Vibrational Quantum States Research Articles

Two-dimensional vibrational potential energy surface for phthalan: The effect of large coupling on vibrational quantum states

The low-frequency analysis of the phthalan ring-puckering vibration shows a highly irregular pattern of energy levels which cannot be adequately described by a one-dimensional potential energy function. Because the ring-puckering mode interacts strongly with the ring-flapping vibration of the same symmetry, a two-dimensional analysis involving these two motions is required. Two-dimensional kinetic energy (reciprocal reduced mass) expansions were calculated for the puckering, flapping, and interaction terms and these were utilized in the calculation of the two-dimensional potential energy surface. This surface does an excellent job of reproducing the irregular pattern of observed energy spacings for the ring-puckering vibration in both the ground and excited flapping states. The potential-energy surface has a barrier to planarity of 35 cm−1 and energy minima at x1=0.09 Å, x2=−0.03 Å, and x1=−0.09 Å, x2=0.03 Å where x1=puckering and x2=flapping. Although the minima correspond to puckered conformations with a slight amount of flapping, the molecule for practical purposes is planar since the energy barrier is so small. The calculations demonstrate that the unusual irregular pattern of the puckering levels arises primarily from the kinetic-energy interactions of the two vibrations.

Thermalization of trapped ions: A quantum perturbation approach

The rate at which external random thermal fluctuations drive transitions between, and cause decoherence of, the near ground vibrational (harmonic oscillator) quantum states of trapped cold ions is of crucial importance in relation to quantum computing. Presented here is an estimate of these rates, for a single trapped ion, based on a quantum perturbation approach where an external thermal energy reservoir is electrically coupled to the ion. The results are for a general system, and it is shown that the relevant parameter in the interpretation of experimentally observed heating rates is the correlation time of the fluctuations. The rates due to the fluctuating electric field associated with blackbody radiation are also considered and shown to be negligible.

Electron Transfer Rates from Vibrational Quantum States

Electron transfer involves changes in molecular geometry that are important for controlling rates. In this work we report the first clear effects of vibrational quantum state on solution phase electron transfer rates. The spontaneous electron transfer rates for the recovery of an ion pair [Co(Cp)2+/V(CO)6-] are studied with picosecond infrared spectroscopy following optical excitation into its charge transfer band. The rates increase about 2-fold for each additional vibrational quantum in the CO stretching mode. These results allow new tests of electron transfer theory.

Photodissociation of acrylonitrile at 193 nm: the CN-producing channel

We report the rotational and vibrational quantum state distribution of the CN(X 2 Σ +) products formed in the 193 nm photolysis of acrylonitrile (vinyl cyanide). The CN product is formed in v = 0 and v = 1 with relative populations of 0.86 and 0.14, respectively. The rotational distributions in both v-levels are well fit to a temperature of approximatelt 1450 K. The results are consistent with a prompt dissociation on the excited electronic potential surface.

Sampling of semiclassically quantized polyatomic molecule vibrations by an adiabatic switching method: Application to quasiclassical trajectory calculations

We apply the adiabatic switching (AS) method to determine the polyatomic classical motions that correspond to selected vibrational quantum states on multidimensional, anharmonic potential energy surfaces, and use these semiclassically quantized motions as initial conditions for quasiclassical trajectory (QCT) calculations of state-to-state reaction dynamics. Specifically, we calculate the classical motion corresponding to the quantum mechanical zero-point vibration of deuterated methane, CD4, and run QCT calculations on the H+CD4→HD(v′,j′)+CD3 reaction. The distribution of CD4 vibrational zero-point energy (ZPE) associated with the AS-sampled motions is compared with that from normal-mode-sampled motions. The spread of total zero-point energy in the AS calculations is much narrower than with normal-mode sampling, and the ZPE’s are appropriately shifted to lower energy due to anharmonic effects. Reverse adiabatic switching is used as an indirect check of the quantum numbers of the adiabatically sampled motion, but numerical limitations made this test inconclusive. The AS method thus appears to be superior to normal-mode sampling, but this superiority cannot be demonstrated conclusively for the fully anharmonic CD4 potential. However, the AS method is shown to perform very well for transformation from one CD4 harmonic potential to another and for transformation from an harmonic to an anharmonic, but decoupled potential in which CD4 is described by Morse oscillators. Evidence is presented that suggests the AS calculations are limited by numerical inaccuracies or intrinsic features of the potential energy surface, both of which are unavoidable. H+CD4→HD(v′,j′)+CD3 QCT calculations of state-to-state dynamics using CD4 with no ZPE, the ZPE from AS sampling, and the ZPE from normal-mode sampling are reported and compared.

