SFn- (n = 1

The best single value for D0°(F4S−F) appears to us to be 1.65 eV, from the ... a Reference 2a.b Reference 27.c Reference 31a.d Reference 31b.e Refe...
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J. Phys. Chem. 1996, 100, 6061-6068

6061

Negative Ion Thermochemistry: The Sulfur Fluorides SFn/SFn- (n ) 1-7) Rollin A. King, John Morrison Galbraith, and Henry F. Schaefer III* Center for Computational Quantum Chemistry, UniVersity of Georgia, Athens, Georgia 30602 ReceiVed: September 6, 1995; In Final Form: NoVember 22, 1995X

The molecular structures and total energies of SFn and SFn- (n ) 1-7) have been predicted using density functional methods. Three significant measures of electron affinity are reported: the adiabatic electron affinity (EAad), the vertical electron affinity (EAvert), and the vertical detachment energy of the anion (VDE). The first S-F ligand dissociation energies D(Fn-1S-F), D(Fn-1S--F), and D(Fn-1S-F-) are also reported. Selfconsistent Kohn-Sham orbitals were obtained using various functional forms and a double-ζ plus polarization (DZP) basis set. The addition of diffuse s- and p-type functions to the basis set lowered the energies of the anions relative to their neutral species and significantly improved the values of the electron affinities. The method (BHLYP) based upon Becke’s half-and-half exchange functional and the Lee-Yang-Parr correlation functional predicted molecular geometries and electron affinities in best agreement with experiment, while the other methods tended to produce bond lengths that were slightly longer and electron affinities which were larger. The BHLYP electron affinities are typically a few tenths of an electronvolt above experiment. Neutral SF7 was found to have no structures that were significantly bound with respect to dissociation. SF7structures with C4V-symmetry and C3V-symmetry were found to lie very close in energy. The adiabatic electron affinities calculated here are in good agreement with experimental results for SF and SF3, but the predicted electron affinities for SF6 vary widely between functionals and are much larger than the accepted experimental value. The density functional results favor a value EAad(SF4) near 1.8 eV. This is a slightly larger value than that predicted by recent experiments which concluded that EAad(SF4) ) 1.5 ( 0.2 eV. The neutral bond dissociation energies D(Fn-1S-F) tend to confirm experiment except for SF5 where the DFT methods predict D(F4S-F) ) 1.09-1.72 eV, which is less than an experimental value of 2.30 ( 0.26 eV. The bond dissociation values of the anions D(Fn-1S--F) and D(Fn-1S-F-) are in agreement with experimentally determined values with the exception of D(F5S-F-) which is predicted to be at least 1 eV larger than an experimental value of 1.10 eV. All density functional schemes predict a vertical detachment energy for SF6- that is at least 0.5 eV more than the recently reported experimental value of 3.16 eV. It is concluded that the density functional methods, while very useful in establishing trends, are not yet quantitatively reliable. However, additional (SFn-SFn-) experiments are required to precisely establish the reliability of the different density functional methods.

I. Introduction The important recent study by Miller, Miller, Viggiano, Morris, Van Doren, Arnold, and Paulson (MMVMVAP)1 on the negative ion-molecule reactions of SF4 and SF4- represents the latest in an ongoing attempt to determine the stability of the SFn- anions relative to their neutral counterparts.2 Although the electron affinity of SF has been experimentally determined to within (0.006 eV,3 the adiabatic electron affinities of the other SFn molecules are much more in doubt, with uncertainties suggested by MMVMVAP of 0.9 eV for SF2, 0.4 eV for SF3, 0.4 eV for SF4, a whopping 1.7 eV for SF5, 0.2 eV for SF6, and unknown for SF7. An overview of previous studies of the structures and electron affinities of SFn is deferred to the Results section. The objective of the present study is to systematically apply several modern forms of density functional theory4 (DFT) to the determination of the electron affinities of the SFn series. Of specific interest is (a) the accuracy of the electron affinities as determined from comparison with experimental results, (b) the variation in the predicted electron affinities between the different DFT methods, (c) the importance of the presence of diffuse functions in the basis set, and (d) the relationship between neutral SFn and its anion as measured by the adiabatic electron X

Abstract published in AdVance ACS Abstracts, March 15, 1996.

0022-3654/96/20100-6061$12.00/0

affinity (EAad), the vertical electron affinity (EAvert), and the vertical detachment energy of the anion (VDE). Over the past 15 years DFT has evolved into a widelyapplicable technique providing predictions of chemical properties on a par with lower-level ab initio methods (e.g., secondorder perturbation theory) while often requiring less effort computationally.5 The application of gradient-corrected density functionals to inorganic complexes has been generally successful and is becoming more common.6 In this research the electron affinities, evaluated as the difference of total energies, are the adiabatic electron affinity,

EAad ) E(optimized neutral) - E(optimized anion) (1) the vertical electron affinity, EAvert ) E(optimized neutral) E(anion at the neutral equilibrium geometry) (2) and the vertical detachment energy of the anion, VDE ) E(neutral at the anion equilibrium geometry) E(optimized anion) (3) II. Methods The quantum chemical computations have been performed using the Gaussian 92/DFT program system.7 The application of DFT utilized here is based upon the self-consistent Kohn© 1996 American Chemical Society

