Chemical Dynamics Simulation of Energy Transfer: Propylbenzene

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Chemical Dynamics Simulation of Energy Transfer: Propylbenzene Cation and N Collisions 2

Hyunsik Kim, Hum Nath Bhandari, Subha Pratihar, and William L. Hase J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00111 • Publication Date (Web): 22 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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The Journal of Physical Chemistry

Chemical Dynamics Simulation of Energy Transfer: Propylbenzene Cation and N2 Collisions

Hyunsik Kim,† Hum Nath Bhandari,‡ Subha Pratihar,† William L. Hase*† †Department

of Chemistry and Biochemistry

‡Department

of Mathematics and Statistics

Texas Tech University Lubbock, Texas, 79409

*email : [email protected] 1 ACS Paragon Plus Environment

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Abstract

Collisional energy transfer of highly vibrationally excited propylbenzene cation in a N2 bath has been studied with chemical dynamics simulations. In this work, an intermolecular potential of propylbenzene cation interacting with N2 was developed from SCS-MP2/6-311++G** ab initio calculations. Using a particle swarm optimization(PSO) algorithm, the ab initio results were simultaneously fit to a sum of three two-body potential, consisting of Ca-N, Cb-N and H-N, where Ca is carbon on benzene ring and Cb is carbon on the propyl side chain. Using the developed intermolecular potential, classical trajectory calculations were performed with a 100.1 kcal/mol excitation energy at 473 K to compare with experiment. Varying the density of the N2 bath, the single collision limit of propylbenzene cation with the N2 bath was obtained at density 20 kg/m3 (28 atm). For the experimental excitation energy and in the single collision limit, the average energy transferred per collision, 〈Δ𝐸𝑐〉, is 1.04 ± 0.04 kcal/mol and in good agreement with the experimental value of 0.82 kcal/mol.

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I. INTRODUCTION Collisional intermolecular energy transfer (IET) between a highly vibrationally excited molecule and bath molecules has been widely studied1-4 to model unimolecular reactions. Understanding the dynamics of collisional energy transfer is very important.5-7 For this reason, there have been many experimental studies of collisional IET for numerous molecules such as benzene,8-11 toluene,12-14 azulene,15-21 hexafluorobenzene,22,23 cycloheptatriene,24 pyrazine,25-32 and alkylbenzene cation.33-36

Moreover, theoretical and computational studies have been

performed for collisional IET of vibrationally excited molecules, including CS2,37-39 SO2,39 benzene,40-43 toluene,44,45 hexafluorobenzene,43,46-48 azulene,49-55 and propylbenzene cation.56 In modeling experiments it is important to understand the efficiency of collisional IET for different bath molecules. As discussed in previous work,56 vibrationally highly exited alkylbenzene cations were prepared by a charge exchange process in a turbulent ion flow tube (TIFT).33-36 In the experiments,33-36 competition between collisional deactivation and dissociation of the excited alkylbenzene cations was studied. For the work reported here, the specific charge exchange process considered35 is that between neutral propylbenzene and O2+ + O2+ + C9H12→O2 + C9H12

∗

(1)

There are three pathways for the charge transfer in (1); i.e. a, b, and c.35 Pathway a is direct charge transfer, b involves (O2---C9H12)+ complex formation, and electronically excited O2 is formed in c. Energy transfer to C9H12+ is largest for pathway a and substantially smaller for c. In modeling the experiments, branching fractions for the three pathways are ga = 0.60, gb = 0.27, and gc = 0.13, and the resulting energy distributions for pathways a and b are shown in Figure 1.35 The maximum 3 ACS Paragon Plus Environment


