1340
J. Phys. Chem. 1981, 85, 1340-1342
tetrachloride and 0.8 kJ/mol for methdcsclohexane. respectively (cf. Figure 41.‘ The discrepancces are to be’expected, however, if one takes into account that the following strongly simplifying assumptions were made: (a) An essential simplification is that the electric field within the cavity was only described by the field Ziproduced by the point charges q1 and qz, whereas the field due to the remaining dipole moments has been neglected, which corresponds to a zero-order approximation.1° (b) The distortions of the lattice caused by the different sizes of the ions and the solvent molecules, and caused by the change in the force field when a solvent molecule is substituted by an ion, have not been taken into account. (c) The two ions were treated as point charges. The only specific characteristic of the ions which has been consideied is their polarizability, but even here the assumption was made that the sum of the polarizabilities of the CC13+ and Cl- ions equals polarizability of CClk This assumption is considered less drastic since the corresponding contri-
bution to the result is rather small. Conclusions Our ab initio calculation does not predict any stability for an isolated contact ion pair between CC13+and C1-. On neutralization of these two isolated ions the neutral CCll molecule is expected to be formed immediately. However, the calculation is not able to exclude any formation of electronically excited states on neutralization of these ions, which could correspond to such ion pairs. In contrast, our simple electrostatic model calculation suggests that solvent effects might well be the reason for the stability of the ion pair in the solvents CCll and methylcyclohexane. The most likely structure would correspond to the solvent separated ion pair (CC13+11 C1-). Acknowledgment. Support bfthe Swiss National Science Foundation is gratefully acknowledged. We also express our appreciation to the ETH Zurich computer center for providing computer time for this study.
Ab Initio Self-Consistent Field Calculations on the Structure of Cubane, Cubene, and the Cubyi Radical W. Schubert, M. Yoshlmlne, and J. Pacansky” IBM Research Laboratory, San Jose, California 95 193 (Received: December 1, 1980)
Extensive SCF calculationsare reported for the structures of cubane, cubene, and the cubyl radical. An estimate is provided for the energy required for scission of a C-H bond in cubane and a 0C-H bond in the cubyl radical. The energetics of both of these reactions are used to understand the geometry of the cubyl radical.
Introduction Ab initio calculations on the ethyl, n-propyl, isopropyl, and tert-butyl radicals have shown that C-H bonds in a /3 position to the radical center and eclipsed to the halffilled p orbital of the radical center are longer than C-H bonds normally encountered in a1kanes.l The feature common to all of these, as shown by thermodynamic and kinetic studies: is that the C-H bonds are weak, requiring only a dissociation energy of -38 kcal/mol for cleavage to give a hydrogen atom and an alkene. In order to investigate this further, we decided to study the structure of a radical that could not readily form an alkene by dissociation of a 0 hydrogen. The activation energy for such a reaction would be quite high, and, as a consequence, the /3 C-H bonds would probably not be affected. Calculations Ab initio restricted Hartree-Fock calculations have been carried out on cubane and cubene while unrestricted Hartree-Fock calculations were performed on the cubyl radical. A gradient method3 was used to optimize all geometrical parameters of the molecules. For cubane, a Da symmetry was imposed on the molecule, whereas the cubyl radical and cubene were subject to a C3”and Czu symmetry constraint, respectively. For all calculations, the (1)J. Pacansky and M. Dupuis, J . Chem. Phys., 68,4276(1978);71, 2095 (1979);73, 1867 (1980);J. Pacansky and M. Yoshimine, ibid. (2)J. A. Kerr, Chem. Reu., 66,465 (1966). (3)A. Komornicki, K. Ishida, K. Morokuma, R. Ditchfield, and M. Conrad, Chem. Phys. Lett., 45, 595 (1977);J. W.McIver, Jr., and A. Komornicki, ibid., 10, 303 (1971);P. Pulay in “Methods of Electronic Structure Theory”, H. F. Schaefer 111, Ed.,Plenum, New York, 1977.