6062 J. Phys. Chem., Vol. 100, No. 15, 1996 Sham procedure4b which is in some respects analogous to conventional Hartree-Fock theories. The geometries and energies have been obtained using four different gradientcorrected methods. The first, designated BLYP, uses Becke’s 1988 exchange functional (B)8 with Lee, Yang, and Parr’s correlation functional (LYP).9 The B3LYP method is an HF/ DFT hybrid method that uses Becke’s semiempirical threeparameter exchange functional (B3)10 with the LYP correlation functional. The BHLYP method (also an HF/DFT hybrid method) was formed from Becke’s half-and-half exchange functional (BH)11 as implemented in Gaussian 9211b along with the LYP correlation functional. Finally, the BP86 method comprised the Becke (B) exchange functional, along with the correlation correction of Perdew (P86).12 A standard double-ζ plus polarization (DZP) basis set was used. The DZ part of the basis set was constructed from the Huzinaga-Dunning-Hay13 set of contracted Gaussian functions. The DZP basis was formed by the addition of a set of five d-type polarization functions on each atom.14 The contraction scheme for this basis is S(11s7p1d/6s4p1d), F(9s5p1d/ 4s2p1d). In order to determine the significance of diffuse functions in the description of the anions, the DZP basis was augmented with diffuse functions; each atom received one additional s-type and one additional set of p-type functions. The diffuse function orbital exponents were determined in an “even tempered sense” as a mathematical extension of the primitive set, according to the prescription of Lee and Schaefer.15 This extended basis will be denoted “DZP++”. All SFn (n ) 1-6) geometries were determined to be minima by the evaluation of their harmonic vibrational frequencies at the DZP BLYP level of theory. Structures with very low vibrational frequencies at this level were confirmed to be minima by the further evaluation of their vibrational frequencies using the other functionals. The C4V-symmetry structure of SF7- was found to have all real harmonic vibrational frequencies at the DZP++ BLYP, DZP++ B3LYP, DZP++ BHLYP, and DZP++ BP86 levels of theory. The C3V-symmetry structure of SF7was found to have all real harmonic vibrational frequencies at the DZP++ B3LYP and the DZP++ BHLYP levels of theory. Throughout all computations, integrals analytically evaluated were accurate to at least 10 digits, and the density was converged to 10-8. For SFn, where n g 2, the “int)finegrid” option was applied in all optimizations and single-point energies. Thermochemical quantities were not corrected for zero-point vibrational energies. However, zero-point vibrational energies at the DZP BLYP level of theory are included in Table 9. The EA(F) has been computed with all functionals for comparison to the accurately known experimental value EA(F) ) 3.401190 ( 0.000004 eV.16 The DZP electron affinities for fluorine are BLYP, 1.93 eV; B3LYP, 2.07 eV; BHLYP, 1.76 eV; and BP86, 2.18 eV. The DZP++ electron affinities for fluorine are BLYP, 3.68 eV; B3LYP, 3.54 eV; BHLYP, 2.94 eV; and BP86, 3.76 eV. The BHLYP method predicts a lower electron affinity for fluorine than do the other functionals. This tendency is also evident for the SFn molecules. III. Assessment of Results in Comparison with Known Values A. SF and SF-. The geometries of the ground state of SF and its anion are given in Figure 1. The SF radical has a 2Π ground state and an experimental bond length of 1.599 ( 0.002 Å.17 The BHLYP method bond lengths compare most favorably with experiment (DZP, 1.599 Å; DZP++, 1.600 Å), while the other methods predict longer bond lengths by at most 0.053 Å. The 1Σ+ ground state of the anion has bond lengths which vary

King et al.

Figure 1. The molecular geometries of the X ˜ 2Π state of neutral SF and the X ˜ 1Σ+ state of the anion SF-.

TABLE 1: The Adiabatic Electron Affinity (EAad) and Vertical Electron Affinity (EAvert) of SF, Along with the Vertical Detachment Energy (VDE) of SF- in eV. Predicted Values Are Not Corrected for Zero-Point Vibrational Energy EAad DZP++ BLYP DZP++ B3LYP DZP++ BHLYP DZP++ BP86

2.32 2.45 2.25 2.47

exptl

2.285 ( 0.006a

a

EAvert

VDE(SF-)

2.16 2.29 2.08 2.32

2.52 2.63 2.44 2.65

Reference 3.

