Collisional Energy Transfer Research Articles

“Third-Body” collision efficiencies for combustion modeling: Hydrocarbons in atomic and diatomic baths

The collisional energy transfer dynamics relevant to the unimolecular kinetics of linear, branched, and cyclic hydrocarbons, including both radicals and saturated and unsaturated molecules, in atomic and diatomic baths is studied via classical trajectories. A set of full-dimensional potential energy surfaces (PESs) suitable for efficient trajectory simulations involving large hydrocarbons (CxHy) colliding with any of seven baths (M=He, Ne, Ar, Kr, H2, N2, O2) is validated against direct dynamics calculations for two small systems. The PESs are then used to calculate Lennard-Jones collision parameters, and a general rule for calculating these parameters based only on the number of carbon atoms and the bath gas is obtained. Next, the PESs are used to calculate low-order moments of the collisional energy transfer function relevant to low-pressure-limit unimolecular kinetics for a total of 266 systems (38 unimolecular reactants in 7 baths), with a focus on the average angular momentum and total energy transferred in deactivating collisions. These moments are used to quantify the relative rotational and total collision efficiencies of the 7 baths for the various hydrocarbon reactants. Trends in the collision efficiencies with respect to the chemical structures of the hydrocarbon reactants are discussed.

Performance of a high-resolution mid-IR optical-parametric-oscillator transient absorption spectrometer.

We report on a mid-IR optical parametric oscillator (OPO)-based high resolution transient absorption spectrometer for state-resolved collisional energy transfer. Transient Doppler-broadened line profiles at λ = 3.3 μm are reported for HCl R7 transitions following gas-phase collisions with vibrationally excited pyrazine. The instrument noise, analyzed as a function of IR wavelength across the absorption line, is as much as 10 times smaller than in diode laser-based measurements. The reduced noise is attributed to larger intensity IR light that has greater intensity stability, which in turn leads to reduced detector noise and better frequency locking for the OPO.

A unified model for simulating liquid and gas phase, intermolecular energy transfer: N₂ + C₆F₆ collisions.

Molecular dynamics simulations were used to study relaxation of a vibrationally excited C6F6* molecule in a N2 bath. Ab initio calculations were performed to develop N2-N2 and N2-C6F6 intermolecular potentials for the simulations. Energy transfer from "hot" C6F6 is studied versus the bath density (pressure) and number of bath molecules. For the large bath limit, there is no heating of the bath. As C6F6* is relaxed, the average energy of C6F6* is determined versus time, i.e., ⟨E(t)⟩, and for each bath density ⟨E(t)⟩ is energy dependent and cannot be fit by a single exponential. In the long-time limit C6F6 is fully equilibrated with the bath. For a large bath and low pressures, the simulations are in the fixed temperature, independent collision regime and the simulation results may be compared with gas phase experiments of collisional energy transfer. The derivative d[⟨E(t)⟩]/dt divided by the collision frequency ω of the N2 bath gives the average energy transferred from C6F6* per collision ⟨ΔE(c)⟩, which is in excellent agreement with experiment. For the ~100-300 ps simulations reported here, energy transfer from C6F6* is to N2 rotation and translation in accord with the equipartition model, with no energy transfer to N2 vibration. The energy transfer dynamics from C6F6* is not statistically sensitive to fine details of the N2-C6F6 intermolecular potential. Tests, with simulation ensembles of different sizes, show that a relatively modest ensemble of only 24 trajectories gives statistically meaningful results.

Three-dimensional analytic probabilities of coupled vibrational-rotational-translational energy transfer for DSMC modeling of nonequilibrium flows

A three-dimensional, nonperturbative, semiclassical analytic model of vibrational energy transfer in collisions between a rotating diatomic molecule and an atom, and between two rotating diatomic molecules (Forced Harmonic Oscillator–Free Rotation model) has been extended to incorporate rotational relaxation and coupling between vibrational, translational, and rotational energy transfer. The model is based on analysis of semiclassical trajectories of rotating molecules interacting by a repulsive exponential atom-to-atom potential. The model predictions are compared with the results of three-dimensional close-coupled semiclassical trajectory calculations using the same potential energy surface. The comparison demonstrates good agreement between analytic and numerical probabilities of rotational and vibrational energy transfer processes, over a wide range of total collision energies, rotational energies, and impact parameter. The model predicts probabilities of single-quantum and multi-quantum vibrational-rotational transitions and is applicable up to very high collision energies and quantum numbers. Closed-form analytic expressions for these transition probabilities lend themselves to straightforward incorporation into DSMC nonequilibrium flow codes.

