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.

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.

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.

First Full-Dimensional Potential Energy and Dipole Moment Surfaces of SF6.

A 15-dimensional analytical form for the potential energy and dipole moment surfaces of the SF6 molecule in the ground electronic state is obtained using ab initio methods. In order to calculate the equilibrium S-F distance, we applied the coupled cluster CCSD(T) method and several versions of the correlation-consistent basis sets from valence triple-zeta (VTZ) and augmented valence triple-zeta (AVTZ) to core-valence quadruple-zeta (CVQZ) with Douglas-Kroll (DK) relativistic corrections that provided good agreement with an empirical equilibrium value. Ab initio electronic energies on 15D grids of nuclear geometries are computed using the CCSD(T) method with VTZ and CVQZ-DK basis sets. The analytical representation of the potential energy surface is determined through an expansion in symmetry-adapted products of nonlinear coordinates up to the 5th order. The influence of additional redundant coordinates on the quality of the fit was investigated. Parameters of full-dimensional dipole moment surfaces are determined up to the 4th order expansion in normal mode coordinates. For validation of ab initio results, the fundamental vibration frequencies and absorption cross sections of the principal sulfur hexafluoride isotopologue are calculated, giving good agreement with cold (180 K) and room temperature (296 K) experimental spectra. Absorption cross sections calculated from our preliminary line list agree much better with these observations than the simulations using SF6 line-by-line lists constructed from effective models included in currently available spectroscopic databases.

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 D2h symmetry of 12C2H4 ([triple bond, length as m-dash]12CH212CH2) to C2v, C2h or Cs. For the very first time, we report ab initio predictions for 12C2D4 ([triple bond, length as m-dash]12CD212CD2) and three Cs 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.

Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules.

A new procedure is presented for building a general kinetic energy operator expressed as a polynomial series expansion of symmetry-adapted curvilinear coordinates for semirigid polyatomic molecules. As a starting point, the normal-mode Watson kinetic energy part is considered and then transformed into its curvilinear counterpart. An Eckart molecular fixed-frame is thus implicitly used. To this end, we exploit symmetry at all stages of the calculation and show how group-theoretically based methods and Γ-covariant tensors help properly invert nonlinear polynomials for the coordinate changes. Such a linearization procedure could also be useful in different contexts. Unlike the usual normal mode approach, the potential part initially expressed in curvilinear coordinates is not transformed in this work, making convergence of the Hamiltonian expansion generally faster. For dimensionality reduction, the final curvilinear kinetic and potential parts are expanded in terms of irreducible tensor operators when doubly and triply degenerate vibrations are involved. The procedure proposed here is general and can be applied to arbitrary Abelian and non-Abelian point groups. Illustrative examples will be given for the H2S (C2v), H2CO (C2v), PH3 (C3v), and SiH4 (Td) molecules.

Symmetry effects in rotationally resolved spectra of bi-deuterated ethylene: Theoretical line intensities of cis, trans, and as-C2H2D2 isotopomers.

In this paper, we report accurate first-principles variational rovibrational spectra predictions for the three double deuterated ethylene isotopologs denoted as cis, trans, and as-12C2H2D2. Calculations were performed in the framework of the normal-mode approach using our ab initio12C2H4 (D2h) Born-Oppenheimer potential energy and dipole moment surfaces. Symmetry breaking effects under bideuterated H → D substitutions (D2h → C2v/C2h) and their impact on infrared spectra are studied from normal mode transformations. All theoretical spectra simulated at 296 K up to J = 38 are in good agreement, both for line positions and in absorption cross sections, with the experiment. Accurate theoretical line lists providing for the first time intensities of rovibrational transitions are computed for the three species in the range (0-4500) cm-1 and will be available on our TheoReTS information system (http://theorets.univ-reims.fr and http://theorets.tsu.ru). These results can be used for remote sensing retrieval of isotopic species using predicted line intensities and experimentally optimized line positions.

Glucocorticoid Treatment of Symptomatic Sarcoidosis in 2 Morbidly Obese Patients.

Corticosteroid management for patients with sarcoidosis requires the need for close monitoring to detect and manage any complications that may arise during treatment.

Cystic Fibrosis: Emerging Understanding and Therapies.

Cystic fibrosis (CF) is the most common life-limiting genetic disease in Caucasian patients. Continued advances have led to improved survival, and adults with CF now outnumber children. As our understanding of the disease improves, new therapies have emerged that improve the basic defect, enabling patient-specific treatment and improved outcomes. However, recurrent exacerbations continue to lead to morbidity and mortality, and new pathogens have been identified that may lead to worse outcomes. In addition, new complications, such as CF-related diabetes and increased risk of gastrointestinal cancers, are creating new challenges in management. For patients with end-stage disease, lung transplantation has remained one of the few treatment options, but challenges in identifying the most appropriate patients remain.

