Search

Mixed quantum/classical theory (MQCT) for the treatment of rotationally inelastic transitions during collisions of two identical molecules, described either as indistinguishable or distinguishable partners, is reviewed. The treatment of two molecules as indistinguishable includes symmetrization of rotational wavefunctions, introduces exchange parity, and leads to state-to-state transition matrix elements different from those in the straightforward treatment of molecules as distinguishable. Moreover, the treatment of collision partners as indistinguishable is eight times faster. Numerical results presented herein for H2 + H2, CO + CO and H2O + H2O systems indicate good agreement of MQCT calculations with full-quantum calculations from the literature and show that an a posteriori correction, applied after treatment of the collision partners as distinguishable, generally produces good results that agree well with the rigorous treatment of collision partners as indistinguishable. This correction for the cross section includes either multiplication by 2 or a summation over physically indistinguishable processes, depending on the transition type. After this correction, the results of the two treatments agree within 5% for most but may reach 10–20% for some transitions. At low collision energies dominated by scattering resonances, these differences can be larger, but they tend to decrease as collision energy is increased. It is also shown that if the system is artificially forced to follow the same collision path in the indistinguishable and distinguishable treatments, then all differences between the results of the two treatments disappear. This interesting finding gives new insight into the collision process and indicates that the indistinguishability of identical collision partners comes into play through the collision path itself, rather than through matrix elements of inelastic transitions. [ABSTRACT FROM AUTHOR]

We re-introduce a semiclassical methodology based on theories developed for the determination of broadening coefficients. We show that this simple and extremely fast methodology provides results that are in good agreement with results obtained using the more sophisticate MQCT approach. This semiclassical methodology could be an alternative approach which allows to provide large sets of collisional data for very complex molecular systems. It saves time both on the determination of potential energy surfaces and on the collisional dynamical calculations. In addition, this paper provides more complete sets of rotational de-excitation cross-sections and rate coefficients of H2O perturbed by a thermal average of water molecules. Those data can be used in the radiative transfer modelling of cometary atmospheres. [ABSTRACT FROM AUTHOR]

Potential energy and permanent dipole moment surfaces of the electronic ground state of formyl negative ion HCO- are determined for a large number of geometries using the coupled-cluster theory with single and double and perturbative treatment of triple excitations ab initio method with a large basis set. The obtained data are used to construct interpolated surfaces, which are extended analytically to the region of large separations between CO and H- with the multipole expansion approach. We have calculated the energy of the lowest rovibrational levels of HCO- that should guide the spectroscopic characterization of HCO- in laboratory experiments. The study can also help to detect HCO- in the cold and dense regions of the interstellar medium where the anion could be formed through the association of abundant CO with still unobserved H-. [ABSTRACT FROM AUTHOR]

Three-body fragmentation of Na[sup +][sub 3] ions to Na[sup +] + Na(3s)+Na(3s) following excitation by He is studied experimentally and theoretically. The three reduced kinetic energies of the products in the center-of-mass are determined for each fragmentation event, and the results are displayed in a Dalitz plot. The fragmentation involves three adiabatic ¹A' electronic states of Na[sup +][sub 3] that become degenerate at the detector. It is possible to determine the final electronic state for each event, and here we show that each of the three product states appears in a particular sector of the Dalitz plot. Theoretical and experimental Dalitz plots for the three-body fragmentation of Na[sup +][sub 3] are presented, and the results are related to various mechanisms for three-body fragmentation of this system. [ABSTRACT FROM AUTHOR]

