Chemical Dynamics Simulations of Energy Transfer for Propylbenzene

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Chemical Dynamics Simulations of Energy Transfer for Propylbenzene Cation and He Collisions Hyunsik Kim, Biswajit Saha, Subha Pratihar, Moumita Majumder, and William Louis Hase J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b07982 • Publication Date (Web): 19 Sep 2017 Downloaded from http://pubs.acs.org on September 27, 2017

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The Journal of Physical Chemistry

Chemical Dynamics Simulations of Energy Transfer for Propylbenzene Cation and He Collisions

Hyunsik Kim, Biswajit Saha, Subha Pratihar, Moumita Majumder, and William L. Hase* Department of Chemistry and Biochemistry Texas Tech University Lubbock, Texas 79409

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


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Abstract

Intermolecular energy transfer (IET) for the vibrationally excited propylbenzene cation (C9H12+) in a helium bath was studied with chemical dynamics simulations. The bond energy bond order (BEBO) relationship and electronic structure calculations were used to develop an intramolecular potential for C9H12+. Spin component scaled (SCS) MP2/6-311++G** calculations were used to develop an intermolecular potential for He + C9H12+. The He + He intermolecular potential was determined from a previous explicitly correlated Gaussian (ECG) electronic structure calculation. For the simulations, C9H12+ was prepared with a 100.1 kcal/mol excitation energy to compare with experiment. The average energy transfer from C9H12+, 〈∆𝐸𝑐 〉, decreased as C9H12+ was vibrationally relaxed and for the initial excitation energy 〈∆𝐸𝑐 〉 = 0.64 kcal/mol. This result agrees well with the experimental 〈∆𝐸𝑐 〉 value of 0.51 ± 0.26 kcal/mol for collisions of He with the ethylbenzene cation. The 〈∆𝐸𝑐 〉 value found for He + C9H12+ collisions is compared with reported values of 〈∆𝐸𝑐 〉 value for He colliding with other molecules.

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I. INTRODUCTION Collisional intermolecular energy transfer (IET) has been widely studied for many years1-4 and is particularly important for modeling unimolecular reactions.5-7 There have been a number of studies of IET for neutral molecule and ions, including those for azulene,8-14 benzene,15-18 toluene-d0 and -d8,1921

hexafluorobenzene,22,23 pyrazine,

24-31

cycloheptatriene,32 SF6- anion,33 and the ethylbenzene,34-35

propylbenzene,36 butylbenzene37 cations. In previous experiments34-37 the charge transfer reaction between an alkylbenzene molecule and O2+, in a turbulent ion flow tube (TIFT), was used to prepare vibrationally excited ethyl-, propyl- and butylbenzene cations. In these studies, the competition between collisional stabilization and dissociation of the excited alkylbenzene cation was studied. To adequately interpret these experiments it is important to understand the efficiency of the inert collision partner for stabilizing the alkylbenzene cation. In the work presented here, chemical dynamics simulations were performed to study intermolecular energy transfer in collisions of vibrationally excited propylbenzene cation with helium. Experimentally,36 vibrationally excited propylbenzene cation is generated by the charge transfer ∗

+ reaction O+ 2 + 𝐶9 𝐻12 → 𝑂2 + 𝐶9 𝐻12 . The experiments considered here were performed at 473 K and

the propylbenzene cation excitation energy is the difference in the ionization energies of O2 and propylbenzene, plus the propylbenzene thermal energy, the sum of which is 35000 cm-1. To compare with experiments,34-36 chemical dynamics simulations were performed to study collision energy transfer from vibrationally excited C9H12+ to a bath of He atoms. A unified gas/condensed phase model38-40 was used to perform the simulations. By comparing the energy transfer dynamics at different bath densities, the value of the C9H12+ + He average energy transfer per collision was obtained and compared with the experimental value. Simulations like the one reported here have been performed previously for C 6F6 + 3 ACS Paragon Plus Environment


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N2 and azulene + N2.38-40 Energy transfer efficiencies determined for these systems may be compared with that found here.

