10261
J. Phys. Chem. 1992,96, 10261-10264
(8) Kato, T.;Kodama, T.; Oyama, M.; O W , S.;Shida,T.; Nakagawa, T.; Matsui, Y.; Suzuki, S.;Shiromaru, H.; Yamauchi, K.;Achiba, Y. Ch" Phys. Lett. 1991, 186, 35. (9) An aging effect is observed for pure C a which is revealed by an appearanceof a weak ESR signal with 1-24 line width and g = 2.0024. The ColleldoILs intensity of this signal also depends on any heat treatment. (10) Chakravarty, S.;Kivelson, S.A.; Salkola, M.I.; Tewari, S . Sclence During about 24 h the ESR signals of Rb3Ca evolve with time. 1992,256, 1306. This is suggested to be related to diffusion of the Rb atoms within (11) Stewart, G. R. Reu. Mod.Phys. 1984.56.755. the Cm crystallites. Near T, the ESR susceptibility is found to (12) Fisk, 2.;Hew, D. W.; Pethick, C. J.; Pines, D.; Smith, J. L.; Thompson, J. D.; Willis, J. 0. Science 1988, 239, 33. change from antiferromagnetic to paramagnetic behavior. The (13) Bames, S.E. Adu. Phys. 1981, 30, 801. magnitude of the ESR susceptibility is described by a two-com(14) Anderson, P. W.; W e b , P. R. Reu. Mod.Phys. 1954, 25, 269. ponent model of localized and conduction electrons. The ESR (15) Fleming, R. M.;Ramircz, A. P.; Raseinsky, M.J.; Murphy, D. W.; signals of K3Ca and Cs3Ca also show a similar timedependent Haddon, R. C.; Zahwak, S. M.;Makhija, A. V. Nature 1991, 352, 787. (16) Duclos, S.J.; Haddon, R. C.; Glarum, S.;Hebard, A. F.; Lyons, K. behavior. B. Science 1991,254, 1625. (17) Gu, C.; Stepniak, F.; Poirier, D. M.; Jost, M.B.; Benning, P. J.; Chcn, Acknowledgment. This research was supported by the Texas Y.; Ohno, T. R.; Martin, J. L.; Weaver, J. H.; Fure, J.; Smalley, R. E. Phys. Center for Superconductivity at the University of Houston under Reu. B 1992, 45, 6348 and references therein. Grant MDA972-88G-OOO2 from the Defense Advanced Research (18) Kinoshita, N.; Tanaka, Y.;Tokumoto, M.;Matsumiya, S. J. Phys. Projects Agency and by the state of Texas. Soc. Jpn. 1991,60,4032. (19) Kortan, A. R.; Kopylov, N.; Glarum, S.;Gyorgy, E.M.; Ramirez, A. RWhy NO. Rb&, 137926-73-9; K3Cw 137232-17-8; C S ~ C ~ , P.; Fleming, R. M.;Thiel, F. A,; Haddon, R. C. Nature 1992, 355, 529. 140883-40-5; Na3Cw 139242-45-8. (20) Jorgensen, J. D.; Pei, S.;Lightfoot, P.; Shi,H.; Paulikas, A. P.; Veal, B. W. Physica C 1990,167, 571. Rdereaees d Notes (21) See for instance: Ashcroft, N. W.; Mermin, N. D. Solid Srare (1) Bensebaa, F.; Xiang, B.; Kevan, L. J. Phys. Chem. 1992, 96, 6118. Physics; Holt, Rinehart and Winston: New York, 1976; p 661. (2) Haddon, R. C.; Hebard, A. F.; Raseinsky, M.J.; Murphy, D. W.; (22) Holczer, K.;Klein, 0.; Grflner, G.; Thompson, J. D.; Diederich, F.; Duclos, S.J.; Lyons, K. B.; Miller, B.; Rosamillia, J. M.;Fleming, R. M.; Whetten, R. L. Phys. Rev. Lett. 1991, 67, 271. Kortan, A. R.; Glarum, S.H.; Makhija, A. V.; Muller, A. J.; Eick, R. H.; (23) Morya, T. Spin Fluctuation in Intinerant Electron Magnetism; Zahurak, S.M.;Tycko, R.; Dabbagh, G.; Thiel, F. A. Nature 1991,350,320. Springer-Verlag: Berlin, 1985. (3) Zhakhidov, A. A,; Ugawa, A.; Imaeda, K.;Yakushi, K.;Inokuchi, H.; (24) Zhang, Z.; Lieber, Ch. M.Mod.Phys. Lett. 1991, BS, 1905. Kikuchi, K.;Ikemoto, I.; Suzuki, S.;Achiba, Y. Solid State Commun. 1991, (25) Chakaravarty, M.;Gelfand, M.P.; Kivelson, S . Science 1991, 254, 79, 939. 166. (4) Glarum, S.H.; Duclos, S.J.; Haddon, R. C. J. Am. Chem. Soc. 1992, (26) Gelfand, M. P.; Lu, J. P . Phys. Rev. Lett. 1992, 66, 1050. 114, 1996. (27) Ogata, H.; Inabe,T.; Hashi, H.; Maruyama, Y.; Achiba, Y.; Suzuki, (5) Tycko, R.; Dabbagh, G.; Roaseinsky, M.J.; Murphy, D. W.; Fleming, S.;Kikuchi, K.;Ikemoto, I. Jpn. J . Appl. Phys. 1992, 31, 166. R. M.;Ramirez, A. P.; Tully, J. C. Science 1991, 253, 884. (28) Ogawa, M.Y.; Hoffman, B. M.;Lee, S.;Yudkowsky, M.; Halperin, (6) Hugha, A. E.;Jain, S.C. Adu. Phys. 1979, 28, 717. W. P. Phys. Rev. Lett. 1986,57, 1177. (7) Allemand, P. M.;Srdanov, G.; Koch,A.; Khemani; K.;Rubin, Y.; (29) Pedersen. H. J.; Scott, J. C.; Bechgaard, K.Solid State Commun. Diederich, F.; Alvarez, M.M.; Anz, S.J.; Whetten, R. L. J. Am. Chem. Soc. 1980, 35, 207. 1991, 112,2780, (30) Yafet, Y. Solid State Phys. 1963, 14, 1.
