J. Phys. Chem. 1985,89, 3053-3060 actions reveal that in these systems waves travel faster in the upward direction, in accordance with the simpler view of convection given above. A further corollary is that waves in an endothermic reaction will display a %verse gravity effect”. W e have not been able to find an endothermic system which propagates chemical waves. The experiments in which tube diameters and depths of solution were varied or in which silica gel or glass powder was added are consistent with the above interpretation but suggest that other factors such as viscosity, diffusion, and heat condktion also play a role in determining the wave velocity. Thus, while it may be possible to minimize or eliminate convection, e.g., by using silica (21) Showalter, K., private communication. (22) Nagypal, I.; Epstein, I. R.; Kustin, K., to be submitted for publication.
3053
gel, one must then consider changes made in the other transport properties before attempting to model the “chemical” portion of the “unperturbed” wave. Whether earlier studies of chemical wave propagation will need to be reinterpreted to take into account the sort of hydrodynamic effects encountered here is a question worthy of consideration. Acknowledgment. This work was made possible by a US.Hungarian Cooperative Grant from the National Science Foundation (INT 8217658) and the Hungarian Academy of Sciences. It was also supported by N S F Grant CHE-8204085. We thank Mr. I. Lengyel and Dr. M. Crowley for experimental assistance, Prof. M. T. Beck for discussions and advice, and Prof. K. Kustin for a critical reading of the manuscript. Registry No. Fe, 7439-89-6; HNO,, 7697-37-2
Comparison between Proton Transfers Involving Carbonyl and Hydroxyl Oxygens Steve Scheiner*t and Eric A. Hillenbrand Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, Illinois 62901 (Received: March 4 , 1985)
Proton transfers between the carbonyl and hydroxyl groups of (H2CO-H-OH2)+ are studied by ab initio methods using a 4-31G* basis set. Also examined for purposes of comparison is (H20-H-OH2)+ in which the carbonyl is replaced by a hydroxyl. Energetics of preton transfer are calculated for a range of fixed values of interoxygen distance R and with all other parameters fully optimized. The (H2COH--OHZ)+configuration li4’4-6kcal/mol lower in energy than (H2CO--HOH2)+ n dis lengthened. The bamer for interhydroxyl for all values of R, although the energy bamers for proton transfer rise as the H b transfer in (H20-H-OHz)+ is consistently 1 kcal/mol higher than the hydroxyl to carbonyl barrier. Transfers are studied also with the angular orientation of one group held fixed with respect to the other. It is found that moving the hydroxyl group to lie along the C = O axis rather than along a carbonyl lone pair direction reverses the relative stabilities of (H2COH--OHz)+ and (H2CO--HOH2)+. Similar reversals occur for (HzOH--OH2)+and (H20--HOH2)+but are of smaller magnitude. In contrast to the above rotations within the plane of the oxygen lone pairs, out-of-plane distortions produce very little change in the relative stabilities of the two configurations. Although such distortions substantially raise the transfer barriers in (H20-H-OHz)+, the barriers in the carbonyl case remain essentially unaffected. The underlying reqsons for the above trends are analyzed in terms of deformation energies of individual configurations which are, in turn, rooted in H-bond strengths, intrinsic flexibilities, charge-dipole interactions, and angular dependence of electron densities.
The prevalence of proton transfers in chemical and biological processes has motivated a great deal of investigation of this elementary reaction step.’-’7 Most early experimental work dealt with transfers occurring in solution and the intrinsic properties of the process were thereby largely masked by solvent effects.I4 More recent techniques have made possible study of reaction 1 in the gas However, the large energy changes involved AH++B-
association
(AH--B)+
proton transfer.
in the association and dissociation steps have made it extremely difficult to isolate the fundamental features of the intermediate proton-transfer step. In order to help fill this gap, recent work in this laboratory has turned to a b initio molecular orbital methods.’8-z2 Previous calculations have shown the energetics of the transfer process to be sensitive to the geometry of the H-bonded complex (AH- -B)+. In addition, the rearrangements of the electron density that accompany the proton transfer have been studied in detqjl and related to the energetics. Whereas the previous calculations have dealt primarily with proton transfers between molecules (represented by A and B in reaction 1) consisting of only simple hydrides such as OHz and NH3, we extend the +prk to include somewhat more complicated groups here. Specifically, we consider the C=O carbonyl moiety NIH Research Career Development Awardee, 1982-87.
which is expected to provide an interesting comparison with the hydroxyl group -OH in which the oxygen is involved in single (1) “Proton Transfer Reactions”, Caldin, E., Gold, V., Eds., Chapman and Hall: London, 1975. (2) Grunwald, E.; Jumper, C. F.; Meiboom, S.J . Am. Chem. SOC.1962, 84. 4664. (3) Caldin, E. F. ‘Fast Reactions in Solution”; Wiley: New York, 1964. (4) Albery, W. J., in ref 1, pp 263-315. (5) Kluger, R.; Wong, M. K.; Dodds, A. K. J . Am. Chem. SOC.1984,106, 1113. (6) Alder, R. W.; Moss, R. E.; Sessions, R. B. J . Chem. SOC.,Chem. Commun. 1983, 999, 1000. (7) Engdahl, K-A; Bivehed, H.; Ahlberg, P.; Saunders, Jr. W. H. J . A m . Chem. SOC.1983,105,4767. (8) Menger, F. M.; Chow, J. F.; Kaiserman, H.; Vasquez, P. C. J . Am. Chem. SOC.1983, 105,4996. (9) Squires, R. R.; Bierbaum, V. M.; Grabowski, J. J.; D e h y , C. H. J . Am. Chem. SOC.1983, 105, 5185. (10) Farneth, W. E.; Brauman, J. I. J . A m . Chem. SOC.1976, 98, 7891. (11) Ausloos, P.; Lias, $. G. J . A m . Chem. SOC.1981, 103: 3641. (12) Mackay, G. I.; Tanner, S. D.; Hopkinson, A. C.; Bohhp, D. K. Con. J . Chem. 1979, 57, 1518. Bohme, D. K.; Rakshit, A. B.; Mackay, G. I. J . Am. Chem. SOC.1982, 104, 1100. (13) Rossetti, R.; Rayford, R.; Haddon, R. C.; Brus, L. E. J. Am. Chem. SOC.1981, 103, 4303. (14) Moylan, C. R.; Brauman, J. I. Annu. Rev. Phys. Chem. 1983,34, 187. (15) Meot-Ner, M. J . Am. Chem. SOC.1984, 106, 1257, 1265, 278. (16) Collyer, S. M.; McMahon, T. B. J . Phys. Chem. 1983, 87, 909. (17) Taft, R. W., in ref 1, pp 31-77. (18) Scheiner, S. J . Am. Chem. Soc. 1981,103,315. Ann. N.Y. Acad. Sci. 1981, 347, 493. J . Phys. Chem. 1982,86, 376. (19) Scheiner, S.J. Chem. Phys. 1982, 77, 4039, 1984, 80, 1982. (20) Scheiner, S.; Harding, L. B. J . Am. Chem. SOC.1981, 103, 2169. Chem. Phys. Lett. 1981, 79, 39. J . Phys. Chem. 1983,87, 1145.
