J. Phys. Chem. A 2010, 114, 9309–9318
9309
Infrared Spectra of CF2dCHD and CF2dCD2: Scaled Quantum-Chemical Force Fields and an Equilibrium Structure for 1,1-Difluoroethylene Donald C. McKean,† Mark M. Law,‡ Peter Groner,§ Andrew R. Conrad,| Michael J. Tubergen,| David Feller,⊥ Michael C. Moore,# and Norman C. Craig*,# School of Chemistry, UniVersity of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, United Kingdom, Chemistry Department, UniVersity of Aberdeen, Meston Walk, Aberdeen AB24 3UE, United Kingdom, Department of Chemistry, UniVersity of MissourisKansas City, Kansas City, Missouri 64110-2499, Department of Chemistry, Kent State UniVersity, Kent, Ohio 44242, Department of Chemistry, Washington State UniVersity, Pullman, Washington 99164-4630, and Department of Chemistry and Biochemistry, Oberlin College, Oberlin, Ohio 44074 ReceiVed: May 17, 2010; ReVised Manuscript ReceiVed: July 16, 2010
Infrared (IR) spectra in the gas phase are reported for CF2dCHD and CF2dCD2 in the region 350-4000 cm-1. Ab initio calculations of an harmonic force-field and anharmonicity constants have been made with an MP2/aug-cc-pVTZ model. These enable a number of Fermi resonances in each species to be analyzed and a complete set of “observed” harmonic frequencies to be derived. The latter are combined with similar data for CF2dCH2 in a scaling of the model harmonic force field to both anharmonic and harmonic frequencies. Inspection of the scale factors reveals minor defects of the model, evident in the out-of-plane wagging modes and in the CF stretch/CF stretch interaction force constant. Fermi resonance treatments involved in all isotopomers studied are compatible with the overall force-field refinement results. The treatment leaves a small anomaly in the 13C shift on ν1. Improved microwave spectra are reported for five isotopic species, and a semiexperimental equilibrium structure for F2CdCH2 is determined and compared favorably with the structure obtained from new high-level ab initio calculations. Centrifugal distortion constants are predicted for the five isotopic species, and those for F2CdCH2 are compared with values fit to microwave spectra. Introduction Infrared (IR) spectra of CF2dCD2 (d2) and CF2dCHD (d1) have not been reported since the original study of Edgell and Ultee in 1954,1 although predictions of fundamental frequencies from a simplified force field have appeared in the literature.2 In a companion study to the present, new spectra of CF2d12CH2 and CF2d13CH2 were reported in gas and liquid argon phases, a series of Fermi resonances (FRs) analyzed, and a set of “observed” harmonic frequencies obtained from experimental fundamental frequencies by applying anharmonic and FR corrections derived with the aid of quantum-chemical (QC) calculations.3 The present study was undertaken with two objectives. The first of these was to obtain improved spectra of d2 and d1 and from these to derive “observed” harmonic frequencies, employing QC calculations. These frequencies could then be combined with similar data for the d0 species in a scaling of the ab initio harmonic force field. The latter should represent the best available harmonic force field for the molecule. A study of the scale factors involved will also provide a measure of the quality of the QC model employed because, for an exact ab initio force field, every scale factor would be unity. For such a test, the number of scale factors should be as large as possible. 1,1Difluoroethylene (11DFE) is found to constitute a favorable * To whom correspondence should be addressed. † University of Edinburgh. ‡ University of Aberdeen. § University of MissourisKansas City. | Kent State University. ⊥ Washington State University. # Oberlin College.
species for a study of this kind because the scale factors are not strongly correlated with each other and each is well determined by the data. The QC calculations involved were vital also to our second objective, which was to determine a semiexperimental equilibrium geometry4,5 for 11DFE. For the source of accurate groundstate rotational constants needed for this geometry, it is usual to look to the microwave (MW) spectrum. Three studies have been conducted, all employing continuous-wave (cw) spectra.6-8 In the first of these, that of Edgell et al.,6 data were reported for the d0, d1, and d2 species. In the second such study, Laurie and Pence observed cw spectra from the two 13C species and reinvestigated the d0 species.7 In the third work, Chauffoureaux reported additional lines (cw) for the two 13C species.8 The improved precision offered by contemporary pulsedbeam, cooled-jet Fourier transform MW spectroscopy led us to reinvestigate the MW spectra of all five isotopomers and thereby upgrade the quality of the ground-state rotational constants. A semiexperimental equilibrium structure has been determined from the new rotational constants and calculated equilibriumrotational constants. We have also computed the equilibrium structure with high-level ab initio methods. The two structures agree closely. MW spectroscopy has not been the only method for determining the structure of 11DFE. We note here three studies by gas-phase electron diffraction (ED).9-11 One of these combined both ED and MW.11 Experimental Section Syntheses. Zinc dehalogenation of F2BrCCFHD and F2BrCCFD2 in refluxing ethanol gave F2CdCHD and F2Cd
10.1021/jp104498n 2010 American Chemical Society Published on Web 08/06/2010
9310
J. Phys. Chem. A, Vol. 114, No. 34, 2010
CD2, respectively.6 The two haloethanes were byproducts of the preparation of the haloethanes used in the synthesis of the d1 and d2 isotopomers of cis- and trans-1,2-difluoroethylene.12 For spectra free of traces of the haloethane starting material, the F2CdCHD and F2CdCD2 samples were purified by preparative gas chromatography on a 5 m column packed with tricresylphosphate coated on Fluoropak 80 particles (Analabs) at room temperature. Spectroscopy. Spectra in the mid-IR region were recorded on a Nicolet 760 Magna Fourier transform spectrometer with a resolution of 0.1 cm-1 and boxcar apodization. A total of 600 scans were accumulated for the background and 300 for the sample. The cell was a 10 cm Wilmad minicell with 2.5 cm potassium bromide windows. Residual lines from atmospheric water and carbon dioxide remain in the spectra because the spectrometer was not purged. Far-IR spectra were recorded on a Perkin-Elmer 1760X spectrometer in a 10 cm cell with either polyethylene or cesium iodide windows. The spectrometer was purged with dry nitrogen gas. A total of 400 scans were accumulated for the background and for the sample. Residual water lines, which arise from water evaporating from the walls of the cell during long scans, were subtracted as well as possible. The mid-IR spectrum of the F2CdCHD species is given in Figure S1a,b of the Supporting Information, and the far-IR spectrum is given in Figure S2 of the Supporting Information. Corresponding spectra for F2CdCD2 are supplied in Figures S3a,b and S4 of the Supporting Information. MW spectra were recorded with a mini pulsed-molecularbeam, a Fourier transform instrument at Kent State University with a spectral range from 10 000 to 22 500 MHz.13 The driver gas was a 30:70 mixture of helium and neon at 2 atm, and the samples were approximately 1 mmol in a 2 L flask. Theoretical Procedures Procedures were identical with those described in a previous work.3 Outputs of cubic and quartic potential constants and Coriolis coefficients from Gaussian03 (G03) calculations,14 using the MP2/aug-cc-pVTZ (macct) model,14-16 were analyzed with the aid of programs previously described,3,17 to derive anharmonicity data with varying numbers of FRs. These programs confirmed that our version of G03 (C.02) was determining anharmonicity constants correctly. FR treatments were carried out as before, with the resulting deperturbed frequency and anharmonicity constants being identified by an asterisk, thus, νi* and xrs*.3 For scaling of the QC force fields, we employed the program ASYM40.18 The scaling procedure is that recommended by Pulay et al., in which each off-diagonal symmetry force constant is scaled by the geometric mean of the scale factors for the two corresponding diagonal force constants.19 In one instance, described below, one off-diagonal force constant was adjusted manually before the programmed scaling. As in our previous work, we use the notation Wrst to represent the corresponding FR interaction matrix element
Wrss ) 0.5φrss[Vr(Vs + 1)(Vs + 2)/8]1/2 for interaction between the states 〈Vr, Vs| and 〈Vr - 1, Vs + 2| and
Wrst ) φrst[Vr(Vs + 1)(Vt + 1)/8]1/2 for interaction between the states 〈Vr, Vs, Vt| and 〈Vr - 1, Vs + 1, Vt + 1|.
