Theory predicts UV/vis-to-IR photonic down conversion mediated by excited state vibrational polaritons

This work proposes a photophysical phenomenon whereby ultraviolet/visible (UV/vis) excitation of a molecule involving a Franck-Condon (FC) active vibration yields infrared (IR) emission by strong coupling to an optical cavity. The resulting UV/vis-to-IR photonic down conversion process is mediated by vibrational polaritons in the electronic excited state potential. It is shown that the formation of excited state vibrational polaritons (ESVP) via UV/vis excitation only involve vibrational modes with both a non-zero FC activity and IR activity in the excited state. Density functional theory calculations are used to identify 1-Pyreneacetic acid as a molecule with this property and the dynamics of ESVP are modeled. Overall, this work introduces an avenue of polariton chemistry where excited state dynamics are influenced by the formation of vibrational polaritons. Along with this, the UV/vis-to-IR photonic down conversion is potentially useful in both sensing excited state vibrations and quantum transduction schemes.

Extracting Inelastic Scattering Cross Sections for Finite and Aperiodic Materials from Electronic Dynamics Simulations

Explicit time-dependent electronic structure theory methods are increasingly prevalent in the areas of condensed matter physics and quantum chemistry, with the broad-band optical absorptivity of molecular and small condensed-phase systems nowadays routinely studied with such approaches. In this paper, it is demonstrated that electronic dynamics simulations can similarly be employed to study cross sections for the scattering-induced electronic excitations probed in nonresonant inelastic X-ray scattering and momentum-resolved electron energy loss spectroscopies. A method is put forth for evaluating the electronic dynamic structure factor, which involves the application of a momentum boost-type perturbation and transformation of the resulting reciprocal space density fluctuations into the frequency domain. Good agreement is first demonstrated between the dynamic structure factor extracted from these electronic dynamics simulations and the corresponding transition matrix elements from linear response theory. The method is then applied to some extended (quasi)one-dimensional systems, for which the wave vector becomes a good quantum number in the thermodynamic limit. Finally, the dispersion of many-body excitations in a series of hydrogen-terminated graphene flakes (and twisted bilayers thereof) is investigated to highlight the utility of the presented approach for capturing morphology-dependent effects in the inelastic scattering cross sections of nanostructured and/or noncrystalline materials.

Tug-of-War between Internal and External Frictions and Viscosity Dependence of Rate in Biological Reactions

The role of water in biological processes is studied in three reactions, namely, the Fe-CO bond rupture in myoglobin, GB1 unfolding, and insulin dimer dissociation. We compute both internal and external components of friction on relevant reaction coordinates. In all of the three cases, the cross-correlation between forces from protein and water is found to be large and negative that serves to reduce the total friction significantly, increase the calculated reaction rate, and weaken solvent viscosity dependence. The computed force spectrum reveals bimodal 1/f noise, suggesting the use of a non-Markovian rate theory.

Vibrational Lifetime of the SCN Protein Label in H2O and D2O Reports Site-Specific Solvation and Structure Changes During PYP's Photocycle

The application of vibrational labels such as thiocyanate  (-S-C≡N) for studying protein structure and dynamics is thriving. Absorption spectroscopy is usually employed to obtain wavenumber and line shape of the label. An observable of great significance might be the vibrational lifetime, which can be obtained by pump probe or 2D-IR spectroscopy. Due to the insulating effect of the heavy sulfur atom in the case of the SCN label, the lifetime of the C≡N oscillator is expected to be particularly sensitive to its surrounding as it is not dominated by through-bond relaxation. We therefore investigate the vibrational lifetime of the SCN label at various positions in the blue light sensor protein Photoactive Yellow Protein (PYP) in the ground state and signaling state of the photoreceptor. We find that the vibrational lifetime of the C≡N stretching mode is strongly affected both by its protein environment and by the degree of exposure to the solvent. Even for label positions where the line shape and wavenumber observed by FTIR are barely changing upon activation of the photoreceptor, we find that the lifetime can change considerably. To obtain an unambiguous measure for the solvent exposure of the labeled site, we show that it is imperative to compare the lifetimes in H₂O and D₂O. Importantly, the lifetimes shorten in H₂O as compared to D₂O for water exposed labels, while they stay largely the same for buried labels. We quantify this effect by defining a solvent exclusion coefficient (SEC). The response of the label's vibrational lifetime to its solvent exposure renders it a suitable universal probe for protein investigations. This applies even to systems that are otherwise hard to address, such as transient or short-lived states, which could be created during a protein's working cycle (as here in PYP) or during protein folding. It is also applicable to flexible systems (intrinsically disordered proteins), protein-protein and protein-membrane interactions.

