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.

Post-Transition-State Direct Dynamics Simulations on the Ozonolysis of Catechol.

On-the-fly dynamics simulations are performed for the reaction of catechol + O3. The post transition state (TS) dynamics is studied at temperatures of 400 and 500 K. The PM7 semiempirical method is employed for calculating the potential energy gradient needed for integrating Hamilton's equations of motion. This semiempirical method provides excellent agreement in terms of energy and geometry of the TSs as well as minimum energy states of the system with respect to B3LYP/6-311+G (2df, 2p) calculated results. In the dynamics, first, a peroxyacid is formed, which further dissociates to different fragments. Four major channels forming CO, CO2, H2O, and small carboxylic acid (SCA) fragments are seen in this reaction. Rates of each of the channels and the overall unimolecular reaction are calculated at both temperatures. Branching ratios of all these product channels are calculated and compared with experiment. The minimum energy profile of CO2, CO, and H2O channels are calculated. A qualitative estimate of activation energies for all the channels are obtained and compared with the explicit TS energies of three product channels, which ultimately correlate with the reaction probabilities.

Unimolecular Dissociation of C6H6-C6Cl6 Complex and Effect of Mode-Mode Coupling.

The unimolecular dissociation dynamics of the C6H6-C6Cl6 (Bz-HCB) complex is studied with initial excitation of all vibrational modes for a temperature range of 1000-2000 K and with mode-specific excitations at 1500 K. The results are compared with those of the C6H6-C6F6 [Bz- HFB] complex. When all modes of Bz-HCB are initially excited, the rate of dissociation is slower with respect to Bz-HFB. However, the rate of dissociation is faster when simulations with nonrandom excitation of the specific vibrational modes are performed. The rate of dissociation of Bz-HCB is found to become slower when a few intramolecular modes are excited along with all inter-fragment modes compared to the simulation when only inter-fragment modes of the same complex are excited. Such an energy-transfer dynamics is absent if both intramolecular and inter-fragment modes are not initially excited. Thus, a "stimulated" resonance energy-transfer dynamics is observed in Bz-HCB dissociation dynamics.

A Photochemical Intramolecular C-N Coupling Toward the Synthesis of Benzimidazole-Fused Phenanthridines.

Herein, we report a direct photochemical dehydrogenative C-N coupling of unactivated C(sp2)-H and N(sp2)-H bonds. The catalysts or additive-free transformation of 2-([1,1'-biphenyl]-2-yl)-1H-benzo[d]imidazole to benzo[4,5]imidazo[1,2-f]phenanthridine was achieved at ∼350 nm of irradiation via ε-hydrogen abstraction. DFT calculations helped to understand that the N-H···π interaction was essential for the reaction to proceed at a lower energy than expected.

Comparison of intermolecular energy transfer from vibrationally excited benzene in mixed nitrogen-benzene baths at 140 K and 300 K.

Gas phase intermolecular energy transfer (IET) is a fundamental component of accurately explaining the behavior of gas phase systems in which the internal energy of particular modes of molecules is greatly out of equilibrium. In this work, chemical dynamics simulations of mixed benzene/N2 baths with one highly vibrationally excited benzene molecule (Bz*) are compared to experimental results at 140 K. Two mixed bath models are considered. In one, the bath consists of 190 N2 and 10 Bz, whereas in the other bath, 396 N2 and 4 Bz are utilized. The results are compared to results from 300 K simulations and experiments, revealing that Bz*-Bz vibration-vibration IET efficiency increased at low temperatures consistent with longer lived "chattering" collisions at lower temperatures. In the simulations, at the Bz* excitation energy of 150 kcal/mol, the averaged energy transferred per collision, ⟨ΔEc⟩, for Bz*-Bz collisions is found to be ∼2.4 times larger in 140 K than in 300 K bath, whereas this value is ∼1.3 times lower for Bz*-N2 collisions. The overall ⟨ΔEc⟩, for all collisions, is found to be almost two times larger at 140 K compared to the one obtained from the 300 K bath. Such an enhancement of IET efficiency at 140 K is qualitatively consistent with the experimental observation. However, the possible reasons for not attaining a quantitative agreement are discussed. These results imply that the bath temperature and molecular composition as well as the magnitude of vibrational energy of a highly vibrationally excited molecule can shift the overall timescale of rethermalization.

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.

Chemical Dynamics Simulations on Association and Ensuing Dissociation of a Benzene-Hexafluorobenzene Molecular System.