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energy available to C9H12+ is the sum of the difference of the O2 and C9H12 ionization energies and the C9H12 473 K thermal energy. For the work reported here, chemical dynamics simulations were performed to study collisional IET of highly vibrationally excited C9H12+ in a N2 bath. The same methodology was used for the simulations as described previously.46,47,55,56 The initial excitation energy of C9H12+ was 35000 cm-1 (see Figure 1) and the simulations were performed for bath densities of 10, 20, 40, 80, 160, and 320 kg/m3 (14-442 atm) at 473 K. In previous work, collisional IET was studied for vibrationally excited C9H12+ in a He bath and excellent agreement was obtained with experiment.56 A motivation for development and application of the bath model, used here for studying IET, is that it does not require identification of a maximum impact parameter for the simulation. Finding this impact parameter is ambiguous and uncertain.57,58

II. POTENTIAL ENERGY The potential energy function for the chemical dynamics simulations is represented as 𝑉𝑇𝑜𝑡 = 𝑉𝑃𝑟𝑝𝑏𝑧 + + 𝑉𝑁2 + 𝑉𝑃𝑟𝑝𝑏𝑧 + ― 𝑁2 + 𝑉𝑁2 ― 𝑁2

(2)

where VTot is the total potential energy, 𝑉𝑃𝑟𝑝𝑏𝑧 + is the intramolecular potential of C9H12+, 𝑉𝑁2 is the N2 intramolecular potential, 𝑉𝑃𝑟𝑝𝑏𝑧 + ― 𝑁2 is the C9H12+-N2 intermolecular potential, and 𝑉𝑁2 ― 𝑁2 is the N2-N2 intermolecular potential. The intramolecular potentials of C9H12+ and N2, and the N2N2 intermolecular potential, were developed in previous work.46,56 The optimized structure of C9H12+ was determined previously56 by B3LYP/6-311++G** calculations and is shown in Figure 2. Mulliken charges on the atoms were calculated at the same level of theory and it was found that the positive charge of C9H12+ is primarily localized on the benzene ring. Thus, in order to develop 4 ACS Paragon Plus Environment

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an accurate N2-C9H12+ intermolecular potential, it was essential to use independent potential energy functions for the phenyl carbons, Ca-N2, and propyl carbons, Cb-N2. To develop the N2-C9H12+ intermolecular potential, eleven different orientations between N2 and C9H12+ were considered, as shown in Figures 3a-3k. In panels a-d, the N2 molecule approaches the benzene ring plane perpendicularly, directly above C3, C4, C6, and the midpoint of the C3-C4 bond, respectively. In panel e, the N2 molecule approaches the benzene ring plane perpendicularly, directly above the midpoint of C3-C4, with the C3-C4 and N-N bonds crossed at a right angle. In panels f and g, the N2 molecule approaches along a C-H bond axes. In panels f and g the N2 and C4-H4 bond axes and N2 and C9-H12 bond axes are collinear, respectively. In panels h-j, the N2 molecule approaches bisecting a HCH angle. The N2 molecule bisects the H6C7H7, H8C8H9, and H10C9H11 angles in panels h, i, and j, respectively. In panel k, the midpoint of N2 bisects the H10C9H11 angle, with the N-N bond axis perpendicular to the H10C9H11 angle plane. For all orientations, ab initio calculations were performed with the SCS-MP2/6-311++G** theory55,56 and all the points were simultaneously fit using a particle swam optimization (PSO) algorithm.59,60 The fit was made with a sum of Ca-N, Cb-N and H-N two-body potential functions, where Ca is phenyl carbon (C1-C6) and Cb is a propyl carbon (C7-C9). Each two-body potential is given by the modified Buckingham function 𝐶

𝐷

V = Ae ―Br + 𝑟𝑛 + 𝑟𝑚

(3)

The fitting parameters are listed in Table 1. Good fits to the ab initio potential energy curves were obtained, as shown in Figures 3a-3k. The short-range, repulsive intermolecular potential is



