J. Phys. Chem. 1986,90, 5910-5914 fast temperature change of w, can be expected, if the system exhibits a change in order of relative stabilities of the two isomers at low temperatures, i.e., the case of the complexes (CO,), and HF-ClF which exhibit a distinct maximum in the temperature course of the ACpo term. A maximum is also encountered in the case of CO-HF; it is, however, absent from the HF-HCl system which exhibits, out.of all the four systems, the highest temperature of the interchange of relative stabilities (in the case of N O dimerization, no interchange of relative stabilities of the two isomers was observed in the temperature interval investigated). The fact that, in regions of fast changes of wi with temperature, the enhancement of value of the ACpo term can be very distinct (as compared with the partial ACpoiterms) is also supported by numerical data of Table I where the ACpo/ACpo,,, ratio of, e.g., the CO-HF system is about 2.8. Two points deserve attention. The first point is a question of possible effects of the R R H O approximation used. Certainly, application of a more sophisticated approach to the partition functions should influence18 the values of the partial thermodynamic terms, though it will generally not be a change in the order of magnitude of the terms. However, an approach beyond the RRHO approximation is now possible only for two18aor at most threelEbatomic clusters. Nevertheless, one can expect considerable cancelling out between the numerator and the denominator in eq 1 so that the corrections to the RRHO approximation should not be critical for the values of wi. The changes in the partial values of thermodynamic quantities owing to the application of higher quality partition functions should not be, moreover, too much different for different isomers. Consequently, the qualitative behavior of the overall term from eq 3 or 4 is not supposed to be influenced by the particular type of qi approximation used. Hence, the reported finding of a pronounced maximum on the curve of temperature dependence of ACpo should be invariant to a particular way of qi evaluation. (1 7) (a) Temperature dependencesof weights w, for (CO,),, HF-HCI, and H F C I F isomers are available in ref 10, 11, and 14. (b) In fact, the term AHo I - AHo, is important, too; as for the two-isomer case the second term in eq 3 is reduced, e.g., to ( A H o , - AHo,) dw,/dT or to wlw2 (Mol AHoz)z/R~. (18) (a) Shin, H. K. Chem. Phys. Lett. 1977, 47, 225. (b) Bernstein, L. S.;Wormhoudt, J. J . Chem. Phys. 1984.80, 4630.
The second point concerns a possible technique to be used for ACpo observation. Clearly enough, the Cpoof a whole gas-phase mixture (i.e., mixture of not only isomeric dimers but also related monomers and even higher oligomers) will, at least at some conditions of observation, mostly be determined by the heat capacities of the monomer units. Hence, a recording of the heat capacity of the whole mixture would not be too useful for proving the predicted effects. It should be much more promising to apply a technique just following the formation of the dimers only, e.g., through measuring equilibrium constants of their formation. Obtaining the latter value is not prevented by the presence of monomers as well as higher oligomers; however, it is still difficult. If such a measurement of the equilibrium constant would be precise enough, even its second temperature derivative could be derivable and meaningful and the overaIl heat capacity change upon dimerization obtainable. Unfortunately, the contemporary measurements are generally not accurate enough to facilitate the second temperature derivative determination, and thus, a further development would be desirable for the purpose. Another line of adjusting observation is varying the temperature and pressure (or even possibly initial ratio of different monomers) in order to enhance just the dimer populations. However, at pressures where molecular complexes occur in substantial amounts, there are nonnegligible deviations from the perfect-gas equation of state to be expected; this may be reflected in the heat capacity term, too. In conclusion it can be stated that a manifestation of isomerism of molecular complexes connected with a fast temperature interchange of stability of the isomers in a temperature region can be expected as a distinct maximum at the temperature course of the overall ACpo term in this temperature region. Acknowledgment. Support from the Japan Society for the Promotion of Science is greatly acknowledged as well as the friendly, creative atmosphere and kind hospitality of Prof. Eiji Osawa and his group and the considerable help of Ms. Teruyo Fujiyoshi with computational aspects. Finally, the valuable, constructive comments of referees are highly appreciated. R@tV NO. (NO)z, 16824-89-8; (CO,),,26796-46-3; HF-HC1, 75979-18-9; HF-CIF, 61981-49-5; CO-HF, 104505-49-9.
