Rotational Spectrum, Structure, and Interaction Energy of the

Sep 29, 2016 - Rotational spectra for four isotopologues of the 1:1 weakly bound complex between trifluoroethylene (HFC═CF2) and carbon dioxide (CO2...
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Rotational Spectrum, Structure, and Interaction Energy of the Trifluoroethylene···Carbon Dioxide Complex Rachel E. Dorris, William C. Trendell, Rebecca A. Peebles, and Sean A. Peebles* Department of Chemistry, Eastern Illinois University, 600 Lincoln Avenue, Charleston, Illinois 61920 United States S Supporting Information *

ABSTRACT: Rotational spectra for four isotopologues of the 1:1 weakly bound complex between trifluoroethylene (HFCCF2) and carbon dioxide (CO2) were recorded using 480 MHz bandwidth chirped-pulse and resonant cavity Fourier transform microwave spectroscopy between 5.0 and 18.5 GHz. Two planar forms are possible: experimental rotational constants, planar moments, and dipole moment components are consistent with the form in which CO2 is positioned at the CHF end of the TFE subunit and is approximately perpendicular to the CC bond; the other form, with CO2 aligned roughly parallel to the CC bond, is not observed, consistent with ab initio relative energy predictions. Symmetry-adapted perturbation theory (SAPT) calculations provided interaction energies for possible structural forms of this complex, and comparisons are made with this and other members of the series of carbon dioxide complexes with fluorinated ethylenes (vinyl fluoride, 1,1-difluoroethylene, cis- and trans-1,2-difluoroethylene, and trifluoroethylene).

1. INTRODUCTION Probing the interactions of carbon dioxide (CO2) with small molecules can lead to an improved understanding of its behavior in a number of applications, including as an important industrial solvent1 or perhaps as a means of optimizing the properties of materials designed for CO2 capture and storage. Although studies of such binary clusters consider only solute− solvent interactions on the smallest possible scale, useful information on the energetics and balance of forces can be obtained. The resulting improved molecular-level understanding of these interactions can therefore contribute to development of models to better describe bulk-scale behavior. For instance, the particular mechanism for the high solubility of some fluorinated compounds in supercritical carbon dioxide is not well understood.2 Systematic studies of binary complexes can therefore lead to insight into the factors responsible for competition between different binding sites and information on the strength of interactions between fluorinated compounds and CO2. Furthermore, systematic fluorination yields insight into subtle variations of interaction strength with the degree and position of fluorination. Previous theoretical work has explored the interactions of CO2 with carbonyl-containing species3−6 or within benzene/ fluorobenzenes···CO2 complexes.7,8 Much interest has also focused on the effects of halogenation on alkane/CO2 interactions.9−12 Work on alkenes has been sparser, although recent calculations provided accurate binding energies for a series of dihalogenated ethylene complexes with CO2.13 As part of a systematic investigation aimed at determining the effects of the position and degree of fluorination of the ethylene subunit on the structure and interaction energy, we recently initiated a series of studies involving gas-phase binary complexes of CO2 with fluoroethylenes. Fluorination causes © XXXX American Chemical Society

significant changes in the electrostatic properties of the alkene because the out-of-plane component of the molecular electric quadrupole moment changes sign when three or more F atoms are attached to ethylene.14 Therefore, the interaction energy will undoubtedly be influenced as fluorination occurs, and it is likely that the energetically preferred position of binding of the CO2 molecule around the fluoroethylene subunit could change. For instance, for a planar fluoroethylene···CO2 complex, two binding sites are usually possible: CO2 can bind either at the CHF end of the molecule, roughly perpendicular to the CC bond (side-bonded), or it can bind approximately parallel to the CC bond (top-bonded). The vinyl fluoride (VF)···CO2 complex15 provides a rare example where spectra for both sideand top-bonded arrangements are observed with comparable intensity, in accordance with ab initio calculations that predicted these two forms to lie very close in energy. Interestingly, a third form, with CO2 stacked above the VF plane, was actually predicted to be most stable by ab initio calculations but was not observed in our experiment. In 1,1difluoroethylene (DFE)···CO2,16 only one planar possibility exists (the top-bonded form), and this was indeed the form observed experimentally. In the triply fluorinated member of this series, trifluoroethylene (TFE)···CO2, both side- and topbonded structures are once again possible, posing the question as to which form will be observed and whether we can predict this reliably beforehand. The present study describes a 2-fold approach to investigating interactions between CO2 and a series of fluorinated ethylenes. First, an analysis of the rotational Received: August 16, 2016 Revised: September 16, 2016