McKean et al. Results Assignments for CF2dCHD. Table 1 lists all of the IR features that we observed for the CF2dCHD sample. Figures S1a,b and S2 of the Supporting Information contain the IR spectra for this species. Several bands ascribed to impurity CF2dCH2 are included. The reduction of symmetry in CF2dCHD means that bands arising from the in-plane A′ modes can have hybrid A/B-type contours, while the three out-of-plane A′′ modes yield pure C-type bands. The only significant assignment problem apart from bands involving FRs arises with ν8 (A′) and ν12 (A′′). In the prior work of Edgell and Ultee, ν8 was assigned to a band at 542 cm-1, while ν12 was left unassigned.1 G03 with the macct model predicts the two bands to have almost coincident anharmonic frequencies and comparable IR intensities, as follows: ν8 545.4 cm-1, 5.2 km mol-1; ν12 547.0 cm-1, 6.0 km mol-1. Figure 1 shows details of the absorption in this region. The dominant Q branch at 546.5 cm-1 is accompanied by weaker ones at 547.5, 545.8, and 543.9 cm-1. The spectrum at 0.1 cm-1 resolution shows many “lines” spaced by approximately 0.35 cm-1 to either side of the band center. This spacing must arise from an A- or B-type band for this oblate-tending top. Other A- and B-type bands in the spectrum have this spacing, which is consistent with the known rotational constants. An A-type band would have a distinct Q branch. Somewhat further out in the wings of the band are distinct “lines” with a spacing of approximately 0.68 cm-1, which must come from a C-type band. Two other C-type bands in the spectrum have this spacing, which is consistent with high-resolution modeling of the band types with known rotational constants. In the present situation, the occurrence of a C-type band due to ν12 is diagnosed. We can predict the position of ν12 with some confidence from the combination band at 1164.3 cm-1, which from its B-type contour can only be due to ν11 + ν12. With x11,12 ) 0.1 cm-1 in the absence of FR and ν11 ) 618.4 cm-1, ν12 is placed at 545.8 cm-1, very close to the main Q branch at 546.5 cm-1. A small FR between ν11 + ν12 and ν5, as suggested by G03, could give exact coincidence with 546.5 cm-1. Placing ν12 at 546.5 cm-1 then permits the assignment of 547.5 cm-1 to ν12 + ν9 - ν9 (x9,12 ) 0.9 cm-1) and 545.8 cm-1 to ν12 + ν6 - ν6 (x6,12 ) -0.7 cm-1) or ν12 + ν11 - ν11 (x11,12 ) -0.6 cm-1). Here we use the notation νj + νi - νi to refer to “hot bands”. With no obvious hot band to explain the 543.9 cm-1 Q branch, the latter might then be due to ν8. However, it might be preferable to use the more intense Q branch at 547.5 cm-1 for ν8. (Neither of these alternatives permits an accurate prediction of the band at 1092.1 cm-1, which might be 2ν8, 2ν12, or ν8 + ν12). The tentative nature of these assignments suggests the need for caution in their adoption, and for the purposes of the FR assessments and force-field refinement below, we choose to place both ν8 and ν12 at 546.5 cm-1. FRs for F2CdCHD. The G03 calculation with the macct model and DelFre ) 100,3 the frequency interval in which an FR is recognized, identifies a total of 14 FRs, affecting ν1, ν2, ν3, ν4, and ν5. However, those involving ν1 and ν2 proved to be trivial, with displacements ∼0.2 cm-1, and have been ignored here. ν4 and ν5. These levels, lying close to each other, are, according to G03, both involved in a strong FR with the level ν10 + ν12, and an interacting polyad of order 8 must be considered because six overtone and combination levels may be involved. Table 2 shows the data involved. Unfortunately, two key frequencies are missing from our spectra, octad levels 3 and 6, the former largely ν10 + ν12. The absence of the latter
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9311 TABLE 1: IR Frequencies Observed for CF2dCDH νobsd/cm-1
assignment
νpreda
νobsd/cm-1
3958.5 vw A? ∼3670 vw 3426.4 vw A? 3258.3 vvw Q 3133.2 w A 3132.2 vw Q 3010.8 vvw B? 2952.4 vw Q 2941.6 vw C
ν1 + ν7 (A′) ν1 + ν12 (A′′) 2ν3 (A′) ν2 + ν6 (A′) ν1 (A′) ν1 + νi - νi (A′) ? ν3 + ν5 (A′) ν2 + ν11 (A′′) ν5 + ν6 + ν10 (A′′) ? ν9 + 3ν10 (A′′) 2ν6 + ν7 (A′) ν3 + ν6 (A′) ν4 + ν10 + ν12 (A′) ν5 + ν10 + ν11 (A′) ? ν6 + 2ν7 (A′) ν6 + ν7 + 2ν9 (A′) ν10 + 2ν11 + ν12 (A′′) ν7 + ν9 + ν10 + ν12 (A′) ν3 + ν7 (A′) ν6 + ν11 + 2ν12 (A′′) ν6 + ν7 + ν10 (A′′) ν4 + 2ν9 (A′) ν4 + ν5 (A′) 2ν6 + ν11 (A′′) ν5+ 2ν11 (A′) ν5 + ν7 + ν9 (A′) 2ν5 (A′) ν2 (A′) ν3 + ν12 (A′′) ν3 + ν8 (A′) ν4 + ν6 (A′) ? ν4 + ν7 (A′) ? ν3 + ν9 (A′) ? ν4 + ν10 (A′′) ν6 + 2ν11 (A′) ? ν5 + ν7 (A′) ν4 + ν11 (A′′)
3958.3 3678.0 3427.4 3258.6
1857.6 w A 1758.4 m A 1756.3 wm Q 1719.4 vs A 1651.5 m A 1618.5 w Q 1611.0 w Q 1537.0 m A ∼1480 vw 1387.7 vw B 1339.1 s B 1301.0 vs B 1240.6 s A 1219.6 s B 1164.3 w B 1092.1 vw Q
2933.2 vw Q 2686.6 vw Q 2643.6 w A? 2633.6 w Q 2593.8 vw Q 2583.2 vw Q 2554.7 vw Q 2546.5 vw Q 2543.4 vw Q 2533.5 vw Q 2526.8 vw Q 2513.6 vw Q 2472.5 vvw Q 2455.0 vw A 2445.9 vvw Q 2432.8 vvw Q 2329.6 m A 2262.6 vw Q 2224.9 w B 2167.9 vw Q 2125.5 w Q 2120.8 vw Q 2117.3 vw Q 2071.7 vvw Q 2066.5 vw Q 2058.7 vw Q 2040.8 vw Q ∼1916 vvw Q
2949.0 2946.2 2929.6 2685.5 2683.2 2644.8 2630.3 2619.2 2581.6 2557.9 2551.7 2547.6 2543.5 2533.9 2525.3 2516.8 2542.9 2470.6 2468.8 2458.0 2464.6 2263.5 2264.8 2239.7 2140.7 2117.2 2083.8 2062.4 2058.4 1929.8
1019.0 vvw Q 930.0 s A 831.6 w Q 827.6 m A 823.8 w Q 818.8 w Q 802.1 wm Q 792.4 w Q 782.0 w Q 771.2 m Q 770.3 ms Q 769.3 ms C 767.8 m Q 694.2 vw Q 685.9 vw Q 622.3 vw Q 618.4 wm Q 617.5 w Q 614.3 vw Q 603.2 vw Q 547.5 wm Q 546.5 m Qb 545.8 wm Q 543.9 wm Q 401.0 w A/B
assignment 2ν6 (A′) ν6 + ν7 (A′) FR ? ν3 (A′) FR 2ν7 (A′) FR ν5 + ν9 (A′) CF2dCH2 2ν10 (A′) FR ? ν6 + ν12 (A′′) ? ν10 + ν11 (A′) FR ν6 + ν9 (A′) FR ν4 (A′) FR 2ν11 (A′) FR ν5 (A′) FR ν11 + ν12 (A′) FR 2ν8 (A′′) ν8 + ν12 (A′′) 2ν12 (A′) ν9 + ν11 (A′′) ν6 (A′) ν7 + νi - νi (A′) ν7 (A′) 2ν7 - ν7 (A′) ν7 + νi - νi (A′) CF2dCH2 ? ? 2ν10 - ν10 (A′′) ν10 + νi - νi (A′′) ν10 (A′′) 2ν10 - ν10 (A′′) 2ν11 - ν8 (A′) ? 2ν11 - ν11 (A′′) ν11 (A′′) ν11 + νi - νi (A′′) ν11 + νi - νi (A′′)
νpreda 1857.8 1756.5
1653.8 1635.2 1530.2 1475.8 1387.1 1330.3 1237.0 1164.3 1093.2 1093.1 1090.2 1019.5
823.9
770.9
767.8 694.1 622.2
ν8 (A′) ?, ν12 + ν9 - ν9 ν12 (A′′) ν12 + νi - νi, i ) 6 or 11 ν8 (A′)? ν9 (A′)
a Based on deperturbed values. Levels involving a single quantum of ν4 or ν5 should lie 14-15 cm-1 below the values quoted in this column. b For the force-field scaling exercise, this peak of uncertain origin is assigned to both ν8 and ν12.