Far-infrared amplified spontaneous emission and collisional energy transfer between the $E\;0_g^ +$Eg+ (3P2) and $D\;0_u^ +$Du+ (3P2) ion-pair states of I2

We report direct observation of far-infrared amplified spontaneous emission from the E 0(g)⁺ ((3)P2) (v(E) = 0 - 3) ion-pair state of I2 by using an optical-optical double resonance technique with the B (3)Πu (0(u)⁺) (v(B) = 19) valence state as the intermediate state. The directional far-infrared emission detected in the wavelength range from 19 to 28 μm was assigned to the vibronic transitions from the E 0(g)⁺ ((3)P2) ion-pair state to the D 0(u)⁺ ((3)P2) ion-pair state. The subsequent UV fluorescence from the D 0(u)⁺ ((3)P2) state was also observed, which consists not only from the vibrational levels populated by the amplified spontaneous emission but also from those populated by collisional energy transfer. Analyses of the vibrational distribution in the D 0(u)⁺ ((3)P2) state revealed that the population transfer through the amplified spontaneous emission was dominant under our experimental conditions.

Rovibrational energy transfer in the He-C3 collision: Potential energy surface and bound states

We present a four-dimensional potential energy surface (PES) for the collision of C3 with He. Ab initio calculations were carried out at the coupled-cluster level with single and double excitations and a perturbative treatment of triple excitations, using a quadruple-zeta basis set and mid-bond functions. The global minimum of the potential energy is found to be -26.9 cm(-1) and corresponds to an almost T-shaped structure of the van der Waals complex along with a slightly bent configuration of C3. This PES is used to determine the rovibrational energy levels of the He-C3 complex using the rigid monomer approximation (RMA) and the recently developed atom-rigid bender approach at the Close Coupling level (RB-CC). The calculated dissociation energies are -9.56 cm(-1) and -9.73 cm(-1), respectively at the RMA and RB-CC levels. This is the first theoretical prediction of the bound levels of the He-C3 complex with the bending motion.

The importance of accurate adiabatic interaction potentials for the correct description of electronically nonadiabatic vibrational energy transfer: a combined experimental and theoretical study of NO(v = 3) collisions with a Au(111) surface.

We present a combined experimental and theoretical study of NO(v = 3 → 3, 2, 1) scattering from a Au(111) surface at incidence translational energies ranging from 0.1 to 1.2 eV. Experimentally, molecular beam-surface scattering is combined with vibrational overtone pumping and quantum-state selective detection of the recoiling molecules. Theoretically, we employ a recently developed first-principles approach, which employs an Independent Electron Surface Hopping (IESH) algorithm to model the nonadiabatic dynamics on a Newns-Anderson Hamiltonian derived from density functional theory. This approach has been successful when compared to previously reported NO/Au scattering data. The experiments presented here show that vibrational relaxation probabilities increase with incidence energy of translation. The theoretical simulations incorrectly predict high relaxation probabilities at low incidence translational energy. We show that this behavior originates from trajectories exhibiting multiple bounces at the surface, associated with deeper penetration and favored (N-down) molecular orientation, resulting in a higher average number of electronic hops and thus stronger vibrational relaxation. The experimentally observed narrow angular distributions suggest that mainly single-bounce collisions are important. Restricting the simulations by selecting only single-bounce trajectories improves agreement with experiment. The multiple bounce artifacts discovered in this work are also present in simulations employing electronic friction and even for electronically adiabatic simulations, meaning they are not a direct result of the IESH algorithm. This work demonstrates how even subtle errors in the adiabatic interaction potential, especially those that influence the interaction time of the molecule with the surface, can lead to an incorrect description of electronically nonadiabatic vibrational energy transfer in molecule-surface collisions.

Chemical Activation through Super Energy Transfer Collisions

Can a molecule be efficiently activated with a large amount of energy in a single collision with a fast atom? If so, this type of collision will greatly affect molecular reactivity and equilibrium in systems where abundant hot atoms exist. Conventional expectation of molecular energy transfer (ET) is that the probability decreases exponentially with the amount of energy transferred, hence the probability of what we label "super energy transfer" is negligible. We show, however, that in collisions between an atom and a molecule for which chemical reactions may occur, such as those between a translationally hot H atom and an ambient acetylene (HCCH) or sulfur dioxide, ET of chemically significant amounts of energy commences with surprisingly high efficiency through chemical complex formation. Time-resolved infrared emission observations are supported by quasi-classical trajectory calculations on a global ab initio potential energy surface. Results show that ∼10% of collisions between H atoms moving with ∼60 kcal/mol energy and HCCH result in transfer of up to 70% of this energy to activate internal degrees of freedom.

