Rotational excitation of diatomic molecular systems. II - H2 /plus/
Hydrogen molecules rotational excitation cross sections by electron impact in adiabatic excitation, discussing polarization and distortion effects
Chang, E. S.↗
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Discrete Rotational Energy for Polyatomic Molecules in Direct Simulation Monte Carlo
Accurate prediction of aerothermodynamic loads in thermal non-equilibrium flows requires precise modeling of internal energy exchange. While previous direct simulation Monte Carlo frameworks have successfully implemented discrete rotational energy models for diatomic species, the treatment of polyatomic molecules has traditionally relied on continuous energy assumptions that break down at low temperatures and neglect critical high-temperature corrections. This study extends the discrete rotational energy models of Boyd and Gimelshein to fully encompass polyatomic molecules. The proposed framework implements quantized rotational energy level sampling for linear, spherical, and symmetric/asymmetric top rotors. Crucially, the model incorporates centrifugal distortion to address the limitations of the rigid-rotor assumption at hypersonic temperatures, and accounts for nuclear spin parity, which dictates the permissible rotational states and macroscopic specific heats at low temperatures. The model is verified through equilibrium sampling procedures, demonstrating agreement with theoretical quantum Boltzmann distributions and accurately reproducing thermophysical properties across a wide range of temperatures.
DSMC↗
Langevin Dynamics modeling of gas-phase ion-ion recombination (Final Technical Report)
A self-consistent trajectory simulation approach to model MN reactions (Fig. 1) which incorporates the probability of electron transfer as a Monte Carlo operator (Fig. 2) was developed and published as Liu et al. J. Chem. Phys. 159, 114111 (2023). The electron transfer probability p ET estimated using the two-state Landau-Zener (LZ) theory was incorporated into classical trajectory simulations to elicit predictions of MN reaction cross-section σ (vacuum) or rate constant β (finite pressure). Electronic structure calculations with multireference configuration interaction (MRCI) and large correlation consistent basis sets were used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the incorporation of electron transfer probability and the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of neutral gas on ions. For H + – H - and Li + – H(D) - pairs, our approach quantitatively agrees with measured speed-dependent cross-sections for up to ~10 5 m/s. For the ion pair Ne + – Cl - , our predictions of the MN rate constant at ~1 torr are a factor of ~2 – 3 higher than the experimentally measured value. Similarly, for Xe + – F - in the pressure range of ~20000 – 80000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently model MN reactions is the basis for inclusion of additional non-classical, and static magnetic and electric field effects. Subsequent work, published as Roy et al. focused on modeling recombination rate constant for three ion pairs (rare gas Ar + cation and halide anions): Ar + – Cl - , Ar + – Br - , Ar + – I - , 2) considering spin-orbit couplings in the electronic structure calculations to obtain high-fidelity estimates of the electron transfer probability and incorporated within the classical trajectory simulations to elicit predictions. In addition to calculations of ion-ion recombination rate constants, a classical trajectory simulation technique (published as Roy et al. J. Chem. Phys. 162(9), 094104 (2023)) that uses quaternions to represent orientation of non-spherical particles (ions or aerosol particles) was developed to simulate the recombination of diatomic or more generally, polyatomic molecules. Finally, several other ion pairs such as Ne + – Cl - , Kr + – Cl - , were explored using the developed semi-classical trajectory simulations to understand various challenges in tackling electronic structure calculations. Using empirical approaches to parameterize the electron transfer radius, trajectory simulations were also used to probe the effect of ion number density on MN rate constant.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Thermodynamic properties and theoretical rocket performance of hydrogen to 100,000 K and 1.01325 x 10 to the 8th power N/sq m
The composition and thermodynamic properties were calculated for 100 to 110,000 K and 1.01325 x 10 to the 2nd power to 1.01325 x 10 to the 8th power N/sq m for chemical equilibrium in the Debye-Huckel and ideal-gas approximations. Quantities obtained were the concentrations of hydrogen atoms, protons, free electrons, hydrogen molecules, negative hydrogen ions, hydrogen diatomic molecular ions, and hydrogen triatomic molecular ions, and the enthalpy, entropy, average molecular weight, specific heat at constant pressure, density, and isentropic exponent. Electronically excited states of H and H2 were included. Choked, isentropic, one-dimensional nozzle flow with shifting chemical equilibrium was calculated to the Debye-Huckel and ideal-gas approximations for stagnation temperatures from 2500 to 100,000 K. The mass flow per unit throat area and the sonic flow factor were obtained. The pressure ratio, temperature, velocity, and ideal and vacuum specific impulses at the throat and for pressure ratios as low as 0.000001 downstream were found. For high temperatures at pressures approaching 1.01325 x 10 to the 8th power N/sq m, the ideal-gas approximation was found to be inadequate for calculations of composition, precise thermodynamic properties, and precise nozzle flow. The greatest discrepancy in nozzle flow occurred in the exit temperature, which was as much as 21 percent higher when the Debye-Huckel approximation was used.