Figure 1. Details of the overlapped ν8 (A/B-type) and ν12 (C-type) bands in the IR spectrum of F2CdCDH at 39 Torr.
9312
J. Phys. Chem. A, Vol. 114, No. 34, 2010
McKean et al.
TABLE 2: Energy Levels and FR Data (cm-1) for the ν4/ν5 System in CF2dCHD
a
octad no.
level
νobsda
νcalcd* b
ν8×8refc
εd
8 7 6 5 4 3 2 1
ν10 + ν11 ν 6 + ν9 ν10 + ν12 ν4 2ν11 ν 7 + ν9 ν5 ν11 + ν12
1387.7 1339.1 ? 1301.0 1240.6 ? 1219.6 1164.3
1386.6 1330.3 1317.1 (1316.4) 1237.0 1228.0 (1234.1) 1165.2
1387.2 1340.5 1328.8 1300.2 1241.2 1233.3g 1219.2g 1164.4
0.5 –1.4 0.8 –0.6 0.4 –0.1
ν6×6refe
W4ijf
1340.6 1328.8 1300.1 1241.3 1233.4g 1219.2g
W5ijf
–5.96 –7.94 18.55
5.91 (–0.55) 22.68
(–0.30) (–1.60)
–5.71 8.65
(–1.35)
–7.36
b
This work, gas phase. Deperturbed value calculated using observed fundamentals and G03 values of deperturbed xij* constants. In parentheses, values derived from refinement to the six observed frequencies using macct values of W. c Perturbed frequencies from the 8 × 8 refinement. d ε ) νobsd - ν8×8ref e Perturbed frequencies from the 6 × 6 refinement, which yields ν4* ) 1315.9 ( 1.9 and ν5* ) 1235.0 ( 2.3 cm-1. f FR parameters from the macct model. In parentheses are small values ignored in both of our treatments. The subscripts i and j refer to the modes involved in the respective overtone or combination level. g These two levels are roughly equal mixtures, in- and out-of-phase, of ν7 + ν9 and ν5. The order of their appearance here has no significance.
is particularly unfortunate because of the very strong correlation between its value and those of ν4* and ν5*. These missing data made it impossible to refine any W interaction parameters in addition to the values of ν4* and ν5* themselves, for which we derived 1316.4 ( 1.3 and 1234.1 ( 1.6 cm-1, respectively. The fit to observed data and the predicted values of the missing levels are shown in column 5 of Table 2. Noticing that levels 1 and 8 involved less than 1% of ν4 or ν5 and aware that the same FRs would be repeated in the polyad involving ν3, we tried a further refinement of ν4* and ν5* from which levels 1 and 8 were omitted. As expected, this procedure produced little change, either to the fit or to the values of ν4* and ν5*, which became 1315.9 ( 1.9 and 1235.0 ( 2.3 cm-1, respectively. These results indicate that the observed fundamental frequencies ν4 and ν5 have been depressed through FR by 14-15 cm-1. ν3. G03 identifies FRs between ν3 and ν5 + ν8, ν6 + ν7, ν4 + ν9, 2ν7, and ν5 + ν9, in descending order of energy. This list, however, omits the further resonances studied above in the regions of ν4 and ν5. Using the reduced dimension of six for the latter, the ν3 polyad then comprises 15 levels as shown in Table 3, together with their estimated deperturbed and perturbed (after FR) values. The polyad levels P10-P15, which involve ν8, are subject to greater error than the others because of uncertainty in the value of ν8. Here only four observed bands could be assigned to members of the polyad, namely, P1, P4, P6, and P9. The % ν3 given in column 7 indicates that P6 is very largely composed of ν3. For ν3*, the refined value is 1719.8 ( 0.4 cm-1, which is only 0.4 cm-1 distant from that of the band observed at 1719.4 cm-1. The cumulative outcome of all of the FR effects on ν3 has therefore been negligible. However, several of the overtone and combination levels elsewhere in the polyad have been displaced far from their deperturbed positions, as seen by comparing columns 3 and 4 in Table 3, by resonances not involving ν3. This result enables us to say with some confidence that the band observed at 1857.6 cm-1 is not ν4 + ν8 but 2ν6, which is not involved in this polyad and is expected at 1857.8 cm-1. The complete set of fundamental frequencies, deperturbed where necessary, is shown in Table 4A, which includes also the G03 harmonic frequencies, anharmonic corrections, and resulting “observed” harmonic frequencies. OWertone and Combination Bands. Table 1 contains a number of suggested assignments for overtone and combination bands. With several exceptions, only binary and ternary transitions have been considered. Values of such levels in column 3 are predicted from the deperturbed fundamental frequencies. Where ν4 and ν5 are involved, the actual transitions are likely to lie 14-15 cm-1 lower than those predicted. (For ν4 + ν5,
TABLE 3: FR Levels (cm-1) for the Polyad Involving ν3 in CF2dCHD no.
level
νcalcd* a
νpredb
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
ν8 + ν10 + ν12 ν8 + ν6 + ν 9 ν4 + ν8 ν8 + 2ν11 ν7 + ν8 + ν 9 ν5 + ν8 ν6 + ν7 ν4 + ν9 ν6 + 2ν9 ν3 ν 4 + ν9 2ν7 ν7 + 2ν9 ν9 + 2ν11 ν5 + ν9
1864.2 1875.3 1858.5 1782.9 1775.0 1779.1 1756.5 1715.5 1732.6 (1719.8)e 1715.5 1653.8 1630.4 1638.2 1635.2
1885.7 1874.2 1844.5 1786.7 1779.4 1764.4 1758.5 1742.7 1727.8 1719.4 1696.7 1651.1 1643.4 1636.1 1616.2
νobsdc
εd
1758.4
–0.1
1719.4
0.0
1651.5
0.4
1618.5
2.3
% ν3 0.0 0.0 0.0 0.1 0.1 0.7 5.0 2.2 9.8 76.5 1.1 3.8 0.4 0.1 0.2
a
Values calculated using deperturbed fundamental frequencies, except for ν3*, and G03 values of deperturbed xrs* constants. b Values of observed levels predicted from the data in column 3, using the following G03 FR matrix elements W3rs (in addition to those involving ν4* and ν5*) (r,s): (4,9) -5.7, (5,8) -3.7; (5,9) -5.9; (6,7) 8.6; (7,7) -13.8 cm-1. ν3* was refined in this calculation. c Frequencies observed in this work: in italics are those used in the ν3* refinement. d ε ) νobsd - νcalcd. e Refined value: 1719.8 ( 0.4 cm-1.
