Optimization of laser-driven intramolecular hydrogen transfer in the presence of dephasing

The coherent control of laser-driven intramolecular hydrogen transfer is considered in the presence of pure dephasing. Emphasis is put on performing the optimization in the presence of dephasing. Simple analytical expressions are obtained for the optimal pulse shape and optimal yield as functions of the dephasing rate constant. It is found that dephasing is not always uncontrollable and destructive, and that the optimal pulse shape is dictated by the minimization of the destructive attributes of the dephasing processes, as much as by steering the coherent component of the dynamics towards the desired goal. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70057/2/JCPSA6-116-4-1629-1.pd

A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solutions

The temporal behavior of optical response functions (ORFs) reflects the quantum dynamics of an electronic superposition state, and as such lacks a well-defined classical limit. In this paper, we consider the importance of accounting for the quantum nature of the dynamics when calculating ORFs of different types. To this end, we calculated the ORFs associated with the linear absorption spectrum and the nonlinear two-pulse photon-echo experiment, via the following approaches: (1) the semiclassical forward-backward approach; (2) an approach based on linearizing the path-integral forward-backward action in terms of the difference between the forward and backward paths; (3) an approach based on ground state nuclear dynamics. The calculations were performed on a model that consists of a two-state chromophore solvated in a nonpolar liquid. The different methods were found to yield very similar results for the absorption spectrum and “diagonal” two-pulse photon echo (i.e., the homodyne-detected signal at time t = t0t=t0 after the second pulse, where t0t0 is the time interval between the two pulses). The different approximations yielded somewhat different results in the case of the time-integrated photon-echo signal. The reasons for the similarity between the predictions of different approximations are also discussedPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87863/2/064506_1.pd

A relationship between semiclassical and centroid correlation functions

A general relationship is established between semiclassical and centroid-based methods for calculating real-time quantum-mechanical correlation functions. It is first shown that the linearized semiclassical initial-value-representation (LSC-IVR) approximation can be obtained via direct linearization of the forward-backward action in the exact path integral expression for the correlation function. A Kubo-transformed two-time correlation function, with the position operator as one of the two operators, is then cast in terms of a carefully crafted exact path integral expression. Linearization of the corresponding forward–backward action, supplemented by the assumption that the dynamics of the centroid is decoupled from that of the higher normal modes, is then shown to lead to the centroid correlation function.© 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70917/2/JCPSA6-118-18-8173-1.pd

Vibrational energy relaxation rate constants from linear response theory

A new approach for the calculation of vibrational energy relaxation rate constants is introduced. The new approach is based on linear response theory, and is shown to have several distinct advantages over the standard Landau–Teller formula, which is based on the Bloch–Redfield theory, namely: (1) weak system–bath coupling is not assumed; (2) selectivity in choosing the vibrational energy relaxation pathway, including non-Landau–Teller pathways, is possible; (3) the validity of rate kinetics can be explicitly verified; (4) direct extraction of the high-frequency tail of the force–force correlation function is avoided. A detailed analysis of the conditions under which the new expression reduces into the Landau–Teller formula, and an application in the case of bilinear coupling to a harmonic bath are provided. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69779/2/JCPSA6-118-16-7562-1.pd

On the calculation of vibrational energy relaxation rate constants from centroid molecular dynamics simulations

We explore the use of centroid molecular dynamics (CMD) for calculating vibrational energy relaxation (VER) rate constants of high-frequency molecular vibrations in the condensed phase. We employ our recently proposed linear-response-theory-based approach to VER [Q. Shi and E. Geva, J. Chem. Phys. 118, 7562 (2003)], to obtain a new expression for the VER rate constant in terms of a correlation function that can be directly obtained from CMD simulations. We show that the new expression reduces to a centroid Landau-Teller-type formula in the golden-rule regime. Unlike previously proposed CMD-based approaches to VER, the new formula does not involve additional assumptions beyond the inherent CMD approximation. The new formula has the same form as the classical Landau–Teller formula, and quantum effects enter it in two ways: (1) The initial sampling and subsequent dynamics are governed by the centroid potential, rather than the classical potential; (2) The classical force is replaced by the corresponding centroid symbol. The application of the new method is reported for three model systems: (1) A vibrational mode coupled to a harmonic bath, with the coupling exponential in the bath coordinates; (2) A diatomic molecule coupled to a short linear chain of Helium atoms; (3) A “breathing sphere” diatomic molecule in a two-dimensional monoatomic Lennard-Jones liquid. It is confirmed that CMD is able to capture the main features of the force–force correlation function rather well, in both time and frequency domains. However, we also find that CMD is unable to accurately predict the high-frequency tail of the quantum-mechanical power spectrum of this correlation function, which limits its usefulness for calculating VER rate constants of high-frequency molecular vibrations. The predictions of CMD are compared with those obtained via the linearized-semiclassical initial-value-representation (LSC-IVR) method, which does yield accurate predictions of high-frequency VER rate constants. The reasons underlying these observations are discussed in terms of the similarities and differences between these two approaches. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71157/2/JCPSA6-119-17-9030-1.pd

