Markovian approximation in the relaxation of open quantum systems

In this paper, we examine the validity of the Markovian approximation and the slippage scheme used to incorporate short time transient memory effects in the Markovian master equations (Redfield equations). We argue that for a bath described by a spectral function, J(omega), that is dense and smoothly spread out over the range omega(d), a time scale of tau(b) approximately 1/omega(d) exists; for times of t > tau(b), the Markovian approximation is applicable. In addition, if J(omega) decays to zero reasonably fast in both the omega --> 0 and omega --> infinity limits, then the bath relaxation time, tau(b), is determined by the width of the spectral function and is weakly dependent on the temperature of the bath. On the basis of this criterion of tau(b), a scheme to incorporate transient memory effects in the Markovian master equation is suggested. Instead of using slipped initial conditions, we propose a concatenation scheme that uses the second-order perturbation theory for short time dynamics and the Markovian master equation at long times. Application of this concatenation scheme to the spin-boson model shows that it reproduces the reduced dynamics obtained from the non-Markovian master equation for all parameters studied, while the simple slippage scheme breaks down at high temperatures.     

Flexible biradicals in liquid and supercritical carbon dioxide: the exchange interaction, the chain dynamics, and a comparison with conventional solvents

X-band time-resolved electron paramagnetic resonance (TREPR) spectra of three flexible biradicals of varying chain length and structure were obtained in liquid and supercritical carbon dioxide (CO2) solutions and compared to conventional solvents. For C16 acyl-alkyl biradical 1a, an average spin exchange interaction between the radical centers, J(avg), was obtained by spectral simulation using a simple model for spin-correlated radical pairs (SCRPs) and a small amount of T2 relaxation from a previously established J modulation mechanism. A large solvent effect on J(avg) was observed for the first time, varying by almost 1 order of magnitude from CO2 (J(avg) = -120 +/- 10 MHz) to heavy mineral oil (-11 +/- 3 MHz) for 1a. For C15 bis(alkyl) biradical 1b, spectra obtained under supercritical conditions are only slightly different from those detected in liquid CO2 but differ from spectra taken in benzene. For C10 acyl-alkyl biradical 2a, more emissive spin polarization due to S-T- mixing is observed in CO2 than in benzene. These results are discussed in terms of solvent properties such as dielectric constant, viscosity, and specific interactions. Both chain dynamics and changes to the equilibrium distribution of end-to-end distances can alter J(avg) and the observed ratio of S-T0 to S-T- mixing; however, faster chain dynamics is concluded to be the most likely cause of the observed effects in these systems.     

Electronic excitation dynamics in multichromophoric systems described via a polaron-representation master equation

We derive a many-site version of the non-Markovian time-convolutionless polaron master equation [Jang et al., J. Chem Phys. 129, 101104 (2008)] to describe electronic excitation dynamics in multichromophoric systems. By treating electronic and vibrational degrees of freedom in a combined frame (polaron frame), this theory is capable of interpolating between weak and strong exciton-phonon coupling and is able to account for initial non-equilibrium bath states and spatially correlated environments. Besides outlining a general expression for the expected value of any electronic system observable in the original frame, we also discuss implications of the Markovian and Secular approximations highlighting that they need not hold in the untransformed frame despite being strictly satisfied in the polaron frame. The key features of the theory are illustrated using as an example a four-site subsystem of the Fenna-Mathews-Olson light-harvesting complex. For a spectral density including a localised mode, we show that oscillations of site populations may only be observed when non-equilibrium bath effects are taken into account. Furthermore, we illustrate how this formalism allows us to identify the electronic and vibrational components of the oscillatory dynamics.     