detected by ESR (3%), the second part comprises the electron pairs which participate in superconductivity, and the third part comprises electron spins arranged antiferromagnetically.
A Correlation between Proton Aff lnities and Intramolecular Hydrogen Bonds in Bifunctional Organic Compounds S . Yambe,* Department of Chemistry, Nara University of Education. Takabatake-cho, Nara 630, Japan I(. Hirao,
Department of Chemistry, College of General Education, Nagoya University, Nagoya 464- 01, Japan
and H.Wasada Department of Chemistry, College of General Education, Gifu University, Gifu 501 - I I , Japan (Received: June 17, 1992; In Final Form: September 15, 1992)
The geometries of diethers, diketones, and diamines and their protonated species are determined with the ab initio calculati~n~ of RHF/3-21G. The theoretical proton affinities (PA's) of MP2/6-31(+)G(**)//RHF/3-21G reproduce well experimental PA's. A good correlation between PA's and hydrogen-bond angles is found. As the alkyl size increases, the angles and ring strains at the sp3 carbons become larger, which leads to a "saturation" of PA values.
I. Iatrodpetioa In protonated polyfunctional organic molecules, intramolecular hydrogen bonds play an important role to stabilize the ions. The intramolecular hydrogen bond gives stabilization by up to 20 kcal/mol in diamines and amino alcohols.' The intramolecular hydrogen bond is also of biological importance in protonated peptide8 and ionic intermediates in enzyme processes. Gas-phase proton affinities (PA's) of many organic molecules have been measured, and a correlation between PA values and the strengths
of the intramolecular hydrogen bonds has been suggested in ions of polyfunctional g r o ~ p . These ~ . ~ studies of protonated di- or polyether compounds stated that the G H + - -0hydrogen bond plays a central role in PA values and that structural information is needed for rationahhg more clearly the differences of the PA's in a series of organic compounds. Although there are many observed PA's related to the intramolecular hydrogen bond, explicit struchuc analyses have not been made and it is tempting to investigate the PA-~tructurecomlation
0022-3654/92/2096- 10261$03.00/0 Q 1992 American Chemical Society
-
10262 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
theoretically. Theoretical interest is also compared between o b served and calculated PA'S of large organic compounds of bifunctional groups. In this work, in order to d e the structural effect on PA's, those of diethers (2-9, diketones (7-9), and
n-4
}
n-5
J
n-3
BSSE
p\,
Me
n-2
}
R
R
MeA(az/\Me H
n-4
HzN-
>0
Step 5. The basis-set superposition error (BSSE) is estimated by the Boys-Bernardi counterpoise method.'O
Me/'\(adn/o\Me
.cstoac
n- 1
AE = MP2(A) - MP2(B) < 0
= E~b(protonated)- &,(neutral)
0
n-0
without the proton and the ghost orbital on the (A) geometry. Step 3. An electronic binding (stabilizing) energy, -AE,is computed.
sbep A The difference of vibrational energies, A&,, is obtained, after all the species 14 neutral and 14 mtonated) are found not to have imadnary abrational frequerkies.