The process of Na[sub 3][sup +] cluster ion fragmentation following excitation by a fast He atom is studied using a theoretical procedure developed earlier. The collision with He leaves Na[sub 3][sup +] in any of three electronic states, and each of these can fragment into three product channels (Na[sub 2][sup +]+Na, Na[sub 2]+Na[sup +] and Na+Na+Na[sup +]). Attention is focused on understanding both the dynamics of the Na[sub 3][sup +]-He interaction and the post-collisional fragmentation of the excited cluster. Four simple fragmentation mechanisms are proposed to describe the major features of the process. Contributions of these mechanisms to different fragmentation pathways are determined and their dependence on the initial internal energy of the cluster is studied. Fragmentation intensity maps are calculated and good agreement with experiment is obtained. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The formation of six ozone isotopomers and isotopologues, 16O16O16O, 18O18O18O, 16O16O18O, 18O18O16O, 16O18O16O, and 18O16O18O, has been studied in electron-irradiated solid oxygen 16O2and 18O2(1  1) ices at 11 K. Significant isotope effects were found to exist which involved enrichment of 18O-bearing ozone molecules. The heavy 18O18O18O species is formed with a factor of about six higher than the corresponding 16O16O16O isotopologue. Likewise, the heavy 18O18O16O species is formed with abundances of a factor of three higher than the lighter 16O16O18O counterpart. No isotope effect was observed in the production of 16O18O16O versus18O16O18O. Such studies on the formation of distinct ozone isotopomers and isotopologues involving non-thermal, non-equilibrium chemistry by irradiation of oxygen ices with high energy electrons, as present in the magnetosphere of the giant planets Jupiter and Saturn, may suggest that similar mechanisms may contribute to the 18O enrichment on the icy satellites of Jupiter and Saturn such as Ganymede, Rhea, and Dione. In such a Solar System environment, energetic particles from the magnetospheres of the giant planets may induce non-equilibrium reactions of suprathermal and/or electronically excited atoms under conditions, which are quite distinct from isotopic enrichments found in classical, thermal gas phase reactions. [ABSTRACT FROM AUTHOR]

A general theoretical procedure is developed that treats the fragmentation of a polyatomic cluster ion following excitation by a fast rare gas atom. The process involves multiple electronic states of the cluster ion that are described by the diatomics-in-molecule (DIM) procedure. The interaction of the cluster ion with the rare gas atom is obtained by extending the DIM model and by including three-center interactions. The atom-cluster collision is treated using the semiclassical path procedure and the sudden approximation for the cluster. Finally, the fragmentation is studied using the trajectory surface hopping procedure. The method is applied to the Na[sub 3][sup +]-He system, which can fragment into three product channels. For each channel doubly differential cross sections are computed and compared with the available experimental data. The calculations give much insight into the fragmentation process of Na[sub 3][sup +]. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We developed a general theoretical approach and a user-ready computer code that permit study of the dynamics of collisional energy transfer and ro-vibrational energy exchange in complex molecule-molecule collisions. The method is a mixture of classical and quantum mechanics. The internal ro-vibrational motion of collision partners is treated quantum mechanically using a time-dependent Schrödinger equation that captures many quantum phenomena including state quantization and zero-point energy, propensity and selection rules for state-to-state transitions, quantum symmetry and interference phenomena. A significant numerical speed up is obtained by describing the translational motion of collision partners classically, using the Ehrenfest mean-field trajectory approach. Within this framework a family of approximate methods for collision dynamics is developed. Several benchmark studies for diatomic and triatomic molecules, such as H 2 O and ND 3 collided with He, H 2 and D 2 , show that the results of MQCT are in good agreement with full-quantum calculations in a broad range of energies, especially at high collision energies where they become nearly identical to the full quantum results. Numerical efficiency of the method and massive parallelism of the MQCT code permit us to embrace some of the most complicated collisional systems ever studied, such as C 6 H 6 + He, CH 3 COOH + He and H 2 O + H 2 O. Application of MQCT to the collisions of chiral molecules such as CH 3 CHCH 2 O + He, and to molecule-surface collisions is also possible and will be pursued in the future.

An updated version of the CO + CO potential energy surface from [R. Dawes, X. G. Wang and T. Carrington, J. Phys. Chem. A 2013, 117 , 7612] is presented, that incorporates an improved treatment of the asymptotic behavior. It is found that this new surface is only slightly different from the other popular PES available for this system in the literature [G. W. M. Vissers, P. E. S. Wormer and A. Van Der Avoird, Phys. Chem. Chem. Phys. 2003, 5 , 4767]. The differences are quantified by expanding both surfaces over a set of analytic functions and comparing the behavior of expansion coefficients along the molecule-molecule distance R . It is shown that all expansion coefficients behave similarly, except in the very high energy range at small R where the PES is repulsive. That difference has no effect on low collision-energy dynamics, which is explored via inelastic scattering calculations carried out using the MQCT program which implements the mixed quantum/classical theory for molecular energy exchange processes. The validity of MQCT predictions of state-to-state transition cross sections for CO + CO is also tested by comparison against full-quantum coupled-states calculations. In all cases MQCT gives reliable results, except at very low collision energy where the full-quantum calculations predict strong oscillations of state-to-state transition cross sections due to resonances. For strong transitions with large cross sections, the results of MQCT are reliable, especially at higher collision energy. For weaker transitions, and lower collision energies, the cross sections predicted by MQCT may be up to a factor of 2-3 different from those obtained by full-quantum calculations.

