J . Phys. Chem. 1987, 91, 1703-1704
Ionization Potential and Hyperfine Splitting Constant of the F;An ab Initio Study
1703
Radical Anion.
Minh Tho Nguyen Research School of Chemistry, Australian National University, Canberra, ACT 2601, Australia
and Tae-Kyu Ha* Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, E TH- Zentrum, CH-8092- Zurich, Switzerland (Received: November 25, 1986)
Employing a RCISD wave function with a DZ+(d) basis set, the isotropic hyperfine splitting (hfs) constant for the F nucleus in the gas-phase radical anion Fz*-is predicted to be aF = 520 50 G. This is much larger than the ESR value of 280.2 G recently obtained from neon matrix experiment, suggesting that matrix shifts of hfs constants are quite important for radical anions. The ionization potential of F;- of 2.8-3.0 eV computed at various levels of theory compares well with the experimental one of 2.96-3.08 eV.
*
Along with other diatomic halogen molecules, molecular fluorine and its radical anion are an important component in several electrically excited gas lasers. Therefore, the attachment of slow electrons to Fz and different phenomena associated with this process have been extensively investigated both experimentally2 and theoretically3 during the past decade. Previously, the radical ion Fz'- has been observed as a defect center in ionic lattices. It has, however, recently been generated and trapped as a free ion in dilute neon matrix at low temperature (-4 K) and characterized by electron spin resonance (ESR) spectro~copy.~Various magnetic parameters of F2'- in a matrix have consequently been determined. Thus, the problem of particular interest is about the shifts in obtained values due to matrix conditions. In this regard, the authors of ref 4 suggested that the neon results should closely reflect the free or gaslike magnetic properties of the ground state of Fz'-. Because gas-phase values are not currently available for direct comparison, these authors4 called for theoretical calculations on relevant magnetic parameters of F2'-. Therefore, we report in this Letter ab initio calculations aimed at determining the spin density and thereby the hyperfine coupling constant of fluorine atom in the gas-phase radical anion F2*-. In addition, as a calibration on the limit of confidence to be expected from our prediction, we have also considered the ionization potential of F;-, e.g., the electron affinity of F2, for which a gas-phase experimental value is a ~ a i l a b l e . ~ We turn first to an evaluation of the ionization potential of F2*-. The calculations were performed using different basis sets ranging ~~
~
~
(1) (a) Searle, S. K.; Hart, G. A. Appl. Phys. Lett. 1975, 27, 243. (b) Mangano, J. A,; Jacob, J. H.; Dodge, J. B. Ibid. 1976, 29, 426. (2) (a) Sides, G. D.; Tieman, T. 0.; Hanraham, R. J. J. Chem. Phys. 1976, 65, 1966. (b) Mahadevan, P.; Hofland, R.Bull. Am. Phys. SOC.1976, 21, 575. (c) Chen, H. L.; Center, R. E.; Trainor, D. W.; Fyfe, W. I. Appl. Phys. Lett. 1977, 30, 99. (d) Schneider, B. I.; Brau, C. A. Ibid. 1978, 33, 569. (e) Nygaard, K. J.; Hunter, S.R.; Fletcher, J.; Foltyn, S. R. Ibid. 1979, 35, 920. (0 McCorkle, D. L.; Christophorou, L. G.; Christodoulides, A. A,; Pichiarella, L. Ibid. 1986, 85, 1966. (3) (a) Gilbert, T. L.; Wahl, A. J. Chem. Phys. 1971, 55, 5247. (b) Rescigno, T. N.; Bender, C. F.; McCurdy, L. W.; McKoy, V. J. Phys. B 1976, 98 2141. (c) Rescigno, T. N.; Bender, C. F. Ibid. 1976, 9, L329. (d) Schneider, B. I.; Hay, P. J. Phys. Reu. A 1976, 13, 2049. (e) Hazi, A. U.; Orel, A. E.; Rescigno, T. N. Phys. Rev. Lett. 1981, 46, 918. (f) Hall, R. J. J . Chem. Phys. 1978, 68, 1803. (9) Drukarev, G.; Pozdneev, S. J . Phys. B 1980, 13, 2611. (h) Kurepa, M. V.; Babic, D. S.; Belic, D. S. Chem. Phys. 1981, 59, 125. (i) Bardsley, J. N.; Wadehra, J. M.J . Chem. Phys. 1983, 78, 1227. (4) Knight, L. B.; Earl, E.; Ligon, A. R.; Cobranchi, D. P. J . Chem. Phys. 1986,85, 1228. (5) (a) Chupka, W. A.; Berkovitz, J.; Gutman, D. J. Chem. Phys. 1971, 55, 2724. (b) Walker, I. C. Annu. Rep. Prog. Chem. Sect. C 1974, 71, 49. (c) Radzig, A. A.; Smirnov, B. M. Reference Data on Atoms, Molecules and Ions; Spinger-Verlag: West Berlin, 1985.