II. POTENTIAL ENERGY FUNCTION The potential energy function for the C9H12+ + He system studied here is written as

VTot = VPBz + VPBz-He + VHe-He

(1)

where VTot is the total potential energy, VPBz is intramolecular potential energy of the propylbenzene cation, and VPBz-He and VHe-He are the propylbenzene cation-He and He-He intermolecular potentials. For the work presented here it was necessary to develop the VPBz and VPBz-He potentials. VHe-He is known from previous work.41 A. Propylbenzene Cation Intramolecular Potential There is not an intramolecular potential available for C9H12+ and an important component of the work presented here was to develop this potential. The optimized structure for C9H12+, as determined by a B3LYP/6-311++G** calculation, is given in Figure 1. The electron for C9H12+ is removed from the benzene ring and the structure of this ring is quite different from that of neutral C9H12. An intramolecular potential for C9H12+, with harmonic force constants, was constructed by two steps. First an intramolecular potential for neutral C9H12 was developed by combining experimental harmonic potentials for benzene42,43 and propane.44 The next step was to rescale this potential using the bond energy bond order (BEBO) model,45 to account for differences in bond lengths between C9H12+ and benzene and propane. The BEBO relationship for rescaling a stretching force constant is written as

𝑠

𝑓𝑖𝑠 = 𝑓𝑖 0 𝑛𝑖

(2) 4

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where 𝑓𝑖𝑠 is the rescaled force constant for stretching bond i of C9H12+, 𝑓𝑖

𝑠0

is the force constant for

stretching bond i of benzene or propane, and n is the bond order for bond i. The bond order is expressed as

𝑛𝑖 = 𝑒𝑥 𝑝(− 𝑎 (𝑅 − 𝑅0 ))

(3)

where a is rescaling factor, 𝑅𝑖 is the equilibrium bond length for C9H12+, and 𝑅𝑖0 is the equilibrium bond length of benzene or propane. This stretching BEBO relationship was extended to harmonic bending rescaling and represented as

𝑏

𝑓𝑗𝑏 = 𝑓𝑗 0 𝑛𝑎 𝑛𝑏

(4)

𝑏

where 𝑓𝑗𝑏 is the of C9H12+ bending force constant for angle j, 𝑓𝑗 0 is the force constant for benzene or propane, and 𝑛𝑎 and 𝑛𝑏 are the orders of the bonds defining the angle j. Previous calculations have shown that B3LYP/6-311++G** theory gives very good harmonic vibrational frequencies for benzene,46-48 and this theory was used to determine harmonic vibrational frequencies for C9H12+. Of interest is that a number of theories do not give accurate vibrational frequencies for benzene, including MP2 and CCSD(T),46,47 and some predict benzene to be nonplanar.47 The rescaling factors a for the force constants, in Eq. (3) were determined by iterative fitting and minimizing the deviation with the B3LYP/6-311++G** harmonic frequencies for of C9H12+. The B3LYP/6-311++G** and intramolecular potential harmonic frequencies for C9H12+ are listed in Table 1. The force constants are given in Table S1 of the Supporting Information. The rescaling factor a is 2.91 and 2.31 Å -1 for the stretches of the phenyl and propyl parts of C9H12+, respectively. For the bends the rescaling factor is 1.71 and 0.01 Å -1, respectively, for the phenyl and propyl parts. For 5 ACS Paragon Plus Environment


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torsions of the propyl group with respect to phenyl the following were used: a 2-fold term is used for the Ca-Ca-C-C torsion, where Ca is an aromatic carbon and C a sp3 carbon of propyl; and a 3-fold term is used for the Ca-C-C-C torsion. The barriers for these torsions are 4.70 and 1.20 kcal/mol, respectively. B. Intermolecular Potentials 1. He-He intermolecular potential In previous work,41 He-He intermolecular potentials have been developed. In an electronic structure calculation,41 using an explicitly correlated Gaussian (ECG) expansion of the wave function, a very accurate He-He potential was derived and fit with an analytic potential energy function. This potential is more complicated than necessary for the He bath in our simulations and the ECG He-He potential was fit with the same modified Buckingham two-body function as used to study IET in our previous simulations;38-40 i.e.