Gas-Phase StabUlties of Symmetric Proton-Held Dlmer Cations Kenzo Hiraoka,* Hajime Takimoto, Faculty of Engineering, Yamanashi University, Takeda-4, Kofu 400, Japan
and Shinichi Yamabe* Department of Chemistry, Nara University of Education, Takabatake-cho, Nara 630, Japan (Received: January 8, 1986; In Final Form: May 13, 1986)
The stabilities of symmetric proton-held dimer cations H+(B)2have been studied, where B is H2, 02,N2, CO, CH4, HF, HzO, alcohols, ethers, and nitrogen-containing hydrocarbons. The general trend is found that the bond energies - N o s for proton-held dimers H+(B)? decrease as the proton affinity of base B increases. This indicates that as the positive charge in the protonated molecules H+B is more dispersed, the bond energies of the proton-held dimers B--H+B are weaker. The electron density on the proton of H+-B is found to reflect the energetic trend.
Introduction In earlier work dealing with proton-held dimers AHB+, where A and B were oxygen and nitrogen n-donor bases, Kebarle and co-workers had observed that for a series in which B was held constant but AH+ was changed the binding energy increased with 0022-3654/86/2090-5910$01.50/0
the acidity of AH+ (i.e., decreased with increasing proton affinity of A).'4 When AH+ was kept constant and B was changed, the (1) Payzant, J. D.; Yamdagni, R.; Kebarle, P. Can.J . Chem. 1971, 49, 3308.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5911
Gas-Phase Stabilities of Proton-Held Dimer Cations binding energy increased with the basicity of B. The binding energy in AHB+ could thus be considered as a partial protdn transfer in which the strength of the interaction increases with the acidity of AH+ and the basicity of B. When it comes to symmetric dimers H+(B)*, the rule cannot be applied since a high proton affinity of B decreases the acidity of BH+ as it idcreases the basicity of the proton acceptor B; i.e., the effects are o p p ~ s e d . Although ~ a vast majority of the proton affinities and the bond energies of the symmetric proton-held dimers H+(B)2has been measured, no detailed investigation has been done that correlates these two kinds of thermochemical data. In this study, we tried to find some correlation between the proton affinities and the bond energies of the proton-held symmetric dimers. The proton affinities of studied bases B are very different, but the changes of the bond energies of the dimers H+(B)2 are found to be rather small. However, it was found that the bond energies of H+(B)2show a systematic decrease with an increase of the proton affinities of bases B. As a criterion of showing these energetic differences, the electron density on the proton of H+-B is taken up. A larger charge dispersal in H+-B (i.e., larger proton affinity) will correspond to an accumulation of the density and will lead to a weaker B--H+-B bonding. Recently, a highly accurate a b initio MO calculation has been done for the evaluation of the thermochemical data for reaction 1 with n = 1.6 The calculated enthalpy change for reaction 1 H+(H20),
+ H 2 0 = H+(H20),+1
(n, n + 1)
(1)
= 35.5 kcal/mol) is somewhat higher than the experimehtal value (-AHo = 3 1.6 kcal/mol) obtained by Kebarle and co-workers.' In this study, a careful measurements of thermochemical data for reaction 1 with n = 1 and 2 have been done with a pulsed-electron-beam mass spectrometer. The thermochemical data for clustering reactions of acetone, tetrahydrofuran (THF), and 2-methyltetrahydrofuran (2-MTHF) have also been measured.
C4H60H++ C4H@ = H+(C4H60),
(3)
Methods of Experimental and ab Initio Calculation The measurements for clustering reactions 1-4 were made with a pulsed-electron-beam mass spectrometer that has been described p r e v i o u ~ l y . ~Small ~ ~ amounts of sample vapors were introduced into 4 Torr of CH4carrier gas through a stainless steel capillary. In the previous measurement~,8.~ the ion source temperature was changed by using the heating and cooling stainless steel jacket. The thermocouple embedded in the ion source block was used for the temperature measurements. The jacket was in thermal contact with the ion source block.9 In such an arrangement, the efficiency of the heat transfer between the ion source and the heating and cooling jacket was found to be very low. For instance, when the jacket temperature was maintained at --150 OC, the ion source temperature could be decreased not lower than --80 OC. The temperature gradient between the ion source and the jacket becomes greater as the jacket temperature gets higher or lower than the room temperature. For the measurements of equilibria for (2) Yamdagni, R.; Kebarle, P. J. Am. Chem. SOC.1971, 93, 7139. (3) Yamdagni, R.; Kebarle, P. J. Am. Chem. SOC.1973, 95, 3504. (4) Davidson, W. R.; Sunner, J.; Kebarle, P . J. Am. Chem. Soc. 1979,101,
1675. ( 5 ) Lau, Y.K.; Saluja, P.P.S.; Kebarle, P.J. Am. Chem. Soc. 1980, 102, 7429. (6) Yamabe, S.;Minato, T.; Hirao, K. J . Chem. Phys. 1984, 80, 1576. (7) Cunningham, A. J.; Payzant, J. D.; Kebarle, P. J . Am. Chem. Soc. 1972, 94, 1627. (8) Hiraoka, K.; Morise, K.; Shoda, T. Inr. J . Mass. Spectrom. Ion Processes 1985, 67, 11. (9) Hiraoka, K.; Morise, K.; Nishijima, T.; Nakamura, S.; Nakazato, M.; Ohkuma, K. Int. J. Mass Spectrom. Ion Processes 1986, 68, 99.