0022-3654 187 I209 1- 1703S01SO10 , ,
I
from the split-valence plus sp-diffuse and d-polarization functions 6-3 1+G(d)6 through a double-{ plus sp-diffuse and d-polarization functions DZ+(d)' to the triple-split-valence plus sp-diffuse and df-polarization functions 6-3 1 1+G (2df).6 The energy differences between the ground states ]Eg+of F2 and 2Xu+ of F2'- were computed at the Hartree-Fock, second-through fourth-order Merller-Plesset perturbation theory* configuration interaction (CI) levels. For perturbation calculations, the unrestricted formalism (UHF, UMP) has been employed for the ion.g In the CI calculations which used the DZ+(d) basis set, the CI matrix formed included all configurations generated from single and double excitations from all valence shell orbitals to all virtual orbitals. These were selected by perturbation theory with an energy threshold of 10" hartree. The S C F calculation which precedes the C I one for F2'- was carried out by an open-shell restricted Hartree-Fock method.I0 Table I summarizes the calculated energies and electron affinity (EA) of F2. At all levels of calculations, the computed electron affinity of F2 lies in the range of 2.6 (RSCF) to 3.0 eV (UMP). These values compare quite well with the experimental ones of 2.965cand 3.08 f 0.1 eV.5a,b It is worth noting that extension of the basis set and/or inclusion of correlation energies in the wave functions create rather small effects on the computed value. The largest change in the absolute value of the EA amounts in fact to 0.19 eV in going from RSCF to CI with large basis sets (Table I). This is quite different with the situation in the evaluation of EA'S of radicals" (open shell for radicals and closed shell for anions) where correlation energy plays an essential role by improving H F values by 0.5-0.7 eV. Further systematic calculations are desirable in order to emphasize whether this is an isolated case or a general trend occurring in the EA'S determination of closed-shell species. Some electronic properties of the molecular and anionic fluorine in their ground states calculated by using CI wave functions are (6) (a) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 23, 218. (b) Frisch, M. J.; Pople, J. A,; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (7) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. The coefficients for sp diffuse functions are the same as in 6-31+G(d). (8) Krishnan, R.; Pople, J. A. Int. J. Quantum Chem. 1978, 14, 91 and references therein. (9) Binkley, J. S.; Frisch, M. J.; DeFrees, S . J.; Raghavachari, K.; Whiteside, R. A,; Schlegel, H. B.; Fluder, E.; Pople, J. A. Program Gaussian-82; Carnegie-Mellon University: Pittsburgh, PA, 1983. (10) (a) Davidson, E. R.; Stenkamp, L. Z. In?. J . Quantum Chem., Quantum Chem. Symp. 1976, No. 10, 21. (b) For the CI calculations, the MELD program package was employed: McMurchie, L.; Elbert, S . T.; Langhoff, S. R.; Davidson, E. R. MELD, University of Washington: Seattle, WA, 1978. (11) (a) Novoa, J. J.; Mota, F. Chem. Phys. Lett. 19858 119, 135; 1986, 123, 399. (b) Baker, J.; Nobes, R . H.; Radom, L. J . Comput. Chem. 1986, 78 349 and references therein.