The accuracy of the pseudopotential approximation. I. An analysis of the spectroscopic constants for the electronic ground states of InCl and InCl3 using various three valence electron pseudopotentials for indium

Spectroscopic constants for InCl and InCl3 are determined by a coupled cluster procedure using relatively large basis sets and an energy-consistent semilocal three valence electron pseudopotential for indium. Possible errors within the pseudopotential approximation are discussed in detail by comparison of available pseudopotentials adjusted through different techniques. Core-polarization corrections and the deviation from a point core approximation are discussed. These corrections, however, do not lead to more accurate bond distances as compared to the experimental results. Differently adjusted three valence electron pseudopotentials yield quite different results for the bond distances of InCl and InCl3. The single-electron adjusted energy-consistent pseudopotential of Igel-Mann et al. [Mol. Phys. 65, 1321 (1988)] yields the best results and therefore, this pseudopotential has been chosen for all further investigations on molecular properties. The Dunham parameters for InCl are calculated by solving the vibrational-rotational Schrödinger equation numerically. A finite field technique is used to determine the dipole moment and dipole-polarizability of diatomic InCl. The dependence of several molecular properties on the vibrational quantum state is determined by calculating the expectation value Pn=〈n‖P(R)‖n〉, where P(R) is the distance dependent molecular property. The P(R) curves show strong linear behavior and therefore, the shape of the Pn curve is mostly determined by anharmonicity effects in the InCl potential curve. For the vibrational ground state, ‖0〉, the calculated property P0 deviates only slightly from the property determined directly at the equilibrium distance, Pe. There is in general satisfying agreement of our calculated values with available experimental results. However, it is concluded that in order to obtain very accurate spectroscopic constants a small core definition for indium has to be preferred.

Rotation-vibration-dissociation interaction in a multicomponent nonequilibrium viscous shock layer

A new, simple and physically adequate method of calculating vibrationally nonequilibrium dissociation constants is proposed on the basis of a dissociation model which takes into account the equilibrium excitation of the rotational degrees of freedom of the molecules and the nonequilibrium excitation of vibrational quantum states. This rotation-vibration-dissociation interaction model contains only the indeterminacy associated with the indeterminacy of the experimental data on the interaction potentials and the collision cross sections of the components. In the case of thermodynamic equilibrium the model gives values of the dissociation constants close to those generally accepted. The use of this model in multicomponent nonequilibrium total viscous shock layer calculations gives values for the shock detachment distance within 5% of the experimental values. The indeterminacy in the values of the vibrational energy lost by air molecules during dissociation and recovered during recombination does not lead to serious errors in the macrocharacteristics of the flow. The nonequilibrium excitation of vibrational degrees of freedom proves to be not so important in computing the macrocharacteristics of the flow as previously assumed and the existing algorithms for calculating chemically nonequilibrium flows on the assumption of thermodynamic equilibrium can be used with satisfactory accuracy for calculating the values of the heat flux, the position of the shock wave, and the temperature and pressure in the shock layer for partially dissociated and ionized air.

Production of a pure, single ro-vibrational quantum-state molecular beam

Electrostatic hexapole focusing is used to produce a beam of ND 3 molecules in a pure, single | JKMϵ〉|±〉≡|1111〉|−〉 rational—vibrational quantum state in the electronic ground state, X , 1A′ 1. Both photodissociation at 193.3 nm and (2+1) REMPI are used to detect the state-selected ND 3 molecules. Calculated focusing curves are shown to be in good agreement with the experimental curves for initial beam temperatures less than 6 K and special simulations confirm the single state nature of the molecular beam by comparisons to the measured population and alignment ( A [2] O=0.5±0.1) of the focused |1111〉|−〉 state.