Me /O\Me n-2
Yamabe et al.
(adnj-NH2
n-5
diamines (11-14) are obtained with ab initio calculations. The experimental values of them have been reported. 1,6, and 10 are standard compounds of monofunctional groups used to check the theoretical PA's relative to the observed ones. It will be shown that the alkyl-chain growth (n larger) leads to saturation of the hydrogen-bond angle and consequently to saturation of the PA's.
-
11. Method of CaIcStions There have been various ab initio calculations on monofunctional compounds.c9 Among them, DeFrees and McLean studied the PA's of small molecules with high-accuracy calculations, MP4/6-31++G**.5 They concluded that the diffuse basis functions and the even orders of perturbations are needed so as to obtain reliable PA's of large molecules. Even by the highaccuracy calculations, however, there are a few kilocalories/mole differences in the PA's of some small molecules between experiment and theory, e.g., 2.5 kcal/mol for methane' and 2.5 kcal/mol for water? For ortho-substituted pyridines, simplification of G* to G(*) has only a negligible effect on the computed PA'S.* In this present work, the PA's of 1-14 are calculated with the following procedure. Step 1. The geometries of neutral and protonated species are fully optimiztd with RHF/3-21G, fdloweed by vibrationalanalyses. Step 2. Four types of singlepoint calculations, MP2/6-31(+)G(**), are made on RHF/3-21G geometries. They are MP2(A), MPZ(B), MPZ(C), and MP2(D). MP2 is the total energy of the second-ordcr Meller-Plesset perturbation method. In 6-3l(+)G(**), (+) means that diffuse sp functions are added to only two heteroatoms (oxygen or Ntrogen), the fvst (*) meam augmentation of six d orbitals on the two heteroatoms, and the second one stands for the addition of a ad of ptype GTOs on each proton (not hydrogen). W ( A ) is thetotal QIC~BYof a protonated species. MPZ(B) is that of a neutral species. MP2(C) is that of a neutral species with a set of ghost orbitals on the proton position of the (A) geometry. MPZ(D) is that of a neutral species
MP2(D) - MP2(C) > 0
Step 6. A theoretical PA ( P h l C )is given by the use of AE, & ? & band , BSSE.
-P&lf
ZG
AE + h E v i b
+ BSSE + (-5/2)RT
(-5/2)RTis the thermal correction of translation and rotation (T = 298.15 K). All the calculations are performed using the GAUSSIAN 90 program" installed on the CONVEX C-220 computer at the Information processing Center of Nara University of Educetion and using the GAUSSIAN 8612program installed on the HITAC M-680H computer at the Institute for Molecular Science. Table I exhibits P h I cvalues and their three components together with reported experimental data, p&@. (I) In general, as methylene groups increase, PA becomes larger. However, at n = 4 (butane) 5 (pentane), the PA's do not change in diether and diamine. While BSSE increases slightly with the size of n, AEdb is almost independent of n. Thus, the sowth of the PLb's comes from that of electronic ener". U s . - (2) The discrescy between P& and P& is not &&matic. In ethers and amines, P L l Cvalues are overestimated, whereas in diketones they are underestimated. The disagreement in 7 ( P h , = 184.61 vs 194.80) is the largest. In view of other data, some part of this disagreement might come from experimental errors such as scatters in van't Hoff plots.2 The trend of the increase in P&lc as n increases is similar to that in PA,,@. (3) A surprising result is found in the P&k values of 13 and 14 (241.84 and 239.22 kcal/mol). This decrease as n increases must be rationalized in terms of the geometric change, n = 4 5. (4) Among 11 protonated species with intmnolacular hydrogen bonds (bridged form), 7H+has the largest ring strain and an open
-
-
d e ' Me bridge form
m+
open form
protonated form might be more stable. However, the bridge form is found to be more stable than the open form by 5.5 kcal/mol
at MP2/6-31(+)G(**). Thus, all the protonated species are of the bridge form. Figure 1 shows the geometries of the protonated diethers. ( 5 ) As n becomes larger, the angle 0-H- -0approaches 180° asymptotically and the proton is shifted midway. Thus, as far as the linearity of the hydrogen bond is concerned, saturation of the PA values at around n = 5 is understandable. A question arises: for n > 5 , do PA values become constant? (6) In S H ' , sp3 C-C-C bond angles are 108.8, 114.8, and 1 17.0°, the latter of which are appreciably larger than the normal angle, 109.5O. It is anticipated that protonated diethers of n > 5 suffer from ring strain at the sp3bond angle, leading to decay in the PA values.