Dynamics of energy transfer and soft-landing in collisions of protonated dialanine with perfluorinated self-assembled monolayer surfaces.

Chemical dynamics simulations are reported which provide atomistic details of collisions of protonated dialanine, ala2-H(+), with a perfluorinated octanethiolate self-assembled monolayer (F-SAM) surface. The simulations are performed at collision energies Ei of 5.0, 13.5, 22.5, 30.00, and 70 eV, and incident angles 0° (normal) and 45° (grazing). Excellent agreement with experiment (J. Am. Chem. Soc., 2000, 122, 9703-9714) is found for both the average fraction and distribution of the collision energy transferred to the ala2-H(+) internal degrees of freedom. The dominant pathway for this energy transfer is to ala2-H(+) vibration, but for Ei = 5.0 eV ∼20% of the energy transfer is to ala2-H(+) rotation. Energy transfer to ala2-H(+) rotation decreases with increase in Ei and becomes negligible at high Ei. Three types of collisions are observed in the simulations: i.e. those for which ala2-H(+) (1) directly scatters off the F-SAM surface; (2) sticks/physisorbs on/in the surface, but desorbs within the 10 ps numerical integration of the simulations; and (3) remains trapped (i.e. soft-landed) on/in the surface when the simulations are terminated. Penetration of the F-SAM by ala2-H(+) is important for the latter two types of events. The trapped trajectories are expected to have relatively long residence times on the surface, since a previous molecular dynamics simulation (J. Phys. Chem. B, 2014, 118, 5577-5588) shows that thermally accommodated ala2-H(+) ions have an binding energy with the F-SAM surface of at least ∼15 kcal mol(-1).

Electronic processes in adatom dynamics at epitaxial semiconductor surfaces studied using MBE-STM combined system

Thermal desorption flux of cation adatoms is modeled in the context of the transition state theory. The model, on the basis of thermally excited electron tunneling to surface adatoms, suggests that the rate of phonon-stimulated electronic transition (In+ + e− → In0) by tunneling is essential to explain the desorption flux at the InAs surface. The adatom thermal desorption is electronic in nature. The importance of an electronic process as one of elemental dynamics of epitaxy, as well as collisional kinetic energy transfer among heavy nuclei of atoms and surface, is emphasized. By means of verifying the equivalence of electrons and phonons as excitation sources in the case of the electronic transition, usefulness of low-temperature scanning tunneling microscopy (LT-STM) as a tool for studying the crystal growth mechanism is explained. A molecular beam epitaxy (MBE) system equipped with the LT-STM provides a promising complement to in situ STM observation during MBE.

Classical Trajectory Study of Energy Transfer in Collisions of Highly Excited Allyl Radical with Argon

Predicting the results of collisions of polyatomic molecules with a bath of atoms is a research area that has attracted substantial interest in both experimental and theoretical chemistry. Energy transfer, which is the consequence of such collisions, plays an important role in gas-phase kinetics and relaxation of excited molecules. We present a study of energy transfer in single collisions of highly vibrationally excited allyl radical in argon. We evolve a total of 52 000 classical trajectories on a potential energy surface, which is the sum of an ab initio intramolecular potential for the allyl and a pairwise interaction potential describing the argon's effect on the allyl. The former is described by means of a permutationally invariant full-dimensional potential, whereas the interaction potential between allyl and argon is obtained by means of a sum of pairwise potentials dependent on nonlinear parameters that have been fit to a set of MP2/avtz counterpoise corrected ab initio energies. Results are reported for energy transfers and related probability densities at different collisional energies. The sensitivity of results to the interaction potential is considered and the potential is shown to be suitable for future applications involving different isomers of the allyl. The impact of highly efficient collisions in the energy transfer process is examined.

ChemInform Abstract: Direct Chemical Dynamics Simulations: Coupling of Classical and Quasiclassical Trajectories with Electronic Structure Theory

AbstractReview: 123 refs.