The phenomena of propensity and inverse propensity are explored using time-dependent mixed quantum classical theory, MQCT, in which the rotational motion of the molecule is treated quantum mechanically, whereas the scattering process is described classically. Good agreement with the results of accurate full-quantum calculations is reported for a closed shell approximation to the NO + Ar system. It is shown that MQCT reproduces both phenomena in a broad range of the final states of the molecule and for various initial rotational states, offering a unique time-dependent insight. It permits seeing that both propensity and inverse propensity occur due to efficient depopulation of some states at the early postcollisional stage of the scattering process, when the molecule exists in a coherent superposition of many excited states that span a very broad range of angular momentum quantum numbers, populated by an efficient stepladder process of many consecutive transitions with small Δ j .

The extension of mixed quantum/classical theory (MQCT) to describe collisional energy transfer is developed for a symmetric-top-rotor + linear-rotor system and is applied to ND 3 + D 2 . State-to-state transition cross sections are computed in a broad energy range for all possible processes: when both ND 3 and D 2 molecules are excited or both are quenched, when one is excited while the other is quenched and vice versa , when the ND 3 state changes its parity while D 2 is excited or quenched, and when ND 3 is excited or quenched while D 2 remains in the same state, ground or excited. In all these processes the results of MQCT are found to approximately satisfy the principle of microscopic reversibility. For a set of sixteen state-to-state transitions available from the literature for a collision energy of 800 cm -1 the values of cross sections predicted by MQCT are within 8% of accurate full-quantum results. A useful time-dependent insight is obtained by monitoring the evolution of state populations along MQCT trajectories. It is shown that, if before the collision, D 2 is in its ground state, the excitation of ND 3 rotational states proceeds through a two-step mechanism in which the kinetic energy of molecule-molecule collision is first used to excite D 2 and only then is transferred to the excited rotational states of ND 3 . It is found that both potential coupling and Coriolis coupling play important roles in ND 3 + D 2 collisions.

Manifestation of the quantum interference effect in the oscillation of scattering cross section is explored using the N 2 + O system as a case study. Calculations are carried out for two electronic PESs of the system, for various initial rotational states of N 2 , in a broad range of N 2 + O collision energies and using three theoretical methods: two versions of the approximate mixed quantum/classical theory (MQCT and AT-MQCT) and the accurate full-quantum coupled-channel method (implemented in MOLSCAT). A good agreement between different methods is observed, especially at high energies. Elastic scattering cross-sections oscillate as a function of collision energy, which is the result of quantum interference. The effects of initial rotational excitation and of the PES properties are studied in detail. For the final (thermally averaged) cross sections, both MOLSCAT and MQCT calculations predict a rather regular pattern of quantum oscillations that persist through a broad range of collision energies and expand into the low-energy regime where quantum scattering resonances are common. The difference between cross sections predicted by MQCT and MOLSCAT decreases from ∼8% at low energies to ∼2% at high energies. Experimental data available at high collision energies are well reproduced.

A new version of the MQCT program is presented, which includes an important addition, adiabatic trajectory approximation (AT-MQCT), in which the equations of motion for the classical and quantum parts of the system are decoupled. This method is much faster, which permits calculations for larger molecular systems and at higher collision energies than was possible before. AT-MQCT is general and can be applied to any molecule + molecule inelastic scattering problem. A benchmark study is presented for H 2 O + H 2 O rotational energy transfer, an important asymmetric-top rotor + asymmetric-top rotor collision process, a very difficult problem unamenable to the treatment by other codes that exist in the community. Our results indicate that AT-MQCT represents a reliable computational tool for prediction of collisional energy transfer between the individual rotational states of two molecules, and this is valid for all combinations of state symmetries (such as para and ortho states of each collision partner).