A

DOI: 10.1021/acs.jpca.6b08286 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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predicted rotational constants and dipole moment components. All optimizations were made at the MP2/6-311++G(2d,2p) level, and basis set superposition error (BSSE) effects were accounted for during the optimization process using the Boys− Bernardi counterpoise correction26 procedure that is integrated into Gaussian 09. The CalcAll keyword requested the computation of the exact Hessian at each optimization step, and ZPE corrections were made using the resulting harmonic vibrational frequencies. 3.2. Symmetry-Adapted Perturbation Theory (SAPT) Calculations. In an attempt to rationalize the order of stability observed for different structural forms of CO2 complexes of VF,15 1,1-DFE,16 and TFE, we applied the Symmetry-Adapted Perturbation Theory (SAPT) methodology.17 In addition to these complexes for which experimental data exists, we included predictions for the as-yet-unpublished cis and trans isomers of 1,2-DFE complexed with CO2; the former complex is currently being characterized experimentally in our laboratory and will be reported in a future publication and the latter complex is composed of two nonpolar moieties, and experimental studies have not yet been initiated. The SAPT2012 program,27 which utilized GAMESS28 as the integral/SCF package, provided interaction energies for each complex using a dimer-centered basis set approach (with the 6-311++G(2d,2p) basis); structures were taken from the Gaussian 09 MP2/6-311+ +G(2d,2p) optimizations as explained in Section 3.1.

spectrum of TFE···CO2 should allow an unambiguous determination of which structural forms are observed in a supersonic expansion. Then, subsequent treatment of TFE··· CO2 and related complexes via the symmetry-adapted perturbation theory (SAPT) method17 will allow the calculation of binding energies for all species so far observed in the fluoroethylene···CO2 series (VF, 1,1-DFE, TFE), as well as for related systems not yet studied experimentally (cis- and trans1,2-DFE). This will allow the variation of contributions to the overall dimer binding energy to be explored as the position and degree of fluorination are varied and a rationalization of why particular structural forms are favored in the gas phase.

2. EXPERIMENTAL METHODS A sample mixture consisting of 1% CO2 (99.8%, SigmaAldrich) and 1% CHFCF2 (98%, Synquest Laboratories) diluted in a He/Ne carrier gas (17.5% He: 82.5% Ne, BOC Gases) was delivered at a rate of 2 Hz and a pressure of 2.5 atm to a General Valve Series 9 pulsed nozzle with a 0.8 mm orifice oriented perpendicularly to the microwave horns. A broadband rotational spectrum spanning the 6.5−18.5 GHz region was constructed from overlapping 480 MHz segments measured on a reduced bandwidth chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer.18 A total of 2000 free induction decays (FIDs) were averaged at each frequency step, with 6 FIDs collected per gas pulse. A LabVIEW program was used to determine the absolute transition frequencies and assemble the scan segments into a full broadband spectrum. Measurements of additional weaker parent isotopologue transitions, transitions falling to lower frequency (down to about 5 GHz), and spectra for 18O-substituted species (see below) were carried out on a resonant cavity FTMW spectrometer of the Balle-Flygare design.19,20 The resonant cavity spectrometer utilized a General Valve series 9 nozzle identical to that in the chirped-pulse FTMW spectrometer, although running at a higher repetition rate of 10 Hz and with only one FID collected per gas pulse. Isotopically enriched samples for the measurement of C18O2- and C18O16O-labeled species were prepared by mixing C18O2 (95% 18O, SigmaAldrich) with C16O2 in a 1:1 ratio; a small drop of H218O (97% 18 O, Sigma-Aldrich) was also added to the bulb to facilitate exchange. Microwave spectra were assigned and fit to a Watson Areduced Hamiltonian in the Ir representation21 using the AABS package of Kisiel22 and Pickett’s SPFIT/SPCAT programs.23 Measurements from both instruments have a frequency reproducibility of ∼4 kHz, so all transition frequencies are weighted equally within SPFIT. Stark effect experiments were carried out on the resonant cavity instrument, allowing the determination of dipole moment components for TFE···CO2. Voltages of up to ±5 kV (corresponding to a maximum electric field strength of ca. 330 V cm−1) were applied to a pair of parallel steel mesh plates placed 31 cm apart within the vacuum chamber and straddling the molecular expansion. Calibration of the applied electric field was carried out by measurement of the J = 1 ← 0 transition of OCS and assuming a dipole moment of μ = 0.71519(3) D.24

4. RESULTS AND DISCUSSION 4.1. Ab Initio Optimizations. The results of MP2/6-311+ +G(2d,2p) geometry optimizations for three possible structures of TFE···CO2 are given in Table 1 and displayed in Figure 1; Table 1. MP2/6-311++G(2d,2p)-Predicted Spectroscopic Parameters, Dipole Moment Components, and Relative Energies for the Three Structures of TFE···CO2a A/MHz B/MHz C/MHz μa/D μb/D μc/D ΔEBSSE/cm−1 (kJ mol−1) ΔEBSSE+ZPE/cm−1 (kJ mol−1)

I side

II stacked

III top

5291 675 599 0.40 1.19 0.00 0 0

3239 1068 964 0.99 0.60 0.86 39 (0.47) 37 (0.45)

3531 834 675 1.24 0.62 0.00 64 (0.77) 55 (0.66)

a

Relative energies are computed either from initial BSSE-corrected MP2/6-311++G(2d,2p) optimization without zero-point energy corrections (ΔEBSSE) or with both BSSE and zero-point energy corrections (ΔEBSSE+ZPE).