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important for the collisional IET.61 The long-range attractive regions of the potential energy curves, and their fits, are illustrated in Figures 4a-4k. The fit is poorest for orientation f. III. SIMULATION METHODOLOGY A condensed-phase version of the VENUS chemical dynamics computer program was used for the simulations reported in this work.62,63 In the experiments,35 C9H12+ is highly vibrationally excited by charge transfer between C9H12 and O2+; i.e. Reaction (1). The maximum excitation energy is a sum of charge exchange exothermicity and the C9H12 thermal excitation at 473 K, and extends to ~35000 cm-1 (100.1 kcal/mol) as shown in Figure 1. The procedure for choosing initial conditions for the vibrationally excited molecule and the bath molecules has been described in detail previously46,55,56 and is only outlined here. The C9H12+ cation was excited randomly with 100.1 kcal/mol of vibrational energy using a quasiclassical microcanonical sampling algorithm.64,65 In adding the vibrational excitation, this algorithm includes the 115.2 kcal/mol zero point energy (ZPE) of C9H12+. As discussed in previous work, 64-72 it is important to include ZPE to obtain good agreement with experiment. For bimolecular reactions, ZPE is an energy component for accessing the transition state barrier.66-68 ZPE is also important for energy transfer dynamics associated with intramolecular vibrational energy redistribution (IVR)70 and post-transition state dynamics,71,72 and for the current study of collisional IET. Initial translational and rotational energies of C9H12+ were chosen by sampling their 473 K Boltzmann distributions. Vibrationally excited C9H12+ was then placed at the center of a cubical box, with its coordinates and momenta fixed, and 1000 N2 bath molecules equilibrated around it for 290 ps to obtain a temperature of 473 K. After the equilibration, a trajectory calculation was performed to study vibrational energy transfer from excited C9H12+ to the N2 bath. The simulations were performed for bath densities of 6 ACS Paragon Plus Environment

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10, 20, 40, 80, 160 and 320 kg/m3 (14-443 atm), and the corresponding sides of the cubical box are 167.2, 132.7, 105.4, 83.7, 66.5, and 52.9 Å. The simulations used periodic boundary conditions (PBC) and a neighbor list algorithm with a 18 Å cut-off distant. It was necessary to integrate the trajectories for the lower densities for longer times to obtain vibrational relaxation of C9H12+. The respective integration times for the lowest to highest density are 2100, 1400, 800, 400, 300, and 200 ps. A total of one hundred trajectories were calculated for each density. As vibrational energy transferred from C9H12+ to the 1000 N2 bath molecules, there was some slight heating of the bath. On the time scale of the simulations, there is negligible energy transfer to N2 vibration.55 With complete equilibration of the C9H12+ vibration, rotation, and translation and the N2 rotation and translation degrees of freedom, the temperature of the bath increases by 24 degrees to 497 K.

IV. RESULTS AND DISCUSSION A. Average Energy versus Time. One-hundred trajectories were calculated for each density and averaged to obtain plots of the average C9H12+ energy, , versus time. The plots are presented in Figure 5 and, as done previously,46,47,55,56 are fit by the bi-exponential function 〈𝐸(𝑡)〉 = [𝐸(0) ―𝐸(∞)](𝑓1exp ( ― 𝑘1𝑡) + 𝑓2exp ( ― 𝑘2𝑡)) +𝐸(∞)

(4)

where 𝐸(0) is the initial energy, 𝐸(∞) the fitted final energy of C9H12+, 𝑓1 + 𝑓2 = 1, and 𝑘1 and 𝑘2 are rate constants. The fitting parameters are listed in Table 2. Rotations and translations of C9H12+ were not heated, and remained as their initial temperature and temperature of the N2 bath. Thus, represents the change in the vibrational energy of C9H12+ versus time. 7 ACS Paragon Plus Environment


