Disentangling the IR spectra of 2,3,3,3-tetrafluoropropene using an ab initio description of vibrational polyads by means of canonical Van Vleck perturbation theory

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Highlights

  • Complete spectroscopic analysis of the IR spectrum of 2,3,3,3-tetrafluoropropene.

  • Accurate determination of absorption cross section data

  • Thorough understanding of polyad mixing in the vibrational spectra.

  • Benchmark of numerical-analytic second order Van Vleck perturbation theory.

Abstract

The vibrational spectra of 2,3,3,3-tetrafluoropropene (2333TFP) are studied in the infrared experimentally and theoretically by the canonical second-order Van Vleck operator perturbation theory (CVPT2) and full quartic potential energy surface (PES). 2333TFP belongs to hydrofluoroolefins (HFOs) considered among the most promising alternatives to the hydrofluorocarbons presently in use in refrigeration. The medium resolution infrared spectra of gaseous 2333TFP were recorded in the range 9500–30 cm1. The integrated IR intensities for all bands falling between 6300–400 cm1 were accurately determined. Theoretical descriptions of up to four-quanta anharmonic vibrational states of 2333TFP are performed using the state-of-the-art numerical-analytic implementation of CVPT2. High quality harmonic frequencies, obtained at different coupled-cluster levels of theory up to the CCSD(T*)-F12c/VTZ-F12 model were combined with the full quartic MP2/cc-pVTZ anharmonic force field to form the hybrid PES. All Fermi and Darling-Dennison resonances were detected using a universal criterion and treated with the variational CVPT2/VCI stage by using two-, three-, and four-quanta harmonic oscillator basis sets. General recommendations for choosing such basis sets in future studies are formulated. In addition to all fundamentals and their resonance satellites, the vibrational analysis led to the assignment of virtually all observed first/second overtone and binary/ternary combination bands. Computed dipole moment first derivatives in the principal axis system yielded reliable predictions of band shapes for fundamental transitions in good agreement with observed counterparts. Computed anharmonic IR intensities showed an excellent agreement with observed data in the measured ranges. The fundamental spectroscopic effect of excited resonances is observed experimentally and explained theoretically as a universal mechanism of formation of vibrational polyads. The efficiency of the CVPT2/VCI approach employed is clearly demonstrated and can be considered as a benchmark for modeling vibrational states and interpretation of vibrational spectra of semi-rigid molecules.

Introduction

Recent years have seen many research projects aimed at finding efficient replacements for hydrofluorocarbons (HFCs), a class of compounds widely used in place of chlorofluorocarbons (CFCs), which were banned by the Montreal Protocol (and its subsequent amendments). Even if HFCs are considered as ozone-friendly alternatives to CFCs, they are generally characterized by rather high values of global warming potential (GWP), thus contributing to climate change. Concerns about how the rapidly growing emissions of HFCs [1] will affect the Earth’s radiative budget [2] prompted many Governments to adopt regulations with respect to HFCs. For example, the European Directive 2006/40/EC about air-conditioning systems in motor vehicles banned by 2017 the use of refrigerants having GWPs larger than 150 [3]. The Kigali amendment (2016) of the Montreal Protocol anticipates the phase-out of HFCs. Their production and consumption should be cut by more than 80 percent over the next 30 years. Consequently, there is an urgent need for eco-friendly, low-GWP alternatives to HFCs.

Among the different classes of compounds considered as viable alternatives to HFCs, the hydrofluoroolefins (HFOs) are the most promising ones. They are characterized by having no adverse effects on the Earth’s ozone layer and by very low values of GWPs. The low GWPs are mainly due to the short atmospheric lifetimes of the HFOs. Otherwise, the presence of C–F bonds would give strong absorption in the infrared region. The likely large-scale industrial use of HFOs in the near future requires a thorough investigation of their physical and chemical properties, as well as of their atmospheric chemistry. In addition, monitoring and detecting HFOs in real-time is highly desirable. Studies of HFOs can be efficiently supported by modern computational methods, such as classical or ab initio molecular dynamics. The atmospheric chemistry of these compounds can be modeled by taking account of their reaction with tropospheric oxidants [4], [5], and by experimentally determining accurate values of their absorption cross-sections [6], [7].

Thanks to the recent advances in high-resolution infrared spectroscopic techniques it is possible to monitor the concentration of gaseous pollutants in real-time and with very high sensitivity [8], [9], [10]. A prerequisite is the availability of accurate spectroscopic data coming from ro-vibrational assignments and line-shape analysis [11], [12]. To provide such data, different methods have been developed in recent decades to help analyze complex spectra as has been done for CFCs. Experimental techniques, such as free-jet expansion [13], [14], [15] or collisional cooling cells [16], [17], [18], can efficiently cool the sample and thus greatly simplify the infrared spectra. Concerning the ro-vibrational assignment and the line-shape analysis, several methods [19], [20], [21], [22], [23], [24], [25], [26], [27], [28] are available to assist. Coupling these data to a proper treatment of the anharmonic couplings [29], [30], it is possible to analyze dense ro-vibrational spectra [12], [31].

