J . Phys. Chem. 1993,97, 12197-12204
12197
Molecular Orbital Study of Acetic Acid Aggregation. 1. Monomers and Dimers Usz16 Turi and J. J. Dannenberg' Department of Chemistry, City University of New York-Hunter College and The Graduate School, 695 Park Avenue, New York, New York 10021 Received: June 14, 1993'
Ab initio and semiempirical (AM1, PM3, and SAM1) molecular orbital studies on monomeric and dimeric acetic acid are reported. The highest-level ab initio calculations (MP2/6-3 1 l++G(d,p)) on the monomeric forms of acetic acid predicted the cis form to be preferred over the trans by 6.1 kcal/mol. Four different dimers were studied. The enthalpy of stabilization at 298 K is 1 1.8 kcal/mol at the MP2/6-3 1G(d) level after correction for BSSE and ZPVE for the cyclic dimer containing two O-H-.O hydrogen bonds, which is 2.4-3.1 kcal/mol more stable than twice the open dimer containing only one O-H.-O interaction. We attribute this difference to cooperativity in the cyclic structure. Vibrational analyses at the MP2/6-3 1G(d) level confirm this assessment. According to the best dimer calculations (MP2/6-3 lG(d)), the hydrogen-bonding enthalpy of a C-H.-O bond is about 0.5-1 .Okcal/mol, while that of a simple O-H-0 is 4.7 kcal/mol. Vibrational analyses on the monomers and dimers are reported and compared to experimental results. We suggest two modifications of vibrational assignments. The semiempirical results are compared with the a b initio calculations.
Introduction How molecules nucleate and crystallize remain fundamental problems in chemistry. We have used molecular orbital (MO) methods to elucidate the nature of the interactions involved in these processes. Previous studies on 1,3-diones1and nitroanilines2 strongly suggest that cooperative effects areextremely important, especially for H-bonding. Cooperativity may also play an important role in other interactions as well.3 Due to the size of the molecules, our previous studies were mostly limited to interactions in one dimension. To critically study these effects in three dimensions, we sought an example of an unusual crystal structure of a small molecule, preferably one where the crystal structure defies simple intuition. Such a case is that of acetic acid. Normally, carboxylic acids crystallizeas dimers similar to those that exist in the gas and liquid phases. For example, the crystal structures of both propionic acid4 and fluoroacetic acid5 consist of associated cyclic dimers. However, acetic acid crystallizes6in long chains that involve C-H-eO as well as O-H-0 bonds. This peculiar behavior makes the examination of the crystal structure of acetic acid especially interesting. Derissen and Smit7 have rationalized this unusual crystal structure using atom-atom potential calculations. Theoretical studies of this type (generally based upon two-body interactions) cannot adequately treat the cooperativity. They neglect the nonadditivity or many-body interactions which are inherent in intermolecular interactions of more than two molecules. In contrast, MO theory is an extremely useful tool in treating the cooperative effects correctly as illustrated in our MO study of 1,3-diones.Ia Another important aspect of the crystal structure of acetic acid is the evaluation of the importance of the C-He-0 hydrogen bonds.8 In a recent study,9 we estimated the strengths of these interactions to vary between -0.5 and -3.8 kcalfmol. In this paper we shall concentrate on the dimerization of acetic acid molecules. Both ab initio and semiempirical molecular orbital methods will be used to evaluate the extent to which both 0-HO and 0-HC H-bonds contribute to the stability of the dimers. Due to the complexity of the problem, the effects of aggregation Abstract published in Aduance ACS Abstracts, October IS, 1993.
