Spectroscopic and ab initio studies of difluoromethyl radicals and

Jan 1, 1992 - G. Copeland , E. P. F. Lee , J. M. Dyke , W. K. Chow , D. K. W. Mok and F. T. Chau. The Journal of Physical Chemistry A 2010 114 (4), 18...
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J. Phys. Chem. 1992,96, 585-594

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Spectroscopic and ab Initio Studies of Difiuoromethyi Radicals and Cations David V. Dearden,+Jeffrey W. Hudgens,* Russell D. Johnson nI,*Bilin P. Tsai,* Chemical Kinetics and Thermodynamics Division, National Institute of Standards and Technology,$ Gaithersburg, Maryland 20899

and Sherif A. Kafafi*J Department of Environmental Chemistry and Biology, Johns Hopkins University School of Hygiene and Public Health, 615 North Wove Street, Baltimore, Maryland 21205 (Received: September 19, 1991)

The structures and optical spectroscopy of the CHF, radical and cation were studied by ab initio molecular orbital calculations and by experiment. Ab initio calculations at the MP2/6-31GS* theory level found that the o timum structure of the k IA, CHF2+cation belongs to the C, point group wkh r(C-F) = 1.2424 A, r(C-H) = 1.0883 and LF-C-F = 119.19O. The optimized structure of the ground state CHFz (X ,A') radical belongs to the C, point group with r(C-F) = 1.3360 A, r(C-H) = 1.0843 A, LF-C-F = 111.5l0,and LH-C-F = 113.65'. The ab initio angle between the F-C-F plane and the C-H bond is am = 44.53O. Vibrational frequencies for each CHF, species were computed. The electronic spectra of CHF, and CDF, radicals were observed between 330 and 430 nm using mass-resolved resonanceenhanced multiphoton ionization (REMPI) spectroscopy. These spectra arose from two-photon reSOnanceS with planar Rydberg states. A third laser photon ionized the radicals. Spectroscopic constants were found for the E (3p) Rydberg state of the CHFz radical (vM = 49 312 (10) cm-', d2(C-F str) = 1365 (8) cm-l, d3(CF2scissors) = 660 (20) cm-', d4(OPL,A)= 1022 (1) cm-I) and of the CDFz radical (vM = 49323 (10) cm-', w"(C-F str) = 1300 (21) cm-I, d3(CF2 scissors) = 650 (15) cm-', d4(0PLA) = 864 (2) cm-I). The REMPI spectra exhibited Y''~ = 1-5 hot bands of the k 'A' radical. Modeling of these hot bands with a quartic double-well potential gives the inversion barrier, Bin"= 2800 (500) cm-l, and @,,, = 49 (6)'.

8,

Introduction This paper reports the first electronic spectra of dfluoromethyl radicals (CHF, and CDF,) which we observed using resonanceenhanced multiphoton ionization (REMPI) spectroscopy. This study continues our systematic investigation of the REMPI spectra of fluorine- and chlorine-substituted methyl radicals. To date, we have reported REMPI spectra of CH2F,' CF3,2 CF2C1,3 CFC12,3CHC12,4and CC135radicals. In previous studies of the CHC1, and CC13 radicals4" we used ab initio theoretical calculations to estimate with good fidelity the vibrational frequencies exhibited in the REMPI spectra. The results of ab initio calculations were also a very useful aid in the analyses of REMPI spectra during the preparation of this paper. In the theoretical section of this paper we provide the framework that supports discussions of structure and spectroscopy. We construct this framework by presenting qualitative molecular orbital theory (QMOT) descriptions and ab initio calculations for CHF, species. These QMOT descriptions outline the principal interactions that cause the geometries and normal-mode frequencies of CHF, radical and cation to differ. Our ab initio results are the first to describe the CHF2+cation and the excited valence states of the CHF, radical. These calculations quantitatively predict structures, vibrational frequencies, and vertical excitation energies. In the experimental section we report the REMPI spectra of CHF, and CDF, radicals between 330 and 430 nm. These spectra measure vibrational frequencies of modes associated with the ground and 3p Rydberg states. The REMPI scheme presented here is suitable for sensitive and selective detection of gas-phase CHF, radicals in other experiments. Data regarding the kinetics, spectroscopy, and structures of CHF, radicals and cations are meager. The reaction of OH with CHzF2 produces CHFz radicals. This reaction is probably the principal degradation mechanism for CHzF2in the atmosphere. The CHF, radical is also formed during the infrared laser induced decomposition of heptafluoropropanesand may be present above

surfaces during the reactive ion etching of semiconductor substrates? ESR spectroscopy has established that the ground state of CHFz radical is nonplanar.1° Infrared absorption studies in argon matrices have measured the frequencies of several vibrational modes of difluoromethyl radicals and cations."-'3 The ionization potential of CHFz is not known with high precision. The difference between the heats of formation of the radical14 and the cationI5indicates that the adiabatic ionization potential lies between IP, = 8.5 and 8.8 eV.

Approximate Descriptions of the CHFz Species QMOT Description of CHF2+Cation. Qualitative molecular orbital theory (QMOT) gives a general outline of the ab initio calculations and reveals the main orbital interactions which cause the differences in geometries and vibrational frequenciesamong the various CHF, radical and cation species. The QMOT descriptions of CHF, species are very similar to those previously described for CHCI, species.6 However, fluorine is more electronegative than chlorine, and the C-F bonds are shorter than the C-Cl bonds. These two factors have profound effects upon the energy ordering of the molecular orbitals of CHF, as compared to the M O s of CHCl,. Figure 1 displays the seven highest filled MOs and four lowest empty MOs of planar, C, CHX2+(X= F, Cl) cations. As shown (1) Hudgens, J. W.; Dulcey, C. S.;Long, G. R.; Bogan, D. J. J . Chem. Phys. 1987, 87, 4546. (2) Duignan, M.; Hudgens, J. W.; Wyatt, J. R. J. Phys. Chem. 1982,86, 4156. (3) Tsai, B. P.; Johnson 111, R. D.; Hudgens, J. W. J . Phys. Chem. 1989, 93, 5334. (4) Long, G. R.; Hudgens, J. W. J . Phys. Chem. 1987, 91, 5870. (5) Hudgens, J. W.; Johnson 111, R. D.; Tsai, B. P.; Kafafi, S.A. J. Am. Chem. SOC.1990, 112, 5763. (6) Kafafi, S. A.; Hudgens, J. W. J . Phys. Chem. 1989, 93, 3474. (7) Howard, C. J.; Evenson, K. M. J . Chem. Phys. 1976, 64, 197. (8) Kato, S.;Makide, Y.; Takeuchi, K.; Tominaga, T. J . Phys. Chem. 1987. 91. 4278. (9) Hayashi, T.; Kikuchi, M.; Fujioka, T.; Komiya, S.Proc. Inr. Ion Eng. Congr. 1983, 3, 1611. (10) Fmenden, R. W.; Schuler. R. H. J. Chem. Phys. 1965, 43, 2704. (1 1) Carver, T. G.; Andrews, L. J. Chem. Phys. 1969,50, 5100. (12) Andrews, L.; Prochaska, F. T. J . Chem. Phys. 1979, 70, 4714. (13) Jacox. M. E. J . Mol. Specrrosc. 1980, 81, 349. (14) Pickard, J. M.; Rodgers, A. S.Inr. J . Chem. Kinet. 1983, 15, 569. (1 5 ) Lias, S.G.; Ausloos, P. Int. J . Mass Spectrom. Ion Proc. 1977, 23, 273. ~

Address correspondenceto these authors. ' NIST/NRC Postdoctoral Associate, 1989-90. Current address: Department of Chemistry, University of Texas at Arlington, Arlington, TX 76019. *Sabbatical fellow from the University of Minnesota at Duluth. I Formerly called the National Bureau of Standards. A. Mellon Foundation Fellow (1989-1992).

0022-3654/92/2096-585$03.00/0

0 1992 American Chemical Society

586 The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 F-Atom Substitution

Relaxation

CHF2+ ,

CHF2+

_ _ _ _-----

-. :

24'

i,

'.'(rgt"

Dearden et al.

MO 16

n

15 23'

14

22' 13

(LUMO!;' 21' @i@ 3b,-'

(HOMO) , -

os&

A

6%

12

Figure 2. Geometric diagram of CHF, species which illustrates the angles used to characterize molecular structure. is the angle formed between the C-H bond and the F-C-F plane as the C-H bond is rotated in the mirror plane. a,,, is the equilibrium angle of a CHF, structure, i.e., the angle at which the total energy is minimized. In planar C, CHF, structures a,,, = . ' 0

(HOMO)

.-

8

6

Figure 1. Seven highest occupied MOs and four lowest empty MOs of the CHC1, and CHF2+cations as obtained from ab initio HF/STO-3G calculations. (a) Orbitals of the CHC12+cation. Correlation lines diagram the relative energy change of each CHC12orbitals as (b) fluorine atoms are substituted for chlorine atoms and (c) the C-F bonds of the CHF2+ cation are shortened to the equilibrium geometry. Energy spacings between levels indicate trends and are not to scale.

in Figure 1, MOs 17', 20', and 21' of CHC12+are PMOS (For clarity in this section we will cite MO numbers which refer exclusively to orbitals of the CHC12+structure). The remaining orbitals are ac-Hand accl MOs. The energy levels of Figure l b show the first-order energy change16of each MO when F atoms are substituted for C1 atoms in CHC12+. Since fluorine is more electronegative than chlorine, F atom substitution is equivalent to an increase in charge density at the halogen atom sites. An increase in bonding overlap between the C and F AOs in the bonding MOs 14'-17' and 19' should cause these levels to become more stable. Our previous computations on CHC12+cation6 showed that MOs 18', lY,and 20' are clustered together. The energy gap between MOs 18' and 20' is C0.4 eV (Figure la). The highest occupied molecular orbital (HOMO) of CHC12+, MO 20', is nonbonding. Because fluorine substitution should increase the through-space antibonding repulsion between the halogen AOs, MO 2U' will be slightly destabilized in CHF2+. F atom substitution should also cause MO 1Y to drop below MO 18' in energy. As is shown in Figure la, MO 18' has antibonding interactions between the F AOs and the C-H lobe. Because fluorine atom substitution increases these antibonding interactions, the energy of MO 18' will also increase. In contrast, because the various AOs in MO 1Y are engaged in bonding interactions and fluorine substitution enhances the electron density, MO 19' should drop below below MO 18' in CHF2+ (Figure lb). When fluorine atoms are substituted into CHC12+,an increase in antibonding interactions between the F and C AOs should (16) (a) Gimarc, B. M. Molecular Structure and Bonding, Academic Press: New York, 1979. (b) Lowe, J. P. Quantum Chemistry; Academic Press: New York, 1978; pp 283-303.

destabilize the virtual MOs 21', 22', and 23' of CHC12+. In contrast, fluorine substitution should stabilize MO 24' through bonding interactions of the F AOs. The net effect of these energy changes should cause MO 24' to lie at lower energy than MO 23' (Figure lb). The energy correlation diagram in Figure 1 shows the energy change of each MO as chemical bonds are permitted to shorten from the equilibrium positions of CHC12+(Figure lb) to those of CHF2+ (Figure IC). Shortening the C-F bonds to their equilibrium values should stabilize the occupied MOs 14'-17' and 19'. Increased out-of-phase interactions between the F AOs will destabilize MO 20'. Even greater destabilization of MO 18' occurs as through-space repulsions between the F AOs and the C-H lobe increase. Because the energy gap between MO 18' and MO 20' is small in CHC12+(Figure la), QMOT analysis suggests that the differential energy increase of MO 18' and MO 20' may switch the order of these MOs in CHF2+(Figure IC). In fact, QMOT analysis cannot predict whether the HOMO of CHF2+has a l or a2symmetry. Explicit ab initio calculations, presented below, show that the HOMO has a l symmetry. To summarize, CHF2+and CHC12+cations have the following differences: (1) in CHF2+QMOT indicates that the HOMO of CHF2+ may be a a-MO of al symmetry. By comparison the HOMO of CHC12+is a ?r-nonbondingMO with a2symmetry. (2) The HOMO-LUMO gap in CHF2+is expected to be larger than the corresponding one in CHC12+. Therefore, the excited valence states of CHF2 species should occur at higher energies than the corresponding states of CHC12 species. (3) As diagrammed in Figure 1, the virtual levels of CHF2+lie in a different order than those of CHC12+. Geometry of the CHF2+Cation. Figure 2 shows the internal angles used to describe structures of CHF2species. In Figure 2 CP is the angle of the C-H bond relative to the F-C-F plane. CPm is the angle of potential energy minima along the out-of-plane bend coordinate. For C, structures CPm = Oo. For nonplanar C, structures ICP,,J > 0. QMOT analysis indicates that the energy minimum of ground-state CHF2+possesses C2,geometry. This prediction is found by examining the fmt-order energy changes of the occupied MOs as the planar C, CHF2+is transformed to a C,geometry by rotating the C-H bond out of the F-C-F plane by an angle, CP. Figure 3 presents the response of each MO as a function of CP. (Henceforth, we will refer to the MOs in Figure 1 using the numbering system of CHF2.) As the C-H bond rotates out of the F-C-F plane, the bonding overlap of the hydrogen s orbital with the carbon pz orbital decreases in a-MOs 6,7,and 12;and thus, their bonding energies diminish (Figure 3). Because a node lies at the C-H bond, the orbital energies of PMOS 8, 10,and 11 are unaffected, to first order, by small C-H out-of-plane rotations. The r-bonding orbital, MO 9, is slightly stabilized by out-of-plane rotations as the hydrogen s-orbital increases its bonding overlap with the carbon pTatomic orbital. In summary, for small @ rotations the bonding of three occupied orbitals decreases, three remain unchanged, and one occupied orbital in-

Difluoromethyl Radicals and Cations

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 587

e

t

,

MO 16 15

14 12 13 11 10

la,

*b,

-----...-

9 8 7 6

90.0

0.0

Angle, 0 Figure 3. Walsh diagram for CHF2species which shows the change in energy of each molecular orbital as a function of the out-of-planeangle, a. The orbital numbers correspond to those for CHFzt from Figure 1. Out-of-plane

creases its bonding slightly. Thus, out-of-plane rotations of the C-H bond above or below the F-C-F plane in CHF2+is destabilizing and CHF2+should prefer a planar geometry. Analyses show that all bond stretching and in-plane bending deformations away from the C, equilibrium structure also increase the total energy. Thus, the potential energy function of each normal mode possesses a single minimum. We expect these vibrational modes of CHF2+can be modeled by nearly harmonic potentials. QMOT Description of the CHF2Radical. Adding an electron to MO 13 in the CHF2+cation produces the ground-stateradical. In the C, point group this configuration is denoted as X ,BI. However, like the CHC12 radical: the ground state of CHF2 is expected to have a nonplanar, C,, equilibLium geometry ([@,,,I> 0) and its ground state is denoted as X 2A’. The nonplanar geometry is preferred because Stabilization energy is obtained from the frontier orbital of the radical, MO 13, as the hydrogen atom is rotated out of the F-C-F plane and the bonding overlap with the carbon px orbital increases (Figures 1 and 3). For small @ rotations the stabilization energy from the frontier orbital (MO 13) dominates the total energy change; therefore, slightly nonplanar C, structures are more stable than planar ones. As @ becomes larger, destabilizing interactions from PMOS 6,7, and 12 will eventually overcome the stabilizing interactions of ?r-MOs 13 and 9. The net effect of these interactions will cause the potential energy function along the 0 rotation (out-of-plane) coordinate to have two energy minima located at +@,, and -a,,. The high electronegativityof the fluorine atoms should cause the equilibrium out-of-planeangle, a , to be greater than the a, of CHCI,. Accordingly, the inversion barrier, Binv,of the CHF, (R2A’) radical should be greater than the Binvof CHC12 (R ,A’). When the ground CHF2 radical is constrained to be planar, the bond lengths and angles of electronic state equilibrium geometry of planar CHF, radical should not differ appreciably from those of the cation. However, the presence of the odd electron in the C-F antibonding ?r*-MO 13 should cause the C-F bonds of the X state radical to be slightly longer than those of the cation. QMOT Description of Electronically Excited CHF2 Radicals. The predominant orbital configurations of the lowest energy states of CHF2 in the C2, point group are ...(4b2)2(la2)2(6al)2(2bl)l % ,B, ...(4b2)2(la2)2(6al)2(7al)1

...(4b2)2(la2)2(6a1)2(9al)1 ...(4b2)2(la2)2(6al)2..(3s)’

A 2A, B ,A, ,Al (3s)

...(4b2)2(la2)2(6al)1(2b,)2

b 2AI

...(4b2)2(1az)2(6a,)2(5b2)’

E 2B2

The A,B, b, and are excited valence states of CHF2. B e u s e @ rotations stabilize MO 14, the energy minima of the A ,Al CHF2 radical should lie at nonplanar C, geometries. In contrast, since @ rotations destabilize the singly occupied MO 15 of the B 2ALradical, the B 2Alradical should have a planar structure. The A and B states have 2Alsymmetry and the HOMOS of these configurations (MO 14 and MO 15, respectively) cross in energy at longer C-F bond distances (Figure 1). Thus, we expect the A and B states to mix and produce states with long C-H bonds. These long C-H bonds arise from the strong antibonding intera_ctions-betweenthe C-p, and H-1s AOs in MO 14. In fact, the A and B states may be dissociative because at the planar configuration both states have greatly diminished barriers to CF2 H formation. The long C-H bond of the A ,Al state of the CHF, radical differs considerably from the corresponding state of the CHC1, radical. In A ,AI CHCl, the C-H interactions of the frontier MO 22’ are bonding (Figure l), which leads to a stable, strongly bound state. As deduced from Figure 3, b ,Al CHF, radical possesses a nonplanar, C, structure, i.e., it is a b ,A’ state. The presence of two electrons in the frontier orbital, ?r*-MO 13, of the b 2A’ radical should pEoduce an inversion barrier that is larger than observed in the X ,A’ radical. The 2B2CHF, radical should possess the longest C-F bond lengths of all CHF2 species studied in this work. The long C-F bonds originate from the strong u-antibonding interactions in the C-F re ions of MO 16. The state is a Rydberg state. Since Rydberg orbitals are diffuse and reside mostly oustide the valence core, electrons in Rydberg orbitals contribute little to chemical bonding. The valence core is essentially the same as the cation. Like CHF2+,all Rydberg states of the CHF, radicals are expected to be planar. The energy of Rydberg states can be estimated using the Rydberg equation

+

e

8

v M = IP,

- 109737/(n - 6)2

-

(1)

where the quantum defect, 6, is 1 for ns states, -0.6 for np states, and -0.1 for nd states.17- Using eq 1, we estimate that the lowest energy Rydberg state, C 2A, (3s) state, will reside near 41 000 cm-I.

Apparatus and Methods ”bearetical Methods. All computationswere performed using the GAUSSIAN 86 series of programs using standard 6-31G* and 6-31G** basis ~ e t s . ~ * JThe ~ restricted Hartree-Fock (HF) method was used to locate the equilibrium geometry of CHF2+. The corresponding unrestricted level of theory, UHF/6-31G*, was used to optimize the ground-state geometry of the planar (C2”) CHF, doublet radical and its lowest two excited states. This level of theory was also applied to determine the nonplanar (C,) CHF, doublet equilibrium geometry. In all UHF calculationsreported in this work, spin contamination from higher spin states was negligible. The largest S2value was slightly less than 0.76 (S2 should be 0.75 for a pure doublet state). In view of this very small spin contamination, no corrections to the UHF wave functions and energies were performed. Throughout the computations the C-F bond lengths were assumed to be equal. Second-order Mailer-Plesset (MP2) perturbation theory geometry optimizations using the 6-31G* basis set were performed on each radical structure to partially account for electron correlation. These optimizations were followed by single-point frozen core calculations at the MP4 level of theory. Single (S),double (17) Robin, M. B. Higher Excited States of Polyatomic Molecules; Academic Press: New York, 1975. (18) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H.B.; Fluder, E. M.; Pople, J. A. Carnegie-Mellon University: Pittsburgh, PA, 1986. (19) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, ,C. M.; Kahn, R. L.;Defrees, D. J.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; Fleuder, E. M.; Pople, J. A. Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984.

588 The Journal of Physical Chemistry, Vol. 96, No. 2, 1992

Dearden et al.

TABLE I: TOWEaergies, Inversion Barriers, Adiabatic Ionization Potentials, and Vertical Excitation Energies Obtained for Difluoromethyl Species Obtaiaed at Different Levels of The~ry electronic total energy,' Bin", IP,, vert. exc species state level of theory hartrees cm-' eV energy, cm-1 HF/6-31G* -236.960082 CHF2+ cation . . ~ MP2/6-31GS -231.421 010 -231.41 0 490 MP2 = FC/6-31GS//MP2/6-31G* MP3 FC/6-3 lG*//MP2/6-3 lG* -231.406 598 MP4SDQ = FC/6-31G*//MP2/6-31G* -231.421 513 MP4SDTQ FC/6-31G*//MP2/6-3lG* -231.436 866 HF/6-31GS* -236.962 286 MP2/6-31G** -231.419985 MP2 = FC/6-3 lG**//MP2/6-31G** -231.411411 MP3 = FC/6-3 lG**//MP2/6-3 1G** -231.413 918 MP4SDQ = FC/6-31GS*//MP2/6-31G** -231.428 900 MP4SDTQ = FC/6-3 1G**//MP2/6-3 1G** -231.444 3 11 CHF2 ground-state UHF/6-31G* -231.263 135 3505 8.33 radical UMP2/6-31GS -237.117638 3116 8.18 UMPZ = FC/6-31G*//UMP2/6-31G* -237.108 494 3183 UMP3 = FC/6-31G*//UMP2/6-31G* 2959 -231.111 604 UMP4SDQ = FC/6-3 lG*//UMP2/6-31G* -231.122 640 3001 UMP4SDTQ = FC/6-3 1GS//UMP2/6-31G* -231.133 685 3043 UHF/6-31GS* -231.265 186 3314 8.32 UMP2/6-31GZ* -231.125 864 3148 8.40 UMPZ FC/6-3 lG**//UMP2/6-3 lG** -231.116511 3118 UMP3 = FC/6-31G**//UMP2/6-3lG** -231.120 243 2962 UMP4SDQ = FC/6-3lGC*//UMP2/6-31G**-231.131 116 3008 UMP4SDTQ = FC/6-31G**//UMP2/6-31G** -231.142 384 3054 CHF2 ground-state UHF/6-31G* -231.241 161 transition structure UMP2/6-31GS -231.103 111 UMPZ = FC/6-31G*//UMP2/6-31G* -237.693918 UMP3 = FC/6-31G*//UMP2/6-31GS -231.698 126 UMP4SDQ FC/6-3 lG*//UMP2/6-3 1G* -231.108 968 UMP4SDTQ = FC/6-3 1G*//UMP2/6-31G1 -237.719 805 UHF/6-31G** -231.249 813 UMP2/6-3 1G* * -231.111 521 UMPZ = FC/6-31G**//UMP2/6-3lG** -231.102089 UMP3 = FC/6-31GS*//UMP2/6-31G** -231.106 148 UMP4SDQ = FC/6-31G**//UMP2/6-31G**-231.111 41 1 UMP4SDTQ = FC/6-31G**//UMP2/6-3lG** -231.128 468 CHF, excited-state UHF/6-31G* -231.159 009 22 840 transition structure UMP2/6-3 1G* -231.618148 21 685 UMPZ = FC/6-3 1G*//UMP2/6-31GS -231.609 841 21 650 UMP3 = FC/6-3 lG*//UMP2/6-31G* -231.609 496 22 420 UMP4SDQ = FC/6-31G*//UMP2/6-31G* -231.624 103 21 615 UMP4SDTQ FC/6-31G*//UMP2/6-31GS -237.638 381 20915 CHFl excited-state UHF/6-31G* -236.999 304 51 885 transition structure UMP2/6-31G* -231.483 164 51 450 UMPZ = FC/6-31G*//UMP2/6-31G* -231.414 501 51 345 UMP3 = FC/6-31G*//UMP2/6-31G* -237.468 295 53410 UMP4SDQ = FC/6-31G*//UMP2/6-31G* -231.481 651 51 5 5 5 UMP4SDTQ = FC/6-31G*//UMP2/6-3 1G* -231.506049 49 945 ~~

1 hartree = 219414 cm-I.

(D), triple (T), and quadruple (Q) excitations froin the starting H F determinant were included in these calculations. The frozen core computations are denoted by MP4SDTQ = FC/6-31G*/ /MP2/6-3 lG* for the CHF2+cation and UMP4SDTQ = FC/ 6-31G*//UMP2/6-31G* for the doublet radicals. For the ground-state structures of the cation and radical similar calculations were also performed using the 6-31G** basis set. All computations were performed on VAX-11/185 and IBM 4381 computers at the National Institute of Standards and Technology Scientific Computing Facility and at the Johns Hopkins University Academic Data Center. ExperimentalApparatus. The apparatus and procedures used to measure REMPI spectra of difluoromethyl radicals have been described in detail.2o Only a brief overview is given here. Radicals were generated in a flow reactor which operated at 250-400 Pa (2-3 Torr) by hydrogen abstraction from CH2F2(or CD2F2)using F atoms produced in a microwave discharge. The radicals effused from the flow reactor into the ionization region of a time-of-flight mass analyzer. The estimated radical density in the ionization (20) Johnson, R. D. 111; Tsai, B. P.;Hudgens, J. W. J . Chem. Phys. 1988, 89,4558.

region is 1O1O Radicals were ionized with the focused output of a pulsed dye laser (energy = 10-20 mJ/pulse; bandwidth = 0.2 cm-I, fwhm; focal length = 150 mm). The ions were mass resolved, and the intensities of the mass peaks of interest were monitored with a gated integrator and averaged and recorded with a computer data-acquisition system, as a function of laser wavelength. The spectra shown here are composites of spectra obtained with the laser dyes (Exciton Chemical Co.):*' PTP (332-350 nm), DMQ (346-377 nm), QUI (368-402 nm), PBBO (386-420 nm), DPS (399-415 nm), and stilbene 420 (412-443 nm). The spectra are uncorrected for the variation in laser pulse energy which occurs over the range of each dye.

Results and Analyses Ab Initio Results. Tables I and I1 list the total energies and the geometrical parameters of CHF2 species at several levels of (21) Certain commercial materials and equipment are identified in this paper in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 589

Difluoromethyl Radicals and Cations

TABLE Ik Minimum b r g y CeOmeMecnl Prrnwters of the Difluorowthyl Cation and Rndicala Obbined rt Different Levels of Theory species electronic state level of theory r(C-H), A r(C-F), A LF-C-F, deg LH-C-F, deg CHF2+cation

2 'AI (C,)

CHF2 ground-state radical

k 2A' (C,)

CHF, ground-state transition structure

k 'BI

CHF2 transition structure

A 2AI (C,)

CHF, transition structure

e 2Bz (C,)

(C,)

HF/6-31G* HF/6-3 1G** MP2/6-3 lG* MP2/6-31G** UHF/6-31G* UHF/6-31G** UMP2/6-31G* UMP2/6-31G** UHF/6-31G* UHF/6-31G** UMP2/6-31G* UMP2/6-3 1G** UHF/6-31G* UMP2/6-31G* UHF/6-31G* UMP2/6-31G*

1.0798 1.0816 1.0925 1.0883 1.0756 1.0772 1 .0882 1.0843 1.0626 1.0627 1.0718 1.0669 3.9798 3.9724 1.0583 1.0678

1.2170 1.2172 1.2427 1.2424 1.3139 1.3139 1.3368 1.3360 1.3095 1.3095 1.3304 1.3298 1.2833 1.3128 1.4273 1.4502

118.04 117.90 1 1 8.24 119.19 111.15 111.07 111.44 111.51 114.80 114.61 115.32 115.18 104.48 104.24 92.94 93.18

120.98 121.05 120.88 120.41 113.77 113.93 113.68 113.65 122.60 122.70 122.34 122.41 127.76 127.88 133.53 133.41

a,,,, deg 0.0 0.0 0.0 0.0 44.52 44.20 44.52 44.53 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

TABLE IIk Cnlculrted and ExperimenWly Observed Vibrational Frequencies of the CHFl+ and the CHFl Rndieal (Cdculrted Harmonic Frequencies from the HF/6-31G* and UHF/6-31C* Optimized Structures of the CHF, Cation and Radial, Respectively, nod Then Reduced by 11% See Text) CHF2+ cation CHF2 radical vibrational motion c, sym ab initio calc, cm-I expt, cm-l c, sym ab initio calc, cm-l expt, cm-I a' 2996 wI C-H sym str 81 3053 1365' a' 1146 1 164b w2 CF2 sym str a1 1347 660" a' 520 w3 CF2 scissors a1 634 1022' a' 991' 949d to4 OPLA bend bl 1073 a" 1339 1317b HCF def b2 1283 1608' a" 1177 1 173b w6 CF2 asym str b2 1625 4508 4506 zero-point energy 38528 3829h ' A frequency of the P (3p) Rydberg radical obtained during this REMPI study. bAr matrix data from ref 11, 13. cAverage ab initio u", = 0-2, 1-3 frequency interval. See text. dAverage v''~ = 0-2, 1-3 frequency interval obtained from the REMPI spectrum. 'Ar matrix data of ref 12. fDerived using the ab initio w l r us,and w6. 'Ab initio ZPE(u4) = 523 cm-'. "Derived using the experimental ZPE(v,) = 504 cm-I and the ab initio wI and w3.

theory. The QMOT descriptions of these species described above are in good agreement with the results of the ab initio computations. The CHF2+cation is planar, and its HOMO is a u-MO of a, symmetry. The virtual MOs of CHF, lie at higher energies than the corresponding ones of CHCl,+. The MO ordering of CHF2+ is depicted in Figure 1. The ground-state geometry of CHF, radical is of ,A' symmetry in the C, point group. As shown in Table 11, the computed out-of-plane angle in the nonplanar radical is a,,, = 44.53O. For comparison, in X ,A' CHCl, the smaller out-of-plane angle, a,,, = 29S0, was obtained at the UMP2/6-31G* level of theory: As predicted with the QMOT analysis, the planar C, CHF, radical has 2BIsymmetry. Table I1 also shows the optimized geometries obtained for the CHF2+cation and for the C, and C, ground-state CHF, radicals using the 6-31G** basis set. Each optimized geometry differs little from the corresponding structure obtained with the 6-31G* basis set, e.g., bond lengths differ by 10.005 A and bond angles differ by 10.2O. For calculations that use the 6-31G* basis set the addition of electron correlation alters the optimum geometries of CHF2 s e e s only slightly. For all species the UMP2/6-31G* calculations lengthened the C-F bond lengths by -0.02 A and changed the bond angles by 1 O S o (Table 11). The out-of-plane angle a,,, is unchanged. An expansion of the 6-31G* basis set to the 6-31G** basis by including hydrogen pAOs also causes small geometric changes. The geometric changes caused by electron correlation with the 6-31G** basis set are also small. The most dramatic change caused by enhancing calculations from the MP2/6-31G* to the I$P2/6-31G** levels is the l o change in LF-C-F observed in the X ,Al CHF2+cation. In Table I the inversion barrier, Bim,& obtained from the energy separation between the k ,A' and X 2BI structures. At the UMP4SDQ = FC/631G* level of theory we obtained Bi, = 3043 cm-I. By comparison, the corresponding barrier in CHC12was calculated at the UHF/6-31G* theory level to be 220 cm-1.6No experimental measurement of Binvfor CHC1, is reported.

Table I11 lists the scaled harmonic vibrational frequencies (HVF), computed at the HF/6-31G* and UHF/6-31G* levels of theory, far the ground states of the CHF,+ cation and the CHF, radical, respectively. At these theory levels the computed HVFs are known to be 9-13% higher than the corresponding experimental v a l ~ e s .To ~ permit comparisons with experimental results, the harmonic ab initio frequencies listed in Table I11 have been arbitrarily reduced by 11%. Because the CHF, is nonplanar, it has two potential energy minima along the v4 (b,) out-of-plane large amplitude (OPLA) bending coordinate. The harmonic w4 OPLA frequency reported by the GAUSSIAN86 program is inappropriate for comparison with experimental measurements. Instead, in Table I11 we report the average of the v''~ = 0-2 and 0'5 = 1-3 intervals obtained by solving the Hamiltonian for the quartic doublewell oscillator with the potential

v = A(Z4 - BZZ)

(2)

after the method described by LaaneZ3and as described in our earlier s t ~ d i e s . ~ ~The ~ J ~mass-weighted ~*~ coefficients, A and B, were derived using the MP2/6-3 1G** optimized structure and the UMP4SDTQ = FC/6-31GS* inversion barrier, Bin,= 3054 cm-I. Tables I and I1 also list the ab initio results for the A ,Al (C,) and ,Bz(C,) states of the CHF, radical. Limitations imposed by the GAUSSIAN86 program constrained-investi ations of excited states. Only planar geometries of the A and states were calculated. The a ,Al state could not be investigated. The ab initio UMP2/6-31G* calculations-estimate that the A ,A1 (C,) state lies 20915 cm-l above :he X ,A' structure. As predicted by the QMOT analysis, the A ,Al (C,) state has an

e

B

(22) Hehre, W.; Radom, L.; Schleyer. P. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Why-Interscience: New York, 1986. (23) Laane, J. Appl. Spectrosc. 1970, 24, 13. (24) Johnson 111, R. D.; Tsai, B. P.; Hudgens, J. W. J. Chem. Phys. 1989, 91, 3440.

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992

590

60000

330

58000

340

350

56000

Two-Photon Energy (Cm I ) 54000 52000 50000

360

370

380

390

400

TABLE IV: Band Maxima Observed in the 2 + 1 m / z 51 REMPI Spectrum of the CHFl Radical between 330 and 430 nm and Their Assignments diffuse band continuum between 430 and 410 nm energy band max two-photon re1 to 3p assgn A.i, nm energy, cm-' origin, cm-'

48000

410

420

430

Laser Wavelength (nm)

Figure 4. Composite REMPI spectrum of the CHF2 radical ( m / z 51) observed between 330 and 440 nm. Two-Photon Energy (cm ' ) 60000

330

58000

340

350

56000

360

54000

370

52000

380

50000

390

400

40000

410

420

430

Laser Wavelength (nm)

Figure 5. Composite REMPI spectrum of the CDF2 radical ( m / z 52) observed between 330 and 440 nm.

abnormally long C-H bond, r(C-H) = 3.97 A (Table 11). This long C-H bond is caused by the odd electron that resides in MO 14 which is strongly C-H antibonding. The ab initio calculations also find that one of the b2 normal modes, comprised largely of C-H moiion, has an imaginary frequency. This result suggests that the A 2Alstate dissociates rapidly to give CF2 H. We note that an expansion of the hydrogen atom basis set should not appreciably reduce the length of the C-H bong. The ab initio calculationj estimate that the E 2B2 (C2J state lies 49 945 cm-] above the X 2A' structure. The ab initio calculations obtained an imaginary harmonic vibrational ftquency for the v4 OPLA mode which indicates that the planar E 2Bz CHF2 structure lies at a saddle point. Thus, we conclude that 2B2 CHF2is nonplanar and belongs to the C,point group. The E 2B2 state should reside lower than the vertical excitation energy listed in Table I. Table I lists the adiabatic ionization potentials for CHF2radical calculated at several levels of theory. IP, is the total energy difference between the radical and cation plus the energy difference between the radical and cation zero-point energies. The UMP2/6-31GS* level of theory obtains IP, = 8.40 eV. Identification of Spectral Carrier. The composite REMPI spectra of CHF, ( m / z 51) and CDF2 ( m / r 52) are presented in Figures 4 and 5, respectively. Difluoromethyl radicals were generated using the hydrogen abstraction reaction CH2F2 + F CHF2 H F

+

+

Dearden et al.

+

The REMPI signals were proportional to reactant concentrations and were not observed in the absence of F2 or when the microwave discharge used to produce F atoms was extinguished. As required of a species that contains one hydrogen atom, the REMPI signal shifted to 1 amu higher mass upon deuteration of the precursor. Structured spectra were observed only at the molecular cation mass. No evidence indicated that the laser light induced fragmentation of the difluoromethyl cations. Thus, all available data support the assignment of these REMPI spectra to the CHF2 and CDF2 radicals. REMPI Spectra of the CHFzand CDF2Radicals. CHF2and CDF2 radicals produce strong REMPI signals between 410 and 330 nm. The spectra of both radicals consist of distinct progressions of vibrational bands. Table IV lists the band maxima observed in the REMPI spectrum of the CHFz radical. Table V lists the band maxima observed in the REMPI spectrum of the CDF2radical. State energies listed in the tables are based upon

420.47 41 3.39 411.39 408.78 407.80 406.51 405.46 404.89 403.86 403.10 402.09 401.1 I 400.1 1 397.63 397.15 396.59 396.28 394.60 394.03 391.95 391.41 390.49 389.22 386.65 384.20 383.78 381.55 381.39 379.17 378.33 376.78 376.30 376.02 374.33 371.89 37 1.06 369.61 368.74 367.29 366.50 364.88 362.65 360.5 1 358.27 356.07 355.26 354.01 352.93 351.97 350.54 349.57 347.74 347.68 347.10 345.82 345.76 345.19 343.74 341.74 340.23 339.86 339.00 338.29 338.00 336.06 335.48 334.45 333.20

47552 48307 48602 48913 49030 49185 49312 49382 49509 49602 49726 49847 49972 50283 50344 50416 50455 50670 50743 51012 51083 5 1203 51370 51711 52042 52099 52402 52425 52732 52850 53066 53134 53173 53414 53764 53884 54096 54223 54438 54555 54797 55134 55461 55808 56152 5628 1 56480 56653 56807 57038 57 197 57498 57508 57604 578 17 57827 57923 58 166 58507 58767 58831 58980 59104 59155 59496 59599 59783 60006

-1 760 -945 -71 1 -400 -282 -1 27

0 69 196 289 414 535 660 97 1 1032 1 IO3 1I 4 3 1358 1431 1700 1771 1891 2058 2399 2729 2786 3090 3112 3420 3537 3754 3822 3861 4101 445 I 4572 4784 491 1 5125 5242 5485 5822 6149 6496 6840 6968 7168 7340 7494 7726 7884 8185 8196 8292 8505 8515 861 1 8854 9194 9454 9519 9667 9792 9843 10184 10287 10471 10694

OTentative assignment. bThis band was not used in the calculation of the average progression interval.

Difluoromethyl Radicals and Cations

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 591

TABLE V: Band Maxima Observed in the 2 + 1 m / z 52 REMPI Spectrum of the O F l Radical between 330 and 430 nm and Their Assignments unresolved band continuum unresolved band continuum between 430 and 410 nm between 430 and 410 nm energy energy band max two-photon re1 to band max two-photon re1 to assignt &in nm energy, cm-’ origin, cm-l assignt A,,, nm energy, cm-l origin, cm-l -2421 366.70 54524 5202 46901 426.31 -1621 419.15 47102 366.55 54548 5225 -1528 47795 418.33 54623 5301 366.04 -796 412.03 48526 54777 365.02 5454 -669 410.95 48654 54916 5654 363.69 -196 49127 406.99 55076 5754 363.03 49323 0 405.38 55193 362.26 5870 49394 71 404.80 55385 631.01 6062 403.72 49526 203 55417 360.80 6095 49847 525 401.11 55484 6161 360.36 49969 646 400.13 55647 6325 359.30 865 398.40 50187 55834 651 1 358.10 950 391.72 50212 55918 357.57 6595 50436 1114 396.43 56050 356.12 6727 50640 1317 394.83 56247 6924 355.47 50727 1405 394.16 56276 355.29 6953 1531 393.17 50854 5633 1 7008 354.95 1748 391.50 51071 56687 7365 352.71 1841 390.79 51164 56771 7449 352.20 51292 1969 389.82 57 129 349.98 7807 388.07 51523 2201 57571 8249 347.30 2274 387.51 51597 57665 346.73 8388 51139 2416 386.45 57780 8457 346.04 51940 2618 384.95 5798 1 8659 344.84 58005 344.70 52033 384.27 8683 2710 58191 8869 343.60 52178 383.20 2855 58387 9065 342.44 52390 38 1.64 3068 58425 342.22 9102 3160 52482 380.97 58581 341.31 9258 3283 52606 380.08 58730 9407 340.44 3500 52823 378.52 58829 9506 339.87 3580 52902 377.95 58912 339.39 9589 53045 3722 376.93 59087 9764 338.39 53261 3938 375.40 59222 9900 337.61 59265 9942 337.37 374.73 53357 4035 59434 10112 336.41 4142 373.97 53465 336.28 59457 10134 53697 4374 312.36 59512 10190 335.97 371.89 53764 444 1 59653 10330 335.18 370.92 53905 4582 59700 334.91 10377 4788 369.51 541 10 59950 10628 333.51 54212 4890 368.81 59999 10677 333.24 54330 5008 368.01 ~~~

