Intra- and intermolecular vibrational energy transfer in tungsten carbonyl complexes W(CO)5(X) (X=CO, CS, CH3CN, and CD3CN)

Vibrational energy relaxation of degenerate CO stretches of four tungsten carbonyl complexes, W(CO)6, W(CO)5(CS), W(CO)5(CH3CN), and W(CO)5(CD3CN), is observed in nine alkane solutions by subpicosecond time-resolved infrared (IR) pump-probe spectroscopy. Between 0 and 10 ps after the vibrational excitation, the bleaching signal of the ground-state IR absorption band shows anisotropy. Decay of the anisotropic component corresponds either to the rotational diffusion of the molecule or to the intramolecular vibrational energy transfer among the degenerate CO stretch modes. The time constant of the anisotropy decay, tauaniso, shows distinct solvent dependence. By comparing the results for the T1u CO stretch of W(CO)6 and the A1 CO stretch of W(CO)5(CS), the time constant of the rotational diffusion, taur, and the time constant of the intramolecular energy transfer among the three degenerate vibrational modes, taue, are determined as 12 and 8 ps, respectively. The tauaniso value increases as the number of carbon atoms in the alkane solvent increases. After 10 ps, the recovery of the bleaching becomes isotropic. The isotropic decay represents the vibrational population relaxation, from v=1 to v=0. In heptane, the time constant for the isotropic decay, tau1, for W(CO)5(CS) and W(CO)6 was 140 ps. The tau1 for the two acetonitrile-substituted complexes, however, shows a smaller value of 80 ps. The vibrational energy relaxation of W(CO)5(CH3CN) and W(CO)5(CD3CN) is accelerated by the intramolecular energy redistribution from the CO ligand to the acetonitrile ligand. In the nine alkane solutions, the tau1 value of W(CO)6 ranges between 124 and 158 ps, showing the apparent V-shaped solvent dependence with its minimum in decane, while the tau1 value shows little solvent dependence for W(CO)5(CH3CN) and W(CO)5(CD3CN).     

Reinterpretation of Dynamic Vibrational Spectroscopy to Determine the Molecular Structure and Dynamics of Ferrocene

Molecular distortion of dynamic molecules gives a clear signature in the vibrational spectra, which can be modeled to give estimates of the energy barrier and the sensitivity of the frequencies of the vibrational modes to the reaction coordinate. The reaction coordinate method (RCM) utilizes ab initio‐calculated spectra of the molecule in its ground and transition states together with their relative energies to predict the temperature dependence of the vibrational spectra. DFT‐calculated spectra of the eclipsed (D_5h) and staggered (D_5d) forms of ferrocene (Fc), and its deuterated analogue, within RCM explain the IR spectra of Fc in gas (350 K), solution (300 K), solid solution (7–300 K), and solid (7–300 K) states. In each case the D_5h rotamer is lowest in energy but with the barrier to interconversion between rotamers higher for solution‐phase samples (ca. 6 kJ mol^?1) than for the gas‐phase species (1–3 kJ mol^?1). The generality of the approach is demonstrated with application to tricarbonyl(η⁴‐norbornadiene)iron(0), Fe(NBD)(CO)₃. The temperature‐dependent coalescence of the ν(CO) bands of Fe(NBD)(CO)₃ is well explained by the RCM without recourse to NMR‐like rapid exchange. The RCM establishes a clear link between the calculated ground and transition states of dynamic molecules and the temperature‐dependence of their vibrational spectra.     

Structure and vibrational dynamics of model compounds of the [FeFe]-hydrogenase enzyme system via ultrafast two-dimensional infrared spectroscopy

Ultrafast two-dimensional infrared (2D) spectroscopy has been applied to study the structure and vibrational dynamics of (mu-S(CH2)3S)Fe2(CO)6, a model compound of the active site of the [FeFe]-hydrogenase enzyme system. Comparison of 2D-IR spectra of (mu-S(CH2)3S)Fe2(CO)6 with density functional theory calculations has determined that the solution-phase structure of this molecule is similar to that observed in the crystalline phase and in good agreement with gas-phase simulations. In addition, vibrational coupling and rapid (<5 ps) solvent-mediated equilibration of energy between vibrationally excited states of the carbonyl ligands of the di-iron-based active site model are observed prior to slower (approximately 100 ps) relaxation to the ground state. These dynamics are shown to be solvent-dependent and form a basis for the future determination of the vibrational interactions between active site and protein.     