A thermally non-equilibrium viscous shock layer past slender blunted cones

Physical-chemical processes in a shock layer past a slender spherically blunted body at high supersonic velocities are investigated. Using a gas-dynamic model, defined by the complete viscous shock-layer equations [1], the steady laminar axisymmetric flow of viscous, heat-conducting, partially dissociated and ionized air under chemical and thermal non-equilibrium is considered throughout the region between the body and the required thin shock wave. Attention is concentrated on the non-equilibrium chemical, ionization, and relaxation kinetics at large distances from the leading stagnation point. Multicomponent diffusion and the reverse influence of dissociation-recombination on the relaxation of vibrational quantum states, i.e. coupling vibration-dissociation-vibration (CVDV), are taken into account. A new model is used to describe dissociation-relaxation process [2]. The model includes the effect of non-equilibrium excitation of vibrations and the equilibrium excitation of rotational molecular modes on the dissociation rate constants. Comparisons with experimentally verified calculations and calculations within the scope of the chemically equilibrium full viscous shock-layer model indicate that the model is physically adequate. The calculations highlighted physical effects in the non-equilibrium viscous shock layer past a slender spherically blunted cone at various distances from the stagnation point.

State-to-state dynamics of atom+polyatom abstraction reactions. II. The H+C2H6/C3H8→H2(v′,J′) +C2H5/C3H7 reactions

The rotational and vibrational quantum state distributions for the H2 products of the H+HR→H2+R reactions (HR=C2H6 and C3H8 ) at 1.6 eV collision energy have been measured using coherent anti-Stokes Raman scattering. Total reaction cross sections have also been determined. For the total cross sections we find 1.5±0.5 Å2 for the ethane reaction and 2.9±0.8 Å2 for the propane reaction. Although several vibrational states are energetically accessible, we observe H2 products only in v′=0 and v′=1, with the majority in the ground vibrational state. The H2 products are on average rotationally cold as well, and 20% or less of the total energy is partitioned to H2 internal energy. However, the quantum state distributions show a positive correlation of H2 product rotational and vibrational energy. That is, the average rotational energy of the H2 in v′=1 is substantially greater than the average rotational energy of the H2 in v′=0. Comparison with state-to-state dynamics results previously obtained for the kinematically and energetically similar H+CD4→HD+CD3 and H+HCl→H2+Cl reactions seems to indicate that this anomalous energy disposal is an intrinsic characteristic of H + alkane hydrogen atom abstraction reactions at high collision energy. We speculate that this anomalous behavior is the result of inelastic encounters between the nascent H2 and alkyl radical products in the reaction exit channel.

Dynamics of H2 elimination from cyclohexadiene

A comprehensive study of the dynamics of H2 elimination from 1,4 and 1,3 cyclohexadiene is reported. Rotational and vibrational quantum state distributions as well as translation energy distributions for the H2 product are measured. State specific detection of H2 is accomplished with a transform limited vacuum ultraviolet–extreme ultraviolet laser system via (1+1) resonance enhanced multiphoton ionization (REMPI). Rate constants for the H2 elimination and 1,4 to 1,3 isomerization reactions are derived. A (v,J) correlation for H2 with v∥J primarily is observed from anisotropy in the Doppler profiles. A clear picture of the transition state configuration of 1,4 cyclohexadiene is provided from the information obtained.