this difference should be about 30 cm-1.) The imprecise nature of the analysis of the ν4/ν5 system suggested that a more detailed analysis of the corresponding overtones and combinations would not be profitable. In fact, quite useful predictions of such levels may well be obtained by using the observed frequencies of ν4 and ν5 rather than the deperturbed ones. CF2dCD2: Assignments and FRs. Table 5 lists all of the features seen in our sample of CF2dCD2. These include several peaks arising from impurity CF2dCHD, whose concentration was estimated to be about 4%. In the Supporting Information, parts a and b of Figure S3 give the mid-IR spectrum and Figure S4 gives the far-IR spectrum of CF2dCD2. As noted in the companion paper,3 G03 uses B1 for the out-of-plane modes and B2 for the in-plane modes. Thus, the G03 numbering of these modes differs from that used in this paper. A significant change from the previous assignments of Edgell and Ultee1 concerns the location of ν7, the asymmetric CD2 stretch. This mode was previously assigned at the same time to a weak IR band in the gas phase at 2354 cm-1 (our value: 2358.8 cm-1) and a Raman band at 2385 cm-1 in the liquid, with the former value being preferred. The resulting ν7 - ν1 splitting of 2358.8 - 2278.8 ) 80.1 cm-1 is incompatible with the ab initio
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9313 TABLE 4: Calculated and Observed Harmonic and Anharmonic Fundamental Frequencies (cm-1) for CF2dCHD and CF2dCD2 A. CF2dCHD mode
ωmacct
νmaccta
∆b
νobsda
ωobsd
A′ 1 2 3 4 5 6 7 8 9 A′′ 10 11 12
3303.9 2433.3 1756.8 1336.6 1260.2 945.6 838.5 550.1 401.4 778.1 642.5 556.4
3171.2 2356.1 1719.2* 1304.4* 1230.1* 930.0 824.6 545.4 400.6 755.1 631.3 547.0
132.7 77.2 37.6 32.2 30.1 15.6 13.9 4.6 0.9 23.0 11.2 9.4
3133.2 2329.6 1719.8* 1315.9* 1235.0* 930.0 827.6 546.5 401.0 769.3 618.4 546.5
3265.9 2406.8 1757.4 1348.1 1265.1 945.6 841.5 551.1 401.9 792.3 629.6 556.9
B. CF2dCD2 mode
ωmacct
νmacctc
∆b
νobsdc
ωobsd
A1 1 2 3 4 5 A2 6 B1 7 8 9 10 B2 11 12
2371.7 1737.5 1096.0 876.0 546.0 521.6 2505.4 1307.2 814.1 376.1 672.7 591.4
2303.8 1704.2* 1072.9* 861.4 541.0 513.8 2424.4* 1276.8* 801.5 374.5 655.2 581.8
67.9 33.3 23.1 14.6 5.0 7.8 80.9 30.4 12.5 1.6 17.5 9.6
2278.8 1704.3* 1072.4* 858.8 542.6 513.3 2392* 1288* 806.3 376.0 660.4 574.6
2346.7 1737.6 1095.5 873.4 547.6 521.1 2472.9 1318.4 818.8 377.6 677.9 584.2
a 10 FRs treated: 3/4,9; 3/5,8; 3/5,9; 3/6,7; 3/7,7; 4/6,9; 4/10,12; 5/7,9; 5/10,12; 5/11,11. Asterisks designate deperturbed frequencies. b ∆ ) ωmacct - νmacct. c 10 FRs treated: 2/4,4; 2/3,5; 2/8,10; 3/5,5; 3/ 6,6; 3/9,10; 3/12,12; 7/2,9; 7/3,8; 8/4,10. Asterisks designate deperturbed frequencies.
value from the macct model of 115.2 cm-1. (The latter value includes a correction of 6.1 cm-1 from FR with ν2 + ν9 above.) This ab initio result leads one to expect ν7 to lie near 2394 cm-1, where, in fact, a very weak B-type IR band can be seen at 2390.1 cm-1 in Figure 2. Although this feature is weak, its structure is consistent with other weak B-type bands in the spectrum. The spacing between the Q-branch “horns” in the R and P branches is consistent with that of other bands. The agreement between the latter and the Raman liquid band at 2385 cm-1 is then most satisfactory. The ab initio IR intensity estimated for ν7 is only 1.2 km mol-1, compared with 24.8 km mol-1 for ν1, so that the weakness of ν7 in the IR spectrum is understandable. The 2358.8 cm-1 band is readily assigned to ν3 + ν8, expected near 2361 cm-1, and is likely to be in FR with ν7 as discussed below. The normally IR-inactive fundamental due to ν6 (A2) was seen as a very weak Q branch at 513.3 cm-1, which agrees excellently with the location of this mode in CF2dCH2 at 708.2 cm-1.3 The 513.3 cm-1 band appeared as a faint shoulder in the far-IR spectrum (Figure S4 of the Supporting Information) and as a distinct but weak feature in the higher resolution midIR spectrum at 113 Torr. Resonances. G03 identifies eight FRs in CF2dCD2 when the option DelFre ) 100 is imposed in conjunction with the macct model: ν7 with ν2 + ν9; ν2 with 2ν4, ν8 + ν10, ν3 + ν5; ν8 with ν4 + ν10; ν3 with ν9 + ν10, 2ν12, and 2ν6. A fourth possible resonance between ν3 and 2ν5 was ignored by the program because k355 is less than 10 cm-1. The cumulative effect of the FRs among the lower levels leads to the expectation of nine
and eight levels in resonance with ν7 (2329.4 cm-1) and ν2 (1703.3 cm-1), respectively. However, observation of all of the ternary and quaternary levels involved is not possible with the present data. Fortunately, the FR shifts involved are all small. ν3. The only FR capable of complete analysis proved to be that involving ν3, for which data are shown in Table 6. This interpretation entailed the assignment of 2ν5, for which purpose we use the Q branch at 1085.7 cm-1. This Q branch is sufficiently near the central Q branch of ν3 at 1076.4 cm-1 to be considered alternatively as a hot band of ν3, i.e., a transition of the type ν3 + νi - νi. However, the G03 values of all of the xrs’s associated with ν3 prove to be negative, implying that all of the hot bands should lie below 1076.4 cm-1 rather than above the latter value. Three such Q branches are, in fact, conspicuous in the spectrum (Table 5). Only if a marked FR shift of the appropriate sign was associated with the upper state of the hot band concerned could a value higher than 1076.4 cm-1 result. No such FR was found, although any involving B-type bands originating from room temperature populations in the B1 ν9 and ν10 states would be hard to detect. With the choice of 2ν5 at 1085.7 cm-1, the deperturbed value of ν3* is estimated (Table 6) to be 1072.4 cm-1, with the overall FR shift being 4.0 cm-1, compared with 1.8 cm-1 from the G03 treatment. The largest effect comes from the interaction with 2ν6, as is the case for ν3 in d0. Refinement of the W values to the observed frequencies shows that our approach using experimental data leads to an increased interaction with 2ν6 but a much smaller one with 2ν12, compared with G03. The G03 value for W355 fits very well with our assignment of 2ν5 at 1085.7 cm-1. The FR shifts calculated in 2ν12 and 2ν5 are so small, both 0.1 cm-1, that the refined values of the corresponding W elements will be enormously sensitive to the macct xrs* values involved. The changes shown in W3,5,5 and W3,12,12 from their G03 values will not therefore be significant. ν8. G03 calculates a FR shift of 1.1 cm-1 from the interaction with ν4 + ν10 below, with separation of the deperturbed levels being 40.4 cm-1. The B-type band from ν4 + ν10 is expected at 1235.3 cm-1 and is unlikely to be detected because it will underlie the A-type band due to ν11 + ν12 observed at 1236.4 cm-1. With a slightly lower estimated separation of the deperturbed levels of 53.2 cm-1, the FR shift on ν8 is estimated to be 0.9 cm-1. The deperturbed value of ν8* is then 1288 cm-1. ν2. The main IR band assigned to ν2 occurs at 1703.3 cm-1. G03 with the macct model finds the deperturbed values of ν2, ν3 + ν5, ν8 + ν10, and 2ν4 to be respectively 1704.2 (0.9), 1612.0 (-0.7), 1648.7 (-1.0), and 1721.6 (0.8), with the parentheses enclosing the FR shifts resulting from these interactions. Of these three overtone or combination levels, only one was securely identified in our spectrum, ν3 + ν5, being assigned to the band at 1617.1 cm-1. Because our value for this band based on observed fundamental frequencies and an estimate of the 3ν5/ ν3 + ν5 FR is 1614.2 cm-1, there is no evidence for involvement of this remote level in an interaction with ν2. A possible value for 2ν4 is a shoulder at about 1718 cm-1, in which case a FR shift of ∼1 cm-1 on ν2, as suggested by the G03 calculation, is acceptable, making ν2* ) 1704.3 cm-1. None of the levels reckoned to be in FR with ν3 + ν5 due to those affecting ν3 could be identified. ν7. An approximate calculation of the unperturbed position of ν2 + ν9 is obtained using the observed value for ν2, 1703.3 cm-1, from which ν2 + ν9 is expected at 1703.3 + 806.3 + 0.4 ) 2510.0 cm-1. A B-type band is seen close to this value at 2512.3 cm-1. The separation of the perturbed levels of ν2 + ν9 and ν7 is then 2512.3 - 2390.1 ) 122.2 cm-1, which is
9314
J. Phys. Chem. A, Vol. 114, No. 34, 2010
McKean et al.