3. COMPUTATIONAL METHODS 3.1. Ab Initio Optimizations. Initial optimizations of possible structures for TFE···CO2 were carried out using Gaussian 0925 to provide approximate relative energies and

Figure 1. Three forms of the TFE···CO2 complex determined by BSSE-corrected optimizations at the MP2/6-311++G(2d,2p) level. Structure I is the side-, II is the stacked-, and III the top-bonded form. B

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The Journal of Physical Chemistry A Table 2. Spectroscopic Parameters for the Normal and 18O-Substituted Species of TFE···CO2a parameterb

CHFCF2···CO2

CHFCF2···C18O2

CHFCF2···C16O(8)18O(9)

CHFCF2···C18O(8)16O(9)

A/MHz B/MHz C/MHz ΔJ/kHz ΔJk/kHz Δk/kHz δJ/kHz Nd Δνrms/kHze Paa/uÅ2g Pbb/uÅ2 Pcc/uÅ2

5355.7872(15) 696.42354(21) 617.32466(15) 0.4103(15) −2.378(10) 30.7(3) 49.5(8) 45 2.8 724.98825(22) 93.67182(22) 0.68948(22)

5111.2215(18) 664.5320(9) 589.01436(22) [0.4103]c [−2.378] [30.7] [49.5] 9 3.5 759.8177(7) 98.1904(7) 0.6860(7)

5189.5777(12) 685.2675(7) 606.32579(17) [0.4103] [−2.378] [30.7] [49.5] 10 2.7 736.8095(5) 96.7013(5) 0.6813(5)

5281.921(8) 674.428(5) 599.0573(18) [0.4103] [−2.378] [30.7] [49.5] 4 0.5f 748.644(4) 94.980(4) 0.701(4)

a

Atom numbers are given in Figure 2. bErrors in parentheses correspond to one standard deviation in the reported parameters. cQuantities in square brackets [] are fixed at values obtained for the parent isotopologue. dNumber of fitted rotational transitions. eΔνrms = [Σ(νobs − νcalc)2/N]1/2 fThe Δνrrms for this species is artificially low because the data set is very small. This rotational constant data was therefore not used for structure determination. gPlanar moments, Paa = 0.5(Ib + Ic − Ia) = Σi miai2 and so forth.

4.3. Dipole Moment. Measured transition frequencies at each applied electric field were fitted directly to μa and μb dipole moment components using the QSTARK program,34 with rotational constants and centrifugal distortion constants held fixed at values determined in Table 2. A fit of 26 separate measurements comprising 4 distinct M components from 3 different rotational transitions gave a satisfactory standard deviation of 3.9 kHz. Output from the last cycle of the QSTARK least-squares fit is given in Supporting Information Table S3. The resulting fitted dipole moment components, μa = 0.246(28) D and μb = 1.23(11) D, giving μtotal = 1.25(11) D, are clearly consistent only with values given in Table 1 for a side-bonded form (structure I). 4.4. Structure Determination. The structure of TFE··· CO2 is defined by three intermolecular parameters, assuming that monomer structures are unchanged from literature values (Supporting Information Table S4)35−37 and that the groundstate structure is planar. These three parameters were chosen as the distance between the F atom geminal to H of TFE and the C atom of CO2 (F5···C7) and the two angles C4−F5···C7 and F5···C7O9 (O atom nearest the H atom of TFE); atom numbers are shown in Figure 2. These values were determined

principal axis coordinates are given in Supporting Information Table S1. The side-bonded form (structure I) is predicted by ab initio optimizations to be about 55 cm−1 more stable than the top-bonded form (structure III) at the BSSE- and ZPEcorrected levels. Interestingly, in terms of stability, the stacked form (structure II) is predicted to lie between the two planar forms, being less stable than the side-bonded structure by 37 cm−1 (BSSE + ZPE). All three forms have quite distinct rotational constants and dipole moment components that should enable easy identification of their rotational spectra, given sufficient intensity. 4.2. Rotational Spectra. Measured transition frequencies are given in Supporting Information, Tables S2a−d, and Table 2 lists fitted spectroscopic parameters for the parent species and three isotopologues containing 18O substitutions (TFE···C18O2 and two possible singly substituted TFE···C18O16O). It is interesting that one of the C18O16O species was observed at significantly better intensity than the other. (The species in which the 18O atom is adjacent to the CH bond of the TFE seemed to be preferred.) This suggests that perhaps some kind of zero-point effects are causing an enhancement of the population of certain isotopic species in the supersonic expansion, as has been observed previously for a variety of different systems.29−31 This observation might be interpreted as evidence of an interaction between the H atom of TFE and the O atom of CO2. An atoms in molecules (AIM)32 or natural bond order (NBO)33 analysis might be able to provide insight into whether there are any significant interactions between these atoms, although such a study is beyond the scope of the present work. Because only four weak transitions were identified for the C18O16O species with the 16O atom closest to the H atom of TFE, that species was not used in the structure analysis (although Kraitchman coordinates derived from its rotational constants are in very good agreement with inertial fits (Section 4.4)). The quantity and position of isotopically labeled species studied restricts the amount of structural information that can be extracted, but it is sufficient to confirm that the experimentally assigned species is the sidebonded form. During assignment of the TFE···CO2 rotational spectrum, rotational transitions belonging to TFE···Ne were also identified; details of the analysis of that rotational spectrum will be reported in a future publication.

