J. Phys. Chem. 1992, 96, 5800-5803
5800
(1 l ) Syage, J. A.; Felker, P. M.; Zewail, A. H. J . Chem. Phys. 1984,81, 2233. (12) Itoh, M.; Sasaki, M. J. Phys. Chem. 1990, 94, 6544. (13) Itoh, M.; Hayashi, A. J . Phys. Chem. 1989, 93, 7789. (14) Itoh, M.; Takamatsu, M.; Kizu.; Fujiwara, Y . J . Phys. Chem. 1991, 95, 9682. (15) Itoh, M.; Mimura, T.; Usui, H.; Okamoto, T. J. Am. Chem. SOC. 1973, 95, 4388.
(16) (a) Itoh, M. J . Am. Chem. SOC.1974, 96, 7390. (b) Itoh, M.; Mimura, T. Chem. Phys. Lett. 1974, 24, 551. (17) Hirayama, S.; Tanaka, F.; Shobatake, K. Chem. Phys. Leu. 1987, 140, 447. (18) Gaweda, M.; Prwhorow, J. Chem. Phys. Lett. 1975, 30, 155. (19) Kebarle, P.; Chouwdhury, S. Chem. Reu. 1987, 87, 513. (20) Castella, M.; Millie, P.; Piuzzi, P.; Caillet, J.; Langlet, J.; Claverie, P.; Tramer, A. J . Phys. Chem. 1989, 93, 3941.
Bond Dissociation Energies of H,NX Compounds. Comparison with CH,X, HOX, and FX Compounds Kenneth B. Wiberg Department of Chemistry, Yale University, New Haven, Connecticut 0651 1 (Received: October 16, 1991)
The bond dissociation energies (BDE) of H2NNH2,HONH,, and FNH2 have been calculated using Pople's G1 procedure, and the known BDE for hydrazine is well reproduced. The BDEs of MeX, H2NX, HOX, and FX derivatives, where X = Me, H2N, HO, and F, are compared, and the differences are related to changes in hybridization, internal Coulombic stabilization, and lone pair-lone pair repulsion.
In another investigation, we made an indirect estimate of the bond dissociation energies of hydrazine, hydroxylamine, and fluoroamine and found that all were close to 65 kcal/mol.' This is in agreement with the known dissociation energy of hydrazine, 66 kcal/mol? The similarity in values for these compounds stands in contrast to the change in dissociation energies for the corresponding methyl derivatives: methylamine, 84.1; methanol, 90.2; and methyl fluoride, 108.2 kcal/mol.2 As a first step in trying to understand the differences in the two series, we have carried out direct calculations of the dissociation energies. In order to have appropriate comparison data, we have examined the following series: CH3X, H2NX, HOX, and FX where X = CH3, NH2, HO, and F. The structures were calculated at the MP2/6-3 lG* theoretical level (Table I), giving geometries which generally agreed satisfactorily with the experimental ~ a l u e s . ~ Energies were calculated at the MP4/6-3 1l++G**, QCISD(T)/631 l++G**, and QCISD(T)/6-31 l++G(Zdf,p) theoretical level^.^ These data are summarized in Table 11. The radicals formed by the dissociation processes also were studied, and their data are included in the table. The calculation of bond dissociation energies is known to present problems. One good solution has been provided by Pople et al. in their G1 procedure.' This involves calculation of the energy at the QCISD(T)/6-3 11+G(2df,p) level, either directly or via a set of calculations. The energies are then corrected for higher level terms (hlc) and for the zero-point energies. The latter are estimated using the HF/6-31GS vibrational frequencies that are scaled by the factor 0.8934.5 The use of the 6-31 1++G(2df,p) basii set in our work, which includes diffuse functions at hydrogens, leads to slightly different higher level correction terms.6 The full calculation of Eo = E(QCISD(T)/6-31 l++G(Zdf,p)) + Ehlc+ EZpEis given in the last column of Table 11. The dissociation energies calculated at the various levels are summarized in Table 111. The MP4 and QCISD(T) values obtained using the 6-3 1l++G** basis set are essentially the same and are somewhat too small as compared to the experimental values.2 The MP2/6-31G* dissociation energies are close to the experimental value. All sets of estimated Do are linearly related to the observed values, as shown in Figure 1 for the MP2 data. Here, the relationship between the MP2 data, after correcting for zero-point energy changes, and the experimental data was BDE(MP2) = 0.8 + 0.988BDE(obs) The rms error was only 1.4 kcal/mol. The good agreement is,