(and cooperativity) leading to the three-dimensional crystal structure will be considered in a separate paper. Spectroscopicloand vapor-density measurements" indicate that acetic acid forms hydrogen-bonded cyclic dimers in the gas phase. From these studies, statistical calculations,I2 and other experimental techniquesl3 (i.e., thermal conductivity measurements), the standard thermodynamic parameters for thedimer formation were determined. The dimer forms to the extent of about 50% at 20 OC. Several previous MO studies on acetic acid monomers and dimer have been reported.13J4
Methods Both semiempirical (AMlI5, PM3,I6andSAM1l7)andvarious levels of ab initio molecular orbital theory have been used in this study. Theapplicabilityof theAM1 method to H-bonding studies has been reviewed elsewhere.18 The AM 1 method has previously been used with success in several hydrogen-bonding studies19 including modeling of the H-bonding between molecules of various nitroanilines in the crystalline state.* We explicitly considered all internal coordinates for the semiempirical optimizations. Ab initio studies on H-bonding systems are very sensitive to basis set and correction for electron correlation, as exemplified in previous studies of the water dimer,20 hydroxamic acids,21 and aggregation of 1,3-diones.la We performed accurate ab initio calculations at the Hartree-Fock (HF)22 and second-order Maller-Plesset (MP2)23levels using several different basis sets. At both levels we used 6-31G, 6-31G(d), 6-31G(d,p), 6-31 lG++(d,p), and D 9 5 + + ( d , ~ )basis ~ ~ sets for acetic acid monomers. For the dimers we employed the first three basis sets at the HF, but only 6-31G and 6-31G(d) at the MP2 level. All internal coordinates were explicitly optimized with a symmetry plane (containing the heavy atoms and a methyl hydrogen eclipsed with the C=O) enforced. Force calculations confirmed convergence to minima on the potential surface.25 We corrected the dimer interaction energies for both basis set superposition error (BSSE) and zero-point vibrational energies (ZPVE). We used the somewhat controversial26 counterpoise (CP)27 method to estimate the BSSE. The ab initio enthalpies28at 298 K were computed for comparison with the semiempirical results. The
0022-3654/93/2097-12197%04.00/0 0 1993 American Chemical Society
Turi and Dannenberg
12198 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
TABLE I: Total Energies of cis Acetic Acid and Relative Energies of trans total energy re1 energy method of cis (hartrees)" of trans (kcal/mol) AM 1 SAM 1 PM3 HF/6-31G HF/6-31G(d) HF/6-3 1G(d,p) HF/D95++(d,p) HF/6-31 l++G(d,p) MP2/6-31G MP2/6-3 1G(d) MP2/6-3 lG(d,p) MP2/D95++(d,p) MP2/6-311++G(d,p)
-103.0 -102.3 -102.0 -227.701 -227.810 -227.822 -227.876 -227.883 -228.135 -228.433 -228.469 -228.567 -228.644
116 0 647 6 171 5 044 2 547 8 590 3 979 1 224 4 032 9 032 4
5.9 7.9 2.6 8.4 7.2 7.1 6.8 6.8 7.1 7.0 6.8 6.3 6.1
Heats of formation (kcal/mol) for semiempirical methods. enthalpy of association is obtained from the calculated energies using eq 1:13,2* AHdim = AEel
+ AEvib- 4 R T
and electr~n-diffraction~~ results.39 Increasing the size of the basis set does not substantially improve the calculated geometries. On the other hand, the MP2 calculations (except 6-3 1G) agree reasonably well with the experimental geometries. Clearly, HF calculations are inadequate to describe the geometry of the monomer. The semiempirical methods do moderately well, especially for bond lengths. Oddly, PM3, which is worst for the relative energies of the conformations, gives the best geometry. All a b initio methods and PM3 predict one of the C-H bonds of the methyl group to be eclipsed with the C = O group at the global minimum. This structure is more stable than staggered by 0.4 kcal/mol using MP2/6-311++G(d,p). Both AM1 and SAM 1 predict, however, that the staggered (relative to the C=O bond) conformation is slightly preferred by 0.04 and 0.12 kcal/ mol, respectively. There are several possible structures for the dimer of acetic acid. Dimer I, containing two OH-0 H-bonds, predominates in both the gas and liquid phases. In dimer 11, one of the C-O-H-0 interactions is replaced by a C-O-H-C. Unlike dimer I, this dimer can participate in the hydrogen-bonded chains and is observed in the crystal structure.