I
I
I
I
t
t
10°1
0
I
100 PRESSURE
I
200 OF W A T E R
300 (mTorr)
Figure 1. Some of the determinations of the temperature and pressure dependences of the equilibrium constants for the reaction H30++ H 2 0 = H+(H20)2.
reaction 1 with n = 1, it was necessary to increase the ion source temperature above 500 OC. It was difficult to get this high temperature with the jacket because the cartridge heaters embedded in the jacket were burnt out due to the overheating. Thus we abandoned the idea of using the jacket for heating and cooling the ion source block. We made a new ion source of solid stainless steel block. The ion source was heated by six cartridge heaters (Watlow E2A55, 120 V, 100 W) that were embedded directly in the ion source block. The ion source temperature above 500 O C could be easily obtained with much less than the maximum hedter capacity. The thermocouple embedded deep in the ion source block and close to the inner wall of the ion source was used for measurement of the ion source temperature. On the top of the ion source, 1-mm-thick mica and 5-mm-thick stainless steel sheets were placed for the base of the ion accelerating grids. The mica sheet works as a heat insulator as well as an electric one. The procedure of the ab initio MO calculation is briefly described. The geometry of the protonated monomer H+-B is optimized with the STO-3G basis set. The electron density is evaluated with the one-point calculation of 4-31G (4-31G// STO-3G). The STO-3G structure is known to be acceptable, as far as covalent bonds are dealt with. The usage of such small basis set arises from the need of determining the geometry of the large-size ~pecies(e.g., 2-methyltetrahydrofuran). The 4-3 1G basis set tends to overestimate the dipole moment (i.e., charge separation between '6 and 6-). However, only the relative values are important in the present analysis, and the 4-3 1G electron density is meaningful. All the MO calculations are carried out with the GAUSSIAN 80 program.I0
Experimental Results An example of the measurements of equilibrium constants for reaction 1 with n = 1 is given in Figure 1. Shown are the experimentally determined equilibrium constants K at different temperatures and pressures. The equilibrium constants are independent of the change of water pressure over 1 order of magnitude. van't Hoff plots of the data for the equilibrium reaction 1 with n = 1 and 2 are shown in Figure 2. The obtained -AHo 1,2 and from Figure 2 are 35.0 kcal/mol and 30.2 cal/mol K, respectively. The obtained values are in good agreement with the recent theoretical values (Le., = 35.5 kcal/mol and = 28.8 cal/mol K)6 but only in fair agreement with the previous experimental values (Le., -W 1,2 = 3 1.6 kcal/mol and = 24.3 cal/mol K) obtained by Cunningham et al.' The van't Hoff plots obtained by Cunningham et al.' are shown in (10) Binkley, J. S.;Whiteside, R. A.; Krishnan, R.; Seeger, R., DeFrees, D. J.; Schlegel, H. B.; Topiol, S.;Kahn, L. R.; Pople, J. A. QCPE 1981, 13, 406.
5912 The Journal of Physical Chemistry. Vol. 90, No. 22, 1986
t
Hiraoka et al.
lo3
n=l
IOZ
L
0
I-
IO'
7
Y
loor
t
-' u
IO
15
2 0
1000 T("K)
IO'
2 .o
1.5
Figure 3. van't Hoff plots for clustering reactions of protonated tetrahydrofuran (THF) and 2-methyltetrahydrofuran (2-MTHF): (0) H+(THF) THF = H+(THF)2; (A) H'(2-MTHF) 2-MTHF = H+(2-MTHF)2. Equilibrium constants given for pressure in Torr.