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To establish the statistical uncertainty in the values, the standard deviation of the mean was calculated from the 100 trajectories used to determine . Representative values, for different times, are given in Figure 5 for the 20 kg/m3 simulation. This uncertainty in the ranges from 1.2 kcal/mol at the short time of 300 ps to 0.9 kcal/mol for the longer time of 1300 ps. The f1 and f2 parameters in Table 2 are similar for the different bath densities. The E(∞) values range from 59.3 to 65.1 kcal/mol as compared to 56.3 kcal/mol for C9H12+ at the final equilibrated bath temperature of 497 K. The sets of C1 and C2 parameters are identical for the two lowest densities, indicating the single collision limit as discussed below. For the higher densities, the C1 are similar, ranging from 0.00011 - 0.00012. In contrast the C2 parameter increases with increase in bath density. The energy transfer dynamics at high densities is important and interesting, and will be considered in future work. B. Single Collision Limit. As discussed in previous work,46,47,55,56 at densities at and below the single collision limit, there is a proportional relationship between the rate constant (k) and bath density (ρ), which is 𝑘 = 𝐶𝜌. Within the single collision limit, the proportionality constant C becomes independent of pressure. With this understanding, the single collision limit may be identified by decreasing the simulation density. As shown in Table 2, the sets of C1 and C2 values are identical for the 10 and 20 kg/m3 bath densities and, thus, independent of pressure. However, at higher densities they change. This observation indicates the single collision limit exists at the 20 kg/m3 (28 atm) bath density. The single collision limit is reached between 20 and 40 kg/m3, but the exact density is not determined here. C. Average Energy Transfer per Collision. 8 ACS Paragon Plus Environment

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In the single collision limit, the average energy transfer per collision, 〈Δ𝐸𝑐〉, of C9H12+ in the N2 bath is given by

〈Δ𝐸𝑐〉 = where

𝑑〈𝐸(𝑡)〉 𝑑𝑡


1

×𝜔

(5)

, the slope of versus t, is the energy transfer per unit time and ω is the collision

frequency. To obtain the C9H12+ + N2 collision frequency, as done in experiment,34,35 the Langevin rate constant (kL) was used and is kL = 2𝜋𝑞 𝛼/𝜇

(6)

where q is the elementary electronic charge, 4.8×10-10 esu, α is the experimental polarizability of N2, 1.7Å3,73 and μ is the C9H12+ + N2 reduced mass. The Langevin rate constant, used in the experimental study,35 is 6.5×10-10 cm3/molecule∙s and that is the rate constant used here. The derivative


was obtained from Eq. (4), using the fitting parameters in Table 2, and combined

with kL to determine 〈Δ𝐸𝑐〉 versus 〈𝐸〉 as shown in Figure 6. The plots for densities of 10 and 20 kg/m3 are similar, but at higher densities the average energy transfer per collision depends on the density. For the analyses made here, the plot of versus for 10 kg/m3 is used. As shown in Figure 1, the energy distribution of vibrationally excited C9H12+ extends from ~ 20,000 to ~ 35,000 cm-1, the latter the initial excitation energy for the simulations reported here. With the 115.1 kcal/mol ZPE of C9H12+ included, these energies correspond to 172.3 - 215.3 kcal/mol. From Figure 6, ranges from 0.79 to 1.16 kcal/mol for these energies. From Figure 1, the maximum in the C9H12+ experimental energy distribution is at ~ 31,500 cm-1. From the simulation at this energy, is 1.04 kcal/mol and in good agreement with the experimental value of 0.82 kcal/mol.35