0022-3654/85/2089-3053~01,50/0 0 1985 American Chemical Society
3054
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
Scheiner and Hillenbrand
TABLE I: Optimized Geometry of (HzCOH- -OHz)' and Isolated Subsystems' R(O0) r(OaHc) r(COa) ?(CHI) r(CH2) r(ObH) 6 cx (3 2.523
B(HICOa) O(H2COa) O(HObH)
(H2CO-H-OH2)' 111.1 153.2
1.018
1.220
1.076
1.079
0.954
5.2
0.966
1.230
1.076
1.078
0.948
H2COHt B(C0H) =
+ OH2
117.6
121.1
107.0
ESCF= -190.03497 au
116.2
121.7
105.3
ED = 30.0 (28.9)b kcal/mol
122.2
122.2
113.0
ED = 36.9 kcal/mol
117.5
HzCO 1.182
1.091
1.091
0.970
+ H30'
"All distances in 8, and angles in degrees. See Figure 1 for definition of parameters. bExperimental value from ref 15.
bonds only. The system chosen for study is (HzCO-H-OHZ)+ in which the central proton is transferred between the formaldehyde and water subunits. To our knowledge, this system has not been studied previously by ab initio molecular orbital methods. For purposes of comparison, calculations are carried out as well for (Hz0-H-OH2)+ in which the carbonyl group is replaced by a hydroxyl. We first investigate the proton transfer between HzCO and HzO in the gas phase. The calculations focus on the strength of the H bond and the nature of the minima in the potential energy hypersurface and hence include full geometry optimizations. The remainder of the paper considers the HzCO and HzO molecules as models of the carbonyl and hydroxyl groups within a larger molecular framework. We accordingly simulate the wide range of lengths and angular characteristics that have been observed for H bonds involving these groups. Choice of Method Since we are considering a transfer betwen two different molecules in (HzCO-H-OHz)+, it is crucial that our theoretical approach accurately portray their relative proton affinities, known from previous gas-phase measurements. Proton affinities were calculated theoretically in the following manner. The difference in energy was computed between the molecules HzCO and HzO on one hand and the respective protonated species HzCOH+ and H30+on the other, with all geometries fully optimized. To this difference was added a correction for zero-point vibrational energies as well as thermal correction terms. All calculations were carried out using the ab initio GAUSSIAN-80 computer codez3and geometries optimized with the gradient schemes included therein. After consideration of a number of different basis sets, the polarized double-valence 4-3 1G* setz4was chosen for the following reasons. First and perhaps most important, the relative proton affinities calculated for HzCO and HzO with this basis set agree very well with experiment. The calculated electronic contributions to the protonation energies are 182.7 and 175.8 kcal/mol, respectively. After subtracting out the corresponding zero-point corrections of 8.5 and 8.6 kcal/mol previously computed by Del Bene et aLZ5 and adding in 1.5 kcal/mol for each system arising from thermal corrections, we arrive at calculated proton affinities of 175.7 and 168.7 kcal/mol, in excellent agreement with the experimental measurements26of 177 and 170 kcal/mol. Most importantly the calculated difference of 7 kcallmol is equal to the difference (2.1) Szczesniak, M. M.; Scheiner, S. J . Chem. Phys. 1982, 77, 4586. Scheiner, S.; Szczesniak, M. M. Bigham, L. D. Int. J. Quantum Chem. 1983, 23, 739. (22) Hillenbrand, E.; Scheiner, S. J . A m . Chem. SOC.1984, 106, 6266. Scheiner, S.; Hillenbrand, E. A. Proc. Natl. Acad. Sci. U.S.A., in press. (23) 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, No. 406.
(24) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724. Hehre, W. J.; Ditchfield, R.; Pople, J. A. Ibid. 1972, 56, 2257. Collins, J. B.; Schleyer, P. v. R.; Binkley, J. S.; Pople, J. A. Ibid. 1976, 64, 5142. (25) Del Bene, J. E. Chem. Phys. Lett. 1983, 94, 213. Del Bene, J. E.; Frisch, M. J.; Raghavachari, K.; Pople, J. A. J . Phys. Chem. 1982, 86, 1529. (26) Wolf, J. F.; Staley, R. H.; Koppel, I.; Taagepera, M.; McIver, Jr., R. J.; Beauchamp, J. L.; Taft, R. W. J . A m . Chem. SOC. 1977, 99, 5417. Marynick, D. S.;Scanlon, K.; Eades, R. A,; Dixon, D. A. J . Phys. Chem. 1981,85, 3364. Aue, D. H.; Bowers, M. T. In "Gas Phase Ion Chemistry", Bowers, M. T., Ed.; Academic Press: New York, 1979; pp 1-51.
\
\--it
-RFigure 1. Geometry of (H2CO-H-OH2)'. This complex belongs to the C, point group, although no prior assumptions were made concerning its symmetry. R represents the distance between 0 atoms and r between Oaand H'. (3 measures the angle between the 0--0 axis and the HOH bisector.
observed e~perimentally.~'(It is this difference, rather than the absolute proton affinities, which is of greatest relevance in studying the proton-transfer process.) A second virtue of this basis set is that it is sufficiently flexible to provide an adequate framework for electron density shifts during the proton transfer. Finally, it is knownzs that basis sets of insufficient quality can lead to incorrect treatment of the protonated water species H30+. Although this moiety is known from experimental data to be pyramidal, inadequate basis sets predict a planar geometry.zs The 4-31G* basis set being used here does in fact leadz9to the correct pyramidal equilibrium geometry for H30+. Moreover, the accuracy of its treatment of the protonated HzCOH+cation is confirmed by calculations including larger basis sets and electron correlation which are described in detail below. Results
The first step in studying the proton transfer in (HzCO-HOHz)+ was a fully geometry optimization of this complex. The molecular arrangement of this system is illustrated in Figure 1 which points out the key geometrical parameters. R represents the interoxygen H-bond length and r the distance between the carbonyl oxygen 0" and the central proton HC. The angle between the OaHcbond and the 0--0internuclear axis is designated 6. LY refers to the angle between the latter 0--0axis and the C=O bond while measures the angle to the H O H bisector. The optimized values of these quantities as well as all other geometrical parameters are contained in the first row of Table I along with the total S C F energy of the system. There are a number of features of this optimized geometry which merit some discussion. First, the H-bond length R is equal t o 2.523 A, significantly longer than the distance of 2.39 A between 0 atoms in the analogous proton-bound dimer (H20-H-OHz)' where the formaldehyde subunit has been replaced by H20. The minimum energy structure of the latter system has the central proton midway between the two oxygens whereas in (HzCO-HOHz)+ the proton is considerably closer to the carbonyl oxygen than to the hydroxyl. Specifically, r(OaHC)= 1.018 A, as com(27) More recent measurements yield a slightly smaller difference of 5.2 kcal/mol (Lias, S. G.; Liebman, J. F.; Levin, R. D. J . Phys. Chem. ReJ Data 1984, 13, 695). (28) Pople, J. A. In "Applications of Electronic Structure Theory", Schaefer, H. F., Ed.; Plenum Press: New York, 1977; pp 1-27 and references contained therein. (29) Scheiner, S. Chem. Phys. Lett. 1982, 93, 540.
