Vibrational relaxation of OH and CH fundamentals of polar and nonpolar molecules in the condensed phase

Studies of vibrational energy flow in various polar and nonpolar molecules that follows the ultrafast excitation of the CH and OH stretch fundamentals, modeled using semiclassical methods, are reviewed. Relaxation rates are calculated using Landau-Teller theory and a time-dependent method, both of which consider a quantum mechanical solute molecule coupled to a classical bath of solvent molecules. A wide range of decay rates are observed, ranging from 1 ps for neat methanol to 50 ps for neat bromoform. In order to understand the flow rates, it is argued that an understanding of the subtle mixing between the solute eigenstates is needed and that solute anharmonicities are critical to facilitating condensed phase vibrational relaxation. The solvent-assisted shifts of the solute vibrational energy levels are seen to play a critical role of enhancing or decreasing lifetimes.     

Time scales and pathways of vibrational energy relaxation in liquid CHBr3 and CDBr3

Molecular dynamics simulations are used in conjunction with Landau-Teller, fluctuating Landau-Teller, and time-dependent perturbation theories to investigate energy flow out of various vibrational states of liquid CHBr3 and CDBr3. The CH stretch overtone is found to relax with a time scale of about 1 ps compared to the 50 ps rate for the fundamental. The relaxation pathways and rates for the CD stretch decay in CDBr3 are computed in order to understand the changes arising from deuteration. While the computed relaxation rate agrees well with experiments, the pathway is found to be more complex than anticipated. In addition to the above channels for CH(D) stretch relaxation that involve only the hindered translations and rotations of the solvent, routes involving off-resonant and resonant excitations of solvent vibrational modes are also examined. Finally, the decay of energy from low frequency states to near-lying solute states and solvent vibrations are studied.     

Vibrational relaxation of the CH stretch fundamental in liquid CHBr3

In continuation of our work on haloforms, the decay of CH stretch excitation in bromoform is modeled using molecular dynamics simulations. An intermolecular force field is obtained by fitting ab initio energies at select CHBr3 dimer geometries to a potential function. The solvent forces on vibrational modes obtained in the simulation are used to compute relaxation rates. The Landau-Teller approach points to a single acceptor state in the initial step of CH stretch relaxation. The time scale for this process is found to be 50-90 ps, which agrees well with the experimental value of 50 ps. The reason for the selectivity of the acceptor is elaborated. Results from a time-dependent approach to the decay rates are also discussed.     

Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.     

Nitrile and thiocyanate IR probes: molecular dynamics simulation studies

Nitrile- and thiocyanate-derivatized amino acids have been found to be useful IR probes for investigating their local electrostatic environments in proteins. To shed light on the CN stretch frequency shift and spectral lineshape change induced by interactions with hydrogen-bonding solvent molecules, we carried out both classical and quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations for MeCN and MeSCN in water. These QM/MM and conventional force field MD simulation results were found to be inconsistent with the experimental results as well as with the high-level ab initio calculation results of MeCN-water and MeSCN-water potential energies. Thus, a new set of atomic partial charges of MeCN and MeSCN is obtained. By using the MD simulation trajectories and the electrostatic potential model recently developed, the CN and SCN stretching mode frequency trajectories were obtained and used to simulate the IR spectra. The C[Triple Bond]N frequency blueshifts of MeCN and MeSCN in water are estimated to be 9.0 and 1.9 cm(-1), respectively, in comparison with those of gas phase values. These values are found to be in reasonable agreement with the experimentally measured IR spectra of MeCN, MeSCN, beta-cyano-L-alanine, and cyanylated cysteine in water and other polar solvents.     

Vibrational relaxation of CN stretch of pseudo-halide anions (OCN-, SCN-, and SeCN-) in polar solvents