of course, a result of cancellation of errors. It will be interesting to see whether this agreement extends to other saturated molecules. The use of the 6-3 1 l++G(Zdf,p) basis that includes two sets of d functions and one set off functions on the non-hydrogenated atoms leads to a considerable decrease in calculated energies and an improvement in the dissociation energies. The inclusion of Pople's higher level corrections further improves the agreement between calculated and observed values, leading to an rms error of 0.7 kcal/mol. The calculations confirm our previous estimate of the dissociation energies of hydroxylamine and fluoroamine and show that they are indeed about the same as that for hydrazine. It now remains to examine the reasons for the differences between the MeX, H2NX, HOX, and FX series (Figure 2). The bond dissociation energies in the MeX series appear to be dominated by chargetransfer effects. After a decrease on going from ethane to methylamine, there is a steady increase in BDE on going from methylamine to methanol and methyl fluoride. The decrease in BDE on going from ethane to methylamine is probably a hybridization effect. Whereas the methyl group is sp3 hybridizul, the amine group uses less s character in its bonds in order to use as much s character as possible to stabilize its lone pair. This results in a C-N-H bond path angle of 106.4O.' It is known that the percent s character has a dramatic effect on BDE's, so that in the series ethane, ethylene, and acetylene the C-H BDE's are 98, 110, and 131 kcal/mol, respectively.8 The increase in BDE from methylamine to methyl fluoride is probably related to the increasing ionic character of the bonds that results from the increasing difference in electronegativity. This is reflected in the charges calculated for the groups in these molecules via numerical integration of the charge density from the MP2 wave functions using appropriately defined atomic volumes (Table IV).9 Pauling showed that ionic character increases bond strengths as a result of the added Coulombic stabilization.1° It is generally thought that the low dissociation energy for fluorine is due to the repulsion of the lone pairs attached to the atoms." It may be an important factor with the H2NX compounds since the nitrogen has a lone pair and could become even more important with the HOX compounds. Repulsive interactions usually lead to changes in geometry, and so we have examined the M-X bond lengths (Figure 3). Here, for consistency, the calculated bond lengths were used. The same conclusion would have been reached using the experimental ~ a l u e s . ~
0022-365419212096-5800$03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 5801
Bond Dissociation Energies of H2NX Compounds TABLE I: Calculated Structures, MP2/6-31G* comwund calc 1.524 ethane rcc 1.093 rCH 107.7 fHCH 1.461 methylamine rCN 1.095 rCHl 1.087 rCHb 1.012 ~ N H 115.4 LNCH, 109.0 fNCHb 107.4 LHCH 105.9 fHNH 1.419 methanol rco 1.085 rCH, 1.092 rCHb 0.962 rOH 106.5 LOCH, 112.5 LOCH, 108.5 LHCH 107.3 fCOH 1.390 methyl fluoride rCF 1.092 rcn 109.8 LHCH 109.1 fHCF 1.484 hydrazine ~ N N 1.016 ~NH. 1.020 rNHb 106.4 fNNH, 111.5 fNNHb 107.0 fHNH
obs 1.532 (2) 1.111 (2) 107.3 (3) 1.471 (2) 1.099 (5)" 1.010 (5) 113.2 108.8 108.0 (5) 107.1 (5) 1.425 (2) 1.094 (3)' 0.945 (3) 107.1 112.1 108.6 (7) 108.5 (5) 1.382 1.095 110.5 108.9 1.447 (5) 1.008 (8)
rON
r~H rOH
fONH LNOH fHNH r~ F
fluoroamine
~ N H
FNH fHNH
hydrogen peroxide
rw rOH
fHOO T
hypofluorous acid
rOF rOH
LFOH fluorine
~ F F
I
1
'-"
109.2 (8) 113.3 (3) 88.9 (15) 1.453 (3) 1.016 (10) 0.962 (5) 103.3 (7) 101.4 (7) 107.1 (10) 1.433 (1) 1.023 (1) 101.1 (1) 106.3 (1) 1.475 (4) 0.950 (5) 94.8 (20) 120.0 (5) 1.442 (1) 0.966 96.8 1.417 (1)
T
hydroxylamine
Observed BDE
Figure 1. Relationship between observed and MP2/6-31GS calculated bond dissociation energies.