Stimulated Raman adiabatic passage in the presence of dephasing

The prospect of employing the stimulated Raman adiabatic Passage (STIRAP) technique under the influence of pure dephasing is explored. A general analysis of how decoherence influences the performance of STIRAP is provided. Starting from a general and fully quantum-mechanical system–bath Hamiltonian, we derive a quantum master equation (QME) that describes the reduced dynamics of a dissipative STIRAP system. The derivation is based on the standard assumptions of (1) weak system–bath coupling; (2) Markovity, in the sense that the relaxation times are long in comparison to the bath correlation time, τc;τc; and (3) weak field–matter interaction, in the sense that the Rabi period of the driving laser fields, Ω−1,Ω−1, is longer than τc.τc. The dissipative term in this QME is the same as it would have been in the absence of the driving fields, because of the assumption of weak field–matter interaction. This type of uncontrollable dephasing is seen to diminish the efficiency of STIRAP, although the actual loss strongly depends on the specific dephasing mechanism. We also derive a more general QME, which is applicable to driving fields of arbitrary intensity. The dissipative term in the new QME is explicitly dependent on the driving fields, and therefore controllable. Intense fields are shown to effectively slow down the dephasing when Ωτc>1,Ωτc>1, which suggests that it may be possible to use STIRAP in order to transfer population between the quantum states of a solute molecule embedded in a solvent. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70266/2/JCPSA6-119-22-11773-1.pd

A semiclassical generalized quantum master equation for an arbitrary system-bath coupling

The Nakajima–Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC–GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard–Jones atoms. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69762/2/JCPSA6-120-22-10647-1.pd

Centroid-based methods for calculating quantum reaction rate constants: Centroid sampling versus centroid dynamics

A new method was recently introduced for calculating quantum mechanical rate constants from centroid molecular dynamics (CMD) simulations [E. Geva, Q. Shi, and G. A. Voth, J. Chem. Phys. 115, 9209 (2001)]. This new method is based on a formulation of the reaction rate constant in terms of the position-flux correlation function, which can be approximated in a well defined way via CMD. In the present paper, we consider two different approximated versions of this new method, which enhance its computational feasibility. The first approximation is based on propagating initial states which are sampled from the initial centroid distribution, on the classical potential surface. The second approximation is equivalent to a classical-like calculation of the reaction rate constant on the centroid potential, and has two distinct advantages: (1) it bypasses the problem of inefficient sampling which limits the applicability of the full CMD method at very low temperatures; (2) it has a well defined TST limit which is directly related to path-integral quantum transition state theory (PI-QTST). The approximations are tested on a model consisting of a symmetric double-well bilinearly coupled to a harmonic bath. Both approximations are quite successful in reproducing the results obtained via full CMD, and the second approximation is shown to provide a good estimate to the exact high-friction rate constants at very low temperatures. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70079/2/JCPSA6-116-8-3223-1.pd

A nonperturbative calculation of nonlinear spectroscopic signals in liquid solution

Nonlinear spectroscopic signals in liquid solution were calculated without treating the field-matter interaction in a perturbative manner. The calculation is based on the assumption that the intermolecular degrees of freedom can be treated classically, while the time evolution of the electronic state is treated quantum mechanically. The calculated overall electronic polarization is then resolved into its directional components via the method of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)]. It is shown that the time dependence of the directional components is independent of laser intensity in the impulsive pulse regime, which allows for flexibility in choosing the procedure for calculating optical response functions. The utility and robustness of the nonperturbative procedure is demonstrated in the case of a two-state chromophore solvated in a monoatomic liquid, by calculating nonlinear time-domain signals in the strong-field, weak-field, impulsive, and nonimpulsive regimes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87874/2/214501_1.pd

Quantum-mechanical reaction rate constants from centroid molecular dynamics simulations

It has been shown recently that in order for real-time correlation functions obtained from centroid molecular dynamics (CMD) simulations to be directly related, without further approximations, to the corresponding quantum correlation functions, one of the operators should be linear in the position and/or momentum [Jang and Voth, J. Chem. Phys. 111, 2357 (1999)]. Standard reaction rate theory relates the rate constant to the flux–Heaviside or the flux–flux correlation functions, which involve two nonlinear operators and therefore cannot be calculated via CMD without further approximations. We present an alternative, and completely equivalent, reaction rate theory which is based on the position–flux correlation function. The new formalism opens the door to more rigorously using CMD for the calculation of quantum reaction rate constants in general many-body systems. The new method is tested on a system consisting of a double-well potential bilinearly coupled to a harmonic bath. The results obtained via CMD are found to be in good agreement with the numerically exact results for a wide range of frictions and temperatures. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71074/2/JCPSA6-115-20-9209-1.pd