TABLE 5: IR Frequencies Observed for CF2dCD2 ν (cm-1) 3975.9 vw A 3566.7 vw B 3459.6 vw B? 3395.7 vw A 3352.4 vvw Q 3323.8 vvw Q 3319.4 vw Q 3314.6 vw Q 3209.5 vvw Q 3184.8 vw Q 3133.2 vw Q 3081.0 vw B 3001.0 vw Q 2986.2 vw B 2945.9 vvw Q 2934.8 vw Q 2927.4 vw Q 2845.1 vw Q 2821.5 vvw Q 2788.5 vw Q 2776.8 w A 2774.0 vw Q 2720.8 vvw Q 2643.4 vvw Q 2633.5 vvw Q 2568.9 wm Q 2555.4 m A 2552.1 wm Q 2512.3 vw B 2466.6 vw Q 2390.1 vvw B 2358.8 w B? 2329.4 w Q 2278.8 ms A 2276.4 ms Q 2274.7 ms Q 2244.5 w Q 2158.6 w Q 2156.6 w Q 2147.9 mw A 2146.0 w Q 2144.2 w Q 2140.3 w Q 2104.3 w Q 2091.6 wm A 2089.4 w Q 2085.7 w Q 2083.8 w Q 2014.7 vvw Q 1932.6 vw A 1879.5 vw B? 1876.8 vw Q 1800.6 vw Q 1758.4 w Q a
assignment ν3 + ν7 (B1) 2ν2 (A1)
1739.9 w Q 1703.3 vs A 1669.3 m Q 1665.1 m Q 1661.4 m A
3454.9 3397.0
1617.1 m Q
ν2 + 2ν9 (A1) ν2 + ν3 + ν5 (A1) ν2 + ν4 + ν11 (B2)
3314.3 3313.1 3209.5
ν1 + ν4 (A1) ν1 + ν9 (B1) ν2 + 2ν11 (A1) ν2 + ν8 (B1) ν4 + ν8 + ν9 (A1) ν1 + ν11 (B2) ν2 + ν11 + ν12 (A1) ν2 + 2ν12 (A1) ν1 + ν5 (A1) ν2 + 2ν5 (A1) ν2 + ν3 (A1) ? ? ? ? 2ν8 (A1) ν2 + ν4 (A1) ? ν2 + ν9 (B1) FR ? ν7 (B1) FR ν3 + ν8 (B1) FR
3133.9 3081.1 3003.9 2984.7 2943.4 2934.9 2925.2 2858.1 2821.3 2786.1 2773.4
ν1 (A1) ν1 + νi - νi (A1) ν1 + νi - νi (A1) ν2 + ν12 (B2) ν2 + ν5 (A1) 2ν3 + νi - νi (A1) 2ν3 + νi - νi (A1) 2ν3 (A1) 2ν3 + νi - νi (A1) 2ν3 + νi - νi (A1) 2ν3 + νi - νi (A1) ? ν8 + ν9 (A1) ν8 + ν9 + νi - νi (A1) ν4 + ν11 + ν12 (A1) ν8 + ν9 + νi - νi (A1) ν8 + ν9 + νi - νi (A1) ? ν3 + ν4 (A1) ν3 + ν9 (B1) ? ν6 + ν8 (B2) ν5 + ν11 + ν12 (A1) FR ν9 + ν10 + ν12 (B2)
ν (cm-1)
νpreda
1608.8 m A 1583.9 w Q 1557.6 wm Q 1537.0 w Q 1400.2 w Q 1339.2 wm B 1288.9 vs B 1239.6 ms Q 1237.7 ms Q 1236.4 ms A 1231.6 ms Q 1199.9 w Q 1183.9 vw Q 1181.8 wm Q 1171.2 wm Q 1150.5 w Q 1136.7 w Q 1085.7 m Q 1080.2 m Q 1076.4 m A 1075.4 m Q 1074.4 m Q 1072.6 m Q 1071.5 m Q 1022.6 m A 1016.2 m Q 929.9 m Q 858.8 s A 857.7 s Q 855.7 s Q 827.8 m Q 806.3 m B 769.4 wm Q 667.7 m Q 662.3 ms Q 660.4 s C 658.1 ms Q 618.4 w Q 576.1 wm Q 575.5 wm Q 574.6 m C 572.1 wm Q 546.5 w Q 543.3 wm Q 543.1 wm Q 542.7 m A 513.3 vw Q 502.0 vw Q 376 w B
2565.8 2559.4
2356.0
2275.6 2245.1 2139.2
2090.7 2088.2
1928.3 1875.4 1800.2
assignment
νpreda
ν2 (A1) FR 13
C? ν8 + ν10 (A1) FR 2ν5 + ν12 (B2) ν3 + ν5 (A1) FR ν4 + 2ν10 (A1) 2ν9 (A1) ν3 + ν6 (A2)? ν9 + 2ν10 (B1) ? ? ν4 + ν5 (A1) ? ν8 (B1) FR 2ν12 + ν11 - ν12 ν11 + ν12 + νi - νi (A1) ν11 + ν12 (A1) ν11 + ν12 + νi - νi (A1) ν5 + ν11 (B2) ν9 + ν10 + νi - νi (A1) ν9 + ν10 (A1) FR ν6 + ν11 (B1) 2ν12 (A1) FR ? 2ν5 (A1) FR ν3 + νi - νi (A1) ν3 (A1) FR ν3 + νi - νi (A1) ν3 + ν5 - ν5 (A1) ν3 + νi - νi (A1) ν3 + νi - νi (A1) 2ν6 (A1) FR 2ν6 + νi - νi (A1) d1 impurity ν4 (A1) ν4 + νi - νi (A1) ν4 + νi - νi (A1) d1 impurity ν9 (B1) d1 impurity ?CO2 ν11 + νi - νi (B2) ν11 (B2) ν11 + νi - νi (B2) d1 impurity ν11 + νi - νi (B2) 2ν12 - ν12 (B2) ν12 (B2) ν12 + νi - νi (B2) d1 impurity ν5 + νi - νi (B2) ν5 + νi - νi (B2) ν5 (A1) ν6 (A2) ν3 - ν12 (B2) ν10 (B1)
1661.5 1660.2 1613.9 1613.8 1609.2 1558.3
1233.6 1203.2 1180.3 1172.3 1150.4 1085.4
1074.4 1027.4
1757.6
Values calculated from deperturbed data, i.e., without corrections for FR.
markedly greater than the unperturbed separation of 81.0 cm-1 ()2506.1 - 2425.1) from the macct model. The displacement of the levels is then estimated to be reduced from the G03 value of 6.1 cm-1 to about 4.3 cm-1. A further interaction is expected between ν7 and ν3 + ν8, predicted at 1076.4 + 1288.9 - 4.4 ) 2360.9 cm-1, again using observed values for ν3 and ν8 instead of deperturbed ones. The IR band at 2358.8 cm-1 is therefore clearly ν3 + ν8. The macct W738 value of 8.44 cm-1 would lead us to expect a FR shift of about 2 cm-1 on ν3 + ν8, which fits well with the above estimate. The joint effects of the combination levels above and below ν7 therefore sum to give a deperturbed position for ν7* of about 2392 cm-1. The interaction of ν7 with these two other levels provides a further possible explanation for the weakness of the fundamental. When the transition moments of two unperturbed transitions have opposite signs, the IR intensity can be transferred from
Figure 2. IR spectrum at 113 Torr in the vicinity of the weak B-type band at 2390 cm-1 assigned to ν7 for F2CdCD2. The series of sharp lines comes from a CO2 impurity.