-
A Correlation in Bifunctional Organic Compounds
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10263
TABLE I: clrleulrted ( P L )and Observed ( P L )Proton Affinities" functional group no. ether
ketone
compd
1 dimethyl ether 2 1,2-dimethoxyethane 3 1,3-dimethoxypropane 4 1,Cdimethoxybutane 5 1,s-dimethoxypentane 6 acetone 7 2,3-butanedione 8 2,4-pentanedione
Mvib
BSSE
[RHF/3-2lG]
[MP2/6-31(+)G(**)]
-202.38 -2 17.22
8.44 8.12
2.91 3.72
-192.51 -206.86
-192.10(") -2M.iW(2)*(3)
-229.3 1
6.78
4.17
-219.84
-213.809')
-236.46
7.22
4.66
-226.06
-221.80(')*(')
-236.89
7.40
4.61
-226.36
-221.80(')
-201.09 -193.58 -21 3.19
7.99 7.67 7.45
2.53 2.79 3.05
-192.05
-1 96.70(')*(16) -194.80(') -207.80(')
-219.91
7.08
3.42
-2 10.89 -2 13.20(')
-239.13 -244.21
10.33 10.51
3.60 4.65
-226.68 -230.53
-220.60(") -225.90(13)
NHz(CH2)jNHz
-251.42
10.06
5.26
-237.58
-234. 10(13)-('4)
NHz(CHz),NH2
-255.74
9.89
5.51
-241.82 -237.60(")0('~)
NH2(CH2)5NH2
-253.68
10.28
5.68
-239.20 -238.10(")
CH30CH3 CH,O(CH2)20CH3 CH30(CH2),0CH3 CH30(CH2)40C-
-P&
-P&,
H3
CH30(CH2)50CH3 CH3COH3 CH3COCOCH3 CH3COCH2COCH3 CH3CO(CH2)2COCH3 CH3NHCH3 NH2(CH2)2NH2
9 2,s-hexanedione amine
AE [MP2/6-31G(+)G(**)]
rational formula
10 dimethylamine 11 1,2-diaminoethane 12 1,3-diaminopropane 13 1,ediaminobutane 14 1,S-diaminopentane
-184.60 -204.17
"In kcal/mol. - P k k = AT + A T Y + ~ ~BSSE (-5/2)RT. -AE is the electronic binding energy, is the difference of vibrational energies, and BSSE is the counterpoise correction of basis-set superposition error. (-5/2)RT is the thermal correction of translation and rotation (T= 298.15 K).
3
F i p e 2. Geometries of protonated diketones.
11H+
12H+
Figwe 1. Geometries of protonated diethers optimiz+d with RHF/3-21G. Empty circles denote hydrogen atoms, and black circles stand for protons.
Figure 2 exhibits three protonated diketones. (7) As expected in 7H+, the hydrogen-bond angle is small (=lOS.Oo). An increase of methylene groups (n larger) leads sensitively to the linearity of the hydrogen bond. Whereas the geometries of neutral molecules are usually of high symmetry, that of 8 is found to be of no symmetry. This anomalous structure
-
8
is ascribed to an intramolecular charge transfer. That is, two carbonyl groups have appropriate positions for intramolecular nucleophilic attack on the unsaturated carbon. In fact, the atomatom bond population along the bold empty arrow is positive (bonding). Figure 3 displays the geometries of protonated diamines.
Figure 3. Geometries of protonated diamines.
(9) Like in protonated diethers, an increase in the alkyl size sharply changes the N-H- - -N hydrogen-bond angle. (10) An anomal is found in hydrogen-bond lengths, 1.494 A in 13H+vs 1.536 k i n 14H+.Usually the larger NH---N angle corresponds to the smaller length. The anomaly originates probably from the strained sp3 angles (1 14.4 and 116.2O) in the
10264 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
Yamabe et al. Recently, Meot-Ner and Siech reported revised values of P&,18 The new values of the amines are much larger than the old ones, e.g., 204.0 (old) 208.3 kcal/mol (new) for ammonia and 220.8 (old) 229.2 kcal/mol (new) for tert-butylamine. At the latter case, the experimental error is 8 kcal/mol. A&, and BSSE are almost independent of the size (n) of the alkyl chains, and the change in the PA values as n increases is ascribed to that in electronic stabilizing energies.