Solution reaction space Hamiltonian based on an electrostatic potential representation of solvent dynamics

Quantum chemical solvation models usually rely on the equilibrium solvation condition and is thus not immediately applicable to the study of nonequilibrium solvation dynamics, particularly those associated with chemical reactions. Here we address this problem by considering an effective Hamiltonian for solution-phase reactions based on an electrostatic potential (ESP) representation of solvent dynamics. In this approach a general ESP field of solvent is employed as collective solvent coordinate, and an effective Hamiltonian is constructed by treating both solute geometry and solvent ESP as dynamical variables. A harmonic bath is then attached onto the ESP variables in order to account for the stochastic nature of solvent dynamics. As an illustration we apply the above method to the proton transfer of a substituted phenol-amine complex in a polar solvent. The effective Hamiltonian is constructed by means of the reference interaction site model self-consistent field method (i.e., a type of quantum chemical solvation model), and a mixed quantum/classical simulation is performed in the space of solute geometry and solvent ESP. The results suggest that important dynamical features of proton transfer in solution can be captured by the present approach, including spontaneous fluctuations of solvent ESP that drives the proton from reactant to product potential wells.     

Nonadiabatic quantum dynamics based on a hierarchical electron-phonon model: exciton dissociation in semiconducting polymers

A hierarchical electron-phonon coupling model is applied to describe the ultrafast decay of a photogenerated exciton at a donor-acceptor polymer heterojunction, via a vibronic coupling mechanism by which a charge-localized interfacial state is created. Expanding upon an earlier Communication [H. Tamura et al., J. Chem. Phys. 126, 021103 (2007)], we present a quantum dynamical analysis based on a two-state linear vibronic coupling model, which accounts for a two-band phonon bath including high-frequency C[Double Bond]C stretch modes and low-frequency ring torsional modes. Building upon this model, an analysis in terms of a hierarchical chain of effective modes is carried out, whose construction is detailed in the present paper. Truncation of this chain at the order n (i.e., 3n+3 modes) conserves the Hamiltonian moments (cumulants) up to the (2n+3)rd order. The effective-mode analysis highlights (i) the dominance of the high-frequency modes in the coupling to the electronic subsystem and (ii) the key role of the low-frequency modes in the intramolecular vibrational redistribution process that is essential in mediating the decay to the charge-localized state. Due to this dynamical interplay, the effective-mode hierarchy has to be carried beyond the first order in order to obtain a qualitatively correct picture of the nonadiabatic process. A reduced model of the dynamics, including a Markovian closure of the hierarchy, is presented. Dynamical calculations were carried out using the multiconfiguration time-dependent Hartree method.     

Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration time-dependent Hartree method

In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.     

Time-dependent quantum transport: An efficient method based on Liouville-von-Neumann equation for single-electron density matrix

Basing on our hierarchical equations of motion for time-dependent quantum transport [X. Zheng, G. H. Chen, Y. Mo, S. K. Koo, H. Tian, C. Y. Yam, and Y. J. Yan, J. Chem. Phys. 133, 114101 (2010)], we develop an efficient and accurate numerical algorithm to solve the Liouville-von-Neumann equation. We solve the real-time evolution of the reduced single-electron density matrix at the tight-binding level. Calculations are carried out to simulate the transient current through a linear chain of atoms, with each represented by a single orbital. The self-energy matrix is expanded in terms of multiple Lorentzian functions, and the Fermi distribution function is evaluated via the Pade? spectrum decomposition. This Lorentzian-Pade? decomposition scheme is employed to simulate the transient current. With sufficient Lorentzian functions used to fit the self-energy matrices, we show that the lead spectral function and the dynamics response can be treated accurately. Compared to the conventional master equation approaches, our method is much more efficient as the computational time scales cubically with the system size and linearly with the simulation time. As a result, the simulations of the transient currents through systems containing up to one hundred of atoms have been carried out. As density functional theory is also an effective one-particle theory, the Lorentzian-Pade? decomposition scheme developed here can be generalized for first-principles simulation of realistic systems.     