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To establish uncertainties in the values, for the low and high values of the standard deviation of the mean, in Figure 5 for the 20 kg/m3 simulation, were fit with the biexponential in Eq. (4). The resulting curves are very similar to that given in Figure 5 for the average . From these curves, values were determined as described above. The resulting values are within ± 0.04 kcal/mol of the values for the average . Thus, for 35,000 cm-1 is 1.16 ± 0.04 kcal/mol and the value is 1.04 ± 0.04 kcal/mol at 31,500 cm-1. D. Comparison 〈𝚫𝑬𝒄〉 Values for collisions of N2 with Different molecules. From experiments,74-78 it is known that low frequency vibrational modes of the excited molecule play an important role in the dynamics of collisional IET. This was found in previous simulations43,47 for C6H643 and C6F6.47 Without changing the potential, the H-atoms of C6H6 were replaced with F-atoms, creating a model benzene with much lower vibrational frequencies. This resulted in a substantial increase in 〈Δ𝐸𝑐〉.43 In a similar study,47 the F-atoms of C6F6 were replaced with H-atoms, increasing the vibrational frequencies. This change decreased the efficiency of collisional IET. With the F-atoms replaced by H-atoms, 〈Δ𝐸𝑐〉 was decreased by a factor of two.47 As discussed in previous work for the C9H12+-He bath system,35 the propylbenzene cation has three groups of vibrational modes; i.e. the phenyl modes, propyl modes, and the modes connecting the phenyl and propyl groups. The low frequency torsion and C-C-C bend modes of the propyl group and phenyl-propyl connecting group are expected to be efficient for transferring energy from vibrationally excited C9H12+. In Table 3 values of 〈Δ𝐸𝑐〉 are listed for collisions of various molecules with N2.12,20,22,24,34,35,46,79 Benzene is the least efficient and C6F6 the most efficient. The next most efficient are the ethyl- and propylbenzene cations. In Table 4, the ten lowest vibrational frequencies 10 ACS Paragon Plus Environment

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of the molecules are listed.35,47,80-84 Benzene has the highest frequencies and C6F6 and the alkylbenzene cations have the lowest, consistent with the smallest 〈Δ𝐸𝑐〉 value for the former and the larger 〈Δ𝐸𝑐〉 values for the latter. Though this comparison in Table 4 is important and informative, it is not quantitative. For example, the vibrational frequencies are lower for the alkylbenzene cations than for C6F6, but 〈Δ𝐸𝑐〉 is larger for C6F6. It is important to develop an accurate model for representing the efficiency of vibrational energy transfer from highly excited molecules. The molecules’ vibrational frequencies are an important property but clearly there are others. One may be gateway modes for efficient collisional IET,75,78,85,86 which could be investigated in simulations with a normal mode Hamiltonian.87

V. SUMMARY Collisional energy transfer dynamics of highly vibrationally excited propylbenzene cation (C9H12+) colliding with N2 were studied at 473 K. An intermolecular potential for C9H12+ interacting with N2 was developed by fitting ab initio SCS-MP2/6-311++G** calculations to twobody modified Buckingham potentials. The intermolecular potential included three two-body potentials representing Ca-N, Cb-N, and H-N interactions, where Ca is phenyl carbon and Cb is a propyl carbon. In the experiment considered here,35 highly vibrationally excited C9H12+ was generated by the charge transfer process described in Reaction (1). For the chemical dynamics simulations C9H12+ was excited randomly with 100.1 kcal/mol (35,000cm-1) of vibrational energy and then allowed to relax in a bath of N2 molecules at 473 K. In order to determine the single collision limit (binary collision limit) for energy transfer from C9H12+, the density of the N2 bath was varied as 11 ACS Paragon Plus Environment