Role of quantum coherence in shaping the line shape of an exciton interacting with a spatially and temporally correlated bath

Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vibrational line shapes, through such concepts as static heterogeneity and motional narrowing. However, the theory does not properly address the effects of quantum coherences on optical line shape, especially in extended systems where a large number of eigenstates are present. In this work, we study the line shape of an exciton in a one-dimensional lattice consisting of regularly placed and equally separated optical two level systems. We consider both linear array and cyclic ring systems of different sizes. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (SLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigenfunctions are known analytically. This identification is particularly useful for long chains where the eigenvalues of TDTM help understanding crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peaks increases beyond the ones obtained from TDTM (constant off-diagonal coupling element J and no fluctuation). (ii) However, in the fast modulation limit when the bath correlation time is small, the spatial correlation is less important. In this limit, the line shape shows motional narrowing with peaks at the values predicted by TDTM (constant J and no fluctuation). (iii) Importantly, we find that the line shape can capture that quantum coherence affects in the two limits differently. (iv) In addition to linear chains of two level systems, we also consider a cyclic tetramer. The cyclic polymers can be designed for experimental verification. (v) We also build a connection between line shape and population transfer dynamics. In the fast modulation limit, both the line shape and the population relaxation, for both correlated and uncorrelated bath, show similar behavior. However, in slow modulation limit, they show profoundly different behavior. (vi) This study explains the unique role of the rate of fluctuation (inverse of the bath correlation time) in the sustenance and propagation of coherence. We also examine the effects of off-diagonal fluctuation in spectral line shape. Finally, we use Tanimura-Kubo formalism to derive a set of coupled equations to include temperature effects (partly neglected in the SLE employed here) and effects of vibrational mode in energy transfer dynamics.

Theoretical study of vibrational energy transfer of free OH groups at the water-air interface

Recent experimental studies have shown that the vibrational dynamics of free OH groups at the water-air interface is significantly different from that in bulk water. In this work, by performing molecular dynamics simulations and mixed quantum/classical calculations, we investigate different vibrational energy transfer pathways of free OH groups at the water-air interface. The calculated intramolecular vibrational energy transfer rate constant and the free OH bond reorientation time scale agree well with the experiment. It is also found that, due to the small intermolecular vibrational couplings, the intermolecular vibrational energy transfer pathway that is very important in bulk water plays a much less significant role in the vibrational energy relaxation of the free OH groups at the water-air interface.

Fluctuations and Relaxation Dynamics of Liquid Water Revealed by Linear and Nonlinear Spectroscopy

Many efforts have been devoted to elucidating the intra- and intermolecular dynamics of liquid water because of their important roles in many fields of science and engineering. Nonlinear spectroscopy is a powerful tool to investigate the dynamics. Because nonlinear response functions are described by more than one time variable, it is possible to analyze static and dynamic mode couplings. Here we review the intra- and intermolecular dynamics of liquid water revealed by recent linear and nonlinear spectroscopic experiments and computer simulations. In particular, we discuss the population relaxation, anisotropy decay, and spectral diffusion of the intra- and intermolecular motions of water and their temperature dependence, which play important roles in ultrafast dynamics and relaxations in water.

Vibrational energy relaxation of large-amplitude vibrations in liquids

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.

Vibrational dynamics of acetate in D2O studied by infrared pump-probe spectroscopy

Solute-solvent interactions between acetate and D(2)O were investigated by vibrational spectroscopic methods. The vibrational dynamics of the COO asymmetric stretching mode in D(2)O was observed by time-resolved infrared (IR) pump-probe spectroscopy. The pump-probe signal contained both decay and oscillatory components. The time dependence of the decay component could be explained by a double exponential function with time constants of 200 fs and 2.6 ps, which are the same for both the COO asymmetric and symmetric stretching modes. The Fourier spectrum of the oscillatory component contained a band around 80 cm(-1), which suggests that the COO asymmetric stretching mode couples to a low-frequency vibrational mode with a wavenumber of 80 cm(-1). Based on quantum chemistry calculations, we propose that a bridged complex comprising an acetate ion and one D(2)O molecule, in which the two oxygen atoms in the acetate anion form hydrogen bonds with the two deuterium atoms in D(2)O, is the most stable structure. The 80 cm(-1) low-frequency mode was assigned to the asymmetric stretching vibration of the hydrogen bond in the bridged complex.