Collision Efficiency of Water in the Unimolecular Reaction CH4 (+H2O) ⇆ CH3 + H (+H2O): One-Dimensional and Two-Dimensional Solutions of the Low-Pressure-Limit Master Equation

The low-pressure-limit unimolecular decomposition of methane, CH4 (+M) ⇆ CH3 + H (+M), is characterized via low-order moments of the total energy, E, and angular momentum, J, transferred due to collisions. The low-order moments are calculated using ensembles of classical trajectories, with new direct dynamics results for M = H2O and new results for M = O2 compared with previous results for several typical atomic (M = He, Ne, Ar, Kr) and diatomic (M = H2 and N2) bath gases and one polyatomic bath gas, M = CH4. The calculated moments are used to parametrize three different models of the energy transfer function, from which low-pressure-limit rate coefficients for dissociation, k0, are calculated. Both one-dimensional and two-dimensional collisional energy transfer models are considered. The collision efficiency for M = H2O relative to the other bath gases (defined as the ratio of low-pressure limit rate coefficients) is found to depend on temperature, with, e.g., k0(H2O)/k0(Ar) = 7 at 2000 K but only 3 at 300 K. We also consider the rotational collision efficiency of the various baths. Water is the only bath gas found to fully equilibrate rotations, and only at temperatures below 1000 K. At elevated temperatures, the kinetic effect of "weak-collider-in-J" collisions is found to be small. At room temperature, however, the use of an explicitly two-dimensional master equation model that includes weak-collider-in-J effects predicts smaller rate coefficients by 50% relative to the use of a statistical model for rotations. The accuracies of several methods for predicting relative collision efficiencies that do not require solving the master equation and that are based on the calculated low-order moments are tested. Troe's weak collider efficiency, βc, includes the effect of saturation of collision outcomes above threshold and accurately predicts the relative collision efficiencies of the nine baths. Finally, a brief discussion is presented of mechanistic details of the energy transfer process, as inferred from the trajectories.

Suprathermal oxygen and hydrogen atoms in the upper Martian atmosphere

The processes of kinetics and transport of hot oxygen and hydrogen atoms in the transition (from the thermosphere to the exosphere) region of the upper Martian atmosphere are studied. The reaction of dissociative recombination of the principal ionospheric ion O2+ with thermal electrons in the ionosphere of Mars served as the source of hot oxygen atoms. The process of momentum and energy transfer in elastic collisions between hot oxygen atoms and atmospheric hydrogen atoms with thermal energies was regarded as the source of hot hydrogen atoms. The kinetic energy distribution functions are determined for suprathermal oxygen and hydrogen atoms. It is shown that the exosphere is populated with a significant number of suprathermal oxygen atoms with kinetic energies ranging up to the escape energy of 2 eV (i.e., the hot oxygen Martian corona is formed). The transfer of energy from hot oxygen atoms to thermal hydrogen atoms creates an additional nonthermal flux of atomic hydrogen escaping from the Martian atmosphere.

High-order fluid model for streamer discharges: I. Derivation of model and transport data

Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. This paper focuses on the derivation of a high-order fluid model for streamers. Using momentum transfer theory, the fluid equations are obtained as velocity moments of the Boltzmann equation; they are closed in the local mean energy approximation and coupled to the Poisson equation for the space charge generated electric field. The high-order tensor in the energy flux equation is approximated by the product of two lower order moments to close the system. The average collision frequencies for momentum and energy transfer in elastic and inelastic collisions for electrons in molecular nitrogen are calculated from a multi-term Boltzmann equation solution. We then discuss, in particular, (1) the correct implementation of transport data in streamer models; (2) the accuracy of the two-term approximation for solving Boltzmann's equation in the context of streamer studies; and (3) the evaluation of the mean-energy-dependent collision rates for electrons required as an input in the high-order fluid model. In the second paper in this sequence, we will discuss the solutions of the high-order fluid model for streamers, based on model and input data derived in this paper.

Frozen rotor approximation in the mixed quantum/classical theory for collisional energy transfer: Application to ozone stabilization

A frozen-rotor approximation is formulated for the mixed quantum/classical theory of collisional energy transfer and ro-vibrational energy flow [M. Ivanov and D. Babikov, J. Chem. Phys. 134, 144107 (2011)]. Numerical tests are conducted to assess its efficiency and accuracy, compared to the original version of the method, where rotation of the molecule in space is treated explicitly and adiabatically. New approach is considerably faster and helps blocking the artificial ro-vibrational transitions at the pre- and post-collisional stages of the process. Although molecular orientation in space is fixed, the energy exchange between rotational, vibrational, and translational digresses of freedom still occurs, allowing to compute ro-vibrational excitation and quenching. Behavior of the energy transfer function through eight orders of magnitude range of values and in a broad range of ΔE is reproduced well. In the range of moderate -500 ≤ ΔE ≤ +500 cm(-1) the approximate method is rather accurate. The absolute values of stabilization cross sections for scattering resonances trapped behind the centrifugal threshold are a factor 2-to-3 smaller (compared to the explicit-rotation approach). This performance is acceptable and similar to the well-known sudden-rotation approximation in the time-independent inelastic scattering methods.

