Dephasing-induced vibronic resonances in difference frequency generation spectroscopy

The difference frequency generation (DFG) signal from a two electronic level system with vibrational modes coupled to a Brownian oscillator bath is computed. Interference effects between two Liouville space pathways result in pure-dephasing-induced, excited-state resonances provided the two excitation pulses overlap and time ordering is not enforced. Numerical simulations of two-dimensional DFG signals illustrate how the ground and excited electronic state resonances may be distinguished.     

Polarization-angle-scanning two-dimensional spectroscopy: application to dipeptide structure determination

Coherent two-dimensional optical spectroscopy based on a heterodyne-detected stimulated photon echo measurement technique requires four ultrashort pulses whose pulse-to-pulse delay times, wavevectors, and frequencies are experimentally controllable variables. In addition, the polarization directions of the four radiations can also be arbitrarily adjusted. We show that the polarization-angle-scanning two-dimensional spectroscopy can be of effective use to selectively suppress either all the diagonal peaks or a cross-peak in a given two-dimensional spectrum. Theoretical relationships between the transition dipole vectors of a given pair of coupled modes or quantum transitions and the polarization angle configuration making the corresponding cross-peak vanish are established. Here, to shed light into the underlying principles of the polarization-angle-scanning two-dimensional spectroscopy, we considered the amide I vibrations of various isotope-labeled dipeptide conformers and show that one can selectively suppress a cross-peak by properly controlling the polarization angle of a chosen beam among them. Once the relative directions of the amide I transition dipole vectors are determined using the polarization-angle-scanning technique theoretically proposed here, they can serve as a set of constraints for determining structures of model peptides. The present work demonstrates that the polarization-controlled two-dimensional vibrational or electronic spectroscopy can provide invaluable information on intricate details of molecular structures.     

The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.     

Separating Vibrational Coherences in Ground/Excited Electronic States of Solvent/Solute Following Non-Resonant/Resonant Impulsive Excitation

In a quest to track down the origin of coherent vibrational motions observed in femtosecond pump-probe transients, whether they arise from ground/excited electronic state of solute or are contributed by the solvent, we demonstrate a method for extricating vibrations under resonant and non-resonant impulsive excitations using a diatomic solute in condensed phase (iodine in carbon tetrachloride) with aid of spectral dispersion of the chirped broadband probe. Most importantly, we show how a sum over intensities for a select region of detection wavelengths and Fourier transform of data over select temporal window untwine contributions from vibrational modes of different origins. Thus, in a single pump-probe experiment, vibrational features specific to solute as well as solvent are disentangled that are otherwise spectrally overlapping and are non-separable in conventional (spontaneous/stimulated) Raman spectroscopy employing narrowband excitation. We envision wide-ranging applications of this method to unveil vibrational features in complex molecular systems.     

How delocalized is N,N,N',N'-tetraphenylphenylenediamine radical cation? An experimental and theoretical study on the electronic and molecular structure

The electronic and molecular structure of N,N,N',N'-tetraphenylphenylenediamine radical cation 1(+) is in focus of this study. Resonance Raman experiments showed that at least eight vibrational modes are strongly coupled to the optical charge resonance band which is seen in the NIR. With the help of a DFT-based vibrational analysis, these eight modes were assigned to symmetric vibrations. The contribution of these symmetric modes to the total vibrational reorganization energy is dominant. These findings are in agreement with the conclusions from a simple two-state two-mode Marcus-Hush analysis which yields a tiny electron-transfer barrier. The excellent agreement of the X-ray crystal structure analysis and the DFT computed molecular structure of 1(+) on one hand as well as the solvent and solid-state IR spectra and the DFT-calculated IR active vibrations on the other hand prove 1(+) adopts a symmetrical delocalized Robin-Day class III structure both in the solid state and in solution.     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment

The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.     

Vibrational coupling in carboxylic acid dimers

The vibrational level splitting in the ground electronic state of carboxylic acid dimers mediated by the doubly hydrogen-bonded networks are investigated using pure and mixed dimers of benzoic acid with formic acid as molecular prototypes. Within the 0-2000-cm(-1) range, the frequencies for the fundamental and combination vibrations of the two dimers are experimentally measured by using dispersed fluorescence spectroscopy in a supersonic jet expansion. Density-functional-theory calculations predict that most of the dimer vibrations are essentially in-phase and out-of-phase combinations of the monomer modes, and many of such combinations show significantly large splitting in vibrational frequencies. The infrared spectrum of the jet-cooled benzoic acid dimer, reported recently by Bakker et al. [J. Chem. Phys. 119, 11180 (2003)], has been used along with the dispersed fluorescence spectra to analyze the coupled g-u vibrational levels. Assignments of the dispersed fluorescence spectra of the mixed dimer are suggested by comparing the vibronic features with those in the homodimer spectrum and the predictions of density-functional-theory calculation. The fluorescence spectra measured by excitations of the low-lying single vibronic levels of the mixed dimer reveal that the hydrogen-bond vibrations are extensively mixed with the ring modes in the S1 surface.     