1.451 1.021 0.971 102.9 101.3 105.3 1.433 1.023 100.9 105.0 1.468 0.976 98.7 121.2 1.444 0.979 97.2 1.4206
I"
.
6
8
7
9
Atomic Number of X
Figure 2. Changes in bond dissociation energies with changes in substituents.
'The
structural determinations assumed a symmetrical methyl group. However, it is known from other data (McKean, D. C.; Boggs, J. E.; Schlfer, L. J . Mol. Strurt. 1984, 116, 313) that the CH bond lengths differ by 0.007 A in methylamine and 0.006 A in methanol.
In the CH3X, H2NX, and HOX series, the homopolar compound (closed symbols) has the longer bond. As noted above, differences in electronegativity normally lead to Coulombic attraction and shorter and stronger bonds. One interpretation of
the changes in bond lengths would be that the homopolar compound has no charge separation and as a result has the longest bond. Another interpretation of the data would be that the covalent radius of the X atom decreases with increasing atomic number because the valence electrons are held more strongly. This could account for the bond length changes in the MeX series. With the HzNX compounds, the bond length increase on going from CH3NH2to H2NNH2could be due to a combination of lone pair repulsion in the latter and the decrease in Coulombic stabilization. The subsequent decrease in bond length would be due to the increased Coulombic stabilization as the difference in electronegativityincreases and to the decrease in covalent radius. Then, with the HOX compounds, the minimum Coulombic stabilization would be found with HOOH. and this does have the
TABLE 11: Energies of Compounds and Radicals comcd CHSCHI CHiNH2 CHJOH CHjF H,NNHI HZNOH HZNF HOOH HOF F2 CHI NH2 HO
F
HF/6-31G* -79.228 76 -95.209 83 -1 15.035 42 -1 39.034 62 -111.16937 -130.978 84 -154.955 78 -1 50.764 79 -174.729 58 -198.677 76 -39.558 99 -55.557 70 -75.382 28 -99.364 96
MP2/6-3 lG* -79.503 97 -95.514 44 -1 15.353 29 -1 39.342 66 -1 11.504 40 -131.33017 -155.298 11 -1 51.134 92 -175.09286 -199.038 82 -39.673 03 -55.693 75 -75.523 21 -99.487 27
MP4/ 6-311++G** -79.655 01 -95.671 35 -115.51663 -139.51498 -1 11.666 26 -1 3 1.496 77 -155.473 80 -1 51.305 76 -175.27200 -199.223 76 -39.75270 -55.778 42 -75.615 53 -99.59068
QCISD(T)/ 6-31 l++G** -79.656 22 -95.67202 -1 15.516 51 -139.514 23 -1 1 1.666 46 -13 1.496 28 -155.471 10 -151.30473 -175.27052 -199.22253 -39.753 04 -55.778 71 -75.615 51 -99.590 53
QCISD(T)/ 6-31 1++G(2df,p) -79.697 72 -95.722 77 -1 15.578 32 -139.587 14 -111.726 12 -131.566 69 -155.55347 -151.38649 -175.363 35 -199.32544 -39.772 45 -55.806 37 -75.652 14 -99.635 23
hlc -0.042 77 -0.042 77 -0.042 77 -0.042 77 -0.042 77 -0.042 77 -0.042 77 -0.042 77 -0.042 77 -0.042 77 -0.018 51 -0.018 51 -0.018 51 -0.018 51
ZPE 0.07 1 22 0.061 53 0.049 40 0.037 86 0.051 85 0.039 47 0.027 18 0.026 17 0.013 92 0.002 53 0.027 65 0.018 36 0.008 13 0.000 00
EO -79.669 27 -95.70401 -115.571 69 -139.59205 -111.71704 -1 31.569 99 -155.56906 -15 1.40309 -175.39220 -199.365 68 -39.763 31 -55.806 52 -75.66252 -99.653 74