Figure 2. Experimentally determined structure of TFE···CO2. The small circle to the right of atom 1 is the center of mass of TFE, and the center of mass of the complex is at the origin of the axes. See the text for details.

by least-squares fits to different combinations of moments of inertia or planar moments38 using Kisiel’s STRFIT program;39 explicit details of the fitting approach are given in Supporting Information, and the results for all fits are listed in Table 3. The fit to planar moments resulted in the lowest deviation between observed and calculated moments of inertia, so it is our preferred structure. Uncertainties reported for this structure in Table 3 are double the values propagated during the fitting C

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The Journal of Physical Chemistry A Table 3. Fitted Structural Parameters for TFE···CO2 and a Comparison with the Analogous Form of VF···CO215,a

RF5···C7/Åb θC4−F5···C7/degb θF5···C7O9/degb RH6···O9/Å θC4−H6···O9/°deg θH6···O9C7/deg Rcm/Åd RMS/u Å2

Ia, Ib

Ia, Ic

Ib, Ic

Paa, Pbb (preferred)c

Paa, Pbb (ref 36)

ab initio (side)

ab initio (top)

VF···CO2(ab initio)

VF···CO2 (expt)

2.915(12) 112.9(9) 83.0(5) 2.745(20) 111.0(8) 116.1(8) 4.5719(6) 0.12

2.916(12) 112.4(9) 82.8(5) 2.725(21) 111.4(9) 116.5(9) 4.5669(5) 0.11

2.883(12) 115.0(9) 82.0(5) 2.771(21) 108.9(9) 117.1(8) 4.5668(5) 0.15

2.897(20) 113.9(1.4) 82.5(8) 2.754(34) 110.0(1.4) 116.6(1.4) 4.5668(10) 0.098

2.915(10) 111.6(7) 82.9(4) 2.670(17) 114.8(8) 116.3(7) 4.5627(5) 0.10

3.047 108.5 81.5 2.693 115.8 117.5 4.656

5.424 13.5 45.5 2.620 137.8 127.2 4.286

2.983 112.3 83.9 2.747 117.8 113.3 3.780

2.935(10) 110.5(1.0) 83.5(1.0) 2.58(10) 121.3(2.0) 114.7(1.0) 3.709(10)

a

Least-squares analyses were performed using pairs of either moments of inertia or planar moments for the normal and two isotopologues. The preferred structure is that resulting from a fit of the three intermolecular structural parameters to Paa and Pbb, using ref 35 for the TFE monomer. b The parameter was allowed to vary during the least-squares fitting routine. cFit to Paa and Pbb with the monomer determined by ref 35. Reported uncertainties for this preferred structure are double the propagated errors reported by STRFIT and encompass the majority of values obtained by fitting different combinations of constants and/or by using ref 36 for the TFE monomer. dRcm = distance between the centers of mass of the monomers.

Table 4. SAPT Interaction Energya Decomposition Results (kJ mol−1) and Percentage Contribution to the Attractive Interaction (in Parentheses) for Fluorinated Ethylene Complexes with CO2b Ees

Eind

Edisp

Eex

ESAPTb

EMP2(BSSE)c

EBd

VF (side) VF (top) VF (stacked)

−8.33 (52.0%) −7.78 (49.7%) −6.65 (42.5%)

−1.34 (8.3%) −1.30 (8.2%) −0.96 (6.1%)

−6.36 (39.7%) −6.61 (42.1%) −8.02 (51.3%)

8.33 8.03 8.43

−7.70 −7.66 −7.19

−6.41 −6.30 −6.44

−5.80(20)e −6.13(10)e

1,1-DFE (top) 1,1-DFE (stacked)

−5.69 (44.8%) −4.43 (34.8%)

−1.00 (7.8%) −0.78 (6.1%)

−6.02 (47.4%) −7.50 (59.1%)

6.49 7.35

−6.22 −5.35

−5.10 −4.86

−5.80(1)f

cis-1,2-DFE (side) cis-1,2-DFE (stacked)

−7.91 (51.0%) −7.29 (44.6%)

−1.34 (8.6%) −1.11 (6.8%)

−6.28 (40.5%) −7.96 (48.7%)

7.99 8.38

−7.54 −7.97

−6.33 −6.81

g

trans-1,2-DFE (side) trans-1,2-DFE (top)

−7.61 (50.6%) −7.99 (49.5%)

−1.21 (8.1%) −1.42 (8.8%)

−6.23 (41.3%) −6.74 (41.7%)

7.87 8.28

−7.18 −7.87

−6.03 −6.45

h

TFE (side) TFE (top) TFE (stacked)

−7.61 (50.2%) −6.11 (45.7%) −5.84 (41.2%)

−1.30 (8.5%) −1.21 (9.0%) −0.87 (6.1%)

−6.23 (41.3%) −6.07 (45.3%) −7.47 (52.7%)

7.82 6.78 7.52

−7.32 −6.61 −6.66

−6.16 −5.39 −5.69

−7.12(15)i

X···CO2 X =

g

h

a Also included are supermolecular interaction energies (EMP2) and pseudodiatomic approximation (EB) values (where available from experimental studies). See Figure 3 for structures. bEes is the electrostatic, Eind is the induction, Edisp is the dispersion, and Eex is the exchange-repulsion contributions to the overall SAPT interaction energy (ESAPT). cEMP2 is the BSSE-corrected supermolecular interaction energy: EMP2 = E(A···B) − E(A) − E(B), where the energy values are for the dimer and isolated monomers, respectively. dEB is an estimate of the binding energy from spectroscopic data using the pseudodiatomic approximation; see the text for details. eReference 15. fReference 16. gCurrently in progress in our laboratory. The observed rotational spectrum appears to be consistent with a stacked structure. hThe trans-1,2-DFE···CO2 rotational spectrum is expected to be weak because it is formed from two nonpolar monomers. iThis work.

