Intermolecular energy transfer probabilities from trajectory calculations: A new approach

Mixed quantum/classical theory (MQCT) approach to the dynamics of molecule-molecule collisions in complex systems

We developed a general theoretical approach and a user-ready computer code that permit study of the dynamics of collisional energy transfer and ro-vibrational energy exchange in complex molecule-molecule collisions. The method is a mixture of classical and quantum mechanics. The internal ro-vibrational motion of collision partners is treated quantum mechanically using a time-dependent Schrödinger equation that captures many quantum phenomena including state quantization and zero-point energy, propensity and selection rules for state-to-state transitions, quantum symmetry and interference phenomena. A significant numerical speed up is obtained by describing the translational motion of collision partners classically, using the Ehrenfest mean-field trajectory approach. Within this framework a family of approximate methods for collision dynamics is developed. Several benchmark studies for diatomic and triatomic molecules, such as H2O and ND3 collided with He, H2 and D2, show that the results of MQCT are in good agreement with full-quantum calculations in a broad range of energies, especially at high collision energies where they become nearly identical to the full quantum results. Numerical efficiency of the method and massive parallelism of the MQCT code permit us to embrace some of the most complicated collisional systems ever studied, such as C6H6 + He, CH3COOH + He and H2O + H2O. Application of MQCT to the collisions of chiral molecules such as CH3CHCH2O + He, and to molecule-surface collisions is also possible and will be pursued in the future.

An advanced bath model to simulate association followed by ensuing dissociation dynamics of benzene + benzene system: a comparative study of gas and condensed phase results

The role of the environment (N₂ molecules) on the association followed by the ensuing dissociation reaction of benzene + benzene system is studied here with the help of a new code setup. Chemical dynamics simulations are performed to investigate this reaction in vacuum as well as in a bath of 1000 N₂ molecules, equilibrated at 300 K. Bath densities of 20 and 324 kg m^-3 are considered with a few results from the latter density. The simulations are performed at three different excitation temperatures of benzene, namely, 1000, 1500, and 2000 K, with an impact parameter range of 0-12 Å for both vacuum and bath models. Higher association probabilities and hence, higher temperature dependent association rate constants are obtained in the condensed phase. In the condensed phase, when a trajectory takes a longer time for the monomers to associate, the associated complex is formed with a longer lifetime and provides a lower rate of ensuing dissociation. Higher association rate and lower dissociation rate in condensed phase dynamics are due to the energy transfer process. Hence, the energy transfer phenomenon plays a decisive role in the association/dissociation dynamics, which is completely ignored in the same reaction when studied in vacuum.

In-silico study on perovskites application in capturing and distorting coronavirus

The COVID-19 pandemic, known as coronavirus pandemic, a global pandemic, emerged from the beginning of 2020 and became dominant in many countries. As COVID-19 is one of the deadliest pandemics in history and has a high rate of distribution, a fast and extensive reaction was needed. Considering its composition, revealing the infection mechanism is beneficial for effective decisions against the spread and attack of COVID-19. Investigating data from numerous studies confirms that the penetration of SARS-CoV-2 occurs along with bonding spike protein (S protein) and through ACE2; Therefore, these two parts were the focus of research on the suppression and control of the infection. Performing lab research on all promising candidates requires years of experimental study, which is time-consuming and not an acceptable solution. Molecular dynamic simulation can decipher the performance of nano-structures in preventing the spread of coronavirus in a shorter time. This study surveyed the effect of three nano-perovskite structures (SrTiO3, CaTiO3, and BaTiO3), a cutting-edge group of perovskite materials with outstanding properties on coronavirus. Various computational parameters evaluate the effectiveness of these structures. Results of the simulation indicated that SrTiO3 performs better in SARS-CoV-2 suppression.