Anharmonic vibrational modes of nucleic acid bases revealed by 2D IR spectroscopy

Polarization-dependent two-dimensional infrared (2D IR) spectra of the purine and pyrimadine base vibrations of five nucleotide monophosphates (NMPs) were acquired in D(2)O at neutral pH in the frequency range 1500-1700 cm(-1). The distinctive cross-peaks between the ring deformations and carbonyl stretches of NMPs indicate that these vibrational modes are highly coupled, in contrast with the traditional peak assignment, which is based on a simple local mode picture such as C═O, C═N, and C═C double bond stretches. A model of multiple anharmonically coupled oscillators was employed to characterize the transition energies, vibrational anharmonicities and couplings, and transition dipole strengths and orientations. No simple or intuitive structural correlations are found to readily assign the spectral features, except in the case of guanine and cytosine, which contain a single local CO stretching mode. To help interpret the nature of these vibrational modes, we performed density functional theory (DFT) calculations and found that multiple ring vibrations are coupled and delocalized over the purine and pyrimidine rings. Generally, there is close correspondence between the experimental and computational results, provided that the DFT calculations include explicit waters solvating hydrogen-bonding sites. These results provide direct experimental evidence of the delocalized nature of the nucleotide base vibrations via a nonperturbative fashion and will serve as building blocks for constructing a structure-based model of DNA and RNA vibrational spectroscopy.     

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.     

Alignment, vibronic level splitting, and coherent coupling effects on the pump-probe polarization anisotropy

The pump-probe polarization anisotropy is computed for molecules with a nondegenerate ground state, two degenerate or nearly degenerate excited states with perpendicular transition dipoles, and no resonant excited-state absorption. Including finite pulse effects, the initial polarization anisotropy at zero pump-probe delay is predicted to be r(0) = 3/10 with coherent excitation. During pulse overlap, it is shown that the four-wave mixing classification of signal pathways as ground or excited state is not useful for pump-probe signals. Therefore, a reclassification useful for pump-probe experiments is proposed, and the coherent anisotropy is discussed in terms of a more general transition dipole and molecular axis alignment instead of experiment-dependent ground- versus excited-state pathways. Although coherent excitation enhances alignment of the transition dipole, the molecular axes are less aligned than for a single dipole transition, lowering the initial anisotropy. As the splitting between excited states increases beyond the laser bandwidth and absorption line width, the initial anisotropy increases from 3/10 to 4/10. Asymmetric vibrational coordinates that lift the degeneracy control the electronic energy gap and off-diagonal coupling between electronic states. These vibrations dephase coherence and equilibrate the populations of the (nearly) degenerate states, causing the anisotropy to decay (possibly with oscillations) to 1/10. Small amounts of asymmetric inhomogeneity (2 cm(-1)) cause rapid (130 fs) suppression of both vibrational and electronic anisotropy beats on the excited state, but not vibrational beats on the ground electronic state. Recent measurements of conical intersection dynamics in a silicon napthalocyanine revealed anisotropic quantum beats that had to be assigned to asymmetric vibrations on the ground electronic state only [Farrow, D. A.; J. Chem. Phys. 2008, 128, 144510]. Small environmental asymmetries likely explain the observed absence of excited-state asymmetric vibrations in those experiments.     

Phonon-mediated path-interference in electronic energy transfer

We present a formalism to quantify the contribution of path-interference in phonon-mediated electronic energy transfer. The transfer rate between two molecules is computed by considering the quantum mechanical amplitudes associated with pathways connecting the initial and final sites. This includes contributions from classical pathways, but also terms arising from interference of different pathways. We treat the vibrational modes coupled to the molecules as a non-Markovian harmonic oscillator bath, and investigate the correction to transfer rates due to the lowest-order interference contribution. We show that depending on the structure of the harmonic bath, the correction due to path-interference may have a dominant vibrational or electronic character, and can make a notable contribution to the transfer rate in the steady state.     

Anharmonicity of amide modes

The principal contributions to the anharmonic coupling of amide vibrations are explored with the objective of comparing recent experiments with density functional theory and evaluating simple models of mode coupling. Experimental information obtained by means of two-dimensional infrared spectroscopy (2D IR) is reasonably well predicted by the computed one- and two-quantum anharmonic modes of amide-A, -I, and -II types in mono-, di- and tripeptides. The expansion of the vibrational energy up to the cubic and quartic coupling of harmonic modes suggested criteria to assess how localized are the forces determining the anharmonicity. The off-diagonal anharmonicity between an amide-A and one other amide mode was shown to be mainly determined by forces involving only these two modes, whereas the off-diagonal anharmonicity of two amide-I modes in peptides depended significantly on forces due to motions other than those of the amide-I type. Both the diagonal and off-diagonal anharmonicities exhibit sensitivity to peptide structures. These results should prove useful in linking 2D IR experimental results to secondary structure. Further, the results are used to evaluate the vibrational exciton model for the mixed-mode anharmonicities of the amide-I transitions.     