process so that they encompass most of the variations of parameters that were observed when other combinations of spectroscopic constants were fitted. Uncertainties reported for other fits are the propagated values. Two structures for the TFE monomer are reported in the literature,35,36 and these result in relatively large differences in fitted intermolecular parameters. All least-squares fits were performed using both TFE monomer geometries, with the result that RMS deviations of fitted constants were consistently slightly lower when the older structure originally proposed by Bhaumik was used.35 In addition, although Leung’s newer monomer structure (which incorporates13C data and ab initio results) better reproduces the observed monomer rotational constants, the planar moments are better reproduced using Bhaumik’s structure. Our favored dimer structure fits use Bhaumik’s TFE structure, although parameters resulting from fits using the Leung monomer lie within reported uncertainties

and are also included in Table 3. The biggest difference between the two TFE monomer structures is in the C1C4− H6 angle, which differs by 5°. This variation seems to translate directly into the θC4−H6···O9 angle in the dimer, which is also consistently about 5° larger in fits utilizing ref 36 for the monomer structure. A separate approach to structure determination was achieved by applying the planar moment scaling procedure described by Bohn.38 Ab initio structure I was used as the model, and its principal axis coordinates were multiplied by a factor of (Pxxexpt/ Pxxmodel)1/2, where Pxx represents planar moments. This method results in a scaled structure that reproduces experimental planar moments exactly, but this structure is naturally dependent on the initial model. In the present case, the scaled coordinates are considerably closer to the model than they are to inertial fit structures. Using the scaled structure to predict 18 O isotopologue rotational constants gives estimates of B and C D

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Figure 3. Structures for the fluoroethylene complexes referred to in Table 4: (a) VF···CO2 side, (b) top, and (c) stacked; (d) 1,1-DFE···CO2 top and (e) stacked; (f) cis-1,2-DFE···CO2 stacked and (g) side; and (h) trans-1,2-DFE···CO2 side and (i) top.

for 18O8 and 18O9 substitution within 1 MHz of the experimental values, making this an excellent route to the prediction of rotational constants for as-yet unassigned isotopologues. Additional structural information may be obtained by using Kraitchman’s equations40 (as implemented in Kisiel’s KRA routine41) to determine principal axis coordinates of atoms for which single isotopic substitution data are available. Coordinates for both oxygen atoms are summarized in Supporting Information Table S5, where they are compared with results from the preferred R0 structure and the two planar ab initio structures. Only the side-bonded structure (structure I) is consistent with derived oxygen atom coordinates, and Rs and R0 structures are in reasonable agreement with each other, keeping in mind that the two methods probe different parts of the dimer potential well and thus are not expected to give identical results. The Rs coordinates give an O−O substitution distance of 2.321 Å, in excellent agreement with ref 37 (2.324 Å). Finally, the R0 structure for TFE···CO2 can be compared to the analogous side-bonded configuration for vinyl fluoride (VF)···CO2.15 Table 3 shows that R0 structures for both TFE··· CO2 and VF···CO2 have large uncertainties, leading to almost all structural parameters being the same to within the reported uncertainties. This masks any genuine structural variation, although ab initio optimizations suggest that the O9···H6 distance is ∼0.06 Å shorter in TFE···CO2, consistent with a stronger interaction resulting from a more polarized C−H bond as more F atoms are added to the ethylene moiety. 4.5. Pseudodiatomic Approximation Interaction Energy. Using the structure determined above and the very good assumption that the dimer’s a axis lies approximately along the direction of the weak interaction (Figure 2), a weak bond stretching force constant and binding energy can be estimated via a pseudodiatomic approximation (eqs 1 and 2)42,43 ks =