+
1000/ T ( " K ) Figure 2. van't Hoff plots for clustering reactions: (0)H30+(H20)rl H 2 0 = H30+(H20),,with n = 1 and 2; (A) (CH3)+20H+ (CH3)$0 = H+((CH3)2CO)2.Equilibrium constants given for pressure in Torr. The broken lines represent the van't Hoff plots obtained by Kebarle and co-workers.'
+
+
TABLE Ik Proton Affiities (PA) and Bond Energies (-AHo) in the Svmmetric Proton-Held Dimer Cations and Proton Electronic Densitv PA,' -AHo, proton molecule kcal/mol kcal/mol electr densityb
TABLE I: Thermochemical Data from Protonated Clusters in Equilibria'
+ H20 = H+(H20)2 H+(H20), + H 2 0 = H+(H2O)3 (CH3)2COH+ + (CH3)ICO = H+((CH3)2C0)2 H'(H20)
C4HSOH' + CdHsO H+(C,HsO), CSHloOH+ + C5HloO = H+(C5Hlo0)2
H2 0 2
N2 35.0 31.6b 20.2 19.5b 29.6 3O.lc 29.9d 27.4'
co
30.2 24.3b 23.6 21.7b 29.3 30.4' 29.1d 26.5e
CH4 HF H2O CHjOH CZHSOH n-C,H,OH i-C3H,0H (CH3)20 (C2H5)20 THF 2-MTHF (CH3)2CO NH3 CH3NH2 (CH3)ZNH (CH3)3N CH3CN pyridine
' A H o in kcal/mol, ASoin cal/(K mol). bReference 7. 'Reference 5. dSolvent molecule B is tetrahydrofuran. CSolventmolecule B is 2-methyltetrahydrofuran.
Figure 2 as a broken line. The slope of the van't Hoff plots obtained by us is slightly steeper than that obtained by Cunningham et al.' In order to examine the reliability of our data for reaction 1 with n = 1, the temperature dependence of equilibrium constants for reaction 1 with n = 2 and reaction 2 were measured. The van't Hoff plots obtained for these reactions (solid lines in Figure 2) are in excellent agreement with those obtained by Kebarle and c o - w o r k e r ~ .The ~ ~ ~observed good agreement may verify the reliability of our thermochemical data for reaction 1 with n = 1. We are afraid that in their early measurements Cunningham et al. had some problem in temperature measurements, especially in the higher temperature region. The new measurements of the van't Hoff plots for reactions 3 and 4 are shown in Figure 3. The thermochemical data obtained are summarized in Table I. Discussion The proton affinities (PAS),the bond energies of the symmetric proton-held dimer cations, and the electronic density on the proton
+
101.3 100.9 118.2 141.9 132.0 95.51 166.5 181.9 188.3 190.8 191.2 192.1 200.2 198.8 203.6 196.7 204.0 214.1 220.6 225.1 188.4 220.8
9.6c 20.6d 16.0d 12.8d 7.4e 29 35.09 33.1h 32' 3 1.6' 3 1.9' 30.7h 29.v 29.98 27.4% 29.68 25.4k 21.7' 20.8' 22.5' 30.2'" 24.6"
0.667 0.376 0.484 0.661 0.348 0.417 0.435 0.443 0.444 0.464 0.449 0.460 0.467 0.479 0.497 0.524 0.534 0.546 0.555 0.455 0.524
'Reference 22. "he electronic density on the proton of H+-B computed with MO of the 4-31G basis set. N 2 > CO. The order is opposite to that of the proton affinities of 02,N2, and CO. The larger proton affinity means that the positive charge is more delocalized in the protonated species. The electronic density on the proton of H+N2and H+CO shows this trend in Table I1 (CO and H2 are isoelectronic). The charge accumulation on the proton enhances the exchange repulsion between B and H+B.