0 1987 American Chemical Society
J . Phys. Chem. 1987, 91, 1704-1707
1704
TABLE I: Total Energies (hartree) and Electron Affinity of F2 (eV) method" UHF/6-3 I+G(d)//UHF/6-31 +G(d)* UMP2/6-3 1+G(d)///UMP2/6-31+G(d)' UMP2/6-3 1+G(d)//UMP4/6-3 l+G(d)d UMP3/6-3 I+G(d)///UMP4/6-3 1 +G(d) UMP4SDQ/6-3 1 +G(d)//UMP4/6-3 l+G(d)e UMP4/6-3 l+G(d)//UMP4/6-31+G(d) UHF/6-31 l+G(2d)//UMP4/6-31+G(d) UMP2/6-31 I+G(2d)//UMP4/6-3 1 +G(d) UHF/6-3 1 I+G(2df)//UMP4/6-3 I+G(d) UMP2/6-3 1 I+G(2df)//UMP4/6-3 I +G(d) RSCF/DZ+(d)//UMP4/6-3 I+G(d)
E(F,'-, ,Z,,+lh -198.795 05 -1 99.169 02 -199.164 43 -199.15855 -199.172 30 -199.181 74 -198.85095 -199.324 26 -198.851 54 -199.366 39 -198.83368 -199.253 49 -199.29235
U F , , '2.') -198.68462 -199.057 79 -199.05285 -199.048 53 -1 99.059 64 -199.071 03 -198.73621 -199.214 71 -198.739 87 -199.259 47 -198.737 24 -199.15026 -199.18968
RCISD/DZ+(d)//UMP4/6-31+G(d)' RCISDQ/DZ+(d)//UMP4/6-3 l+G(d)z
EA(F,) 3.00 3.03 3.04 2.99 3.06 3.01 3.12 2.98 3.04 2.90 2.62 2.81 2.79
"The first desingator indicates the energy level while the second indicates the geometry employed. bThe (U)HF/6-31+G(d) bond lengths are 1.347 8, (F,) and 1.910 8, (F2*-). 0.95), it may also be expected that the value obtained from a multireference MCSCF-CI treatment could be only slightly different from the present uFvalue. Therefore, we would predict that the isotropic hyperfine splitting constant for the F nucleus in the gas-phase radical anion F2 is about = 520 f 50 G considering variation in the level of calculation. This is thus far larger than the neon matrix value of 280.2 G reported in ref 4. Such an important shift can partly be accounted for by the diffuse nature of the radical anion which can be seen by its large quadrupole and second moments with respect to those of the neutral molecule (Table 11). In any case, matrix shifts for hfs constants of anions should be much larger than those observed for corresponding radical cations. Studies on peculiar interactions responsible for such matrix shifts as well as magnetic properties of other halogen radical anions are currently under way.
aio
Acknowledgment. The authors thank the ETH-Zurich Computer Centre for a grant of computer time and Mrs. L. M. Phuong for friendly assistance. Registry No. F2*-, 12184-85-9.
Picosecond Transient Grating Experiments in Sodium Vapor: Velocity and Polarization Efiects Todd S. Rose, William L. Wilson, G . Wackerle, and M. D. Fayer* Department of Chemistry, Stanford University, Stanford, California 94305 (Received: December 5, 1986)
-
The picosecond transient grating technique is applied to the 2S1/2 and 2P3,2transitions in sodium vapor. A population grating is generated by using parallel polarization for the two excitation pulses. T h e signal decay is directly related to the velocity distribution of the atoms. When the polarizations of the excitation pulses are perpendicular, a polarization grating is formed, and oscillations corresponding to the ground- and excited-state hyperfine splittings a r e observed.
Recently, there has been considerable interest in the nonlinear optical properties of sodium vapor. Four-wave mixing (FWM) 0022-3654/87/2091-1704$01.50/0
experiments have been performed in the frequency domain in order to obtain information concerning the third-order susceptibility 0 1987 American Chemical Society