by about 0.08 Å with the same basis. Again, the DZP++ BHLYP bond length (1.717 Å) is in superb agreement with the experimental value of 1.717 ( 0.015 Å.3 The DZP++ electron affinities of SF are given in Table 1. The electron affinities calculated using the DZP++ basis are greater than those computed using the DZP basis, as expected, since the stabilization of the anion due to the addition of diffuse functions will be greater than the stabilization of the neutral species. The adiabatic electron affinities predicted by the DZP basis are generally 0.6-0.9 eV lower than those predicted using the DZP++ basis for the entire series of SFn molecules. Clearly, using a basis set including diffuse functions in the computation of electron affinities is of paramount importance. Therefore, the electron affinities computed with the DZP basis are reported in Supporting Information but are not futher discussed. The DZP++ adiabatic electron affinities calculated with the BLYP (2.32 eV) and BHLYP (2.25 eV) methods are closest to the precise experimental value of 2.285 ( 0.006 eV from laser photoelectron spectrometry,3 and all functionals produce EAad values which lie within 0.19 eV of the experimental value. The range of VDE(SF-) is 2.44-2.65 eV, and thus, the anion is quite stable with respect to electron detachment. The bond dissociation energies D(Fn-1S-F), D(Fn-1S-F-), and D(Fn-1S-F) are provided in Tables 7 and 8. An experiment by Hildenbrand18 measured D0(S-F) ) 3.51 ( 0.05 eV. The DZP++ BHLYP method gives a poor result of D(S-F) ) 2.92 eV, while the DZP++ BLYP and the DZP++ BP86 methods predict dissociation energies that are somewhat larger than experiment (BLYP, 3.74 eV; BP86, 3.85 eV). In best agreement with experiment is the DZP++ B3LYP method which predicts a value of D(S-F) ) 3.46 eV. The fluoride dissociation values

Negative Ion Thermochemistry

J. Phys. Chem., Vol. 100, No. 15, 1996 6063

Figure 2. The C2V-symmetry geometry of the X ˜ 1A1 state of SF2 and the D∞h-symmetry geometry of the X ˜ 2Πu (2A1) state of SF2-.

TABLE 2: The Adiabatic Electron Affinity (EAad) and Vertical Electron Affinity (EAvert) of SF2, Along with the Vertical Detachment Energy (VDE) of SF2- in eV. Predicted Values Are Not Corrected for Zero-Point Vibrational Energy EAad ++

DZP BLYP DZP++ B3LYP DZP++ BHLYP DZP++ BP86

2.04 2.00 1.69 2.08

exptl

0.2 e EAad e 1.6a

estimate of MMVMVAP

0.7 e EAad e 1.6a

a

EAvert

VDE(SF2-)

0.02 -0.02 -0.35 0.10

4.35 4.79 5.08 4.46

Reference 1.

for D(S-F-) ) 2.23-2.56 eV are in agreement with Polack’s value of D0(S-F-) ) 2.40 ( 0.09 eV3 with the DZP++ BLYP method giving the best value of 2.39 eV. B. SF2 and SF2-. The geometries of the 1A1 ground state of neutral SF2 and the 2A1 (2Πu) ground state of SF2- are displayed in Figure 2. The bond angle of SF2 is 1-3° larger than that reported by Ziegler and Gutsev2b who used the local spin density approximation with Becke’s nonlocal gradient correction (LSDA/B) along with a triple-ζ STO basis set augmented with two 3d-type polarization functions. The BHLYP method once again produced the best agreement with the experimental geometry of Kirchoff, Johnson, and Powell19 given in the figure. Ziegler also reported a slightly bent structure (178.6°) for the SF2- ground state geometry. In the present study, the addition of diffuse functions for the B3LYP and BHLYP methods has a significant (10°) effect and changes the molecule to a linear geometry. The electron affinities of SF2 are reported in Table 2. The DZP++ BHLYP EAad and EAvert are lower than those obtained with the other functionals as is often the case for the other SFn molecules. The DZP++ electron affinities are in agreement with

Figure 3. The Cs-symmetry molecular structure of the X ˜ 2A′ state of SF3 and the C2V-symmetry structure of the X ˜ 1A1 state of SF3-.

the 1.97 eV calculated by Ziegler, but only the DZP++ BHLYP value of 1.69 eV comes near the range suggested by MMVMVAP of 0.7 e EAad(SF2) e 1.6 eV. As previously reported by Ziegler, the 2B2 state of SF2- was found to be the lowest energy state at the geometry of neutral SF2. Thus, the EAvert values were calculated using the 2B2 state energy for SF2- at the neutral equilibrium geometry. The DZP++ BHLYP bond dissociation value D(FS-F) ) 3.10 eV is far lower than the dissociation energies predicted by the other methods (DZP++ BLYP, 3.75 eV; DZP++ B3LYP, 3.54 eV; DZP++ BP86, 3.90 eV). In this case, only the DZP++ BP86 value of 3.90 eV achieves the experimental estimate 3.98 ( 0.19 eV of Kiang based partially on previous thermochemical data.20 C. SF3 and SF3-. The geometries of the 2A′ ground state of the SF3 radical and the 1A1 ground state of SF3- are displayed in Figure 3. SF3 was found to have a nonplanar Cs-symmetry structure with a torsional angle looking down the planar SF axis of 158-167°. This geometry is in agreement with the theoretical work of Volatron21 and Irikura.22 The geometry is in conflict with the theoretical results of Ziegler2b who reported a C2Vsymmetry planar structure. The C2V-symmetry structure of Ziegler was found to have an imaginary B1 frequency of 75i at the DZP/BLYP level of theory. However, the SF3 molecule seems to be nonrigid since the Cs-symmetry structure was found to be only 0.0028 eV (0.064 kcal/mol) lower in energy than the planar form, and a C3V-symmetry pyramidal structure was found to be only 0.58 eV (13.5 kcal/mol) higher than the Cssymmetry structure at the above level. So23 theoretically determined the geometry of SF3 under C2V-symmetry constraints and reported a 2B1 electronic ground state (the same ground state reported by Ziegler). The 2B1 electronic ground state of the planar form becomes the 2A′ state reported here as the molecule falls to a lower symmetry.

