relaxation of a dissipative Morse oscillator. Here, too, the SCIVR series converges rapidly as the first two terms are sufficient to provide the quantum mechanical relaxation with an estimated accuracy on the order of a few percent. The results in this case are compared with computations obtained using the classical Wigner approximation for the relaxation dynamics.     

From aromaticity to self-organized criticality in graphene

The unique properties of graphene are rooted in its peculiar electronic structure where effects of electron delocalization are pivotal. We show that the traditional view of delocalization as formation of a local or global aromatic bonding framework has to be expanded in this case. A modification of the π-electron system of a finite-size graphene substrate results in a scale-invariant response in the relaxation of interatomic distances and reveals self-organized criticality as a mode of delocalized bonding. Graphene is shown to belong to a diverse class of finite-size extended systems with simple local interactions where complexity emerges spontaneously under very general conditions that can be a critical factor controlling observable properties such as chemical activity, electron transport, and spin-polarization.     

Extended charge decomposition analysis and its application for the investigation of electronic relaxation

A general and comprehensive molecular orbital method for the investigation of the electronic relaxation contribution to redox processes is presented. This method is based on the population analysis of the molecular orbitals of the final electronic state in terms of the occupied and unoccupied molecular orbitals of the Koopmans’ state. The DFT calculations for oxidation and reduction of transition-metal species indicate a dramatic magnitude of electronic relaxation in these systems. The passive molecular orbitals play a more significant role in electronic relaxation than the redox-active molecular orbital that directly participates in the redox process. The mechanism of electronic relaxation in the oxidation of Fe^II and Cu^I species varies from the ligand to metal 3d charge transfer (LMCT) interactions to the ligand to metal 4s,4p LMCT. For systems with significant electronic delocalization, electronic relaxation becomes smaller leading to much smaller contributions to the redox processes. Dedication: This contribution is to celebrate Philip Stephen’s seminal contributions to theory and experiment. An erratum to this article can be found at     

Relaxation time, diffusion, and viscosity analysis of model asphalt systems using molecular simulation

Molecular dynamics simulation was used to calculate rotational relaxation time, diffusion coefficient, and zero-shear viscosity for a pure aromatic compound (naphthalene) and for aromatic and aliphatic components in model asphalt systems over a temperature range of 298-443 K. The model asphalt systems were chosen previously to represent real asphalt. Green-Kubo and Einstein methods were used to estimate viscosity at high temperature (443.15 K). Rotational relaxation times were calculated by nonlinear regression of orientation correlation functions to a modified Kohlrausch-Williams-Watts function. The Vogel-Fulcher-Tammann equation was used to analyze the temperature dependences of relaxation time, viscosity, and diffusion coefficient. The temperature dependences of viscosity and relaxation time were related using the Debye-Stokes-Einstein equation, enabling viscosity at low temperatures of two model asphalt systems to be estimated from high temperature (443.15 K) viscosity and temperature-dependent relaxation time results. Semiquantitative accuracy of such an equivalent temperature dependence was found for naphthalene. Diffusion coefficient showed a much smaller temperature dependence for all components in the model asphalt systems. Dimethylnaphthalene diffused the fastest while asphaltene molecules diffused the slowest. Neat naphthalene diffused faster than any component in model asphalts.     

Continuum Model for Electronic Polarization Based on a Novel Dielectric Response Function

A generalized response function based on the use of dielectric spectra for dielectric relaxation process is derived. We apply the general response function to the special case in order to examine how special dielectric relaxation functions developed by other authors for solvent relaxation can be derived based on our formulations. Three typical solvents, water, methanol, and acetonitrile are used to investigate the electronic polarization processes of polar solvents. The solvent electronic polarization process is shown after a linear variation with the external electric field imposed on the solvent. The results show a conclusion that the electronic polarization of the solvents will accompany the electronic transition synchronously, without time lag.     

Polymerization-induced viscoelastic phase separation in polyethersulfone-modified epoxy systems

The polymerization-induced phase-separation process of polyethersulfone (PES)-modified epoxy systems was monitored in situ continuously on a single sample throughout the entire curing process by using optical microscopes, time-resolved light scattering (TRLS), scanning electronic microscopes (SEM), and a rheometry instrument. At specific PES content a viscoelastic transformation process of phase inversion morphology to bicontinuous was found with an optical microscope. The rheological behavior during phase separation corresponds well with the morphology development. Light-scattering results monitoring the phase-separation process of systems with final phase inversion morphology show a typical exponential decay procedure of scattering vector qm. The characteristic relaxation time of phase separation can be described well by the WLF equation.     

Fluorescence Lifetimes: Effect of Precision of Relaxation Times from Fluorescence Depolarization Data

Abstract

The fluorescence lifetime τ enters into the Perrin-Weber equation used to determine rotational relaxation times of proteins by the steady-state depolarization method. If is either too short or too long, the relaxation time cannot be measured with precision. With reasonable assumptions as to photometric precision, it has been possible to compute the precision of relaxation time assays for different lifetime:relaxation time ratios, thus also determining the “optimum” lifetimes for different systems. These results provide a basis for designing experiments requiring optimal conditions, and also provide insight into the amount of allowable deviation from optimal conditions. The short lifetimes of intrinsic protein fluorescence can often be used to determine the global relaxation rate of the macromolecule with acceptable precision.     