5802 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992
Wiberg
TABLE 111: Calculated Bond Dissociation Energies, Including Zero-Point Energy Correction (kcal/mol) MP4/ QCISD/ QCISD/ compd HF/6-31G* MP2/6-31G* 6-31 l++G** 6-311++G** 6-311++G(2df,p) 59.5 CHICHI 89.1 83.9 84.2 85.9 CHJNH2 48.7 82.9 78.3 78.3 80.6 CHIOH 50.5 90.0 84.6 84.3 87.9 CHiF 63.0 108.0 101.3 100.7 106.2 H2NNH2 24.4 63.9 59.2 58.9 61.1 HZNOH 16.2 62.9 56.4 55.9 59.1 15.3 67.9 60.2 58.4 64.7 HiNF HOOH -6.1 49.3 40.7 40.0 45.4 HOF -14.2 48.1 31.7 36.8 44.0 F2 -34.3 38.8 25.0 24.4 32.9
G1 89.5 84.2 91.5 109.8 65.3 63.3 68.3 49.0 41.1 36.5
obs (0 K)’ 88.0 f 0.3 83.9 f 1.5 90.6 f 0.4 108.7 f 2.0 66.2 f 2.1 49.4 f 1.0 37.0 f 0.0
“The data were taken from: ref 2 and Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.;Chapman and Hall: London, 1986. TABLE I V Calculated Group Charges (MP2/6-31G*) comDd (A-B) charge on A comDd (A-B) charge on A CH3-CHJ 0.000 HZN-OH 0.204 0.348 H2N-F 0.369 CHI-NH2 CHI-OH 0.551 HO-OH 0.000 CHI-F 0.665 HO-F 0.169 H 2N-N H 2 0.000 F-F 0.000
0.68 20
40
30 %S
Figure 4. Relationship between the carbon covalent radius and the percent s character.
135
Atomic Number of X
Figure 3. Relationship between calculated bond length and the atomic number of the substituent atoms.
longest bond length in the series. It would be helpful to have appropriate covalent radii of the C, N, 0,and F atoms in the CH3, NH2, and HO groups. With ethane, there are no Coulombic factors and no repulsive interactions between the attached hydrogen,I2 and so the carbon covalent radius is usually taken as one-half the C-C bond length.1° Similarly, the covalent radiis of fluorine has been taken as the difference between the C-F bond length in methyl fluoride and the covalent radius of a methyl carbon. However, the C-F bond length is subject to two effects: the change in the carbon covalent radius with the change in hybridization that occurs when it is bonded to an electronegative atom such as fluorineI3 and the bond-shortening Coulombic interactions that result from the formation of a polar C-F bond. The covalent radius does change with hybridization as is seen in the M e - C bond lengths for propane, propene, and propyne (1.526, 1.501, and 1.459 A, respectively, from experimental data3 and 1.5248, 1.4980, and 1.4611 A at the MP2/6-31GS theoretical level14). Taking one-half the C-C single bond length as the covalent radius of a methyl group with sp3hybridization (0.763 A (expt) based on propane, 0.762 A (calc)), the covalent radii for approximately sp2- and sp-hybridized carbons are 0.738 and 0.696 A (expt) or 0.736 and 0.699 A (calc). A plot of these radii against percent s character is shown in Figure 4. Both sets of data give essentially the same curve. The C-F bond lengths in the fluoromethanes decrease with increasing fluorine substitution, and this probably results from
Y
li21
I
1.304
o
I
2
3
Carbon charge
Figure 5. Relationship between CF bond lengths and carbon charges.