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9315 TABLE 6: FR Data (cm-1) for ν3 in CF2dCD2 pentad no.
level
νobsda
νcalcd* b
νmacct* c
νmacctd
xij* e
W3ij,macctf
εg
W3ij,refh
5 4 3 2 1
ν9 + ν10 2ν12 2ν5 ν3 2ν6
1181.9 1150.5 1085.7 1076.4 1022.6
1181.3 1150.4 1085.4 (1072.4) 1027.4
1175.0 1164.6 (1079.6)i 1072.9 1028.3
1182.1 1151.5 1085.9 1073.9 1023.7
–1.03 0.56 0.06j
–9.4 –9.5 1.8i
–7.7 –2.1 1.0
0.35
13.2
–0.2 –1.0 –0.2 2.5 –1.1
a
15.5
b
This work, gas phase. Deperturbed value calculated using observed fundamentals and macct values of deperturbed xij* constants. c G03 prediction of deperturbed levels from the macct model. d G03 prediction of observed levels from the macct model. e Deperturbed anharmonicity constant xii* or xij* from the macct model. The subscripts i and j refer to the modes involved in the respective overtone or combination levels. f FR parameter from the macct model. g Fit to νobsd obtained using W3ij,macct. h W3ij values giving exact fits to νobsd. i No FR identified in the G03 treatment due to the small magnitude of W3ij. j This datum was calculated from the G03 output using our xrs program.
the weaker band to the stronger one. This interpretation implies, of course, that the unperturbed combination band must have some intrinsic IR intensity. The complete list of chosen fundamental frequencies, together with the resulting “observed” harmonic frequencies, is included in Table 4B. Force Field and Scale Factors. The macct harmonic force field was scaled on frequency data for the d0, d1, and d2 species, first to the deperturbed (anharmonic) fundamental frequencies and then to the “observed” harmonic ones, using a conventional set of symmetry coordinates as defined in Table S1 of the Supporting Information. During the refinement, the symmetry coordinates were regrouped into sets of nine A′ and three A′′ so as to be able to refine simultaneously the frequency data for the d0, d1, and d2 species. The observed frequencies for F2dC13CH2 were not used in the scaling process. Thus, predictions for 13C frequencies reflect the quality of the model. No problem arose in trying to distinguish between A1 and B1 or between A2 and B2 frequencies during this procedure. A total of 11 scale factors were employed, one for each symmetry coordinate, except for the two CH stretches, for which a common factor was employed. As a means of probing the relative effects of anharmonicity and the interaction force constant on the CH stretches, the CH scale factor was scaled only to the antisymmetric stretching frequency of the d0 species, which is thought to be unaffected by FR. While ASYM40 automatically scales off-diagonal symmetry force constants by the geometric mean of the scale factors for the corresponding diagonal ones, one can always make manual adjustments to the off-diagonal values. A significant improvement in the fit to the B2 and A′′ frequency data was effected by a small reduction of about 5% in the computed value of F11,12. Table 7 lists the scale factors thus determined, while the harmonic force constants are available in Table S2 of the Supporting Information. Table 8 shows the frequency fit for both types of refinement. This last table also includes predictions of the frequencies of the 13CF2d12CH2 species, which has not yet been studied. Scale Factors. Table 7 shows that there is a satisfactory improvement in the average scale factor from 0.96 to 1.00 in passing from use of anharmonic to harmonic data, with a corresponding diminution of the standard deviation. However, several symptoms of imperfection in the macct model remain. The scale factors for the two out-of-plane B2 wagging modes are significantly less and greater respectively than the average value, suggesting a fundamental weakness of the model for this type of vibration. That this discrepancy occurs in both anharmonic and harmonic refinements indicates that the problem is associated with the harmonic wagging symmetry force constants. Another weakness of the harmonic macct force field is identified in the difference 1.0217 - 0.9932 ) 0.0285 (0.0025)
TABLE 7: Scale Factors for the Anharmonic and Harmonic macct Force Fields for 11DFE νobsd coord. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 average σaver a
sym. A1 A1 A1 A1 A1 A2 B1 B1 B1 B1 B2 B2
motion νsCH2 νsCF2 νCdC δsCH2 δsCF2 τCH2 νasCH2 νasCF2 FCH2 FCF2 wCH2 wCF2
sf(ν)
ωobsd σsf
a
0.8953 0.9704 0.9564 0.9474 0.9896 0.9639 0.8953a 0.9663 0.9747 1.0070 0.9827 0.9197 0.9557 0.0356
0.0001 0.0039 0.0033 0.0027 0.0023 0.0023 0.0001 0.0031 0.0041 0.0032 0.0025 0.0023 0.0025 0.0013
sf(ω)
σsf a
0.9751 0.9932 1.0023 1.0030 1.0057 0.9970 0.9751a 1.0217 1.0111 1.0028 1.0427 0.9480 0.9981 0.0242
0.0018 0.0019 0.0017 0.0014 0.0012 0.0012 0.0018 0.0016 0.0020 0.0015 0.0013 0.0012 0.0016 0.0003
Constrained equal.
between the two νCF scale factors. This difference can arise from errors in the anharmonicity assessments or from an incorrect stretch/stretch interaction valence constant. The latter situation is more characteristic of B3LYP calculations than those from MP2 models, and for C-Cl bond stretches at least it is independent of anharmonic corrections.20 In contrast, for 11DFE the corresponding anharmonic scale factors are identical within the limits of error. This outcome may mean that the anharmonic corrections calculated here are imperfect. However, it may still be possible for both the interaction νCF/νCF constant and the anharmonicity correction to be erroneous to a small degree, with an accidental cancellation occurring in the anharmonic refinement. We now examine the error vectors of Table 8 in detail. CH and CD Stretching Frequencies. From the anharmonic refinement results for CF2dCH2 in part A of Table 8, ν1 is predicted as 6.2 cm-1 below the value of 3075.2 cm-1 obtained from our FR analysis in the νCH region.3 A somewhat larger disagreement would arise with the value of 3085 cm-1 predicted from earlier work of Duncan et al.,3,21 which may lend some support to our FR analysis result. However, ν1 in d1 is also predicted as 6.7 cm-1 below its observed position, which is a matter for concern in a situation where FR is thought to be negligible. A comparison with the νCD values in d2 and d1 is less exact because of the need to incorporate a factor to represent the differing effects of anharmonicity in the νCH and νCD stretching transitions. Here we have used our customary factor of 1.011 to offset this anharmoncity effect. To a large extent, all of these anomalies disappear upon passing to the harmonic refinement results in part B of Table 8, where the corresponding maximum error vector entries ε are seen to be on the order of 2-3 cm-1. This improvement is in large measure due to slightly differing anharmonicity corrections for the symmetric and antisymmetric stretching motions, as
9316
J. Phys. Chem. A, Vol. 114, No. 34, 2010
McKean et al.
TABLE 8: Comparison of Observed Frequencies and Frequency Shifts (cm–1) with Those Calculated from Scaled macct Force Fields for 11DFE Species A. Fit to Observed Fundamental Frequencies 12
mode A1 1 2 3 4 5 A2 6 B1 7 8 9 10 B2 11 12
CF2d12CH2
νobsd
CF2d12CH2
13 c
a,b
3075.2* 1735.0* 1375.8* 925.8 549.6 708.2 3175.6 1305.0* 953.8 436.9 802.1 609.5
ε
νpred
δνcalcd
6.2 –4.6 –4.4 –0.5 0.0 –2.2 0.0 –2.0 –1.0 –0.4 –0.4 –0.5
3068.9 1699.1 1374.7 925.0 547.7 710.4 3175.6 1271.4 954.1 435.6 802.1 590.9
0.2 40.5 5.5 1.3 1.9 0.0 0.0 35.6 0.8 1.7 0.4 19.0
12 d
νobsd
CF2d13CH2
b
δνobsd
3071.4* 1714.2* 1373.8* 915.0 546.0 708.4 3161.3 1303.3* 945.1 434.4 795.1 608.5
d
12
δνcalcd
3.8 20.8 (2.0) 10.8 3.6 0.2 14.3 (1.7) 8.7 2.5 7.0 1.0
6.2 20.9 2.1 10.7 2.8 0.0 13.6 1.9 9.0 2.6 7.3 1.1
CF2d12CD2
νobsd
12 c
a,b
2278.8 1704.3* 1072.4* 858.8 542.6 513.3 2392.0* 1288.0* 806.3 376.0 660.4 574.6
CF2d12CHD
ε
mode
νobsda,b
εc
4.1e 5.2 1.6 0.3 0.1 1.2 –5.4e 0.1 0.8 0.4 0.9 0.4
A′ 1 2 3 4 5 6 7 8 9 A′′ 10 11 12
3133.2 2329.6 1719.8* 1315.3* 1235.0* 930.0 827.6 546.5 401.0 769.3 618.4 546.5
6.7 –1.3e 0.2 1.0 3.3 –0.6 0.4 –0.1 –0.1 –1.0 –0.3 0.9
B. Fit to Observed Harmonic Frequencies 12
12
13
CF2d CH2 a
mode
ωobsd
A1 1 2 3 4 5 A2 6 B1 7 8 9 10 B2 11 12
3204.0 1775.9 1418.5 940.8 554.5 721.8 3313.9 1337.5 973.4 437.8 828.3 619.5
c
12
12
CF2d CH2
ε
ωpred
δωcalcd
1.9 –1.0 0.1 0.7 0.1 –0.6 –0.1 0.1 –0.4 –0.1 0.5 0.1
3202.0 1736.1 1412.5 938.6 552.5 722.4 3314.0 1300.9 973.2 436.2 827.4 600.1
0.1 40.8 5.9 1.4 1.9 0.0 0.0 36.5 0.6 1.7 0.4 19.3
d
CF2d13CH2
ωobsd
δωobsd
3199.3 1753.7 1417.2 929.8 550.8 721.9 3298.4 1335.7 964.5 435.3 820.6 618.5
4.7 22.2 1.3 11.0 3.7 –0.1 15.5 1.8 8.9 2.5 7.7 1.0
d
12
CF2d12CD2 a
δωcalcd
ωobsd
6.4 21.9 1.9 10.8 2.8 0.0 14.2 1.7 9.2 2.7 7.6 1.0
2346.7 1737.3 1096.5 873.4 547.6 521.1 2472.9 1318.4 818.8 377.6 677.9 584.2
ε
12 c
2.4 0.6 0.4 –1.6 0.2 0.3 –1.2 –1.1 0.2 0.6 –0.7 –0.4
CF2d12CHD
mode
ωobsda
εc
A′ 1 2 3 4 5 6 7 8 9 A′′ 10 11 12
3265.9 2406.8 1757.4 1347.9 1265.1 945.6 841.5 551.1 401.9 792.3 629.6 555.9
3.4 2.8 0.6 2.2 –0.1 0.5 –0.4 –0.3 –0.5 0.2 0.4 0.1
a In italics, data used in the scale factor refinement. b Asterisks signify deperturbed frequencies. c ε ) obsd - calcd. d δν ) ν(12C) - ν(13C) or δω ) ω(12C) - ω(13C). e After multiplication of the calculated frequency by 1.011 to offset the differing effect of anharmonicity on νCH and νCD stretching frequencies.