Influence of aggregates and solvent aromaticity on the emission of conjugated polymers

The influence of aggregates and solvent aromaticity on the photophysics and fluorescence dynamics of two conjugated polymers is studied. The two polymers are derivatives of poly(p-phenylene vinylene) (PPV) containing different kinked moieties along the main chain. The polymers contain 2,6-diphenylpyridine and m-terphenyl kinked moieties and they are abbreviated as PN and PC, respectively. The insertion of kinked segments along the main chain shifts the emission spectrum from the yellow-orange spectral region, common to PPV derivatives, to the blue-green spectral region. The results show that in dilute solutions the polymers decay monoexponentially, while in concentrated ones the fluorescence decays biexponentially, indicating fluorescence quenching. This is attributed to an energy transfer process from polymer chains to aggregates that occurs within a few tens of picoseconds. By comparing the photophysics and fluorescence dynamics of polymer PN in a nonaromatic and an aromatic solvent, we conclude that the polymer conformation adopted in the aromatic solvent leads to a higher fluorescence quantum yield and a longer fluorescence lifetime. Furthermore, the fluorescence quenching of PN because of aggregates is faster and more efficient in the aromatic than in the nonaromatic solvent. These results can be explained through a more extended chain conformation of PN in the aromatic solvent.     

Dissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin and harmonic baths

The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the surrogate Hamiltonian approach. This method is based on constructing a system-bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results are compared to calculations that include a finite number of harmonic modes carried out by using the multiconfiguration time-dependent Hartree method of Nest and Meyer [J. Chem. Phys. 119, 24 (2003)]. In the weak coupling regime, at zero temperature and for small excitations of the primary system, both methods converge to the Markovian limit. When initially the primary system is significantly excited, the spin bath can saturate restricting the energy acceptance. An interaction term between bath modes that spreads the excitation eliminates the saturation. The loss of phase between two cat states has been analyzed and the results for the spin and harmonic baths are almost identical. For stronger couplings, the dynamics induced by the two types of baths deviate. The accumulation and degree of entanglement between the bath modes have been characterized. Only in the spin bath the dynamics generate entanglement between the bath modes.     

Continuum limit semiclassical initial value representation for dissipative systems

In this paper, we consider a dissipative system in which the system is coupled linearly to a harmonic bath. In the continuum limit, the bath is defined via a spectral density and the classical system dynamics is given in terms of a generalized Langevin equation. Using the path integral formulation and factorized initial conditions, it is well known that one can integrate out the harmonic bath, leaving only a path integral over the system degrees of freedom. However, the semiclassical initial value representation treatment of dissipative systems has usually been limited to a discretized treatment of the bath in terms of a finite number of bath oscillators. In this paper, the continuum limit of the semiclassical initial value representation is derived for dissipative systems. As in the path integral, the action is modified with an added nonlocal term, which expresses the influence of the bath on the dynamics. The first order correction term to the semiclassical initial value approximation is also derived in the continuum limit.     

On the Use of Accelerated Molecular Dynamics to Enhance Configurational Sampling in Ab Initio Simulations

We have implemented the accelerated molecular dynamics approach (Hamelberg, D.; Mongan, J.; McCammon, J. A. J. Chem. Phys. 2004, 120 (24), 11919) in the framework of ab initio MD (AIMD). Using three simple examples, we demonstrate that accelerated AIMD (A-AIMD) can be used to accelerate solvent relaxation in AIMD simulations and facilitate the detection of reaction coordinates: (i) We show, for one cyclohexane molecule in the gas phase, that the method can be used to accelerate the rate of the chair-to-chair interconversion by a factor of ～1 × 10(5), while allowing for the reconstruction of the correct canonical distribution of low-energy states; (ii) We then show, for a water box of 64 H(2)O molecules, that A-AIMD can also be used in the condensed phase to accelerate the sampling of water conformations, without affecting the structural properties of the solvent; and (iii) The method is then used to compute the potential of mean force (PMF) for the dissociation of Na-Cl in water, accelerating the convergence by a factor of ～3-4 compared to conventional AIMD simulations.(2) These results suggest that A-AIMD is a useful addition to existing methods for enhanced conformational and phase-space sampling in solution. While the method does not make the use of collective variables superfluous, it also does not require the user to define a set of collective variables that can capture all the low-energy minima on the potential energy surface. This property may prove very useful when dealing with highly complex multidimensional systems that require a quantum mechanical treatment.     

Simulated and NMR-derived backbone dynamics of a protein with significant flexibility: a comparison of spectral densities for the betaARK1 PH domain.