Photodynamics of extended molecular systems. II. Application to the photodissociation of CH3I from vibrationally excited initial states

Photodissociation cross sections have been calculated using a collisional time-correlation function (TCF) approach to light–molecule interactions. The method is based on separating the total TCF into the molecular dipole TCF of the target and the electric-field TCF of the light source. A norm-conserving time-dependent self-consistent-field approximation is implemented for the molecular dipole TCF of the target, which factors into a primary-region TCF, a secondary-region TCF, and a time-dependent phase factor. We present an application to the photodissociation of CH3I from vibrationally excited initial states with up to three quanta in the C–I and CH3 umbrella modes. The dynamics of energy transfer between the primary and the secondary region and its effect on the line shape functions for each initial vibrational state are systematically studied. The evolution of the primary- and secondary-region amplitudes is considered first for the initially excited (1,0) and (0,1) states of CH3I and shows the contrast between the fast oscillations of the primary-region amplitude and the slow oscillations of the secondary-region amplitude. A detailed study of the photodissociation dynamics of CH3I from the other vibrationally excited initial states is presented next. We fixed the number of vibrational quanta in the secondary-region dynamics, and studied the effect of increasing the vibrational excitation energy in the primary-region dynamics. Some of the vibrational energy given to the primary-region dynamics is transferred to the secondary-region dynamics. The reverse situation, vibrational energy transfer from the secondary to the primary region, is also obtained by fixing the vibrational quantum states in the primary-region dynamics and varying the excitation energy in the secondary region.

Laser Vibrational Spectroscopy of Transient, Weakly Bound, and Reactive Molecules

Using laser spectroscopic techniques, namely Stimulated Emission Spectroscopy (SES) and Stark Level Crossing Spectroscopy, in combination with molecular beam techniques, we can now study vibrational levels with energies from zero to tens-of-thousands wavenumbers with sub-Doppler resolution and single rotational level selectivity. Molecular species with concentrations as low as 10−4 Torr can be studied. Low-frequency intermolecular van der Waals vibrational levels in a weakly bound complex can be directly observed for the elucidation of intermolecular forces. Short-lived radicals can be studied at high vibrational excitation. The dissociation behavior of a molecule with vibrational energy higher than the dissociation barrier can be examined with single vibrational quantum state resolution.

A theoretical study of the dissociation of H2/Cu

We present calculations for the dissociative adsorption of hydrogen molecules on a Cu surface as a function of initial translational energy and vibrational quantum state. Classical, semiclassical, and fully quantum calculations are performed and the results compared. The potential energy surface was based upon a total energy calculation for H2 on a small Cu cluster and has been previously employed in dynamical simulations. Our results show that for low primary beam energies, dissociation occurs primarily via tunneling through the activation barrier in the vibrational coordinate. Populating the initial vibrational states is shown to enhance reactivity, but not simply by a total energy shift. By changing the hydrogen isotope it is shown that tunneling effects can persist up to quite high molecular masses. This occurs because the activation barrier lies in the vibrational coordinate, where the reduced mass of the molecule determines the dynamics.

Vibrational overlap integrals between the neutral and ion states of NH 3 and ND 3: Application to the vibrational dependence of the NH 3+( v2)+NH 3(0) symmetric charge transfer reaction

Vibrational overlap integrals have been calculated for the transition between the neutral ground state and the ion state of NH 3 and ND 3 for the ν 2 vibrational bending mode. Calculations were performed by numerically solving the Schrödinger equation. The vibrational overlap integrals were used to simulate the dependence of the cross-section for the NH 3 +( v 2)+NH 3(0)→NH 3( v 2″)+NH 3 +( v 2′) symmetric charge-transfer reaction on the initial vibrational quantum state of the ion. The cross-sections show a gradual increase with v 2, in agreement with experiment.

Dynamics of the reactions of Zn(4s4p 3P1) with H2, HD, and D2: Rotational and vibrational quantum-state distributions of ZnH (ZnD) products

The complete initial vibrational and rotational quantum state distributions of ZnH(ZnD) products in the reactions of Zn(4s4p 3P1) with H2, HD, and D2 have been determined using a laser ‘‘pump-and-probe’’ technique. The most striking result is that the quantum-state distributions of ZnH (or ZnD) products are essentially unchanged when the mass of the leaving atom is doubled, from H to D. It is suggested that this indicates that simple impulsive bond breaking cannot play a large role in the reaction of Zn(3P1) with H2, and that potential surface anisotropy in the decomposition of bent H–Zn–H insertion intermediates could be responsible for the rotational energy distributions of the products. Similar isotopic results for reactions of Cd(5s5p 3P1), Hg(6s6p 3P1), and O(1D2) with H2, HD, and D2 are noted, and the general implications of the lack of an isotope effect are discussed in detail. The branching ratio of ZnD vs ZnH formation in the reaction of Zn(3P1) with HD was determined to be 1.1±0.2 and it was pointed out that several ‘‘insertion’’ reactions have now been shown to have branching ratios for reaction with HD which are very near 1.0, inconsistent with earlier qualitative arguments that such processes should lead to high branching ratios.