identified in our previous paper.3 Our tentative conclusion is that the macct model is giving a reliable description of this part of the force field and that there is no evidence for an imperfect CH/CH stretch/stretch interaction force constant, as was the case with the CF bond stretches. Other Motions. Errors of -4.6 and 5.2 cm-1 on ν2 in d0 and d2 are markedly reduced where the harmonic frequency ω2 is concerned, leaving no evidence for the presence of significant error in the ν2 FR analyses. The same is true to a smaller extent for ν3 and ν8. The less exact FR analyses for ν4 and ν5 in d1 yield values within 3 cm-1 of those predicted by either refinement, a result that must be considered satisfactory in view of the approximate nature of the FR treatment of ν4 and ν5. Asymmetry in the fit to ν6 (a2) in d0 and d2 arises from the joint refinement of the A2 torsional force constant with data from the three d1 A′′ modes. Again improvement results from the use of harmonic frequencies. 13 C Shifts. Observed and calculated values of the 13C shifts are in general agreement with two exceptions, those on ν1 and ν5. The former is, in principle, covered by the errors associated with the FR analyses of ν1, if these errors are considered to be independent of each other. However, the possibility of more systematic errors in these νCH FR analyses must be acknowledged. The disagreement between observed (3.6 cm-1) and calculated (2.8 cm-1) 13C shifts in ν5 (d0) is unexplained. Semiexperimental Equilibrium Structure of 11DFE. Reference has already been made to the improved accuracy obtainable by pulsed-jet Fourier transform MW spectroscopy. In the case of the d1 and d2 species, the improvement over the earlier work amounts to about 3 orders of magnitude.6,22 Our new frequency measurements for lines in the d0, d1, d2, and two 13C species are shown in Table S3 of the Supporting
Information. A-type selection rules apply. The accuracy of the MW lines for the two deuterium isotopomers was compromised to some extent by the fine structure arising from the quadrupole coupling of deuterium nuclei. Table 9 gives the new ground-state rotational constants accompanied by full sets of quartic centrifugal distortion constants. All of the quartic centrifugal distortion constants were fitted for the normal species. Scale factors were defined from the ratio of the observed and calculated (macct model) centrifugal distortion constants of the normal species and used to adjust predicted values for the other isotopomers, as needed. Footnote a in Table 9 provides the calculated centrifugal distortion constants for the normal species for comparison with the observed values in this table. The comparison is quite good. The somewhat less accurate ground-state rotational constants for 11DFE reported in two high-resolution IR studies23,24 are in acceptable agreement with the new values in Table 9. In another study, ground-state rotational constants for 11DFE were fitted with centrifugal distortion constants up to the sextic level for a wide range of MW data.25 The values reported in this study agree with those in Table 9 within the cited uncertainties. Vibration-rotation constants (R’s) were computed in several ways. One method used harmonic contributions computed from the force field scaled to fit “observed” harmonic frequencies. The second used harmonic contributions from the force field scaled to fit anharmonic frequencies. The third and fourth methods used harmonic contributions derived from the average of the scale factors of the first and second methods. For all cases, the anharmonic contributions came from the cubic force constants calculated with the macct model. The computation of R sums was done with the program VibRot.4 The fifth method used the R’s computed by G03 with the macct model. Table
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9317 TABLE 9: Ground-State Rotational Constants for 11DFE and Its Isotopomers (in MHz) constant
F2CdCH2a
F213CdCH2
F2Cd13CH2
F2CdCHD
F2CdCD2
A B C δJ δK ∆K ∆JK ∆J std. dev. κc ∆d no. lines
11002.564(5) 10428.992(5) 5345.379(5) 0.0020(1) 0.0060(4) 0.0073(8) 0.0018(9) 0.0048(3) 0.0084 0.797223 0.1531 15(4)
11003.744(7) 10425.526(7) 5344.764(7) 0.00200b 0.00599b 0.0072(5) 0.0020(5) 0.00485b 0.0155 0.795646 0.1529 11(2)
11002.486(8) 9991.412(5) 5227.920(5) 0.00181b 0.00613b 0.0059(7) 0.0026(2) 0.0054(2) 0.0126 0.649818 0.1547 10(1)
10926.68(2) 9545.15(2) 5086.74(1) 0.00158b 0.00628b 0.0073(25) 0.0027(14) 0.00390b 0.0567 0.526869 0.1543 9
10589.925(7) 8993.222(5) 4856.113(4) 0.00144b 0.00534b 0.0071(4) 0.0019(2) 0.0372(7) 0.0207 0.443057 0.1525 12
a Calculated values (macct) for centrifugal distortion constants in kHz are δJ ) 1.98, δK ) 5.53, ∆K ) 7.53, ∆JK ) 1.59, and ∆J ) 4.73. Calculated from the macct model and scaling on the d0 species. See the text. c Asymmetry parameter. d Inertial defect, ∆ ) Ic - Ia - Ib. e In parentheses is the number of lines from ref 7 that were given 0.1 weight in the fit. Two of the lines for F2Cd13CH2 were omitted because of large deviations. b
TABLE 10: Structure of 11DFE
parameter rCC/Å rCH/Å rCF/Å RCCH/deg RHCH/deg RCCF/deg RFCF/deg
ED/MW rg, rza 1.340(6) 1.091(9) 1.315(3) 119.0(4)
MW r0b
macctc re
macct R’sd re
R’s ave. scale factor, ωobsdbasede re
1.313(3) 1.074(6) 1.325(2)
1.3213 1.0750 1.3197 119.19 121.61 125.18 109.64
1.3174(5) 1.0753(2) 1.3157(3) 119.40(1) 121.21(2) 125.16(2) 109.68(3)
1.3175(4) 1.0753(1) 1.3157(2) 119.40(1) 121.21(2) 125.16(2) 109.68(3)
121.1(8) 124.7(3) 108.9(3)
R’s many scale factors, ωobsdbasedf re
CCSD(T)/aug-ccpVnZ model, extrapol,g re
1.3175(3) 1.0754(1) 1.3157(2) 119.40(1) 121.21(2) 125.16(2) 109.68(2)
1.3181 1.0750 1.3157 119.38 121.24 125.14 109.72
From ED and MW data. From MW data.7 c Structure found with the macct model. d R’s computed with the macct model. e Harmonic contributions to R’s computed with the average scale factor from scaling of the force constants to the ωobsd values. f Harmonic contributions to R’s computed after scaling of the force constants to the ωobs values. g Ab initio calculation with complete basis set extrapolation of geometric parameters found with CCSD(T)/aug-cc-pVnZ models and corrections for core/valence electron correlations, relativity and higher order correlation recovery. a
11 b
