Semiclassical extension of the Landau-Teller theory of collisional energy transfer

A semiclassical version of the quantum coupled-states approximation for the vibrational relaxation of diatomic molecules in collisions with monatomic bath gases is presented. It is based on the effective mass approximation and a recovery of the semiclassical Landau exponent from the classical Landau-Teller collision time. For an interaction with small anisotropy, the Landau exponent includes first order corrections with respect to the orientational dependence of the collision time and the effective mass. The relaxation N(2)(v=1)-->N(2)(v=0) in He is discussed as an example. Employing the available vibrationally elastic potential, the semiclassical approach describes the temperature dependence of the rate constant k(10)(T) over seven orders of magnitude across the temperature range of 70-3000 K in agreement with experimental data and quantum coupled-states calculations. For this system, the hierarchy of corrections to the Landau-Teller conventional treatment in the order of importance is the following: quantum effects in the energy release, dynamical contributions of the rotation of N(2) to the vibrational transition, and deviations of the interaction potential from a purely repulsive form. The described treatment provides significant simplifications over complete coupled-states calculations such that applications to more complex situations appear promising.     

Efficient quantum-classical method for computing thermal rate constant of recombination: application to ozone formation

Efficient method is proposed for computing thermal rate constant of recombination reaction that proceeds according to the energy transfer mechanism, when an energized molecule is formed from reactants first, and is stabilized later by collision with quencher. The mixed quantum-classical theory for the collisional energy transfer and the ro-vibrational energy flow [M. Ivanov and D. Babikov, J. Chem. Phys. 134, 144107 (2011)] is employed to treat the dynamics of molecule + quencher collision. Efficiency is achieved by sampling simultaneously (i) the thermal collision energy, (ii) the impact parameter, and (iii) the incident direction of quencher, as well as (iv) the rotational state of energized molecule. This approach is applied to calculate third-order rate constant of the recombination reaction that forms the (16)O(18)O(16)O isotopomer of ozone. Comparison of the predicted rate vs. experimental result is presented.     

A Modified statistical theory of collisional energy transfer in thermal reactions

A fully statistical kernel describing the probability of energy transfer in collisions between polyatomic reactant (A) and heat bath (M) molecules in a thermal system is developed, proceeding through the formation of an intermediate collision complex (AM) whose internal degrees of freedom are assumed to exchange energy. After pointing out that this kernel does not give a quantitatively useful answer, the kernel is modified by introducing the concept that the collision complex lifetime is due to orbiting collisions, and that the (AM) lifetime must equal collision duration. This puts two constraints on the internal degrees of freedom of (AM): (1) those that correlate with relative translation and intrinsic rotation of separated A and M (= transitional modes) can contain only an amount of energy not exceeding E_*, which is the maximum energy for which orbiting can occur; (2) those that correlate with internal degrees of freedom of M must have a density of states such that, subject to constraint (1), the lifetime of (AM) is equal to collision duration. It turns out, quite unambiguously, that the appropriate density of states is equivalent to just one oscillator of M participating in energy exchange. Calculations of average amount of energy transferred (Δ E>) in the system CH₃NC + M show good quantitative agreement with experiment for both polar and non-polar M. The modified theory does not give any appreciable dependence of Δ E> on the size of M because collision duration is assumed to depend only on the long-range part of the potential.     

A three-dimensional He-NaH potential energy surface for rovibrational energy transfer studies

A three-dimensional potential energy surface for the He-NaH van der Waals complex is calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connected triples [CCSD(T)] level of theory. Estimates of CCSD(T) interaction energies for an infinitely large basis set is obtained using a basis set extrapolation scheme. The He-NaH potential energy surface is much different than the He-LiH surface. In particular, the He-NaH system has a binding energy of De=19.73 cm(-1) in comparison to De=176.7 cm(-1) for He-LiH. These minima are at the theta=180 degrees linear geometry where the helium is located at the metal end of the metal hydride. The He-NaH and He-LiH potentials are very similar for the theta=0 degrees linear geometry. The He-NaH potential energy surface supports one vibrational bound state with E=-1.48 cm(-1). Since this energy is smaller than the accuracy of the potential energy surface, the existence of a bound He-NaH complex is questionable.     

