An efficient algorithm for capturing quantum effects in classical reactive scattering: application to D + H+3 → H2D+ + H.

Motivated by a recent semiclassical analysis of chemical reaction thresholds [Bonnet et al., J. Chem. Phys., 2022, 157, 094114], we present an efficient algorithm for including zero-point energy (ZPE) effects in classical reactive scattering. The algorithm is an extension of the quasi-classical trajectory (QCT) Gaussian binning method. We apply it to the astrophysically important D + H+3 reaction, where there are significant quantum effects and where application of other methods is problematic [Braunstein et al., Phys. Chem. Chem. Phys., 2022, 24, 5489]. The rate constants computed with the new, general algorithm closely match recent Ring Polymer Molecular Dynamics (RPMD) [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] and experimentally derived [Bowen et al., J. Chem. Phys., 2021, 154, 084307] ones spanning ∼4 orders of magnitude from 70 to 1500 K.

Capturing quantum effects with quasi-classical trajectories in the D + H+3 → H2D+ + H reaction.

We present quasi-classical trajectory (QCT) cross sections, rate constants, and product state distributions for the D + H+3 → H2D+ + H reaction. Using the same H+4 potential surface, the rate constants obtained from several QCT-based methods correcting for zero-point effects by Gaussian binning the product H2D+ are compared to ring polymer molecular dynamics (RPMD) rate constants [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] which include quantum effects and to recent experimentally derived rate constants [Bowen et al., J. Chem. Phys., 2021, 154, 084307]. QCT with standard binning predicts rate constants that increase slowly as the temperature decreases from 1500 to 100 K. In contrast, the RPMD rate constants decrease rapidly with decreasing temperature. By 100 K, the QCT standard binning rate constant is more than 3 orders of magnitude larger than the RPMD rate constant. We show that QCT with Gaussian binning and proper normalization captures the zero-point effects and reproduces the RPMD rate constants over a large temperature range. Furthermore, the simple technique of counting only reactive trajectories with vibrational energy above the product zero-point energy matches the RPMD results well down to ∼300 K. The present Gaussian binned rate constants are in fair agreement with new experimentally derived rate constants from 100 to 1500 K. However, because the Gaussian binned rate constants do not include tunneling, important at lower temperatures, and the RPMD and experimentally derived rate constants have significant differences, the roles of the competing effects of zero-point energy, internal excitation of the H+3, and quantum tunneling are not simple and require further study for a consistent picture of the dynamics. Since rate constants for complex forming reactions, such as the title reaction, are difficult to converge with RPMD, alternative QCT-based methods, which include quantum effects and in addition provide product state distributions as described here, are highly desirable.

Classical dynamics of H2O vibrational self-relaxation.

The vibrational self-relaxation rate constants of the (001), (100), (020), and (010) states of H2O from 295 to 2500 K are calculated, using ∼1.6 × 10(6) classical trajectories with Gaussian binning for determining product vibrational quantum numbers. The calculations use a new H2O-H2O potential surface obtained by fitting 1.25 × 10(5) ab initio geometry points at the CCSD(T)//cc-pvtz level of theory. The resulting vibrational self-relaxation rate constants are generally within a factor of 2 of the measured data, which are large in magnitude and tend to increase with decreasing temperature. At lower temperatures, the calculations show long-lived (20 ps and longer) H2O-H2O collision complexes which accompany vibrational relaxation. Product rotational and translational energy distributions are investigated, and joint vibrational state and molecule-specific relaxation rate constants are presented.

Classical dynamics of state-resolved hyperthermal O((3)P) + H2O((1)A1) collisions.

Classical dynamics calculations are performed for O((3)P) + H2O((1)A1) collisions from 2 to 10 km s(-1) (4.1-101.3 kcal mol(-1)), focusing on product internal energies. Several methods are used to produce ro-vibrationally state-resolved product cross sections and to enforce zero-point maintenance from analysis of the classical trajectories. Two potential energy surfaces are used: (1) a recently developed set of global reactive surfaces for the three lowest triplet states which model OH formation, H elimination to make H + OOH, O-atom exchange, and collisional excitation and (2) a non-reactive surface used in past classical and quantum collision studies. Comparisons to these previous studies suggest that for H2O vibrational excitation, classical dynamics which include gaussian binning procedures and/or selected zero-point maintenance algorithms can produce results which approximate quantum scattering cross sections fairly well. Without these procedures, the classical cross sections can be many orders of magnitude greater than the quantum cross sections for exciting the bending vibration of H2O, especially near threshold. The classical cross section over-estimate is due to energy borrowing from stretching modes which dip below zero-point values. For results on the reactive surfaces, the present calculations show that at higher velocities there is an unusually large amount of product internal excitation. For OOH, where 40% of available collision energy goes into internal motion, the excited product vibrational and rotational energy distributions are relatively flat and values of the OOH rotational angular momentum exceed J = 100. Other product channel distributions show an exponential fall-off with energy consistent with an energy gap law. The present detailed distributions and cross sections can serve as a guide for future hyperthermal measurements of this system.