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 3055
Proton Transfers Involving C O and OH Oxygen
TABLE II: Geometries of (H2CO-H-OH2)+ during the Proton-Transfer Process for R = 2.75 k
r(OaHC)
r(COa)
1.oo 1.3 1.4 1.5 1.735
All distances in
1.224 1.212 1.208 1.204 1.197
r(CH,)
r(CHz)
r(ObH)
1.075 1.078 1.079 1.08 1 1.083
1.078 1.080 1.08 1 1.083 1.085
0.952 0.956 0.959 0.961 0.965
6 7.6 0.5 -0.1 -0.5 -3.9
(Y
P
107.5 118.6 121.6 125.3 140.3
155.4 136.9 132.9 130.7 127.6
@(HICOB) B(HzCOa) 117.2 118.1 118.7 119.3 120.5
121.1 122.1 122.2 122.2 122.1
B(HObH) 106.4 108.2 108.8 109.6 111.3
A; angles in degrees.
pared to 1.512 for the distance between HE and Ob. We therefore designate this structure as (H2COH--OH,)+; a search of the configuration space indicated that there is no second minimum corresponding to (H,CO- -HOHz)+ on the energy hypersurface. It may be noted that the central proton is situated 5' off of the 0--0axis in the equilibrium geometry. As will be described in greater detail below, this deviation from a linear H bond may be attributed in part to interactions with the lone pairs of the OHz subunit. The angle O(C0H) within the H2COH+subunit, equal to the sum of a and 6, is 116.3' in the complex. This value is within about 1' of the angle in the isolated H2COH+cation, listed along with the optimized geometry of H 2 0 in the second row of Table I. The difference in energy between the sum of these two subunits and the complex provides a measure of the dissociation energy of the complex, listed as ED,the last entry in the second row. The theoretical value of 30.0 kcal/mol compares quite favorably with a previous experimental e ~ t i m a t e of ' ~ 28.9. An alternative dissociation pathway of the complex involves products H2C0and H30+and has been calculated to require 36.9 kcal/mol; the last row of Table I contains the optimized geometries of the relevant species. In the gas phase, then, formation of the H-bonded complex (HzCOH- -OHz)+ from isolated reactants (H2COH)+ and HzO is exothermic by about 30 kcal/mol. Since there is no second minimum on the surface, decomposition to H 2 C 0 and (H,O)+ occurs without passing through (H2CO--HOH2)+ as an intermediate. Dependence on Znteroxygen Distance. We now shift our attention to the proton-transfer process occuring between the carbonyl and hydroxyl groups within the framework of an intramolecular H bond where the length of the bond is determined by structural restraints of the whole molecule. The transfer of the central proton between oxygen atoms in (H2CO-H-OHz)+ was hence examined for a series of three different H-bond lengths varying between 2.55 and 2.95 A. For each fixed value of R,the proton-transfer potential contains two minima corresponding to the configurations (H2COH--OH,)+ and (H,CO- -HOH2)+. Each geometry was fully optimized, subject only to the constraint of fixed R. Geometry optimizations were carried out as well for values of r(OaHc) intermediate between these two extremes, Le., along the proton-transfer coordinate. The maximum in the transfer potential was located by a saddle point search for a single negative eigenvalue in the second derivative matrix. The changes occurring in the geometry of the complex as the proton is shifted between the two oxygen nuclei are described in Table 11. As the proton is shifted away from the formaldehyde, its internal C=O bond length becomes shorter and the two CH bonds elongate. These changes are consistent with a transition from a structure with a great deal of H2COH+ character to one more closely resembling H,CO, the parameters of which are contained in Table I. Similar arguments apply to the increases observed in the internal O(HC0) angles. In an analogous vein, the OH, subunit undergoes geometry changes consonant with a transition from H 2 0to H30+as the proton approaches it. More interesting perhaps are the variations in the intermolecular parameters. Motion of the proton away from H 2 C 0 shifts it from beneath the 0--0axis (positive 6) to above as the transfer proceeds. At the same time the CH, group of formaldehyde bends away from the 0--0axis, with a increasing by 33' from 107.5' to 140.3'. The OHz subunit also rotates with respect to the H-bond axis; the H O H bisector bends by 28' toward the axis as the proton approaches.
These rather drastic reorientations may be understood in terms of interactions between the subunits. Let us consider first the (H,COH- -OH,)+ configuration where the H-bonding interaction places the central proton close to the 0--0axis. The equilibrium value of is determined by two competing effects. A lone pair of H 2 0 may best align itself with the central proton when 0 is about 125' (assuming hybridization of the sp3 type). On the other hand, the dipole moment of OH, points directly along the H O H bisector; hence, an orientation with @ = 180' would best align this dipole with the positive charge of H,COH+. The net result in the complex is a compromise between these two effects and @ = 155'. Now since p is greater than 125', the OH, lone pair is oriented below the 0--0axis which pulls the central proton below the axis as well and leads to a positive value of 6. 6 in turn influences the equilibrium value of a since their sum will tend toward the optimized O(C0H) angle in H2COH+ of 117.5'. The above arguments are essentially reversed when the proton is situated on the H20 subunit in (H2CO--HOH,)+. A lone pair of H,CO can most effectively point toward the central proton when cy is approximately 120° (assuming sp2 hybridization) whereas the H,CO dipole moment, oriented along the C = O axis, can best align itself with the positive charge of H30+when a is closer to 180'. The net result of 140.3' in the last row of Table I1 is again a compromise between these two effects. In analogy with the previous case, the H2C0 lone pair is rotated away from the 0--0 axis due to the large value of a. In this case, the lone pair is oriented above the axis and a negative sign of 6 results. The small value of p is necessary to accommodate the pyramidalization of the H 3 0 + subunit. For a H-bond length of 2.75 A, configuration (H,COH--OH,)+ is 5.7 kcal/mol lower in energy than (H2CO--HOHz)+,consistent with the greater proton affinity of H,CO. An energy barrier of 14.5 kcal/mol is present for conversion of the first configuration to the second; the bamer for proton transfer in the reverse direction is 8.8 kcal/m01.~~These two barriers are shown as a function of the H-bond length R in Figure 2 where the notation is as follows. COH-0 refers to transfer from the carbonyl to hydroxyl; CO+-HO to the reverse process. The energy of one minimum relative to the other, AE,is of course identical with the numerical difference between the two barrier heights. The parallel nature of the two solid curves in Figure 2 indicates that AE is essentially constant over the range of H-bond lengths being considered here. Extrapolation of the curves to the horizontal axis of Figure 2 shows that the barrier for CO+HO transfer will vanish when R decreases to approximately 2.49 A. This barrier disappearance corresponds to transition from double- to single-well character of the proton-transfer potential. Thus, when the H-bond length is shorter than 2.49 A, configuration (HzCOH- -OH,)+ is expected to be the only minimum in the potential. A primary objective of this paper is a detailed comparison between the proton-transfer properties of the carbonyl and hydroxyl groups. Therefore, calculations similar to those described above were carried out for (H20-H-OH,)+ in which water is substituted for H,CO. The barriers computed for proton transfer are indicated by the dashed curve in Figure 2 with the notation OH-0. It may be noted that this curve is parallel to and lies between those computed for the carbonyl-hydroxyl system. (The symmetry of this system is such that the two wells in each potential
-.
