Rotational Excitations in CO–CO Collisions at Low Temperature: Time-Independent and Multiconfigurational Time-Dependent Hartree Calculations

Mixed quantum/classical theory for rotationally inelastic scattering of identical collision partners revised

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.

Mixed quantum/classical theory (MQCT) approach to the dynamics of molecule-molecule collisions in complex systems

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 H2O and ND3 collided with He, H2 and D2, 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 C6H6 + He, CH3COOH + He and H2O + H2O. Application of MQCT to the collisions of chiral molecules such as CH3CHCH2O + He, and to molecule-surface collisions is also possible and will be pursued in the future.

Mixed quantum/classical calculations of rotationally inelastic scattering in the CO + CO system: a comparison with fully quantum results

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.

Symmetry Breaking: A Classic Example of Quantum Interference Captured by Mixed Quantum/Classical Theory

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 Δj.

Rovibrational states calculations of the H2O-HCN heterodimer with the multiconfiguration time dependent Hartree method

Water and hydrogen cyanide are two of the most common species in space and the atmosphere with the ability of binding to form dimers such as H2O-HCN. In the literature, while calculations characterizing various properties of the H2O-HCN cluster (equilibrium distance, vibrational frequencies and rotational constants) have been done in the past, extensive calculations of the rovibrational states of this system using a reliable quantum dynamical approach have yet to be reported. In this work, we intend to mend that by performing the first calculation of the rovibrational states of the H2O-HCN van der Waals complex on a recently developed potential energy surface. We use the block improved relaxation procedure implemented in the Heidelberg MultiConfiguration Time-Dependent Hartree (MCTDH) package to compute the states of the H2O-HCN isomer, from which we extract the transition frequencies and rotational constants of the complex. We further adapt an approach first suggested by Wang and Carrington-and supported here by analysis routines of the Heidelberg MCTDH package-to properly characterize the computed rovibrational states. The subsequent assignment of rovibrational states was done by theoretical analysis and visual inspection of the wavefunctions. Our simulations provide a Zero Point Energy (ZPE) and intermolecular vibrational frequencies in good agreement with past ab initio calculations. The transition frequencies and rotational constants obtained from our simulations match well with the available experimental data. This work has the broad aim to propose the MCTDH approach as a reliable option to compute and characterize rovibrational states of van der Waals complexes such as the current one.

Collisonal energy transfer in the CO-CO system

An accurate determination of the physical conditions in astrophysical environments relies on the modeling of molecular spectra. In such environments, densities can be so low ($n << 10^{10}$ cm$^{-3}$) that...

Molecular square dancing in CO-CO collisions

Knowledge of rotational energy transfer (RET) involving carbon monoxide (CO) molecules is crucial for the interpretation of astrophysical data. As of now, our nearly perfect understanding of atom-molecule scattering shows that RET usually occurs by only a simple "bump" between partners. To advance molecular dynamics to the next step in complexity, we studied molecule-molecule scattering in great detail for collision between two CO molecules. Using advanced imaging methods and quasi-classical and fully quantum theory, we found that a synchronous movement can occur during CO-CO collisions, whereby a bump is followed by a move similar to a "do-si-do" in square dancing. This resulted in little angular deflection but high RET to both partners, a very unusual combination. The associated conditions suggest that this process can occur in other molecule-molecule systems.

The Leiden Atomic and Molecular Database (LAMDA): Current Status, Recent Updates, and Future Plans

The Leiden Atomic and Molecular Database (LAMDA) collects spectroscopic information and collisional rate coefficients for molecules, atoms, and ions of astrophysical and astrochemical interest. We describe the developments of the database since its inception in 2005, and outline our plans for the near future. Such a database is constrained both by the nature of its uses and by the availability of accurate data: we suggest ways to improve the synergies among users and suppliers of data. We summarize some recent developments in computation of collisional cross sections and rate coefficients. We consider atomic and molecular data that are needed to support astrophysics and astrochemistry with upcoming instruments that operate in the mid- and far-infrared parts of the spectrum.

Rotationally inelastic scattering of O3–Ar: state-to-state rates with the multiconfigurational time dependent Hartree method

The rates of state-changing collisions are compared for different isotopologues of ozone from quantum scattering calculations with the MCTDH method.