TABLE I: Comparison of the Experimental and Theoretical Structural Parameters for Cubanea the oretical
bond lengths, A
bond angles, deg
C-C
1.572
C-H
1.076
GC-C
90.0
C-CH
125.3
exptl
1.553 i 0.003 1.549 i 0.003 1.01 i 0.05 1.11 i 0.05 90.5 i 0.3 89.6 i 0.3 89.3 i 0.3 127i 2 126 i 2 123 * 2
a D4hsymmetry; 4-31Gbasis set; total energy, -306.928 037 au.
split valence 4-31G basis set was used. This basis set is computationally efficient and known to give reasonable results. The calculations were done with the program HOND0.4
Results and Discussion The structural parameters resulting from the geometry optimization of cubane (Figure 1) are shown in Table I. According to this calculation, the edge of the cube formed by the carbon atoms is 1.572 A long. This C-C bond is considerably longer than those found in alkanes which are ca. 1.53-1.54 A long. The relatively long C-C bonds in cubane may be attributed to the nonbonded interactions (4) M. Dupuis, J. Rys, and H. F. King, J . Chem. Phys., 65,111 (1976); M. Dupuis and H. F. King, ibid., 68,3998 (1978).
QQ22-3654/81/2085-134Q$Q1.25/0 0 1981 American Chemical Society
Structure of Cubane, Cubene, and the Cubyl Radical
H
Flgure 1. Structure of cubane with
H"
The Journal of Physlcal Chemlstty, Vol. 85, No. 10, 1981 1341
.H
D,,,symmetry. H"
H2
Flgure 3. Structure of cubene.
TABLE 111: Optimized Structural Parameters for Cubenea bond lengths. C,-C, 1.367 C,-C, , A
c;-c;
bond angles, deg
Figure 2. Structure of the cubyl radical with C B vsymmetry.
TABLE 11: Optimized Structural Parameters for the Cubyl Radicala bond length, A C,-C, 1.562 C,-C, bond angles, deg
a
1.577 1.074 c,-c, 1.572 C,-H, 1.075 C,-H, 1.075 C,-H, C,-C,-C, 91.9 C,-C,-C, 88.7 C,-C,-C, 90.0 C,-C,-C, 90.7 C,-C,-C, 89.9 C,-C,-C, 90.4 C,-C,-H, 126.8 C,-C,-H, 125.4 C,-C,-H, 125.1 C,-C,-H, 125.3 C,-C,-H, 125.0
C,, symmetry; 4-31Gbasis set; total energy,
-306.284 170 au.
between carbon atoms. The shortest nonbonded distances between the carbon atoms in cubane is 2.22 A. In propane, for example, the nonbonded distance between the end carbon atoms is found to be -2.58 A.5 In response to the stronger repulsion between the carbon atoms in cubane, the bonded carbon atoms try to keep farther apart than in other C-C single bonds. The C-H bonds in cubane are 1.073 A. This is shorter than the C-H bonds calculated in open-chain hydrocarbons,' where they range from 1.08 to 1.09 A. The C-H bond length in cubane almost equals the C-H bond length for ethylene, 1.076 A. Also shown in Table I are the C-C and C-H bond lengths determined by X-ray diffraction.* Considering the large uncertainty of the experimental C-H bond lengths, the computed results provide a good geometric description of the cubane system. This provides a basis for the degree of reliability of the computed geometric differences between cubane and the cubyl radical. The results of the calculations for the cubyl radical (Figure 2) are shown in Table 11. The carbon skeleton of the molecule no longer forms a cube. The arrangement of the carbon atoms looks like a cube deformed by pushing one corner toward the center of the cube. The C1-C2bonds are shorter than the C-C bonds in cubane, whereas the C&3 bonds are longer than the C-C bonds in cubane. The C3-C4bonds have the same length as those in cubane within 0.001 A. In essence, the radical center in the cubyl system influences the geometry of the bonds a to the radical center similar to that observed for other acyclic (5) The computed geometry for propane' was used to find the nonbonded distance between the end carbon atoms. (6)E. B. Fleischer, J. Am. Chem. SOC.,86, 3889 (1964).