In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer., (© 2022. The Author(s).)

Reconstructing the history of biological productivity and atmospheric oxygen partial pressure ( p O 2 ) is a fundamental goal of geobiology. Recently, the mass-independent fractionation of oxygen isotopes (O-MIF) has been used as a tool for estimating p O 2 and productivity during the Proterozoic. O-MIF, reported as Δ' 17 O, is produced during the formation of ozone and destroyed by isotopic exchange with water by biological and chemical processes. Atmospheric O-MIF can be preserved in the geologic record when pyrite (FeS 2 ) is oxidized during weathering, and the sulfur is redeposited as sulfate. Here, sedimentary sulfates from the ∼1.4-Ga Sibley Formation are reanalyzed using a detailed one-dimensional photochemical model that includes physical constraints on air-sea gas exchange. Previous analyses of these data concluded that p O 2 at that time was <1% PAL (times the present atmospheric level). Our model shows that the upper limit on p O 2 is essentially unconstrained by these data. Indeed, p O 2 levels below 0.8% PAL are possible only if atmospheric methane was more abundant than today (so that p CO 2 could have been lower) or if the Sibley O-MIF data were diluted by reprocessing before the sulfates were deposited. Our model also shows that, contrary to previous assertions, marine productivity cannot be reliably constrained by the O-MIF data because the exchange of molecular oxygen (O 2 ) between the atmosphere and surface ocean is controlled more by air-sea gas transfer rates than by biological productivity. Improved estimates of p CO 2 and/or improved proxies for Δ' 17 O of atmospheric O 2 would allow tighter constraints to be placed on mid-Proterozoic p O 2 ., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

A numerical approach is developed to capture the effect of rotation-vibration coupling in a practically affordable way. In this approach only a limited number of adjacent rotational components are considered to be coupled, while the couplings to other rotational components are neglected. This partially coupled (PC) approach permits to reduce the size of Hamiltonian matrix significantly, which enables the calculations of ro-vibrational states above dissociation threshold (scattering resonances) for large values of total angular momentum. This method is employed here to reveal the role of the Coriolis effect in the ozone formation reaction at room temperature, dominated by large values of total angular momentum states, on the order of J = 24 and 28. We found that, overall, the effect of ro-vibrational coupling is not minor for large J . Compared to the results of symmetric top rotor approximation, where the ro-vibrational coupling is neglected, we found that the widths of scattering resonances, responsible for the lifetimes of metastable ozone states, remain nearly the same (on average), but the number of these states increases by as much as 20%. We also found that these changes are nearly the same in symmetric and asymmetric ozone isotopomers 16 O 18 O 16 O and 16 O 16 O 18 O. Therefore, based on the results of these calculations, the Coriolis coupling does not seem to favor the formation of asymmetric ozone molecules and thus cannot be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes.

A theoretical approach is developed for the description of all possible recombination pathways in the ozone forming reaction, without neglecting any process a priori , and without decoupling the individual pathways one from another. These pathways become physically distinct when a rare isotope of oxygen is introduced, such as 18 O, which represents a sensitive probe of the ozone forming reaction. Each isotopologue of O 3 contains two types of physically distinct entrance channels and two types of physically distinct product wells, creating four recombination pathways. Calculations are done for singly and doubly substituted isotopologues of ozone, eight rate coefficients total. Two pathways for the formation of asymmetric ozone isotopomer exhibit rather different rate coefficients, indicating large isotope effect driven by ΔZPE-difference. Rate coefficient for the formation of symmetric isotopomer of ozone (third pathway) is found to be in between of those two, while the rate of insertion pathway is smaller by two orders of magnitude. These trends are in good agreement with experiments, for both singly and doubly substituted ozone. The total formation rates for asymmetric isotopomers are found to be somewhat larger than those for symmetric isotopomers, but not as much as in the experiment. Overall, the distribution of lifetimes is found to be very similar for the metastable states in symmetric and asymmetric ozone isotopomers.