4.6. Symmetry-Adapted Perturbation Theory (SAPT) Interaction Energies for the Fluoroethylene···CO2 Series. Table 4 compares SAPT interaction energies (ESAPT) for various structural forms of the CO2 complexes of VF, 1,1-DFE, and cis- and trans-1,2-DFE and TFE as well as individual contributions to this total binding energy (electrostatic (Ees), induction (Eind), dispersion (Edisp), and exchange−repulsion (Eex)). Structures of all complexes considered are shown in Figure 3 (except for TFE···CO2, which is pictured in Figure 1). A final summary of the SAPT output for each complex as well as details of how the interaction energy is decomposed into the various terms, according to ref 45, can be found in Supporting Information Tables S6−S10. Table 4 also includes interaction energies computed from a supermolecular approach (i.e., as a difference between BSSE-corrected dimer and monomer energies) and finally, where a complex has been studied experimentally, values obtained from a pseudodiatomic treatment of the spectroscopic data, as outlined above in Section 4.5 for the present case. Beginning with the title complex TFE···CO2, SAPT predicts interaction energies for top- and side-bonded structures of −7.32 and −6.61 kJ mol−1, a difference of 0.71 kJ mol−1, which lies between the BSSE-corrected (0.77 kJ mol−1) and (BSSE + ZPE)-corrected (0.66 kJ mol−1) differences from the initial ab initio predictions given in Table 1. In general, the addition of ZPE corrections to the supermolecular interaction energy does not change the relative energy ordering and decreases the absolute value of the interaction energy by roughly 1.2 to 1.5 kJ mol−1, so all further supermolecular interaction energies will refer to ZPE-uncorrected values. The stacked (II) and topbonded (III) forms are predicted to be less stable than the sidebonded form (I) by MP2 optimizations (Table 1 and EMP2 values in Table 4), in agreement with SAPT calculations, although SAPT suggests that these two higher-energy forms have much more similar interaction energies (−6.61 kJ mol−1 (top) and −6.66 kJ mol−1 (stacked)) than the MP2 results indicate. We can now compare results for other members of this series, beginning with the three possible structures of VF···CO2 (top, side, and stacked; Table 4). It is notable that the stacked form of VF···CO2, which in the initial study15 was predicted by MP2 optimizations to be slightly more stable (as shown by the supermolecular energies (EMP2) in Table 4), is now predicted by the SAPT methodology to be less stable than the top- and side-bonded forms (both of which were observed in our microwave spectrum)15 by about 0.5 kJ mol−1. It appears that the similarity in binding energy of top- and side-bonded forms

16π 4(μR cm)2 [4B4 + 4C 4 − (B − C)2 (B + C)2 ] hDJ (1)

1 EB = ksR cm 2 72

(2)

In these expressions, μ, Rcm, and DJ are the reduced mass, center-of-mass separation, and Watson S reduction centrifugal distortion constant (DJ = 0.410(15) kHz, calculated using ΔJ and δk and the relationship DJ = ΔJ − [(2δk(B − C))/(2A − B − C)]),44 respectively. This yields ks = 4.08(5) N m−1 and EB = 7.12(15) kJ mol−1. E

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actually positive for the stacked structure of 1,1-DFE···CO2, suggesting it is not bound at the HF level, consistent with the atypically large dispersion contribution in this case (see above). This highlights the need for reliable descriptions of dispersion interactions for an accurate prediction of the structure and relative stabilities of these complexes. It is interesting that the top-bonded forms of VF, TFE, and trans-1,2-DFE have CO2 located in roughly the same position (interacting with an FC CH edge of the fluoroethylene), and this leads to similar contributions and overall binding energies in these three cases. Curiously, however, in the case of top-bonded 1,1-DFE···CO2, where the same interaction is once again present, all attractive terms (and the overall binding energy) are smaller. 4.7. Comparison of Pseudodiatomic, SAPT, and Supermolecular Interaction Energies. Finally, a comparison of interaction energies may be made with binding energies estimated from a pseudodiatomic approximation using spectroscopic data (eqs 1 and 2) and the supermolecular method (the most readily accessible value during the initial survey of possible structures); these are listed under EB and EMP2, respectively, in Table 4. It is clear that the rather crude estimate of binding energy afforded by a pseudodiatomic approximation does capture some important characteristics of the interactions and correctly predicts almost identical binding strengths for both planar forms of VF···CO2 (EB values overlap to within the uncertainties). However, a comparison of EB between complexes of different fluorinated ethylenes fails to follow the trends in interaction energy (e.g., in the case of 1,1DFE..CO2, the pseudodiatiomic value is about the same as that for VF···CO2, although SAPT and supermolecular values suggest that the former complex is less strongly bound by over 1 kJ mol−1). By contrast, EMP2 values are all fairly consistently smaller than the SAPT values, ranging from about 82 to 91% of the SAPT interaction energies, thereby correctly reproducing much of the relative energy ordering. However, care is needed because the range of supermolecular interaction energies, with respect to the SAPT values, is large enough to allow the relative stability ordering to change. For example, in the case of VF···CO2 it is sufficient to change the stacked structure from most stable (as predicted by the supermolecular interaction energy) to 0.5 kJ mol−1 less stable (as predicted by SAPT). It appears that the supermolecular interaction energy, as calculated in the present study, does not provide results that are reliably consistent with experimental observations. If several structures with similar supermolecular interaction energies are predicted, then further information (either SAPT or experimental) would be required in order to obtain a reasonably reliable estimate of the true interaction energy ordering.