Modeling Collisional Transitions in Thermal Unimolecular Reactions: Successive Trajectories and Two-Dimensional Master Equation for Trifluoromethane Decomposition in an Argon Bath

Collisional transition processes in thermal unimolecular reactions are modeled by collision frequency, Z, and probability distribution function, P(E, J; E', J'), which describes the probabilities of collisional transitions from the initial state specified by the total energy and angular momentum, (E', J'), to the final states, (E, J). The validity of the collisional transition model, consisting of Z and P(E, J; E', J'), is assessed here for the title reaction. The present model and its parameters are derived from the moments of transition probabilities calculated by classical trajectory simulations. The model explicitly accounts for coupling between the energy and angular momentum transfer and the dependence of transition probability on the initial state. The performance of the model is evaluated by comparing the rate constants calculated by solving the two-dimensional master equation with those obtained from the classical trajectory calculations of the sequence of successive collisions. The rate constants are also compared with available experimental data. The present collisional transition model is found to perform fairly well for predicting the pressure-dependent rate constants. The uncertainty in the prediction and sensitivities of the rate constants to the model parameters are discussed. A simplified version of the model is proposed, which performs as well as the full model. The simplifications and robust procedures for calculating the model parameters are described.

A Competition between Dissociation Pathway and Energy Transfer Pathway: Unimolecular Dissociation of a Benzene-Hexafluorobenzene Complex in Nitrogen Bath

The unimolecular dissociation of a benzene-hexafluorobenzene complex at 1000, 1500, and 2000 K is studied inside a bath of 1000 N₂ molecules kept at 300 K using chemical dynamics simulation. Three bath densities of 20, 324, and 750 kg/m³ are considered. The dissociation dynamics of the complex at a 20 kg/m³ bath density is found to be similar to that in the gas phase, whereas the dynamics is drastically different at higher bath densities. The microcanonical/canonical dissociation rate constants for the three bath densities are calculated and fitted to the Arrhenius equation. The activation energies are found to be similar to the gas-phase one. However, the pre-exponential factor is lower and decreases with the increase in bath density. The vibrational degree of freedom of the complex more effectively participates in the collisional energy transfer to the N₂ bath, whereas the translational and rotational degrees of freedom of N₂ receive the transferred energy. The energy transfer efficiency increases with the increase in bath density. The time scale of the energy transfer pathway is more than that of the dissociation pathway, and negligible direct dissociation of the complex is observed from the simulation at the highest bath density.

Collision Frequency for Energy Transfer in Unimolecular Reactions

Pressure dependence of unimolecular reaction rates is governed by the energy transfer in collisions of reactants with bath gas molecules. Pressure-dependent rate constants can be theoretically determined by solving master equations for unimolecular reactions. In general, master equation formulations describe energy transfer processes using a collision frequency and a probability distribution model of the energy transferred per collision. The present study proposes a novel method for determining the collision frequency from the results of classical trajectory calculations. Classical trajectories for collisions of several polyatomic molecules (ethane, methane, tetrafluoromethane, and cyclohexane) with monatomic colliders (Ar, Kr, and Xe) were calculated on potential energy surfaces described by the third-order density-functional tight-binding method in combination with simple pairwise interaction potentials. Low-order (including non-integer-order) moments of the energy transferred in deactivating collisions were extracted from the trajectories and compared with those derived using some probability distribution models. The comparison demonstrates the inadequacy of the conventional Lennard-Jones collision model for representing the collision frequency and suggests a robust method for evaluating the collision frequency that is consistent with a given probability distribution model, such as the exponential-down model. The resulting collision frequencies for the exponential-down model are substantially higher than the Lennard-Jones collision frequencies and are close to the (hypothetical) capture rate constants for dispersion interactions. The practical adequacy of the exponential-down model is also briefly discussed.