Vibrational energy relaxation of the bend fundamental of dilute water in liquid chloroform and d-chloroform

The population lifetimes of the bend fundamental of dilute water in liquid chloroform (8.5 ps) and d-chloroform (28.5 ps) display an interesting solvent isotope effect. As the lowest excited vibrational state of the molecule, the water bend fundamental relaxes directly to the ground state with about 1600 cm-1 of energy released to the other degrees of freedom. The strong solvent isotope effect along with the large energy gap indicates the participation of solvent vibrational modes in this vibrational energy relaxation process. We calculate the vibrational energy relaxation rates of the water bend in chloroform and d-chloroform using the Landau-Teller formula with a new potential model developed and parametrized self-consistently to describe the chloroform-water interaction. The computed values are in reasonable agreement with the experimental results, and the trend for the isotope effect is correct. It is found that energy transfer to the solvent vibrations does indeed play an important role. Nevertheless, no single dominant solvent accepting mode can be identified; the relaxation appears to involve both the bend and the C-Cl stretches, and frequency changes of all of these modes upon deuteration contribute to the observed solvent isotope effect.     

Vibrational relaxation of CH3I in the gas phase and in solution

Transient electronic absorption measurements reveal the vibrational relaxation dynamics of CH(3)I following excitation of the C-H stretch overtone in the gas phase and in liquid solutions. The isolated molecule relaxes through two stages of intramolecular vibrational relaxation (IVR), a fast component that occurs in a few picoseconds and a slow component that takes place in about 400 ps. In contrast, a single 5-7 ps component of IVR precedes intermolecular energy transfer (IET) to the solvent, which dissipates energy from the molecule in 50 ps, 44 ps, and 16 ps for 1 M solutions of CH(3)I in CCl(4), CDCl(3), and (CD(3))(2)CO, respectively. The vibrational state structure suggests a model for the relaxation dynamics in which a fast component of IVR populates the states that are most strongly coupled to the initially excited C-H stretch overtone, regardless of the environment, and the remaining, weakly coupled states result in a secondary relaxation only in the absence of IET.     

Temperature-dependent solvent effect on the kinetic energy distribution on p-cresol molecule as building block of calixarene capsules

The solvent effect on the kinetic energy distribution of p-cresol molecule was investigated by quantum-chemical (QM) method and molecular dynamics (MD) simulations, then the consequences were checked experimentally by photoluminescence (PL) and differential scanning calorimetry (DSC) methods. Results of QM calculations highlight the coupling of two vibrational normalmodes of p-cresol molecule in the presence of ethanol while no similar coupling was observed in methanol. MD simulations show that the normalmode coupling in ethanol is more pronounced at higher temperature and it is preferably based on the molecular friction of the cresol molecule with its environment. The theoretical observations were also proved experimentally. The dissociation rate of calixarene–phenol complexes were measured by DSC method. The decreased dissociation rate of the calixarene–phenol complexes observed in ethanol reflects the increased motion of the methyl groups of cresol units of calixarene in the ethanol solvent, a property which was predicted by the theoretical results. Our findings are applicable to many areas of chemistry where the formation and dissociation rates play important role: e.g., in the development of chemical molecular sensors or developing molecular containers for drugs towards pharmaceutical applications.     