Tracking energy transfer from excited to accepting modes: application to water bend vibrational relaxation

We extend, via a reformulation in terms of Poisson brackets, the method developed previously (Rey et al., J. Phys. Chem. A, 2009, 113, 8949) allowing analysis of the pathways of an excited molecule's ultrafast vibrational relaxation in terms of intramolecular and intermolecular contributions. In particular we show how to ascertain, through the computation of power and work, which portion of an initial excess molecular energy (e.g. vibrational) is transferred to various degrees of freedom (e.g. rotational, translational) of the excited molecule itself and its neighbors. The particular case of bend excess energy relaxation in pure water is treated in detail, completing the picture reported in the work cited above. It is shown explicitly, within a classical description, that almost all of the initial water bend excitation energy is transferred-either indirectly, via Fermi resonance centrifugal coupling to the bend-excited water's rotation, or directly via intermolecular coupling- to local water librations, only involving molecules in the first two hydration shells of the vibrationally excited water molecule. Finally, it is pointed out that the Poisson bracket formulation can also be applied to elucidate the microscopic character of solvation and rotational dynamics, and should prove useful in developing a quantum treatment for energy flow in condensed phases.

Temperature dependence of vibrational frequency fluctuation of N(3) (-) in D(2)O

We have studied the temperature dependence of the vibrational frequency fluctuation of the antisymmetric stretching mode of N(3) (-) in D(2)O by three-pulse infrared (IR) photon echo experiments. IR pump-probe measurements were also carried out to investigate the population relaxation and the orientational relaxation of the same band. It was found that the time-correlation function (TCF) of the frequency fluctuation of this mode is well described by a biexponential function with a quasistatic term. The faster decay component has a time constant of about 0.1 ps, and the slower component varies from 1.4 to 1.1 ps in the temperature range from 283 to 353 K. This result indicates that liquid dynamics related to the frequency fluctuation are not highly sensitive to temperature. We discuss the relationship between the temperature dependence of the vibrational frequency fluctuation and that of the molecular motion of the system to investigate the molecular origin of the frequency fluctuation of the solute. We compare the temperature dependence of the frequency fluctuation with that of other dynamics such as dielectric relaxation of water. In contrast to the Debye dielectric relaxation time of D(2)O, the two time constants of the TCF of the frequency fluctuation do not exhibit strong temperature dependence. We propose a simple theoretical model for the frequency fluctuation in solutions based on perturbation theory and the dipole-dipole interaction between the vibrational mode of the solute and the solvent molecules. This model suggests that the neighboring solvent molecules in the vicinity of the solute play an important role in the frequency fluctuation. We suggest that the picosecond component of the frequency fluctuation results from structural fluctuation of the hydrogen-bonding network in water.

Vibrational relaxation of NO-(v=1) in icosahedral (Ar)12NO- clusters

Relaxation dynamics of NO(-)(v=1) in icosahedral (Ar)(12)NO(-) clusters are studied using classical dynamics and semiclassical procedures over the temperature range of 100-300 K. The minimum energy of the equilibrium configuration (-9875 cm(-1)) needed in the study is determined by varying the cluster size z in (Ar)(z)NO(-). NO(-)(v=1) is embedded in the cluster, which is filled with low frequency motions: 39 cm(-1) for the argon modes, 77 cm(-1) for the Arc...NO(-) substructure vibration, 109 cm(-1) for the librational frequency of restricted rotation, and 128 cm(-1) for oscillatory local translation. Dynamics calculations show that in the early time period (<20 ps), part of the vibrational energy rapidly transfers to rotation, but most energy transfers to Ar atoms on a long time scale (approximately 1 ns). The long time scale leads to the relaxation rates of 0.403 ns(-1) at 100 K and 0.453 ns(-1) at 300 K. The rates calculated using analytical formulations vary nearly linearly from 0.288 ns(-1) at 100 K to 0.832 ns(-1) at 300 K. Although the temperature dependence is stronger in the latter, both approaches give the rates on a nanosecond time scale. The principal energy transfer pathway is from NO(-) vibration to Ar vibrations via oscillatory local translation, while the NO(-) rotation is in a librational state. The energy transfer probabilities are two orders of magnitude larger than the vibration-to-translation probabilities in the gas phase collision Ar-NO(-)(v=1).