Collisional Intermolecular Energy Transfer from a N2 Bath at Room Temperature to a Vibrationlly "Cold" C6F6 Molecule Using Chemical Dynamics Simulations

Chemical dynamics simulations were performed to study collisional intermolecular energy transfer from a thermalized N₂ bath at 300 K to vibrationally "cold" C₆F₆. The vibrational temperature of C₆F₆ is taken as 50 K, which corresponds to a classical vibrational energy of 2.98 kcal/mol. The temperature ratio between C₆F₆ and the bath is 1/6, the reciprocal of the same ratio for previous "hot" C₆F₆ simulations (J. Chem. Phys. 2014, 140, 194103). Simulations were also done for a C₆F₆ vibrational temperature of 0 K. The average energy of C₆F₆ versus time is well fit by a biexponential function which gives a slightly larger short time rate component, k₁, but a four times smaller long time rate component, k₂, compared to those obtained from the "hot" C₆F₆ simulations. The average energy transferred per collision depends on the difference between the average energy of C₆F₆ and the final C₆F₆ energy after equilibration with the bath, but not on the temperature ratio of C₆F₆ and the bath. The translational and rotational degrees of freedom of the N₂ bath transfer their energies to the vibrational degrees of freedom of C₆F₆. The energies of the N₂ vibrational mode and translational and rotational modes of C₆F₆ remain unchanged during the energy transfer. It is also found that the energy distribution of C₆F₆ broadens as energy is transferred from the bath, with an almost linear increase in the deviation of the C₆F₆ energies from the average C₆F₆ energy as the average energy of C₆F₆ increases.

Chemical Dynamics Simulations of Intermolecular Energy Transfer: Azulene + N2 Collisions

Chemical dynamics simulations were performed to investigate collisional energy transfer from highly vibrationally excited azulene (Az*) in a N2 bath. The intermolecular potential between Az and N2, used for the simulations, was determined from MP2/6-31+G* ab initio calculations. Az* is prepared with an 87.5 kcal/mol excitation energy by using quantum microcanonical sampling, including its 95.7 kcal/mol zero-point energy. The average energy of Az* versus time, obtained from the simulations, shows different rates of Az* deactivation depending on the N2 bath density. Using the N2 bath density and Lennard-Jones collision number, the average energy transfer per collision ⟨ΔEc⟩ was obtained for Az* as it is collisionally relaxed. By comparing ⟨ΔEc⟩ versus the bath density, the single collision limiting density was found for energy transfer. The resulting ⟨ΔEc⟩, for an 87.5 kcal/mol excitation energy, is 0.30 ± 0.01 and 0.32 ± 0.01 kcal/mol for harmonic and anharmonic Az potentials, respectively. For comparison, the experimental value is 0.57 ± 0.11 kcal/mol. During Az* relaxation there is no appreciable energy transfer to Az translation and rotation, and the energy transfer is to the N2 bath.

Dissipation and transport dynamics in a ratchet coupled to a discrete bath

We investigate a particle in a ratchet potential (the system) coupled to an harmonic bath of N=1-500 degrees of freedom (the discrete bath). The dynamics of the energy exchange between the system and the discrete bath is studied in the transition regime from low to high values of N . First manifestation of dissipation (energy lost by the system) appears for the bath composed of 10 less, similar N less, similar 20 oscillators, as expected. For low values of N , beside small dissipation effects, the system experiences the bath-induced particle transfer between different potential wells from the ratchet. We show that this effect decreases the mobility of particles along the ratchet. The hopping probability along the ratchet and the energy decay rates for the system are shown to obey the power law for late times, a behavior typical of discrete baths which for low and intermediate values of N always induce a non-Markovian process. The exponential decay is recovered for high bath frequencies distribution and for high values of N , where the Markovian limit is expected. Moreover, by including the external oscillating field with intensity F , we show that current reversal occurs in two situations: By increasing N and by switching from low to high frequencies distribution of the bath. The mobility of particles is shown to have a maximum at F=0.1 , which is N independent (for higher values of N ).

Building transition probabilities for any condition using reduced cumulative energy transfer functions in H2O–H2O collisions

The energy transfer process between highly vibrationally excited H(2)O in thermal equilibrium with a gas bath of H(2)O at different internal energies and temperatures has been studied by classical trajectory calculations. The results were analyzed using a cumulative probability distribution Q(DeltaE) of the amount of energy transferred, obtained by direct count of the number of trajectories that transfer an amount of energy equal to or greater than a certain value DeltaE. Scaling Q(DeltaE) in terms of the mean down and up energies transferred for each group of trajectories results in a unique distribution. This fact and the use of detailed balance constrains were used to propose a methodology that make it possible to build the whole P(E('),E) for any condition by knowing DeltaE and a series of parameters that depend only on the system under study.

