Algorithms for Sampling a Quantum Microcanonical Ensemble of Harmonic Oscillators at Potential Minima and Conical Intersections

Unimolecular dissociation of C6H6-C6H5Cl, C6H6-C6H3Cl3, and C6H6-C6Cl6 complexes using machine learning approach

The application of Machine Learning (ML) algorithms in chemical sciences, particularly computational chemistry, is a vastly emerging area of modern research. While many applications of ML techniques have already been in place to use ML based potential energies in various dynamical simulation studies, specific applications are also being successfully tested. In this work, the ML algorithms are tested to calculate the unimolecular dissociation time of benzene-hexachlorobenzene, benzene-trichlorobenzene, and benzene-monochlorobenzene complexes. Three ML algorithms, namely, Decision-Tree-Regression (DTR), Multi-Layer Perceptron, and Support Vector Regression are considered. The algorithms are trained with simulated dissociation times as functions (attributes) of complexes' intramolecular and intermolecular vibrational energies. The simulation data are used for an excitation temperature of 1500 K. Considering that the converged result is obtained with 1500 trajectories, an ML algorithm trained with 700 simulation points provides the same dissociation rate constant within statistical uncertainty as obtained from the converged 1500 trajectory result. The DTR algorithm is also used to predict 1000 K simulation results using 1500 K simulation data.

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.

Dynamical Behavior of Aromatic Trimer Complexes in Unimolecular Dissociation Reaction at High Temperatures. Case Studies on C6H6-C6F6-C6H6 and C6H6 Trimer Complexes

The intramolecular vibrational energy redistribution (IVR) dynamics during unimolecular dissociation of aromatic trimers at high temperatures is the primary interest of this study. Chemical dynamics simulations are performed for the unimolecular dissociation of benzene-hexafluorobenzene-benzene (Bz-HFB-Bz) and benzene trimer (Bz-trimer) complexes at a temperature range of 1000-2000 K. Partial dissociation of both the complexes is observed, which leads to a dimer and a monomer in the dynamics. However, the probability of such dissociation was found much lower in the case of the Bz-trimer, which further decreases with the increase of temperature. The rate of partial dissociation of Bz-HFB-Bz is faster at 1500, 1800, and 2000 K, whereas the rate of complete dissociation of the Bz-trimer is significantly faster than Bz-HFB-Bz at all temperatures. This is just the opposite of the corresponding dimer's dissociation, where benzene-hexafluorobenzene (Bz-HFB) dissociates at a faster rate than the benzene dimer (Bz-dimer). Thus, the dissociation dynamics of the trimer is different than that of the dimer. Simulations with excited intramolecular and intermolecular modes of the trimer complexes reveal that energy flows from intermolecular to intramolecular modes of Bz-HFB-Bz more freely than the Bz-trimer, and the dissociation process becomes slower for the former. Calculated activation energies for both types of dynamics are much lower than the corresponding binding energies, which may be due to the anharmonicity. The Arrhenius equation with an anharmonic correction factor is considered to recalculate the activation energy and pre-exponential factor.

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.

Sampling initial positions and momenta for nuclear trajectories from quantum mechanical distributions

We compare algorithms to sample initial positions and momenta of a molecular system for classical trajectory simulations. We aim at reproducing the phase space quantum distribution for a vibrational eigenstate, as in Wigner theory. Moreover, we address the issue of controlling the total energy and the energy partition among the vibrational modes. In fact, Wigner's energy distributions are very broad, quite at variance with quantum eigenenergies. Many molecular processes depend sharply on the available energy, so a better energy definition is important. Two approaches are introduced and tested: the first consists in constraining the total energy of each trajectory to equal the quantum eigenenergy. The second approach modifies the phase space distribution so as to reduce the deviation of the single mode energies from the correct quantum values. A combination of the two approaches is also presented.

Graph theory-based reaction pathway searches and DFT calculations for the mechanism studies of free radical-initiated peptide sequencing mass spectrometry (FRIPS MS): a model gas-phase reaction of GGR tri-peptide

Graph theory-based reaction pathway searches (ACE-Reaction program) and density functional theory calculations were performed to shed light on the mechanisms for the production of [a_n + H]⁺, x_n⁺, y_n⁺, z_n⁺, and [y_n + 2H]⁺ fragments formed in free radical-initiated peptide sequencing (FRIPS) mass spectrometry measurements of a small model system of glycine-glycine-arginine (GGR). In particular, the graph theory-based searches, which are rarely applied to gas-phase reaction studies, allowed us to investigate reaction mechanisms in an exhaustive manner without resorting to chemical intuition. As expected, radical-driven reaction pathways were favorable over charge-driven reaction pathways in terms of kinetics and thermodynamics. Charge- and radical-driven pathways for the formation of [y_n + 2H]⁺ fragments were carefully compared, and it was revealed that the [y_n + 2H]⁺ fragments observed in our FRIPS MS spectra originated from the radical-driven pathway, which is in contrast to the general expectation. The acquired understanding of the FRIPS fragmentation mechanism is expected to aid in the interpretation of FRIPS MS spectra. It should be emphasized that graph theory-based searches are powerful and effective methods for studying reaction mechanisms, including gas-phase reactions in mass spectrometry.

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 k_asso( 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 k_asso( 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 k_asso( T) at 1000 and 2000 K. The Arrhenius parameters, using the k_asso( 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.

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.

The effect of molecular dynamics sampling on the calculated observable gas-phase structures

In this study, we compare the performance of various ab initio molecular dynamics (MD) sampling methods for the calculation of the observable vibrationally-averaged gas-phase structures of benzene, naphthalene and anthracene molecules. Nose-Hoover (NH), canonical and quantum generalized-Langevin-equation (GLE) thermostats as well as the a posteriori quantum correction to the classical trajectories have been tested and compared to the accurate path-integral molecular dynamics (PIMD), static anharmonic vibrational calculations as well as to the experimental gas electron diffraction data. Classical sampling methods neglecting quantum effects (NH and canonical GLE thermostats) dramatically underestimate vibrational amplitudes for the bonded atom pairs, both C-H and C-C, the resulting radial distribution functions exhibit nonphysically narrow peaks. This deficiency is almost completely removed by taking the quantum effects on the nuclei into account. The quantum GLE thermostat and a posteriori correction to the canonical GLE and NH thermostatted trajectories capture most vibrational quantum effects and closely reproduce computationally expensive PIMD and experimental radial distribution functions. These methods are both computationally feasible and accurate and are therefore recommended for calculations of the observable gas-phase structures. A good performance of the quantum GLE thermostat for the gas-phase calculations is encouraging since its parameters have been originally fitted for the condensed-phase calculations. Very accurate molecular structures can be predicted by combining the equilibrium geometry obtained at a high level of electronic structure theory with vibrational amplitudes and corrections calculated using MD driven by a lower level of electronic structure theory.

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.