State-to-state inelastic rotational cross sections in five-atom systems with the multiconfiguration time dependent Hartree method

We present a MultiConfiguration Time Dependent Hartree (MCTDH) method as an attractive alternative approach to the usual quantum close-coupling method that approaches some computational limits in the calculation of rotational excitation (and de-excitation) between polyatomic molecules (here collisions between triatomic and diatomic rigid molecules). We have performed a computational investigation of the rotational (de-)excitation of the benchmark rigid rotor H₂O-H₂ system on a recently developed Potential Energy Surface of the complex using the MCTDH method. We focus here on excitations and de-excitations from the 0₀₀, 1₁₁, and 1₁₀ states of H₂O with H₂ in its ground rotational state, looking at all the potential transitions in the energy range 1-200 cm^-1. This work follows a recently completed study on the H₂O-H₂ cluster where we characterized its spectroscopy and more generally serves a broader goal to describe inelastic collision processes of high dimensional systems using the MCTDH method. We find that the cross sections obtained from the MCTDH calculations are in excellent agreement with time independent calculations from previous studies but does become challenging for the lower kinetic energy range of the de-excitation process: that is, below approximately 20 cm^-1 of collision energy, calculations with a relative modest basis become unreliable. The MCTDH method therefore appears to be a useful complement to standard approaches to study inelastic collision for various collision partners, even at low energy, though performing better for rotational excitation than for de-excitation.

Interaction of H2O with CO: potential energy surface, bound states and scattering calculations

We present the first scattering calculations for the H₂O–CO system based on a high accuracy potential energy surface.

Infrared spectrum and intermolecular potential energy surface of the CO–O2 dimer

The spectrum of the weakly-bound radical complex CO–O₂ is studied for the first time.

MQCT. I. Inelastic Scattering of Two Asymmetric-Top Rotors with Application to H2O + H2O

A mixed quantum/classical theory (MQCT) for the inelastic collision of two asymmetric-top rotor molecules is developed. In this method, the quantum state-to-state transitions between the rotational states of molecules (internal) are treated quantum mechanically using the time-dependent Schrodinger equation, whereas their relative translational motion (responsible for scattering) is treated classically, using the average trajectory approach. Two versions of the formula for transition matrix elements are presented: a straightforward approach that uses numerical multidimensional quadrature over all the internal degrees of freedom and a more standard analytic approach that uses the expansion of the PES over the basis set of spherical harmonics. Adaptation to the case of identical molecules scattering is presented and is applied to the rotational excitation of two water molecules, H₂O + H₂O, using the PES from recent literature. Calculations of collisional excitation from the ground state of the system into a number of low-lying excited rotational states are carried out in a broad range of energies. Analysis of computed opacity functions shows a rather unusual scattering regime, dominated by a strong anisotropic long-range interaction (dipole-dipole). The coupled-states (CS) approximation is tested and found to agree semiquantitatively (within a factor of 2) with the fully coupled version of the method. Differential cross sections for the elastic scattering indicate a very narrow forward scattering peak.

Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them

In order to identify the origin of possible errors in the mixed quantum/classical approach to inelastic scattering [A. Semenov and D. Babikov, J. Chem. Phys. 140, 044306 (2014) and A. Semenov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 141, 114304 (2014)], a simplified model is considered that consists of one intermolecular degree of freedom and two intramolecular states, coupled by a simple potential. For this system, analytic derivations are carried out to determine (i) the exact quantum mechanical solution of the inelastic scattering problem, (ii) a simplified version of it with all oscillatory terms neglected, and (iii) the Ehrenfest solution in which the translational motion is described by the mean-field trajectory while the internal molecular motion is treated by the time-dependent Schrodinger equation. It is shown that the appropriate choice of velocity for the mean-field trajectory permits to enforce microscopic reversibility and gives results in excellent agreement with full-quantum results. The average velocity method of Billing is rigorously derived as a limiting case (of this more general approach), when reversibility is enforced locally, at the initial moment of time only. It is demonstrated that errors of state-to-state transition probabilities in the Ehrenfest approach occur at lower values of total energy E if the magnitudes of excitation energy ΔE, potential energy difference between the two states ΔV, and coupling of two states V₁₂ are large. Possible ways of applying this concept to rotational transitions in real molecules are explored, using examples from CO + CO inelastic scattering.

Inelastic Scattering of Identical Molecules within Framework of the Mixed Quantum/Classical Theory: Application to Rotational Excitations in H2 + H2

Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes.