8399
J. Phys. Chem. 1993,97, 8399-8402
Ab Initio Study of Several Electronic States of the CF2 Radical Z.-L. Cai Department of Chemistry, East China Institute of Technology, Nanjing 210014, People's Republic of China Received: February 19, 1993
The equilibrium geometries, excitation energies, force constants, and vibrational frequencies for several lowlying electronic states X lA1, 3B1, lB1, 3A2, lA2, 3B2, and 1B2 of the CF2 radical have been calculated a t the MRSDCI level with a triple-zeta plus double polarization (TZ + 2P) basis set. Our calculations imply that the X 'A1 3B2 and X 'A1 lBz transitions may correspond to new band systems near 1500 and 1350 A in the absorption spectrum of CF2 of ref 14. Our calculated excitation energies and vibrational frequencies for the ground state X 'A1 and excited states 3B1,lB1, 3B2,and lB2 of CF2 are in good agreement with available experimental data. Electronic transition dipole moments, oscillator strengths for the lB1- X 'A1 and lB2 X 'A1 transitions, and radiative lifetimes for the lB1 and lBz states are calculated by using the MRSDCI wave functions, predicting results in reasonable agreement with available experimental results.
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We have studied seven low-lying electronic states of the CF2 radical, X 'Al, 3BI, lB1, 3Az, lA2, 3B2, and lB2, by means of multireference single and double excitation configuration interaction (MRSDCI) calculations with a triple-zeta plus double polarization (denoted as TZ + 2P) basis set. In this paper, we report theoptimized equilibrium geometries, calculatedexcitation energies, force constants, and vibrational frequencies for these electronic states. We will also report electronic transition properties for the 1B1 X 'A1 and lB2 X 'A1 transitions. These calculated results will be compared with available experimental data.
I. Introduction
The CF2 radical is well-known, since it is believed to be created in the upper atmosphere by the photodissociation of chlorofluoromethanes, and it is an important intermediate in discharge environments containing CF4, which is currently widely used as a source of F atoms and as a process gas in plasma etching applications. In recent years, there has been an increasing interest in understanding the chemistry of CF2. The CF2 spectrum of the ground state X 'A1 has been extensively investigated by various high-resolution spectroscopic methods.1-11 There were several studies of the absorption, laser-induced fluorescence, emission, and chemiluminescence spectra for the electronic excited states II. Calculations of CF2.12-23The excitationenergies, vibrational frequencies,and The basis set used in our calculations consists of the (9s, 5p) radiative lifetime for some electronic excited states of CFZwere Cartesian Gaussian functions for C and F in the [Ss, 3p] obtained. In 1967, Mathews13 studied the UV absorption contraction,given by Dunning,s3augmented by two uncontracted spectrum of CF2 and discovered well-resolved subbands corred-functionswith exponents 0.35 and 1.2 for carbon and fluorine, spondingtoX 'AI lB1 transition. Theyobservednewabsorption yielding a total of 78 contracted basis functions. bands near 1350 and 1500 A as well but did not assign them in The MRSDCI calculationswere performed using the program detail. package MELDF34on a VAX 8350 computer. The equilibrium geometry of the ground state of CF2 was CI, the SCF (RHF) virtual orbitals were transformed measured by absorptionand microwave s p e c t r ~ s c o p y ; ~ .the ~ * ~ J ~ * ~ Before ~ into K-orbital~,'~ which have been shown to mimic frozen natural most accurate values obtained for the C-F bond length and the orbitals of the system. In the MRSDCI calculations, all the F-C-F bond angle are 1.300 A and 104.94'. The equilibrium single excitations from the (multi-)referenceconfigurationswere geometry of the excited state IBIwas also measured by absorption included, as well as the most important double excitations, as spectroscopy,l3 and the bond length and angle are 1.32 A and selected by second-order perturbation theory36 with a selection 122.3O, respectively. No experimental geometries have been threshold T = 15.8phartree. The reference space in our MRSDCI reported for other