of VF···CO2 arises from a chance cancelation of various contributions to the overall binding. Results for the first difluorinated species (1,1-DFE···CO2) reveal the two forms to have the smallest interaction energies of all complexes studied in the present work (a trend that is mirrored by EMP2 results and reflected in the three attractive terms (Ees, Eind, and Edisp) being among the smallest of all values listed in Table 4). For the remaining difluorinated ethylenes (cis- and trans-1,2DFE···CO2), it is possible to compare our present SAPT results with recent ZPE- and BSSE-corrected CCSD(T)/aug-ccpVTZ//MP2/aug-cc-pVDZ calculations,13 although the stacked form of cis-1,2-DFE···CO2 that our SAPT calculations predict to be most stable (see further discussion below) was not considered in the previous work so we will restrict our comparisons to top- and side-bonded forms. Note also that Trung’s results for a stacked form of trans-1,2-DFE···CO2, in which CO2 is aligned parallel to the C−H bonds, revealed it to be significantly less strongly bound13 than the two planar forms, so it is not considered here. Our present results are in good agreement with Trung’s values for cis-1,2-DFE···CO2 (sidebonded = −6.6 kJ mol−1) and trans-1,2-DFE···CO2 (sidebonded = −6.3 kJ mol−1; top-bonded = −6.5 kJ mol−1), with consistent relative stabilities, although our SAPT interaction energies are about 1 kJ mol−1 more negative (more strongly bound) than the BSSE + ZPE values of Trung (consistent with the inclusion of ZPE corrections in that work). As mentioned above, our SAPT results for the stacked form of cis-1,2-DFE··· CO2 (Figure 3f, a structure not considered by Trung) predict this form to be the most stable, consistent with our recent observations of the rotational spectrum for this complex. All complexes have SAPT interaction energies in the range ca. 5.4 to 8 kJ mol−1 with no clear single indicator (such as monomer polarity) to correlate with increasing binding energy. For instance, the top-bonded form of trans-1,2-DFE···CO2, which comprises only nonpolar monomers, is predicted to be similarly strongly bound to the analogous form of VF···CO2 and more tightly bound than top-bonded 1,1-DFE···CO2. Interaction energies for these complexes are comparable to that calculated for the slipped parallel form of the CO2 dimer (∼6.2 kJ mol−1),46 so the complexation of CO2 with a fluoroethylene is energetically comparable to complexation with itself (i.e., we might expect solvent−solvent and solute−solvent interactions to be of similar magnitude in the present cases). Table 4 shows that dispersion terms dominate the attractive portion of the interaction energy for all nonplanar (stacked) structures considered. For stacked forms of the complexes of VF, 1,1-DFE, cis-1,2-DFE, and TFE, the dispersion term is greater than the electrostatic term [with overall contributions of dispersion (electrostatic) terms to the attractive portion of the interaction energy calculated to be 51.3 (42.5), 59.0 (34.8), 48.9 (44.6), and 52.7% (41.2%), respectively]. However, in the planar forms, dispersion typically contributes a slightly smaller 40−45%, and the electrostatic term dominates (comprising 45−50% of the attractive terms). In all cases, induction contributions to the attractive portion of the interaction are relatively small (∼6−9%). The only planar structure in which dispersion is dominant is top-bonded 1,1-DFE···CO2, which is also the weakest bound complex studied here (as described above), and even then the electrostatic (44.8%) and dispersion (47.4%) contributions are almost equal. Note that the EHF int term in the SAPT output (the Hartree−Fock supermolecular interaction energy, see Supporting Information Table S7) is

5. CONCLUSIONS A single side-bonded form of TFE···CO2 was observed by rotational spectroscopy; this structure was predicted to be the most stable by MP2/6-311++G(2d,2p) optimizations. More sophisticated SAPT calculations provided interaction energies for TFE···CO2 and several other complexes of fluoroethylenes with carbon dioxide, showing that in cases where the difference in interaction energies has been more than about 0.5 kJ mol−1 only the most stable form has so far been observed. SAPT calculations also predicted the stacked structure to be favored for cis-1,2-difluoroethylene···CO2, and indeed, recent experimental studies have suggested that this is the form that is consistent with our experimental measurements. Spectral F