𝑉(𝑟) = A exp(−B𝑟) −

C 𝑟n

+

D 𝑟m

(5)

The fitting was performed with a genetic/nonlinear least square algorithm,38,39,49 and the fitted parameters are: A = 10699.72 kcal/mol; B = 4.465666 Å -1; C = 27.44961 kcal Å n/mol; and D = 7.634441 kcal Å m/mol; n = 6; and m = 13. The ECG potential has a potential energy well depth of 0.0219 kcal/mol and an equilibrium He-He separation of 2.96 Å . For the fitted potential by Eq. (5) these values are -0.0214 kcal/mol and 2.96 Å . A CCSD(T) calculation at the complete basis set (CBS) limit was performed for the He-He potential to compare with the ECG potential. They are nearly identical as shown in Figure 2. The CCSD(T) potential energy well depth and equilibrium He-He separation are -0.0211 kcal/mol and 2.98 Å , respectively, and in excellent agreement with the ECG values. The CCSD(T) fitted parameters are: A = 14325.72 kcal/mol; B = 4.610436 Å -1; C = 24.77965 6 ACS Paragon Plus Environment

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kcal Å n/mol; and D = 41.63444 kcal Å m/mol; n = 6; and m = 13. The ECG He-He potential given by Eq. (5) was used for the simulations reported here. To determine the sensitivity of the simulation results to the He-He potential, a less accurate potential was determined using SCS-MP2/6-311++G** and the potential energy curve is shown in Figure 2. The well depth and equilibrium He-He separation for the potential energy curve are -0.00174 kcal/mol and 3.60 Å , respectively. The potential energy curve was fit by Eq. (5) and the parameters are: A = 6126.290 kcal/mol; B = 4.153770 Å -1; C = 112.6921 kcal Å n/mol; and D = 383.0279 kcal Å m/mol; n = 8; and m = 11. As discussed in Section IV, the ECG and SCS-MP2 He-He intermolecular potentials gave the same IET dynamics. 2. Intermolecular potential for He + C9H12+ Though a MP2-type theory does not give an accurate He-He intermolecular potential, MP2 has given accurate potential for other intermolecular systems.50-52 For Ar + CF4,51 MP2 potential energy curves are in very good agreement with those determined with CCSD(T). MP2 theory was used to calculate intermolecular potential energy curves for the previous studies of IET for C6F6 + N2 and Azulene + N2.38,39 Some of the possible shortcomings of MP2 for intermolecular potentials are improved by using spin-component-scaled (SCS) MP2.53,54,55 However, for Azulene + N2, MP2 and SCS-MP2 give nearly identical potential energy curves39 indicating the accuracy of MP2. For the work presented here, intermolecular potential energy curves were calculated for He + C9H12+ using SCS-MP2 with the 6-311++G** basis set. The curves were calculated for the eight orientations in Figure 3. In panels 3a and 3b, He approaches along the C3-H3 and C9-H12 bond axes, respectively. For panels 3c, 3d and 3e, He approaches by bisecting the H6-C7-H7, H8-C8-C9, and H10-C9-H11 angles, respectively. In panels 3f, 3g, and 3h, He approaches directly above C3, C4 and C6 on the phenyl part of C9H12+, respectively. These He + C9H12+ potential energy curves were simultaneously fit with a sum of C-He and H-He two-body potentials as given by Eq. (5), using a 7 ACS Paragon Plus Environment


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genetic/nonlinear least square algorithm.38,39,49 The SCS-MP2/6-311++G** potential energy curves and fits are given in Figure 3. The He-C fitted parameters are A = 12471.09, B = 3.331057, C = -3170.885, D = 5103.914, n = 8, and m = 11; the He-H fitted parameters are A = 2491.538, B = 3.638871, C = 362.392, D = 592.6049, n = 9, and m = 12. The units of A, B, C, and D are kcal/mol, Å -1, kcal-Å n/mol, and kcal-Å m/mol, respectively.