Classical simulation of quantum energy flow in biomolecules

Based on a comparison of classical and quantum-mechanical perturbation theory, the validity of classical nonequilibrium molecular dynamics simulations to describe vibrational energy redistribution in biomolecules is studied. Adopting a small model peptide in aqueous solution as an example, the theory correctly predicts quantum correction factors that need to be applied to the results of classical simulations in order to match the correct quantum results.

Complex-time velocity autocorrelation functions for Lennard-Jones fluids with quantum pair-product propagators

We use the pair-product approximation to the complex-time quantum mechanical propagator to obtain accurate quantum mechanical results for the symmetrized velocity autocorrelation function of a Lennard-Jones fluid at two points on the thermodynamic phase diagram. A variety of tests are performed to determine the accuracy of the method and understand its breakdown at longer times. We report quantitative results for the initial 0.3 ps of the dynamics, a time at which the correlation function has decayed to approximately one fifth of its initial value.

Photodissociation of alkyl iodides in helium nanodroplets. I. Kinetic energy transfer

The photodissociation of (fluorinated) alkyl iodides in helium nanodroplets at a wavelength of 266 nm has been investigated by means of ion imaging techniques. It is found that a significant fraction of the created fragments escapes from the helium droplets. The speed and kinetic energy distributions of these fragments are found to be notably modified with respect to the corresponding gas phase distributions. The fragments, furthermore, show a speed dependent angular distribution. The loss of kinetic energy as well as the reduction of the anisotropy parameter show a strong mass dependence. These observations point to a nonthermal escape process in which the kinetic energy and momentum transfer from the fragments to the solvent is governed by binary collisions with the individual helium atoms making up the droplet. Monte Carlo simulations based on hard-sphere binary collisions substantiate this interpretation of the data.

Comparison between the Landau–Teller and flux-flux methods for computing vibrational energy relaxation rate constants in the condensed phase

The calculation of vibrational energy relaxation (VER) rate constants in the condensed phase is usually based on the Landau-Teller formula, which puts them in terms of the Fourier transform, at the vibrational frequency, of the autocorrelation function of the force exerted on the relaxing mode by the bath modes. An alternative expression for the VER rate constant puts it in terms of the autocorrelation function of the vibrational energy flux. In this paper, we compare the predictions obtained via those two methods in the case of iodine in liquid xenon. We find that the computational cost underlying both methods is comparable and that they predict similar VER rates. However, while the calculation of the VER rate via the Landau-Teller formula is somewhat more direct, the predictions obtained via the flux-flux formula are in somewhat better agreement with the VER rates obtained from nonequilibrium molecular dynamics simulations.

Vibrational energy relaxation of azide in water

Vibrational lifetimes of the asymmetric stretch fundamental of azide anion in normal and heavy water have been measured experimentally, with results in the range of a few picoseconds. This is an interesting problem for theoretical study because of the competition between intramolecular (relaxation to the other excited vibrational states of azide) and purely intermolecular (relaxation to azide's ground vibrational state) pathways. In addition it is important to understand the origin of the solvent isotope effect. Building on the seminal work of Morita and Kato [J. Chem. Phys. 109, 5511 (1998)], the authors develop a simple model based on a two-dimensional description of the azide stretching vibrations. A novel aspect of their theory is the use of an "on-the-fly" optimized quantum mechanical/molecular mechanical approach to calculate the system-bath coupling. Their theoretical lifetimes are in good agreement with experiment for azide in both normal and heavy water. They find that the predominant relaxation pathway is intramolecular. The solvent isotope effect arises from the different librational frequencies in normal and heavy water.

The Ehrenfest method with quantum corrections to simulate the relaxation of molecules in solution: Equilibrium and dynamics

The use of the Ehrenfest method to simulate the relaxation of molecules in solution is explored. Using the cyanide ion dissolved in water as a test model, the independent trajectory (IT) and the bundle of trajectories (BT) approximations are shown to provide very different results for the time evolution of the vibrational populations of the solute. None of these approximations reproduce the Boltzmann equilibrium vibrational populations accurately. A modification of the Ehrenfest method based on the use of quantum correction factors is thus proposed to solve this problem. The simulations carried out using the modified Ehrenfest method provide IT and BT relaxation times which are closer to each other and which agree quite well with previous hybrid perturbative results.