two-photon preparation of the resonant excited states. The basis for this photon-order assignment is discussed below. The vibrational selection rules which govern the REMPI spectra of difluoromethyl radicals are Avi = 0, f l , f 2 ..., for the symmetric v , , v2, and vj vibrational modes and Auj = 0, f 2 , f 4 ..., for the antisymmetric v4, v5, and v6 modes. Calculations show that the v4 = 0, 1 energy levels of X 2A’ difluoromethyl radicals are essentially degenerate. At ambient temperatures these levels will possess nearly the same thermal populations. Hence, because the u4 = 0, 1 levels are degenerate, vibrational progressions involving the v4 OPLA mode will appear identical to those governed by the Av4 = 0, f l , f 2..., selection rule and the frequency intervals observed along the v4 progression will directly exhibit the energy level structure of the upper state. Paddon-Row et al.25 have calculated the frequency and deuterium isotope shift of each normal mode of the CHF2 and CDF2 radicals based upon structures calculated at the UHF/3-21G theory level. The spectrum of the CHF2 radical exhibits three distinct vibrational progressions which terminate at 405.46, 394.60, and 384.20 nm. Each progression is comprised of 6-1 1 bands which are evenly separated by an average interval of 2hv = 1032 cm-I. The spectrum of the CDF2 radical exhibits seven vibrational ( 2 5 ) Paddon-Row, M. N.; Wong, S . S . J . Mol. Struct. (THEOCHEM) 1987, 150, 109.

progressions which terminate at 412.03, 405.38, 401.1 1,400.13, 394.83, 389.82, and 384.95 nm. Each progression possesses 6-1 1 members that are evenly separated by an average interval of 2hv = 865 cm-’. The CHF2/CDF2 isotope ratio of these vibrational intervals is 1.2 which matches the isotope ratio previously calculated by Paddon-Row et al.25for the v4 OPLA vibration of difluoromethyl radicals. This observed ratio also matches the isotope ratio obtained using standard formulas for reduced masses of XYZ2 species.26 Thus, we assign the source of these intervals to the v4’ OPLA mode of the upper electronic state. The uniformity of vibrational intervals along each progression indicates that the v4 OPLA mode is essentially harmonic and that the excited state has a planar structure. Since only the Rydberg states of CHF2radical are planar, we assign the upper state which produces these spectra to Rydberg states. Attributing the spectra to Rydberg states clarifies the photoabsorption process that produces the ion signals. The adiabatic 8.5-8.8 eV will ionization potential for CHF2 radical of IP, permit the CHF2 radical to ionize after absorbing three laser photons. As estimated by simple calculations using eq 1, all Rydberg states of the CHFz radical reside at energies greater than

-

( 2 6 ) Herzberg, G . Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand Co.: New York, 1945; pp 179-180.

592

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992

TABLE VI: SUaDrrmry of the Spectroscopic Coasbats for the P (3p) Rydberg State of Difluoromethyl Radicals Obtained from REMPI SDectra

(3p) Rydberg state CHF,. cm-' CDF,. cm-l 49312 i 10 49323 i 10 1365 f 8 1300 f 21 660 i 20 650 f 15 1022 f 1 864 i 2

swtroscodc const TO w 2 (al) CF2 sym str wj (al) CF3 scissors w4 (b,) OPLA bend

-41 000 cm-'. Therefore, the Rydberg states that produce the spectra are prepared by absorbing two laser photons. After each Rydberg radical absorbs a third l e r photon, it ionizes by ejecting the Rydberg electron to form the X ,Al cation, Le., the ion signals are generated through a 2 1 REMPI mechanism. Table VI summarizes the spectroscopic constants of the upper electronic states which produce the REMPI spectra. In the spectrum of the CHF2 radical the REMPI band at 405.46 nm (2hv = 49 3 12 an-I) is assigned as an electronic origin. This band terminates a vibrational progression of 11 members which we have assigned as a series of 4; bands where n = 0, 1, 2, 3, ...,and m = 0, 1, 0, 1. These assignments give w ' ~= 1022 f 1 cm-I. The corresponding origin the CDF, spectrum lies at 405.38 nm (2hv = 49 323 cm-I). The 4; progression that advances to the blue of this origin gives wf4 = 864 f 2 cm-'. These on in assignments are supported by the small 11-cm-I shift of the Oo%bands between the CDF2 and the CHF, radical spectra. Sensible solutions of the Rydberg formula (eq 1) for these origins yield n = 33nd 6 = 0.64.7. Thus, we attribute these REMPI spectra to the F (3p) Rydberg state of the difluoromethyl radical. The 3p Rydberg states have ,Al, ,B1, and 2B2symmetries. However, no data were collected which would resolve among these symmetry assignments. The solutions of eq 1 for the P (3p) origins caused us to expect that these 2 + 1 REMPI spectra would display a 4p Rydberg origin somewhere between 328 and 339 nm. However, no REMPI bands between 300 and 350 nm were assigned to 4p Rydberg states. The apparent increase in intensity that begins near 348 nm and extends to the blue suggests the presence of an unresolved electronic state. Transition strengths to 4p Rydberg states are smaller than tkose to 3p Rydberg states. -Thus, an obscuration of the 4p X spectrum by the 3p X spectrum is expected. If a 4p Rydberg state origin were assigned near 348 nm, this assignment would indicate that the ionization potential of the difluoromethyl radical is IP, 8.5 eV. Most REMPI bands that lie to the blue of each P (3p) Rydberg origin are combination bands that originate from the uf4 OPLA mode combining with either the J2CF2 symmetric stretch mode and/or with the J3CF, scissors mode. In the CHF, spectrum the 2;4!,, (n = 0-9) progression terminates at 394.60 nm and the 2:4:,1 (n = 0 - 5 ) progression terminates at 384.20 nm. In the CDF2 spectrum the 214t;,l( n = 0-10) progression terminates at 394.83 nm and the 2!4{,, (n = 0 - 5 ) progression terminates at 384.95 nm. These as_ignmentsinvolving the d2CF2 symmetric stretch mode of the F (3p) Rydberg state yield wf2 = 1365 i 8 cm-l for CHF, and wf2 = 1300 f 21 cm-I for CDF2. Yeak bands originating from the J3CF2 scissors vibration of the F (3p) state appear in these spectra. In the CHF, spectrum a weak 3; band appears at 400.11 nm. The 3A4; and 3b4; bands are also assigned. In the CDF, spectrum the 3;4& ( n = 0-7) progression terminates at 400.13 nm. Combination difference? of the assignments involving the v3 CF2 scissors mode of the F (3p) Rydberg state yield wf3 = 660 f 20 cm-I for CHF, and w', = 650 f 15 cm-l for CDF,. The spectrum of the CDF, radical also displays a weak 2$;4!,, (n = 0-6) progression separated by 871 f 10 cm-l which terminates at 389.82 nm. The CDF2 REMPI spectrum exhibits two progressions that originate from the nearly degenerate df4= 2,3 vibrational levels of the ground state. We assign the progression that terminates at 412.03 nm to 4; (n = 0-9, x = 2, 3, 2, 3, ...) hot-band transitions. The 10 members of this progression are separated by 2hv = 867 f 13 cm-I. The combination differences give 2 d f 4= [4! - 4;] = 792 f 6 cm-I and 3wff4= [4;+l - 4F'] = 795 f 2 cm-I

+

-

-

-

Dearden et al. TABLE M:-E d f d Vihtiad Lercls Of the S 2A' Strtes of CHF, d CDF2 Radkda rad the uff4Levels Calculated Urhg a Quartic DotlMcWell Potentid

difference quantum obsd wff4vib calc wff4vib (obsd - calc), no. uf; energy, cm-' energy, cm-I cm-l CHF2 Radical" (Bi, = 2715 f 400 cm-I, 0, = 43.7O i 8°)b 0 1 2 3 4 5 6 I

0 945 (10) 953 (20) 1760 (20)

