Eitan Geva

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.

A derivation of the mixed quantum-classical Liouville equation from the influence functional formalism

We show that the mixed quantum-classical Liouville equation is equivalent to linearizing the forward-backward action in the influence functional. Derivations are provided in terms of either the diabatic or adiabatic basis sets. An application of the mixed quantum-classical Liouville equation for calculating the memory kernel of the generalized quantum master equation is also presented. The accuracy and computational feasibility of such an approach is demonstrated in the case of a two-level system nonlinearly coupled to an anharmonic bath.

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 a...

Two-Dimensional Infrared Spectroscopy of Metal Carbonyls

Metal carbonyl complexes offer both rich chemistry and complex vibrational spectroscopy due to strong coupling among the carbonyl stretches. Using two-dimensional infrared (2DIR) spectroscopy, it is possible to resolve the underlying transitions between vibrational energy levels, determine the orientations and relative magnitude of the corresponding transition dipole moments, measure the coupling between modes due to the anharmonicity of the potential, and probe energy redistribution among the modes as well as energy relaxation to other degrees of freedom. Measurements on metal carbonyl complexes have played, and continue to play, a crucial role in facilitating the development of 2DIR spectroscopy. These compounds have provided powerful demonstrations of the unique ability of 2DIR spectroscopy to resolve vibrational structure and dynamics in multimode systems. In addition, invaluable new information has been obtained on metal-to-ligand charge transfer processes, solvent-solute interactions and fluxionality. Since transition metal complexes play important roles in catalysis and as dye sensitizers for semiconductor nanoparticle photocatalysis, detailed probes of equilibrium and phototriggered dynamics should aid our understanding of these key catalytic systems. The richness and level of detail provided by the 2DIR spectra of metal carbonyl complexes turn them into extremely useful model systems for testing the accuracy of ab initio quantum chemical calculations. Accurate modeling of the 2DIR spectra of solvated metal carbonyl complexes requires the development of new theoretical and computational tools beyond those employed in the standard analysis of one-dimensional IR spectra, and represents an ongoing challenge to currently available computational methodologies. These challenges are further compounded by the increasing interest in triggered 2DIR experiments that involve nonequilibrium vibrational dynamics on multiple electronic potential surfaces. In this Account, we review the various metal carbonyl complexes studied via 2DIR spectroscopy and outline the theoretical approaches used in order to model the spectra. The capabilities of 2DIR spectroscopy and its interplay with modern ab initio calculations are demonstrated in the context of the metal carbonyl complex Mn(2)(CO)(10) recently studied in our lab. Continued progress in experimental implementation and theoretical analysis will enable transient 2D spectroscopy to provide structurally sensitive details of complex, highly interacting nonequilibrium processes that are central to diverse chemical transformations.

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.

A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system-bath coupling

The Nakajima–Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system’s dynamics. The standard approach is based on using a perturbative treatment of the system–bath coupling for calculating this kernel, and is therefore restricted to systems weakly coupled to the bath. In this paper, we propose a new approach for calculating the memory kernel for an arbitrary system–bath coupling. The memory kernel is obtained by solving a set of two coupled integral equations that relate it to a new type of two-time system-dependent bath correlation functions. The feasibility of the method is demonstrated in the case of an asymetrical two-level system linearly coupled to a harmonic bath.

Ab Initio Study of the Emissive Charge-Transfer States of Solvated Chromophore-Functionalized Silsesquioxanes

Recent experimental advances in the ability to tune the optical properties of silsesquioxanes by functionalizing them with photoactive ligands have made these compounds attractive candidates for building blocks of photovoltaic materials. We employ state-of-the-art ab initio methodologies to determine the nature of the excited charge-transfer (CT) states that give rise to a large red-shift between absorption and emission in these molecules, in comparison to the corresponding red-shift in the individual ligand. The calculations are based on time-dependent density functional theory and employ the recently developed Baer-Neuhauser-Livshits range-separated hybrid (RSH) functional. Solvent effects are accounted for via a combination of charge-constrained density functional theory and the polarizable continuum model. We find that the experimentally observed red-shift is consistent with identifying the emissive state as a ligand-to-ligand, rather than a ligand-to-silsesquioxane, CT state. We also find that the enhanced red-shift cannot be explained without accounting for solvation effects, and we demonstrate the importance of using a RSH functional to obtain reliable predictions regarding the emissive state.

