Large Amplitude Vibrational Motion Research Articles

Solvent effects on the thioamide rotational barrier: an experimental and theoretical study.

The solvent effect on the C-N rotational barriers of N,N-dimethylthioformamide (DMTF) and N,N-dimethylthioacetamide (DMTA) has been investigated using ab initio theory and NMR spectroscopy. Selective inversion recovery NMR experiments were used to measure rotational barriers in a series of solvents. These data are compared to ab initio results at the G2(MP2) theoretical level. The latter are corrected for large amplitude vibrational motions to give differences in free energy. The calculated gas phase barriers are in very good agreement with the experimental values. Solvation effects were calculated using reaction field theory. This approach has been found to give barriers that are in good agreement with experiment for many aprotic, nonaromatic solvents that do not engage in specific interactions with the solute molecules. The calculated solution-phase barriers for the thioamides using the above solvents are also in good agreement with the observed barriers. The solvent effect on the thioamide rotational barrier is larger than that for the amides because the thioamides have a larger ground-state dipole moment, and there is a larger change in dipole moment with increasing solvent polarity. The transition-state dipole moments for the amides and thioamides are relatively similar. The origin of the C-N rotational barrier and its relation to the concept of amide "resonance" is examined.

Vibrational promotion of electron transfer.

By using laser methods to prepare specific quantum states of gas-phase nitric oxide molecules, we examined the role of vibrational motion in electron transfer to a molecule from a metal surface free from the complicating influence of solvation effects. The signature of the electron transfer process is a highly efficient multiquantum vibrational relaxation event, where the nitrogen oxide loses hundreds of kilojoules per mole of energy on a subpicosecond time scale. These results cannot be explained simply on the basis of Franck-Condon factors. The large-amplitude vibrational motion associated with molecules in high vibrational states strongly modulates the energetic driving force of the electron transfer reaction. These results show the importance of molecular vibration in promoting electron transfer reactions, a class of chemistry important to molecular electronics devices, solar energy conversion, and many biological processes.

PFI-ZEKE photoelectron spectra of the methane cation and the dynamic Jahn-Teller effect

High resolution pulsed-field-ionization (PFI) zero-kinetic-energy (ZEKE) photoelectron spectroscopy has been used to record the photoelectron spectra of CH4, CDH3, CD2H2 and CD4. The observed extensive progression of rotationally resolved transitions between 100,800 cm-1 and 104,100 cm-1 reveals for the first time the complex energy level structure of the methane cation. The high resolution enabled the determination of accurate values for the adiabatic ionization potentials of the different isotopomers. Based on a simple one-dimensional model for the pseudorotation in the different isotopomers, progress has been made towards the understanding of the Jahn-Teller effect at low energies. The static Jahn-Teller distortion in the ion could be determined directly from the vibrationless photoelectron transition in CD2H2. The analysis of the rotational structure in this spectrum with a rigid rotor model leads to an approximate experimental C2v structure. The dynamics of the other methane isotopomers near the adiabatic ionization potentials is dominated by large amplitude vibrational motions between equivalent structures. The corresponding ground state tunneling motions takes place on a picosecond time scale.

Molecular structure of a conformer of glycine by microwave spectroscopy

We have observed and assigned the rotational spectra of 18O-glycine and, for the amino and hydroxy groups, all monodeutero and dideutero isotopically substituted species of the conformer of glycine which has the most intense microwave spectrum, gly(2). The derived spectroscopic data made possible the first complete gas-phase structural determination of an aminoacid. The values for the molecular parameters determined in a least-squares fit are well resolved and in harmony with the results for similar molecules and the predictions of high-level ab initio calculations. Calculation of the ab initio potential energy function for the amino torsion at the MP2/6-31G∗∗ level confirms that a large-amplitude vibrational motion is associated with the gly(2) species. It was found that the standard deviations in the results from the least-squares fit of the molecular parameters of both gly(2) were anomalously large. A similar effect was found in a test molecule—formamide. We conclude that when the experimentally derived rotational constants for a molecule are vibrationally averaged over a large-amplitude motion the explicit inclusion of LAM rotation–vibration interaction appears necessary to achieve more precise results.