Collision dynamics of O(3P) + DMMP using a specific reaction parameters potential form.

Starting from previous benchmark CBS-QB3 electronic structure calculations (Conforti, P. F.; Braunstein, M.; Dodd, J. A. J. Phys. Chem. A 2009, 113, 13752), we develop two global potential energy surfaces for O((3)P) + DMMP collisions, using the specific reaction parameters approach. Each surface is simultaneously fit along the three major reaction pathways: hydrogen abstraction, hydrogen elimination, and methyl elimination. We then use these surfaces in classical dynamics simulations and compute reactive cross sections from 4 to 10 km s(-1) collision velocity. We examine the energy disposal and angular distributions of the reactive and nonreactive products. We find that for reactive collisions, an unusually large amount of the initial collision energy is transformed into internal energy. We analyze the nonreactive and reactive product internal energy distributions, many of which fit Boltzmann temperatures up to ~2000 K.

Global potential energy surfaces for O((3)P) + H2O((1)A1) collisions.

Global analytic potential energy surfaces for O((3)P) + H(2)O((1)A(1)) collisions, including the OH + OH hydrogen abstraction and H + OOH hydrogen elimination channels, are presented. Ab initio electronic structure calculations were performed at the CASSCF + MP2 level with an O(4s3p2d1f)/H(3s2p) one electron basis set. Approximately 10(5) geometries were used to fit the three lowest triplet adiabatic states corresponding to the triply degenerate O((3)P) + H(2)O((1)A(1)) reactants. Transition state theory rate constant and total cross section calculations using classical trajectories to collision energies up to 120 kcal mol(-1) (∼11 km s(-1) collision velocity) were performed and show good agreement with experimental data. Flux-velocity contour maps are presented at selected energies for H(2)O collisional excitation, OH + OH, and H + OOH channels to further investigate the dynamics, especially the competition and distinct dynamics of the two reactive channels. There are large differences in the contributions of each of the triplet surfaces to the reactive channels, especially at higher energies. The present surfaces should support quantitative modeling of O((3)P) + H(2)O((1)A(1)) collision processes up to ∼150 kcal mol(-1).

Energetics and dynamics of the reactions of O(3P) with dimethyl methylphosphonate and sarin.

Electronic structure and molecular dynamics calculations were performed on the reaction systems O((3)P) + sarin and O((3)P) + dimethyl methylphosphonate (DMMP), a sarin simulant. Transition state geometries, energies, and heats of reaction for the major reaction pathways were determined at several levels of theory, including AM1, B3LYP/6-311+G(d,p), and CBS-QB3. The major reaction pathways for both systems are similar and include H-atom abstraction, H-atom elimination, and methyl elimination, in rough order from low to high energy. The H-atom abstraction channels have fairly low barriers (approximately 10 kcal mol(-1)) and are close to thermoneutral, while the other channels have relatively high energy barriers (>40 kcal mol(-1)) and a wide range of reaction enthalpies. We have also found a two-step pathway leading to methyl elimination through O-atom attack on the phosphorus atom for DMMP and sarin. For sarin, the two-step methyl elimination pathway is significantly lower in energy than the single-step pathway. We also present results of O((3)P) + sarin and O((3)P) + DMMP reaction cross sections over a broad range of collision energies (2-10 km s(-1) collision velocities) obtained using the direct dynamics method with an AM1 semiempirical potential. These excitation functions are intended as an approximate guide to future hyperthermal measurements, which to our knowledge have not yet examined either of these systems. The reaction barriers, reaction enthalpies, transition state structures, and excitation functions are generally similar for DMMP and sarin, with some moderate differences for methyl elimination energetics, which indicates DMMP will likely be a good substitute for sarin in many O((3)P) chemical investigations.

Hyperthermal atomic oxygen source for near-space simulation experiments.

A hyperthermal atomic oxygen (AO) beam facility has been developed to investigate the collisions of high-velocity AO atoms with vapor-phase counterflow. Application of 4.5 kW, 2.4 GHz microwave power in the source chamber creates a continuous discharge in flowing O(2) gas. The O(2) feedstock is introduced into the source chamber in a vortex flow to constrain the plasma to the center region, with the chamber geometry promoting resonant excitation of the TM(011) mode to localize the energy deposition in the vicinity of the aluminum nitride (AlN) expansion nozzle. The approximately 3500 K environment serves to dissociate the O(2), resulting in an effluent consisting of 40% AO by number density. Downstream of the nozzle, a silicon carbide (SiC) skimmer selects the center portion of the discharge effluent, prior to the expansion reaching the first shock front and rethermalizing, creating a beam with a derived 2.5 km s(-1) velocity. Differential pumping of the skimmer chamber, an optional intermediate chamber and reaction chamber maintains a reaction chamber pressure in the mid-10(-6) to mid-10(-5) Torr range. The beam has been characterized with regard to total AO beam flux, O(2) dissociation fraction, and AO spatial profile using time-of-flight mass spectrometric and Kapton-H erosion measurements. A series of reactions AO+C(n)H(2n) (n=2-4) has been studied under single-collision conditions using mass spectrometric product detection, and at higher background pressure detecting dispersed IR emissions from primary and secondary products using a step-scan Michelson interferometer. In a more recent AO crossed-beam experiment, number densities and predicted IR emission intensities have been modeled using the direct simulation Monte Carlo technique. The results have been used to guide the experimental conditions. IR emission intensity predictions are compared to detected signal levels to estimate absolute reaction cross sections.