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10, 20, 40, 80, 160 and 320 kg/m3 (14-443 atm). A total of 100 trajectories were calculated for each density and the results averaged. In Figure 5, the average vibrational energy of C9H12+ is plotted versus time for all densities. The results are well fit by the bi-exponential function in Eq. (4) and the fitting parameters are listed in Table 2. The 20 kg/m3 density is in the single collision limit, which occurs between the densities of 20 and 40 kg/m3. From Eq. (5) the average energy transferred per collision, 〈Δ𝐸𝑐〉, is obtained and 〈Δ𝐸𝑐〉 vs 〈𝐸〉 is plotted in Figure 6 for the different densities. The plots are similar for the 10 and 20 kg/m3 densities, indicating the single collision limit, but at higher densities 〈Δ𝐸𝑐〉 decreases with increase in density. As shown in Figure 1, the most probable energy in the distribution of vibrational energy for C9H12+ is ~ 31,500 cm-1 and for this energy the simulation 〈Δ𝐸𝑐〉 is 0.81 kcal/mol. For comparison, the experimental 〈Δ𝐸𝑐〉 for C9H12+ is 0.82 kcal/mol.35 In Table 3, 〈Δ𝐸𝑐〉 of various molecules colliding with N2 are compared. Amongst the molecules in Table 3, benzene is the least efficient in collisional IET, with 〈Δ𝐸𝑐〉 = 0.17 kcal/mol. The most efficient collisional IET is C6F6, for which 〈Δ𝐸𝑐〉 is 1.74 kcal/mol from simulation46 and 1.60 kcal/mol from experiment.22 The propylbenzene cation has relatively efficient energy transfer, with 〈Δ𝐸𝑐〉 of 1.04 ± 0.04 kcal/mol from the current study and 0.82 kcal/mol from experiment.35 As discussed in previous work,43,47,56,74-78 vibrational modes with low frequencies are important in collisional IET. This is seen for the molecules in Table 3, by comparing their low vibrational frequencies in Table 4. However, vibrational frequencies are not the only property affecting collisional IET, since frequencies are lower for C9H12+ than C6F6, but C6F6 has a larger 〈Δ𝐸𝑐〉. There is considerable interest in developing a theoretical model for predicting the efficiency of collisional IET and 〈Δ𝐸𝑐〉. 12 ACS Paragon Plus Environment

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Acknowledgements The research reported here is based upon work supported by the Air Force Office of Scientific Research (AFOSR) grant FA9550-16-1-0133 and the Robert A. Welch Foundation Grant No. D-0005. Support was also provided by the High Performance Computing Center (HPCC) at Texas Tech University, under the direction of Alan Sill. Some of the computations were also performed on the Chemdynm cluster of the Hase Research Group. The authors wish to thank Al Viggiano for helpful discussions.



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44. Lim, K. F. Quasiclassical Trajectory Study of Collisional Energy Transfer in Toluene Systems. I. Argon Bath Gas: Energy Dependence and Isotope Effects. J. Chem. Phys. 1994, 100, 7385-7399. 45. Bernshtein, V.; Oref, I. Trajectory Calculations of Relative Center of Mass Velocities in Collisions between Ar and Toluene. J. Chem. Phys. 1996, 104, 1958-1965. 46. Paul, A. K.; Kohale, S. C.; Pratihar, S.; Sun, Rui.; North, S. W.; Hase, W. L. A Unified Model for Simulating Liquid and Gas Phase, Intermolecular Energy Transfer: N2 + C6F6 Collisions. J. Chem. Phys. 2014, 140, 194103. 47. Paul, A. K.; Kohale, S. C.; Hase, W. L. Bath Model for N2 + C6F6 Gas-Phase Collisions. Details of the Intermolecular Energy Transfer Dynamics. J. Phys. Chem. C 2015, 119, 1468314691. 48. Paul, A. K.; Donzis, D.; Hase, W. L. Collisional Intermolecular Energy Transfer from a N2 Bath at Room Temperature to a Vibrationally “Cold” C6F6 Molecule Using Chemical Dynamics Simulations. J. Phys. Chem. A 2017, 121, 4049-4057. 49. Lim, K. F.; Gilbert, R, G. The a priori Calculation of Collisional Energy Transfer in Highly Vibrationally Excited Molecules: The Biased Random Walk Model. J. Chem. Phys. 1986, 84, 6129-6140. 50. Lim, K. F.; Gilbert, R. G. Modeling Collisional Energy Transfer in Highly Excited Molecules. J. Chem. Phys. 1990, 92, 1819-1830. 51. Clarke, D. L.; Oref, I.; Gilbert, R. G. Collisional Energy Transfer in Highly Excited Molecules: Calculations of the Dependence on Temperature and Internal, Rotational, and Translational Energy. J. Chem. Phys. 1992, 96, 5983-5998 52. Clarke, D. L.; Gilbert, R. G. Collisional Energy Transfer in Highly Excited Molecules: Deuteration Effects. J. Phys. Chem. 1992, 96, 8450-8453. 53. Heidelbach, C.; Fedchenia, I. I.; Schwarzer, D.; Schroeder, J. Molecular-Dynamics Simulation of Collisional Energy Transfer from Vibrationally Highly Excited Azulene in Compressed CO2. J. Phys. Chem. 1998, 108, 10152-10161. 54. Heidelbach, C.; Vikhrenko, V. S.; Schwarzer, D.; Schroeder, J. Molecular Dynamics Simulation of Vibrational Relaxation of Highly Excited Molecules in Fluids. II. Nonequilibrium Simulation of Azulene in CO2 and Xe. J. Phys. Chem. 1999, 110, 5286-5299. 18 ACS Paragon Plus Environment