electronic states of CFZ. calculations for the selectivestates consisted of 8-14 configurations A few ab initio studies for the ground state X 'A1 and the first generated from six selected s p a m r b i t a l products whose coefexcited state 3B1of CF2 have been reported in the ficients are not less than 0.045. The energy values are denoted Most of these studies except for refs 28, 29, 31, and 32 were by E and E (full CI) corresponding to MRSDCI energy at the carried out at the Hartree-Fock (HF) level. The excitation energy configuration selection threshold T and the energy estimated for and geometries for these two electronic states were calculated at the entire basis (full CI) according to the Davidson f0rmula.3~ different levels (from HF/6-3 lG* to CASSCF/( 1ls7p2d/ The square of the electronic transition dipole moment for a 7s4p2d)). In 1987 and 1988, Carter and G ~ d d a r d ~calculated *.~~ general transition +b +a is given by the expression the excitation energy fromX 'A1 to 3B1at different configuration interaction (CI) levels (from GVB-RCI to CCCI) and found that their RCI* IICI and CCCI results are in good agreement with previous experiment. In 1990, Francisco et al.3l calculated in which c,er,is in the length form of the electronic dipole moment the geometry of the X state at the MP2/6-31GS level and operator summed over all electrons. The oscillator strengths are obtained good agreement with experiment. In 1991, Peterson et obtained from the expression al.32 calculated the geometry and some spectroscopic properties of the X 'A1 state at the CASSCF level with a 1ls7p2d/7s4p2d basis set, and their results were also in good agreement with the experimental data. No theoretical studies of other electronic Finally, the radiative lifetimes are calculated from the relationship states of CF2 have been reported.
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0022-3654/93/2097-8399$04.00/0
0 1993 American Chemical Society
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Cai
8400 The Journal of Physical Chemistry, Vol. 97, No. 32, 1993 TABLE I: CF2 Summary of Technical Details of the CI Calculationsa state X 'A1 'BI 'BI 'Az 3B~
'Bz
total ref set 8 6 9 12 10 14 10
selected threshold 15.8 15.8 15.8 15.8 15.8 15.8 15.8
selected SACsItotal SACS 8 89711 404 854 26 54411 905 645 16 34711 871 251 27 49313 796 802 16 38512 281 679 29 62914 382 183 17 29912 283 522
zp"Cp' 0.92 0.92 0.92 0.91 0.91 0.91 0.91
a SACSdenotes spin-adaptedconfigurations. Threshold is in phartrec. LYC: denotes total contribution to the final wave function from the reference set. 7
TABLE II: Optimized Geometric Parameters and Excitation Energies for the Low-LyingElectronic States of the C F 2 Radical
= 1.5/vye
with ;(M)in units of cm-l. In our study,we assume that the CF2 radical has a Cb geometry in each of the seven electronic states. Therefore, only two geometric parameters, bond length R(C-F) and bond angle LFC-F, were considered in searching for the optimized geometries by using finite difference methods. The vibrational frequency calculations were performed under the assumption of valence f0rce3~and by using the following scheme: For each electronic state of CF2, the energy values of nine points in the vicinity of the equilibrium geometry were calculated by varying the bond length in increments of 0.005 A while the bond angle was fixed at the optimized value. The potential curve for the symmetric stretch was obtained by parabolic fits to these nine points using the least-squares methods. The force constant kl was evaluated from the coefficient of the quadratic term. Similarly, the potential curve for the bending mode as a function of the bond angle was obtained by parabolic fits to another nine points near the equilibrium geometry at the least-squares methods, leading to the force constant ka. The frequencies of three vibrational modes (symmetric ( V I ) , asymmetric (v3) stretching, and bending (v2) fundamental frequencies) were deduced from the values of kl and ks under the assumption of valence force. Using the above scheme, one can predict quite accurate force constants (kl and ka) and vibrational frequency (VI, v2, and v3) values for the XY2 molecules (for example, see refs 3 8 4 1 (for NFz, OF2+,NF2+, and NO,-)).