(1)
where AEvib is the vibrational energy change upon dimerization and Evib is given by eq 2:
c H 3 y 0 \ H
0
For these calculations we used the C P corrected energies as A&. The AMPAC 2.129(AM1),AMPAC4S30(PM3 andSAMl), GAUSSIAN9231(ab initio), PCMODEL32 (generation of input and graphics), and MOTECC-9033 (illustration of vibrations) programs were used on IBM RS/6000 RISC and Ulysses System 386/486 workstations.
Results and Discussion Energies and Geometries. Acetic acid can exist in either the cis or trans conformation. The cis form is calculated to be more stable by 2.6-8.4 kcal/mol (Table I). The best calculations 0
0
)I
I
0
H
Trans
Cis
[MP2/6-31 lG++(d,p)] predict the difference to be 6.1 kcal/ mol. Aside from the calculations using 6-31G, all the a b initio calculations predict differences in the range 6.1-7.2 kcal/mol. Among the semiempirical methods, AM1 predicts 5.9 (close to the best ab initio value); SAM1, 7.9 kcal/mol (at the high end of the ab initio values); and PM3,2.6 kcal/mol (much less than any of the ab initio results). The cis structure probably owes its energetic preference to a combination of a weak internal H-bond and repulsion between the lone pairs on the hydroxyl and carbonyl oxygens that would occur in the trans conformation. As the cis form is more stable and the structure experimentally observed in both the gas-phase and crystal structures, the trans form is not likely to be important in the aggregation process. While one might expect the most stable conformer to exist in the crystal structure, this is not always the case. The crystal structures of (4-chlorophenyl)propiolic acid,341,3-cyclohexanedione,~a.3~ and formohydroxamic acid2I.'6 are among experimental examples of cases where the monomeric and crystalline structures differ. The calculated geometrical parameters of cis-acetic acid are collected in Table 11. The geometries (Table 11) predicted by the HF calculations are generally in poor agreement with experimental microwave37
cH3y0h, 0
I1 Table I11 collects the hydrogen-bonding energies of the optimized dimers I and 11. With the exception of HF/6-3 lG, the ab initio methods all predict AH of -1 1.2 to -1 1.8 kcal/mol for I. Reported experimental values are -13.8 to -17.0 kcal/ m01,10JlJ3which aresomewhat greater. Among thesemiempirical methods, SAM1 predicts -8.1 kcal/mol; PM3, -8.9 kcal/mol; and AMI, -6.4 kcal/mol. Multiplying the AM1 value by 1.9, as we suggested in a previous study,la gives -12.2 kcal/mol. One must consider the reasons for the discrepancies between the calculated and experimental enthalpies. We believe they come from overcorrection of the calculations. The uncorrected binding energies are all too large. Correction for BSSE or ZPVE reduces them to the approximate experimental range; however, correction for both lowers the values too much. The