YiJing Yan

Exact quantum master equation via the calculus on path integrals.

An exact quantum master equation formalism is constructed for the efficient evaluation of quantum non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. A novel truncation scheme is further proposed and compared with other approaches to close the resulting hierarchically coupled equations of motion. The interplay between system-bath interaction strength, non-Markovian property, and required level of hierarchy is also demonstrated with the aid of simple spin-boson systems.

Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach

A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.

Time‐resolved fluorescence and hole‐burning line shapes of solvated molecules: Longitudinal dielectric relaxation and vibrational dynamics

We develop a microscopic theory of time‐ and frequency‐resolved fluorescence and hole‐burning measurements of polar, polyatomic molecules in a polar solvent. The line shapes are expressed in terms of gas phase spectroscopic parameters of the solute, vibrational relaxation rates, laser pulse shapes, and the dynamics of a solvation coordinate. These dynamics are then related to the frequency and wave vector dependent dielectric function of the solvent. Both fluorescence and hole‐burning line shapes are predicted to show significant line narrowing at short times, and to undergo broadening and a red shift as the solvent relaxes. We propose hole burning as an alternative to fluorescence measurements in probing solvation dynamics. The time scale of the solvent induced line shift and line broadening is found to be independent of the shape of the solute, in contrast with previous work. The effects of vibrational relaxation are distinguished from those of solvent relaxation.

Electronic dephasing, vibrational relaxation, and solvent friction in molecular nonlinear optical line shapes

The role of solvation dynamics in molecular nonlinear optical line shapes is analyzed using a reduced description based on the time evolution of the density matrix in Liouville space. Langevin equations are used to treat the coupling of the solvent to the molecular electronic and nuclear degrees of freedom. Electronic dephasing is calculated using a solvation coordinate which satisfies a generalized Fokker–Planck equation, and vibrational relaxation is related to the solvent viscosity and friction. The combined effect of both processes is incorporated into appropriate multitime correlation functions which are evaluated using a Liouville‐space generating function. The present eigenstate‐free approach is particularly suitable for calculating spectral line shapes as well as rate processes (isomerization, electron transfer) of large polyatomic molecules in condensed phases.

Optical control of molecular dynamics: Molecular cannons, reflectrons, and wave‐packet focusers

We consider the control of molecular dynamics using tailored light fields, based on a phase space theory of control [Y. J. Yan et al., J. Phys. Chem. 97, 2320 (1993)]. This theory enables us to calculate, in the weak field (one‐photon) limit, the globally optimal light field that produces the best overlap for a given phase space target. We present as an illustrative example the use of quantum control to overcome the natural tendency of quantum wave packets to delocalize on excited state potential energy curves. Three cases are studied: (i) a ‘‘molecular cannon’’ in which we focus an outgoing continuum wave packet of I2 in both position and momentum, (ii) a ‘‘reflectron’’ in which we focus an incoming bound wave packet of I2, and (iii) the focusing of a bound wave packet of Na2 at a turning point on the excited state potential using multiple light pulses to create a localized wave packet with zero momentum. For each case, we compute the globally optimal light field and also how well the wave packet produce...

Efficient hierarchical Liouville space propagator to quantum dissipative dynamics

We propose an efficient method to propagate the hierarchical quantum master equations based on a reformulation of the original formalism and the incorporation of a filtering algorithm that automatically truncates the hierarchy with a preselected tolerance. The new method is applied to calculate electron transfer dynamics in a spin-boson model and the absorption spectra of an excitonic dimmer. The proposed method significantly reduces the number of auxiliary density operators used in the hierarchical equation approach and thus provides an efficient way capable of studying real time dynamics of non-Markovian quantum dissipative systems in strong system-bath coupling and low temperature regimes.

Eigenstate‐free, Green function, calculation of molecular absorption and fluorescence line shapes

Green function techniques are used to develop a simple and efficient method towards the calculation of optical absorption, excitation, and dispersed fluorescence spectra of large harmonic polyatomic molecules. The molecular line shapes are expressed in terms of Fourier transforms of appropriate correlation functions which may be explicitly evaluated. Closed expressions are derived for a general harmonic molecule with two electronic states including equilibrium displacements, frequency changes, and Dushinsky rotation, within the Condon approximation. A simple method for extracting the complete set of parameters characterizing the ground and the electronically excited states from supersonic beam absorption and emission spectra is presented. Detailed calculations are performed for a model system with ten vibrational modes, and the sensitivity of the various experimental observables to Dushinsky rotation is analyzed.

Photon echoes of polyatomic molecules in condensed phases

A theory of optical echo spectroscopies of large polyatomic molecules in condensed phases is developed. Using phase space correlation functions, we examine the interrelationships among the following optical measurements: ordinary photon echo, stimulated photon echo, accumulated photon echo, incoherent accumulated photon echo, and pump–probe absorption. Conditions for the elimination of inhomogeneous broadening in these experiments are specified. A multimode Brownian oscillator model is used to account for high frequency molecular vibrations, as well as solvent modes, and electronic dephasing processes. The effects of quantum beats, spectral diffusion, and homogeneous dephasing on the echo signals are studied and compared in detail with pump–probe and hole burning spectroscopy.

Theory of open quantum systems

A quantum dissipation theory is constructed with the system–bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the correlated driving-dissipation effects can be accounted for exactly in terms of local-field correction. Remarks on a class of widely used phenomenological quantum master equations that neglects the bath dispersion-induced dissipation are also made in contact with the present theory.

Performance of Several Density Functional Theory Methods on Describing Hydrogen-Bond Interactions

We have investigated eleven density functionals, including LDA, PBE, mPWPW91, TPSS, B3LYP, X3LYP, PBE0, O3LYP, B97-1, MPW1K, and TPSSh, for their performances on describing hydrogen bond (HB) interactions. The emphasis has been laid not only on their abilities to calculate the intermolecular hydrogen bonding energies but also on their performances in predicting the relative energies of intermolecular H-bonded complexes and the conformer stabilities due to intramolecular hydrogen bondings. As compared to the best theoretical values, we found that although PBE and PBE0 gave the best estimation of HB strengths, they might fail to predict the correct order of relative HB energies, which might lead to a wrong prediction of the global minimum for different conformers. TPSS and TPSSh did not always improve over PBE and PBE0. B3LYP was found to underestimate the intermolecular HB strengths but was among the best performers in calculating the relative HB energies. We showed here that X3LYP and B97-1 were able to give good values for both absolute HB strengths and relative HB energies, making these functionals good candidates for HB description.