Comment on the Paper ``Oxygen Monofluoride (OF, 2π): HartreeFockWavefunction, Binding Energy, Ionization Potential, Electron Affinity, Dipole andQuadrupole Moments, and Spectroscopic Constants. A Comparison ofTheoretical and Experimental Results'' by P. A. G. O'Hare and A. C. WahlJoel F. Liebman Citation: The Journal of Chemical Physics 56, 4242 (1972); doi: 10.1063/1.1677851 View online: http://dx.doi.org/10.1063/1.1677851 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/56/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Arsenic monofluoride (AsF, 3Σ): Dissociation enthalpy, ionization potential, electron affinity, dipolemoment, spectroscopic constants, and ideal gas thermodynamic functions from a HartreeFockmolecular orbital investigation J. Chem. Phys. 59, 6495 (1973); 10.1063/1.1680029 Near Hartree—Fock Calculations of the Force Constants and Dipole Moment Derivatives in Methane J. Chem. Phys. 56, 2109 (1972); 10.1063/1.1677506 Oxygen Monofluoride (OF, 2π): Hartree–Fock Wavefunction, Binding Energy, Ionization Potential,Electron Affinity, Dipole and Quadrupole Moments, and Spectroscopic Constants. A Comparison ofTheoretical and Experimental Results J. Chem. Phys. 53, 2469 (1970); 10.1063/1.1674349 Force Constants and DipoleMoment Derivatives of Molecules from Perturbed Hartree–FockCalculations. II. Applications to Limited BasisSet SCF–MO Wavefunctions J. Chem. Phys. 49, 1730 (1968); 10.1063/1.1670300 Accuracy of Computed Spectroscopic Constants from Hartree—Fock Wavefunctions for DiatomicMolecules J. Chem. Phys. 40, 243 (1964); 10.1063/1.1724878

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4242 LETTERS TO THE EDITOR

range. Our potential energy values are in reasonable agreement with those synthesized potentials of Ollison at small interatomic distances. The discrepancy be­tween the experimental determinations is difficult to resolve. One is forced to conclude that either the hydrogen beam of Leonas is extremely impure with massive amounts of H2+ being present or more im­portantly that the geometry of his apparatus is poorly defined. If this latter difficulty is in fact the root of the discrepancy, then the integration that Leonas et at. carry out to relate their theoretical value of the scatter­ing cross section to their experimental measurements of the average total scattering cross section will be wrong and will lead to inaccurate values for their potential energy functions.

* Work supported by Grant No. GM-13966 of the National Institutes of Health, Division of General Medical Sciences.

t Alfred P. Sloan Foundation Fellow.

Comments

THE JOURNAL OF CHEMICAL PHYSICS

1 R. G. Gann and J. Dubrin, J. Chern. Phys. 47, 1867 (1967). 2 R. G. Gann and J. Dubrin, J. Chern. Phys. 50,535 (1969). 3 R. G. Gann, W. M. Ollison, and J. Dubrin, J. Am. Chern. Soc.

92,450 (1970). 'C. Rebick and J. Dubrin, J. Chern. Phys. 53,2079 (1970). • J. E. Nicholas, F. Bayrakceken, and R. D. Fink, J. Phys.

Chern. 75, 841 (1971). 6 J. E. Nicholas, F. Bayrakceken, and R. D. Fink, J. Chern.

Phys. 56,1008 (1972). 7 I. Amdur and J. E. Jordan, in Molecular Beams, edited by J.

Ross (Wiley, New York, 1966), Chap. 2. 8 D. Bohrn, Quantum Theory (Prentice-Hall, Englewood Cliffs,

N.J., 1951), p. 528. 9 E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill,

New York, 1938). 10 R. D. Fink, J. S. King, Jr., and J. H. Freeman, J. Chern.

Phys. 50,2773 (1969). 11 Y. N. Belyaev, N. V. Karnyshov, and V. B. Leonas, Proc.

Intern. Con£. Phys. Electron. At. Collisions, 6th, Cambridge, Mass., 1969,525 (1970).

12 J. E. Jordan, S. O. Colgate, I. Amdur, and E. A. Mason, J. Chern. Phys. 52,1143 (1970).

13 W. Kolos and L. Wolniewiciz, J. Chern. Phys. 43,2429 (1965). 14 W. M. Ollison, Ph.D. dissertation, Massachusetts Institute

of Technology, 1969. 161. Amdur and E. A. Mason, J. Chern. Phys. 25, 624 (1956).