Femtosecond primary events in bacteriorhodopsin and its retinal modified analogs: revision of commonly accepted interpretation of electronic spectra of transient intermediates in the bacteriorhodopsin photocycle

Femtosecond primary events in bacteriorhodopsin (BR) and its retinal modified analogs are discussed. Ultrafast time resolved electronic spectra of the primary intermediates induced in the BR photocycle are discussed along with spectral and kinetic inconsistencies of the previous models proposed in the literature. The theoretical model proposed in this paper based on vibrational coupling between the electronic transition of the chromophore and intramolecular vibrational modes allows us to calculate the equilibrium electronic absorption band shape and the hole burning profiles. The model is able to rationalize the complex pattern of behavior for the primary events in BR and explain the origin of the apparent inconsistencies between the experiment and the previous theoretical models. The model presented in the paper is based on the anharmonic coupling assumption in the adiabatic approximation using the canonical transformation method for diagonalization of the vibrational Hamiltonian instead of the commonly used perturbation theory. The electronic transition occurs between the Born-Oppenheimer potential energy surfaces with the electron involved in the transition being coupled to the intramolecular vibrational modes of the molecule (chromophore). The relaxation of the excited state occurs by indirect damping (dephasing) mechanisms. The indirect dephasing is governed by the time evolution of the anharmonic coupling constant driven by the resonance energy exchange between the intramolecular vibrational mode and the bath. The coupling with the intramolecular vibrational modes results in the Franck-Condon progression of bands that are broadened due to the vibrational dephasing mechanisms. The electronic absorption line shape has been calculated based on the linear response theory whereas the third order nonlinear response functions have been used to analyze the hole burning profiles obtained from the pump-probe time-resolved measurements. The theoretical treatment proposed in this paper provides a basis for a substantial revision of the commonly accepted interpretation of the primary events in the BR photocycle that exists in the literature.     

Polarized pump-probe measurements of electronic motion via a conical intersection

Polarized femtosecond pump-probe spectroscopy is used to observe electronic wavepacket motion for vibrational wavepackets centered on a conical intersection. After excitation of a doubly degenerate electronic state in a square symmetric silicon naphthalocyanine molecule, electronic motions cause a approximately 100 fs drop in the polarization anisotropy that can be quantitatively predicted from vibrational quantum beat modulations of the pump-probe signal. Vibrational symmetries are determined from the polarization anisotropy of the vibrational quantum beats. The polarization anisotropy of the totally symmetric vibrational quantum beats shows that the electronic wavepackets equilibrate via the conical intersection within approximately 200 fs. The relationship used to predict the initial electronic polarization anisotropy decay from the asymmetric vibrational quantum beat amplitudes indicates that the initial width of the vibrational wavepacket determines the initial speed of electronic wavepacket motion. For chemically reactive conical intersections, which can have 1000 times greater stabilization energies than the one observed here, the same theory predicts electronic equilibration within 2 fs. Such electronic movements would be the fastest known chemical processes.     

Dynamics of a multimode system coupled to multiple heat baths probed by two-dimensional infrared spectroscopy

Reduced equation of motion for a multimode system coupled to multiple heat baths is constructed by extending the quantum Fokker-Planck equation with low-temperature correction terms (J. Phys. Soc. Jpn. 2005, 74, 3131). Unlike such common approaches used to describe intramolecular multimode vibration as a Bloch-Redfield theory and a stochastic theory, the present formalism is defined by the molecular coordinates. To explore the correlation among different modes through baths, we consider two cases of system-bath couplings. One is a correlated case in which two modes are coupled to a single bath, and the other is an uncorrelated case in which each mode is coupled to a different bath. We further classify the correlated case into two cases, the plus- and minus-correlated cases, according to distinct correlation manners. For these, one-dimensional and two-dimensional infrared (2D-IR) spectra are calculated numerically by solving the equation of motion. It is demonstrated that 2D-IR spectroscopy has the ability to analyze the correlation of fluctuation-dissipation processes among different modes.     

Chemical imaging of single 4,7,12,15-tetrakis[2.2]paracyclophane by spatially resolved vibrational spectroscopy

Single 4,7,12,15-tetrakis[2.2]paracyclophane were deposited on NiAl(110) surface at 11 K. Two adsorbed species with large and small conductivities were detected by the scanning tunneling microscope (STM). Their vibrational properties were investigated by inelastic electron tunneling spectroscopy (IETS) with the STM. Five vibrational modes were observed for the species with the larger conductivity. The spatially resolved vibrational images for the modes show striking differences, depending on the coupling of the vibrations localized on different functional groups within the molecule to the electronic states of the molecule. The vibrational modes are assigned on the basis of ab initio calculations. No IETS signal is resolved from the species with the small conductivity.