Chemical dynamics simulations are performed to study the association of benzene (Bz) and hexafluorobenzene (HFB) followed by the ensuing dissociation of the Bz-HFB complex. The calculations are done for 1000, 1500, and 2000 K with an impact parameter ( b) range of 0-10 Å at each temperature. Almost no complexes are observed to form at b = 8 and 10 Å. Following three different methods of calculation of the temperature-dependent association rate constant kasso( T), the values obtained are 1.67 × 10-10, 1.86 × 10-10, and 2.05 × 10-10 cm3/molecule·s with a standard deviation of approximately 0.1 × 10-10 cm3/molecule·s for T = 1500 K. Among those values of kasso( T), the middle one is obtained by considering a relative translational energy of 3 RT/2 at T = 1500 K, and the same is followed to calculate kasso( T) at 1000 and 2000 K. The Arrhenius parameters, using the kasso( T) values at three temperatures, are 0.203 × 10-10 cm3/molecule·s for the pre-exponential factor and -5.79 kcal/mol for the activation energy. The absolute value of the latter is similar to the Bz + HFB association energy of 5.93 kcal/mol. The ensuing dissociation dynamics of the complex is significantly different from the unimolecular dissociation dynamics, and an exponential function fits the N( t - t0)/ N( t0) curves comparatively well. The ensuing dissociation is also observed to be independent of time for a statistically large sample size.

A Better Understanding of the Unimolecular Dissociation Dynamics of Weakly Bound Aromatic Compounds at High Temperature: A Study on C6H6-C6F6 and Comparison with C6H6 Dimer.

Chemical dynamics simulations are performed to study the unimolecular dissociation of the benzene (Bz)-hexafluorobenzene (HFB) complex at five different temperatures ranging from 1000 to 2000 K, and the results are compared with that of the Bz dimer at common simulation temperatures. Bz-HFB, in comparison with Bz dimer, possesses a much attractive intermolecular interaction, a very different equilibrium geometry, and a lower average quantum vibrational excitation energy at a given temperature. Six low-frequency modes of Bz-HFB are formed by Bz + HFB association which are weakly coupled with the vibrational modes of Bz and HFB. However, this coupling is found much stronger in Bz-HFB compared to the same in the Bz dimer. The simulations are done with very good potential energy parameters taken from the literature. Considering the canonical (TST) model, the unimolecular dissociation rate constant at each temperature is calculated and fitted to the Arrhenius equation. An activation energy of 5.0 kcal/mol and a pre-exponential factor of 2.39 × 1012 s-1 are obtained, which are of expected magnitudes. The responsible vibrational mode for dissociation is identified by performing normal-mode analysis. Simulations with random excitations of high-frequency Bz and HFB modes and low-frequency inter-Bz-HFB vibrational modes of the Bz-HFB complex are also performed. The intramolecular vibrational energy redistribution (IVR) time and the unimolecular dissociation rate constants are calculated from these simulations. The latter shows good agreement with the same obtained from simulation with random excitation of all vibrational modes.

Non-statistical intermolecular energy transfer from vibrationally excited benzene in a mixed nitrogen-benzene bath.

A chemical dynamics simulation was performed to model experiments [N. A. West et al., J. Chem. Phys. 145, 014308 (2016)] in which benzene molecules are vibrationally excited to 148.1 kcal/mol within a N2-benzene bath. A significant fraction of the benzene molecules are excited, resulting in heating of the bath, which is accurately represented by the simulation. The interesting finding from the simulations is the non-statistical collisional energy transfer from the vibrationally excited benzene C6H6 * molecules to the bath. The simulations find that at ∼10-7 s and 1 atm pressure there are four different final temperatures for C6H6 * and the bath. N2 vibration is not excited and remains at the original bath temperature of 300 K. Rotation and translation degrees of freedom of both N2 and C6H6 in the bath are excited to a final temperature of ∼340 K. Energy transfer from the excited C6H6 * molecules is more efficient to vibration of the C6H6 bath than its rotation and translation degrees of freedom, and the final vibrational temperature of the C6H6 bath is ∼453 K, if the average energy of each C6H6 vibration mode is assumed to be RT. There is no vibrational equilibration between C6H6 * and the C6H6 bath molecules. When the simulations are terminated, the vibrational temperatures of the C6H6 * and C6H6 bath molecules are ∼537 K and ∼453 K, respectively. An important question is the time scale for complete energy equilibration of the C6H6 * and N2 and C6H6 bath system. At 1 atm and 300 K, the experimental V-T (vibration-translation) relaxation time for N2 is ∼10-4 s. The simulation time was too short for equilibrium to be attained, and the time for complete equilibration of C6H6 * vibration with translation, rotation, and vibration of the bath was not determined.