Energy transfer between azulene and krypton: Comparison between experiment and computation

Trajectory calculations of collisional energy transfer between excited azulene and Kr are reported, and the results are compared with recent crossed molecular beam experiments by Liu et al. [J. Chem. Phys. 123, 131102 (2005); 124, 054302 (2006)]. Average energy transfer quantities are reported and compared with results obtained before for azulene-Ar collisions. A collisional energy transfer probability density function P(E,E'), calculated at identical initial conditions as experiments, shows a peak at the up-collision branch of P(E,E') at low initial relative translational energy. This peak is absent at higher relative translational energies. There is a supercollision tail at the down-collision side of the probability distribution. Various intermolecular potentials are used and compared. There is broad agreement between experiment and computation, but there are some differences as well.

Relaxation dynamics of highly vibrationally excited picoline isomers (E(vib) = 38 300 cm(-1)) with CO2: the role of state density in impulsive collisions

Strong collisions of highly vibrationally excited picoline isomers and CO2 (00(0)0) were investigated using high resolution transient IR absorption probing to investigate the role of donor state density. Vibrationally excited 3-picoline and 4-picoline (3-methylpyridine and 4 methylpyridine) with E(vib) = 38300 cm(-1) were prepared by 266 nm excitation followed by rapid internal conversion. Transient IR probe measurements of the nascent rotational and translational energy gain in CO2 (00(0)0) show that large DeltaE collisions for 3- and 4-picoline are similar to those for excited 2-picoline. The probability distributions for the large DeltaE energy transfer of the three isomers have similar dependence on DeltaE. The results are compared with other earlier results demonstrating that the shape of the large DeltaE probability distribution correlates with the DeltaE dependence of the donor vibrational state density. The results are discussed in terms of the GRETCHEN model for collisional relaxation.

Energy transfer of highly vibrationally excited azulene: Collisions between azulene and krypton

The energy-transfer dynamics between highly vibrationally excited azulene molecules and Kr atoms in a series of collision energies (i.e., relative translational energies 170, 410, and 780 cm(-1)) was studied using a crossed-beam apparatus along with time-sliced velocity map ion imaging techniques. "Hot" azulene (4.66 eV internal energy) was formed via the rapid internal conversion of azulene initially excited to the S4 state by 266-nm photons. The shapes of the collisional energy-transfer probability density functions were measured directly from the scattering results of highly vibrationally excited or hot azulene. At low enough collision energies an azulene-Kr complex was observed, resulting from small amounts of translational to vibrational-rotational (T-VR) energy transfer. T-VR energy transfer was found to be quite efficient. In some instances, nearly all of the translational energy is transferred to vibrational-rotational energy. On the other hand, only a small fraction of vibrational energy is converted to translational energy (V-T). The shapes of V-T energy-transfer probability density functions were best fit by multiexponential functions. We find that substantial amounts of energy are transferred in the backward scattering direction due to supercollisions at high collision energies. The probability for supercollisions, defined arbitrarily as the scattered azulene in the region 160 degrees <theta<180 degrees and DeltaEd>2000 cm(-1) is 1% and 0.3% of all other collisions at collision energies 410 and 780 cm(-1), respectively.

Energy Transfer between Polyatomic Molecules. 3. Energy Transfer Quantities and Probability Density Functions in Self-Collisions of Benzene, Toluene, p-Xylene and Azulene