CDF2 Radical' (Bi, = 2860 I 2 792 (6) 3 795 (2) 4 1512 (40) 5 1525 (30) 6 7

0 0.008 948.6 949.6 1760 1796 2325 2588 3022

-4 3 0

* 400 cm-', 0, = 5 3 . 7 O f 0.0003 794.14 794.18 1518.1 1520.7 21 12 2171

-2 +1 -6 +5

" V (cm-I) = 118.19(Z4 - 9.5822); ZPE(v4) = 504 cm-I. b O , is calculated using r(C-H) = 1.0843 A. c V (cm-I) = 90.29(Z4 11.0522); ZPE(v4) = 416 cm-I.

where n = 0,2,4,6,8 (Table V). A second hot-band progression comprised of nine members separated by 2hv = 866 f 15 cm-I runs parallel to the 4: progression and terminates at 401.1 1 nm. Each member of the 401.1 1-nm progression lies 1320 cm-I higher in energy than a corresponding band in the 41: progression. These separations sup rt assignments of the 401.11-nm progression to a series of 204F p" (m = 0-8, y = 2,3,2,3, ...) hot bands. In the CDF2 spectrum we assign the very weak band at 418.33 nm as the 4: transition. This 4: assignment is supported by assignments of the 4: and 2b4: hot bands. The CHF, spectrum also exhibits df4hot-band structure. The 4; and 4: bands are assigned to the weak 413.39- and 420.47-nm bands, respectively (Table IV). The 4: band appears more strongly at 404.89 nm. These assignments receive further support from the corresponding combination bands which include 2; transitions (Table IV). Table VI1 tabulates the ground-state wN4 energy levels of CHF2and CDF, radicals which we evaluated from the REMPI spectra. Potential Energy Fmction of tbe V"4 OPLA Vibrational Mode. The irregular vibrational intervals displayed by the df4OPLA mode (Table VII) are symptomatic of the nonplanarity of the X 2Afdifluoromethyl radicals. These energy levels can be described approximately by the Hamiltonian which has the quartic double-well potential energy surface of eq 2. Using a least-squares procedure, the observed df4vibrational energy levels were fit to obtain coefficients of eq 2 for the CHF, and CDF, radicals. Table VI1 lists these coefficients and the calculated df4OPLA energy levels of each isotopic radical. The residuals of these fits are smaller than the measurement uncertainties. The inversion barriers calculated from the double-well coefficients are Bhv = 2715 400 em-' for the CHF, radical and Bi, = 2860 f 400 cm-' for the CDF2 radical. To interpret the equilibrium coordinate value, 2 ,we have adopted the ab initio bond length, r(C-H) 1.0843 (Table 11). The 2"s give a,,, = 43.7O f 8' for CHF2 and @,, = 53.7O f 8 O for CDF, radicals. The large uncertainties in Bin"and a,,, originate principally from the large magnitude of a, and are amplified by the sparsity and relatively poor precision of the data. More accurate detmninations of the Binvand a,,, will require observations of df4energy levels that lie near or above the inversion barrier. Thus, we report the average experimental values of Binv= 2800 500 em-' and a,,, = 49O f 6O. F i p r e 6 diagrams the vfr4OPLA mode potential function of the X ,Af CHF2 radical. The experimentally observed intervals between vibrational levels of the CHF, radical are also shown.

-

*

w

*

The Journal of Physical Chemistry, Vol. 96, No. 2, 1992 593

Difluoromethyl Radicals and Cations 4000

7

3500 -

I

3000 -

= -E

2500

-

2000

-

1000

-80

-60

-40

-20

0

20

40

60

80

OUT-OF-PLANE ANGLE, P (degrees)

Figure 6. Schematic of the potential energy function along the vN4 OPLA mode of the CHF2 radical as a function of the bending angle, CP. The small energy separations between the u4 = 0-1, 2-3 vibrational energy levels are not depicted. All energies are in cm-'.

As is typical of vibrations described by doubleminimurn potentials, the V"4 = 0-1 vibrational levels form a nearly degenerate pair separated by 0.008 cm-l. The v''~ = 2-3 levels which lie 1260 cm-'below the inversion bamer are also nearly degenerate. Pairs of higher vibrational levels do not separate significantly until the crest of the inversion barrier is surmounted-which in the CHF2 radical first occurs for the Jr4= 6-7 levels. N

Discussion We have assigned the REMPI spectrum of the CHF2 radical to originate from a 3p Rydberg state that exhibits vibrational structure between 47 500 and 60000 cm- (Table 111). The ion signals which produced the spectrum were generated by a 2 + 1 REMPI mechanism. The assignment of vibrational hot bands enabled a determination of the ground state V"4 OPLA potential energy function. The ab initio structures calculated for the CHF2 radical and cation (Table 11) conform with the QMOT descriptions. The CHF2+cation is planar and the CHF2 radical is nonplanar with a C, point group structure. The ab initio results show that the C-F bond length in the cation is shorter than in the radical. The QMOT description indicates that the longer C-F bond length of the radical arises from the out-of-phase repulsions between the carbon and fluorine px AOs in the SOMO, **-MO 13 (Figure 1). The difference in C-H bond lengths between the (planar) CHF2+cation and C , CHF2 radical is ~ 0 . 0 2A. As the C2, radical relaxes to the C, structure, the C-H bond lengthens 0.006 A (Table 11). The C-H bond lengthens because the C, structure cannot accommodate as much overlap between the carbon and hydrogen AOs as occurs in the C, structure. As expected, the C-F bonds of the cation are shorter than those of the radical reflecting the repulsion between the carbon and fluorine *-orbitals of MO 13. The out-of-plane angle 9 , calculated by ab initio theory is one measure of the convergence of the CHF2 radical structure. The UHF/MNDO and RHF/MNDO computations by M o h o et ale2' obtained small out-of-plane angles of 9, = 16.7' and a,, = 11.5O, respectively.28 ST0/3G calculations by Leroy et al. obtained CP, = 40.1°.29 At the UHF/4-31G level Leroy and Peeters30and Pasto et aL31obtained 9, = 42.4O. At the UHF/6-21G level of theory Paddon-Row et al.32 calculated 0, = 41.3'. At the

-

UHF/6-31GZ level our calculations and those of Luke et al.33find e,,, = 44.52'. The ab initio calculation of the CHF2 radical geometry appears to have essentially converged at the UHFJ631G* level. Higher levels of theory introduce insignificant changes in structure (Table 11). The addition of electron correlation at the UMP2/6-31G* level leaves the out-of-plane angle essentially unchanged at 9, = 44.5'. The enhanced 6-31G** basis set also gives essentially the same 9,. The less precise experimental value, obtained from the REMPI spectra, is a,, = 49 (6)'. This paper presents the first ab initio calculations of the CHF2+ cation (Table 11). Table I11 lists the scaled vibrational frequencies obtained from the HF/6-31G* calculations. Only the w6 (9) CF2 antisymmetric stretch frequency of the cation is experimentally known. The scaled ab initio 0 6 frequency computed at the HF/6-31G* level agrees closely with the observed. For CHF2+a more complete comparison of the ab initio results with experimental data is facilitat_edby adopting the w2, w3, and w4 vibrational frequencies of the F (3p) CHF2 Rydberg radical as surrogates for those of the cation. Such substitutions are reasonable because the chemical bonds in the valence shells of CHF2Rydberg radicals closely resemble those in the cation. Table I11 shows that the theoretical and experimental frequencies agree very well. The scaled ab initio w2, w j , and w4 frequencies differ from the 3p Rydberg radical frequencies by 1%, 7%, and 5%. respectively. Table I11 also presents the scaled vibrational frequencies of the 2 2A1CHF2 radical derived from the UHF/6-31G* ab initio calculations. Table I11 also lists the experimental values of the w2, w 5 , and w6 vibrational frequenciesof CHF2 radicals in an Ar matrix which were reported by Carver and Andrewsl' and by Jacox.') The close agreement between the observed and calculated frequencies suggests that the other unobserved harmonic modes, wIand w3, probably lie close to the scaled ab initio frequencies of Table 111. Our analyses of the REMPI spectrum obtained the inversion barrier, Bhv= 2800 f 500 cm-l. This value is significantly smaller than Bi, = 3500 an-',which was obtained at the UHF/6-31G* theory level (Table I) during this study and also previously by Luke et al.33 Good agreement between theory and experiment is obtained for all higher levels of theory. Electron correlation at the UMP2 level greatly reduces Bin".But much smaller changes are observed when the basis set is expanded to the 6-31G** level or when additional electron correlations are added to the calculations (Table I). Thus, we conclude that the ab initio calculations have converged to the 'true" inversion barrier of the CHF2 radical and that this barrier resides near Binv 3050 cm-I. The average u4 = 0-2 and u4 = 1-3 frequency interval calculated from the ab initio Bin"and 9, is 52 cm-' larger than the experimental interval (Table 111). This difference probably arises from the simplifications incorporated into the double-well potential model so that least-squares fits of data were possible. These simplifications include (1) that the u4 vibrational path is comprised of changes in the 9 angle only (Le., bond lengths and LF-C-F are constant as 9 changes) and (2) the reduced mass of the vibration does not vary with 9.The good agreement between the experimental and ab initio frequencies indicates that the quartic double-well potential approximates the v4 OPLA vibrational potential energy function adequately. In our earlier work on CHC12species the number of electrons included in the calculations were too numerous to permit calculations of fourth-order frozen core calculations which included triple substitutions (UMP4SDQ = FC/6-31G*). For CHF2 species Table I lists the results of calculations which included triple substitutions (UMP4SDTQ = FC/6-3 1G*). Triple substitutions change the magnitude of Bi, by only 35 cm-I, or 1%. Similarly an insignificant 464x1-I change is also obtained using the 6-31G** N