Optical paralysis in electronically congested systems: application to large-amplitude vibrational motion of ground state Na 2

The possibility of using phase coherent optical pulse sequences to generate large-amplitude vibrational motion while locking excited state population has been demonstrated by us previously [Kosloff et al., Phys. Rev. Lett.69 (1992) 2172]. While the approach is compatible in principle with strong fields, in practice strong fields excite many higher electronic states and may produce multiphoton ionization, processes that are frequently neglected in model calculations. Here we demonstrate that it is possible to lock any number of unwanted electronic excitations by a single condition on the instantaneous phase of the pulse sequence. We call this scheme “optical paralysis”. Since only the phase of the field is determined by this condition, the amplitude of the field is still unspecified and can be chosen to achieve some desired objective, e.g. monotonic increase of the ground-state vibrational energy. The scheme is demonstrated by solving the time-dependent Schrödinger equation for nine coupled electronic states of Na 2, with energy deposited in the ground state and a single excited state while the population in all other excited states is kept locked.

Dynamics of proton attachment to water cluster: Proton transfer, evaporation, and relaxation

A proton attachment dynamics to a water cluster is investigated by using a classical molecular dynamics calculation. It is found that three dynamical stages are involved: (1) ultrafast (∼10−14 s) proton attachment to a water molecule of the cluster which followed by (2) the fast (∼10−13 s) sequential proton transfer over several water molecules on the cluster surface and then, (3) the gradual (∼10−11 s) proton penetration to the cluster core. In the first two stages, the large kinetic energy of the order of hundreds kcal/mol is released to the system, which results in the evaporation of a few water molecules from the cluster. The water molecules evaporating in these early stages have large vibrational and translational energies. The mechanism of the energy relaxation and the proton transfer in each process are investigated. The large amplitude vibrational motion promotes sequential concerted proton exchange transfers in the earlier stages (1) and (2). The precise configurational matching of the hydrogen bond coordination and the O–O distance fluctuation are the most important factors to determine the direction and the rate of the proton transfer in the stage (3).

Dense molecular hydrogen: Order, disorder, and localization

Recently discovered high-pressure transitions in hydrogen isotopes (H 2, D 2 and HD) exhibit phenomena associated with order, disorder, and localization in their vibrational, rotational, and electronic excitations. Rotational disorder persists in hcp phase I to very high pressures, despite the dramatic increase in intermolecular coupling. Symmetry breaking of hcp occurs on passage into phase II with decreasing temperature, where the axis of rotational quantization adopts specific orientations. Above 150 GPa, a radical symmetry breaking occurs, which is characterized by a large increase in infrared vibron intensity, quasiclassical orientational ordering, and loss of even and odd rotational parity. Synchrotron infrared measurements reveal no evidence for intraband electronic excitations down to 0.15 eV in phase III. Metallization in the molecular solid appears to be controlled by the orientational state, and possibly by order-disorder associated with large-amplitude vibrational motion. The P-T phase diagram to 200 GPa is surprisingly rich, exhibiting both triple and tricritical points.

The missing conformers of glycine and alanine: relaxation in seeded supersonic jets