III. SIMULATION PROCEDURE In this work, a condensed-version of the VENUS chemical dynamics computer program was used.56,57 For the experiments considered here, C9H12+ is vibrationally excited by charge transfer between O2+ and C9H12 at 473 K.36 The excitation energy of C9H12+ is the charge transfer exothermicity plus the 473 K thermal energy, which is 35000 cm-1 (100.1 kcal/mol). The C9H12+ ion was assumed to be excited randomly, the RRKM model,58 and quasi-classical microcanonical sampling59,60 was used to select its initial conditions. This sampling procedure explicitly includes the C9H12+ zero-point energy (ZPE)39,40 of 115.2 kcal/mol and previous work59-64 has shown that ZPE should be included to obtain good agreement with experiment. The initial C9H12+ translational and rotational energies were sampled from their 473 K Boltzmann distributions. After energy was added to C9H12+, a molecular dynamics (MD) simulation38-40,65 was performed to equilibrate a He bath at 473 K around C9H12+. The bath consisting of 1000 He atoms and C9H12+ were placed in a cubical box, with C9H12+ in the middle. The He atoms were place randomly around C9H12+ and, with the coordinates and velocities of C9H12+ held fixed, the bath was equilibrated for 218 ps to attain an equilibrium temperature of 473 K. After this equilibration, the constraints on the C9H12+ coordinates and velocities was released and the simulation trajectory of collisional deactivation of vibrationally excited C9H12+ was initiated. For the simulation, periodic boundary conditions (PBC) and a neighbor list algorithm with 18 Å cut-off were applied. Following previous work,39 to determine the 8 ACS Paragon Plus Environment

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bath densities for the simulation, the value of the mean free path for C9H12+ + He was compared to that for Azulene + N2 and was quite close. Thus, same density range as for Azulene + N2 system was used for the current simulation and it is 10, 20, 40 and 80 kg/m3. For each density 100 trajectories were calculated, each for 400 ps and their results averaged. The length of the sides of the cubical box is 88.2 Å , 70.1 Å , 55.7 Å and 44.4 Å for 10, 20, 40 and 80 kg/m3, respectively.

IV. RESULTS AND DISCUSSION In the work presented here, simulations were performed with the ECG He-He and SCS-MP2/6311++G** He + C9H12+ intermolecular potentials. A. Average Energy versus Time Plots of the average vibrational energy of C9H12+ versus time, for densities of 10, 20, 40 and 80 kg/m3 (pressures of 8.75 – 70.0 atm), are given in Figure 4. The average energies were obtained from 100 trajectories for each density and are well fit to bi-exponential equation

⟨𝐸(𝑡)⟩ = (𝐸(0) − 𝐸(∞)) × [𝑓1 exp(−𝑘1 𝑡) + 𝑓2 exp(−𝑘2 𝑡)] + 𝐸(∞)

(6)

where 𝐸(0) is the initial energy of vibrationally excited C9H12+, 𝐸(∞) is the fitted final C9H12+ energy, 𝑓1 + 𝑓2 = 1, and 𝑘1 and 𝑘2 are rate constants. The fitting parameters are listed in Table 2. B. Single Collision Limit As described previously,38-40,65 in the single collision limit the rate of intermolecular energy transfer is proportional to pressure. For this condition the rate constant, 𝑘 , has a proportionality constant with the bath density (i.e. pressure), which is 𝐶 = 𝑘/𝜌, where ρ is density. In the single collision limit the proportionality constant is independent of pressure.38-40,65 In this work, two rate constants, 𝑘1 and 𝑘2 , were obtained by the bi-exponential fit in Eq. (6) and the constants 𝐶1 and 𝐶2 are 9 ACS Paragon Plus Environment