Relaxation of internal energy and collisional energy transfer

Using the exponential model for the collisional transition probability, it is shown that relaxation of average internal energy is a measure of bulk-average energy transfer ?ΔE?. This is a macroscopic property which is a complicated function of both time and initial excitation and is only distantly related to average energy transferred per collision ?ΔE?, a microscopic property.     

A semiclassical theory for nonseparable rovibrational motions in curved space and its application to energy quantization of nonrigid molecules

The nonseparability of vibrational and rotational motions of a nonrigid molecule placed in the rotationally isotropic space induces several important effects on the dynamics of intramolecular energy flow and chemical reaction. However, most of these studies have been performed within the framework of classical mechanics. We present a semiclassical theory for the motions of such nonrigid molecules and apply to the energy quantization of three body atomic cluster. It is shown numerically that the semiclassical spectum given without the correct account of the rotational symmetry suffers from unnecessary broadening of the resultant spectral lines and moreover from spurious peaks.     

70 years of Landau-Teller theory for collisional energy transfer. Semiclassical three-dimensional generalizations of the classical collinear model

This article, in historical retrospective, describes the development of the celebrated Landau-Teller (LT) model of 1936 for vibrational-translational energy exchange in collisions of an atom with a diatomic molecule. We discuss semiclassical generalizations of the classical LT model and generalizations of the collinear LT model to account for the effects of rotation of the diatom on the vibrational relaxation rate. The former is based on the recovery of the Landau semiclassical exponent from the classical LT encounter time, and the latter on the definition of a 1-D driving mode within the manifold of the translational and rotational degrees of freedom of the colliding partners. The utility of generalized LT models is illustrated by three case studies that exemplify weak and strong effects of the rotation as well as the efficiencies of different driving modes in the vibrational relaxation of highly asymmetric diatoms.     

Semiclassical time-correlation function approach to collisional energy transfer into many-atom systems

Cross sections for energy transfer into many-body systems can be expressed in terms of time-correlation functions (TCFS ) of transition operators. A semiclassical version is presented by treating internal motions as quantized and relative motions as classical. The time evolution of internal motions can be calculated in the Heisenberg picture and avoids expansions in target states. The decoupling of fast and slow internal motions is treated and applied to vibrational–rotational decoupling in polyatomic molecules. Results are presented for Li⁺-CO₂ collisions.     

Accuracy of the IOS approximation for highly inelastic R-T collisional energy transfer

Rate constants for rotational excitation of CO by collisions with He atoms computed within the infinite order sudden (IOS) approximation are compared with accurate quantum (coupled-states) and classical trajectory values. Taking the IOS energy as the initial kinetic energy for upward. 0 → J, transitions is found to overestimate the rates, especially for higher J (larger inelasticity). Taking the IOS energy as the initial energy for downward, J → 0, transitions underestimates the rates by a comparable amount. The geometric average of IOS rates computed in these two ways is found to provide accurate values.     

Classical rotational and centrifugal sudden approximations for atom—molecule collisional energy transfer