problem arises from the fact that C P correction reduces the depth of the potential well. Since the vibrational frequencies are calculated for the original potential well, they are too large, leading to an artificially excessive ZPVE. In principle, the ZPVE should be calculated on the BSSE corrected surface. The effect of CP correction of the potential surface upon the intermolecular vibrations has been illustrated by Bouteillier.40 We have encountered this phenomenon in other work.9 Moreover, the validity of the C P correction for BSSE remains controversial.26 Also, the accuracy of the experimental reports has been questioned by Mathews and Sheets,Iob who attributed the larger reported stabilizations to problems involving surface adsorption. Their preferred value (-14.21 kcal/mol), however, is still larger than those calculated here. Table I1 also presents the geometrical data for dimers I and 11. As in the case of the cis monomer, the HF calculations agree poorly with the experimental gas-phase structure. Only MP2/ 6-3 1G(d) agrees adequately with experiment. Curiously, all ab initio methods (except HF/6-3 1G) predict similar association energies (Table 111) despite the fact that the HF methods predict poor geometries for both the monomeric and dimeric acids. Del
MO Study of Acetic Acid Aggregation
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12199
TABLE II: Optimized Structures of cis-Acetic Acid Monomer, Dimers I and I' AMI
SAMl
monomer dimer I dimer Il
1.364 1.356 1.357 1.362
1.234 1.238 1.237 1.238
1.486 1.487 1.488 1.484
0.971 0.976 0.976 0.97 1
1.1167 1.1167 1.1163 1.1211
monomer dimer I dimer I1
1.385 1.368 1.372 1.383
1.249 1.259 1.256 1.255
1.521 1.524 1.524 1.520
0.971 0.988 0.986 0.971
1.0959 1.0961 1.0961 1.1053
monomer dimer I dimer I1
1.218 1.228 1.225 1.226 1.211 1.227 1.219 1.220 1.187 1.201 1.193 1.195 1.187 1.201 1.193 1.196 1.190 1.183 1.249 1.264 1.256 1.256 1.217 1.233 1.223 1.226 1.216 1.221 1.210
1.497 1.499 1.500 1.492 1.489 1.489 1.491 1.487 1.502 1.501 1SO4 1.499 1.501 1SO3 1.498 1.SO5 1.500 1.508 1 SO7 1.510 1.504 1s o 0 1.499 1SO3 1.494 1 .500 1SO6 1.501
0.952 0.967 0.967 0.953 0.954 0.973 0.967 0.955 0.952 0.966 0.961 0.953 0.948 0.962 0.957 0.948 0.950 0.946 0.985 1.004 0.995 0.986 0.979 0.990 0.980 0.970 0.973 0.967
1.0973 1.0974 1.0973 1.1148 1.0775 1.0772 1.0776 1.0772 1.0793 1.0794 1.0797 1.0783 1.0794 1.0794 1.0797 1.0786 1.0798 1.0797 1.0934 1.0931 1.0935 1.0933 1.OM3 1.0883 1.0884 1.0883 1.0830 1.0864 1.0877
0.970 0.946 0.97s 1.038 1.011
MP2/6-3 1G(d,p) MP2/D95++(d,p) MP2/6-31 l++G(d,p) experiment microwaved microwave gas electron diffraction/ gas electron diffraction/ neutron diffraction*
monomer monomer monomer
1.355 1.339 1.341 1.348 1.355 1.326 1.336 1.345 1.332 1.308 1.318 1.325 1.331 1.306 1.316 1.323 1.333 1.331 1.403 1.368 1.381 1.391 1.361 1.330 1.344 1.352 1.360 1.365 1.358