Isotopic and symmetry breaking effects on phosphine spectra under H → D substitutions from ab initio variational calculations.

Variationally computed infrared spectra in the range [0-5000] cm-1 are reported for the deuterated PH2D and PHD2 molecules from accurate potential energy and dipole moment surfaces initially derived for the major isotopologue PH3( C 3 v ). Energy level and line intensity calculations were performed by using a normal-mode model combined with isotopic and symmetry transformations for the H → D substitutions. Theoretical spectra were computed at 296 K up to J max = 30 and will be made available through the TheoReTS information system (http://theorets.univ-reims.fr, http://theorets.tsu.ru). For the very first time, ab initio intensity predictions of PH2D/PHD2 are in good qualitative agreement with the literature. This work will be useful for spectral intensity analysis for which accurate spectral intensity data are still missing.

Highly excited vibrational levels of methane up to 10 300 cm-1: Comparative study of variational methods.

In this work, we report calculated vibrational energy levels of the methane molecule up to 10 300 cm-1. Two potential energy surfaces constructed in quite different coordinate systems with different analytical representations are employed in order to evaluate the uncertainty of vibrational predictions. To calculate methane energy levels, we used two independent techniques of the variational method. One method uses an exact kinetic energy operator in internal curvilinear coordinates. Another one uses an expansion of Eckart-Watson nuclear motion Hamiltonian in rectilinear normal coordinates. In the Icosad range (up to five vibrational quanta bands-below 7800 cm-1), the RMS standard deviations between calculated and observed energy levels were 0.22 cm-1 and 0.41 cm-1 for these two quite different approaches. For experimentally well-known 3v3 sub-levels, the calculation accuracy is estimated to be ∼1 cm-1. In the Triacontad range (7660-9188 cm-1), the average error of the calculation is about 0.5 cm-1. The accuracy and convergence issues for higher energy ranges are discussed.

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

Fluorine containing molecules have a particularly long atmospheric lifetime and their very big estimated global warming potentials are expected to rapidly increase in the future. This work is focused on the global theoretical prediction of infrared spectra of the tetrafluoromethane molecule that is considered as a potentially powerful greenhouse gas having the largest estimated lifetime of over 50 000 years in the atmosphere. The presence of relatively low vibrational frequencies makes the Boltzmann population of the excited levels important. Consequently, the "hot bands" corresponding to transitions among excited rovibrational states contribute significantly to the CF4 opacity in the infrared even at room temperature conditions but the existing laboratory data analyses are not sufficiently complete. In this work, we construct the first accurate and complete ab initio based line lists for CF4 in the range 0-4000 cm-1, containing rovibrational bands that are the most active in absorption. An efficient basis set compression method was applied to predict more than 700 new bands and subbands via variational nuclear motion calculations. We show that already at room temperature a quasi-continuum of overlapping weak lines appears in the CF4 infrared spectra due to the increasing density of bands and transitions. In order to converge the infrared opacity at room temperature, it was necessary to include a high rotational quantum number up to J = 80 resulting in 2 billion rovibrational transitions. In order to make the cross-section simulation faster, we have partitioned our data into two parts: (a) strong & medium line lists with lower energy levels for calculation of selective absorption features that can be used at various temperatures and (b) compressed "super-line" libraries of very weak transitions contributing to the quasi-continuum modelling. Comparisons with raw previously unassigned experimental spectra showed a very good accuracy for integrated absorbance in the entire range of the reported spectra predictions. The data obtained in this work will be made available through the TheoReTS information system (http://theorets.univ-reims.fr, http://theorets.tsu.ru) that contains ab initio born line lists and provides a user-friendly graphical interface for a fast simulation of the CF4 absorption cross-sections and radiance under various temperature conditions from 80 K to 400 K.

Internal- and rho-axis systems of molecules with one large amplitude internal motion: The geometry of rho.

The internal-axis system (IAS) of molecules with a large amplitude internal motion (LAM) is determined by integrating the kinematic equation of the IAS by Lie-group and Lie-algebraic methods. Numerical examples on hydrogen peroxide, nitrous acid, and acetaldehyde demonstrate the methods. By exploiting the special product structure of the solution matrix, simple methods are devised for calculating the transformation to the rho-axis system (RAS) along with the value of the parameter ρ characterizing a RAS rotational-LAM kinetic energy operator. The parameter ρ so calculated agrees exactly with that one obtained by the Floquet method as shown in the example of acetaldehyde. Geometrical interpretation of ρ is given. The advantageous property of the RAS over the IAS in retaining simple periodic boundary conditions is numerically demonstrated.