Evaluation of quantum correlation functions from classical data: Anharmonic models

The previously introduced method of evaluating quantum mechanical time correlation functions using as input only classical simulation data is generalized and applied to two anharmonic model systems, as a further test. The quantum correction approach utilizes the relation between a general quantum correlation function and its classical analog. For the tested models, we obtain numerical results of nonlinear correlation functions with comparable accuracy to that of the centroid molecular dynamics method, although the present method is much simpler to implement and not limited to real valued quantum correlation functions.

Quantized time correlation function approach to nonadiabatic decay rates in condensed phase: Application to solvated electrons in water and methanol

A new, alternative form of the golden rule formula defining the nonadiabatic transition rate between two quantum states in condensed phase is presented. The formula involves the quantum time correlation function of the energy gap, of the nonadiabatic coupling, and their cross terms. Those quantities can be inferred from their classical counterparts, determined via molecular dynamics simulations. The formalism is applied to the problem of the nonadiabatic p-->s relaxation of an equilibrated p-electron in water and methanol. We find that, in both solvents, the relaxation is induced by the coupling to the vibrational modes and the quantum effects modify the rate by a factor of 2-10 depending on the quantization procedure applied. The resulting p-state lifetime for a hypothetical equilibrium excited state appears extremely short, in the sub-100 fs regime. Although this result is in contrast with all previous theoretical predictions, we also illustrate that the lifetimes computed here are very sensitive to the simulated electronic quantum gap and to the strongly correlated nonadiabatic coupling.

Quantum dynamics in simple fluids

We use quantum-correction factors to calculate approximately the quantum velocity time-correlation function (TCF) of supercritical Lennard-Jones argon from the classical TCF. We find that for this quite classical system, several different quantum-correction schemes yield essentially identical results for the real and imaginary parts of the quantum TCF, and also agree well with the recent forward-backward semiclassical dynamics (FBSD) results of Wright and Makri [J. Chem. Phys. 119, 1634 (2003)]. We also consider a more quantum-mechanical fluid of lighter atoms (neon) at a lower temperature. In this case different quantum-correction schemes give different results. FBSD calculations show that the harmonic quantum correction factor works the best for this system

CONNECTING CHEMICAL DYNAMICS IN GASES AND LIQUIDS

▪ Abstract  Modern ultrafast spectroscopic techniques provide new opportunities to study chemical reaction dynamics in liquids and hold the possibility of obtaining much of the same detailed information available in gases. Vibrational energy transfer studies are the most advanced of the investigations and demonstrate that it is possible to observe state-specific pathways of energy flow within a vibrationally excited molecule (intramolecular vibrational relaxation) and into the surrounding solvent molecules (intermolecular energy transfer). Energy transfer in liquids and gases share many common aspects, but the presence of the solvent also alters the relaxation in both obvious and subtle ways. Photodissociation is amenable to similarly detailed study in liquids, and there are informative new measurements. Bimolecular reactions have received the least attention in state-resolved measurements in liquids, but the means to carry them much further now exist. Studying photodissociation and bimolecular reaction of molecules prepared with initial vibrational excitation in liquids is a realistic, but challenging, goal.

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water.

Light-scattering study of vibrational relaxation in liquid xylenes

Brillouin spectra obtained in dynamic light-scattering experiments are reported for the three isomeric xylenes (ortho-, meta-, and paradimethylbenzenes) between 288 and 363 K. Limiting sound velocities and relaxation times, as obtained from the polarized spectra using the theory developed by Mountain [J. Res. Natl. Bur. Stand. 70A, 207 (1966)], reveal the existence of a relaxation process. Our results suggest that the relaxation process in liquid xylenes has a purely vibrational nature. Vibrational-translational energy exchanges in xylenes are analyzed in terms of available molecular models and compared to those previously obtained for toluene and benzene. The results presented here confirm the important role played by the molecular geometry in the vibrational relaxation process, as the relative arrangement of the methyl groups has significant effect in determining the relaxing vibrational modes.