As a promising substitute of 1,1,1,2-tetrafluoroethane (HFC-134a, R-134a), 2,3,3,3-tetrafluoropropene (H2C=CF–CF3), also designated HFO-1234yf (the ID derived from hydrofluoroolefin, HFO) or R-1234yf, has received growing attention. In this work we will use a chemically sound acronym 2333TFP rather than the aforementioned technical codes. New routes of synthesis [32], [33], as well as the kinetics of atmospheric degradation were investigated [7], [34], [35], and its properties in the liquid state were simulated by both classical molecular dynamics and ab initio quantum chemical techniques [36]. The recently announced decisions of the European Union and of the U.S. Environmental Protection Agency regarding the substitution of the 1,1,1,2-tetrafluoroethane with 2333TFP bolstered the interest in this compound. For assessing the environmental impact of the future emissions of this substance and for use in monitoring it, a complete characterization of its spectroscopic properties is desirable. The microwave spectrum in the 6–18 GHz region [37], as well as its microwave spectrum from an investigation of its complexes with Ar [38], is available, but the gas-phase vibrational spectrum is incompletely analyzed. Not all the fundamentals are clearly identified [39].

In the present work we report on the results coming from a combined experimental and theoretical study of IR spectra of 2333TFP. The analysis of its vibrational spectrum has led to the assignment of all the fundamentals and of many combination and overtone bands in the range 9500–30 cm1. Accurate values of absorption cross sections were also determined for all the important features up to 6200 cm1. Vibrational analysis of the gas-phase infrared spectra was guided by high-level quantum chemical calculations. For the harmonic part of the force field, an accurate description was obtained using two different approaches. The first is based on composite schemes, which comprises a highly correlated treatment of the electronic structure at the coupled-cluster level of theory, including single and double excitations with a perturbative treatment of triple excitations, CCSD(T) [40], an extrapolation to the complete basis set (CBS) limit and corrections for core-correlation effects. The second approach, with the calculations carried out at CCSD(T*)-F12c/VTZ-F12 level of theory [41], relies on the fast convergence of explicitly correlated methods towards the complete basis set limit.

For providing more comprehensive experimental IR data and for performing an effective check of accepted theoretical methods of predicting IR spectra, we have made measurements of IR spectra in the near-infrared region of 9500–4000 cm1. As was noted in ref. [42], the molecular mechanisms standing behind the absorption of electromagnetic radiation in the NIR involve excitations of non-fundamental vibrations, which include overtones and combination modes. In this sense, NIR spectroscopy distinctively sets itself apart from the other kinds of vibrational spectroscopy (mid-infrared, MIR; far-infrared, FIR; and Raman), in which the principal chemical information originates from fundamental vibrational transitions. Unlike these latter ones, theoretical NIR predictions unequivocally require computationally intensive anharmonic approaches. Hence, NIR spectral simulations have remained rather rare in the literature until recent advances in theory and computer technology made such studies feasible for molecules that are beyond a few atoms in complexity. Besides, the presence of four low-frequency fundamentals of 2333TFP in the far infrared (FIR,  ∼ 400–30 cm1) prompted our new spectral measurements in this region as well.

The vibrational Schrödinger equation for a semi-rigid polyatomic molecule can be solved using rather different methods. They include either classic quantum-mechanical theoretical approaches: the variational configuration interaction (VCI) method [43], [44], [45], [46], [47], the second-order perturbation theory (VPT2) [48], [49], [50], [51], [52], [53], [54], [55], [56], or more recently established ones, such as the vibrational self-consistent field (VSCF) method and its extensions [57], [58], [59], [60], [61], [62], [63], [64], or the vibrational coupled cluster method (VCC) [65], [66]. It should be noted that these methods based on the Watson Hamiltonian are meaningful only for semi-rigid molecules and will not work for non-rigid molecules exhibiting complex nuclear motion.

The case of the nine-atom 2333TFP molecule with 21 degrees of freedom probably leaves only one suitable option – the second-order vibrational perturbation theory with the full quartic potential energy surface (PES). There are several alternatives for realization of VPT2; identical results can be obtained using different theoretical strategies. First, the traditional Rayleigh-Schrödinger perturbation theory can be applied in the first order followed by the evaluation of diagonal matrix elements, which leads to expressions for anharmonic constants [67]. Resonance coupling matrix elements can be obtained using the same approach [68]. Second, the Hamiltonian operator can be subjected to canonical unitary transformations within the Van Vleck perturbation theory [69], [70], [71], [72], [73], [74], [75], [76], [77], [78]. The resulting transformed Hamiltonian with the preserved energy spectrum commutes with the zero-order harmonic Hamiltonian and hence can be directly integrated in harmonic wave functions, yielding anharmonic and resonance constants. Within this approach, there are two practical possibilities: (1) necessary transformations can be performed in a general analytic form with derivation of closed expressions for anharmonic constants etc, or (2) canonical transformations can be done in full operator form with subsequent integration at the final stage. The former option is more traditional and dominant in the literature, while the latter one is rather laborious but more flexible, extendable to higher orders and convenient for evaluation of transition probabilities.