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.

Zero-Point Energy Constraint for Unimolecular Dissociation Reactions. Giving Trajectories Multiple Chances To Dissociate Correctly.

A zero-point energy (ZPE) constraint model is proposed for classical trajectory simulations of unimolecular decomposition and applied to CH4* → H + CH3 decomposition. With this model trajectories are not allowed to dissociate unless they have ZPE in the CH3 product. If not, they are returned to the CH4* region of phase space and, if necessary, given additional opportunities to dissociate with ZPE. The lifetime for dissociation of an individual trajectory is the time it takes to dissociate with ZPE in CH3, including multiple possible returns to CH4*. With this ZPE constraint the dissociation of CH4* is exponential in time as expected for intrinsic RRKM dynamics and the resulting rate constant is in good agreement with the harmonic quantum value of RRKM theory. In contrast, a model that discards trajectories without ZPE in the reaction products gives a CH4* → H + CH3 rate constant that agrees with the classical and not quantum RRKM value. The rate constant for the purely classical simulation indicates that anharmonicity may be important and the rate constant from the ZPE constrained classical trajectory simulation may not represent the complete anharmonicity of the RRKM quantum dynamics. The ZPE constraint model proposed here is compared with previous models for restricting ZPE flow in intramolecular dynamics, and connecting product and reactant/product quantum energy levels in chemical dynamics simulations.

Dynamics of Na(+)(Benzene) + Benzene Association and Ensuing Na(+)(Benzene)2* Dissociation.

Chemical dynamics simulations were used to study Bz + Na(+)(Bz) → Na(+)(Bz)2* association and the ensuing dissociation of the Na(+)(Bz)2* cluster (Bz = benzene). An interesting and unexpected reaction found from the simulations is direct displacement, for which the colliding Bz molecule displaces the Bz molecule attached to Na(+), forming Na(+)(Bz). The rate constant for Bz + Na(+)(Bz) association was calculated at 750 and 1000 K, and found to decrease with increase in temperature. By contrast, the direct displacement rate constant increases with temperature. The cross section and rate constant for direct displacement are approximately an order of magnitude lower than those for association. The Na(+)(Bz)2* cluster, formed by association, dissociates with a biexponential probability, with the rate constant for the short-time component approximately an order of magnitude larger than that for the longer time component. The latter rate constant agrees with that of Rice-Ramsperger-Kassel-Marcus (RRKM) theory, consistent with rapid intramolecular vibrational energy redistribution (IVR) and intrinsic RRKM dynamics for the Na(+)(Bz)2* cluster. A coupled phase space model was used to analyze the biexponential dissociation probability.

Chemical Dynamics Simulations of Benzene Dimer Dissociation.

Classical chemical dynamics simulations were performed to study the intramolecular and unimolecular dissociation dynamics of the benzene dimer, Bz2 → 2 Bz. The dissociation of microcanonical ensembles of Bz2 vibrational states, at energies E corresponding to temperatures T of 700-1500 K, were simulated. For the large Bz2 energies and large number of Bz2 vibrational degrees of freedom, s, the classical microcanonical (RRKM) and canonical (TST) rate constant expressions become identical. The dissociation rate constant for each T is determined from the initial rate dN(t)/dt of Bz2 dissociation, and the k(T) are well-represented by the Arrhenius eq k(T) = A exp(-E(a)/RT). The E(a) of 2.02 kcal/mol agrees well with the Bz2 dissociation energy of 2.32 kcal/mol, and the A-factor of 2.43 × 10(12) s(-1) is of the expected order-of-magnitude. The form of N(t) is nonexponential, resulting from weak coupling between the Bz2 intramolecular and intermolecular modes. With this weak coupling, large Bz2 vibrational excitation, and low Bz2 dissociation energy, most of the trajectories dissociate directly. Simulations, with only the Bz2 intramolecular modes excited at 1000 K, were also performed to study intramolecular vibrational energy redistribution (IVR) between the intramolecular and intermolecular modes. Because of restricted IVR, the initial dissociation is quite slow, but N(t) ultimately becomes exponential, suggesting an IVR time of 20.7 ps.

Potential energy surfaces for the HBr(+) + CO2 → Br + HOCO(+) reaction in the HBr(+) (2)Π3/2 and (2)Π1/2 spin-orbit states.