monomer monomer monomer dimer I solid (11)
1.357 1.323 1.364 1.334 1.321
1.209 1.243 1.214 1.231 1.206
1.494 1.500 1.520 1.506 1.501
X-ray diffraction'
solid (11)
1.319
1.226
1.479
PM3
HF/6-3 1G
HF/6-3 1G(d)
HF/6-3 lG(d,p)
HF/D95++(d,p) HF/6-31 I++G(d,p) MP2/6-3 1G
MP2/6-3 1G(d)
monomer dimer I dimer I1 monomer dimer I dimer I1 monomer dimer I dimer I1 monomer monomer monomer dimer I dimer I1 monomer dimer I dimer I1
1.501
1.OW
1.1178 1.1176 1.1176 1.1163 1.1182 1.0967 1.0970 1.0970 1.0959 1.0980 1.0979 1.0980 1.0979 1.0973 1.0821 1.0821 1.0822 1.0825 1.0838 1.0838 1.0840 1.0841 1.0840 1.0839 1.0841 1.0842 1.0842 1.0842 1.0967 1.0967 1.0967 1.0971 1.0921 1.0921 1.0922 1.0925 1.0868 1.0903 1.0918
1.090 1.086 1.102 1.102 1.078 1.050 1.052
3.067 3.076
2.710 2.741
3.284
116.5 117.3 117.3 116.1
129.3 128.2 128.4 129.3
109.8 110.5 110.5 109.9
2.975
119.8 121.3 121.0 118.8
128.9 126.3 127.1 129.0
107.7 109.0 109.2 107.9
115.7 117.5 117.5 114.6 121.7 122.6 122.8 120.4 122.4 123.6 123.6 121.3 122.3 123.6 123.6 121.2 122.2 122.3 122.1 123.4 123.3 120.7 122.6 124.3 124.1 121.1 122.7 122.5 122.7
129.1 126.8 127.3 128.7 126.3 123.9 124.6 126.4 125.8 123.6 124.4 126.1 125.7 123.5 124.3 126.0 125.7 125.8 126.9 123.8 125.0 126.9 126.4 123.3 124.6 126.7 126.3 126.3 126.3
109.9 112.1 112.4 110.0 113.8 115.8 115.9 114.2 108.1 110.8 110.5 108.5 108.3 111.0
123.8 122.4 122.8 123.4 121.9
126.2 123.4 126.6 123.6 124.9
121.3
124.9
2.741 2.741
2.934
2.714 2.763
3.402
2.794 2.863
3.479
2.779 2.855
3$461
2.763 2.833 2.742 2.828
2.684 2.631
3.393
3.349
3.429
2.624
110.8
108.7 108.6 108.8 109.6 112.6 112.3 110.8 105.5
109.1 108.5 106.0 105.4 105.7 105.9 105.9 108.4 107.01 110.01 110.5
For dimer 11, first entries correspond to the acetic acid molecule whose O H is the H-bond donor. Bond lengths are in angstroms and bond angles in degrees. H is in the plane of the heavy atoms. e H is out of the plane of the heavy atoms. Reference 37a. Reference 37b. f Reference 38. 8 Estimated value. At -140 OC. Reference 6c. The results of ref 6b interpolated to -140 "C by ref 6c.
*
'
TABLE IIk Hydrogen-Bonding Energies (kcal/mol) of Acetic Acid Dimers I and I1 hydrogen-bonding energies method HF/6-31G HF/6-3 1G(d) HF/6-3 1G(d,p) MP2/6-31G MP2/6-3 1G(d) AM1 S A M1
PM3 expt"
dimer I I1 I I1 I I1 I I1 I I1 I I1 I I1 I I1 I I
without corr
after CP
after ZPVE
after CP+ZPVE
-19.5 -11.5 -15.6 -8.8 -15.5 -8.8 -18.8 -11.2 -19.1 -11.2
-16.7 -9.6 -13.1 -7.1 -13.2 -7.2 -13.2 -7.4 -13.5 -7.3
-17.8 -10.2 -14.0 -7.6 -14.0 -7.7 -16.8 -9.8 -17.4 -9.9
-15.0
-8.4 -11.5 -6.0 -11.7
enthalpies at 298.15 K -15.0
-8.0 -1 1.3
-5.6 -1 1.6
-6.1
-5.7
-11.3 -5.9 -11.8
-1 1.2
-6.0
-5.6 -1 1.8
-5.7 -6.4 4.9 -8.1 -5.0 -8.9 -5.4 -13.8 to-17.0 -14.2b
Referenccs 10, 11, and 13 for dimer I. Our preferred value from ref 10b for dimer I.