Relaxation and dephasing in open quantum systems time-dependent density functional theory: Properties of exact functionals from an exactly-solvable model system

The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum systems time-dependent density functional theory (OQS-TDDFT) within the master equation approach were established. It was proven that the exact time-dependent density of a many-electron open quantum system evolving under a master equation can be reproduced with a closed (unitarily evolving) and non-interacting Kohn-Sham system. This potentially offers a great advantage over previous approaches to OQS-TDDFT, since with suitable functionals one could obtain the dissipative open-systems dynamics by simply propagating a set of Kohn-Sham orbitals as in usual TDDFT. However, the properties and exact conditions of such open-systems functionals are largely unknown. In the present article, we examine a simple and exactly-solvable model open quantum system: one electron in a harmonic well evolving under the Lindblad master equation. We examine two different representitive limits of the Lindblad equation (relaxation and pure dephasing) and are able to deduce a number of properties of the exact OQS-TDDFT functional. Challenges associated with developing approximate functionals for many-electron open quantum systems are also discussed.     

An alternative way of characterising the bonding in compounds featuring main-group elements and with the potential for multiple bonding: on the dissociation of binary main-group hydrides

Herein the bonding in compounds featuring main-group elements and with the potential for multiple bonding is studied theoretically by examination of their fragmentation into two fragments that still exhibit the same structure as they had in the molecule prior to dissociation. The fragments were calculated both in their electronic ground state and in an excited electronic state, in which the number of unpaired electrons is equal to the maximal number of bonds in the compounds before dissociation. The energies of the fragmentation processes (DeltaE(frag)) can be more directly linked to the bond strengths than the dissociation energies (DeltaE(diss)), because of the absence of any secondary effects like relaxation of the electronic state or of the geometry of the fragments. These relaxation energies of the fragments (DeltaE(frag)) are also studied herein. The energies derived in this work allow for an accurate comparison of the bonding properties in main-group-element hydrides. The trends of the fragmentation and relaxation energies are discussed in detail. It will be shown that the relaxation energies allow for a classification of the bonds ("classical" sigma and pi bonds or donor-acceptor interactions), while the fragmentation energies are good quantitative measures for the total bond strength. Similar calculations are on the way to explore the bonding in systems in which the hydrogen atoms are replaced by organic groups or halogen atoms.     

Semiclassical treatment of thermally activated electron transfer in the intermediate to strong electronic coupling regime under the fast dielectric relaxation

The generalized nonadiabatic transition-state theory (NA-TST) (Zhao, Y.; et al. J. Chem. Phys. 2004, 121, 8854) is used to study electron transfer with use of the Zhu-Nakamura (ZN) formulas of nonadiabatic transition in the case of fast dielectric relaxation. The rate constant is expressed as a product of the well-known Marcus formula and a coefficient which represents the correction due to the strong electronic coupling. In the case of general multidimensional systems, the Monte Carlo approach is utilized to evaluate the rate by taking into account the multidimensionality of the crossing seam surface. Numerical demonstration is made by using a model system of a collection of harmonic oscillators in the Marcus normal region. The results are naturally coincident with the perturbation theory in the weak electronic coupling limit; while in the intermediate to strong electronic coupling regime where the perturbation theory breaks down the present results are in good agreement with those from the quantum mechanical flux-flux correlation function within the model of effective one-dimensional mode.     

Effects of the strain rate and temperature in stress–strain tests: study of the glass transition of a polyamide-6

In this work new insights are presented on the measurement of the tangent and secant moduli from stress–strain curves in polymeric systems. Expressions for the strain-rate and strain dependence of both moduli are derived for systems characterised by a distribution of relaxation times. The equivalent frequency of the stress–strain experiments is shown to be dependent on the strain rate and on the strain at which the measurements are carried out. Such considerations enable using quasi-static tensile stress–strain tests to study relaxational processes in polymeric materials. The tensile behaviour of a 30% glass fibre reinforced polyamide 6 was characterised at different strain rates and temperatures, covering the glass transition region. A master curve of the tangent modulus as a function of strain rate was successfully constructed by simple horizontal shifting of the isothermal data. The temperature dependence of the shift factors was well described by the WLF equation. It was also possible to fit the master curve considering a polymeric system with a distribution of relaxation times, relevant parameters such as the KWW β parameter being extracted. The results were found to be consistent with dynamic mechanical analysis results.     

Quantum chemistry studies of electronically excited nitrobenzene, TNA, and TNT

The electronic excitation energies and excited-state potential energy surfaces of nitrobenzene, 2,4,6-trinitroaniline (TNA), and 2,4,6-trinitrotoluene (TNT) are calculated using time-dependent density functional theory and multiconfigurational ab initio methods. We describe the geometrical and energetic character of excited-state minima, reaction coordinates, and nonadiabatic regions in these systems. In addition, the potential energy surfaces for the lowest two singlet (S(0) and S(1)) and lowest two triplet (T(1) and T(2)) electronic states are investigated, with particular emphasis on the S(1) relaxation pathway and the nonadiabatic region leading to radiationless decay of S(1) population. In nitrobenzene, relaxation on S(1) occurs by out-of-plane rotation and pyramidalization of the nitro group. Radiationless decay can take place through a nonadiabatic region, which, at the TD-DFT level, is characterized by near-degeneracy of three electronic states, namely, S(1), S(0), and T(2). Moreover, spin-orbit coupling constants for the S(0)/T(2) and S(1)/T(2) electronic state pairs were calculated to be as high as 60 cm(-1) in this region. Our results suggest that the S(1) population should quench primarily to the T(2) state. This finding is in support of recent experimental results and sheds light on the photochemistry of heavier nitroarenes. In TNT and TNA, the dominant pathway for relaxation on S(1) is through geometric distortions, similar to that found for nitrobenzene, of a single ortho-substituted NO(2). The two singlet and lowest two triplet electronic states are qualitatively similar to those of nitrobenzene along a minimal S(1) energy pathway.