A 7.6 ns molecular dynamics trajectory of the betaARK1 PH domain in explicit water with appropriate ions was calculated at 300 K. Spectral densities at omega = 0, omega(N), and 0.87omega(H) and the model-free parameters were evaluated from the experimental as well as the simulated data, taking the anisotropic overall motion of the protein into account. Experimental and simulated spectral densities are in reasonable general agreement for NH bond vectors, where the corresponding motions have converged within the simulation time. A sufficient sampling of the motions for NH bonds within flexible parts of the protein requires a longer simulation time. The simulated spectral densities J(0) and J(omega(N)) are, on average, 4.5% and 16% lower than the experimental data; the corresponding numbers for the core residues are about 6%; the high-frequency spectral densities J(0.87omega(H)) are lower by, on average, 16% (21% for the core). The simulated order parameters, S(2), are also lower, although the overall disagreement between the simulation and experiment is less pronounced: 1% for all residues and 6% for the core. The observed systematic decrease of simulated spectral density and the order parameters compared to the experimental data can be partially attributed to the ultrafast librational motion of the NH bonds with respect to their peptide plane, which was analyzed in detail. This systematic difference is most pronounced for J(0.87omega(H)), which appears to be most sensitive to the slow, subnanosecond time scale of internal motion, whereas J(0) and J(omega(N)) are dominated by the overall rotational tumbling of the protein. Similar discrepancies are observed between the experimentally measured (15)N relaxation parameters (R(1), R(2), NOE) and their values calculated from the simulated spectral densities. The analysis of spectral densities provides additional information regarding the comparison of the simulated and experimental data, not available from the model-free analysis.     

Crooks equation for steered molecular dynamics using a Nosé-Hoover thermostat

The Crooks equation [Eq. (10) in J. Stat. Phys. 90, 1481 (1998)], originally derived for microscopically reversible Markovian systems, relates the work done on a system during an irreversible transformation to the free energy difference between the final and the initial state of the transformation. In the present work we provide a theoretical proof of the Crooks equation in the context of constant volume, constant temperature steered molecular dynamics simulations of systems thermostated by means of the Nosé-Hoover method (and its variant using a chain of thermostats). As a numerical test we use the folding and unfolding processes of decaalanine in vacuo at finite temperature. We show that the distribution of the irreversible work for the folding process is markedly non-Gaussian thereby implying, according to Crooks equation, that also the work distribution of the unfolding process must be inherently non-Gaussian. The clearly asymmetric behavior of the forward and backward irreversible work distributions is a signature of a non-Markovian regime for the folding/unfolding of decaalanine.     

Molecular modeling and simulation of conjugated polymer oligomers: ground and excited state chain dynamics of PPV in the gas phase

The ground and excited state dynamics of poly(p-phenylenevinylene) (PPV) chains is studied through an implementation of mixed quantum/classical molecular dynamics simulation. The model used in the simulations combines the semiempirical Pariser-Parr-Pople (PPP) Hamiltonian to treat the pi molecular electronic structure with a mechanical force field capturing all other aspects. Nuclear degrees of freedom are treated classically. We first validate the model by simulating PPV chains of various length, and evaluate the absorption spectra. The thermal disorder contribution to the breadth of the first absorption band is estimated to be 0.2 eV at T = 300 K. To investigate the relationship between the emission and chain conformation, we simulate an isolated ten unit chain of PPV in the ground and the lowest excited state. The emission spectrum, red-shifted with respect to absorption of about 0.2 eV as found in experiments, shows a structured line shape that we relate to the photoinduced CC bond distortions. In accord with earlier studies, the exciton self-traps in the middle of the chain. We introduce two collective variables that reflect geometrical distortion, and find these to be effective in describing the contribution of chain conformation to the emission spectrum. The collective variables are also shown to be effective in describing the bond relaxation dynamics after photoexcitation. Such a relaxation is found to occur in approximately 100 fs and is guided by a compensatory release of energy between the double and single bonds in the vinylene junctions and p-phenyl rings. Finally, we find that the chain has a very slight preference for a more planar conformation in the excited state, compared to the ground state. However, the thermal motions induce the chain to explore out-of-plane conformations in both the ground and the excited states with an amplitude significantly greater than this difference.     