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TABLE 3: The Adiabatic Electron Affinity (EAad) and Vertical Electron Affinity (EAvert) of SF3, Along with the Vertical Detachment Energy (VDE) of SF3- in eV. Predicted Values Are Not Corrected for Zero-Point Vibrational Energy EAad DZP++ BLYP DZP++ B3LYP DZP++ BHLYP DZP++ BP86

3.14 3.36 3.27 3.19

exptl estimate of MMVMVAP a

b

EAvert

VDE(SF3-)

2.58 2.60 2.28 2.61

3.58 3.87 3.88 3.62

TABLE 4: The Adiabatic Electron Affinity (EAad) and Vertical Electron Affinity (EAvert) of SF4, Along with the Vertical Detachment Energy (VDE) of SF4- in eV. Predicted Values Are Not Corrected for Zero-Point Vibrational Energy EAad DZP++ BLYP DZP++ B3LYP DZP++ BHLYP DZP++ BP86

2.62 2.45 1.99 2.54

2.9 ( 0.1a 3.07 ( 0.2b

exptl

1.5 ( 0.2a 2.35 ( 0.1b

2.9 ( 0.2c

estimate of MMVMVAP

c

Reference 24. Reference 2f. Reference 1.

Figure 4. The C2V-symmetry molecular structure of the X ˜ 1A1 state of the SF4 and the C4V-symmetry structure of the X ˜ 2A1 state of SF4-.

The SF3- anion is planar with C2V-symmetry. The bonds have been elongated from the neutral structure, but the smaller F-S-F bond angle has remained virtually constant. The electron affinities of SF3 are reported in Table 3. The DZP++ adiabatic electron affinities (3.14-3.36 eV) are above Harland’s experimental value of 2.9 ( 0.1 eV.24 The predictions are also greater than the estimate of Miller for EAad(SF3) ) 2.9 ( 0.2 eV. An extremely large range of dissociation energies is predicted for D(F2S-F). The DZP++ BHLYP value of 1.69 eV is severely low, while the DZP++ BLYP value of 2.69 eV is in the best agreement with the experimentally-based estimate of Kiang20 (2.74 ( 0.31 eV). The DZP++ B3LYP and DZP++ BP86 methods predicted 2.29 and 2.81 eV, respectively. D. SF4 and SF4-. The C2V-symmetry geometry of the 1A1 ground state for SF4 and the C4V-symmetry geometry of the 2A1 ground state for SF4- are given in Figure 4. The geometries vary by as much as 1.6° and 0.08 Å from the experimental geometry from Tolles and Gwinn.25 The BHLYP method gave the shortest and most accurate bond lengths with the B3LYP

a

EAvert

VDE(SF4-)

0.53 0.40 -0.04 0.53

4.62 4.84 4.82 4.58

1.5 ( 0.2c

b

Reference 26. Reference 2a. c Reference 1.

method competing for the best overall geometry including bond angles. The BLYP method predicted the worst geometry with bond lengths that were 0.08 Å too long as well as poor bond angles. The electron affinities of SF4 are given in Table 4. Again, the BHLYP method gives the lowest EAad and EAvert. Viggiano experimentally concluded in 1991 that EAad(SF4) ) 1.5 ( 0.2 eV.26 All of the DZP++ electron affinities lie significantly above this range, with the BHLYP being the lowest at 1.99 eV. Our results lie closer to those of Ziegler (whose LSDA/B value was 2.56 eV) and the experimental estimate of Babcock and Streit of 2.35 ( 0.1 eV.2a The predicted neutral bond dissociation energies D(F3S-F) for DZP++ BLYP (3.54 eV), DZP++ B3LYP (3.49 eV), and DZP++ BP86 (3.75 eV) are near the experimental result of MMVMVAP of 3.74 ( 0.34 eV1 while the DZP++ BHLYP value (3.25 eV) is again lower. The dissociation energies of the anion D(F3S-F-) ) 2.29-2.53 eV are closer to Babcock’s experimentally-based estimate of 2.60 ( 0.16 eV2a than to the experimental result of MMVMVAP of 1.84 ( 0.14 eV.1 E. SF5 and SF5-. The C4V-symmetry geometry of the 2A1 ground state of SF5 and the similar C4V-symmetry structure of the 1A1 ground state of the SF5- are given in Figure 5. The electron affinities of SF5 are given in Table 5. Ziegler was unable to explain the discrepancy between his predicted EAad of 4.79 eV and the experimental estimate of Fenzlaff27 of 3.8 ( 0.14 eV. The EAad’s we report are in the range 4.29-4.74 eV and are also higher than Fenzlaff’s value, though the DZP++ BHLYP value of 4.29 eV is much closer to this experimental estimate. The large values for EA(SF5) support the higher value for EA(SF5) suggested by MMVMVAP of EA(SF5) ) 4.2 eV which results from reevaluating Fenzlaff’s experimental work with an updated, larger bond dissociation energy D(F5S-F).33a The dissociation energies D(F4S-F) ) 1.09-1.72 eV are much lower than Kiang’s estimate of 2.30 ( 0.26 eV.20 Thus, the DFT results support the proposal of MMVMVAP that the bond dissociation energy D(F4S-F) is much lower than previous experiments18,20,28 have indicated (MMVMVAP suggested D(F4S-F) ) 1.1-1.5 eV). The best single value for D0°(F4SF) appears to us to be 1.65 eV, from the G2 computations of Irikura.22 The dissociation energies D(F4S-F-) are in the range 2.44-2.64 eV and are above Larson’s experimental value of 1.90 eV.29 F. SF6 and SF6-. The octahedral geometry of the 1A1g ground state of SF6 and the octahedral geometry of the 2A2g ground state of SF6- are given in Figure 6. Again the BHLYP method is in the best agreement with the experimental bond length.30 The adiabatic electron affinities calculated for SF6 are widely varying. The BHLYP method predicted the smallest EAad ) 1.61 eV which is still half of an electronvolt above the accepted experimental values.2d,31 The other methods predicted very poor electron affinity values in the range 2.66-3.22 eV.