(30) The energy barriers referred to here correspond to the roton transfer within the already existing H bond, e.g., (HzCOH--OH2)P (H,CO-HOH?)+. rather than considering reactants or products as the dissociated subunits.
3056
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
Scheiner and Hillenbrand
TABLE 111: Energetics of Proton Transfer for Fixed Values of a#
(HXO-H-OH,)' E'(COCH0) AEb
E'(COH-4)
a,deg
107.5 140.3 180
15.9 13.0 11.3
a,deg
7.1 10.9 18.8
(H20-H-OH2)' E'(OCH0) AEe
E'(OH-4)
107.5 131.4 180
8.8 2.1 -1.5
11.4 10.2 9.6
8.7
2.7 1 .o
9.2 11.5
-1.9
GE(C0H- -0)'
6E(CO- -HO)d
0 3.6 14.6
3.1 0 1.4
bE(0H- -0V
6E(O--HO)g 4.3 1 .o 0.1
1.6 0 2.1
"All entries in kcal/mol; R = 2.75 A. *E(H2CO--HOH2)+ - E(H2COH--OH2)+. '(H2COH--OH2)+: E ( a ) - E(107.5'). d(H2CO--HOH2)+: E ( a ) - E(140.3'). 'E(H20--HOH2)+ - E(H20H--OH2)+. f(H,OH--OH2): E ( a ) - E(131.4'). g(H20--HOH2)+:E ( a ) - E(160.8').
-1.I
h
20
5
1
/
P'/
O H d O / // / / i o
',/ 0
2.35
I
I ' I
I
2.55
l
l
l
l
l
2.75
l
l
l
l
i
2
l
95
R(O0) . 8 .
Figure 2. Proton-transfer barriers computed for (H2CO-H-OH2)+(solid curves) and (H20-H-OH2)+ (broken curve). In all cases, R is the
interoxygen separation. Barriers for transfer from H2C0 to OH2 are denoted as COH-4; CO-HO refers to transfers in the reverse direction.
are equal in energy and the barriers in the forward and reverse directions are identical.) W e conclude from Figure 2 that, for equivalent H-bond lengths, thk energy barrier for proton transfer from carbonyl to hydroxyl is about 4 kcal/mol higher than for transfer between hydroxyls. On the other hand, the transfer from hydroxyl to carbonyl involves a bamer 1 kcal/mol lower than the interhydroxyl process. As described above, the energetics in Figure 2 were extracted from potentials involving full geometry optimizations at each stage of proton transfer, subject only to the constraint of constant R(0--0).Previous has suggested that, in certain cases, potentials obtained in this manner may be closely reproduced by using the "rigid molecule" approximation in which all nuclei are frozen in place durine the transfer with the exception of the central proton itself. The appropriateness of this approximation was tested for the (HzCO-H-OHz)+ system as follows. The structure of the complex was frozen in the geometry corresponding to the left well (HzCOH--OHz)+with R = 2.75 A, described in the first row of Table 11, and the proton then shifted across to the OHz subunit. The results were quite different than energetics calculated with full geometry optimizations during the transfer. For example, the right well, corresponding to (HzCO--HOHZ)+,was found to be 12.1 kcal/mol higher in energy than the left, in contrast to the value of 5.7 kcal/mol obtained when both configurations are fully optimized.
On the other hand, rather good agreement with optimized transfer energetics is possible with judicious choice of a relatively small number of parameters for optimization. The data in Table I1 indicate that the maximum change in any bond length during the transfer is about 0.02 A. Internal bond angles are also rather constant, varying by less than 5'. The parameters undergoing the greatest change are the intermolecular orientation angles a and @,both of which vary over a range of approximately 30'. Protpn transfer was therefore considered within a limited optimization mode whereby a and /3 are optimized at each stage of transfer while all other parameters are held fixed at the values in the first row of Table 11. In addition, the central proton was constrained to lie along the 0--0axis throughout the course of the transfer Le., 6 = 0'. The barriers for forward COH-0 and reverse C O c H O transfer computed in this manner for R = 2.75 A were 14.5 and 7.7 kcal/mol, respectively, which compare quite favorably with the values of 14.5 and 8.8 kcal/mol obtained with full geometry optimizations. Good agreement was found also for R = 2.95 A where the limited optimization barriers are 24.7 and 17.4 kcal/mol, as compared with 24.8 and 18.6 kcal/mol. We conclude that, whereas accurate transfer energetics require some geometry optimization, reasonably reliable values may be obtained by reqtricting these optimizations to intermolecular orientation angles while keeping the internal geometries of each subunit fixed. Angular Dependence. The same structural restraints which maintain H bonds at lengths other than what would be observed in the absence of external forces may be expected to lead as well to deviations from the optimal angular orientation. This presumption is indeed verified by recent surveys3' of the geometry of the H bond involving a carbonyl and hydroxyl in which a wide spectrum of C 4 - - 0 angles are observed. For this reason, whereas the intermolecular angles were allowed to freely change during the proton transfers studied in the previous section, one of these angles is held fixed in the present section in order to enforce a certain degree of rigidity. Specificqlly, we hold a constant which corresponds to a fixed C=O- -0 angle with the hydroxyl in a given orientation with respect to the carbonyl group. All other geometrical parameters are fully optimized as the proton is shifted between the carbonyl and hydroxyl groups, with the exception of the H-bond length R which is held equal to 2.75 A. We consider three different fixed values of a. The first is 107.5', the angle found in the optimized (HzCOH--OHz)+ configuration (see Table 11). The optimized value of a in the right well (HzCO--HOH2)+,140.3', is chosen as the second. The third angle is 180' and corresponds to placement of the hydroxyl oxygen directly along the C=O axis. The previous surveys of a large number of relevant crystals3] indicate that our three values of a a v e r the full spectrum of angles generally encountered in such bonds. It is emphasized that the angle which is being specified here is a(C==O- -0)which involves the heavy atoms only. There are no restrictions imposed upon the position of the central proton which is free to follow its lowest energy path between the two subunits. (31) Taylor R.; Kennard, 0.;Versichel, W. J . Am. Chem. SOC.1983, 105, P. Ibid. 1984, 106, 1018.