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78. Koifman, I.; Dashevskaya, E. I.; Nikitin, E. E.; Troe, J. Rotational Gateway for the Vibrational Energy Transfer from Excited Nonlinear Triatomic Molecules. J. Phys. Chem. 1995, 99, 15348-15353. 79. Nakashima, N.; Yoshihara, K. Laser Flash Photolysis of Benzene. VIII. Formation of Hot Benzene from the S2 State and its Collisional Deactivation. J. Chem. Phys. 1983, 79, 2727-2735. 80. Goodman, L.; Ozkabak, A. G.; Thakur, S. N. A Benchmark Vibrational Potential Surface: Ground-State Benzene. J. Phys. Chem. 1991, 95, 9044-9058. 81. Paulick, W.; Jung, C.; Kempka, U.; Suhnel, J.; Gustav, K. Interpretation of the Vibrational Spectra and Calculation of the Geometries of Cycloheptatriene, 7-d-Cycloheptatriene and Phenyl Substituted Cycloheptatrienes. J. Mol. Struct. 1981, 85, 235-240. 82. LaLau, C.; Snyder, R. G. A Valence Force Field for Alkyl Benzenes, Toluene, p-Xylene, mXylene, and Some of their Deuterated Analogues. Spectrochim. Acta. 1971, 27A, 2073-2088. 83. Chao, R. S.; Khanna, R. K. Resonance Raman Spectra and Vibrational Assignments of Azulene-d0 and Azulene-d8. Spectrochim. Acta. 1977, 33A, 53-62. 84. Green, J. H. S.; Harrison, D. J. Thermodynamic Properties of Fluorine Compounds 19. Hexafluorobenzene,

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Page 22 of 41

Table 1. Intermolecular Potential Fitting Parametersa 　

A

B

C

D

m

n

Ca-N 5648.934 2.707638 -972.58 18028.8 6 10 Cb-N 21717.57 2.908793 -12283 24197.86 8 11 H-N 13586.09 3.737048 -3458.17 8283.791 9 12 aUnits of the parameters are A in kcal/mol, B in Å-1, C in kcal Ån/mol and D in kcal Åm/mol.


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Density(kg/m3)

E(∞)

f1

f2

k1

k2

C1

C2

10 20 40 80 160 320

59.3 63.3 63.5 64.3 65.1 64.5

0.35 0.36 0.37 0.38 0.39 0.36

0.65 0.64 0.63 0.62 0.61 0.64

0.001382 0.002764 0.004851 0.008828 0.019547 0.035514

0.000799 0.001599 0.003102 0.004889 0.007325 0.009845

0.000138 0.000138 0.000121 0.00011 0.000122 0.000111

0.0000799485 0.0000799485 0.0000775623 0.0000611105 0.0000457831 0.0000307667

Table 2. Bi-exponential Function Fitting Parametera

a. k1 and k2 have a unit of ps-1.



Page 24 of 41

Table 3. 〈Δ𝐸𝑐〉 Values for Collision of N2 with Various Molecules excitation Ea

〈Δ𝐸𝑐〉a

T(K)

Ref.