Dynamics of hyperthermal collisions of O(3P) with CO.

The dynamics of O(3P) + CO collisions at a hyperthermal collision energy near 80 kcal mol-1 have been studied with a crossed molecular beams experiment and with quasi-classical trajectory calculations on computed potential energy surfaces. In the experiment, a rotatable mass spectrometer detector was used to monitor inelastically and reactively scattered products as a function of velocity and scattering angle. From these data, center-of-mass (c.m.) translational energy and angular distributions were derived for the inelastic and reactive channels. Isotopically labeled C18O was used to distinguish the reactive channel (16O + C18O 16OC + 18O) from the inelastic channel (16O + C18O 16O + C18O). The reactive 16OC molecules scattered predominantly in the forward direction, i.e., in the same direction as the velocity vector of the reagent O atoms in the c.m. frame. The c.m. translational energy distribution of the reactively scattered 16OC and 18O was very broad, indicating that 16OC is formed with a wide range of internal energies, with an average internal excitation of approximately 40% of the available energy. The c.m. translational energy distribution of the inelastically scattered C18O and 16O products indicated that an average of 15% of the collision energy went into internal excitation of C18O, although a small fraction of the collisions transferred nearly all the collision energy into internal excitation of C18O. The theoretical calculations, which extend previously published results on this system, predict c.m. translational energy and angular distributions that are in near quantitative agreement with the experimentally derived distributions. The theoretical calculations, thus validated by the experimental results, have been used to derive internal state distributions of scattered CO products and to probe in detail the interactions that lead to the observed dynamical behavior.

The convergence of complete active space self-consistent-field configuration interaction including all single and double excitation energies to the complete basis set limit.

Examination of the convergence of full valence complete active space self-consistent-field configuration interaction including all single and double excitation (CASSCF-CISD) energies with expansion of the one-electron basis set reveals a pattern very similar to the convergence of single determinant energies. Calculations on the lowest four singlet states and the lowest four triplet states of N(2) with the sequence of n-tuple-zeta augmented polarized (nZaP) basis sets (n=2, 3, 4, 5, and 6) are used to establish the complete basis set limits. Full configuration-interaction (CI) and core electron contributions must be included for very accurate potential energy surfaces. However, a simple extrapolation scheme that has no adjustable parameters and requires nothing more demanding than CAS(10e(-),8orb)-CISD/3ZaP calculations gives the R(e), omega(e), omega(e)X(e), T(e), and D(e) for these eight states with rms errors of 0.0006 Angstrom, 4.43 cm(-1), 0.35 cm(-1), 0.063 eV, and 0.018 eV, respectively.

The convergence of complete active space self-consistent-field energies to the complete basis set limit.

Examination of the convergence of full valence complete active space self-consistent-field energies with expansion of the one-electron basis set reveals a pattern very similar to the convergence of single determinant Hartree-Fock energies. Calculations on 26 molecular examples with the sequence of ntuple-zeta augmented polarized (nZaP) basis sets (n=2, 3, 4, 5, and 6) are used to evaluate complete basis set extrapolation schemes. The most effective extrapolation reduces the rms one-electron basis set truncation errors from 3.03, 0.58, and 0.12 mhartree to 0.23, 0.05, and 0.014 mhartree for the 3ZaP, 4ZaP, and 5ZaP basis sets, respectively.

Beam configurations for 3D tomographic intensity modulated radiation therapy.

We extend the theory of three-dimensional (3D) tomographic intensity modulated radiation therapy (IMRT). The geometry consists of two-dimensional modulated beams on a sphere centred in the tumour. The theory provides an efficient algorithm for computing beam modulation patterns that approximately 'reconstruct' the prescribed dose function. In this paper optimum beam numbers are estimated from dose function spherical harmonics using the 3D projection-slice theorem. An extension to three dimensions of the 'Bow Tie' criterion for beam numbers is derived. The effects of insufficient beam front sampling and beam numbers are characterized with a configuration-dependent matrix. Factors that independently increase beam numbers, such as tumour size and shape, are related to the spherical harmonic content in the dose function. Examples of tomographic IMRT reconstruction with a 3D concave tumour are given.