Solvated Charge Transfer States of Functionalized Anthracene and Tetracyanoethylene Dimers: A Computational Study Based on a Range Separated Hybrid Functional and Charge Constrained Self-Consistent Field with Switching Gaussian Polarized Continuum Models.

We benchmark several protocols for evaluating the energies of excited charge transfer (CT) states of organic molecules dissolved in polar liquids. The protocols combine time-dependent density functional theory using range-separated hybrid functionals, constrained density functional theory, dispersion corrected functional, and a dielectric continuum model for representing the solvent. We compare the different protocols against well-established experimental measured charge transfer state energies in solvated dimers of functionalized anthracene and tetracyanoethylene. We find that using the range-separated hybrid functional for the charge-transfer state energies and the combination of constrained density functional theory with the recently improved switching Gaussian polarizable continuum model (PCM) provide good agreement with the experimental values of the solvated CT states. We also find that using dispersion corrected solvated geometries for the weakly coupled donor-acceptor dimers considered here leads to improved agreement with experimental measured values.

A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solution. II. The signature of excited state dynamics on two-dimensional spectra

Optical response functions are known to reflect quantum dynamics in a superposition state and as such, lack a well-defined classical limit. In a previous paper we considered the importance of accounting for the quantum nature of the dynamics by comparing the linear absorption spectrum and homodyne-detected time-integrated two-pulse photon-echo signal as calculated via the semiclassical forward-backward approach, linearized semiclassical approach, and standard approach which is based on equilibrium ground state dynamics [Shi and Geva, J. Chem. Phys. 122, 064506 (2005)]. In the present paper, we extend the comparison to the case of heterodyne-detected and time-resolved nonlinear time-domain rephasing and nonrephasing signals generated in three-pulse experiments and the corresponding frequency-domain two-dimensional spectra. The comparison is performed in the context of a two-state chromophore solvated in a nonpolar liquid. It is shown that the inherent insensitivity of the standard method to the nonequilibrium dynamics on the excited state potential surface gives rise to two-dimensional spectra which are symmetrical relative to the diagonal. In contrast, accounting for the effect of nonequilibrium excited state dynamics, as is the case within the forward-backward and linearized semiclassical methods, is found to give rise to two-dimensional spectra that become increasingly asymmetrical relative to the diagonal as the waiting time between the second and third pulses becomes larger. It is argued that the emergence of the asymmetry provides a useful probe of nonequilibrium solvation on the excited state potential surface.

Ab initio calculation of the electronic absorption of functionalized octahedral silsesquioxanes via time-dependent density functional theory with range-separated hybrid functionals.

Recent advances in the ability to functionalize octahedral silsesquioxanes with different photoactive ligands, and thereby tune their optical properties, suggest that these molecules may serve as potential building blocks of light-harvesting, photovoltaic, and photonic devices. In this paper we report extensive ab initio calculations of the excitation energies underlying the absorption spectra of these systems. The calculations are based on density functional theory for the ground electronic state and time-dependent density functional theory for the excited electronic states. The ability of the commonly used B3LYP functional to reproduce the experimentally observed absorption excitation energies is compared to that of recently developed range-separated hybrid functionals. The importance of pairing the range-separated hybrid functionals with basis sets that include diffuse and polarization basis functions is demonstrated in the case of vinyl-functionalized silsesquioxanes. Absorptive excitation energies are then calculated and compared with experiment for octahedral silsesquioxanes functionalized with larger ligands. The tunability of optical properties is demonstrated by considering the effect on the excitation energies of functionalizing the ligands with electron-donating or -withdrawing groups.