Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF4

Using nested tensor train contracted basis functions with group theoretical techniques to compute (ro)-vibrational spectra of molecules with non-Abelian groups

In this paper, we use nested tensor-train contractions to compute vibrational and ro-vibrational energy levels of molecules with five and six atoms. At each step, we fully exploit symmetry by using symmetry adapted basis functions obtained from an irreducible tensor method. Contracted basis functions are determined by diagonalizing reduced dimensional Hamiltonian matrices. The size of matrices of eigenvectors, used to account for coupling between groups of coordinates, is reduced by discarding rows and columns. The size of the matrices that must be diagonalized is thus substantially reduced, making it possible to use direct eigensolvers, even for molecules with five and six atoms. The symmetry-adapted contracted vibrational basis functions have been used to compute J = 0 energy levels of the CH3CN (C3v) and J > 0 levels of CH4.

Unrivaled accuracy in measuring rotational transitions of greenhouse gases: THz CRDS of CF4

Tetrafluoromethane CF4 is the most abundant perfluorocarbon in the atmosphere, where it is designated as PFC-14. This greenhouse gas is very stable, has an atmospheric lifetime of 50 000 years, and a high greenhouse warming potential 6500 times that of CO2. Over the last 15 years, its atmospheric concentration has increased at a rate of 0.8 ppt per year. The accurate quantification of CF4 is key to understanding the contribution of its emissions to the radiative forcing budget, and the most precise spectroscopic parameters possible are hence required. In this study, a novel high finesse THz cavity, providing an interaction length in excess of 1 km, has enabled highly resolved spectra, and quantification of the weak transitions of CF4 by cavity ring-down spectroscopy (CRDS). More than 50 pure rotational P6 - P6 : ν3 - ν3 lines of CF4 have been measured, yielding both position and intensity with unequalled precision. Several tetrahedral splittings are fully resolved and measured with sub-MHz accuracy. Moreover, CRDS-THz allows determining absolute intensities and, using a global fit of the ν2 polyad series, a CF4 dipole parameter, namely 3,3, has been fitted to 106.38(53) mD. This value is in very good agreement with that of the ab initio-based parameter deduced from a dipole moment surface. For the first time, a set of ab initio effective dipole moment parameters is derived for the computation of the transitions of the type Pn - Pn (n = 0,…, 8) and the resulting line list composed of 25 863 transitions can be used to model the whole CF4 rotational spectrum. Finally, the TFMeCaSDa database is updated and is available for future spectroscopic and monitoring activities.

Accurate ab initio potential energy surface, rovibrational energy levels and resonance interactions of triplet ( X ~ 3 B1 ) methylene

In this work, we report rovibrational energy levels for four isotopologues of methylene (CH2 , CHD, CD2 , and 13 CH2 ) in their ground triplet electronic state (X ~ 3 B1 ) from variational calculation up to ~10,000 cm-1 and using a new accurate ab initio potential energy surface (PES). Triplet methylene exhibits a large-amplitude bending vibration and can reach a quasilinear configuration due to its low barrier (~2000 cm-1 ). To construct the ab initio PES, the Dunning's augmented correlation-consistent core-valence orbital basis sets were employed up to the sextuple-ζ quality [aug-cc-pCVXZ, X = T, Q, 5, and 6] combined with the single- and double-excitation unrestricted coupled cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. We have shown that the accuracy of the ab initio energies is further improved by including the corrections due to the scalar relativistic effects, DBOC and high-order electronic correlations. For the first time, all the available experimental rovibrational transitions were reproduced with errors less than 0.12 cm-1 , without any empirical corrections. Unlike more "traditional" nonlinear triatomic molecules, we have shown that even the energies of the ground vibrational state (000) with rather small rotational quantum numbers are strongly affected by the very pronounced rovibrational resonance interactions. Accordingly, the polyad structure of the vibrational levels of CH2 and CD2 was analyzed and discussed. The comparison between the energy levels obtained from the effective Watson A-reduced Hamiltonian, from the generating-function approach and from a variational calculation was given.

A numerical-tensorial "hybrid" nuclear motion Hamiltonian and dipole moment operator for spectra calculation of polyatomic nonrigid molecules

The analysis and modeling of high-resolution spectra of nonrigid molecules require a specific Hamiltonian and group-theoretical formulation that differs significantly from that of more familiar rigid systems. Within the framework of Hougen-Bunker-Johns (HBJ) theory, this paper is devoted to the construction of a nonrigid Hamiltonian based on a suitable combination of numerical calculations for the nonrigid part in conjunction with the irreducible tensor operator method for the rigid part. For the first time, a variational calculation from ab initio potential energy surfaces is performed using the HBJ kinetic energy operator built from vibrational, large-amplitude motion, and rotational tensor operators expressed in terms of curvilinear and normal coordinates. Group theory for nonrigid molecules plays a central role in the characterization of the overall tunneling splittings and is discussed in the present approach. The construction of the dipole moment operator is also examined. Validation tests consisting of a careful convergence study of the energy levels as well as a comparison of results obtained from independent computer codes are given for the nonrigid molecules CH2, CH3, NH3, and H2O2. This work paves the way for the modeling of high-resolution spectra of larger nonrigid systems.