The vibrational relaxation dynamics of pseudo-halide anions XCN- (X = O, S, Se) in polar solvents were studied to understand the effect of charge on solute-to-solvent intermolecular energy transfer (IET) and solvent assisted intramolecular vibrational relaxation (IVR) pathways. The T1 relaxation times of the CN stretch in these anions were measured by IR pump/IR probe spectroscopy, in which the 0-1 transition was excited, and the 0-1 and 1-2 transitions were monitored to follow the recovery of the ground state and decay of the excited state. For these anions in five solvents, H2O, D2O, CH3OH, CH3CN, and (CH3)2SO, relaxation rates followed the trend of OCN- > SCN- > SeCN-. For these anions and isotopes of SCN-, the relaxation rate was a factor of a few (2.5-10) higher in H2O than in D2O. To further probe the solvent isotope effect, the relaxation rates of S12C14N-, S13C14N-, and S12C15N- in deuterated methanols (CH3OH, CH3OD, CH3OH, CD3OD) were compared. Relaxation rate was found to be affected by the change of solvent vibrational band at the CN- stretching mode (CD3 symmetric stretch) and lower frequency regions, suggesting the presence of both direct IET and solvent assisted IVR relaxation pathways. The possible relaxation pathways and mechanisms for the observed trends in solute and solvent dependence were discussed.     

Surface hopping simulation of the vibrational relaxation of I2 in liquid xenon using the collective probabilities algorithm

A surface hopping simulation of the vibrational relaxation of highly excited I(2) in liquid xenon is presented. The simulation is performed by using the collective probabilities algorithm which assures the coincidence of the classical and quantum populations. The agreement between the surface hopping simulation results and the experimental measurements for the vibrational energy decay curves at different solvent densities and temperatures is shown to be good. The overlap of the decay curves when the time axis is linearly scaled is explained in terms of the perturbative theory for the rate constants. The contribution of each solvent atom to the change of the quantum populations of the solute molecule is used to analyze the mechanism of the relaxation process     

Phenol-benzene complexation dynamics: quantum chemistry calculation, molecular dynamics simulations, and two dimensional IR spectroscopy

Molecular dynamics (MD) simulations and quantum mechanical electronic structure calculations are used to investigate the nature and dynamics of the phenol-benzene complex in the mixed solvent, benzene/CCl4. Under thermal equilibrium conditions, the complexes are continuously dissociating and forming. The MD simulations are used to calculate the experimental observables related to the phenol hydroxyl stretching mode, i.e., the two dimensional infrared vibrational echo spectrum as a function of time, which directly displays the formation and dissociation of the complex through the growth of off-diagonal peaks, and the linear absorption spectrum, which displays two hydroxyl stretch peaks, one for the complex and one for the free phenol. The results of the simulations are compared to previously reported experimental data and are found to be in quite reasonable agreement. The electronic structure calculations show that the complex is T shaped. The classical potential used for the phenol-benzene interaction in the MD simulations is in good accord with the highest level of the electronic structure calculations. A variety of other features is extracted from the simulations including the relationship between the structure and the projection of the electric field on the hydroxyl group. The fluctuating electric field is used to determine the hydroxyl stretch frequency-frequency correlation function (FFCF). The simulations are also used to examine the number distribution of benzene and CCl4 molecules in the first solvent shell around the phenol. It is found that the distribution is not that of the solvent mole fraction of benzene. There are substantial probabilities of finding a phenol in either a pure benzene environment or a pure CCl4 environment. A conjecture is made that relates the FFCF to the local number of benzene molecules in phenol's first solvent shell.     

Vibrational energy relaxation of small molecules and ions in liquids

A theoretical/computational framework for determining vibrational energy relaxation rates, pathways, and mechanisms, for small molecules and ions in liquids, is presented. The framework is based on the system—bath coupling approach, Fermi’s golden rule, classical time-correlation functions, and quantum correction factors. We provide results for three specific problems: relaxation of the oxygen stretch in neat liquid oxygen at 77 K, relaxation of the water bend in chloroform at room temperature, and relaxation of the azide ion anti-symmetric stretch in water at room temperature. In each case, our calculated lifetimes are in reasonable agreement with experiment. In the latter two cases, theory for the observed solvent isotope effects illuminates the relaxation pathways and mechanisms. Our results suggest several propensity rules for both pathways and mechanisms.     