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listed in Table 2. Their values at densities 10 and 20 kg/m3 are almost identical, whereas those at 40 and 80 kg/m3 are quite different. From this comparison one may conclude that the single collision limit is obtained at a density 20 kg/m3 (17.5 atm). C. Average Energy Transfer per Collision In the single collision limit the average energy transfer per collision, 〈𝛥𝐸𝑐 〉, is given by

〈𝛥𝐸𝑐 〉 =

where

𝑑〈𝐸(𝑡)〉 𝑑𝑡


1

×𝜔

(7)

is the energy transfer unit time and 𝜔 is the collision frequency. The Langevin rate

constant (𝑘𝐿 ) was used for the collisional frequency in analyzing experiments of energy transfer for ion-neutral molecular collisions35 and kL is

𝛼

𝑘𝐿 = 2𝜋𝑞 √𝜇

(8)

where q is elementary electronic charge, 4.8 × 10−10 𝑒𝑠𝑢, 𝛼 is the experimental value of polarizability of He, 0.205Å 3

66

and μ is C9H12+ and He reduced mass.


is the derivative of Eq. (6) with the fit

parameters in Table 2. Using this information and Eq. (7), the average energy transfer 〈𝛥𝐸𝑐 〉 versus 〈𝐸(𝑡)〉 may be calculated and is plotted in Figure 5. The values for 〈Δ𝐸𝑐 〉 are nearly identical for the densities of 10 and 20 kg/m3. For higher ρ there are significant changes in 〈Δ𝐸𝑐 〉 . For the experimental C9H12+ excitation energy of 100.1 kcal/mol, the single collision energy transfer, 〈𝛥𝐸𝑐 〉, is 0.64 ± 0.02 kcal/mol. Another model for determining 〈𝛥𝐸𝑐 〉 is to use the He + C9H12+ intermolecular potential to calculate the collision frequency ω.38 The expression used for ω to interpret experiments is38,39 10 ACS Paragon Plus Environment

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1

7

2

𝜔 = 4.415 × 10 × 𝜎 ×

𝑇 −2 𝑝 (𝜇)

∗ × Ω12

(9)

with 𝑘𝑇

∗ Ω12 = [0.636 + 0.567 × log ( 𝜖 )]

−1

(10)

where σ and ε are Lennard-Jones parameters, p is the pressure(torr), T is the temperature(K), μ is the reduced mass in amu, and Ω is the collision integral. Values for σ and ε may be determined from the angle averaged interaction between He and C9H12+ shown in Figure 6a, and σ is 6.50 Å and ε is -0.0101 kcal/mol (5.08 K). The resulting value for ω is 3.67 × 1012 sec-1 and larger than the Langevin value of 1.68 × 1012 sec-1. 〈𝛥𝐸𝑐 〉 is 0.30 kcal/mol ± 0.02 kcal/mol for this angle-averaged ω. Though the simulations are not performed under equilibrium conditions, another model for the He + C9H12+ intermolecular potential is to weight each random orientation by the Boltzmann term exp[V(orient)/kBT] for its potential V(orient).67 This weighting emphasizes the most attractive He + C9H12+ interactions and its potential energy curve is given in Figure 6b; the σ and ε parameters are 3.30 Å and -0.913 kcal/mol (459.4 K). The collision frequency is ω = 2.58 × 1012 sec-1 and the resulting 〈𝛥𝐸𝑐 〉 is 0.43 kcal/mol ± 0.02 kcal/mol. D. Comparison 〈𝜟𝑬𝒄 〉 Values for Collisions of He with Various Molecules Listed in Table 3 are 〈𝛥𝐸𝑐 〉 values for various molecules colliding with He, in addition to the result of the current study. Propylbenzene cation has the most efficient collisional energy transfer with He, which is similar to that for ethylbenzene cation. The least efficient is benzene. From experiments it is known that the excited molecule’s vibrational modes play an important role in IET, with most of the energy transfer occurring from low frequency modes.68-72 These dynamics were found in simulations for C6F6 and a model in which the C6F6 intramolecular potential was retained, but the F-atoms changed to H-atoms, substantially increasing the vibrational frequencies.40 is approximately a factor of 11 ACS Paragon Plus Environment