Negative Ion Thermochemistry

J. Phys. Chem., Vol. 100, No. 15, 1996 6065 TABLE 6: The Adiabatic Electron Affinity (EAad) and Vertical Electron Affinity (EAvert) of SF6, Along with the Vertical Detachment Energy (VDE) of SF6- in eV. Predicted Values Are Not Corrected for Zero-Point Vibrational Energy EAad DZP++ BLYP DZP++ B3LYP DZP++ BHLYP DZP++ BP86 exptl

estimate of MMVMVAP e

Figure 5. The C4V-symmetry molecular structure of the X ˜ 2A1 state of the SF5 and the C4V-symmetry structure of the X ˜ 1A1 state of SF5-.

TABLE 5: The Adiabatic Electron Affinity (EAad) and Vertical Electron Affinity (EAvert) of SF5, Along with the Vertical Detachment Energy (VDE) of SF5- in eV. Predicted Values Are Not Corrected for Zero-Point Vibrational Energy EAad DZP++ BLYP DZP++ B3LYP DZP++ BHLYP DZP++ BP86 exptl

estimate of MMVMVAP e

4.74 4.70 4.29 4.69

EAvert

VDE(SF5-)

3.58 3.36 2.59 3.44

5.59 5.76 5.59 5.61

g3.70 ( 0.31a 3.8 ( 0.14b g2.8 ( 0.1c 3.8 ( 0.15d 2.65-4.35e

a Reference 2a. b Reference 27. c Reference 31a. d Reference 31b. Reference 1.

The recent photodetachment experiments by Datskos32 yielded a VDE of 3.16 eV. All of the DFT predicted values are larger than this value with the smallest being the BHLYP value of 3.66 eV. As with EAad this lowest estimate for VDE(SF6-) is about half an electronvolt greater than the experimental value. The bond dissociation energies D(F5S-F) ) 3.49-3.79 eV are less than experimental values near 4 eV,33 with the BLYP method giving the lowest result in this instance. The dissociation energies D(F5S-F-) ) 2.35-3.04 eV are much greater than the experimentally-based estimate of Babcock of D298(F5SF-) ) 1.10 ( 0.21 eV.2a For the dissociation to a fluorine atom, the DZP++ BHLYP prediction D(F5S--F) ) 1.01 eV is nearest the experimentally-based estimate of 1.1 ( 0.1 eV from

3.22 2.66 1.61 3.00 g0.6 ( 0.1a 1.15 ( 0.15b g0.7c 1.05 ( 0.1d

EAvert

VDE(SF6-)

1.47 0.70 -0.53 1.22

4.69 4.39 3.66 5.02 3.16e 3.2g

1.05 ( 0.10f

a Reference 31a. b Reference 31b. c Reference 31c. d Reference 2d. Reference 32. f Reference 1. g Reference 2c.