Influence of temperature on thymine-to-solvent vibrational energy transfer

At the instant following the non-radiative deactivation of its ππ* electronic state, the vibrational modes of thymine possess a highly non-equilibrium distribution of excitation quanta (i.e., >4 eV in excess energy). Equilibrium is re-established through rapid (5 ps) vibrational energy transfer to the surrounding solvent. The mechanisms behind such vibrational cooling (VC) processes are examined here using femtosecond transient grating and two-dimensional photon echo spectroscopies conducted at 100 K and 300 K in a mixture of methanol and water. Remarkably, we find that this variation in temperature has essentially no impact on the VC kinetics. Together the experiments and a theoretical model suggest three possible mechanisms consistent with this behavior: (i) vibrational energy transfer from the solute to solvent initiates (directly) in intramolecular modes of the solute with frequencies >300 cm(-1); (ii) the relaxation induced increase in the temperature of the environment reduces the sensitivity of VC to the temperature of the equilibrium system; (iii) the time scale of solvent motion approaches 0.1 ps even at 100 K. Mechanism (i) deserves strong consideration because it is consistent with the conclusions drawn in earlier studies of isotope effects on VC in hydrogen bonding solvents. Our model calculations suggest that mechanism (ii) also plays a significant role under the present experimental conditions. Mechanism (iii) is ruled out on the basis of long-lived correlations evident in the photon echo line shapes at 100 K. These insights into photoinduced relaxation processes in thymine are made possible by our recent extension of interferometric transient grating and photon echo spectroscopies to the mid UV spectral region.     

The role of CN and CO ligands in the vibrational relaxation dynamics of model compounds of the [FeFe]-hydrogenase enzyme

The vibrational dynamics of (μ-propanedithiolate)Fe(2)(CO)(4)(CN)(2)(2-), a model compound of the active site of the [FeFe]-hydrogenase enzyme, have been examined via ultrafast 2D-IR spectroscopy. The results indicate that the vibrational coupling between the stretching modes of the CO and CN ligands is small and restricted to certain modes but the slow growth of off-diagonal peaks is assigned to population transfer processes occurring between these modes on timescales of 30-40 ps. Analysis of the dynamics in concert with anharmonic density functional theory simulations shows that the presence of CN ligands alters the vibrational relaxation dynamics of the CO modes in comparison to all-carbonyl model systems and suggests that the presence of these ligands in the enzyme may be an important feature in terms of directing the vibrational relaxation mechanism.     

Femtosecond IR spectroscopy of peroxycarbonate photodecomposition: S1-lifetime determines decarboxylation rate

The ultrafast photofragmentation of arylperoxycarbonates R-O-C(O)O-O-tert-butyl (R = naphthyl, phenyl) is studied using femtosecond UV excitation at 266 nm and mid-infrared broadband probe pulses to elucidate the dissociation mechanism. Our experiments show that the rate of fragmentation is determined by the S1-lifetime of the peroxide, i.e., the time constants of S1 decay and of CO2 and R-O* formation are identical. The fragmentation times are solvent dependent and for tert-butyl-2-naphthylperoxycarbonate (TBNC) vary from 25 ps in CH2Cl2 to 52 ps in n-heptane. In the case of the tert-butylphenylperoxycarbonate (TBPC) the decomposition takes 5.5 ps in CD2Cl2 and 12 ps in n-heptane. The CO2 fragment is formed vibrationally hot with an excess energy of about 5000 cm(-1). The hot CO2 spectra at high energy can be modeled assuming Boltzmann distributions with initial vibrational temperatures of ca. 2500 K which relax to ambient temperature with time constants of 280 ps in CCl4 and 130 ps in n-heptane. In CCl4 the relaxed spectra at 1.5 ns show 3.5% residual excitation in the n = 1 level of the asymmetric stretch vibration.     