This paper is the third and last in a series of papers that deal with collisional energy transfer, CET, between aromatic polyatomic molecules. Paper 1 of this series (J. Phys. Chem. B 2005, 109, 8310) reports on the mechanism and quantities of CET between an excited benzene and cold benzene and Ar bath. Paper 2 in the series (J. Phys. Chem., in press) discusses CET between excited toluene, p-xylene and azulene with cold benzene and Ar and CET between excited benzene colliding with cold toluene, p-xylene and azulene. The present work reports on CET in self-collisions of benzene, toluene, p-xylene and azulene. Two modes of excitation are considered, identical excitation energies and identical vibrational temperatures for all four molecules. It compares the present results with those of papers 1 and 2 and reports new findings on average vibrational, rotational, and translational energy, <DeltaE>, transferred in a single collision. CET takes place mainly via vibration to vibration energy transfer. The effect of internal rotors on CET is discussed and CET quantities are reported as a function of temperature and excitation energy. It is found that the temperature dependence of CET quantities is unexpected, resembling a parabolic function. The density of vibrational states is reported and its effect on CET is discussed. Energy transfer probability density functions, P(E,E'), for various collision pairs are reported and it is shown that the shape of the curves is convex at low temperatures and can be concave at high temperatures. There is a large supercollision tail at the down wing of P(E,E'). The mechanisms of CET are short, impulsive collisions and long-lived chattering collisions where energy is transferred in a sequence of short internal encounters during the lifetime of the collision complex. The collision complex lifetimes as a function of temperature are reported. It is shown that dynamical effects control CET. A comparison is made with experimental results and it is shown that good agreement is obtained.

Test of a chemical timing method for measuring absolute vibrational relaxation rate constants for S1 p-difluorobenzene

A chemical timing (CT) method for measuring absolute rate constants for collisional vibrational relaxation has been tested for the 5(1) state of S(1) p-difluorobenzene (pDFB) where an alternative method exists to provide benchmark values. The CT method was originally developed to treat vibrational energy transfer (VET) in large molecules excited to high vibrational levels where the intramolecular vibrational redistribution (IVR) resulting from large vibrational state densities completely eliminates vibrational structure in the emission spectrum. Here we apply the same method to a low-lying state (5(1) with epsilon(vib) = 818 cm(-1)) located in the low-density region of the vibrational manifold where IVR plays no role. For high vibrational levels, the chemical timing method involves addition of high O(2) pressures (kTorr) to a low-pressure pDFB sample, introducing vibrational structure in the fluorescence spectrum. Response of this spectrum to vibrational relaxation by Ar is then examined. For levels such as 5(1), the fully structured fluorescence spectrum allows the rate constant for single-collision VET into the surrounding vibrational field to be measured directly without the presence of O(2). The measurements of 5(1) VET have been repeated with various O(2) pressures (kTorr) for comparison with the O(2)-free benchmark. In the presence of O(2), the rate constant for VET by Ar is (4.0 +/- 0.5) x 10(6) Torr(-1) s(-1) and independent of high O(2) pressure variations. The rate constant as found by the standard O(2)-free method is (3.6 +/- 0.4) x 10(6) Torr(-1) s(-1). This comparison suggests that the chemical timing method is capable of providing a reasonably accurate measure of the VET rate constant for high vibrational levels provided that details of the kinetics are known.

Energy Transfer between Polyatomic Molecules. 1. Gateway Modes, Energy Transfer Quantities and Energy Transfer Probability Density Functions in Benzene−Benzene and Ar−Benzene Collisions

We report collisional energy transfer, CET, quantities for polyatomic-polyatomic collisions and use excited benzene collisions with cold benzene bath, B-B, as our sample system and compare our results with the CET of excited benzene with Ar bath. We find that the gateway mode for both systems is the out-of-plane modes and that in B-B CET, vibration to vibration, V-V, is the dominant channel. Rotations play a mechanistic role in the CET but the net rotational energy transfer is small compared to V-V. The shape of the down side of the energy transfer probability density function, P(E,E'), is convex for B-B collisions and it becomes less so as the temperature increases. In Ar-B collisions, P(E,E') is concave and it becomes less so as the temperature decreases. We report average vibrational, rotational, and translational energy transferred, <DeltaE>, as function of temperature for various initial conditions.