In this work, we have employed a state-of-the-art implementation of the operator version of the second order canonical Van Vleck vibrational perturbation theory (CVPT2) [79], [80], [81], [82] developing earlier works by Sibert [83], [84]. There are two major features of our implementation of CVPT2: the original Hamiltonian is transformed into harmonic oscillator ladder operators and canonical transformations are performed in mixed numerical-analytic form. More details will be provided below in Section 3 (Theory).

The outline of this paper is as follows. The conditions of experimental IR spectra measurements are presented in Section 2. Theoretical details of the numerical-analytic version of the second-order canonical Van Vleck operator perturbation theory followed by a small-size variational stage (CVPT2/VCI) are described in Section 3. The details of theoretical calculations, such as the evaluation of the equilibrium geometry of 2333TFP, its harmonic and anharmonic force field, the dipole moment surface, prediction of approximate vibration-rotation band contours, vibrational assignments of normal modes and fine practical details about the CVPT2 calculations are outlined in Section 4. The main discussion about the vibrational assignments of the IR spectra of 2333TFP followed by the juxtaposition of the experimental and theoretical harmonic frequencies and IR intensities is given in Section 5. The final Section 6 (Conclusions) summarizes the key results of this research including some interesting theoretical observations.

Section snippets

Experimental details

The sample of 2333TFP was purchased from ABCR (with a stated purity  > 97%) and used without any purification. New room-temperature gas-phase IR spectra employed for the vibrational analysis were measured in the range 9500–50 cm1 by using the Bruker IFS 120/5HR spectrometer (located at the Centre for Astrochemical Studies, MPE Garching) with a resolution ranging from 0.05 to 0.02 cm1 and employing a cell with an optical path length of 20 cm. For the measurements in the range 9500–400 cm1 the

Theory

In this Section we provide the essential details of the operator form of the canonical Van Vleck perturbation theory (CVPT2) that we employed for modeling the vibrational polyads of 2333TFP. These details are essential for understanding the treatment of vibrational resonances and our method of evaluating IR transition probabilities. The usual form of VPT2 provides a set of analytic expressions for evaluating anharmonic and resonance constants [49], [50]. This approach solves the Schrödinger

Equilibrium geometry, normal modes and quartic force field

The equilibrium structure of the 2333TFP molecule belongs to the symmetry point group Cs, and its normal modes correspond to the following breakdown of irreducible representations: Γ=14A+7A. The geometrical structure and numbering of atoms are presented in Fig. 1. The center of mass is located almost on the C–CF3 bond near atom C3, and the principal a-axis is practically aligned with the same bond.

Full optimization of the molecular geometry was performed using three different levels of

Discussion

Following a spectroscopic tradition, we will discuss vibrational assignments going from higher to lower wavenumbers as found in eight spectral wavenumber ranges (in cm1): 9500–5000 (Fig. 5), 5000–3900 (Fig. 6), 3200–3000 (Fig. 7), 2900–2250 (Fig. 8), 2250–1500 (Fig. 9), 1500–1000 (Fig. 10), 1000–500 (Fig. 11), and 500–30 (Fig. 12). An additional range of 3900–3200 cm1 is contaminated with absorptions due to a trace of H2O likely present in the sample of 2333TFP and has very few important

Conclusions

This study reached several objectives. First, we obtained detailed gas phase near-, mid- and far-infrared spectra at medium resolution of an industrially important compound 2,3,3,3-tetrafluoropropene (2333TFP). The record of its absorption peaks is helpful for monitoring the chemistry of Earth’s atmosphere and for other analytic purposes. Second, practical approaches to theoretical interpretations of molecular vibrational spectra significantly differ depending on the size of a molecule studied.

Declaration of Competing Interest

The authors declare that they do not have any financial or nonfinancial conflict of interests.

Acknowledgments

One of the authors (A.C.P.) gratefully acknowledges financial support by University Ca’ Foscari Venezia (ADiR funds), and the computing facilities of SCSCF (Sistema per il Calcolo Scientifico di Ca’ Foscari, a multiprocessor cluster system owned by Universita’ Ca’ Foscari Venezia).

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    Electronic Supplementary Information (ESI) available: Spectra reporting the vibrational assignments in different infrared regions and the computed sextic centrifugal distortion constants. See DOI: 10.1016/j.saa.2019.00.000.

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