Lifshitz.31a The DZP++ B3LYP prediction (1.65 eV) is nearer to the experimental result of 1.35 ( 0.1 eV from Chen,31b while the DZP++ BLYP prediction (1.97 eV) and the DZP++ BP86 prediction (2.11 eV) are larger. G. SF7 and SF7-. The molecular geometries of SF7 and SF7- were also investigated. No significant minimum was found on the potential energy surface of neutral SF7. The C4Vsymmetry structure for neutral SF7 with an axial F2 group similar to the one reported by Gutsev34 had a degenerate imaginary vibrational frequency of 26i at the DZP BLYP level of theory, and at the DZP++ BLYP level this stationary point was absent and the loosely bound axial fluorine atom dissociated to beyond 5.5 Å. The D5h-symmetry structure was optimized and found to have two large imaginary vibrational frequencies each leading to dissociation. Other geometries of C2-symmetry and C3Vsymmetry were also explored, but still no significantly bound minimum was found for SF7. For the SF7- anion, Gutsev34 used the LSDA/B method to explore possible geometries of C5V-symmetry, Cs-symmetry, and C4V-symmetry and predicted a C4V-symmetry geometry similar to the one he predicted for neutral SF7. Hiraoka et al.35 recently measured the dissociation of F-(SF6) experimentally and performed 6-31(+)G(*) HF SCF computations. On the basis of these computations, Hiraoka concluded that the C4V-symmetry structure of Gutsev was a transition state and lay about 2 kcal/ mol higher in energy than the true minimum which is of C3Vsymmetry. In this study, structures of C4V-symmetry and C3Vsymmetry of the 1A1 ground state were found for SF7-, and the geometries are shown in Figure 7. The C4V-symmetry structure was confirmed to be a minimum by the evaluation of its harmonic vibrational frequencies at the DZP++ BLYP, DZP++ B3LYP, DZP++ BHLYP, and DZP++ BP86 levels of theory. The C3V-symmetry structure had all real harmonic vibrational frequencies at the DZP++ B3LYP and the DZP++ BHLYP levels of theory. The DZP++ BHLYP method predicted that the C4Vsymmetry structure was higher in energy than the C3V-symmetry structure by 0.06 eV (1.5 kcal/mol), while the DZP++ B3LYP method predicted that the C4V-symmetry structure was lower in energy than the C3V-symmetry structure by 0.15 eV (3.5 kcal/ mol). The D5h-symmetry structure of SF7- was found to have all real vibrational frequencies with the DZP++ BLYP method but lay about 1.4 eV (32 kcal/mol) higher in energy than the C4V-symmetry structure. The DZP++ vertical detachment energies for the C4V-symmetry SF7- are BLYP, 5.22 eV (120.3 kcal/ mol); B3LYP, 4.14 eV (95.5 kcal/mol); BHLYP, 3.18 eV (73.4 kcal/mol); and BP86, 5.12 eV (118.2 kcal/mol). For the DZP++ dissociation energies D(F6S-F-), the BHLYP value of 0.17 eV is near the experimental measurement of Hiraoka35 (0.23 eV),

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TABLE 7: The First Bond Dissociation Energies of the Ground State of SFn in eV (kcal/mol). Predicted Values Are Not Corrected for Zero-Point Vibrational Energy channel

DZP++ BLYP

DZP++ B3LYP

DZP++ BHLYP

DZP++ BP86

exptl

G2g

3.51 ( 3.52 ( 0.07b 3.98 ( 0.19b 2.74 ( 0.31b e3.6c 3.65 ( 0.13b 3.74 ( 0.34d 2.30 ( 0.26b 3.95 ( 0.14b 4.35 ( 0.10e 3.90 ( 0.15f

3.58

SF f S + F

3.74 (86.2)

3.46 (79.7)

2.92 (67.3)

3.85 (88.9)

SF2 f SF + F SF3 f SF2 + F SF4 f SF3 + F

3.75 (86.6) 2.69 (61.9) 3.54 (81.6)

3.54 (81.7) 2.29 (52.7) 3.49 (80.5)

3.10 (71.4) 1.69 (39.0) 3.25 (74.9)

3.90 (90.0) 2.81 (64.9) 3.75 (86.5)

SF5 f SF4 + F SF6 f SF5 + F

1.53 (35.2) 3.49 (80.5)

1.37 (31.6) 3.69 (85.1)

1.09 (25.1) 3.69 (85.0)

1.72 (39.7) 3.79 (87.4)

0.05a

3.88 2.35 4.12 1.65 4.60

a Reference 18. b Reference 20. c Reference 24. d Reference 1. e Reference 33a. f Reference 33b. g Reference 22, values are the average of G2 and G2(MP2) calculations recently reported by Irikura, who suggests an uncertainty in the bond energies of 0.07 eV.

Figure 6. The Oh-symmetry molecular structure of the X ˜ 1A1g state of SF6 and the Oh-symmetry structure of the X ˜ 2A2g state of SF6-.

the B3LYP value of 0.39 eV is somewhat larger, and the BLYP value (1.04 eV) and the BP86 value (0.89 eV) are considerably larger. IV. Predictions of Unknown Values The reliability of the prediction of molecular geometries by the B3LYP method has been recently observed in a study of metal fluorides.36 We conclude from the present study that the BHLYP hybrid method predicts SFn geometries more reliably than the B3LYP method and that both hybrid methods outperform the pure DFT methods BLYP and BP86.

Figure 7. The C4V-symmetry and the C3V-symmetry molecular structures of the X ˜ 1A1 state of SF7-.

For the neutral molecules no experimental geometries are known for SF3 and SF5. These geometries are predicted in Figures 3 and 5, respectively. SF3 is predicted to have a

Negative Ion Thermochemistry

J. Phys. Chem., Vol. 100, No. 15, 1996 6067

TABLE 8: The Dissociation Energies for the Ground States of the SFn- Anions in eV (kcal/mol). Predicted Values Are Not Corrected for Zero-Point Vibrational Energy. channel

DZP++ BLYP

DZP++ B3LYP

DZP++ BHLYP

DZP++ BP86

SF f S + SF- f S- + F SF2- f SF + FSF2- f SF- + F SF3- f SF2 + FSF3- f SF2- + F SF4- f SF3 + F-

2.39 (55.0) 3.92 (90.4) 2.12 (49.0) 3.48 (80.2) 2.15 (49.6) 3.78 (87.2) 2.48 (57.2)

2.36 (54.4) 3.68 (84.8) 2.00 (46.2) 3.10 (71.5) 2.10 (48.4) 3.64 (84.0) 2.40 (55.3)