This effect decreases the attractive term, the charge-transfer interaction, and gives the smaller - A P . For nondipolar solvent molecules Bs, there is no electrostatic contribution. The tendency is clearly seen in the hydrogen molecule affinities of 02H+,N2H+, and OCH', which are also shown in Figure 4.12*23 Since the solvent molecule H2is common for all these cluster ions, the bond energies of these clusters can be regarded as a scale of positive charge availability on the hydrogen atom in the cation BH+. For a-electron molecules H2 and CH4, the similar tendency is also observed. The protonation of H2and CH4gives the geometric distortion to give the less acidic (0.667 and 0.661 in Table 11) hydrogens. It is worthwhile to note that -AH0(H3+--H2) is much lower than -AHo(02H+- -02), although the proton affinities of H2 and O2are almost the same. In these clusters without the electrostatic term, the charge-transfer interaction is the dominant attractive (exothermic) component for AHo. In the cluster H3+--H2, the solvent hydrogen molecule approaches one of the three corner protons of H3+axially and the electrons partially transfer to the vacant orbital of H3+.24925 H
&'IH In such an arrangement of species in the cluster, the overlap of (13) Hiraoka, K.; Kebarle, P. J. Am. Chem. Soc. 1975, 97, 4179. (14) Grimsrud, E. P.; Kebarle, P. J . Am. Chem. Sm. 1973, 95, 7939. (15) Larson, J. W.; McMahon, T. B. J. Am. Chem. Soc. 1982,104,6255. (16) Lias, S.G.; Liebman, J. F.; Levin, R. D. J. Phys. Chem. Ref.Datu 1984, 13,695. (17) Bomse, D. S.;Beauchamp, J. L. J . Phys. Chem. 1981, 85, 488. (18) Meot-Ner, M. J . Am. Chem. SOC.1978, 100, 4694. (19) Meot-Ner, M. J. Am. Chem. Soc. 1984,106, 1257. (20) Tang, I. N.; Castleman, A. W., Jr. J . Chem. Phys. 1975, 62, 4576. (21) Meot-Ner, M.; Sieck, L. W. J . Am. Chem. SOC.1983, 105, 2956. (22) Lias, S.G.; Liebman, J. F.;Levin, R. D. J . Phys. Chem. Ref.Datu 1984,13,695. (23) Hiraoka, K.; Kebarle, P. J. Chem. Phys. 1975,63, 1688. (24) Yamabe, S.; Hirao, K.; Kitaura, K. Chem. Phys. Lett. 1978,56,546 (25) Hirao, K.; Yamabe, S.Chem. Phys. 1983, 80, 237.
O3
NH,
2-MTHF
0
Q.
(CH,),N
CH3NHz.
20
(CH,),NH
150
190
170
210
230
PROTON AFFINITY ( k c a l / m o l ) Figure 5. Dependence of the bond energies -AHo of proton-held symmetric dimers on the proton affinities.
the molecular orbitals of these two species cannot be great because the electrons of H2 are mainly distributed along the molecular axis. Besides, the exchange repulsion between the a l MO of H3+ and the ugMO of H2prevent the closer approach. These effects make the charge-transfer interaction relatively weak. On the other hand, in the case of 02H+--02, the central proton is attacked by highly directional sp2 orbitals of two O2 molecules.1*26 Such an interaction makes the overlap of the molecular
orbitals greater and thus the bond energy becomes stronger. For symmetric clusters of nondipolar solvent molecules (electrostatic term absent), the presence or absence of lone-pair orbitals gives the crucial difference of the charge-transfer interaction, i.e., W s . Figure 5 shows the dependence of the bond energies of H+(B)2 on the proton affinities for B that is protic and aprotic solvent molecules. When B is a polar solvent molecule, the bonding power B- -H+B is mainly electrostatic as in hydrogen bond systems. Therefore, the electronic density of the proton of H+-B is the most significant criterion to determine the strength of the electrostatic attraction and the exchange repulsion. In Table 11, the general tendency that the larger proton electronic density corresponds to the smaller -AHo is observed. For H 2 0 and alcohols, a linear decrease in - N o s is observed with an increase of PAS. It is evident that the bond energies of proton-held dimers bonded by hydrogen bonds decrease as the PAS of molecules B increase. For ethers, a similar linearity seems to exist as in the case for H20and alcohols. However, the values of -AHolocate somewhat lower than the extrapolated line for H20 and alcohols. For H+(ROH), two protons H, and H, are equivalent.