S4 of the Supporting Information reports the equilibrium rotational constants determined for the five isotopomers by the five methods, as found by the procedure described before.5 The very small inertial defects of about -0.001 amu Å2 for these planar molecules indicate that the equilibrium rotational constants are close to the true values. Geometric parameters came from a global fit to all of the moments of inertia. Little difference was found between the geometric parameters determined by the five methods. Thus, Table 10 gives in columns 5-7 the geometric parameters for 11DFE found by only three of the methods: the R’s computed with the macct model and the two variations derived from scaling to the ωobsd values. Parameters obtained from scaling to anharmonic frequencies, νi, differed principally from the values in Table 10 by having somewhat larger uncertainties. The simplest procedure of using R’s computed directly by G03 with the macct model gives results as good as the best procedure involving selective scaling of the harmonic force constants. We consider the bond lengths in the semiexperimental equilibrium structure in the next-to-last column to be good to 0.001 Å and the angles good to 0.1°. The last column in Table 10 gives the geometric parameters computed with a high-level ab initio treatment. Models were CCSD(T)/aug-cc-pVnZ, where values for geometric parameters at increasing n were extrapolated to a complete basis set limit and corrections were made for core/valence electron correlation, relativity effects, and higher order correlation.26 Excellent agreement was found between the semiexperimental structure and the ab initio structure. This agreement helps to confirm the two methods. Table 10 includes the geometric parameters from the combined ED/MW study of Mijlhoff et al.11 in column 2 and the r0
parameters determined by Laurie and Pence7 in column 3. The uncertainties in the values for the r0 structure reflect the results of using different combinations of moments of inertia for the fit.7 Except for the rCF bond length, the agreement between the r0 structure and the re structure is surprisingly good. Although exact agreement between different models is not expected, the bond parameters derived from the latest ED study in combination with MW data are surprisingly discrepant for the CdC and CH bonds.11 We offer no explanation for these differences. The equilibrium parameters predicted by the macct model are in column 4 of Table 10. The agreement between the predicted macct structure and the new equilibrium structure is acceptable. Significant deviations are found only for the C-F and CdC bond lengths, which we ascribe to limitations of the basis set. In our prior paper on 11DFE,3 an equilibrium C-H bond length of 1.0762(11) Å was determined from the correlation between bond lengths and frequencies for stretching of isolated C-H bonds.27 The close agreement, within 0.0009 Å, between the above prediction and our new equilibrium value of 1.0754 Å emphasizes the value of this correlation, as well as giving some support to the values of νCH on which the prediction was based. Conclusions 1. New IR data for CF2dCHD and CF2dCD2 yield improved values of fundamental band centers and help to identify FRs in a number of situations. 2. Gaussian03 calculations with the macct model yield anharmonicity data from which predictions of “observed” harmonic frequencies are made.
9318
J. Phys. Chem. A, Vol. 114, No. 34, 2010
3. Harmonic force fields are obtained by scaling the model harmonic force field to both observed anharmonic and “observed” harmonic frequencies for the present molecules in conjunction with similar data for CF2dCH2. The overall fit to observed data in all three species suggests that the FR analyses made throughout are self-consistent and sound. 4. Slight defects in the QC model are identified in scale factor variations found for the two B2 out-of-plane wagging modes and also for C-F stretching. 5. A semiexperimental equilibrium structure is determined from new MW measurements for five isotopomers and calculated vibration-rotation constants. This structure is in good agreement with the equilibrium structure found with new ab initio calculations. The structure predicted by the macct model is in reasonably good agreement with the semiexperimental structure. The re C-H bond length of 1.0754 Å is in good agreement with the value of 1.0762(11) Å found previously from the correlation between the equilibrium bond length and the isolated CH stretching frequency. Acknowledgment. Most of the work at Oberlin College was supported by Dreyfus Senior Scientist Mentor grants. We are grateful to Eric A. Entemann for preparing the deuteriumcontaining haloethanes. The installation of the Beowulf computer cluster at Oberlin College was supported by the National Science Foundation (Grant 0420717). Supporting Information Available: Gas-phase spectra in the mid-IR for F2CdCHD (Figure S1a,b), far-IR spectrum for this species (Figure S2), corresponding figures for F2CdCD2 (Figures S3a,b and S4), definitions of symmetry coordinates (Table S1), scaled harmonic force constants in symmetry coordinate space (Table S2), MW lines for five isotopic species (Table S3), and equilibrium rotational constants used in the structure fitting (Table S4). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Edgell, W. F.; Ultee, C. J. J. Chem. Phys. 1954, 22, 1983–1992. (2) Oskam, A.; Elst, R. J. R. Neth. Chem. Soc. 1975, 94, 143–148. (3) McKean, D. C.; Van Der Veken, B. J.; Herrebout, W.; Law, M. M.; Brenner, M. J.; Nemchick, D. J.; Craig, N. C. J. Phys. Chem. A 2010, 114, 5728–5742. (4) Groner, P.; Warren, R. D. J. Mol. Struct. 2001, 599, 32–325. (5) Craig, N. C.; Groner, P.; McKean, D. C. J. Phys. Chem. A 2006, 110, 7461–7469.
McKean et al. (6) Edgell, W. F.; Kinsey, P. A.; Amy, J. W. J. Am. Chem. Soc. 1957, 79, 2691–2693. (7) Laurie, V. W.; Pence, D. T. J. Chem. Phys. 1961, 38, 2693–2697. (8) Chauffoureaux, J. C. J. Phys. (Paris) 1967, 28, 344–348. (9) Karle, I. J.; Karle, J. J. Chem. Phys. 1950, 18, 963–967. (10) Carlos, J. L., Jr.; Karl, R. R., Jr.; Bauer, S. H. J. Chem. Soc., Faraday Trans. 2 1974, 70, 177–178. (11) Mijlhoff, F. C.; Renes, G. H.; Kohata, K.; Oyanagi, K.; Kutchitsu, K. J. Mol. Struct. 1977, 39, 241–252. (12) Craig, N. C.; Entemann, E. A. J. Chem. Phys. 1962, 36, 243–248. (13) Conrad, A. R.; Teumelsan, N. H.; Wang, P. E.; Tubergen, M. J. J. Phys. Chem. A 2010, 114, 336–342. (14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T., Jr.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (15) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007–1023. (16) Woon, D. F.; Dunning, T. H. J. Chem. Phys. 1993, 98, 1358–1371. (17) McKean, D. C.; Craig, N. C.; Law, M. M. J. Phys. Chem. A 2008, 112, 6760–6771. (18) Hedberg, L.; Mills, I. M. J. Mol. Spectrosc. 2000, 203, 82–95. Hedberg, L.; Mills, I M. J. Mol. Spectrosc. 1993, 160, 117–142. (19) Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J. Am. Chem. Soc. 1983, 105, 7037–7047. (20) McKean, D. C.; Craig, N. C.; Law, M. M. J. Phys. Chem. A 2008, 112, 10006–10016. (21) Duncan, J. L.; Nivellini, G. D.; Tullini, F.; Fusina, L. Chem. Phys. Lett. 1990, 165, 362–368. (22) Reference 11 gives the impression that Chauffoureaux had observed lines of the d1 and d2 species, but none were reported in ref 8. Chauffoureaux did, however, fit the MW lines reported in ref 6 for the d1 and d2 species to Hamiltonians with symmetric top centrifugal distortion constants, thereby improving on the rigid rotor fits made to only three lines each of the d1 and d2 species in ref 7. (23) Lafferty, W. J.; Sattler, J. P.; Worchesky, T. L.; Ritter, K. J. J. Mol. Spectrosc. 1981, 87, 416–428. (24) De Lorenzi, A.; Girogianni, S.; Gambi, A.; Visioni, R.; Stoppa, P.; Ghersetti, S. J. Mol. Spectrosc. 1992, 151, 322–333. (25) Zerbe-Foese, H.; Guarnieri, A.; Stiefvater, O. L. Z. Naturforsch. 1995, 51a, 53–62. (26) Feller, D.; Craig, N. C., in preparation. (27) Demaison, J.; Rudolph, H. D. J. Mol. Spectrosc. 2008, 248, 66–76.
JP104498N