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two smaller for the C6H6 model. C6F6 its with heavy atoms and low vibrational frequencies has a large . Propylbenzene cation has three groups of vibrational modes; i.e. benzene modes, propyl modes, and modes for the propyl-benzene connection. Energy transfer from the benzene modes is expected to be inefficient, with the majority of the energy transfer occurring from the propyl and propyl-benzene connection modes. Particularly efficient modes for IET may be the torsions and low frequency bends. Ethylbenzene and propylbenzene cations, each with an alkyl sidechain, are expected to have similar 〈Δ𝐸𝑐 〉 values.36 The experimental 〈𝛥𝐸𝑐 〉 for ethylbenzene cation is 0.51 ± 0.26 kcal/mol.35 From this work, 〈Δ𝐸𝑐 〉 for the propylbenzene cation is 0.64 ± 0.02 kcal/mol and in good agreement with the value for the ethylbenzene cation. In future work it would be interest to simulate energy transfer dynamics for linear alkanes to determine the efficiency of IET for alkyl groups. E. Effect of Varying the He-He Intermolecular Potential Of interest is to determine how varying the He + He intermolecular potential affects the collisional energy transfer. Multiple He + He intermolecular potentials were determined as discussed in Section II.B. As shown in Figure 2, ECG, CCSD(T), and SCS-MP2 electronic structure theories were used to calculate He + He potential energy curves, which were fit with Eq. (5). The results presented above were determined with the ECG potential energy curve and, as shown in Figure S1 of the Supporting Information, using either the CCSD(T) and SCS-MP2 potential energy curve gives statistically the same result as found with the ECG curve for a He bath density of 20 kg/m3. For the 100.1 kcal/mol experimental C9H12+ excitation energy, the single collision energy transfer, 〈𝛥𝐸𝑐 〉, is 0.61 ± 0.02 and 0.64 ± 0.02 kcal/mol for the CCSD(T) and SCS-MP2 curves, respectively, in comparison to the above ECG value of 0.64 ± 0.02 kcal/mol. The exact form of the He-He intermolecular potential, if approximately correct, is not expected to influence the IET and the similarity of these three numbers illustrates the robustness of the simulation with 100 trajectories. 12 ACS Paragon Plus Environment

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V. SUMMARY In this work here, IET was studied for collisions between He and vibrationlly excited propylbenzene cation, C9H12+, at 473K. An intramolecular potential for C9H12+ was developed by using the BEBO model and scaled force constants for benzene and propane to fit the B3LYP/6-311++G** harmonic frequencies for C9H12+. A high-level He-He intermolecular potential was determined previously41 from an explicitly correlated Gaussian (ECG) electronic structure calculation and accurately fit by the two-body potential in Eq. (5). This potential was supplemented by CCSD(T) and SCS-MP2 potentials, to investigate the effect of the He-He potential on the IET. The He + C9H12+ intermolecular potential was determined by a SCS-MP2/6-311++G** calculation and fit by a sum of He-C and He-H two-body potentials. Experimental studies have been performed of the unimolecular decomposition of C9H12+ vibrationally excited with 35000 cm-1 (100.1 kcal/mol) of energy by the charge transfer reaction O+ 2 + + 𝐶9 𝐻12 → 𝑂2 + 𝐶9 𝐻12 and 473 K thermal excitation.36 This vibrationally excited C9H12+ was

collisionally stabilized by a He bath. The 100.1 kcal/mol excitation energy was used for simulation of He + C9H12+ collisional energy transfer reported here. A unified liquid and gas phase model was used for the simulation.38-40,65 The density of the He bath surrounding C9H12+ was varied to obtain the binary, independent collision limit. For each density, a simulation was performed with 100 trajectories, each integrated for 400 ps, and the results averaged. From a simulation at a fixed density, the average vibrational energy of C9H12+ versus time, 〈𝐸(𝑡)〉, is determined. In the binary, single collision limit the slope of this line divided by the collision frequency ω equals the average energy transfer per collision, 〈Δ𝐸𝑐 〉. For C9H12+ excited with 100.1 kcal/mol of vibrational energy and collisionally stabilized by He, a value of 〈Δ𝐸𝑐 〉 = 0.64 ± 0.02 kcal/mol was determined from the simulations reported here, with the experimental value used for ω. 13 ACS Paragon Plus Environment