Near-resonant energy transfer from highly vibrationally excited OH to N2

The probability per collision P(T) of near-resonant vibration-to-vibration energy transfer (ET) of one quantum of vibrational energy from vibrational levels nu=8 and nu=9 of OH to N(2)(nu=0), OH(nu)+N(2)(0)-->OH(nu-1)+N(2)(1), is calculated in the 100-350 K temperature range. These processes represent important steps in a model that explains the enhanced 4.3 microm emission from CO(2) in the nocturnal mesosphere. The calculated energy transfer is mediated by weak long-range dipole-quadrupole interaction. The results of this calculation are very sensitive to the strength of the two transition moments. Because of the long range of the intermolecular potential, the resonance function, a measure of energy that can be efficiently exchanged between translation and vibration-rotation degrees of freedom, is rather narrow. A narrow resonance function coupled with the large rotational constant of OH is shown to render the results of the calculation very sensitive to the rotational distribution, or the rotational temperature if one exists, of this molecule. The calculations are carried out in the first and second orders of perturbation theory with the latter shown to give ET probabilities that are an order of magnitude larger than the former. The reasons for the difference in magnitude and temperature dependence of the first- and second-order calculations are discussed. The results of the calculations are compared with room temperature measurements as well as with an earlier calculation. Our calculated results are in good agreement with the room temperature measurements for the transfer of vibrational energy for the exothermic OH(nu=9) ET process but are about an order lower than the room temperature measurements for the exothermic OH(nu=8) ET process. The cause of this discrepancy is explored. This calculation does not give the large values of the rate coefficients needed by the model that explains the enhanced 4.3 microm emission from CO(2) in the nocturnal mesosphere.     

Frequency- and time-domain femtosecond vibrational sum frequency generation from CO adsorbed on Pt111

We have studied the effects of intermolecular and intramolecular coupling on the C-O stretching vibration of CO adsorbed on Platinum (111) by means of femtosecond broadband vibrational sum frequency generation (VSFG). Resonant intermolecular coupling is investigated through the coverage dependence of the VSFG signal. The experimental observations can be accurately modeled as lateral coupling of the molecular transition dipole moments; this coupling is invoked in the nonlinear optical response model as a local field correction. The linear polarizability, which appears in this model, is modified by both the dipole-dipole coupling and the population of bridged adsorption sites. By extending the formalism to include these effects, we deduce a vibrational polarizability of 0.32 A(3) from the data. Intramolecular coupling to the frustrated translational mode is observed as temperature dependence of the C-O stretch. The present data can be described either by pertubative or nonpertubative lineshape models from the literature. Measurements of the temperature dependence of the vibrational free induction decay indicate a population relaxation time T(1) of (0.8+/-0.1) ps, in agreement with the observed low-temperature linewidth. Moreover, the ability of this time-domain method to discriminate spectral inhomogeneity yields clear evidence of the order-disorder transition near 275 K. Above this temperature an inhomogeneous linewidth component of (12+/-3) cm(-1) is observed. This value allows us to estimate the structural heterogeneity of the disordered phase, which result agrees with published Monte Carlo simulations.     

Solvation-driven excited-state dynamics of [Re(4-Et-Pyridine)(CO)3(2,2'-bipyridine)]+ in imidazolium ionic liquids. A time-resolved infrared and phosphorescence study

Excited-state dynamics of [Re(Etpy)(CO)3(bpy)]+ was studied in three imidazolium ionic liquids by time-resolved IR and emission spectroscopy on the picosecond to nanosecond time scale. Low-lying excited states were characterized by TD-DFT calculations, which also provided molecular dipole moment vectors in the relevant electronic states. TRIR spectra in ionic liquids show initial populations of two excited states: predominantly bpy-localized 3IL and 3MLCT, characterized by nu(CO) bands shifted to lower and higher frequencies, respectively, relative to the ground state. Internal conversion of 3IL to the lowest triplet 3MLCT occurred on a time scale commensurate with solvent relaxation. The nu(CO) IR bands of the 3MLCT state undergo a dynamic shift to higher wavenumbers during relaxation. Its three-exponential kinetics were determined and attributed to vibrational cooling (units of picoseconds), energy dissipation to the bulk solvent (tens of picoseconds), and solvent relaxation, the lifetime of which increases with increasing viscosity: [EMIM]BF4 (330 ps) < [BMIM]BF4 (470 ps) < [BMIM]PF6 (1570 ps). Time-resolved phosphorescence spectra in [BMIM]PF6 show a approximately 2 ns drop in intensity due to the 3IL --> 3MLCT conversion and a dynamic Stokes shift to lower energies with a lifetime decreasing from 1.8 ns at 21 degrees C to 1.1 ns at 37 degrees C, due to decreasing viscosity of the ionic liquid. It is proposed that solvent relaxation predominantly involves collective translational motions of ions. It drives the 3IL --> 3MLCT conversion, increases charge reorganization in the lowest excited-state 3MLCT, and affects vibrational anharmonic coupling, which together cause the dynamic shift of excited-state IR bands. TRIR spectroscopy of carbonyl-diimine complexes emerges as a new way to investigate various aspects of solvation dynamics, while the use of slowly relaxing ionic liquids offers new insight into the photophysics of Re(I) carbonyl polypyridyls.     