The application of centrifugal and rotational sudden approximations to classical trajectory studies of rotational energy transfer in atom—molecule collisions to examined. Two different types of approximations are considered: a centrifugal sudden (CS) approximation, in which the orbital angular momentum is assumed to be constant during collisions, and a classical infinite order sudden (CIOS) approximation, in which the CS treatment is combined with an energy sudden approximation to totally decouple translational and rotational equations of motion. The treatment of both atom plus linear and nonlinear molecule collisions is described, including the use of rotational action-angle variables for the rotor equations of motion. Applications of both CS and CIOS approaches to rotational energy transfer in He + I₂ collisions are presented. We find the calculated CS and CIOS rotationally inelastic cross sections are in generally good agreement [errors of (typically) 10–50%] with accurate quasiclassical (QC) ones, with the CS results slightly more accurate than CIOS. Both methods are less accurate for small |Δj| transitions than for large |Δj| transitions. Computational savings for the CS and CIOS applications is about a factor of 3 (per trajectory) compared to QC. We also present applications using the CS method to rotational energy transfer in He, Ar, Xe + O₃ collisions, making comparisons with analogous QC results of Stace and Murrell (SM). The agreement between exact and approximate results in these applications is generally excellent, both for the average energy transfer at fixed impact parameters, and for rotationally inelastic cross sections. Results are better for He + O₃ and Ar + O₃ than for Xe + O₃, and better at low temperatures than at high. Since SM's quasiclassical treatment considered only total internal energy transfer without attempting a partitioning between vibration and rotation, while our CS calculation considers only rotational energy transfer, the observed good agreement between our and SM's cross sections indicates that most internal energy transfer in He, Ar, Xe + O₃ is rotational. The relation of this result to models of the activation process in thermal unimolecular rate constant determination is discussed.     

Selection rules for collisional energy transfer in homonuclear diatomics. rotationally inelastic collisions

We have made a precise study of the circular polarisation of rotationally resolved features of laser-excited iodine. The J′ = 19, ν′ = 16 level of ³II⁺_ou was excited using circularly polarised dye-laser fluorescence and a quantitative data on polarisation features representing inelastic transfer of ΔJ′ = 30 was recorded. The experimental circular polarisation ratios were compared to those predicted by two totally conserving models, ΔM = 0 and Δθ = 0. The agreement between experimental points and the predictions based on the former lead to the formation of a new selection due on rotationally inelastic transfer namely, ΔM = 0.     

Statistical theory of collisional energy transfer in molecular collisions. trans-stilbene deactivation by argon, carbon dioxide, and n-heptane

Recent advances in experimental techniques have made it possible to measure the full conditional probability density P(E, E') of the energy transfer between two colliding molecules in the gas phase, one of which is highly energized and the other in thermal equilibrium at a given temperature. Data have now become available for trans-stilbene deactivation by the three bath gas molecules Ar, CO2, and n-heptane (C7H16). The initial energies of trans-stilbene are set to 10 000, 20 000, 30 000, and 40 000 cm (-1). The results show that exceptionally large amounts of energy are transferred in each collision. By application of our partially ergodic collision theory (PECT), we find that the energy transfer efficiency betaE ranges from a rather normal value of 0.15 for n-heptane at the highest excitation energy to 0.93-nearly in the ergodic collision limit-for the argon bath gas at high excitation energy. Generally, the PECT produces a good fit of the data except for the nearly elastic peak in the case of n-heptane, where PECT produces a rounded and downshifted peak in contrast to a sharply defined elastic maximum of the monoexponential functional fit produced from the original experimental data obtained by kinetically controlled selective ionization in the work of the group of Luther in G?ttingen. This problem is analyzed and found to be related partly to the lack of treatment of glancing collisions in the theory with a remaining uncertainty due to the weak dependence of energy transfer efficiency on nearly elastic collisions. A summary of the present state of understanding shows that collisional activation and deactivation of reactant molecules is more efficient and more statistical than has been previously realized.     

Fluctuating energy level Landau-Teller theory: application to the vibrational energy relaxation of liquid methanol

State-to-state vibrational energy relaxation (VER) rates of the OH-stretch fundamental to select vibrational modes of liquid methanol are presented. The rates are calculated via a modified, fluctuating Landau-Teller (FLT) theory approach, which allow for dynamical vibrational energy level shifts. These rates are then compared to previously published results from Gulmen and Sibert [J. Phys. Chem. A 2004, 108, 2389] for the traditional Landau-Teller (LT) method as well as results calculated through time-dependent perturbation theory (TD), which naturally allow for the fluctuation. For the first time, this method is applied to a polyatomic molecular system, and the FLT theory greatly reduces the discrepancy between the LT and TD results or, at a minimum, is comparable to the LT approach with very little additional computational cost.     