Certain conformers of glycine and alanine that are predicted by ab initio calculations to be among those of the lowest energy have not been detected in jet spectroscopy studies of these amino acids, although others of similar or higher predicted energy are observed. Selective conformational relaxation of the missing conformers to lower energy species during the free jet expansion, broadly consistent with the criteria established by Ruoff et al. and by Felder and Günthard, has been found to provide a satisfactory explanation. Relevant regions of the molecular potential energy hypersurface have been modelled via ab initio calculations [ MP2 6–31 G(d,p) ] and these show that glycine 4 (see Fig. 3) and glycine 7 can relax to glycine 1, leading to the conclusion, in accordance with observation, that only the latter and glycine 2 should be detected in the jet. In the case of alanine, the ab initio study of the molecular potential energy hypersurface has yielded revised data on predicted spectroscopic constants for some conformers. Because of the combined effects of relaxation and conformational coalescence through large-amplitude vibrational motion, the revised data do not change the interpretation of the previous spectroscopic study of alanine. The barrier separating conformers 2 and 3 (see Fig. 8) is predicted to be no more than 129 cm −1, so that in addition to alanine 1 only a single additional coalesced conformer { 2, 3}, undergoing a large-amplitude motion in a double-minimum potential, is expected to appear in the jet spectrum rather than two separate species. The ab initio calculations on alanine indicate that conformers 4 and 5 are separated by a low energy barrier and a similarly low barrier separates 4 from the much lower energy conformer 1. The resulting coalesced { 4, 5} is effectively a “ledge” on one wall of the potential well containing 1, and is occupied via an excited vibrational state of 1. In this light, the conformer { 4, 5} is not expected to be observed in the jet, as the vibrational relaxation of low-frequency vibrational modes is known to be very efficient in free jet expansions. Overall, no conflicts are found to remain between the experimental observations of jet spectra and the ab initio calculations for glycine and alanine, provided that the scope of such calculations is broadened from a narrower focus on equilibrium structures to consideration of the potential hypersurface. This approach should be important in the correct interpretation of the spectra of other multi-conformational species in free jet expansions.

Toward preresonant impulsive Raman preparation of large amplitude vibrational motion

This article investigates a new approach to the optical generation of large-amplitude coherent molecular vibrations in condensed media. On the basis of analytical results using pulse propagators in the classical Franck approximation, we are led to investigate the efficacy of driving vibrational motion in the electronic ground state by impulsive stimulated Raman scattering with a timed sequence of electronically preresonant femtosecond laser pulses. Numerically exact computations are performed on a model system of dilute molecular Iodine in a low-temperature host crystal. Vibrational relaxation is incorporated via Redfield theory. The results indicate that under a variety of conditions, chemically significant (greater than 0.1 Å) displacements can be produced in a Raman active mode with a fair measure of control over wave packet spreading, and without substantial population loss due to electronic absorption.

Unraveling of transition dipole and dynamical contributions to resonance Raman intensities

The short-time behavior of resonance Raman correlation functions and the shape of the nuclear potential for the ground electronic state is shown to determine the shapes of both the excited state potential and the transition dipole moment. This is demonstrated for models involving large-amplitude vibrational motion.

Effects of the initial vibrational excitation of O 2 on bond dissociations in the O 2(gas) + H(ads) collision

The collision-induced dissociation of adatom and gas molecule bonds in the O 2(g)/H(ads)/surface system has been studied at different initial vibrational excitation of the oxygen molecule. At low excitation, all trajectories lead to O 2 trapping on an adatom site for several to many picoseconds, and adatom dissociation is more efficient than O 2 dissociation. As reagent excitation increases, the residence time of trapped O 2 decreases, and at the same time both adatom and O 2 bond dissociation probabilities increase. Near the dissociation threshold, the O 2 probability rises very rapidly with increasing initial excitation while the adatom probability decreases as a result of preferential energy transfer to a large amplitude vibrational motion of the highly excited O 2 bond. Even at such excitation, a significant fraction of O 2 does not dissociate while adatom does, in which case the desorbing H atom acquires a large kinetic energy and deexcites O 2 through impulsive interactions.

A semirigid bender analysis of ring puckering in cyclopentene

The large-amplitude ring puckering vibration of cyclopentene has been investigated using the semirigid bender model. The structure of the molecule throughout the puckering motion was defined by assuming the atoms follow minimum potential energy paths, derived from ab initio molecular orbital predictions. The double-minimum potential function, determined by fitting rotational and vibrational spectra, has a barrier to planarity of 230 cm −1 and a ring puckering angle of 25.4°. This method of combining ab initio predictions with the semirigid bender method is suitable for modeling large-amplitude vibrational motion of nonrigid molecules with substantial energy barriers and has the advantage of more accurately locating the potential minima.