Inhomogeneous multiscale dynamics in harmonic lattices

We use projection operators to address the coarse-grained multiscale problem in harmonic systems. Stochastic equations of motion for the coarse-grained variables, with an inhomogeneous level of coarse graining in both time and space, are presented. In contrast to previous approaches that typically start with thermodynamic averages, the key element of our approach is the use of a projection matrix chosen both for its physical appeal in analogy to mechanical stability theory and for its algebraic properties. We show that thermodynamic equilibrium can be recovered and obtain the fluctuation dissipation theorem a posteriori. All system-specific information can be computed from a series of feasible molecular dynamics simulations. We recover previous results in the literature and show how this approach can be used to extend the quasicontinuum approach and comment on implications for dissipative particle dynamics type of methods. Contrary to what is assumed in the latter models, the stochastic process of all coarse-grained variables is not necessarily Markovian, even though the variables are slow. Our approach is applicable to any system in which the coarse-grained regions are linear. As an example, we apply it to the dynamics of a single mesoscopic particle in the infinite one-dimensional harmonic chain.     

Ab initio dynamics study of poly-para-phenylene vinylene

We present an ab initio dynamics investigation within a density-functional perturbation theory framework of the properties of the conjugated polymer poly-para-phenylene vinylene (PPV) in both the isolated chain and crystalline states. The calculated results show that for an isolated chain, most of the vibrational modes correspond to experimentally observed modes in crystalline PPV. However, additional hitherto unidentified modes have been observed in experiment and our calculations on crystalline material have allowed us to assign these. We also present the results of calculations of the polarizability and permittivity tensors of the material, which are in reasonable agreement with the typical values for conjugated polymers. Dynamical Born effective charges [S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001)] are calculated and compared with atomic charges obtained from Mulliken population analysis [M. D. Segall, C. J. Pickard, R. Shah, and M. C. Payne, Mol. Phys. 89, 571 (1996)] and we conclude that effective charges are more appropriate for use in the study of the dynamics of the system. Notable differences are found in the infrared-absorption spectra obtained for the isolated chain and crystalline states, which can be attributed to the differences in the crystalline packing effects, which clearly play a key role in influencing the lattice dynamics of PPV.     

Communication: vacuum ultraviolet laser photodissociation studies of small molecules by the vacuum ultraviolet laser photoionization time-sliced velocity-mapped ion imaging method

We demonstrate that the vacuum ultraviolet (VUV) photodissociation dynamics of N(2) and CO(2) can be studied using VUV photoionization with time-sliced velocity-mapped ion imaging (VUV-PI-VMI) detection. The VUV laser light is produced by resonant sum frequency mixing in Kr. N(2) is used to show that when the photon energy of the VUV laser is above the ionization energy of an allowed transition of one of the product atoms it can be detected and characterized as the wavelength is varied. In this case a β parameter = 0.57 for the N((2)D°) was measured after exciting N(2)(o(1)Π(u), v(') = 2, J(') = 2) ← N(2)(X(1)Σ(g) (+), v(") = 0, J(") = 1). Studies with CO(2) show that when there is no allowed transition, an autoionization resonance can be used for the detection of a product atom. In this case it is shown for the first time that the O((1)D) atom is produced with CO((1)Σ(+)) at 92.21 nm. These results indicate that the VUV laser photodissociation combined with the VUV-PI-VMI detection is a viable method for studying the one-photon photodissociation from the ground state of simple molecules in the extreme ultraviolet and VUV spectral regions.     

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.     

Quantum conditions on dynamics and control in open systems

Quantum conditions on the control of dynamics of a system coupled to an environment are obtained. Specifically, consider a system initially in a system subspace H(0) of dimensionality M(0), which evolves to populate system subspaces H(1), H(2) of dimensionalities M(1), M(2). Then, there always exists an initial state in H(0) that does not evolve into H(2) if M(0)>dM(2), where 2相似文献