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For comparison, the experimental 〈Δ𝐸𝑐 〉 = 0.51 ± 0.26 kcal/mol for He + ethylbenzene cation collisions at a 100.1 kcal/mol excitation energy. Similar values of 〈Δ𝐸𝑐 〉 are expected for collisions of He with the propylbenzene and ethylbenzene cations, as found here. Values of 〈Δ𝐸𝑐 〉 for He colliding with different molecules are compared in Table 3. Of this molecules, the propylbenzene cation is the most efficient for transferring vibrational energy. The least efficient is benzene, transferring only 0.08 kcal/mol per collision, nearly an order of magnitude smaller than for propylbenzene cation. There is not a quantitative model for describing the efficiency of IET in gas phase collisions. Experiments show that these dynamics are related to the density of states of the vibrationally excited molecules,73 which is consistent with the decrease in found here (see Figure 5) as is lowered and the state density decreased. Also, as discussed above in Section IV.D, low frequency modes are important for enhancing IET. It is possible that model simulation studies could be performed to develop an accurate model for predicting the efficiency of IET and values. Previous simulations have shown that it is not important to include mode anharmonicity in the simulation model39,74 and it may be possible to use a normal mode Hamiltonian,75 with uncoupled modes, to study mode specific IET. Using the fully coupled Hamiltonian, as is done here, one could excite specific modes, but intramolecular vibrational energy redistribution76 from the initially prepared vibrational state would complicate interpretation of the simulation results. Mode specific IET may be studied, with the fully coupled Hamiltonian, by increasing force constants for some of the modes, making them spectators and not participating in IET.77 This was done for collisions of Aratoms with peptide ions and torsions were found to be highly efficient for IET.77 The IET property determined directly from gas-phase experiments and simulations is the rate of energy transfer, which is a product of the collision frequency and the average energy transfer.78 To determine a value for a model is used to define the collision cross section, σc, and frequency, ω. For the work presented here, an experimental model for σc is used to determine for comparison 14 ACS Paragon Plus Environment

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with experiment. In future work, one may consider the possibility of obtaining σc directly from the simulations. This has been considered previously,74,77 and it would be of interest to see if there are models which recover the experimental model for σc. In summary, this study and previous studies show that chemical dynamics simulations using a unified liquid and gas phase models gives accurate 〈Δ𝐸𝑐 〉 values for collisional stabilization of vibrationally excited molecules, as compared to experiment. In future work, additional studies of IET will be performed for different vibrationally excited molecules and collision partners.

Supporting Information Comparison of the proylbenzene cation average vibrational energy versus time for a He bath density of 20 kg/m3 calculated with the ECG, CCSD(T)/CBS limit, and SCS-MP2/6-311++G** He + He intermolecular potentials; and force constants for the propylbenzene cation intramolecular potential.

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 Philip W. Smith. Some of the computations were also performed on the Chemdynm cluster of the Hase Research Group.