Molecular dynamics simulations and instantaneous normal-mode analysis of the vibrational relaxation of the C-H stretching modes of N-methylacetamide-d in liquid deuterated water

Nonequilibrium molecular dynamics (MD) simulations and instantaneous normal mode (INMs) analyses are used to study the vibrational relaxation of the C-H stretching modes (ν(s)(CH?)) of deuterated N-methylacetamide (NMAD) in aqueous (D2O) solution. The INMs are identified unequivocally in terms of the equilibrium normal modes (ENMs), or groups of them, using a restricted version of the recently proposed Min-Cost assignment method. After excitation of the parent ν(s)(CH?) modes with one vibrational quantum, the vibrational energy is shown to dissipate through both intramolecular vibrational redistribution (IVR) and intermolecular vibrational energy transfer (VET). The decay of the vibrational energy of the ν(s)(CH?) modes is well fitted to a triple exponential function, with each characterizing a well-defined stage of the entire relaxation process. The first, and major, relaxation stage corresponds to a coherent ultrashort (τ(rel) = 0.07 ps) energy transfer from the parent ν(s)(CH?) modes to the methyl bending modes δ(CH?), so that the initially excited state rapidly evolves into a mixed stretch-bend state. In the second stage, characterized by a time of 0.92 ps, the vibrational energy flows through IVR to a number of mid-range-energy vibrations of the solute. In the third stage, the vibrational energy accumulated in the excited modes dissipates into the bath through an indirect VET process mediated by lower-energy modes, on a time scale of 10.6 ps. All the specific relaxation channels participating in the whole relaxation process are properly identified. The results from the simulations are finally compared with the recent experimental measurements of the ν(s)(CH?) vibrational energy relaxation in NMAD/D?O(l) reported by Dlott et al. (J. Phys. Chem. A 2009, 113, 75.) using ultrafast infrared-Raman spectroscopy.     

Proton-coupled electron transfer in soybean lipoxygenase: dynamical behavior and temperature dependence of kinetic isotope effects

The dynamical behavior and the temperature dependence of the kinetic isotope effects (KIEs) are examined for the proton-coupled electron transfer reaction catalyzed by the enzyme soybean lipoxygenase. The calculations are based on a vibronically nonadiabatic formulation that includes the quantum mechanical effects of the active electrons and the transferring proton, as well as the motions of all atoms in the complete solvated enzyme system. The rate constant is represented by the time integral of a probability flux correlation function that depends on the vibronic coupling and on time correlation functions of the energy gap and the proton donor-acceptor mode, which can be calculated from classical molecular dynamics simulations of the entire system. The dynamical behavior of the probability flux correlation function is dominated by the equilibrium protein and solvent motions and is not significantly influenced by the proton donor-acceptor motion. The magnitude of the overall rate is strongly influenced by the proton donor-acceptor frequency, the vibronic coupling, and the protein/solvent reorganization energy. The calculations reproduce the experimentally observed magnitude and temperature dependence of the KIE for the soybean lipoxygenase reaction without fitting any parameters directly to the experimental kinetic data. The temperature dependence of the KIE is determined predominantly by the proton donor-acceptor frequency and the distance dependence of the vibronic couplings for hydrogen and deuterium. The ratio of the overlaps of the hydrogen and deuterium vibrational wavefunctions strongly impacts the magnitude of the KIE but does not significantly influence its temperature dependence. For this enzyme reaction, the large magnitude of the KIE arises mainly from the dominance of tunneling between the ground vibronic states and the relatively large ratio of the overlaps between the corresponding hydrogen and deuterium vibrational wavefunctions. The weak temperature dependence of the KIE is due in part to the dominance of the local component of the proton donor-acceptor motion.     