VOLUME 56, NUMBER 8 15 APRIL 1972

Comment on the Paper "Oxygen Monofiuoride (OF, 2II): Hartree-Fock Wavefunction, Binding Energy, Ionization Potential, Electron Affinity, Dipole and Quadrupole Moments, and Spectroscopic Constants. A Comparison of Theoretical and Experimental Results"

by P. A. G. O'Hare and A. C. Wahl JOEL F. LIEBMAN*

Inorganic Chemistry Section, National Bureau of Standards, Washington, D. C. 20234

(Received 15 December 1971)

O'Hare and Wahll recently reported highly accurate ab initio calculations on the bonding and energetics of 2IJ OF, 3~ OF+, and l~ OF-. While I accept their quantum mechanical and thermodynamic calculations, I believe direct synthetic inferences from their work can mislead unless one also considers spin conservation. From vertical electron affinity calculations, they obtain a 6.G298o of -2.2 kcal mol-l (-9.2 kJ mol-I) for the reaction l~ OF-~3 P O+IS F-. For light atoms, spin conservation is a good approximation and hence this reaction should not proceed as written. In the absence of potential curves for l~ OF- and the appropriate triplet state (3~ or 3IT?) trustworthy predissociation rates cannot be computed. Let us thus consider the energetics of the spin allowed decomposi­tion reactions of l~ OF-. One can either form ID O+IS F- or 2p 0-+2P F. The ID state of 0 lies 15867.862 cm-l (188.7 kJ mol-I) above the 3P.2 If 6.S is the same for the two states of 0, then the reaction yielding ID O+IS F- has a 6.G298

o of + 179.5 kJ mol-I.

To compute the energetics of the other process, we must know the electron affinities of 0 and F. These are, respectively, 141.8 and 332.7 kJ mol-I.3 We thus conclude 2p 0-+2p F is higher in energy than 3p O+IS F- by 190.9 kJ mol-I. Equating the entropy for 0-+ F and 0+ F- 4 we find a 6.G298

o of 181.7 kJ mol-l for the reaction yielding 2p 0-+2P F.

In agreement with O'Hare and WahJ,l we may conclude "from the thermodynamic point of view, OF- is likely to be marginally stable at room tempera­ture." However, kinetic considerations based on spin conservation suggest a long lived and highly stable species. Analogous reasoning suggests other diatomic anions for the VIa and VIla elements would be likewise stabilized. Spin conservation is less valid here but intrinsic thermodynamic stability should be higher5 and the curve crossing should occur at larger inter­nuclear separation.

We have just seen how conservation of spin increases the likelihood of isolation of OF-. Conservation of spin

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LETTERS TO THE EDITOR 4243

does not always facilitate the "production" of a desired product. Consider the possibility of OF+ salts. The OF+ ion was calculated to have a dissociation energy of around 300 kJ mol-l (3.2 eV) and an electron affinity of 1264 kJ mol-l (13.1 eV). The reaction OF2+SbF5-OF+ SbF6- (or OF+ Sb2Fll-) is suggested in analogy to the known KrF2+SbF6---+KrF+ Sb2Fll-.6

However, no reaction is observed either with the neat compounds or in AsF6 solution.7 More extreme reaction conditions, with the Lewis acids SbF6 or AsF5, "merely" give O2+ salts.s Spin conservation provides an explana­tion for the lack of formation of OF+. OF2, SbF6, and SbF6- (or Sb2Fll-) are all singlets; one may surmise on the basis of conservation of spin that singlet OF+ would be the initial product. The 3~_1~ splitting may be estimated as around 130 kJ mol-l

from the corresponding splitting in NF and O2.9 The reaction yielding an excited state ion would be relatively endoergic by 130 kJ mol-I. Furthermore, the electron affinity of I~OF+ is higher than that of the ground state by the same value since both 3~ OF++e-~II OF and l~ OF++e-~ OF are spin-allowed processes. We may thus conclude either OF+ does not form or is rapidly converted to OF. As several reaction mechanisms may be written connecting OF with 02+,lO it is not surprising no OF+ salts have been obtained.

I wish to thank Dr. L. C. Allen, Dr. V. H. Dibeler, and Dr. A. D. Franklin for many fruitful discussions, and the NRC for my NRC-NBS Postdoctoral As­sociateship.