Crossed beams and theoretical studies of the dynamics of hyperthermal collisions between Ar and ethane

Crossed molecular beams experiments and classical trajectory calculations have been used to study the dynamics of Ar+ethane collisions at hyperthermal collision energies. Experimental time-of-flight and angular distributions of ethane molecules that scatter into the backward hemisphere (with respect to their original direction in the center-of-mass frame) have been collected. Translational energy distributions, derived from the time-of-flight distributions, reveal that a substantial fraction of the collisions transfer abnormally large amounts of energy to internal excitation of ethane. The flux of the scattered ethane molecules increased only slightly from directly backward scattering to sideways scattering. Theoretical calculations show angular and translational energy distributions which are in reasonable agreement with the experimental results. These calculations have been used to examine the microscopic mechanism for large energy transfer collisions ("supercollisions"). Collinear ("head-on") or perpendicular ("side-on") approaches of Ar to the C-C axis of ethane do not promote energy transfer as much as bent approaches, and collisions in which the H atom is "sandwiched" in a bent Ar...H-C configuration lead to the largest energy transfer. The sensitivity of collisional energy transfer to the intramolecular potential energy of ethane has also been examined.

Dynamics of energy transfer in peptide-surface collisions

Classical trajectory simulations are performed to study energy transfer in collisions of protonated triglycine (Gly)(3) and pentaglycine (Gly)(5) ions with n-hexyl thiolate self-assembled monolayer (SAM) and diamond [111] surfaces, for a collision energy E(i) in the range of 10-110 eV and a collision angle of 45 degrees. Energy transfer to the peptide ions' internal degrees of freedom is more efficient for collision with the diamond surface; i.e., 20% transfer to peptide vibration/rotation at E(i) = 30 eV. For collision with diamond, the majority of E(i) remains in peptide translation, while the majority of the energy transfer is to surface vibrations for collision with the softer SAM surface. The energy-transfer efficiencies are very similar for (Gly)(3) and (Gly)(5). Constraining various modes of (Gly)(3) shows that the peptide torsional modes absorb approximately 80% of the energy transfer to the peptide's internal modes. The energy-transfer efficiencies depend on E(i). These simulations are compared with recent experiments of peptide SID and simulations of energy transfer in Cr(CO)(6)(+) collisions with the SAM and diamond surfaces.

MassKinetics: a theoretical model of mass spectra incorporating physical processes, reaction kinetics and mathematical descriptions

A theoretical framework and an accompanying computer program (MassKinetics, www.chemres.hu/ms/ masskinetics) is developed for describing reaction kinetics under statistical, but non-equilibrium, conditions, i.e. those applying to mass spectrometry. In this model all the important physical processes influencing product distributions are considered: reactions, including the effects of acceleration, collisions and photon exchange. These processes occur simultaneously and are taken into account by the master equation approach. The system is described by (independent) product, kinetic energy and internal energy distributions, and the time development of these distributions is studied using transition probability functions. The product distribution at the end of the experiment corresponds to the mass spectrum. Individual elements in this scheme are mostly well known: internal energy-dependent reaction rates are calculated by transition state theory (RRK or RRKM formalisms). In the course of collisions, energy transfer and other processes may occur (the latter usually resulting in the 'loss' of ion signal). Collisions are characterized by their probability and by energy transfer in a single collision. To describe single collisions, three collision models are used: long-lived collision complexes, partially inelastic collisions and partially inelastic collisions with cooling. The latter type has been developed here, and is capable of accounting for cooling effects occurring in collision cascades. Descriptions of photon absorption and emission are well known in principle, and these are also taken into account, in addition to changes in kinetic energy due to external (electric) fields. These changes in the system occur simultaneously, and are described by master equations (a set of differential equations). The usual form of the master equation (taking into account reactions and collisional excitation) was extended to consider also radiative energy transfer, kinetic energy changes, energy partitioning and ion loss collisions. Initial results show that close to experimental accuracy can be obtained with MassKinetics, using few or no adjustable parameters. The model/program can be used to model almost all types of mass spectrometric experiments (e.g. MIKE, CID, SORI and resonant excitation). Note that it was designed for mass spectrometric applications, but can also be used to study reaction kinetics in other non-equilibrium systems.