5761. Murray-Rust, P.;Glusker, J.
Proton Transfers Involving CO and OH Oxygen The salient features of the potential curves for proton transfer for each of these three values of a are contained in Table 111. In addition to the barriers for transfer in either direction contained therein, the succeeding column lists the difference in energy between the two minima: AE = E(H2CO--HOH2)+- E(H2COH-OH2)+. As in the previous case allowing variation of a,when a is fixed at 107S0, the right well is considerably higher in energy than the left well (by 8.8 kcal/mol). This quantity is substantially reduced when CY is lowered to 140'; in fact, when the hydroxyl lies along the C = O direction, Le., a = 180°, the right well is lower than the left and A E becomes negative. Concomitant with this sign reversal in AE, the barrier for transfer from carbonyl to hydroxyl is reduced as the latter group is swung around toward the C=O axis, while the opposite trend of an increased barrier for transfer in the other direction is observed. The above patterns may be summarized as a greater tendency for the central proton to be associated with the H 2 0 rather than with the H 2 C 0 as the water molecule is moved toward the C=O axis. The reversal in sign of AE is in some ways rather surprising and warrants further scrutiny. In order to probe this matter more deeply, we have included in the last two columns of Table I11 the distortion energies 6E required to impose a given value of a on each configuration. More specifically, GE(C0H- -0)represents the energy needed to change the angle a of (H2COH--OH2)+from its optimal value of 107.5' to some other value. As may be seen in the penultimate column of Table 111, increasing a to 140' raises the energy of the (H2COH--OH2)+configuration by 3.6 kcal/mol while the much higher distortion energy of 14.6 is required to increment a to 180'. In an exactly analogous fashion, 6E(CO-HO) describes the energy increase observed when a in the (H2CO--HOH2)+configuration is changed from its optimum value (140'); these quantities are listed in the last column of the table. The distortion energies in Table I11 provide some insight into the reversal in relative energies of the (H2COH--OH2)+ and (H2CO--HOH2)+configurations which occurs when the hydroxyl group is moved toward the C=O axis. As may be seen in the last column, the energy of the latter configuration is relatively insensitive to the angle a,varying by at most 3 kcal/mol and with a minimum near the middle of the 107'-180° range. In contrast, the minimum for the (H2COH--OH2)+configuration occurs at a = 107' and increasing this angle to 180' results in a 15 kcal/mol rise in energy. The latter distortion energy is sufficient to raise the left well in the transfer potential high enough to surpass the energy of the right well, thereby reversing the sign of AE. The reversal of stability of (H2COH--OH2)+ and (H2CO-HOH2)+ is thus rooted in the large energy required to shift the OH2subunit of the former configuration from a = 107' to 180'. We therefore address ourselves now to an understanding of this large distortion energy. In the optimized (H2COH--OH2)+ configuration, the hydroxyl oxygen lies 107' from the C = O axis and close to a carbonyl lone pair direction. The central proton is situated approximately along the 0--0axis, leading to a strong H bond. At the same time the angle B(C0H) in the H2COH subunit of the complex is within 2' of its equilibrium value in the isolated H2COH+cation. When the H20subunit is rotated toward the C=O axis, there are two opposing forces operating upon the central proton. While rotation along with the H 2 0 will help maintain a linear 0-H- -0 arrangement and a strong H bond, this motion will occur at the expense of inducing a strain energy into the H2COHsubunit which prefers a B(C0H) of about 117'. In the case of (H2COH--OH2)+,it is the latter force which is the stronger. In the optimized geometry of this configuration with a = 180°, the central proton is found 55' from the 0--0axis and with B(COH) = 125'. The H bond is severely weakened by this extremely nonlinear 0-H- -0arrangement and the configuration is destabilized accordingly. The situation is somewhat different in the case of (H2CO-HOH2)+which involves interaction between a neutral H2C0and H,O+ cation. As described above, the equilibrium value of a here is 140' due to competition between two opposing factors. The carbonyl lone pairs may best interact with the central proton for angles around 120' while larger angles near 180' produce the
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 3057 greatest ion-dipole stabilization. The net result of these two opposing forces is a rather flat potential in the region between 107' and 180' and hence fairly small distortion energies. The influence of zero-point vibrational effects on the above results was checked in the following manner. It is reasonable to assume that the variation of the angle between the two subunits will not substantially affect the internal vibrations within each subunit. However, since the bonding of the central proton to the two subunits is affected by the intermolecular angle, some variation in the relevant vibrations may be expected. It was found that the total change in zero-point vibrational energy involving this proton was rather small. The vibrational contribution to GE(C0H- -0) and 6E(CO- -HO) in Table I11 is on the order of 0.2 kcal/mol or less over the full range of 72' in a. By changing the angle of orientation of the OH2 relative to the carbonyl group, the relative energies of (H2COH--OH2)+ and (H2CO--HOH2)+ have shifted by a total of more than 16 kcal/mol. An interesting and important question to which we now address ourselves is whether this is a feature unique to the carbonyl oxygen or is instead a general property of H bonds involving any 0 atom. We have approached this question by comparison of the above system to (H20-H-OH2)+ where the carbonyl oxygen has been replaced by the hydroxyl of water. The geometry of this system is precisely the same as (H2CO-H-OH2)+ in Figure 1 except that a refers to the angle between the 0--0axis and the bisector of the left OH2 subunit rather than to the C=O bond of H2C0. The two hydrogens of this OH2, like those on the right, are located above and below the plane of the paper which represents a symmetry plane. Also lying in this plane are the lone pairs of the OH2, like the analogous pairs of H 2 C 0 . As in the previous case of (H2CO-H-OH2)+, proton-transfer potentials were generated for (H20-H-OH2)+ for a range of different angles a,and all with R = 2.75 A. The corresponding properties of these transfer potentials are presented in the lower half of Table 111. It may be seen that increasing a from 107' to 180' changes the sign of AE from positive to negative, as was observed for (H2CO-H-OH2)+. However, the magnitude of this sign change is much smaller than in the latter system, undergoing a total change of 4.6 kcal/mol as compared to 16.3 kcal/mol in (H2CO-H-OH2)+. The distinction between the two systems is even more dramatic if one considers the change undergone by AE in swinging the water around from the linear (a = 180') case to the value of a which is optimal for each system. Whereas this optimized angle is 107.5' for (H2COH- -OH2)+and the change in AE is 16.3 kcal/mol, the corresponding values for ( H 2 0 H - OH2)+ are 131.4' and only 2.9 kcal/mol. In order to analyze the underlying reasons for this disparity, we again turn to the distortion energies, included in the last two columns of Table 111. The distortion energies of the ( H 2 0 H - OH2)+ configuration immediately point out one important difference between the two systems. Whereas the energy of the equivalent (H2COH--OH2)+ configuration was very sensitive to a with a minimum at 107', this function is much flatter for (H20H--OH2)+and the minimum occurs at the higher value of 131'. The behavior of the two systems is more alike with respect to the distortion energies of the (H2CO--HOH2)+ and ( H 2 0 - HOH2)+ configurations in the last column which vary by 3 or 4 kcal/mol over the entire 73' range of a. From the data in Table 111, the greater magnitude of the reversal in AE for the carbonyl case may be ascribed to the much higher sensitivity of the energy of (H2COH--OH2)+to the angle a than of (HIOH- -OH2)+. The instability introduced into (H2COH--OH2)+by increase of this angle from 107' to 180' has in turn been attributed to the weakening of the H bond caused by the nonlinearity of the 0 - H - - 0 atoms. In the case of (H20H--OH2)+,the H bond is not significantly weakened because the central proton remains along the 0--0axis as the right hand OH2 unit is rotated from 107' to 180'. Hence, the distortion energies in the penultimate column of Table I11 are not very high. A central question is therefore why does the proton remain along the 0--0axis in the latter system and not in the case of the carbonyl group?