HI. Results and Discussion A. GroundStateX'AI. Theground stateX 'A1 wascalculated as the lowest singlet root in the secular equation for the A, irreducible representation of the Cb group. The reference space in the MRSDCI calculations for the X lA1 state consisted of eight configurations. The main description for this state comes from the configurations A summary of the CI technical details for all states can be found in Table I. The C I energies of the X 'A1 state at the equilibriumgeometry are E = -237.22797 and E(ful1 CI) = -237.35970 hartrees. The optimized geometric parameters for the X 1Al state are shown in Table 11. The equilibrium geometric parameters of the X 'Al state were measured from absorption and microwavespectroscopy, and the bond length and angle are 1.300 A and 104.94 A, respectively (see Table 11).3J+'J3.14 There were some theoretical studies for the geometry of the X 'A1 state.27.31J2In 1977, Bauschlicher et al.27calculated the geometry of the X 'A1 state at the HF/DZ+P level, and their bond length and angle were 1.291 A and 104.7', respectively, which were in agreement with experimental data. In 1990, Francisco et al.31 obtained the geometry of the ground state of CF2 from their HF/6-3 lG* and MP2/6-3 lG* calculations, but there were large disrepancies
MRSDCI/TZ+ZP CASSCFI (1 ls7p2d/7s4p2d)a HF/6-31G* MP2/6-3 1G* HF/DZ+PC exptd MRSDCI/TZ+ZP HF/DZ+PC GVB-RCI(PPY RCI*IICI(PPY RCI*IICI(OptY CCCY HF/6-31G* 8 expth MRSDCI/TZ+ZP exptl MRSDCI/TZ+ZP MRSDCI/TZ+2P MRSDCI/TZ+ZP exptf MRSDCI/TZ+ZP exptf
1.2980 1.2975
104.80 0.0 104.84
1.283 1.315 1.291 1.300 1.3016 1.303
104.5 104.2 104.7 104.94 119.10 118.2
1.304
118.4
1.3234 1.32 1 SO79 1 S232 1.5121
122.04 122.30 73.50 73.42 86.92
1.5287
85.28
2.4236 (2.4028). 1.9311 2.0114 2.2546 2.5978 2.4979 2.4588 4.6396 (4.6483)e 4.6160 6.3094 (6.2730p 6.5250 (6.4330)e 7.7594 (7.6224). 1.8430 9.0567 (8.9212). 9.0198
a Reference 32. Reference 31. e Reference 27. References 3,7, 9, 13, 14. e Values in parentheses were evaluated from the estimated full CI energies. JReferences 28, 29.8 Reference 30. References 2&23. Reference 14.
between their theoretical values and previously experimental ones. In 1991, Peterson et a1.32calculated the geometric parameters at the CASSCF/( 1ls7p2d/7s4p2d) level and obtained good agreement with the experimental ones. Obviously, our calculated geometric parameters are very close to previous CASSCF ones and also in good agreement with experiment. The force constants of the X 'A1 state, calculated on the MRSDCI/TZ+ZP energy surface by means of the valence force assumption, are listed in Table 111. The vibrational frequencies calculated from our predicted force constants are also listed in Table 111. The vibrational frequenciesof the X state of CF2 (in gas and Ar) have been widely investigated experimentally and theoreti~ally,~~2~~~6~*~1~12,14.32 and some results are shown in Table I11 for comparison. Our calculated values of u1, u2, and u3 are in good agreement with experimental data (see Table 111). It is noted that our calculated vibrational frequencies are also close to previous CASSCF 0nes.32 B. and 1B1 States. The 3B1 and 1B1 states were treated as the lowest triplet and singlet roots in the secular equation for the B1 irreducible representation, respectively. The reference configurations for these two states consisted of six and nine configurations,respectively. The main description for these two states comes from the configuration ( 1-5a1)2(6a1) ( 1b1)'(2b1)
The optimized values for the bond length and angle are 1.3016
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A and 119.10' for the 3B1 state and 1.3234 A and 121.84' for
the lB1 state. The calculated excitation energy for the X 'A1 3B1 transition (electron spin forbidden), as the difference of the CI energiesat the corresponding optimizedgeometries of the two states, is 2.4236 (2.4028) eV (the value from the estimated full CI energiesis given in parentheses). The geometriesand excitation energiesfor the 3Bl and 1B1states have already been investigated experimentallyand theoretically.14*20-23*27-30 In 1967, Mathews14 obtainedthe bond length and angle for the lB1 stateand excitation energy for X 'Al lBI from his absorption spectrum. Several authors also obtained the excitation energy for X lAl 3B1 from chemiluminescence.2*23 In 1977, Bauschlicher et al?7 calculated the geometry of the 3B1state and excitation energy for X 'A1