Patch, R. W.↗
Pathway toward Optical Cycling and Laser Cooling of Functionalized Arenes
Rapid and repeated photon cycling has enabled precision metrology and the development of quantum information systems using atoms and simple molecules. Extending optical cycling to structurally complex molecules would provide new capabilities in these areas, as well as in ultracold chemistry. Increased molecular complexity, however, makes realizing closed optical transitions more difficult. Building on already established strong optical cycling of diatomic, linear triatomic, and symmetric top molecules, recent work has pointed the way to cycling of larger molecules, including phenoxides. The paradigm for these systems is an optical cycling center bonded to a molecular ligand. Theory has suggested that cycling may be extended to even larger ligands, like naphthalene, pyrene, and coronene. For this paper, we study optical excitation and fluorescent vibrational branching of CaO-[illus. chemical structure], SrO-[illus. chemical structure], and CaO-[illus. chemical structure] and find only weak decay to excited vibrational states, indicating a promising path to full quantum control and laser cooling of large arene-based molecules.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Theoretical study of the BeLi, BeNa, MgLi, MgNa, and AlBe molecules and their negative ions
The alkaline earth-alkali diatomics are found to have weak bonds, because the diffuse alkali valence s orbitals cannot form a bond of sufficient strength to pay the promotion energy of the alkaline-earth atoms. This leads to van der Waals bonding in the neutrals as well as the negative ions. In fact, the negative ions have larger binding energies than the neutrals as a result of the much larger polarizability of the negative ion. The binding energy of AlBe is significantly larger than the Be-alkali molecules, due to a covalent contribution to the bonding. The binding energy in AlBe(-) is considerably larger than AlBe; the binding energy of the X 3Sigma(-) state of AlBe(-) is computed to be 1.36 eV, as compared with 0.57 eV for the X 2Pi state of AlBe.
Bauschlicher, Charles W., Jr.↗
On the prospects of optical cycling in diatomic cations: effects of transition metals, spin–orbit couplings, and multiple bonds
Molecules with optical cycling centers (OCCs) are highly desirable in the context of fundamental studies as well as applications (e.g., quantum computing) because they can be effectively cooled to very low temperatures by repeated absorption and emission (hence, cycling). Charged species offer additional advantages for experimental control and manipulation. Here, we present a systematic computational study of a series of diatomic radical-cations made of a d-block metal and a p-block ligand, that are isoelectronic (in their valence shell) to the successfully laser-cooled neutral molecules. Using high-level electronic structure methods, we characterize state and transition properties of low-lying electronic states and compute Franck-Condon factors. The computed branching ratios and radiative lifetimes reveal that the electronic transitions analogous to those successfully used in the laser cooling of neutral molecules are less than optimal in the cations. We propose alternative transitions suitable for optical cycling and highlight trends that could assist future designs of OCCs in charged or neutral molecules.
74 ATOMIC AND MOLECULAR PHYSICS↗
Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory
The dipole moment is the molecular property that most directly indicates molecular polarity. The accuracy of computed dipole moments depends strongly on the quality of the calculated electron density, and the breakdown of single-reference methods for strongly correlated systems can lead to poor predictions of the dipole moments in those cases. Here, we derive the analytical expression for obtaining the electric dipole moment by multiconfiguration pair density functional theory (MCPDFT), and we assess the accuracy of MC-PDFT for predicting dipole moments at equilibrium and nonequilibrium geometries. We show that MC-PDFT dipole moment curves have reasonable behavior even for stretched geometries, and they significantly improve upon the CASSCF results by capturing more electron correlation. Herein, the analysis of a dataset consisting of 18 first-row transition metal diatomics and 6 main-group polyatomic molecules with multireference character suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned deviation of 0.2–0.3 D with respect to the best available dipole moment reference values. We explored the dependence of the predicted dipole moments upon the choice of the on-top density functional and active space, and we recommend the tPBE and hybrid tPBE0 on-top choices for the functionals combined with the moderate correlated participating orbital scheme for selecting the active space. With these choices, the mean unsigned deviations (in debyes) of the calculated equilibrium dipole moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT, 0.24 for HMCPDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results are encouraging because the computational cost of MC-PDFT or HMC-PDFT is largely reduced compared to the CASPT2 and MRCISD+Q methods.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The significance of far-infrared spectra of the interstellar medium
This paper deals with the analysis of interstellar clouds through infrared and submillimeter observations. The determination of temperature, density, state of ionization and abundance of different chemical constituents is discussed for clouds exhibiting a range of optical depths. There is a preferred choice of spectral features useful for examining different types of gaseous complexes. The prospects for improving the understanding of chemical reaction schemes in interstellar clouds are outlined. Prime advances may be expected in improved data on the abundance of atoms; diatomic hydrides; other small, hydrogen-containing molecules; and their ions.
Harwit, M.↗
The V-T energy transfer in collisions of diatomics
A general approach evaluating the transition probabilities for the V-T exchange, involving highly excited levels and the Delta-v greater than 1 transitions, in diatomic gases is presented. Examples of numerical results are given for a number of transitions in nitrogen and oxygen molecules in the ground electronic states. The approach can be used for the V-T exchange involving diatomic molecular ions.