N

(27) M o h o , L. M.; Poblet, J. M.; Canadel, E. J. Chem. SOC.,Perkin Trans. 2 1982, 1217-1221. (28) The tendency of MNDO theory of underestimate bond angles like am is well-known. See ref 22 and: Clark, T. A. A Handbook of- Computarional . Chemistry; Wiley-Interscience: New York, 1985. (29) Leroy, G.;Peeters, D.; Khakil, C. W. M. Noun J. Chim. 1980,4,403. (30) Leroy, G.; Pecten, D. J. Mol. Sfruct. (THEOCHEM) 1981,85, 133. (31) Pasto, D. J.; Krasnansky, R.;Zercher, C. J . Org. Chem. 1987, 52, 3062.

(32) Paddon-Row, M. N.; Thomson, C.; Ball, J. R. J. Mol. Struct. (THEOCHEM) 1987, 150, 93. This UHV/6-31 calculation of the CHF2 radical also obtained the structure: r(C-H) = 1.069 A, r(C-F) = 1.346 A, LF-C-F = 111.9O. and LF-C-H = 114.9O. (33) Luke, B. T.; Loew, G. H.; McLean, A. D. J . Am. Chem. SOC.1987, 109. 1307.

J. Phys. Chem. 1992, 96, 594-603

594

basis set. Therefore, we expect that the addition of triple substitutions into calculations of the chlorinated analogs will have only a small effect upon the calculated Bi,,'s. Acknowledgment. Dr. S . A. Kafafi acknowledges the financial support of the A. Mellon Foundation. We extend our gratitude to NIST Scientific Computing Division and The Johns Hopkins

University School of Public Health Academic Data Center for the allocated computer time on the VAX-11/785 and IBM 4381, respectively, to complete this work. B.P.T. thanks the University of Minnesota for support through the Bush Sabbatical Program. Registry No. CHF2+,35398-31-3; CHF2radical, 2670-13-5; CDF2 radical, 23841-32-9; D, 7782-39-0.

Metastable Polymers of the Nitrogen Oxides. 2. Open-Chain Polymers of the Nitric Oxide Dimers and of Nitrous Oxide: A MNDOIAM1 Study Walter H. Jones Department of Chemistry, The University of West Florida, 1 1 000 University Parkway, Pensacola, Florida 32514-5750 (Received: April 23, 1991; In Final Form: August 30, 1991)

The previous MNDO/AMl study of (SN), and its (NO), analogue is extended to open-chain oligomers of ONNO and NNO. Thermodynamic and kinetic comparisons are made of the neat oligomers and of a number of derivative species, the most pertinent of which, on the basis of similarities to the infinite polymers, are HO(NONO),H, HO(ONNO),H, and HO(NNO),H. Oligomers of up to eight monomer units are investigated. All of the oligomerizations are endothermic. AM1 correctly indicates that the cis-ONNO species is more stable than the trans but gives poor geometry; it can however be argued, on the basis of structural differences between the polymer and the monomer (which has been extensively investigated theoretically by others), that the results for the polymer may be meaningful. A cyclic, high-energy ONNO dimer is found also on the AM1 surface, in qualitative agreement with published ab initio treatments. For all of the oligomersof the nitrogen oxides, charge transfer in the chain (generally N to 0) is less uniform and pronounced than in their polythiazyl counterparts. Thermodynamically, it is concluded that cis,truns-(ONNO), oligomers are favored over (NONO), oligomers. Kinetic analyses, based on presumed homolytic scission of the weakest bond (selected by a bond enthalpy-bond order treatment), also suggest that the most stable nitric oxide polymers would be derived from the symmetricaldimer and that the barriers to decomposition may be significant. The most interesting results arise from study of open-chain oligomers of nitrous oxide: AM1 and MNDO give good geometries and reasonable energies for the monomer and afford oligomers which are similar in structure to polythiazyl, in being straight, planar cis,trans chains with reasonable kinetic stability. These results, in concert with previous theoretical analyses of the importance of low-lying electronic states in the decomposition of nitrous oxide, suggest that metastable polymers of that monomer may be formed at the extreme pressures which have become experimentally accessible in recent years.

Introduction In a previous paper' it was shown MNDO/AMl calculations satisfactorily reproduce the crystal geometry of polythiazyl, (SN),, which is a fibrous metal at ordinary temperatures and becomes a superconductor below 0.33 K. It was also reported that openchain oligomers of NO, analogous to (SN),, may be found on the MNDO/AMl potential energy hypersurfaces. Such species may represent metastable polymers which possess enhanced physical and/or electrical properties and are formed at extreme pressures, polymerization being facilitated by the low-lying excited electronic states. The purpose of analyzing such hypothetical species is to attempt to provide theoretical guidance to experimental efforts. Even if the proposed molecules should not in themselves prove practical, they may serve as models for investigations of more complex materials of interest. In the present study we confine ourselves to assessment of the theoretical feasibility of forming such polymers; estimation of the thermal, electrical, and mechanical properties of such molecules will be the subject of further effort (cf. ref 2). The process of forming polythiazyl is generally thought3 to occur through solid-state polymerization of the known cyclic dimer, viz.

7-y N-S

+

7-y N-S

-

-N

9-N,

S-N

9-N,

S-

and the analogous (NO),, species correspond to oligomers of the unsymmetrical dimer, NONO. The most stable dimer of nitric ( 1 ) Jones, W. H. J . Phys. Chem. 1991, 95, 2588-2595. ( 2 ) Bardo, R. D.; Jones, W. H. In Asay, J. R.; et al., Eds. Shock Waves in Condensed Mutter--1983; Elsevier: Amsterdam, 1984; Chapter XIII, pp 10, 621-624. (3) Another possibility is discussed briefly in ref 1 .

oxide is, however, the symmetrical cis-ONNO, and if the initial step in the polymerization were formation of that dimer, the open-chain polymer might be (ONNO),,. The other symmetrical dimer, NOON, has not been observed but would afford the same polymer. Copolymers among the possible dimers may be envisioned, but it seems worthwhile to consider only individual polymers of the known species. Oligomers of nitrous oxide are unknown, but similar open-chain polymers may be written. Nitrous oxide is of particular interest here because long ago4 it was shown that its decomposition is facilitated by participation of a low-lying excited state, and such considerations led to the analysis that indicated a large pressure-induced reduction of the activation energy for bond scission in the nitrogen oxide^.^ Reduction of the activation energy for a reaction of course reduces the activation energy for the reverse reaction, and the numbers recorded here and in the first paper of this series suggest that there may be a corresponding reduction in activation energy for formation of high-energy, metastable, open-chain oligomers of nitric oxide. We here submit also calculations which suggest the possibility of similar nitrous oxide species. We have found in addition that N 2 0 might form cyclic oligomers; further, the hypersurface contains some interesting polycyclic oligomers of (NO),, of the type \ AN'0. I

/ NO ..

l

/ l

NO.N \

(4) Stern, A. E.; Eyring, H. J . Chem. Phys. 1935, 3,778-785. (5) Bardo, R. D. Proceedings of the Seventh Symposium (International) on Detonation; Office of Naval Research: Washington, D.C., 1981; pp 93-103.

0022-365419212096-594%03.00/0 0 1992 American Chemical Society