3058 The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
Scheiner and Hillenbrand
a
TABLE IV: Calculated Distortion Energies (kcal/mol) of H2COH+
basis set
SCF
MP2
MP3
In Plane, E(180') - E(117.5')" 4-31G* 6-31 1G**
23.3 23.4
24.0 24.8
24.0 24.8
Out of Plane, E(18') - E(O0)* 4-31G* 6-311G**
0.0 0.1
-0.4 0.3
-0.3
"Angle refers to B(C0H). *Angle refers to bend out of molecular plane. The answer to this question is related to the flexibility of the H2COH+and H30+subunits. The equilibrium value of B(C0H) in the former isolated cation is 1 17.5' and the energy rises quickly with distortions from this angle. For example, bending the proton from this position to B(C0H) = 180' requires 23.3 kcal/mol, as calculated with the 4-3 l G * basis set (and including geometry optimizations of both structures). This value is probably a realistic one; calculations involving basis sets up to 6-3 1 1G** and including electron correlation via M P 3 theory32lead to essentially identical results, as may be seen in Table IV. On the other hand, the corresponding energy required to bend the proton in H30+from its equilibrium position (in a pyramidal arrangement) to a planar geometry corresponding to a = 180' is only 1.8 kcal/mol. Returning now to the complexes (HzCOH- -OH2)+ and (H20H--OHz)+,it is clear that the rigidity of the B(C0H) angle in HzCOH prevents the central proton from following the water as it rotates down to a = 180'. On the other hand, such a rotation of the proton in ( H 2 0 H --OH2)+ costs less than 2 kcal/mol in terms of distortion energy in HzOH so the proton is free to remain along the 0--0axis, thereby maintaining the strength of the H bond. In summary, then, the more dramatic reversal in AE observed in the case of the carbonyl is due to the greater intrinsic inflexibility of the C O H angle which removes the proton from the 0--0axis when a approaches 180'. Out-ofplane Distortions. The previous section has dealt with motions of the proton-accepting water molecule within the plane of the carbonyl oxygen lone pairs. Of interest as well are motions of the molecule out of this plane and the resulting effects upon the proton-transfer process. Figure 3a illustrates the definition of angle 4, between the 0--0axis and C=O bond, which measures the deviation of the oxygen atom of OHz from the plane of the carbonyl lone pairs. The geometry of the complex is such that the projection of the 0--0 axis into the carbonyl lone pair plane is collinear with the C=O axis; hence, the in-plane angle a between the C=O bond and the projection of the 0--0 axis is 180'. Potentials were calculated for proton transfer between the 0 atoms with an interoxygen separation R of 2.75 8, for a series of several fixed values of 4. The geometries of each configuration were fully optimized subject only to the above constraints. Again, no restrictions were imposed on the central proton which was allowed to follow its lowest energy path between the two oxygen atoms. The barriers to transfer in either direction as well as the difference in energy between the two minima are listed in Table V for out-of-plane rotations of up to 40'. As mentioned above, the configuration with 4 = '0 corresponds to a fully linear C= 0--0arrangement; hence, the potential summarized in the first row of Table V corresponds to that in the last line of Table 111 where a = 180O. It may be noted that, in the case of zero out-of-plane rotation, the (H2COH--OH2)+ configuration is higher in energy than (H2CO--HOH2)+by 7.5 kcal/mol and that the barrier for transfer from carbonyl to hydroxyl is 1 1.3 kcal/mol. Rotating the water by 20' out of the plane changes these quantities very little. If the distortion is increased to 40°,the magnitude of AE is reduced (32) Pople, J. A.; Binkley, J. S.;Seeger, R.Inr. J . Quantum Chem. 1976, 10, 1.
b
H' Figure 3. Definition of $J which measures rotation of OH2 out of the lone pair plane of (a) HzCO and (b) HOH. Dashed lines represent the C = O axis in a and the HOH bisector in b. The central hydrogen atom involved in the H bond has been removed for purposes of clarity. No symmetry constraintswere imposed on either system. Puckering of the CH2 group was allowed in a but the degree of pyramidalization of the C atom was found to be quite small in all cases.