Kunc, Joseph A.↗
Relaxation of higher vibrational states in diatomic gases
A general and computationally efficient approach evaluating the transition probabilities for the V-T exchange, involving highly excited levels and the transitions of delta-v of more than 1, in diatomic gases is presented. The role of the repulsive part of the intermolecular potential on the transition probability is also investigated. Examples of numerical results are given for number of transitions in nitrogen and oxygen molecules in the ground electronic states. The approach can be used for interactions involving diatomic molecular ions.
Kunc, J. A.↗
Collision integrals for isotopic hydrogen molecules.
The study was undertaken to determine the effects of reduced mass and differences in asymmetry on the collision integrals and thermal diffusion factors of isotopic hydrogen systems. Each system selected for study consisted of two diatoms, one in the j = 0 rotation state and the other in the j = 1 state. The molecules interacted with a Lennard-Jones type potential modified to include angular terms. A set of cross sections and collision integrals were obtained for each system.
Brown, N. J.↗
SpectrumSDT: A program for parallel calculation of coupled rotational-vibrational energies and lifetimes of bound states and scattering resonances in triatomic systems
In this work, we present SpectrumSDT – a program for calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Large-amplitude vibrational motion is treated explicitly using hyper-spherical coordinates. Three options for the rotational-vibrational interaction are supported: uncoupled (symmetric top rotor), partially coupled (to include interaction between several nearest states only) and full-coupled (vibrating asymmetric-top rotor). In addition to energies and lifetimes, SpectrumSDT is able to integrate ro-vibrational wave functions over the user-defined regions of potential energy surface, which helps to classify these states. In this release of the code, SpectrumSDT is limited to ABA-type molecules with wave functions that do not extend into the regions near Eckart singularities.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Molecule formation by inverse predissociation
The general theory of inverse predissociation is described, and is applied to specific molecules. The list of molecules which can be formed by radiative association will be lengthened considerably by considering this phenomenon. Typical rate constants for diatoms will lie in the range 10 to the minus 16th power to 10 to the minus 20th power cu cm/sec/molecule, with the heavy atom molecules such as CN, CO, or NO generally having larger rates than the hydrides. An attempt is made to point out what molecular characteristics determine the radiative association rate and also to make estimates of what rates may be expected for various interstellar molecules. The formal theory is developed, and the molecular properties are discussed which determine the inverse predissociation rate. The details of the theory as applied to specific interstellar molecules are studied.
Julienne, P. S.↗
Collisional narrowing effects in the Raman Q-branch spectral profiles of N2, CO, and NO
A description is presented of coherent Raman spectroscopic studies of N2, CO, and NO molecules. It is pointed out that the Q-branch Raman spectra of these simple diatomics are characterized by lines which overlap with increasing pressure as a result of collisional line broadening. Attention is given to Q-branch vibrational spectra and their determination, the spectral line shape of isolated lines, the line overlap regime, fitting laws, and the isotropic Raman spectrum of NO. It is found that the room temperature spectra of the considered molecules at low pressure (approximately 0.2 atm) may be treated as a sum of isolated lines. It is possible to extract J-dependent pressure-broadening coefficients. With increasing pressure, collisional narrowing occurs and the description of the spectrum must include the effects of interference among neighboring lines.
Hurst, W. S.↗
The computation of radiation from nonequilibrium hypersonic flows
The results of the solution of the equations that describe a hypersonic ionized flow about an elliptically blunted cone are presented. The flow conditions correspond to those of the proposed Aeroassist Flight Experiment (AFE) vehicle at altitudes between the perigee at 78 km and the approximate limit of the continuum regime at 90 km. For the free-stream velocities of interest, about 9 km/sec, the flowfield is out of thermo-chemical equilibrium, electronically excited, ionized and radiating. The gas consists of eight-chemical species including free electrons. The thermal state of the gas is modeled with a translational-rotational temperature, four vibrational temperatures for the diatomic species and an electron-electronic temperature. The electronic excitation of molecules is included. The nonequilibrium air radiation from each fluid element is computed and the radiative heat flux at the body surface is determined. The stagnation point radiative heating result agrees with previous calculations.
Candler, Graham↗
Model for nuclear spin product-state distributions of ultracold chemical reactions in magnetic fields
Based on a theoretical model where the nuclear spins remain unchanged during a collision, we provide an analytical and general expression for the nuclear spin state-to-state distribution of an ultracold diatom-diatom chemical reaction in a magnetic field, for given rotational transitions of the molecules. It simply requires knowledge of the field-dependent eigenfunctions of the molecular reactants and products of the chemical reaction. The final state-to-state distribution drastically changes with the magnetic field. When the distribution is summed over all the final products, a simplified expression is found where only the knowledge of the eigenfunctions of the molecular reactants is required. The present theoretical formalism has been successfully used to explain the magnetic field behavior of the product-state distribution in chemical reactions of ultracold KRb molecules [Hu et al., Nat. Chem. 13, 435 (2021)].
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Algebraic description of atom-molecule interactions
We describe a new method based on algebraic techniques, which leads to a model of atom-diatom collisions.
Santiago, R. D.↗