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Electronic States of the CF2 Radical
The Journal of Physical Chemistry, Vol. 97, No. 32, 1993 8401
TABLE IIk Calculated Force Constants (kland h)and vibrational Frequencies ( v ) for the Low-LyingElectronic States of tbe a* Radical state kl (mdyn/A) ki OW") k d P (mdyn/A) v1 (cm-1) v2 (cm-1) v3 (cm-1) X 'Ai 5.230 82 3.291 26 1.953 50 1284 642 1181 12500
expt (in gas)* 1225 expt (in Ar)' 1222 'B1
4.992 92
1.574 08
0.929 12
1025
expt (in gas)d 'BI
4.539 02
1.430 98
0.817 06
1153
expt (in gas)' expt (in Ary 3A2 3B2
3.720 81 3.511 65 8.718 03
3.820 72 3.736 29 6.439 41
1.680 35 1.610 37 2.816 34
B2
5.666 12
4.292 94
1.837 00
'Ai
1141 1111 1654
expt (in gas)d 1339
expt (in gas)d O
679" 661 668 53 1 517 507 496 496(2) 553 54 1 772 825 628 625
1145" 1114 1102 1198 96 1 825 80 1 1395 1124
Reference 32. Referencea 2, 6, 8, 10-12, 14. References 1, 4. References 17, 20, 22, 23. References 12, 14. /References 6, 15, 18.
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TABLE Iv: Calculated Values of tbe Properties Dependent upon the Electronic Transition Dipole Moment (&) for the lB1 X 'A1 and 1% X 'Al Band Systems oscillator radiative EN2 (au) strength/, (au) lifetime T (ns) 'BI-w X 'A1 0.176 25 0.02003 54 expt (in gasp 61 (3) expt (in Ar)* 27 'B2 X 'A1 0.063 75 0.014 15 20 Referencea 16, 17. Reference 18. 3B1 at HF/DZ+P. In 1987 and 1988, Carter and Goddard28J9 calculated the excitation energy for X 'A1 'B1 at different CI levels (from GVB-RCI to CCCI). In 1989, Baird et al.3O calculated the geometric parameters of the 'B1 state at the HF/ 6-3 1G* level. These experimental and theoretical data are shown in Table I1 for comparison. Obviously, our calculated geometric parameters of the 1B1state and excitation energy from X 'A1 to 1B1 are in good agreement wih the experimental data. Our calculated excitation energy for X 'A1 3B1is very close to a previous CCCIvalue of 2.4979 eV28pand also in good agreement with the experimental value of 2.4588 eV form chemiluminescence.2C-23 Our calculated bond length of the 3B1 state is very close to previous HF/DZ+P and HF/6-31G* ones, but the bond angle of the 3B1state is larger than previous theoretical ones. We believe that our optimized geometric parameters of the3BIstate aremoreaccurate than previous abinitiocalculations, although there are no experimental data for comparison. In our ab initio calculations, electron correlation energy was well considered using the MRSDCI method with a T Z 2P basis set, and this argument that MRSDCI calculations can correctly predict the experimental geometry (excitation energies and other spectroscopic properties) of small molecules has been tested extensively.39-'5 The force constants and vibrational frequencies for these two states have been calculated and are shown in Table 111. Our calculated results are in good agreement with experimental data (in gas and Ar).6,12,14,1~.17.18,~,22.23 For the 1B1 X 'AI transition, the electronic transition properties have been calculated by using the MRSDCI wave functions of these two states, with the same program package. The calculated values of the square of the electronic transition dipole moment (C(%12), the oscillator strength for the absorption (taking AE * 4.6396 eV), and the radiative lifetime ( 7 ) for the lBl state are given in Table IV. There is only experimentalradiative lifetimedata reported in the literature.1618 Our calculated radiative lifetime value of 54 ns is close to the experimental one of 61(3) in gas and is 2 times larger than that in Ar. C. md 'A2 States. The 3A2 and 1A2 states were treated as the lowest triplet and singlet roots in the secular equation for
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the A2 irreducible representation, respectively. The main description for these two states comes from the configuration