H2
a
1.575 1.555 c.-c. CZ-H: 1.073 C,-C,-C, 93.8 C,-C,-C, 86.2 C,-C,-C, 89.6 C,-C,-C, 90.4 C,-C,-H, 129.0 C,-C,-H, 123.2
Ci-C; C,-H. .
1.570 1.590 1.073
C,-C,-C, C,-C,-C, C,-C,-C, C,-C,-H, C,-C,-H, C,-C,-H,
97.3 83.4 95.7 128.6 125.5 124.8
(
I
C,, symmetry; 4-31Gbasis set; total energy,
-305.616 603 au.
alkyl radicals,' i.e., the a bonds are shorter than the C-C bonds in the parent hydrocarbon. The bond angle at the radical site is somewhat larger than 90'; the C1-C2-C3 angle, however, is slightly smaller than 90'. This distortion of the angles may be explained by the tendency of the carbon atoms C1 and C2 to distort toward a planar geometry. All other angles between carbon atoms remain practically unchanged when going from cubane to the cubyl radical. All of the C-H bonds in the cubyl radical are found to be slightly shorter than in cubane. Furthermore, the C2-H2 bonds are shorter than the C3-H3 and C4-H4 bonds, but the differences are very small. This result contrasts with the findings for alkyl radicals, where the C-H bonds in the p position to the radical site and eclipsed with the halffilled p orbital are markedly longer than those in y and higher positions.' The results for cubene (Figure 3) are summarized in Table 111. The effect of forming a double bond along one edge of the cube is to deform the cube by moving this edge toward the center of the cube. As in the case of the cubyl radical this may be attributed to the tendency of the atoms C1 and C2 to distort toward a planar geometry. This tendency also explains the rather long bond length C2-C3. As the atoms C1 move toward the center of the cube, the atoms C3move away, resulting in unusually long carboncarbon bonds. The C1-C1double bond is found to be 1.322 A, which is slightly longer than that for ethylene. The C-H bond lengths are practically the same as those in cubane and the cubyl radical. The energetics for the thermal /3 C-H scission reaction of an alkyl radical to form an alkene and a hydrogen atom have been studied by kinetic methods.2 In general, it is found that the activation energy for this process is -40 kcal/mol, which indicates that the p C-H bonds, for the radicals studied, are rather weak. For example, the AH for p C-H bond sdission in the n-propyl radical is 39 kcal/mol (see eq 1). In contrast to this 98 kcal/mol are CH3CH2CH2 .-* CH,CH'=CH2 + H* (1) CHSCHzCH3 .-* CHSCH2CH2 + H. (2) required to rupture a C-H bond in propane2 (see eq 2). This may be approximately shown theoretically by com-
J. Phys. Chem. 1981, 85, 1342-1349
1342
paring the SCF total energies obtained by using the 4-31G basis set for propane,l,4 propene,' the n-propyl radical, and the hydrogen atom.8 In this manner, the computed energies for eq 1and 2 are 37 and 82 kcal/mol, respectively. In contrast to the n-propyl radical is the energy required for C-H bond rupture in cubane and the cubyl radical, Le., for reactions 3 and 4. Since experimental measurements
+ H* C8He + H*
C8H8 -F C&7*
(3)
C8H7*-P
(4)
are not available for this system, the results of the ab initio calculations in this report will be used. When one uses the total energies for cubane, cubene, and the cubyl radical, the AH for rupture of a C-H bond in cubane, as indicated in eq 3,is found to be 91 kcal/mol. The AH for the @ C-H bond scission reaction in the cubyl radical, as shown in eq 4,is 106 kcal/mol. Because of the neglect of correlation energy in the SCF total energies, only two significant statements may be made about the energetics of reactions 3 and 4. The first is that the C-H bond energies in cubane and the cubyl radical are about equal. The second is that the energy required for @ C-H scission is clearly much (7) Total energy for propene was taken from J. S. Binkley, J. A. Pople, and W. J. Hehre, Chem. Phys. Lett., 36, 1 (1975). (8) R. Ditchfield, W. J. Hehre, and J. A. Pople, J. Chem. Phys., 54,724 (1971).