2.23 (51.3) 3.20 (73.7) 1.85 (42.6) 2.54 (58.6) 2.03 (46.7) 3.27 (75.5) 2.29 (52.9)

2.56 (59.1) 3.99 (92.0) 2.22 (51.1) 3.51 (81.0) 2.24 (51.6) 3.92 (90.4) 2.53 (58.3)

SF4- f SF3- + F SF5- f SF4 + F-

3.02 (69.5) 2.59 (59.7)

2.58 (59.5) 2.53 (58.3)

1.96 (45.2) 2.44 (56.2)

3.10 (71.6) 2.64 (60.9)

SF5- f SF4- + F SF6- f SF5 + FSF6- f SF5- + F

3.65 (84.1) 3.04 (70.0) 1.97 (45.5)

3.62 (83.5) 2.80 (64.6) 1.65 (38.0)

3.39 (78.2) 2.35 (54.3) 1.01 (23.2)

3.86 (89.1) 3.03 (69.9) 2.11 (48.7)

SF7- f SF6 + FSF7- f SF6- + F

1.04 (24.0) 1.49 (34.4)

0.39 (8.9) 1.27 (29.4)

0.17 (4.0) 1.51 (34.7)

0.89 (20.5) 1.65 (38.0)

-

a

F-

exptl 2.40 ( 0.09a

2.60 ( 0.16b 1.8 ( 0.3c 1.84 ( 0.14d g2.60 ( 0.16b 1.90e 1.10 ( 0.21b 1.1 ( 0.1f 1.35 ( 0.1g 0.23h

Reference 3. b Reference 2a. c Reference 26. d Reference 1. e Reference 29. f Reference 31a. g Reference 31b. h Reference 35.

nonplanar Cs-symmetry structure. For the anions, experimental geometries are available only for SF- with the DZP++ BHLYP method agreeing precisely with the experimental bond length. The geometries of the other anions are presented in Figures 2-7. Summarizing the DFT adiabatic electron affinities, it is predicted that EAad(SF5) > EAad(SF3) > [EAad(SF), EAad(SF4), and EAad(SF6)] > EAad(SF2). The adiabatic electron affinity of SF5 is exceptionally large. Since SF5 is an open-shell molecule, a large vertical electron affinity is anticipated, and in fact the EAvert(SF5) was calculated to be 2.59-3.58 eV, near the results for EAvert(SF3). Because SF5 has four S-F bonds that undergo a large increase in bond length (about 0.13 Å) upon the addition of an electron, the adiabatic correction is significant, and the adiabatic electron affinity is significantly larger (1.3-2.0 eV greater) than the vertical electron affinity. The EAad(SF5) is also seen to be consistent with the results for the other SFn molecules when considering the EAad(SF5) is about 1 eV larger than EAad(SF3) which is further about 1 eV larger than EAad(SF). Thus, the neutral SFn species that formed closed-shell anions have larger electron affinities. Conversely, the closed-shell SFn neutrals have smaller electron affinities. In contrast with the situation for the EAad values, no experimental vertical electron affinities are known to the authors. For the SFn molecules, all the DFT vertical electron affinities are between 2.08 and 3.44 eV where n is odd and between -0.53 and 1.47 eV where n is even. EAvert(SF2) is predicted to be very close to zero, which differs significantly from EAad(SF2) due to the dramatic change in geometry upon the addition of an electron. There is very little difference between EAvert(SF) and EAad(SF) because the geometries of the neutral and the anion are very similar. The adiabatic and vertical electron affinities are provided in Tables 1-6. The only known experimental vertical detachment energy for the SFn- series is that of Datskos32 for SF6-. All of the vertical detachment energies are predicted to be quite positive with the least being VDE(SF-) ) 2.44-2.65 eV and the next smallest being VDE(SF3-) ) 3.58-3.88 eV. The vertical detachment energies are presented in Tables 1-6. The energies for dissociation of a fluorine atom or a fluoride ion from the SFn- anions are given in Table 8. For SFn-, where n ) 1, 2, 3, and 5, all methods predict that dissociation to fluoride ion is a lower energy process than the dissociation of a fluorine atom, i.e., D(Fn-1S-F-) < D(Fn-1S--F). For SF4-, all methods, except the BHLYP method, predict similarly that the dissociation to a fluoride ion requires less energy. For SF6-, all methods predict that dissociation to a fluorine atom is a lower

TABLE 9: The Zero-Point Vibrational Energies of the SFn-SFn- Series at the DZP BLYP Level of Theory in eV (kcal/mol) SF SF2 SF3 SF4 SF5 SF6

neutral

anion

0.049 (1.13) 0.11 (2.58) 0.17 (3.96) 0.28 (6.52) 0.36 (8.24) 0.51 (11.88)