The optimized geometric parameters for these two states are listed in Table 11. The calculated excitation energies for X 'Al 3A2(spin forbidden) and X 'A1 'A2 (dipole forbidden) are 6.3094 and 6.5250 eV, respectively. For the and 'A2 states, we have also calculated force constants and vibrational frequencies by means of the valence force assumption, and they are presented in Table 111. In our previous work with OF2+, NF2+, and NO2- 39-41 (above the X lA1, 3B~,andlB1 states of the CF2 radical), we found that the calculations on the MRSDCI surface by means of valence force assumption can predict quite accurately the force constants and vibrational frequencies of the excited states of small molecules. So we believe that our calculated results for the 3A2and 1A2state are accurate, although there are no experimental data for comparison. D. 3B2 and IB2 States. The JB2 and IBz states were treated as the lowest triplet and singlet roots in the secular equation for the B2 irreducible representation, respectively. The main description for these two states comes from the configuration
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For the 3B2and lB2 states, the optimized geometric parameters and excitation energies have been calculated and are shown in Table 11. In 1967, Mathews14observed the UV absorption spectrum of CF2 and found two new band systems near 1500 and 1350 A, with a progression of red-degraded bands separated by about 825 cm-1 and a single progression of headless bands separated by about 625 cm-l as well, but he did not assign them in detail. Our calculated excitation energies for X 'Al 3A2and X lA1- IA2 are very close to being above the energy levels of CF2. We may assign the absorption band systems near 1500 and 1350 A, respectively, to the X 'A1 3A2and X 'A1 1A2 transitions. The force constants and vibrational frequencies for the 3B2 and 1Bz states have also been calculated and are listed in Table 111. Our calculated values of u3 for these states are in good agreement with the observed ones of 825 and 625 cm-l, which further supports our above assignment for the two band systems near 1500 and 1350 A. For the1B2-.X 'A1 transition, whichiselectrondipoleallowed, the electronictransition properties have also been calculated based on the MRSDCI wave functions of these two states (Table IV). The calculated radiative lifetime for the lA2 state is 20 ns, which is smaller than that of the 1B1 state.
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8402 The Journal of Physical Chemistry, Vol. 97, No. 32, 1993
IV. Summary The equilibrium geometries,excitationenergies, force constants and vibrational frequencies for several electronic states, X IA1, 3B1, IB1,3A2, lA2, 3B2 and 1B2, of CF2 have been calculated at the MRSDCI with a TZ + 2P basis set. (i) Our calculations imply that the X 'A1 3B2and X 'AI 'B2 transitions may correspond to two new band systems near 1500 and 1350 A of ref 14. (ii) Our calculated geometric parameters for the X 'A1 and lB1states are in good agreement with the experimental data. (iii) Our calculated excitation energies for X 'AI -3Bl, lB1, 3B2, and 1B2 are in good agreement with the experimental data. (iv) Our calculated vibrational frequencies for the X 'AI, )B1, IB1, 3B2, and lB2 states are also in good agreement with available experiment data. (v) Some electronic transition properties with thelBI 4 X 'AIand 1B2-X 'A1 transitions havebeencalculated by using the MRSDCI wave functions. Our calculated radiative lifetime of the IB1 state is good agreement with experiment.
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References and Notes (1) Milligan, D. E.; Mann, D. E.; Jacox, M. E.; Mitsch, R. A. J. Chem. Phvs. 1964. 41. 1199. ' (2) Herr, K.C.; Pimentel, G. C. Appl. Opt. 1965, 4, 25. (3) Powell, F. X.; Lide, D. R., Jr. J. Chem. Phys. 1966,45, 1067. (4) Milligan, D. E.; Jacox, M. E. J. Chem. Phys. 1968, 48, 2265. (5) Snehn, A. High Temp. Sci. 1970, 2, 70. (6) Lefohn, A. S.; Pimentel, G. C. J. Chem. Phys. 1971, 55, 1213. (7) Kirchhoff, W. H.; Lide, D. R., Jr.; Powell, F. X. J . Mol. Spectrosc. 1973, 47, 491. (8) Davies, P. B.; Lewis-Bevan, W.; Russell, D. K. J. Chem. Phys. 1981, 75, 5602. (9) Charo, A.; De Lucia, F. C. J. Mol. Spectrosc. 1982, 94, 363. (10) Davies, P. B.; Hamilton, P. A.; Elliott, J. M.; Rice, M. J. J. Mol. Spectrosc. 1983, 102, 193. (1 1) Burkholder, J. B.; Howard, C. J.; Hamilton, P. A. J . Mol. Specrrosc. 1988,127, 362. (12) Venkateswarlu, P. Phys. Rev. 1950, 77, 676. (13) Mathews, C. W. J. Chem. Phys. 1966,45, 1068. (14) Mathews, C. W. Can. J. Phys. 1967, 45, 2355.