higher than that for the other alkyl radicals discussed above. The cubyl radical should therefore behave quite differently from alkyl radicals. Whereas a long C-H bond in a @ position to the radical site is found for alkyl radicals, no such long C-H bond is found for the cubyl radical. If the long C-H bond in alkyl radicals indicates that the radical itself looks much like the transition state for the reaction toward the alkene, @ C-H bond scission in the cubyl radical should not be an important thermal reaction. This view is supported by the binding energies for C-H bonds in a @ position to the radical site. For the cubyl radical, it is found that the @ C-H bonds remain strong, indicating that the cubyl radical should not readily form cubene by dissociating another hydrogen.
Conclusions The only significant structural changes that occur when an open shell is formed in cubane is that the radical center has a more planar geometry with shorter a C-C bonds. Unlike the situation in other alkyl radicals, like, for example, the ethyl, n-propyl, and tert-butyl radicals, the @ C-H bonds in the cubyl radical have the same length as those in cubane. Since the energy required for the @ C-H bond scission is approximately that required for the dissociation of a C-H bond in cubane, then the geometry of the cubyl radical is probably not affected by the transition state for this reaction.
Rate Constants, Branching Ratios, and Energy Disposal for Nf(b,a,X) and HF( v ) Formation from the H NFp Reaction
+
R. J. Malinst and D. W. Setser" Dapattment of Chemlstty, Kansas State Unlversky, Manhattan, Kansas 66506 (Recelvd: December 2, 1980)
The rate constant and energy disposal for the H + NF2reaction has been measured by observing infrared and visible chemiluminescencein a fast-flow, low concentration, flowing-afterglow apparatus at room temperature. The rate constant was determined by comparing the HF(u) emission intensity to the HCl(u) emission intensity from the H + Cl, reaction. The rate constant for formationof HF(u21)is 3.8 X lo-', cm3molecde-l s-'. Allowance for HF(V=O)formation gives a total rate constant which is about a factor of 3 larger. The observed HF(u1,u2,ug,u4) distribution is 0.75:0.200.04:0.01. The NF(a1A-X3Z-) emission also was observed; the NF(alA) vibrational distribution is uGu1:uz = 0.730.190.08. Comparison of the NF(blZ+)and NF(alA) emission intensities and using the HF(u=4) emission, which is energeticallyallowed only for formation of NF(X3Z-),gave NF(X):NF(a):NF(b) branching fractions of 0.07:0.91:0.02. By comparing the NF(a1A-X3Z-) intensity from H + NF, to the HF(34) emission intensity from the H + C1F reaction and by using the known rate constant and energy disposal for H + ClF, the radiative lifetime of NF(alA) was determined to be -5.6 s. The M),1-1, and 2-2 band wavelengths of the NF(a1A-X3Z-) transition yielded w: = 1184 cm-l and W ~ X : = 8.5 cm-'.
Introduction Reactions which generate electronically excited-state products have received considerable interest recently because of their potential application as chemical pumps for lasers. For less applied reasons, such reactions are of interest because the chemiluminscence identifies the populations in the product quantum states, which serves as an excellent probe of the reactions dynamics. Few Air Force Weapons Laboratory, Kirtland Air Force Base, NM 87117. 0022-3654/81/2085-1342$01.25/0
chemical reactions give chemiluminescence that permits observation of all products; however, one example is hydrogen atoms plus NF2 radicals which generates electronically excited NF and vibrationally excited HF products.'"' The internal energy of both HF and NF can be (1) J. M. Herbelin and N. Cohen, Chem. Phys. Lett., 20,606 (1973).
(2)J. M.Herbelin, Chem. Phys. Lett., 42,367 (1976). (3) M.A. Kwok and J. M. Herbelin in "Electronic Transition Lasers 11", L. E. Wilson, S. N. Suchard, and J. I. Steinfeld, Ed., MIT Press, Boston, 1977.
0 1981 American Chemical Society