the increasing positive charge at carbon.I5 Using the Weinhold-Reed natural population analysis,16the charge at carbon was found by Reed and SchleyerIs to increase almost linearly with the number of fluorines. We have examined these compounds using H F / 6 3 1 1 G * * wave functionst4and Bader’s theory of atoms in molecules? A plot of the bond length against the carbon charge is shown in Figure 5. The bond length extrapolated to no fluorines (Le., eliminating the Coulombic interaction) is 1.421 A. In methyl fluoride, the H-C-F bond path angle is 106.7’ and the H - C - H bond path angle is 1 12.1 O,I7 leading to 18% s character in the bond. The appropriate C covalent radius would be 0.792 A, leading to a fluorine covalent radius of 0.629 A. This is very close to the value obtained just from the bond lengths of ethane and methyl fluoride and shows that the bond lengthening effect in the methyl group due to the hybridization change and the bond shortening
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 5803
Bond Dissociation Energies of H2NX Compounds TABLE V Covalent Radii rrA atom
hybrid
MP2
obs
SP3 SP2 SP
0.762 0.735 0.699 0.699 0.657 0.628
0.766 0.738 0.696 0.705 0.659 0.616
C N PH2)
0 (OH) F
TABLE VI: Bond Elongation c o m d Ar(MP2l Adexptl H2NNH2 0.040 0.037 HqNOH 0.089 0.094 0.105 0.112
c o m d AdMP2l A d e x d l 0.152 0.157 0.163
HOOH HOF F2
0.157 0.167 0.185
08
for the same reason as in the HzNX series. Finally, in the FX group, the factors that contribute to the methylamine/hydrazine decrease in BDE will continue throughout the series, with the minimum in internal Coulombic stabilization and maximum in lone pair-lone pair repulsion being reached at F2. It is interesting to note that the bond elongation increases with increasing number of opposed lone pairs but levels off after four opposed pairs is reached (Le., with hydrogen peroxide). This may be due to any of a number of factors, but it may be possible that fluorine will effectively only present two lone pairs to an opposed atom and will place the third lone pair at the rear of the bond to the attached atom. The large calculated lone pair repulsion for hydrogen peroxide may seem surprising in view of the small trans rotational barrier (1.1 kcal/mol).18 However, the charge distribution about the 0.0 bond is essentially cylindrically symmetrical, and there is no indication of discrete lone pairs. Therefore, there should be little angular dependence for the lone pair repulsion. Calculations. The ab initio calculationswere carried out using GAUSSIAN-~O'~and used standard basis sets. The charges were calculated using PRO AIM.*^
Acknowledgment. This investigation was supported by a grant from the National Science Foundation. Paul Rablen, Christopher Hadad, and David Nakaji made significant contributions toward the development of the ideas presented herein.
07
References and Notes
06 00
02
04
06
Group charge
Figure 6. Relationship between the covalent radii and the group charge.