Comparisons of classical chemical dynamics simulations of the unimolecular decomposition of classical and quantum microcanonical ensembles

Previous studies have shown that classical trajectory simulations often give accurate results for short-time intramolecular and unimolecular dynamics, particularly for initial non-random energy distributions. To obtain such agreement between experiment and simulation, the appropriate distributions must be sampled to choose initial coordinates and momenta for the ensemble of trajectories. If a molecule's classical phase space is sampled randomly, its initial decomposition will give the classical anharmonic microcanonical (RRKM) unimolecular rate constant for its decomposition. For the work presented here, classical trajectory simulations of the unimolecular decomposition of quantum and classical microcanonical ensembles, at the same fixed total energy, are compared. In contrast to the classical microcanonical ensemble, the quantum microcanonical ensemble does not sample the phase space randomly. The simulations were performed for CH(4), C(2)H(5), and Cl(-)---CH(3)Br using both analytic potential energy surfaces and direct dynamics methods. Previous studies identified intrinsic RRKM dynamics for CH(4) and C(2)H(5), but intrinsic non-RRKM dynamics for Cl(-)---CH(3)Br. Rate constants calculated from trajectories obtained by the time propagation of the classical and quantum microcanonical ensembles are compared with the corresponding harmonic RRKM estimates to obtain anharmonic corrections to the RRKM rate constants. The relevance and accuracy of the classical trajectory simulation of the quantum microcanonical ensemble, for obtaining the quantum anharmonic RRKM rate constant, is discussed.     

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).     

Intramolecular vibrational energy redistribution in the highly excited fluoroform molecule: a quantum mechanical study using the multiconfiguration time-dependent Hartree algorithm

The present paper is devoted to a detailed study of the intramolecular vibrational energy redistribution in fluoroform initiated by a local mode excitation of the CH stretch [nnu(CH) (n=1,...,4)]. All nine internal degrees of freedom are explicitly taken into account and the full quantum mechanical simulation is performed by means of the multiconfiguration time-dependent Hartree algorithm. The existence of different time scales considerably complicates the dynamics. The mode-to-mode energy transfer is analyzed by calculating the evolution of the partial energies of all vibrational modes. This study emphasizes the crucial role played by the two-dimensional FCH bending modes which act as an energy reservoir. The fast energy flow into these bending modes significantly hinders an energy flow from the CH chromophore. Finally, our results are compared with those obtained previously with the wave operator sorting algorithm approach.     

Intramolecular hydrogen bonding in disubstituted ethanes: general considerations and methodology in quantum mechanical calculations of the conformational equilibria of succinamate monoanion

The importance of intramolecular hydrogen bonding between the carboxylate oxygen and amide proton of succinamate anion has been investigated by quantum mechanical simulations as a function of solvent for comparison with conformational equilibria estimated by NMR spectroscopy. The focus is on those methodological considerations of general interest to the conformational equilibrium problem, which are also particularly relevant to the quantum calculations. The roughly planar symmetry of the amide and carboxylate substituents of succinamate anion and the possibility of intramolecular hydrogen-bond formation together suggest that the orientational degrees of freedom of the substituents could play an important role in the equilibrium of the CH2-CH2 torsion. To test this hypothesis, two-dimensional potential-energy surfaces (PESs) were mapped out from the quantum mechanical calculations, with coordinates corresponding to the CH2-CH2 torsional and amide group rotational degrees of freedom. The Boltzmann populations obtained from two-dimensional PESs and those obtained from a one-dimensional adiabatic surface for the CH2-CH2 torsion were compared with the experimental results. In these comparisons, the agreement of calculated gauche fractions with corresponding experimental values was checked, as well as the agreement between predicted coupling constants and those determined from experimental spectra. In polar protic and aprotic solvents, where highly polar trans conformations can be stabilized by dipole-dipole and hydrogen-bonding interactions with the solvent, the orientational degree of freedom of the amide substituent appears to play a sufficiently important role in the CH2-CH2 torsional equilibrium that it cannot be safely ignored in the simulations.     

Nonadiabatic effects on peptide vibrational dynamics induced by conformational changes