somewhat to -5.9 kcal/mol and the transfer barriers are changed by less than 1 kcal/mol. It is thus clear that rotations of the water out of the plane of the carbonyl lone pairs produce very little effect upon the energetics of proton transfer in (H2CO-H-OH2)+. It is instructive to again contrast this behavior with the analogous (H20-H-OH2)+ where the carbonyl oxygen is replaced by a hydroxyl. The geometry of this system is presented in Figure 3b where 4 again represents the angle between the 0--0axis and the lone pair plane. It is reemphasized that, in contrast to H2C0, the lone pairs of H 2 0lie in a plane perpendicular to the molecular plane; hence, out-of-plane distortions correspond to rotations within the HOH plane. The energetics of the proton transfers are listed in the second half of Table V where the data may be compared to the previous carbonyl case. Once again, AE is negative and is only slightly influenced by the angle 4. However, examination of the energy barriers points out a significant distinction between the carbonyl and hydroxyl cases. Whereas the barrier heights are almost constant over a 40' range of 4 for carbonyl, varying by less than 1 kcal/mol, 40' distortions in the hydroxyl case lead to increases in the barrier heights of 6 times that amount. In order to gain some insight into the fundamental causes of this difference in behavior, we again analyze distortion energies of various configurations. The term GE(C0H- -0)listed in the penultimate column of Table V is defined as the energy required to increase the angle 4 in the (H2COH--OH2)+configuration from 0'. Similarly, the increase in energy of the (H2CO--HOH2)+ configuration resulting from a rotation of the water out of the plane by 4 is represented by BE(C0- -HO). Thus, the values of these two quantities in the first row of Table V, corresponding to no out-of-plane rotation, are zero. It may be noted that the distortion energies for (H2CO-HOH2)+are generally quite small. For example, rotating the water by 40' out of the carbonyl lone pair plane increases the energy of (H2COH--OHz)+by only 0.4 kcal/mol. A clue to the insensitivity of the energy of this configuration to 4 may be obtained from the optimized position of the central proton. For all values of 4, this proton is located well off the 0--0axis, preferring instead to lie in the carbonyl lone pair plane with a O(C0H) angle of about 118'. (This fact may again be attributed to the strong pull on a proton toward this position in HzCOH+.) Therefore, the H bond between this cation and the OH2 subunit is already quite weak, even with $= Oo, and removal of the water from the carbonyl plane does little to further weaken the interaction. The dependence of the energy upon 4 is somewhat greater in the (H2CO--HOH2)+configuration since increase of 4 rotates the
Proton Transfers Involving C O and OH Oxygen
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 3059
TABLE V: Proton-Transfer Energetics for Distortions Out of Plane Containing 0 Lone Pairsa
(HJSH-OHZ)' E~(COH-O)
E+(CO+HO)
AE
20 40
11.3 11.2 12.1
18.8 18.5 18.0
-7.5 -7.3 -5.9
9,deg
E~(OH-O)
6.dea 0
0
9.6 10.7 15.7
20 40
" R = 2.75
(H2O-H-OH2)' Ef(OcH0) AE 11.5 12.9 17.3
-1.9 -2.2 -1.6
6E(COH- -0)
6E(CO- -HO)
0
0
0.1 0.4
0.2 1.9
6E(OH- -0)
bE(0- -HO)
0 1.1 5.1
0 0.8 5.4
A; all entries in kcal/mol.
(H30)+cation away from the negative end of the dipole moment that lies along the C = O bond axis, decreasing the charge-dipole attraction. In contrast to the low distortion energies characteristic of (H2CO-H-OH2)+, the e ergies required to raise the water molecule out of the plane o the lone pairs of the hydroxyl group are quite a bit higher, as may be seen from the data for (H20H-OH2)+ in Table V. Whereas the low distortion energies of (HzCOH--OHz)+ may be ascribed to a H bond which has already been severely weakened by a very nonlinear 0-H- -0arrangement when a = 180°,this is not the case for ( H 2 0 H --OH2)+. Due to the small difference in energy between planar and pyramidal H30+, the central proton is able to remain along the 0--0axis as the right-hand OH2 is rotated around in the plane of the hydroxyl lone pairs. Hence, even when a = 180°, the H bond is quite strong in the ( H 2 0 H --OH2)+configuration. However, the situation is quite different if the OHz subunit is rotated out of the lone pair plane. The bending force constant for motion of a proton of H30+in this direction is quite high and prevents the proton from following the OH2subunit, thereby destabilizing the system by weakening the H bond. For example, when d, is equal to 40°, the central proton is pulled off the HOH bisector by only 7 S 0 , leading to a B(O0H) angle of 32.5'. The much greater difficulty of rotating the proton out of the lone pair plane in H30+than in H2COH+ is confirmed by calculations of these isolated cations. Whereas a bend of 20° increases the energy of H30+by 8.9 kcal/mol, an analogous bend destabilizes H2COH+ by only 0.02. The corresponding energy increases for 40° are 32.5 and 0.4 kcal/mol, respectively. This large discrepancy is not an artifact of the basis set being used as calculations with 6-31 1G** and including MP3 lead to very similar results (see Table IV). The relatively high distortion energies 6E(O--HO) for ( H 2 0 -HOH2)+are due to a number of factors. First is the fact that rotating H30+out of the lone pair plane pulls this cation off the direction of the dipole moment of the other OH2 subunit which points along the d, = 0' direction. However, a similar factor is in operation as well in (H2CO--HOH2)+ and led to distortion energies of much smaller magnitude. The second factor contributing to the higher distortion energies in ( H 2 0 - -HOH2)+is related to the covalent interactions between the H 2 0subunit and the central proton of HOH2+. From simple theories of bonding, it is clear that this stabilizing force will be directly related to the magnitude of the electron density of H 2 0 in the direction of the proton. For purposes of comparison, the electron density of both H 2 0and H 2 C 0 were calculated as a function of the angle d,. The density of H 2 C 0 was found to be extremely insensitive to the angle d,, being nearly constant over the range from 0' to 40°. In fact, the density is at its lowest in the lone pair plane, i.e., @ = 0'. In sharp contrast, a maximum occurs a t d, = Oo for H 2 0 and the density decreases markedly as the reference point is rotated out of the lone pair plane. This sharp reduction diminishes the capacity of HzO to H bond effectively with the H30+subunit as the latter is rotated out of the plane and leads to the high distortion energies in the last column of Table V. A final factor contributing to the higher distortion energies in (H,O- -HOH,)+ involves the electrostatic interaction between the (HOH2)+ cation and the quadrupole moment of the neutral
P
subunit on the left. The out-of-plane rotation of the cation magnifies its interaction with the component of the quadrupole tensor which is perpendicular to the lone pair plane. In the case of H20, this component is positive in sign and of large magnitude33 so its repulsive interaction with the cation leads to a large distortion energy in (H20--HOH2)+. In contrast, the relevant quadrupole component of H2C0 is nearly zero;33 the absence of the latter repulsion reduces the distortion energy in (H2CO--HOH2)+. Whereas the small changes in AE in (H2CO-H-OH2)+ over a 40' range of 4 may be traced to the insensitivity of the individual (H2COH--OH2)+and (H2CO--HOH2)+configurations to outof-plane rotations, the situation is quite different in (H20-HOH2)+where the energies of both minima in the proton transfer potentials increase sharply with d,. The nearly constant nature of AE in the latter system may instead by attributed to the approximately equal distortion energies of the (H20H--OH2)+and ( H 2 0 - -HOH2)+ configurations. The increases in the proton-transfer barriers in (H20-H-OH2)+ that are a consequence of out-of-plane distortions are linked to a number of factors.22 First is the fact that the reduced electron density of water out of its lone pair plane (see above) destabilizes the configuration in which the proton is midway between the two H20 subunits. Secondly, the latter configuration is further raised in energy by the misalignment of the HOH dipole moment and the partial positive charge on the proton.
