Induced Dipole Surfaces Research Articles

Trajectory-based Simulation of Far-infrared Collision-induced Absorption Profiles of CH4–N2 for Modeling Titan’s Atmosphere

Abstract We report the results of the trajectory-based simulation of far-infrared collision-induced absorption (CIA) due to CH4–N2 pairs at temperatures between 70 and 400 K. Our analysis utilizes recently calculated high-level potential energy and induced dipole surfaces. Treating collision partners as rigid rotors, the time evolution of interaction-induced dipole is accumulated over a vast ensemble of classical trajectories and subsequently transformed into a CIA spectrum via Fourier transform. In our calculations, both bound and unbound states are properly accounted for, and the rigorous theory of lower-order spectral moments is addressed to check the accuracy of simulated profiles. Classically derived trajectory-based profiles are subject to two approximate desymmetrization procedures so that resulting profiles conform to the quantum principle of detailed balance. The simulated profiles are compared to laboratory measurements and employed for modeling Titan’s spectra in the 50–500 cm−1 range. Based on the desymmetrized simulated profiles, a new semiempirical model for CH4–N2 CIA is proposed for modeling Titan’s infrared spectra. Synthetic spectra derived using this model yield an excellent agreement with the data recorded by the Composite Infrared Spectrometer aboard the Cassini spacecraft at low and high emission angles.

Simulation of collision-induced absorption spectra based on classical trajectories and ab initio potential and induced dipole surfaces. II. CO2-Ar rototranslational band including true dimer contribution.

This paper presents further development of the new semi-classical trajectory-based formalism described in Paper I [Chistikov et al., J. Chem. Phys. 151, 194106 (2019)]. We report the results of simulation and analysis of the low-frequency collision-induced absorption (CIA) in CO2-Ar, including its true dimer component. Our consideration relies on the use of ab initio intermolecular potential energy and induced dipole surfaces for CO2-Ar calculated in an assumption of a rigid CO2 structure using the CCSD(T) method. The theory, the details of which are reported in Paper I [Chistikov et al., J. Chem. Phys. 151, 194106 (2019)], permits taking into account the effect of unbound and quasi-bound classical trajectories on the CIA in the range of a rototranslational band. This theory is largely extended by trajectory-based simulation of the true bound dimer absorption in the present paper. The spectra are obtained from a statistical average over a vast ensemble of classical trajectories restricted by properly chosen domains in the phase space. Rigorous classical theory is developed for two low-order spectral moments interpreted as the Boltzmann-weighted average of the respective dipole functions. These spectral moments were then used to check the accuracy of our trajectory-based spectra, for which both spectral moments can be evaluated independently in terms of specific integrals over the trajectory-based calculated spectral profiles. Good agreement between the spectral moments calculated as integrals over the frequency domain or the phase space largely supports the reliability of our simulated CIA spectra, which conform with the available microwave and far-infrared observations.

Continuum absorption of millimeter waves in nitrogen

We report the results of experimental study for the N2 absorption in the millimeter wavelength range at pressure and temperature ranging, respectively, from 750 to 1500 Torr and from 265 to 310 K. The obtained data are shown to be in a good agreement with the previously published experimental results, as well as with the predictions issued from available empirical models of nonresonant absorption and from the simulation of the N2–N2 rototranslational collision-induced absorption performed recently using the classical trajectories method relying on complete ab initio potential and induced dipole surfaces. Analysis of the first spectral moments leads to a conclusion that the role of true bound (N2)2 dimer absorption is negligible at least in the range of atmospheric temperatures. New experimental data reported in this paper are supported by our theoretical modelling being however somewhat in excess of the data presented in the HITRAN/CIA database for the same spectral range. We consider our data as an update of the previously available so-called “dry” atmospheric continuum which is conventionally employed nowadays in the mm-waves propagation models.

Simulation of collision-induced absorption spectra based on classical trajectories and ab initio potential and induced dipole surfaces. I. Case study of N2-N2 rototranslational band.