New Theoretical Infrared Line List for the Methyl Radical with Accurate Vibrational Band Origins from High-Level Ab Initio Calculations

In the present work, high-level ab initio calculations were carried out for the ground electronic state of the methyl radical (CH₃). Dunning's augmented correlation-consistent orbital basis sets were employed up to the quintuple-ζ valence quality with the core-valence electron correlation [aug-cc-pCV5Z] combined with the single- and double-excitation unrestricted coupled-cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. The explicitly correlated version of the coupled-cluster approach [RHF-UCCSD(T)-F12x{x = a, b}] was additionally applied with the core-valence cc-pCVQZ-F12 basis set in order to study convergence with respect to the basis set size. The contributions beyond the coupled-cluster level of the theory like Douglas-Kroll-Hess scalar relativistic Hamiltonian, diabatic Born-Oppenheimer corrections, and high-order electronic correlations have been included into the ab initio potential energy surfaces (PESs). It is shown that the theoretical band origins of CH₃ converge gradually to the experimental values when applying the ab initio PESs using the aug-cc-pCVXZ [X = T, Q, and 5] basis sets. For the first time, all available experimental band origins of the gaseous CH₃ are reproduced within an accuracy of 0.2 cm^-1 using a newly developed PES extrapolated to the complete basis set limit [CBS(TQ5Z)]. The reached accuracy is one order of magnitude better than that of the best available calculations. A new theoretical infrared line list was generated for astrophysical applications using an ab initio dipole moment surface computed at the RHF-UCCSD(T)/aug-cc-pCVQZ level of the theory. The manifestation of a large-amplitude motion in CH₃ is also discussed.

Novel methodology for systematically constructing global effective models from ab initio-based surfaces: A new insight into high-resolution molecular spectra analysis

In this paper, a novel methodology is presented for the construction of ab initio effective rotation-vibration spectroscopic models from potential energy and dipole moment surfaces. Non-empirical effective Hamiltonians are obtained via the block-diagonalization of selected variationally computed eigenvector matrices. For the first time, the derivation of an effective dipole moment is carried out in a systematic way. This general approach can be implemented quite easily in most of the variational computer codes and turns out to be a clear alternative to the rather involved Van Vleck perturbation method. Symmetry is exploited at all stages to translate first-principles calculations into a set of spectroscopic parameters to be further refined on experiment. We demonstrate on H₂CO, PH₃, CH₄, C₂H₄, and SF₆ that the proposed effective model can provide crucial information to spectroscopists within a very short time compared to empirical spectroscopic models. This approach brings a new insight into high-resolution spectrum analysis of polyatomic molecules and will be also of great help in the modeling of hot atmospheres where completeness is important.

New Ab Initio Potential Energy Surfaces for NH3 Constructed from Explicitly Correlated Coupled-Cluster Methods

Accurate calculation of ab initio potential energy surfaces (PESs) for the NH₃ molecule is a difficult task because of the poor convergence of the standard CCSD(T) method with respect to the basis size. Currently, the best available NH₃ PESs contain empirically refined parameters. In this paper, we show that CCSD(T)/aug-cc-pCV6Z calculations are not sufficient to properly describe the PES over a large range of nuclear configurations. However, the PES obtained by the extrapolation of the CCSD(T)/aug-cc-pCVXZ (X = T, Q, 5, and 6) energies to the complete basis set limit is closer to that based on the explicitly correlated CCSD(T)-F12a method using the cc-pCVQZ-F12 orbital basis set. All of the ab initio PESs constructed in this work include the following corrections: one electron relativistic effects, diagonal Born-Oppenheimer correction, and high-order electronic correlations (CCSDT, CCSDTQ, and CCSDTQP). Finally, the root-mean-square deviation between the predicted band centers obtained from our final "pure" ab initio PES and the experimental ones in the spectral region [0-7000] cm^-1 is divided by two compared to the most accurate ab initio PES available in the literature.

Towards a complete elucidation of the ro-vibrational band structure in the SF6 infrared spectrum from full quantum-mechanical calculations

The first accurate and complete theoretical room-temperature rotationally resolved spectra in the range 300-3000 cm-1 are reported for the three most abundant isotopologues (32SF6, 33SF6 and 34SF6) of the sulfur hexafluoride molecule. The literature reports that SF6 is widely used as a prototype molecule for studying the multi-photon excitation processes with powerful lasers in the infrared range. On the other hand, SF6 is an important greenhouse molecule with a very long lifetime in the atmosphere. Because of relatively low vibrational frequencies, the hot bands of this molecule contribute significantly to the absorption infrared spectra even at room temperature. This makes the calculation of complete rovibrational line lists required for fully converged opacity modeling extremely demanding. In order to reduce the computational costs, symmetry was exploited at all stages of the first global variational nuclear motion calculations by means of irreducible tensor operators. More than 2600 new vibrational band centers were predicted using our empirically refined ab initio potential energy surface. Highly excited rotational states were calculated up to J = 121, resulting in 6 billion transitions computed from an ab initio dipole moment surface and distributed over more than 500 cold and hot bands. The final line lists are made available through the TheoReTS information system (http://theorets.univ-reims.fr, http://theorets.tsu.ru). For the first time, the major (ro)vibrational band structures in the wavenumber range corresponding to the strongest absorption in the infra-red are completely elucidated for a seven-atom molecule, providing excellent agreement with the observed spectral patterns. It is shown that the obtained results are more complete than all available line lists, permitting reliable modelling of the temperature dependence of the molecular opacity.