Benzene Cycloheptatriene Toluene Azulene

52000 40000 52000 30600

59 109 130 198

294 473 300 300

79 24 12 20

Ethylbenzene cation Propylbenzene cation(This work) Propylbenzene cation(exp) C6F6(simulation) C6F6(exp)

35000 31500 31500 30000 30000

251 283 288

473 473 473

34 This work

609

298

46

560

298

22

molecules

35

a. The units of excitation E and 〈Δ𝐸𝑐〉 are in cm-1.


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Table 4. The 10 Lowest Vibrational Frequencies of Various Molecules.a Molecules Benzene Cycloheptatriene Toluene Azulene Propylbenzene cationb Propylbenzene cationc C6F6 (simulation)47 C6F6 (exp)

10 Lowest Vibrational Frequencies 398 223 189 83 91 125 137

398 291 220 240 100 100 125 137

608 355 348 304 114 104 172 201

608 405 407 323 193 226 197 210

674 421 467 331 272 254 271 248

707 428 522 406 310 304 271 267

847 657 622 486 371 359 277 267

847 712 698 542 405 374 285 313

ref 967 743 732 562 488 437 285 313

967 788 680 503 557 379 365

80 81 82 83 35 35 47 84　

a. The unit of the vibrational frequencies is cm-1. b. The vibrational frequencies are for a developed analytic intramolecular potential.35 c. The vibrational frequencies are from B3LYP/6-311++G** calculcation.35



Page 26 of 41

Figure Captions

Figure 1. Energy distributions g(E,T) (in 1/cm-1) of excited C9H12+ from the charge transfer O2+ + n-C9H12 at 473 K. The distributions are for the assumed branching ratios ga = 0.60 (curve at higher energies and gb = 0.27 (curve at lower energies); see the text. (Adapted from ref. 35).

Figure 2. a) Optimized structure of C9H12+ by B3LYP/6-311++G**. b) This represent the definition of Ca(●), Cb(●) and H(●) in the work reported here. The corresponding indices are C1C6, C7-C9 and all H1-H12, respectively.

Figure 3. Intermolecular potential energies of C9H12+ and N2 for 11 different orientations. The red circles (●) are the SCS-MP2/6-311++G** ab initio calculations and black solid lines (‐) are the fits to the ab initio calculations. The x-axis is energy in kcal/mol and y-axis is distance in Å.

Figure 4. Intermolecular potential energies of C9H12+ and N2 for 11 different orientations, illustrating the long-range attractive interactions. The red circles (●) are the SCS-MP2/6311++G** ab initio calculations and black solid lines (‐) are the fits to the ab initio calculations. The x-axis is energy in kcal/mol and y-axis is distance in Å.


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Figure 5. Average energy of C9H12+ vs time for bath densities 10, 20, 40, 80, 160, 320 kg/m3. There are 1000 N2 molecules in the bath. 100 trajectories were calculated for each density and averaged. The initial energy is a sum of the C9H12+ excitation energy and ZPE of 115.2 kcal/mol. The uncertainties shown for the 20 kg/m3 simulation are standard deviations of the mean. Figure 6. Plot of average energy transfer per collision, 〈Δ𝐸𝑐〉, versus average energy 〈𝐸〉 of propylbenzene cation in N2 bath densities of 10, 20, 40, 80, 160, 320 kg/m3. In the inset, the plot of 〈Δ𝐸𝑐〉 versus [〈𝐸〉 ―𝐸(∞)] is represented for same densities.



Page 28 of 41

Figure 1.


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Figure 2.



Page 30 of 41

Figure 3.


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Figure 4.



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Figure 5.


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Figure 6.



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TOC


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Figure 1.

ACS Paragon Plus Environment


Figure 2.


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Figure 3. 317x241mm (150 x 150 DPI)



Figure 4. 239x184mm (96 x 96 DPI)


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Figure 5.



Figure 6.


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TOC 84x47mm (96 x 96 DPI)


Chemical Dynamics Simulation of Energy Transfer: Propylbenzene

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