THE JOURNAL OF CHEMICAL PHYSICS

* NRC-NBS Postidoctoral Research Associate, 1971-1972. 1 P. A. G. O'Hare and A. C. Wahl, J. Chern. Phys. 53, 2469

(1970) . 2 C. E. Moore, Nat!. Std. Ref. Data Ser., Nat!. Bur. Std. (U.S.)

34 (1970). (The currently advocated conversion factors are 1 eV=8065.73 cm-1 =96.4870 kJ mol-1 =23.0609 kcal mole-I.)

3 These values were obtained by averaging the experimental electron affinities given by R. S. Berry, Chern. Rev. 69, 533 (1969) .

• The preferred values of S298.15° (cal delcl.mol-I) are: 0, 38.47; 0-, 37.712; F, 37.917; and F-, 34.768 LD. R. Stull and H. Prophet (Eds.), Nat!. Std. Ref. Data. Ser., Nat!. Bur. Std. (U.S.) 37 (1971)J S298.15° for O+F- is 75.24 cal deg-l·mol-1

while for O+F is 75.63 cal deg-"mol-' and thus the errors in equating the entropies are essentially negligible.

6 O'Hare and Wahl also studied ClO- O. Chern. Phys. 54, 3770 (1971)J, SF-, and SeF- [ibid. 54, 2848( 1971)]' Analogous logic is applicable to their NF- and PF- [ibid. 54, 4563 (1971) J for which one must consider separation to the 2D state of the pnicogen +'SF-.

s There is inconclusive evidence whether XeF+ Sb2Fll- (and by inference KrF+ Sb2Fll-) should be described as an ion pair with only small distortions from the free ions (N. Bartlett et at., Chern. Commun. 1968, 1048 or essentially a covalent, fluorine­bonded, molecule (V. M. McRae, R. D. Peacock, and D. R. Russell, Chern. Commun. 1969, 62). Ab initio calculations on KrF+ and KrF have been performed including a many-configura­tion CI and a large basis set [B. Liu and H. F. Schaeffer III, J. Chern. Phys. 55, 2369 (1971)]. The former has a calculated dissociation energy of 183 kJ mol-I; the latter is unbound. Using the experimental ionization potential of Kr (1350.7 kJ mol-I, Ref. 2), we conclude KrF+ has an electron affinity of 1167 kJ mol-I. No calculations of equivalent accuracy exist for XeF+.

7 E. W. Lawless and I. C. Smith, Inorganic High Energy Oxidizers (Dekker, New York, 1968), p. 215.

8 J. B. Beal, Jr., C. Pupp, and W. E. White, Inorg. Chern. 8, 828 (1969). The typical reaction conditions are 2:1 OF2 :AsF6

at 200°C and 200 atm for 6 days give around an 80% yield of O2+ AsFs-.

9 The vertical NF splitting was calculated as 173.4 kJ mol-1

(Ref. 5) while for O2 it is 92.0 kJ mol-I [see, for example, C. S. Foote, Accounts Chern. Res. 1,104 (1968)].

10 J. F. Liebman (unpublished).

VOLUME 56, NUMBER 8 15 APRIL 1972

Comment on a Group-Theoretical Method for Multicenter Integral Evaluation

KENNETH G. KAY

Department of Chemistry, Kansas State University, Manhattan, Kansas 66502

AND

JOSEPH S. ALPER

Department of Chemistry, University of Massachusetts, Boston, Massachusetts 02116

(Received 10 November 1971)

In two recently published papers, Alperl has derived closed analytical expressions for multicenter molecular integrals over hydrogenic orbitals characterized by in­tegral principal quantum numbers. We have discovered an error in one of the equations of the derivation and wish to take this opportunity to correct it. The error affects the formulas for the two-center integrals with unequal n and the three- and four-center integrals.

The error arises in the interpretation of the addition

theorem for ~ spherical harmonics. The quantity on the right-hand side of Eq. (1-61) is not an expansion for WNLM(k-kl ) , i.e., the spherical harmonic whose argument is the point on the four-dimensional hyper­sphere corresponding to the vector k-kl in three­dimensional momentum space. Instead, Eg. (1-61) is the addition theorem for R4 spherical harmonics and k-kl means the point on the hypersphere obtained by taking the difference of the two points on the sphere

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