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(3) Raveendran, P.; Wallen, S. L. Cooperative C−H···O Hydrogen Bonding in CO2−Lewis Base Complexes: Implications for Solvation in Supercritical CO2. J. Am. Chem. Soc. 2002, 124, 12590−12599. (4) Sui, R.; Lo, J. M. H.; Charpentier, P. A. Infrared and Computational Studies on Interactions of Carbon Dioxide and Titania Nanoparticles with Acetate Groups. J. Phys. Chem. C 2009, 113, 21022−21028. (5) San-Fabián, E.; Ingrosso, F.; Lambert, A.; Bernal-Uruchurtu, M. I.; Ruiz-López, M. F. Theoretical Insights on Electron Donor-Acceptor Interactions Involving Carbon Dioxide. Chem. Phys. Lett. 2014, 601, 98−102. (6) Azofra, L. M.; Scheiner, S. Tetrel, Chalcogen, and CH··O Hydrogen Bonds in Complexes Pairing Carbonyl-Containing Molecules with 1, 2, and 3 Molecules of CO2. J. Chem. Phys. 2015, 142, 034307. (7) Torrisi, A.; Mellot-Draznieks, C.; Bell, R. G. Impact of Ligands on CO2 Adsorption in Metal-Organic Frameworks: First Principles Study of the Interaction of CO2 with Functionalized Benzenes. I. Inductive Effects on the Aromatic Ring. J. Chem. Phys. 2009, 130, 194703. (8) Besnard, M. I.; Cabaço, M.; Danten, Y. Transient Complex Formation in CO2-Hexafluorobenzene Mixtures: A Combined Raman and Ab Initio Investigation. J. Phys. Chem. A 2009, 113, 184−192. (9) Diep, P.; Jordan, K. D.; Johnson, J. K.; Beckman, E. J. CO2− Fluorocarbon and CO2−Hydrocarbon Interactions from FirstPrinciples Calculations. J. Phys. Chem. A 1998, 102, 2231−2236. (10) Raveendran, P.; Wallen, S. L. Exploring CO2-Philicity: Effects of Stepwise Fluorination. J. Phys. Chem. B 2003, 107, 1473−1477. (11) Tafazzoli, M.; Khanlarkhani, A. Investigation of the Enhanced Solubility of Fluorinated Methanes in CO2 by Monte Carlo Simulation: Absolute Free Energy of Solvation and Structural Properties of Solution. J. Supercrit. Fluids 2007, 40, 40−49. (12) Diao, K.-S.; Wang, F.; Wang, H.-J. Ab Initio Theoretical Study of the Interactions Between CFCs and CO2. J. Mol. Struct.: THEOCHEM 2009, 913, 195−199. (13) Trung, N. T.; Thu Trang, N. T.; Ngan, V. T.; Quang, D. T.; Nguyen, M. T. Complexes of Carbon Dioxide with Dihalogenated Ethylenes: Structure, Stability and Interaction. RSC Adv. 2016, 6, 31401−31409. (14) Gierke, T. D.; Tigelaar, H. L.; Flygare, W. H. Calculation of molecular electric dipole and quadrupole moments. J. Am. Chem. Soc. 1972, 94, 330−338. (15) Christenholz, C. L.; Dorris, R. E.; Peebles, R. A.; Peebles, S. A. Characterization of Two Isomers of the Vinyl Fluoride···Carbon Dioxide Dimer by Rotational Spectroscopy. J. Phys. Chem. A 2014, 118, 8765−8772. (16) Anderton, A. M.; Peebles, R. A.; Peebles, S. A. Rotational Spectrum and Structure of the 1,1-Difluoroethylene···Carbon Dioxide Complex. J. Phys. Chem. A 2016, 120, 247−253. (17) Jeziorski, B.; Moszynski, R.; Szalewicz, K. Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes. Chem. Rev. 1994, 94, 1887−1930. (18) Obenchain, D. A.; Elliott, A. A.; Steber, A. L.; Peebles, R. A.; Peebles, S. A.; Wurrey, C. J.; Guirgis, G. A. Rotational Spectrum of Three Conformers of 3,3-Difluoropentane: Construction of a 480 MHz Bandwidth Chirped-Pulse Fourier-Transform Microwave Spectrometer. J. Mol. Spectrosc. 2010, 261, 35−40. (19) Balle, T. J.; Flygare, W. H. Fabry-Perot Cavity Pulsed Fourier Transform Microwave Spectrometer with a Pulsed Nozzle Particle Source. Rev. Sci. Instrum. 1981, 52, 33−45. (20) Newby, J. J.; Serafin, M. M.; Peebles, R. A.; Peebles, S. A. Rotational spectrum, structure and modeling of the OCS−CS2 van der Waals dimer. Phys. Chem. Chem. Phys. 2005, 7, 487−492. (21) Watson, J. K. G. In Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier: New York, 1977; Vol. 6. (22) Kisiel, Z.; Pszczołkowski, L.; Medvedev, I. R.; Winnewisser, M.; De Lucia, F. C.; Herbst, E. Rotational Spectrum of Trans-Trans Diethyl Ether in the Ground and Three Excited Vibrational States. J. Mol. Spectrosc. 2005, 233, 231−243.

analysis is ongoing, and that species will be described in a future publication. The pseudodiatomic approximation, although crude, seems to correctly predict when two forms are close in energy (although there is only one example in the present data set, and this value is available only after rotational spectra for more than one form have been assigned). A more reliable prediction of the relative magnitude of interaction energy (before spectral measurements are made) is the supermolecular interaction energy; this has been shown to recover roughly 80−90% of the SAPT interaction energy, although this range is still wide enough to obscure which structural form is likely to be most stable. A comparison of SAPT interaction energy results and MP2 calculations for this series of complexes suggests that some caution is needed when interpreting what is likely to be the most stable formBSSE-corrected optimizations and ZPE corrections should certainly be applied, but for this particular set of fluoroethylene···CO2 complexes there is some ambiguity, when studied at the MP2/6-311++G(2d,2p) level, as to the preferred orientation in the gas phase. Higher-level calculations and those with larger basis sets (such as aug-cc-pVTZ or even higher) would be beneficial to determining if this can be resolved.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b08286. Full citations for Gaussian 09 (ref 25) and SAPT (refs 27 and 28); details of the structure-fitting procedure; principal axis coordinates obtained from MP2/6-311+ +G(2d,2p) optimizations for structures I−III and experimentally determined structure I; tables of experimental rotational transition frequencies for the normal and all isotopic species; results of dipole moment fitting with QSTARK; literature monomer structures; oxygen atom principal axis coordinates derived from Kraitchman single isotopic substitution calculations; and full results for SAPT calculations for VF···CO2, 1,1-DFE···CO2, cis1,2-DFE···CO2, trans-1,2-DFE···CO2, and TFE···CO2 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (217) 581-2679. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National Science Foundation Research at Undergraduate Institutions grants CHE-1214070 (support for R.E.D. and W.C.T.) and CHE-0809387 (instrument construction).

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REFERENCES

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