Summary The foregoing sections have reported the energies of proton transfer as a function of intermolecular distance and orientation. When all geometrical parameters are allowed to readjust during the transfer process, the dependence upon H-bond length is rather uniform. Over a range of interoxygen distance between 2.55 and 2.95 A, the (H2COH--OH2)+ configuration is consistently lower in energy than (HzCO--HOH2)+ by 4-6 kcal/mol. The barrier for transfer from carbonyl to hydroxyl is higher than the reverse barrier by an equal amount and remains so although both barriers rise quickly as the H bond is elongated. Substitution of H 2 C 0 by HOH leads to energetics falling directly between the above two cases: bamers for interhydroxyl transfer are 1 kcal/mol higher than those involving shift from hydroxyl to carbonyl over the entire range of H-bond length. The two groups involved in the H bond undergo considerable reorientation during the course of the above transfers, rotating with respect to one another by 30'. Energetics were also studied in which the molecular orientation, like the H-bond length, was held fixed. It was observed that the relative energies of the (H2COH--OHz)+ and (H2CO--HOH2)+configurations depend upon the particular angular features chosen for the H bond. For example, whereas the former configuration is more stable than the latter by 8.8 kcal/mol when the hydroxyl is situated along the direction of a carbonyl lone pair, reorienting the hydroxyl to lie along the C=O axis reverses the order of stability and (H2CO--HOH2)+is found lower in energy by 7.5 kcal/mol. A (33)Calculated with the 4-31G8basis set and confirmed by experimental measurements: van Duijneveldt-vande Rijdt, J. G.C. M.;van Duijneveldt, F. B. THEOCHEM 1982, 89, 185.
J. Phys. Chem. 1985,89, 3060-3066
3060
similar reversal in stability is observed in the case of interhydroxyl transfer although the energy differences involved are of considerably smaller magnitude. In contrast to reorientations within the plane of the oxygen lone pairs which lead to marked changes in relative energies of minima in the proton-transfer potentials, these energies are little affected by rotations out of this plane. On the other hand, out-of-plane distortions are found to significantly raise energy barriers to proton transfers between hydroxyl groups although there is little sensitivity to such distortions in the carbonyl case. The latter disparity between these two types of oxygen atoms is due in large part to
the fact that the electron density of hydroxyl decreases quickly as the reference point is rotated out of the lone pair plane while the density of carbonyl is insensitive to such rotations. Acknowledgment. We are grateful to Professor A. Jorgensen for assistance with the calculations testing the accuracy of limited geometry optimizations. Allocations of computer time were provided by Southern Illinois University. This work was supported by grants from the National Institutes of Health (GM29391 and AM01059) and the Research Corp. Registry No. H2C0, 50-00-0; OH3, 13968-08-6; H 2 0 , 7732-18-5.
Enthalpy/Entropy and Volume/Entropy Actlvatlon Ratios and Solute-Solvent Interactions J. C. Phillips A T & T Bell Laboratories, 10-371, Murray Hill, New Jersey 07974 (Received: September 14, 1984; In Final Form: January 16, 1985)
The role of solvent structure in determining solutesolvent interactions and contributing to chemical reaction activation energies is discussed in terms of solute-induced solvent solidification(the traditional “iceberg” model of aqueous solvation) and ionization (a radically new mechanism). Solvent solidification is the principal response to nonpolar (“structure-making”) solutes while solvent ionization makes the dominant contribution for polar (“structure-breaking”) solutes. Each first-order reaction channel is characterized by values of AV and AS which are known for water and methanol. The model yields results in excellent quantiative agreement with (Hepler) plots of AV and AS for proton ionization equilibrium constants of acids and for Twigg plots of ligand exchange activation energies for transition-metal ion complexes. A particularly interesting application of the model is the successful explanation of trunk and branch slopes in the Cabani plot of model amino acids X(CH2),Y with X and Y equal to COOH- or NH3+.
1. Introduction Experimental studies of chemical reactions have undergone several quantitative revolutions in the past 30 years. Taube, in his pioneering review’ in 1952, was able to distinguish only between “fast” and “slow” reactions (on a time scale of 1 min). Quantitative data on activation enthalpies AIP and activation entropies AS“ became availableZ for both slow and fast reactions during the 1960s. These have been greatly enhanced by very accurate measurement^^*^ of activation volumes Avd during the 197Os, again over a wide range of reaction rates. These revolutions in experimental technique and depth and breadth of data may be regarded as normative products of the more general revolution in scientific instrumentation which has taken place concurrently. However, it is striking that few or no corresponding advances have been made in the conceptual framework used to discuss chemical reactions in general and solutesolvent interactions in particular. Chemical reactions such as ligand substitution and exchange for complex ions in solution are still described in terms of classical Bjerrum electrostrictive models5 or geometrical models of the Hughes-Ingold type.5 In these models ligand substitution of, e.g., an octahedral complex MX, ( M = transition-metal ion), occurs through a transition state containing either MX6Y or MX5, corresponding to increasing or decreasing the metal coordination number by one. The central (1) Taube, H. Chem. Reo. 1952, 50, 69. (2) Bennetto, H.P.; Caldin, E. F. J . Chem. SOC.A , 1971, 2198. (3) Twigg, M. V. Inorg. Chim. Acta 1977, 24, L84. (4) Palmer, D. A.; Kelm, H. Cmrd. Chem. Reo. 1981,36,89. The present paper provides the thermodynamic relation linking aP and A P which these reviewers demand (p 188). ( 5 ) Bjerrum, N. K . Dansk. Vidensk. Selsk. Skr. 1906,4,7. Ingold, C. K. “Structure and Mechanism in Organic Chemistry”; Cornell University Press: Ithaca, NY, 1953; Chapter V.
shortcoming of geometrical models was already remarked by Taube in his early review,’ namely the coordination number in the transition state is not a physical observable. In geometrical descriptions the solvent plays the passive role of a source or sink for the entering or leaving ligands (X or Y, respectively). On the other hand, in classical continuum models the thermochemical parameters A P , ASa, and Avd of the reaction are to be related to the solvent only through electrostrictive macroscopic (or quasi-macroscopic) parameters such as the solvent dielectric constant and compressibility (or empirical “polarity” indices).6 A different approach to solute-solvent interactions emphasizes the strongly correlated molecular structure of the solvent, such as hydrogen bonding in HzO. This nonlinear approach explains negative (hydrophobic) entropies and large heat capacities of aqueous solution:4 and for pictorial purposes it is often described as the “iceberg” model.1° The central limitations to this approach are the relatively small data baseg and the large magnitudes of solvation energies. 2. Enthalpy-Entropy Relations Enthalpy-entropy activation ratios in chemical reactions provide a large data base which has been discussed extensively in terms of compensation temperatures
T, = AH*/ASa
(1)
where various choices have been made for AH*, the solvent contribution to W . In a simple model solute (u) and solvent (6) Abboud, J. L.; Kamlet, M. J.; Taft, R. W. J . Am. Chem. SOC.1977, 99, 8325. (7) Eley, D. D. Trans. Faraday SOC.1939, 35, 1281. (8) Frank, H. S . J. Chem. Phys. 1945, 13, 493. (9) Ntmethy, G.; Scheraga, H. A. J . Chem. Phys. 1962, 36, 3401. (IO) Frank, H. S.;Evans, M. W. J. Chem. Phys. 1945, 13, 507.
0022-3654/85/2089-3060$01.50/0 0 1985 American Chemical Society