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Table 1. Vibrational Frequencies for C9H12+ Vibrational frequenciesa B3LYPb Potentialc B3LYPb Potentialc 91.41 83.21 1219.04 1158.60 100.02 114.33 1243.89 1161.50 104.42 100.24 1255.04 1197.40 225.59 271.81 1283.92 1286.20 253.79 193.26 1322.23 1228.90 304.92 309.65 1351.99 1364.90 358.66 370.55 1403.37 1518.30 373.95 404.75 1408.21 1375.60 437.23 488.26 1433.51 1532.00 556.75 503.41 1474.46 1550.70 565.50 616.35 1487.14 1559.30 648.40 586.66 1491.78 1575.80 762.57 666.46 1498.77 1655.70 770.80 743.41 1511.72 1679.30 803.20 753.59 1547.27 1604.20 817.80 845.80 1655.71 1715.50 847.11 824.90 3031.37 2987.50 896.45 872.75 3049.80 3037.90 965.23 873.39 3057.65 3042.70 973.55 952.48 3082.73 3085.40 995.05 983.61 3090.12 3087.30 1013.75 1008.60 3101.61 3092.80 1018.23 1025.20 3113.64 3119.20 1022.93 1015.90 3173.30 3175.10 1048.21 1073.50 3188.90 3175.30 1062.36 1032.90 3193.46 3192.50 1115.48 1080.10 3203.22 3182.30 1180.46 1150.50 3230.14 3189.90 1211.26 1155.70 a. Frequencies are in cm-1. b. Frequencies for B3LYP/6-311++G** calculations. c. Frequencies for the intramolecular potential used for the simulations.


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Table 2. Parameters for Fits to 〈𝐸(𝑡)〉 Density(kg/m3) f1 f2 k1 k2 C1 C2 10 0.24 0.76 0.005441 0.002805 0.000544 0.000281 20 0.26 0.74 0.010806 0.00561 0.00054 0.000281 40 0.021 0.979 0.02057 0.009039 0.000514 0.000226 80 0.037 0.963 0.037022 0.140633 0.000463 0.001758 The units of 𝑘 are in ps-1. C1 and C2 are k1/ρ and k2/ρ, where ρ is the density.



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Table 3. 〈Δ𝐸𝑐 〉 Values for Collisions of He with Different Molecules Molecules

Excitation Ea

〈Δ𝐸𝑐 〉a

T(K)

Ref.

Benzene Cycloheptatriene Toluene Azulene Ethyl-cycloheptatriene Isopropyl-cycloheptatriene HFB(C6F6) Ethylbenzene cation Propylbenzene cation

24000 40000 52000 30600 41600 41800 24000 35000 35000

27 61 75 83 84 120 170 180 224

300 300 300 300 300 300 300 473 473

15 32 20 13 68 68 22 35 This work

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


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Figure Captions Figure 1. Optimized C9H12+ structure obtained with B3LYP/6-311++G** theory.

Figure 2. Plot of He-He potentials from an electronic structure calculation using an explicitly correlated Gaussian (ECG) expansion of the wave function, CCSD(T) calculation at the complete basis set (CBS) limit, and SCS-MP2/6-311++G** calculation.

Figure 3. Intermolecular potential energy for C9H12+ + He for eight different orientations. The red circles are the SCS-MP2/6-311++G** calculations and the solid lines is the fit to these calculations with the modified Buckingham potential in Eq. (5).

Figure 4. Average vibrational energy of C9H12+ vs time for bath densities 10, 20, 40 and 80kg/m3. Each density were averaged over 100 trajectories. There are 1000 He atoms in the bath.

Figure 5. Plot of average energy transfer per collision, 〈𝛥𝐸𝑐 〉, versus average energy, 〈𝐸(𝑡)〉, of C9H12+ in He bath for densities of 10, 20, 40 and 80 kg/m3. In the inset, 〈𝛥𝐸𝑐 〉 vs [〈𝐸(𝑡)〉 − 〈𝐸(∞)〉] is described for all densities.

Figure 6. Angle averaged He + C9H12+ interaction energy potentials versus center-of-mass separation: (a) C9H12+ is randomly oriented by its Euler angles; and (b) each random orientation is weighted by a Boltzmann factor for the orientation’s intermolecular potential.



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Figure 1.


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Figure 2.



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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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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


285x207mm (96 x 96 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1746x1349mm (96 x 96 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


321x245mm (96 x 96 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1746x1349mm (96 x 96 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1746x1349mm (96 x 96 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

222x307mm (150 x 150 DPI)


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TOC 82x47mm (150 x 150 DPI)


Chemical Dynamics Simulations of Energy Transfer for Propylbenzene

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