Time dependent thermal lensing measurements of V–T energy transfer from highly excited NO2

The time dependent thermal lensing technique has been used to measure the vibrational relaxation of NO2 (initially excited at 21 631 cm−1) by Ar, Kr, and Xe. The energy transfer analysis was carried out in terms of 〈〈ΔE〉〉, the bulk average energy transferred per collision. This quantity was found to have a very strong dependence on vibrational energy, with a marked increase at energies greater than about 10 000 cm−1, where several electronic excited states (2B2, 2B1, and 2A2) mix with the ground state (2A1). This effect may be due to large amplitude vibrational motions associated with the coupled electronic states. Even at low energies, deactivation is faster than in other triatomic systems, probably because NO2 is an open shell molecule and electronic curve crossings provide efficient pathways for vibrational deactivation. The V–T rate constant for deactivation of NO2(010) by argon is estimated to be (5.1±1.0)×10−14 cm3 s−1. Results obtained for NO*2–NO2 collisions gave 〈〈ΔE〉〉 values in good agreement with literature results from fluorescence quenching experiments, indicating that V–T may be more important than V–V energy transfer in the quenching process.

Energies and lifetimes of predissociative states of van der Waals molecules: Self-consistent field calculations for I2(v)He, I2(v)Ne

The self-consistent field (SCF) approximation for coupled anharmonic vibrations is applied to the calculation of vibrational energy levels (predissociation resonances) of collinear models of I2 (v)He and I2 (v)Ne, with vibrational quantum number v between 5 and 30. The predissociation lifetimes of these same states are obtained from a distorted wave Born approximation calculation with self-consistent field states taken as the initial states of the complex, and with correlation between the modes taken as the interactions leading to decay. Although the binding energies of the van der Waals complex are very small (order of several cm−1 ), the SCF eigenvalues are in remarkable agreement with the exact numerical values. The lifetimes obtained from the SCF-distorted wave Born approximation (DWBA) are compared with calculations in which the initial state is treated more simply, assuming separability of the modes involved. Results then show that the DWBA with SCF initial states is considerably more accurate than with the more primitive initial state choice. We conclude from these results that the self-consistent field method offers a very accurate description of large-amplitude vibrational motions in van der Waals clusters, with good quantitative results for both the energy levels and predissociation dynamics of these species.

Sub-Doppler infrared spectroscopy in slit supersonic jets. A study of all three van der Waals modes in ? 1-excited ArHCl

Direct absorption tunable difference frequency i.r. laser spectroscopy has been used to study the vibrational dynamics of ArHCl complexes cooled in a slit supersonic jet expansion. As a result of large-amplitude vibrational motion in these weakly bound complexes, transitions to each of the three van der Waals modes are observed as combination bands built on the fundamental HCl stretch, thus permitting detailed study of low-frequency, intermolecular modes with a near-infrared laser source. Our measurements of the (11 10)Π(‘perpendicular’) bend state under uncongested supersonic jet (10 K) conditions dictate a complete reassignment of the vibrational band, which resolves a recent controversy between near- and far-i.r. studies. The bathochromically shifted (1200)Σ(‘parallel’) bend provides strong support for the presence of a secondary minimum in the potential at the inverted ArClH configuration. The unexpectedly large strength of combination band transitions to the (1001)Σ van der Waals stretch state suggests the importance of bend–stretch coupling in the potential as a mechanism for stealing intensity from the bends. This is further substantiated by Coriolis analysis of the rotational levels, in which strong J-dependent mixing of all three vibrations is observed. The molecular constants are in excellent agreement with both far-i.r. experimental results and semiempirical predictions for the Ar + HCl (v= 0) surface, indicating only a small change in the intermolecular potential upon vibrational excitation of the HCl.

A generalized internal axis method for high barrier tunneling problems, as applied to the water dimer

When more than one large-amplitude vibrational motion is present in a molecule, it is often not possible to define a global internal-axis-method (IAM) coordinate system and set of basis functions. In the present work, a method is presented for extending the IAM treatment to tunneling problems in such cases, using as an illustration a model for the water dimer with three large-amplitude vibrational coordinates. The method involves the construction of two different sets of local IAM-like coordinate systems. The first of these contains n coordinate systems, one for the small neighborhood surrounding each of the n equilibrium frameworks. The second contains on the order of n 2 2 coordinate systems, one for each feasible tunneling path between each pair of frameworks. Basis functions written in the second set of local IAM-like coordinates are used to determine the complex phase factors associated in this method with tunneling matrix elements of the phenomenological rotational Hamiltonian in the high barrier limit. These phase factors govern the way in which the various real tunneling frequencies in the molecule constructively and/or destructively interfere in the Hamiltonian matrix elements and final energy expressions. Various mathematical approximations are involved in using the local IAM-like basis sets to obtain matrix elements; the full extent of the adverse effects of these approximations will not be known until an attempt to fit experimental data is carried out.