Cai (15) Bondybey, V. E. J. Mol.Spectroac. 1976,63, 164. (16) King, D. S.;Schenck, P.K.; Stephenson, J. C. J. Mol, Spectrasc. 1979, 78, 1. (17) Toby, S.; Toby, F. S.J . Phys. Chcm. 1980,84206. (18) Smith, C. E.; Jacox, M. E.; Mllligan, D. E. J . Mol. Spectrosc. 1976, 76, 381. (19) Ibuki, T.; Hiraya, A.; Shobatake, K. J. Chem. Phys. 1989,90,6290. (20) Koda, S. Chem. Phys. Lett. 1978,55, 353. (21) Koda, S.J. Phys. Chem. 1979,83, 2065. (22) Koda. S. Chem. Phvs. 1982. 66. 383. (23) Zhou; S.; Zhan, M.: Qiu, Y.';Liu, S.;Shi, J.; Li, F.; Yao, J. Chem. Phys. Lett. 1985, 121, 395. (24) Harrison, J. F. J. Am. Chem. Soc. 1971,93, 4112. (25) Staemmler, V. Theor. Chim. Acta 1974, 35, 309. (26) Rothenbera. S.:Schaefer. H. F. I11 J. Am. Chem. Soc. 1975. 95. 2095. (27) Bauschlicher, C. W., Jr.; Schaefer, H. F. 111; Bagus P. S . J. Am. Chem. Soc. 1977, 99,' 7106. (28) Carter, E. A.; Goddard, W. A. I11 J . Phys. Chem. 1987, 91,4651. (29) Carter, E. A.; Goddard, W. A. I11 J. Chem. Phys. 1988,88, 1752. (30) Baird, N. C.; Kuhn, M.;Lauriston, J. M.; Can. J. Chem. 1989,67, 1952. (31) Francisco, J. S.; Goldstein, A. N.;Li, Z.; Zhao, Y.; Williams, I. H. J. Phys. Chem. 1990,94,4791. (32) Peterson, K. A.; Mayrhofer, R. C.; Sibcrt, E. L. 111; Woods,R. C. J. Chem. Phys. 1991,94,414. (33) Dunning, T. H., Jr. J. Chem. Phys. 1970,53, 2823. (34) Davidson, E. R. MELDF, QCPE 580, Indiana University, Bloomington, IN 1988. (35) Feller, D.; Davidson, E. EL J. Chem. Phys. 1981, 74, 3977. (36) Tanaka, K.; Davidson, E.B. J. Chem. Phys. 1979, 70,2904. (37) Herzberg, G. Molecular Spectra and Molecular Structure: Van Nostrand: Princeton, 1951; Vol. 2. (38) Cai, Z.-L.; Sha, G.-H.; Zhang, C.-H.; Huang, M.-B. Chem. Phys. Lett. 1991, 178, 273. (39) Cai, Z.-L.; Xiao, H.-M. Chem. Phys. 1992, 166, 361. (40) Cai, Z.-L. Chem. Phys. Lett. 1993,202,70. (41) Cai, Z.-L. J. Chem. Soc., Faraday Trans. 1993,89,991. (42) Cai, Z.-L. Wang, Y.-Fd;Xiao, H.-M. Chem. Phys. Lett. 1992,190, 381. (43) Cai, Z.-L.; Wang, Y.-F.; Xiao, H.-M. Chem. Phys. Lett. 1992,191, 533. .. (44)Cai, Z.-L.; Wang, Y.-F.; Xiao, H.-M. J.Chem Soc.,Faraday Trans. 19!?2,88, 1611. (45) Cai, Z.-L.; Wang, Y.-F.; Xiao, H.-M. Chem. Phys. 1992,164,377.
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