Scattering resonances above dissociation threshold are computed for four isotopically substituted ozone species: 16O18O16O, 16O16O18O, 18O16O18O and 16O18O18O, using a variational method with accurate treatment of the rotation-vibration coupling terms (Coriolis effect) for all values of the total angular momentum J from 0 to 4. To make these calculations numerically affordable, a new approach was developed which employs one vibrational basis set optimized for a typical rotational excitation (J,Λ), to run coupled rotation-vibration calculations at several desired values of J. In order to quantify the effect of Coriolis coupling, new data are contrasted with those computed using the symmetric-top rotor approximation, where the rotation-vibration coupling terms are neglected. It is found that, overall, the major properties of scattering resonances (such as their lifetimes, the number of these states, and their cumulative partition function Q) are all influenced by the Coriolis effect and this influence grows as the angular momentum J is raised. However, it is found that the four isotopically substituted ozone molecules are affected roughly equally by the Coriolis coupling. When the ratio η of partition functions for asymmetric over symmetric ozone molecules is computed, the Coriolis effect largely cancels, and this cancelation seems to occur for all values of J. Therefore, it does not seem grounded to attribute any appreciable mass-independent symmetry-driven isotopic fractionation to the Coriolis coupling effect.

Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only. For many physics and chemistry problems, the diagonalization of complex matrices is required. For example, the calculation of quantum scattering resonances can be formulated as a complex eigenvalue problem where the real part of the eigenvalue is the resonance energy and the imaginary part is proportional to the resonance width. In the present work, we generalize the QAE to treat complex matrices: first complex Hermitian matrices and then complex symmetric matrices. These generalizations are then used to compute a quantum scattering resonance state in a 1D model potential for O + O collisions. These calculations are performed using both a software (classical) annealer and hardware annealer (the D-Wave 2000Q). The results of the complex QAE are also benchmarked against a standard linear algebra library (LAPACK). This work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device.

A hierarchy of approximate methods is proposed for solving the equations of motion within a framework of the mixed quantum/classical theory (MQCT) of inelastic molecular collisions. Of particular interest is a limiting case: the method in which the classical-like equations of motion for the translational degrees of freedom (scattering) are decoupled from the quantum-like equations for time evolution of the internal molecular states (rotational and vibrational). In practice, trajectories are pre-computed during the first step of calculations with driving forces determined solely by the potential energy surface of the entrance channel, which is an adiabatic trajectory approximation. Quantum state-to-state transition probabilities are computed in the second step of calculations with an expanded basis and very efficient step-size adjustment. Application of this method to H 2 O + H 2 rotationally inelastic scattering shows a significant computational speedup by 2 orders of magnitude. The results of this approximate propagation scheme are still rather accurate, as demonstrated by benchmarking against more rigorous calculations in which the quantum and classical equations of motion are held coupled and against the full-quantum coupled-channel calculations from the literature. It is concluded that the AT-MQCT method (the adiabatic trajectory version of MQCT) represents a promising tool for the computational treatment of molecular collisions and energy exchange.

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational-vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric ( 18 O 16 O 18 O) and asymmetric ( 18 O 18 O 16 O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric ( 16 O 18 O 16 O) and asymmetric ( 16 O 16 O 18 O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

Several alternative methods for the description of the interaction between rotation and vibration are compared and contrasted using hyperspherical coordinates for a triatomic molecule. These methods differ by the choice of the z -axis and by the assumption of a prolate or oblate rotor shape of the molecule. For each case, a block-structure of the rotational-vibrational Hamiltonian matrix is derived and analyzed, and the advantages and disadvantages of each method are made explicit. This theory is then employed to compute ro-vibrational spectra of singly substituted ozone; roughly, 600 vibrational states of 16 O 18 O 16 O and 16 O 16 O 18 O isomers combined, with rotational excitations up to J = 5 and both inversion parities (21600 coupled ro-vibrational states in total). Splittings between the states of different parities, so-called K -doublings, are calculated and analyzed. The roles of the asymmetric-top rotor term and the Coriolis coupling term are determined individually, and it is found that they both affect these splittings, but in the opposite directions. Thus, the two effects partially cancel out, and the residual splittings are relatively small. Energies of the ro-vibrational states reported in this work for 16 O 18 O 16 O and 16 O 16 O 18 O are in excellent agreement with literature (available for low-vibrational excitation). New data obtained here for the highly excited vibrational states enable the first systematic study of the Coriolis effect in symmetric and asymmetric isotopomers of ozone.