Excited-state characters and dynamics of [W(CO)(5)(4-cyanopyridine)] and [W(CO)(5)(piperidine)] studied by picosecond time-resolved IR and resonance Raman spectroscopy and DFT calculations: roles of W --> L and W --> CO MLCT and LF excited states revised

The characters, dynamics, and relaxation pathways of low-lying excited states of the complexes [W(CO)(5)L] [L = 4-cyanopyridine (pyCN) and piperidine (pip)] were investigated using theoretical and spectroscopic methods. DFT calculations revealed the delocalized character of chemically and spectroscopicaly relevant molecular orbitals and the presence of a low-lying manifold of CO pi-based unoccupied molecular orbitals. Traditional ligand-field arguments are not applicable. The lowest excited states of [W(CO)(5)(pyCN)] are W --> pyCN MLCT in character. They are closely followed in energy by W --> CO MLCT states. Excitation at 400 or 500 nm populates the (3)MLCT(pyCN) excited state, which was characterized by picosecond time-resolved IR and resonance Raman spectroscopy. Excited-state vibrations were assigned using DFT calculations. The (3)MLCT(pyCN) excited state is initially formed highly excited in low-frequency vibrations which cool with time constants between 1 and 20 ps, depending on the excitation wavelength, solvent, and particular high-frequency nu(CO) or nu(CN) mode. The lowest excited states of [W(CO)(5)(pip)] are W --> CO MLCT, as revealed by TD-DFT interpretation of a nanosecond time-resolved IR spectrum that was measured earlier in a low-temperature glass (Johnson, F. P. A.; George, M. W.; Morrison, S. L.; Turner, J. J. J. Chem. Soc., Chem. Commun. 1995, 391-393). MLCT(CO) excitation involves transfer of electron density from the W atom and, to a lesser extent, the trans CO to the pi orbitals of the four cis CO ligands. Optical excitation into MLCT(CO) transition of either complex in fluid solution triggers femtosecond dissociation of a W-N bond, producing [W(CO)(5)(solvent)]. It is initially vibrationally excited both in nu(CO) and anharmonicaly coupled low-frequency modes. Vibrational cooling occurs with time constants of 16-22 ps while the intramolecular vibrational energy redistribution from the v = 1 nu(CO) modes is much slower, 160-220 ps. No LF excited states have been found for the complexes studied in a spectroscopically relevant range up to 6-7 eV. It follows that spectroscopy, photophysics, and photochemistry of [W(CO)(5)L] and related complexes are well described by an interplay of close-lying MLCT(L) and MLCT(CO) excited states. The high-lying LF states play only an indirect photochemical role by modifying potential energy curves of MLCT(CO) states, making them dissociative.     

Ultrafast dynamics of the azobenzene-coumarin complex: investigation of cooling dynamics measured by an integrated molecular thermometer