This paper presents theoretical formalism and some results of the collision-induced absorption (CIA) spectral simulation based on the classical trajectory analysis. Our consideration relies on the use of ab initio potential energy and dipole moment surfaces for two interacting rigid monomers. Rigorous intermolecular Hamiltonian is represented and used in the body-fixed reference frame. The complete set of dynamical equations with Boltzmann-weighted initial conditions is solved to render a large number of classical trajectories. The spectral shape is calculated as an ensemble-averaged Fourier spectrum issued from the time-dependent induced dipole along individual scattering trajectories. Considering a pair of N2 molecules as an example, we have calculated the rototranslational CIA band profiles at T = 78, 89, 109, 129, 149, 179, 228, 300, and 343 K. The classical trajectory-based spectral shape was corrected to satisfy the quantum principle of detailed balance. Good accuracy of our semiclassical approach was demonstrated by comparison with available experimental data as well as with results of the previously published purely quantum simulation by Karman et al. [J. Chem. Phys. 142, 084306 (2015)] in which the same ab initio calculated N2-N2 potential energy and induced dipole moment surfaces were used.

Interacting He and Ar atoms: Revised theoretical interaction potential, dipole moment, and collision-induced absorption spectra

Coupled cluster quantum chemical calculations of the potential energy surface and the induced dipole surface are reported for the He-Ar van der Waals collisional complex. Spectroscopic parameters are derived from global analytical fits while an accurate value for the long-range dipole coefficient D7 is obtained by perturbation methods. Collision-induced absorption spectra are computed quantum mechanically and compared with existing measurements.

Collision-induced spectra and current astronomical research

Collision-induced spectra are the spectra of complexes of two or more atoms or molecules in a “fly-by” collisional encounter. Collision-induced absorption (CIA) has been observed in many dense gases and gas mixtures, in most cases at infrared frequencies in the form of quasi continua, and also in liquids and solids. CIA spectra of several binary complexes have been computed using modern quantum chemical methods, combined with molecular scattering theory, which couples the collisional complex to the radiation field as usual in other spectroscopic work. Binary collisional systems, such as H2 interacting with another H2 molecule, or with a helium or hydrogen atom, are first candidates for such computational work, owing to their small number of electrons and the astrophysical interest in such systems. The computed CIA spectra are found to be in close agreement with existing laboratory measurements of such spectra. Laboratory measurements exist at a limited selection of temperatures around 300 K and lower, but theory currently also provides CIA data for temperatures up to 9000 K and for higher frequencies (well into the visible), on a dense grid of temperatures and frequencies. For such calculations, detailed potential energy surfaces (PES) of the supermolecular complexes, along with the induced dipole surfaces (IDS), are needed so that the rotovibrational matrix elements of PES and IDS may be computed for the molecules involved, which may be highly rotovibrationally excited. Modern astronomical research needs opacity tables for analyses of the atmospheres of “cool” objects, such as cool white dwarfs, solar and extrasolar planets and their big moons, cool main sequence stars, and “first” stars, which are briefly described in a concluding section.

Ab initio and multipolar characterisation of the induced dipole surface for CH4–CH4: Application to dipole-forbidden absorption in the Titan’s atmosphere

The present paper aims to further characterise the induced dipole surface for CH4–CH4 through either multipolar expansion or CCSD(T) ab initio calculations. Our calculations extend to evaluation of the collision-induced integrated intensity of absorption in the far infrared as well as to classical determination of the equilibrium constant for true bound methane dimer formation. Height profiles are simulated for the dimer mole fraction as well as for the portion of true bound dimer absorption in the integrated collision-induced absorption taking the Titan’s atmosphere as an example.

CCSD(T) potential energy and induced dipole surfaces for N2–H2(D2): Retrieval of the collision-induced absorption integrated intensities in the regions of the fundamental and first overtone vibrational transitions

The present work aims at ab initio characterization of the integrated intensity temperature variation of collision-induced absorption (CIA) in N(2)-H(2)(D(2)). Global fits of potential energy surface (PES) and induced dipole moment surface (IDS) were made on the basis of CCSD(T) (coupled cluster with single and double and perturbative triple excitations) calculations with aug-cc-pV(T,Q)Z basis sets. Basis set superposition error correction and extrapolation to complete basis set (CBS) limit techniques were applied to both energy and dipole moment. Classical second cross virial coefficient calculations accounting for the first quantum correction were employed to prove the quality of the obtained PES. The CIA temperature dependence was found in satisfactory agreement with available experimental data.