due to Coulombic interactions cancel. The value is in good agreement with the commonly quoted value (0.64)'O which was derived from the ethane and methyl fluoride lengths using older experimental values. In view of the cancellation of the correction terms for methyl fluoride, it was reasonable to expect similar cancellation for methylamine and methanol. Then, the covalent radii of an amino nitrogen and a hydroxy oxygen could be estimated from the bond lengths. The values thus obtained are given in Table V, along with the corresponding values derived from the experimental data. It was interesting to note that the radii thus obtained were linearly related to the charges (Table IV and Figure 6). It is now possible to calculate the bond lengthening due to lone pair repulsion making use of the covalent radii. The values are given in Table VI. There is fairly good agreement between the Ar values derived from the calculated and experimental structural data, and the elongation increases with the number of opposed lone pairs. The origin of the changes in bond dissociation energies now becomes more clear. With the HINX series (Figure 2), the decrease in BDE from methylamine to hydrazine results from the loss of the internal Coulombic attraction in the former and the lone pair-lone pair repulsion in the latter. On going from hydrazine to hydroxylamine and fluoroamine, the internal Coulombic attraction would be expected to increase, but this appears to be offset by the increased lone pair-lone pair repulsion which can be seen in the increasing Ar values (Table V). The same factors apply to the HOX series, except here the factors which reduce the BDE of hydrazine with respect to methylamine will continue until hydrogen peroxide is reached. The curve then flattens out
(1) Wiberg, K. B.; Glaser, R. J. Am. Chem. SOC.1992, 114, 841. (2) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed.; J . Phys. Chem. Ref. Data 1985 (Suppl. 1). (3) Callomon, J. H.; Hirota, E.; Kuchitsu, K.; Lafferty, W. J.; Maki, A. G.;Pote, C. S.Lundolt-Bornstein; New Series Vol. H/7; Springer-Verlag: Berlin, 1976. Callomon, J. H.; Hirota, E.; Iijima, T.; Kuchitsu, K.; Lafferty, W. J. Lundolt Bornstein; New Series Vol. 11/15; Springer-Verlag: Berlin, 1987. HOF Kim, H.; Pearson, E. F.;Appelman, E. H. J. Chem. Phys. 1972, 56, 1. Pearson, E. F.; Kim, H. J. Chem. Phys. 1972, 57, 4230. H I N F Christen, D.; Minkwitz, R.; Nuss, R. J. Am. Chem. SOC.1987, 109, 7020. (4) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. ( 5 ) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys. 1989, 90, 5622. (6) The higher level correction for a valence electron pair is taken as the difference between the calculated and correct energies for H2 (0.006 11 hartree) and that for a single electron is taken as the corresponding difference for a hydrogen atom (O.OO018 hartree). (7) Wiberg. K. B.; Breneman, C. M. J . Am. Chem. Soc. 1990,112,8765. (8) Ervin, K. M.; Gronert, S.;Barlow, S.E.; Gilles, M. K.;Harrison, A. G.;Bierbaum, V. M.;DePuy, C. H.; Lineberger, W. C.; Ellison, G.B. J . Am. Chem. Soc. 1990, 112, 5750. (9) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Clarendon Press: Oxford, 1990. (10) Pauling, L. The Nature of the Chemical Bond; Cornell University Press: Ithaca, NY, 1939. (1 1) Caldow, G.L.; Coulson, C. A. Trans. Faraday SOC.1962, 58, 633. (12) Bader, R. F. W.; Cheeseman, J. R.; Laidig, K. E.; Wiberg, K. B.; Breneman, C. J . Am. Chem. Soc. 1990, 112, 6530. (13) Bent, H. A. Chem. Rev. 1961,61, 275. (14) Unpublished results, this laboratory. (15) Reed, A. E.; Schleyer, P. v. R. J. Am. Chem. Soc. 1987,109,7362. Cf.: Huheey, J. E. Inorganic Chemistry, 3rd ed.; Harper and Row: New York, 1983; p 262. (16) Reed, A. E.; Weinhold, F. J . Am. Chem. SOC.1986, 108, 3586. (17) Wiberg, K. B.; Breneman, C. M.J. Am. Chem. Soc. 1990,112,8765. (18) Hunt, R. H.; Leacock, R. A.; Peters, C. W.; Hecht, K. T. J . Chem. Phys. 1965, 42, 1931. Helminger, P.; Bowman, W. C.; De Lucia, F. C. J . Mol. Specrrosc. 1981, 85, 120. (19) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.;Gonzolez, C.; Defrees, D. J.; Fox, D. J.; Whitehead, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Fleuder, E. M.; Topiol, S.;Pople, J. A. Gaussian 90; Gaussian, Inc.: Pittsburgh, PA, 1988. (20) Biegler-Konig, F. W.; Bader, R. F. W.; Tang, T.-H. J . Compur. Chem. 1982,3, 317. Bader, R. F. W.; Tang, T.-H.; Tal, Y.; Biegler-KBnig, F. W. J. Am. Chem. SOC.1982, 104, 946.