The energy dissipation mechanism from photoexcited azobenzene (Az) was studied by femtosecond time-resolved UV absorption spectroscopy using 7-amino-4-trifluoromethylcoumarin (ATC) as a probe. The distance between the probe molecule and Az was fixed by covalently linking them together through a rigid proline spacer. Picosecond dynamics in THF solutions were studied upon excitation into the S1 state by a 100 fs laser pulse at 480 nm. Transient absorption spectra obtained for Az-Pro-ATC combined the S1 state absorption and vibrationally excited ground-state absorption of ATC. Correction of the transient spectrum of Az-Pro-ATC for the S1 absorption provided the time-resolved absorption spectrum of the ATC hot band. Three major components were observed in the transient kinetics of Az-Pro-ATC vibrational cooling. It is proposed that in ca. 0.25 ps after the excitation, the S1 state of azobenzene decays to form an initial vibrationally excited nonthermalized ground state of Az-Pro-ATC that involves vibrational modes of both azobenzene and coumarin. This hot ground state decays in ca. 0.32 ps to the next, vibrationally equilibrated, transient state by redistributing the energy within the molecule. Subsequently, the latter state cools by transferring its energy to the closest solvent molecules in ca. 5 ps; then, the energy diffuses to the bulk solvent in 13 ps.     

Intramolecular vibrational coupling contribution to temperature dependence of vibrational mode frequencies

High-frequency vibrational modes in molecules in solution are sensitive to temperature and shift either to lower or higher frequencies with the temperature increase. These frequency shifts are often attributed to specific interactions of the molecule and to the solvent polarization effect. We found that a substantial and often dominant contribution to sensitivity of vibrational high-frequency modes to temperature originates from anharmonic interactions with other modes in the molecule. The temperature dependencies were measured for several modes in ortho-, meta-, and para-isomers of acetylbenzonitrile in solution and in a solid matrix and compared to the theoretical predictions originated from the intramolecular vibrational coupling (IVC) evaluated using anharmonic density functional theory calculations. It is found that the IVC contribution is essential for temperature dependencies of all high-frequency vibrational modes and is dominant for many modes. As such, the IVC contribution alone permits predicting the main trend in the temperature dependencies, especially for vibrational modes with smaller transition dipoles. In addition, an Onsager reaction field theory was used to describe the solvent contribution to the temperature dependencies.     

Langevin model of the temperature and hydration dependence of protein vibrational dynamics

The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes.     

Intramolecular vibrational dynamics in S1 p-fluorotoluene. I. Direct observation of doorway states

Picosecond time-resolved photoelectron spectroscopy is used to investigate intramolecular vibrational redistribution (IVR) following excitation of S(1) 18a(1) in p-fluorotoluene (pFT) at an internal energy of 845 cm(-1), where ν(18a) is a ring bending vibrational mode. Characteristic oscillations with periods of 8 ps and 5 ps are observed in the photoelectron signal and attributed to coupling between the initially excited zero-order bright state and two doorway states. Values for the coupling coefficients connecting these three vibrational states have been determined. In addition, an exponential change in photoelectron signal with a lifetime of 17 ps is attributed to weaker couplings with a bath of dark states that play a more significant role during the latter stages of IVR. A tier model has been used to assign the most strongly coupled doorway state to S(1) 17a(1) 6a(2)('), where ν(17a) is a CH out-of-plane vibrational mode and 6a(2)(') is a methyl torsional level. This assignment signifies that a torsion-vibration coupling mechanism mediates the observed dynamics, thus demonstrating the important role played by the methyl torsional mode in accelerating IVR.     

Dynamics of proton transfer and vibrational relaxation in dilute hydrofluoric acid

The molecular mechanisms in both vibrational relaxation and proton transfer (PT) associated with infrared (IR)-induced PT in a dilute hydrofluoric acid solution at ambient temperature are studied by molecular dynamics (MD) simulations with the multistate empirical valence bond model. To investigate the solvation dynamics, a collective solvent coordinate and its perpendicular bath modes are defined from the diabatic energy gap and their motions are examined by the generalized Langevin equation (GLE) formalism. The GLE analysis using the equilibrium MD simulation shows that the major solvent reorganizations in the PT are represented by the libration and hindered translation. In particular, the libration gives the stronger coupling to the solvent reorganization and the faster relaxation. The nonequilibrium MD simulation demonstrated that both the HF stretching vibration and the solvent reorganization relax on a similar time scale and thus compete in the PT. It also supported the "presolvation mechanism" for the PT in this system.