Quantum mechanical (QM) + molecular mechanics (MM) models are developed to represent potential energy surfaces (PESs) for the HBr(+) + CO2 → Br + HOCO(+) reaction with HBr(+) in the (2)Π3/2 and (2)Π1/2 spin-orbit states. The QM component is the spin-free PES and spin-orbit coupling for each state is represented by a MM-like analytic potential fit to spin-orbit electronic structure calculations. Coupled-cluster single double and perturbative triple excitation (CCSD(T)) calculations are performed to obtain "benchmark" reaction energies without spin-orbit coupling. With zero-point energies removed, the "experimental" reaction energy is 44 ± 5 meV for HBr(+)((2)Π3/2) + CO2 → Br((2)P3/2) + HOCO(+), while the CCSD(T) value with spin-orbit effects included is 87 meV. Electronic structure calculations were performed to determine properties of the BrHOCO(+) reaction intermediate and [HBr⋯OCO](+) van der Waals intermediate. The results of different electronic structure methods were compared with those obtained with CCSD(T), and UMP2/cc-pVTZ/PP was found to be a practical and accurate QM method to use in QM/MM direct dynamics simulations. The spin-orbit coupling calculations show that the spin-free QM PES gives a quite good representation of the shape of the PES originated by (2)Π3/2HBr(+). This is also the case for the reactant region of the PES for (2)Π1/2 HBr(+), but spin-orbit coupling effects are important for the exit-channel region of this PES. A MM model was developed to represent these effects, which were combined with the spin-free QM PES.

Energy and temperature dependent dissociation of the Na(+)(benzene)1,2 clusters: importance of anharmonicity.

Chemical dynamics simulations were performed to study the unimolecular dissociation of randomly excited Na(+)(Bz) and Na(+)(Bz)2 clusters; Bz = benzene. The simulations were performed at constant energy, and temperatures in the range of 1200-2200 K relevant to combustion, using an analytic potential energy surface (PES) derived in part from MP2/6-311+G* calculations. The clusters decompose with exponential probabilities, consistent with RRKM unimolecular rate theory. Analyses show that intramolecular vibrational energy redistribution is sufficiently rapid within the clusters that their unimolecular dynamics is intrinsically RRKM. Arrhenius parameters, determined from the simulations of the clusters, are unusual in that Ea is ∼10 kcal/mol lower the Na(+)(Bz) → Na(+) + Bz dissociation energy and the A-factor is approximately two orders-of-magnitude too small. Analyses indicate that temperature dependent anharmonicity is important for the Na(+)(Bz) cluster's unimolecular rate constants k(T). This is consistent with the temperature dependent anharmonicity found for the Na(+)(Bz) cluster from a Monte Carlo calculation based on the analytic PES used for the simulations. Apparently temperature dependent anharmonicity is quite important for unimolecular dissociation of the Na(+)(Bz)1,2 clusters.

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

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

Space-time contours to treat intense field-dressed molecular states.

In this article we consider a molecular system exposed to an intense short-pulsed external field. It is a continuation of a previous publication [A. K. Paul, S. Adhikari, D. Mukhopadhyay et al., J. Phys. Chem. A 113, 7331 (2009)] in which a theory is presented that treats quantum effects due to nonclassical photon states (known also as Fock states). Since these states became recently a subject of intense experimental efforts we thought that they can be treated properly within the existing quantum formulation of dynamical processes. This was achieved by incorporating them in the Born-Oppenheimer (BO) treatment with time-dependent coefficients. The extension of the BO treatment to include the Fock states results in a formidable enhancement in numerical efforts expressed, in particular, in a significant increase in CPU time. In the present article we discuss an approach that yields an efficient and reliable approximation with only negligible losses in accuracy. The approximation is tested in detail for the dissociation process of H(2) (+) as caused by a laser field.

Photodissociation of H2(+) upon exposure to an intense pulsed photonic Fock state.

Producing and controlling nonclassical light states are now the subject of intense experimental efforts. In this paper we consider the interaction of such a light state with a small molecule. Specifically, we develop the theory and apply it numerically to calculate in detail how a short pulse of nonclassical light, such as the high intensity Fock state, induces photodissociation in H(2)(+). We compare the kinetic energy distributions and photodissociation yields with the analogous results of quasi-classical light, namely a coherent state. We find that Fock-state light decreases the overall probability of dissociation for low vibrational states of H(2)(+) as well as the location of peaks and line shapes in the kinetic energy distribution of the nuclei.