Electron impact ionisation cross sections of highly vibrationally excited Li2molecules

Relative ionisation cross section of Li2 molecules, excited by optical pumping into vibrational quantum states up to v"=21, have been measured in a molecular-beam laser experiment as a function of the electron impact energy. The vibrational distribution of the excited Li2 beam is fully characterised by an experimentally tested exact calculation based on the known transition dipole moment of Li2. The experimental results can be largely explained by a simple photoionisation model, which indicates a maximum increase of the ionisation cross section of about 70% for v"=20 at an impact energy of 12 eV. The best fit requires an additional 5% increase in the cross section at v"=20, which is attributed to a dynamic effect not predicted by the model.

Initial distribution of vibrational and rotational quantum states of magnesium oxide(X1.SIGMA.+) produced in the reaction of magnesium(3s3p1P1) with carbon dioxide

Initial distribution of vibrational and rotational quantum states of magnesium oxide(X1.SIGMA.+) produced in the reaction of magnesium(3s3p1P1) with carbon dioxide

Multiphoton ionization of ammonia: Mass analysis and photoelectron spectra

Mass and photoelectron spectra following the resonantly enhanced four-photon ionization of ammonia have been recorded. The mass spectral data show that extensive fragmentation occurs at a distinct wavelength threshold. This threshold energetically corresponds to the minimum number of photons required to reach the first excited state of the ion. The branching ratio for the various fragments (H+, H+2, N+, NH+, NH+2, NH+3) is independent of the neutral resonantly excited vibronic state, and the ratios differ from those recorded by conventional ionization techniques. Photoelectron energy measurements show that low (∼0 eV) kinetic energy electrons are produced following ionization of all but one of the resonantly excited Rydberg states investigated. The origin of these zero energy electrons is thought to be due to vibrational autoionization. Internal conversion may give rise to the neutral vibronic levels responsible for the autoionization. For one excited state, higher electron energies are recorded corresponding to direct ionization. This mechanism leaves the positive ion in a single vibrational quantum state which is the same vibrational state as that of the initially excited neutral-ammonia with cross sections governed by the Franck–Condon principle. The results suggest that the fragmentation occurs entirely within the ionic manifold.

Vibrational energy transfer from highly excited anharmonic oscillators. Dependence on quantum state and interaction potential

In order to elucidate the general features of vibrational deactivation of highly excited anharmonic oscillators, we present quasiclassical trajectory calculations on prototype collinear I2 (v)-inert gas collision systems. The results for vibrational-translational energy transfer reveal several interesting trends as a function of initial vibrational quantum state, projectile mass, and projectile–oscillator interaction potential. (1) Vibrational deactivation is inefficient from all quantum levels and for all projectile masses. The average energy transfer per collision ΔE is strongly peaked at intermediate vibrational levels (v≊80) and is observed to be at most ≊−kbT. Furthermore, when scaled to h/ω(E), the ’’local’’ oscillator energy spacing, ΔE can be accurately represented by a simple power law in vibrational quantum number over a wide range of bound states. (2) Energy transfer is progressively less efficient from levels in the neighborhood of and approaching dissociation. (3) Vibrational energy loss for high levels of initial vibrational excitation (v≳90) is rather insensitive to the nature of the interaction potential. Smooth exponential and hard-sphere interaction results differ by less than an order of magnitude. This observed insensitivity motivates the development of an analytic collision model, in which simple hard-sphere geometry and dynamics are used to calculate ΔE. The model results are in qualitatively good agreement with trajectory calculations and also indicate that nonuniform sampling of the anharmonic oscillator velocity and phase are responsible for decreased energy transfer efficiency from high vibrational states.