- -
di-amine
Acknowledgment. We thank Miss Sayuri Tagou and Miss Yoshiko Tanaka for their assistance in the computations. The present research is supported in part by a Grant-in-Aid for Scientific Research on Priority Area "Theory of Chemical Reactions" from the Ministry of Education, Science and Culture. RNO. 1, 115-10-6; 2, 110-71-4; 3, 17081-21-9; 4, 13179-96-9;
,I
250
B j
d
240
--
230
--
190 --
I I
,
I
,
1
5, 111-89-7; 6, 67-64-1; 7,431-03-8; 8, 123-54-6; 9, 110-13-4; 10, 12440-3; 11, 107-15-3; 12, 109-76-2; 13, 110-60-1; 14, 462-94-2.
References pad Notes
210 200 -
I
0
a.''
,...".. O+-....-,"di-ketone 0
/
(1) (a) Yamdagni, R.; Kebarlc, P. J . Am. Chem.Soc. 1973,95,3504. (b) Meot-Ner (Mautner), M.; Hamlet, R.; Hunter, E. P.; Field, F. H. Ibid. 1980. 102,6393. (2) Meot-Ncr (Mautner), M. J. Am. Chem. Soc. 1983, 105, 4906. (3) Sharma, R. B.; Blades, A. T.; Kebarle, P. J . Am. Chem. Soc. 1984, 106, 510. (4) Meot-Ner (Mautner), M.; Liebman, I. F.; Del Bene, J. E. J . Org. Chem. 1986.51. 1105. ( 5 ) DeFrccs, D. J.; McLean, A. D. J. Compur. Chem. 1986, 7 , 321. (6) Schmicdekamp,A.; Smith, R. H., Jr.; Michejda, C. J. J. Org. Chem.
180
Figure 5. P&-Pkk afinitica.
,
I
I
I
plot for showing the correlation of two proton
alkyl chain of 14H' and gives the reault of PA& 13) > P&( 14) in Table I. For n > 5, the PA would gradually decrease after "saturation". Figure 4 shows a relationship between the PA values and the calculated hydrogen angles. Three groups follow the same trend toward saturation.
IV. Concluding Remarks The proton affinities of organic molecules of bifunctional groups have been calculated. The role of intramolecular hydrogen bonds in protonated species has been described in terms of two opposing components, its linearity and ring strain at sp3carbons. As the alkyl size increases, PA values go to saturation. Agreement between the computed and observed PA values is not perfect but satisfactory, because PA values are generally difficult properties to reproduce. F i i 5 show a plot of P h vs P& values taken from Table I. Another source would be in experimental data.
--.
1988.53.3433. --, ~
A'
(7) Martin, J. M. L.; Francois, J. P.; Gijbels, R. J . Compur. Chem. 1989, 10, 346. (8) Williams. M. L.: Greadv. J. E. J . Comou?. Chem. 1989. 10. 35. (9) Pople, J. A,; Head-Gordon, M.; Fox, D. 5.; Raghavachari,'K.;'Curtiss, L. A. J. Chem. Phys. 1989,90, 5622. (10) Boys, S. F.; Bemardi, F. Mol. Phys. 1970, 19, 553. (11) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreeman, J. B.; Schleael. H. B.: Raahavachari. K.: Robb. M. A.: Binklev. J. S.: Gonzalez. C.: DeFrk, D. J.; Fox~D.J.; Whiteeide, R. A.; Seeger, R.;keliG, C. F.; &ker; J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople. J. A. Gaussian 90,Reuision F; Gaussian, Inc.: Pittsburgh, PA, 1990. (12) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; DeFrets, D. J.; Setger, R.; Whiteside, R. A,; Fox, F. J.; Fluder, E. M.; Topiol, S.;Pople, J. A. Gaussian 86; CamegieMeUonQuantum Chemistry Publishing Unit, Carnegie-Mellon University: Pittsburgh, PA 15213. (13) Aue, D. H.; Webb, H. M.;Bowers, M. T. J. Am. Chem. Soc. 1973, 95, 2699. (14) Lias, S. G.; Liebman, J. F.; Levin, R. D. J . Phys. Chem. ReJ Data 1984,13,695. (15) Sen Sharma, D. K.; Kebarle, P. Can. J . Chem. 1981, 59, 1592. (16) Bromilow, J.; Abboud, J. L. M.; Lebrilla, C. B.; Taft, R. W.; Scorrano, G.; Lucchini, V. J . Am. Chem. Soc. 1981, 103, 5448. (17) Aue, D. H.; Webb, H. M.; Davidson, W. R.; Vidal, M.; Bowers, M. T.; Goldwhite, H.; Vertal, L. E.; Douglas, J. E.; Kallman, P. A.; Kenyon, G. L. J . Am. Chem. Soc. 1980, 102, 5151. (18) Meot-Ner (Mautner), M.; Siech, L. W. J. Am. Chem.Soc. 1991,113, 4448.