0.032 (0.75) 0.072 (1.67) 0.15 (3.41) 0.19 (4.49) 0.31 (7.09) 0.34 (7.91)

energy process than the dissociation to a fluoride ion. Experimental results for D(Fn-1S-F-) have been determined for SF-, SF4-, SF5-, SF6-, and SF7-, while the fluoride dissociation energies for SF2- and SF3- are unknown. The experimental value of D(Fn-1S--F) has been determined only for SF6-. V. Concluding Remarks The recent experimental paper by Miller, Miller, Viggiano, Morris, Van Doren, Arnold, and Paulson1 makes the SFn-SFnfamily one of the best characterized in terms of electron affinities and thermochemistry. Nevertheless the number of gaps and serious uncertainties creates problems for the characterization of theoretical methods, such as the four density functional schemes carefully investigated here. For the SFn and SFn- structures, there are six known experimental bond distances. With the DZP++ basis set the average errors for the four density functional schemes are 0.069 Å (BLYP), 0.034 Å (B3LYP), 0.003 Å (BHLYP), and 0.053 Å (BP86). Similarly, three bond angles are reliably known from experiment. The average errors of the DFT methods are 1.2° (BLYP), 0.5° (B3LYP), 0.7° (BHLYP), and 1.0° (BP86). Clearly the HF/DFT hybrid methods are superior in the prediction of molecular geometries, with the BHLYP method being the best method investigated. The pure DFT methods BLYP and BP86 consistently predict bond lengths which are 0.07 and 0.05 Å too long and also perform worse in the prediction of bond angles. For the SFn electron affinities, only the sulfur monofluoride system has a precisely determined experimental EAad, namely, 2.285 ( 0.006 eV.3 The BHLYP method predicts 2.25 eV, and the BLYP method predicts 2.32 eV, and these are the best of the density functional schemes. Although the experimental EAad of SF2 is quite uncertain (0.2-1.6 eV), only the BHLYP value (1.69 eV) gives a reasonable match. For SF5, although above the experimental EAad of Chen (3.8 ( 0.15),31b the

6068 J. Phys. Chem., Vol. 100, No. 15, 1996 BHLYP EAad of 4.29 eV still provides the best harmony with experiment. Furthermore, the BHLYP EAad of 4.29 eV is in accord with EAad(SF5) ) 4.2 eV which results from the reevaluation of the experimental results in light of a new D0(F5S-F) bond dissociation energy,33a which is larger than previously believed. For SF6, again the BHLYP method gives by far the smallest (1.61 eV) prediction, which lies above the 1.15 ( 0.15 eV experimental value of Chen.31b It certainly would be highly desirable to have precise Lineberger-type measurements3 of the electron affinities of SFn (n ) 2-6). But it is already clear that the BHLYP method is superior to the other three DFT schemes for the prediction of SFn electron affinities. The density functional schemes give rather scattered results for the neutral dissociation energies D(Fn-1S-F). In comparison to the experimental results in Table 7, for SF3, the BLYP method is best; for SF2, SF5, and SF6, BP86 is best; for SF, B3LYP is best. The BHLYP method, clearly best for electron affinities, provides the worst D(Fn-1S-F) values (of the four DFT methods) for SF, SF2, SF3, SF4, and SF5. The bond dissociation energies D0(Fn-1S--F) are unknown experimentally except for D0(F5S--F) where the BHLYP method predicts a value (1.01 eV) in agreement with experiment, while all of the other functionals predict much larger values (1.65-2.11 eV). In every case (except for a slight difference in SF7-) the dissociation values D(Fn-1S--F) fall in the order BP86 > BLYP > B3LYP > BHLYP. For the bond dissociation to a fluoride ion D(SFn-1-F-), the functional results are more consistent and the order of the functional values is not as clear as for the dissociation to a fluorine atom, but the BHLYP method still predicts the smallest value in every case. For SF-, the BLYP prediction is best; for SF4-, the BHLYP method is best; for SF5-, it is uncertain; and for SF6-, the BHLYP method is best, with the BLYP and BP86 methods providing the worst performance. Clearly, precise new thermochemical experiments would be greatly appreciated for the SFn and SFn- systems. Acknowledgment. This research was supported by the U.S. Air Force Office of Scientific Research, Grant AFOSR-95-10057. We thank Drs. Tom Miller, Robert A. Morris, John F. Paulson, and Albert A. Viggiano for helpful discussions. We thank Alexey Timoshkin (St. Petersburg State University, Russia) for carrying out preliminary computations. Supporting Information Available: One table listing the adiabatic electron affinities and vertical electron affinities of SFn (n ) 1-6), along with the vertical detachment energy of SFn- in electronvolts (2 pages) using the unaugmented DZP basis. Ordering information is given on any current masthead page. References and Notes (1) Stevens Miller, A. E.; Miller, T. M.; Viggiano, A. A.; Morris, R. A.; Van Doren, J. M.; Arnold, S. T.; Paulson, J. F. J. Chem. Phys. 1995, 102, 8865. (2) (a) Babcock, L. M.; Streit, G. E. J. Chem. Phys. 1981, 75, 3864. (b) Ziegler, T.; Gutsev, G. L. J. Chem. Phys. 1992, 96, 7623. (c) Mock, R. S.; Grimsrud, E. P. Chem. Phys. Lett. 1991, 184, 99. (d) Grimsrud, E. P.; Chowdhury, S.; Kebarle, P. J. Chem. Phys. 1985, 83, 1059. (e) Hay, P. J. J. Chem. Phys. 1982, 76, 502. (f) Compton, R. N.; Reinhardt, P. W.; Cooper, C. D. J. Chem. Phys. 1978, 68, 2023.

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