Vladimir Chernyak

Exciton-migration and three-pulse femtosecond optical spectroscopies of photosynthetic antenna complexes

A theory for four-wave-mixing signals from molecular aggregates, which includes effects of two-exciton states, static disorder, and coupling to a phonon bath with an arbitrary spectral density, is developed. The third-order polarization is rigorously partitioned into a coherent and a sequential contribution. The latter is given by a sum of an exciton-hopping and a ground state (bleaching) terms, both expressed using the doorway-window representation. Applications are made to photon-echo and pump-probe spectroscopies of the B850 system of the LH2 antenna in purple bacteria.

MULTIDIMENSIONAL FEMTOSECOND CORRELATION SPECTROSCOPIES OF ELECTRONIC AND VIBRATIONAL EXCITONS

Femtosecond visible and infrared analogues of multiple-pulse nuclear magnetic resonance techniques provide novel snapshot probes into the structure and electronic and vibrational dynamics of complex molecular assemblies such as photosynthetic antennae, proteins, and hydrogen-bonded liquids. A classical-oscillator description of these spectroscopies in terms of interacting quasiparticles (rather than transitions among global eigenstates) is developed and sets the stage for designing new pulse sequences and inverting the multidimensional signals to yield molecular structures. Considerable computational advantages and a clear physical insight into the origin of the response and the relevant coherence sizes are provided by a real-space analysis of the underlying coherence-transfer pathways in Liouville space.

Density-matrix representation of nonadiabatic couplings in time-dependent density functional (TDDFT) theories

Closed expressions for nonadiabatic coupling between the ground and an excited electronic state of a molecule are derived by representing the time-dependent density functional (TDDFT) equations in a form of classical dynamics for the Kohn-Sham (KS) single-electron density matrix. Applicability of Krylov-space-type fast algorithms to nonadiabatic TDDFT as well as the representivity of the time-dependent charge density of a driven system are discussed.

Polarons, localization, and excitonic coherence in superradiance of biological antenna complexes

A real-space formulation of time-resolved fluorescence of molecular aggregates is developed using the one-exciton density matrix ρ(t) of the optically driven system. A direct relationship is established between the superradiance enhancement factor Ls and the exciton coherence size Lρ associated with the off-diagonal density matrix elements in the molecular representation. Various factors which affect the latter, including finite temperature, energetic disorder, coupling with phonons, and polaron formation are explored. The theory is applied for the interpretation of recent measurements in the B850 system of the LH2 photosynthetic complexes.

Resonant nonlinear polarizabilities in the time-dependent density functional theory

The response of the density matrix to an external field is calculated in the adiabatic time-dependent density functional (TDDFT) theory by mapping the equation of motion for the driven single-electron density matrix into the dynamics of coupled harmonic oscillators. The resulting nonlinear response functions and the closed expressions for nonlinear frequency-dependent polarizabilities are derived. These expressions include transition densities and frequencies calculated in the linear response TDDFT, and higher order functional derivatives of the exchange-correlation functional. Limitations of the applicability of the traditional sum over states approach for computing the nonlinear response to the TDDFT are discussed.

Multidimensional femtosecond spectroscopies of molecular aggregates and semiconductor nanostructures: The nonlinear exciton equations

A unified description of nonlinear optical spectroscopies of molecular aggregates (starting with the Frenkel-Heitler-London Hamiltonian) and semiconductors (starting with the two-band model) is developed using the nonlinear exciton equations (NEE). The equations follow explicitly the complete set of one-, two-, and three-point dynamical exciton variables relevant for the third-order response. Effects of nuclear motions are incorporated through relaxation superoperators calculated perturbatively in exciton-phonon coupling. A Greens function expression for the third-order response is derived by solving the NEE using a new truncation scheme based on factorizing the three-point relaxation kernels. These results set the stage for designing multidimensional spectroscopies of excitons and analyzing them using coherence-transfer pathways.

FEMTOSECOND PHOTON ECHOES IN MOLECULAR AGGREGATES

Two-pulse four-wave-mixing signals from molecular aggregates, including effects of two-exciton states, static disorder, and exciton-phonon interaction represented by arbitrary spectral densities are calculated. Three types of contributions to the signal are identified. The first, reflecting exciton self-correlation, is similar to the photon echo from disordered two-level systems and dominates the signal for long time-delays. The second is related to correlations of one-exciton states, whereas the third reflects correlations between one- and two-exciton states. The information gained by completely resolving the signal field (both amplitude and phase) is analyzed using Wigner spectrograms.

Multidimensional femtosecond spectroscopies of vibrational motions in liquids: Semiclassical expansion

Fifth- (χ(5)) and seventh- (χ(7)) order electronically off-resonant Raman spectroscopies in molecular liquids are investigated using a new semiclassical expansion of the optical response which applies for weak anharmonicities and low temperatures. The leading contribution can be calculated using classical equations of motion for nuclear wave packets, even when the system itself may be highly nonclassical. Two sources of nonlinearities which generate the signals—the nonlinear dependence of the polarizability on nuclear coordinates and vibrational anharmonicities—are identified. Formal analogy between the present equations and the time-dependent Hartree–Fock equations used in electronic nonlinear spectroscopy suggests specific experimental signatures of the various nonlinearities.

Collective coordinates for nuclear spectral densities in energy transfer and femtosecond spectroscopy of molecular aggregates

A theory for Frenkel exciton dynamics in molecular aggregates which incorporates coupling to vibrational motions (intramolecular, intermolecular and solvent) with multiple spectral densities of arbitrary nature and interpolates between the coherent and the incoherent limits is developed. A rigorous procedure for identifying the relevant collective nuclear coordinates necessary to represent a given set of spectral densities is obtained. Additional coordinates are required as the temperature is lowered. Exciton dynamics is calculated by following the evolution of wavepackets representing the electronic density matrix in the collective coordinates phase space. The signatures of excitonic and nuclear motions in ultrafast fluorescence spectroscopy are explored using a hierarchy of reduction schemes with varying numbers of collective coordinates.

Size‐consistent quasiparticle representation of nonlinear optical susceptibilities in many‐electron systems

The optical response of a many‐electron system is calculated by mapping it onto a coupled set of classical oscillators representing the electron–hole pair components of the reduced single‐ electron‐density matrix. This classical representation is rigorously established using a Poisson bracket relation. Expressions for the nonlinear optical susceptibilities obtained using a Green’s‐function solution of the oscillator equations of motion are used to analyze the size scaling of the off‐resonant response and the resonant structure of the response.