Ro-vibrational quenching of CO (v = 1) by He impact in a broad range of temperatures: A benchmark study using mixed quantum/classical inelastic scattering theory

The mixed quantum/classical approach is applied to the problem of ro-vibrational energy transfer in the inelastic collisions of CO(v = 1) with He atom, in order to predict the quenching rate coefficient in a broad range of temperatures 5 < T < 2500 K. Scattering calculations are done in two different ways: direct calculations of quenching cross sections and, alternatively, calculations of the excitation cross sections plus microscopic reversibility. In addition, a symmetrized average-velocity method of Billing is tried. Combination of these methods allows reproducing experiment in a broad range of temperatures. Excellent agreement with experiment is obtained at 400 < T < 2500 K (within 10%), good agreement in the range 100 < T < 400 K (within 25%), and semi-quantitative agreement at 40 < T < 100 K(within a factor of 2). This study provides a stringent test of the mixed quantum/classical theory, because the vibrational quantum in CO molecule is rather large and the quencher is very light (He atom). For heavier quenchers and closer to dissociation limit of the molecule, the mixed quantum/classical theory is expected to work even better.

Resonant energy transfer between highly vibrationally excited RbH(RbD) and H2(D2)

An experimental study of vibrational relaxation and V–V and V–R energy transfer in RbH-H2 collisions and their isotopic variants has been performed. In RbH (v″=17, 18, 21)+H2, single quantum relaxation accounts for only about 30% of the total relaxation out of v″ states, and multiquantum relaxation makes significant contribution. For RbH (v″=18), Δv=2 relaxation is about twice as large as Δv=1. The significant fraction (24%) of the initial population for RbH (v″=21) prepared by overtone pumping, relaxes to much lower vibrational levels (Δv=−8). The time scales is much shorter than the known collisional lifetimes of the intervening vibrational levels and thus a sequential single-quantum relaxation mechanism can be explicitly ruled out. V–V energy transfer is suitable explanation. Energy transfer between RbD (X1Σ+v″=21–30) and D2 has been also investigated. V–R and V–V resonance behavior has been also confirmed.

Alignment Selection of the Metastable CO(a 3Π1) Molecule and the Steric Effect in the Aligned CO(a 3Π1) + NO Collision

The aligned metastable CO(a (3)Π1) molecular beam was generated by an electronic excitation through the Cameron band (CO a (3)Π1 ← X (1)Σ(+)) transition. Beam characterization of the aligned molecular beam of CO(a (3)Π1) was carried out by (1 + 1) REMPI detection via the b (3)Σ(+) state. The REMPI signals showed the clear dependence on the polarization of the pump laser, and the experimental result was well reproduced by the theoretical simulation. This agreement confirms that aligned metastable CO(a (3)Π1) can be generated and controlled by rotating polarization of the pump laser. By using this technique, a single quantum state of CO(a (3)Π1) can be selected as a metastable molecular beam. The steric effect in the energy-transfer collision of CO(a (3)Π1) with NO forming the excited NO was carried out with this aligned CO(a (3)Π1) molecular beam. We find that the sideways orientation of CO(a (3)Π1) is more favorable in the formation of the excited NO(A (2)Σ(+), B (2)Π) than that for the axial collisions. The obtained steric effect was discussed with the aid of the spatial distribution of CO(a (3)Π1) molecular orbitals, and we find that specific rotational motion of CO(a (3)Π1) in each state may not be a dominant factor in this energy-transfer collision.

Global ab initio ground-state potential energy surface of N4

We present a global ground-state potential energy surface for N4 suitable for treating high-energy vibrational-rotational energy transfer and collision-induced dissociation in N2-N2 collisions. To obtain the surface, complete active space second-order perturbation theory calculations were performed for the ground singlet state with an active space of 12 electrons in 12 orbitals and the maug-cc-pVTZ triple zeta basis set. About 17,000 ab initio data points have been calculated for the N4 system, distributed along nine series of N2 + N2 geometries and three series of N3 + N geometries. The six-dimensional ground-state potential energy surface is fitted using least-squares fits to the many-body component of the electronic energies based on permutationally invariant polynomials in bond order variables.