Terahertz Rotational Spectroscopy of Greenhouse Gases Using Long Interaction Path-Lengths

Even if on-board mm-wave/THz heterodyne receivers have been developed to measure greenhouse gases (GHGs) atmospheric profiles, rotational spectroscopy rests under-exploited for their monitoring unlike IR rovibrational spectroscopy. The present study deals with the ability of THz spectroscopy using long interaction path-lengths for GHG laboratory investigations. High-resolution THz signatures of non-polar greenhouse molecules may be observed by probing very weak centrifugal distortion induced rotational transitions. To illustrate, new measurements on CH4 and CF4 have been carried out. For CH4, pure rotational transitions, recorded by cw-THz photomixing up to 2.6 THz in a White type cell adjusted to 20 m, have allowed to update the methane line list of atmospheric databases. Concerning CF4, Fabry-Perot THz absorption spectroscopy with a km effective pathlength was required to detect line intensities lower than 10−27 cm−1/(moleccm−2). Contrary to previous synchrotron-based FT-FIR measurements, the tetrahedral splitting of CF4 THz lines is fully resolved. Finally, quantitative measurements of N2O and O3 gas traces have been performed in an atmospheric simulation chamber using a submm-wave amplified multiplier chain coupled to a Chernin type multi-pass cell on a 200 m path-length. The THz monitoring of these two polar GHGs at tropospheric and stratospheric concentrations may be now considered.

A Decade with VAMDC: Results and Ambitions

This paper presents an overview of the current status of the Virtual Atomic and Molecular Data Centre (VAMDC) e-infrastructure, including the current status of the VAMDC-connected (or to be connected) databases, updates on the latest technological development within the infrastructure and a presentation of some application tools that make use of the VAMDC e-infrastructure. We analyse the past 10 years of VAMDC development and operation, and assess their impact both on the field of atomic and molecular (A&M) physics itself and on heterogeneous data management in international cooperation. The highly sophisticated VAMDC infrastructure and the related databases developed over this long term make them a perfect resource of sustainable data for future applications in many fields of research. However, we also discuss the current limitations that prevent VAMDC from becoming the main publishing platform and the main source of A&M data for user communities, and present possible solutions under investigation by the consortium. Several user application examples are presented, illustrating the benefits of VAMDC in current research applications, which often need the A&M data from more than one database. Finally, we present our vision for the future of VAMDC.

Derivation of ρ-dependent coordinate transformations for nonrigid molecules in the Hougen-Bunker-Johns formalism

In this paper, we report a series of transformations for the construction of a Hamiltonian model for nonrigid polyatomic molecules in the framework of the Hougen-Bunker-Johns formalism (HBJ). This model is expressed in normal mode coordinates for small vibrations and in a specific coordinate ρ to describe the large amplitude motion. For the first time, a general procedure linking the "true" curvilinear coordinates to ρ is proposed, allowing the expression of the potential energy part in the same coordinate representation as the kinetic energy operator, whatever the number of atoms. A Lie group-based method is also proposed for the derivation of the reference configuration in the internal axis system. This work opens new perspectives for future high-resolution spectroscopy studies of nonrigid, medium-sized molecules using HBJ-type Hamiltonians. Illustrative examples and computation of vibrational energy levels on semirigid and nonrigid molecules are given to validate this method.

A global view of isotopic effects on ro-vibrational spectra of six-atomic molecules: a case study of eleven ethylene species

In this work, we present a global view of the impact of isotopic substitutions on the spectra of eleven ethylene isotopologues obtained from variational calculations using accurate ab initio potential energy and dipole moment surfaces. This may lead to some important changes in the molecular spectra due to symmetry breaking effects lowering the initial D_2h symmetry of ¹²C₂H₄ ([triple bond, length as m-dash]¹²CH₂¹²CH₂) to C_2v, C_2h or C_s. For the very first time, we report ab initio predictions for ¹²C₂D₄ ([triple bond, length as m-dash]¹²CD₂¹²CD₂) and three C_s species: ¹²CHD¹³CH₂, ¹³CHD¹²CH₂ and ¹²C₂HD₃ ([triple bond, length as m-dash]¹²CD₂¹²CHD). To this end, we have considered the normal-mode approach based on our reduced Eckart-Watson Hamiltonian combined with ethylene ab initio surfaces. This work will contribute to the complete theoretical studies of the deuterated and ¹³C-enriched ethylene isotopologues. A total of 1252 vibrational levels are computed and all the corresponding transitions in the energy range of ≤3100 cm^-1 are predicted and compared to 151 bands assigned from experimental spectra analyses.