Group theoretical treatment of the planar internal rotation problem in (HF) 2

The HF dimer is believed to exhibit an internal rotation tunneling process between two planar but nonlinear equilibrium configurations, during which tunneling the roles of the hydrogen-bonded and the free hydrogen atom are interchanged. This process can be represented schematically with labeled atoms as H lF aH 2F b ⇄ F aH lF bH 2, and gives rise to a permutation-inversion group G 4 containing four operations. In the present work the vibration-rotation-tunneling problem in (HF) 2 is treated group theoretically in three ways: (i) by allowing tunneling only through a trans planar C 2 h intermediate, (ii) by allowing tunneling only through a cis planar C 2 v intermediate, and (iii) by considering the trans and cis tunneling processes both to occur, though not necessarily with the same probability. The molecular symmetry groups used for these treatments are (i) the point group C 2 h , (ii) the point group C 2 v , and (iii) a double group, which might be thought of as G 4 † = C 2h † = C 2v † . Nonplanar tunneling paths are not considered, since the internal axis method (IAM) coordinate system used here cannot easily be adapted to nonplanar internal rotation motions in this molecule. Various-details of energy level diagrams, symmetry species for operators, selection rules for spectroscopic transitions, and statistical weights are presented for the (HF) 2 tunneling problem, as well as some speculation on the general question of when point groups, permutation-inversion groups, or double groups are preferable for treating large-amplitude vibrational motion problems.

The selection of coordinate systems for describing large-amplitude nuclear motion in triatomic molecules

A family of mass-scaled coordinate systems is presented for the triatom i75n which the kinetic energy operator for large-amplitude vibrational motion is diagonal (unlike that in current local-mode theories). For any particular potential, a procedure is described to choose the coordinate system in which the hamiltonian most closely approaches separability. This optimal system is applied to the calculation of vibrational excitation energies of water and related isotopic molecules. The relationship of the family of large- amplitude coordinates to normal coordinates is discussed.

Intramolecular and intermolecular interactions in methyl substituted pentanes as revealed by high energy CH-stretching overtone spectra

The overtone spectra of pentane and 12 methyl substituted pentanes are measured in the liquid phase in the region of the pure local mode overtones corresponding to ΔvCH = 3, 4, 5, and 6. The local mode structure of the spectra is discussed. The local mode frequencies ωCH and diagonal local mode anharmonicities XCH for the methyl oscillators are obtained from an analysis of the spectra. The change in ωCH and XCH with increased methyl substitution is related to a barrier to large amplitude vibrational motion arising from steric crowding. The height of this barrier is obtained from dissociation energies calculated from ωCH and XCH by taking the local methyl CH stretching potential to be a Lippincott–Schroeder potential. The methyl steric interactions are described in terms of nonbonded Lennard-Jones and Morse potentials. The parameters for these nonbonded potentials are calculated from the barrier heights and structural information obtained from molecular models for their least strained conformations. These parameters are used to identify a positional dependence in methyl steric hindrance. Force constants evaluated from the nonbonded potentials are correlated with bulk liquid properties.

Quantum theory of large amplitude vibrational motions in a one-dimensional Morse chain

By introducing appropriately generalized annihilation and creation operators for oscillators interacting by Morse potentials and generalized coherent states, we have derived the quantal equations of motion for displacements in a one-dimensional chain of Morse oscillators. The equations of motion derived have the same mathematical structures as their classical analogs which have been studied before. Since they are essentially identical in structure, it is possible to infer from the classical studies that the quantal system also would exhibit solitary waves and solitons. It is pointed out in the paper that the formalism used here for anharmonic systems should also be useful for other fields of study related to high amplitude vibrational motions of polyatomic molecules for which the usual normal mode analysis is not suitable.