/H
R)--Q ''\I
'.HA
46i
\04A
/"-R
He
(26) Yamabe, S.;Hirao, K. J . Am. Chem. SOC.1981, 103, 2176
5914
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
In the cluster RO(H)- -H,+ROH,, the 0--Hb electrostatic attraction is effective as well as the 0--Ha attraction. This 0--H, secondary effect strengthens the ROH- -H+ROH bonding energy. On the other hand, the proton H, is not available in ethers, which results in the smaller -AHo. For the aprotic solvent (CH3)2C0,-AHo is even lower than those for ethers, reflecting the larger proton electronic density (0.497) in Table 11. A rather drastic decrease in the values of -AHo is observed for NH3 and amines as shown in Figure 5. Since nitrogen is less electronegative than oxygen, the positive charge of the protonated nitrogen bases can be more delocalized than that of the protonated oxygen bases. In addition, on the protonation of NH3 and amines, well-defined sp3 hybridization orbitals are realized and the positive charge is dispersed most uniformly in the protonated species. This well-dispersed positive charge in H+B is considered to make the mainly electrostatic interaction between the protonated species and solvent molecules weaker. As shown in Table 11, the gas-phase basicity order of aliphatic amines are NH, C CH,NH2 C (CH3)2NH < (CH&N. The calculated proton electronic densities of protonated amines H+Bs increase in the same order. These results suggest the order of -AHo as NH, > CH3NH2> (CH3)2NH> (CH&N. However, as shown in Figure 5, -AH’’for (CH&N is larger than those for (CH3)2NHand CH3NH2. The observed inconsistency may be due to the experimental error in the determination of bond energies -AHo for amines. Lee and co-workers measured PA = 95.5 kcal/mol for H F and -AHo = 25 kcal/mol for H+(HF)2by the molecular beam photoionization method.27 The data do not fit our PA vs. -AHo correlation in Figure 5 at all. The electron density on two protons of H2F+,0.348, indicates that the value of -AHo obtained by Lee and co-workers is too small. To judge the energetic accuracy, the 6-3 1G** geometry optimization is made. Theoretical data, PA = 127 kcal/mol and -AHQ = 34 kcal/mol, are obtained. A theoretical study of H+(HF)2was reported primarily by Kraemer et a1.28a Recently, Pople et al. estimated these energies with the more rigorous wavefunction, MP4SDQ/6-3 1 + G(d,p).28b They gave PA = 121 kcal/mol and -AHo = 32 kcal/mol. In view of our and these theoretical results, -AHo for HF- -H+FH should lie between 30 and 35 kcal/mol. (27) Tiedeman, P. W.; Anderson, S. L.; Seyer, S. T.; Hirooka, T.; Ng, Y. C.; Mahan, 9. H.; Lee, Y. T. J . Chem. Phys. 1979, 71, 605. (28) (a) Diercksen, G. H. F.; von Niessen, W.; Kraemer, W. P. Theor. Chim. Acta 1973, 31, 205. (b) Del Bene, J. E.; Frisch, M. J.; Pople, J. A. J . Phys. Chem. 1985, 89,3669.
Hiraoka et al. Concluding Remarks
When the proton affinity of a molecule B increases, the bond energy of the symmetric proton-held dimer cation H+(B), generally decreases. The bonds in proton-held dimers are strongly electrostatic by nature but still include an essential charge transfer.29 For nondipolar solvent molecules, the extent of how the exchange repulsion attenuates the charge-transfer interaction is the crucial factor. The experimental results indicate that the positive charge on the protic hydrogen atom in the protonated molecule BH+ plays a most important role for the determination of the bond energies of H+(B)2. The intrinsic molecular properties of B are reflected characteristically on the bond energies of H+(B)2. The qualitative interpretation of the bond energies of proton-held dimers is given. Finally, two isoelectronic clusters are exhibited to clarify our discussion. The optimized geometries are taken from l i t e r a t ~ r e . ~ ” ~
H 20 PA. 166.5 kcallmol
NH3 PA= 204.0 kcallmol
Acknowledgment. K.H. is greatly indebted to Professor P. Kebarle of the University of Alberta for his help. The financial support of the Grant-in-Aid from the Ministry of Education is gratefully acknowledged. We thank the Institute for Molecular Science for the allotment of the CPU time of the HITAC M-200H computer. Registry No. Hz, 1333-74-0; 02,7782-44-7; N2, 7727-37-9; CO, 630-08-0; CH4,74-82-8; HF, 7664-39-3; Hz0,7732-18-5; CH3OH, 6756-1; CzH50H, 64-17-5; n-C3H70H, 71-23-8; i-C3H70H, 67-63-0; (CHJ20, 1 1 5-10-6; (CZH5)20,60-29-7; THF, 109-99-9; 2-MTHF, 9647-9; (CH3)2CO, 67-64-1; NH3, 7664-41-7; CHjNH2, 74-89-5; ( C H,),NH, 124-04-3; (CH3),N, 75-50-3; CH3CN, 75-05-8; pyridine, 110-86- 1 . (29) Hirao, K.; Yamabe, S.; Sano, M. J. Phys. Chem. 1982, 82, 2626. (30) Hirao, K.; Fujikawa, T.; Konishi, H.; Yamabe, S . Chem. Phys. Lett. 1984, 104, 184.