Infrared absorption by collisional H2–He complexes at temperatures up to 9000 K and frequencies from 0 to 20 000 cm−1

Quantum chemical methods have been used elsewhere to obtain the potential energy surface (PES) and the induced dipole surface (IDS) of H(2)-He collisional complexes at eight different H-H bond distances, fifteen atom-molecule separations, and 19 angular orientations each [X. Li, A. Mandal, E. Miliordos, and K. L. C. Hunt, J. Chem. Phys. 136, 044320 (2012)]. An atom-molecule state-to-state scattering formalism is employed, which couples the collisional molecular complex to the electromagnetic radiation field. In this way, we obtain theoretical collision-induced absorption (CIA) spectra of H(2)-He complexes for frequencies from 0 to 20,000 cm(-1) and temperatures up to 9000 K. The work is based on the fundamental theory and is motivated by current research of certain astronomical objects, such as cool white dwarf stars, cool main sequence stars, M dwarfs, exoplanets, so-called "first" stars. We compare our theoretical results to existing laboratory measurements of CIA spectra; very close agreement of theory and measurement is observed. We also discuss similar previous theoretical efforts.

Comparison of the Calculated Collision-Induced Absorption Spectra by Dense Hydrogen-Helium, Deuterium-Helium, and Tritium-Helium Gas Mixtures

We have recently determined the induced dipole surface (IDS) and potential energy surface (PES) of collisional H2-He complexes. We have used these surfaces to compute the binary collision-induced absorption spectra of H2 molecules interacting with He atoms and of D2 molecules interacting with He atoms. Here we extend these calculations to the case of T2 molecules interacting with He atoms. Whereas the electronic structure of X2-He is virtually the same for all hydrogen isotopes X = H, D, or T, the collisional dynamics and molecular scattering wave functions are different for the different collisional pairs. We have calculated spectra up to a temperature of 9000 K and frequencies up to 20,000 cm−1. Here we compare the calculated collision-induced absorption spectra for the different hydrogen isotopes. While we have observed reasonable agreement between our calculations and laboratory measurements for the collisional H2-He and D2-He complexes, there are no laboratory measurements for T2-He collisional complexes, and one must rely on the fundamental theory, supported by the agreement between theory and experiment for the other isotopes.

Note: Collision-induced infrared absorption by gaseous deuterium

A recent potential energy surface and an induced dipole surface obtained by advanced quantum chemical methods for collisional H2–H2 complexes [Li et al., Int. J. Spectroscopy.2010 (to be published)] are used to compute the infrared collision-induced absorption spectrum of dense deuterium gas. The computed spectra are in agreement with existing laboratory measurements.

Is sonoluminescence due to collision-induced emission?

We estimate the collision-induced emission (CIE) intensity and profile in the visible and near UV region of the spectrum of ${N}_{2}\ensuremath{-}X$ pairs where $X$ represents another ${\mathrm{N}}_{2}$ molecule or an argon atom, etc. of shock waves believed to exist in sonoluminescence experiments. Calculated profiles consist of superimposed high overtone bands and resemble the measured profiles. Intensities calculated on the basis of a few, simple assumptions concerning the induced dipole surface compare favorably with measurements. The agreement obtained suggests that CIE is an attractive alternative to bremsstrahlung to explain sonoluminescence. The CIE source is optically thin, and the spectral emission profile is not related to Planck's law.

Is sonoluminescence collision-induced emission?

An estimate is attempted of the collision-induced emission (CIE) intensity and spectral profile in the visible and near UV region of the spectrum of N2–χ pairs, where χ represents another N2 molecule or an argon atom, etc., for conditions that correspond to shock waves believed to exist in sonoluminescence experiments. Calculated profiles consist of superimposed high overtone bands and resemble measured profiles of sonoluminescence spectra. The intensities calculated on the basis of a few, simple assumptions concerning the induced dipole surface compare favorably with measurements. The agreement obtained suggests that collision-induced emission is a viable or even an attractive alternative to bremsstrahlung to explain sonoluminescence. According to the theory presented, the CIE source is optically thin so that the spectral emission profile is not related to Planck’s radiation law.