Quantum dynamical simulations of vibrational spectroscopy have been carried out for glycine dipeptide (CH(3)-CO-NH-CH(2)-CO-NH-CH(3)). Conformational structure and dynamics are modeled in terms of the two Ramachandran dihedral angles of the molecular backbone. Potential energy surfaces and harmonic frequencies are obtained from electronic structure calculations at the density functional theory (DFT) [B3LYP/6-31+G(d)] level. The ordering of the energetically most stable isomers (C(7) and C(5)) is reversed upon inclusion of the quantum mechanical zero point vibrational energy. Vibrational spectra of various isomers show distinct differences, mainly in the region of the amide modes, thereby relating conformational structures and vibrational spectra. Conformational dynamics is modeled by propagation of quantum mechanical wave packets. Assuming a directed energy transfer to the torsional degrees of freedom, transitions between the C(7) and C(5) minimum energy structures occur on a sub-picosecond time scale (700...800 fs). Vibrationally nonadiabatic effects are investigated for the case of the coupled, fundamentally excited amide I states. Using a two state-two mode model, the resulting wave packet dynamics is found to be strongly nonadiabatic due to the presence of a seam of the two potential energy surfaces. Initially prepared adiabatic vibrational states decay upon conformational change on a time scale of 200...500 fs with population transfer of more than 50% between the coupled amide I states. Also the vibrational energy transport between localized (excitonic) amide I vibrational states is strongly influenced by torsional dynamics of the molecular backbone where both enhanced and reduced decay rates are found. All these observations should allow the detection of conformational changes by means of time-dependent vibrational spectroscopy.     

Vibrational solvatochromism and electrochromism of infrared probe molecules containing C≡O, C≡N, C=O, or C-F vibrational chromophore

Solvatochromic vibrational frequency shifts of a few different infrared (IR) probe molecules have been studied by carrying out quantum chemistry calculations for a number of their water clusters. We are particularly focused on the vibrational solvatochromic and electrochromic effects on the CO, CN, and CF stretch modes in carbon monoxide, acetone, 4-cyanopyridine, p-tolunitrile, fluorobenzene, and 3-fluoropyridine. Using multiple interaction site antenna model, we show that their solvatochromic vibrational frequency shifts can be successfully described by considering spatially nonuniform electrostatic potential generated by the surrounding water molecules. It turns out that the CO and CF stretch mode frequencies are approximately proportional to the solvent electric field projected onto the bond axes, whereas the vibrational frequencies of the nitrile stretch mode in 4-cyanopyridine and p-tolunitrile are not. Consequently, it is confirmed that the vibrational Stark tuning rates of the CO and CF stretching modes can be directly used to describe their solvatochromic frequency shifts in condensed phases. However, the nitrile stretch mode frequency shift induced by solvent electrostatic potential appears to be more complicated than its electrochromic phenomenon. To examine the validity of the distributed interaction site model for solvatochromic frequency shifts of these vibrational chromophores, we thus calculated the vibrational Stark tuning rates of the CO, CN, and CF stretch modes and found that they are in good agreement with the experimental results found in literatures. This confirms that a collection of properly chosen distributed interaction sites can be an excellent electric antenna sensing local electrostatics that affects on vibrational frequencies of IR probe modes.     

Computational experiments on the intramolecular energy flow in macromolecules

The microscopic details of the flow of energy in a single chain of polyethylene containing 300 atoms is discussed. The intramolecular dynamics of the polyethylene molecule is studied as a function of CH stretch excitation, temperature, and pressure. The rate of energy flow from CH stretching modes is found to be very rapid and irreversible, occurring on a timescale of less than 0.5 ps at low temperatures, and increases with temperature. A general characteristic two-phase energy flow behavior is observed, where there is initially a very rapid flow (due to the decay of the initial excitation) followed by a slower flow (due to energy redistribution throughout the system). The mechanism for the initial facile energy flow is shown to involve strong resonant pathways. In particular, a CH stretch/HCH bend Fermi (1:2) resonance is shown to dominate the short-time dynamics and facilitates the overall process of energy redistribution. The increase in the rate of energy flow as a function of the backbone temperature is found to be due to the increase in the density of the bath states for energy redistribution which subsequently results in the formation of new low-order resonant interactions (1:1, etc). The long-time dynamics, associated to complete redistribution of the initial CH stretch energy with all of the 894 available vibrational modes, occurs within a time of 2 ps. This timescale corresponds to the time for intramolecular redistribution. A comparison of the intramolecular redistribution time to that of intermolecular redistribution (redistribution in the condensed or solid phase as opposed to a single chain) is also made. A preliminary study of energy flow in a crystal of polyethylene (system containing 19 polyethylene chains) shows that the energy flow exhibits two very different time behaviors. The first is for the intramolecular redistribution as in the single chain study and the second is for intermolecular (chain-to-chain) redistribution. The timescale for intermolecular redistribution is found to be on the order of 0.2 ns at room temperature and pressure, about two orders of magitude larger than the intramolecular timescale.