Intra- and intermolecular energy transfer in highly excited ozone complexes

The energy transfer of highly excited ozone molecules is investigated by means of classical trajectories. Both intramolecular energy redistribution and the intermolecular energy transfer in collisions with argon atoms are considered. The sign and magnitude of the intramolecular energy flow between the vibrational and the rotational degrees of freedom crucially depend on the projection K(a) of the total angular momentum of ozone on the body-fixed a axis. The intermolecular energy transfer in single collisions between O(3) and Ar is dominated by transfer of the rotational energy. In accordance with previous theoretical predictions, the direct vibrational de-excitation is exceedingly small. Vibration-rotation relaxation in multiple Ar+O(3) collisions is also studied. It is found that the relaxation proceeds in two clearly distinguishable steps: (1) During the time between collisions, the vibrational degrees of freedom are "cooled" by transfer of energy to rotation; even at low pressure equilibration of the internal energy is slow compared to the time between collisions. (2) In collisions, mainly the rotational modes are "cool" by energy transfer to argon.     

Stochastic theory of collisional energy transfer: nature of convergence of master equation transition probabilities and moments as a function of cumulant expansion order

Closed form expressions for collisional energy transfer transition probabilities and moments are determined for the forced oscillator model by solving cumulant expansion master equation in second, fourth, sixth and infinite order. This enables a study of convergence properties of the cumulant expansion.     

Applications of quantum-classical and quantum-stochastic molecular dynamics simulations for proton transfer processes

Quantum-classical and quantum-stochastic molecular dynamics models (QCMD/QSMD) are formulated and applied to describe proton transfer processes in three model systems - the proton bound ammonia-ammonia dimer in an external electrostatic field; malonaldehyde, which undergoes a quantum tautomeric rearrangement; and phospholipase A₂, an enzyme which induces a water dissociation process in its active site followed by proton hopping to a histidine imidazole ring. The proton dynamics are described by the time-dependent Schrödinger equation. The dynamics of the classical atoms are described using classical molecular dynamics. Coupling between the quantum proton (s) and the classical atoms is accomplished via conventional or extended Hellmann-Feynman forces, as well as the time-dependence of the potential energy function in the Schrödinger equation. The interaction of the system with its environment is described by stochastic forces. Possible extensions of the models as well as future applications in molecular structure and dynamics analysis will be briefly discussed.     

The new theory of electron transfer: application to the photosynthetic reaction centre

Based on recent developments in the theory of electron transfer, we prove that a non-polar environment is needed to maintain the high efficiency and chemical integrity of the photosynthetic reaction centre. We also determine the Gibbs energy diagram for the primary act of charge separation in photosynthesis, and propose an equivalent circuit that captures the principal features of the entire acceptor side of the electron transport chain in photosystem II.     

Higher energy states in the CO dimer: millimeter-wave spectra and rovibrational calculations

New extensive millimeter-wave measurements of the 12C16O dimer have been made, and more than 300 new spectral transitions have been observed in the frequency range 81-135 GHz. A joint analysis of these and previous millimeter-wave data yielded the precise location of 33 new energy levels of A+ symmetry and 20 levels of A- symmetry. These energy levels are located at 8-18 cm(-1) above the zero-point level. Some of them belong to already known stacks, and others make up 9 new stacks of the dimer. Newly determined stacks have K=0, 1, and, for the first time, 2, where K is the projection of the total angular momentum on the intermolecular axis. The energy levels from accompanying rovibrational calculations with the use of a recently developed hybrid CCSD(T)/DFT-SAPT potential are in very good agreement with experiment. Analysis of the calculated wave functions revealed that two new stacks of A+ symmetry with K=2 correspond to overall rotation of the dimer while the other newly observed stacks belong to the geared bend overtone modes. The ground vibrational states of the two "isomers" found are more or less localized at the two minima in the potential surface, whereas all the geared bend excited states show a considerable amount of delocalization.