Bene has suggested that HF/6-31G(d) is a good basis set for H-bond calculations due to a fortuitous cancellation of errors.41 The present results support that conclusion with respect to the interaction energies, but not for the optimized geometries. The ab initio methods (again except 6-31G) predict I1 to have
H-bonding enthalpiesof-5.6 to-5.7 kcal/mol (Table 111). Among thesemiempirical methods, PM3 is closest (-5.4 kcal/mol), while AM1 and SAMl predict slightly weaker interactions. We have previously suggestedthat AM1 is accurate for CH-0 interactions, while SAMl overestimates them and PM3 is e r r a t i ~ . ~
12200 The Journal of Physical Chemistry,Vol. 97, No. 47, 1993
Turi a n d Dannenberg
TABLE I V Hydrogen-Bonding Energies (kcal/mol) of Acetic Acid Dimers 111 and IV hydrogen-bonding energies method HF/6-31@
dimer
without w r r
after CP
after ZPVE
-
-
-
-4.3 -6.3 -3.3 -6.2 -3.4 -8.1 -5.1 -8.0 -5.2
-3.2 -5.3 -2.1 -5.3 -2.2 -5.8 -2.4 -5.6 -2.5
-3.6 -5.5 -2.6 -5.5 -2.7 -7.1 -4.2 -7.1 -4.4
111 IV I11 IV III IV 111 IV I11 IV I11 IV I11 IV
HF/6-31G(d) HF/6-3 lG(d,p) MP2/6-3 1G MP2/6-31G(d) AM1 SAM 1
after CP+ZPVE -2.5 -4.5 -1.5 -4.6 -1.6 -4.8 -1.5 -4.7 -1.6
enthalpies at 298.15 K
-1.8 -4.4 -0.8 -4.5 -0.9 -4.8 -1 .o -4.7 -1.1 -2.8 -3.6 -1.9 -2.8 -3.2 -2.1
111
PM3
IV a
No minimum observed at the HF/6-3 1G level.
TABLE V
Calculated and Experimental Frequencies of Acetic Acid Monomer. Hartrce-Fock IV I1 I11
Moeller-Pltsset I11 IV
vibrations
AM1
PM3
SAM1
I
v
I
I1
V
exp
r(CH3) A” r(O-H) A“ 6(C-(2-0) A‘
23.0 521.3 418.1
37.5 506.4 394.7
56.3 527.8 406.7
110.4 588.4 452.6
100.8 587.2 451.1
102.9 584.6 452.0
98.9 579.2 454.7
96.3 582.3 452.2
99.8 549.4 423.8
90.5 557.6 427.6
90.7 554.7 426.6
58.4(0.6) 531.3 (48.8) 429.1 (3.9)
43.4 542.1 426.1
6(O=C-0) A’ 570.1 r(C-C==O) A” 589.1 u(C-C) A’ 1100.2
466.4 556.8 570.2 597.1 961.5 1027.7
621.6 701.1 930.8
637.4 725.3 938.3
638.0 721.3 937.4
640.4 705.6 931.7
636.3 706.7 935.4
568.0 652.9 845.4
585.9 695.3 888.3
584.4 690.5 888.0
589.2 (38.6) 640.8 (82.9) 880.9 (6.7)
579.8 644.9 877.8
p,(CH,) A’
1038.7
977.5 1004.7 1127.8 11 13.9 1106.6 1101.3 1104.3 1027.3 1035.4 1032.2 1015.8 (69.7)
1025.4
p,(CH3) A”
1073.4 1007.6 1046.8 1205.0 1183.8 1175.5 1170.3 1172.2 1122.9 1103.8 1098.3 1072.3 (5.4)
u(C-0) A’
1549.7 1450.0 1433.9 1298.4 1355.1 1346.3 1339.0 1343.9 1190.7 1239.8 1232.0 1222.9 (218.8) 1224.3
6(0-H) A’
1430.4 1240.6 1285.3 1483.4 1483.5 1474.0 1453.4 1461.8 1370.8 1388.1 1382.2 1349.6 (43.5)
1356.8
6,(CH,) A‘
1412.8 1355.4 1344.0 1584.4 1574.1 1562.8 1546.6 1555.7 1482.7 1469.3 1465.7 1428.8 (66.2)
1446.7
6,’(CH3) A’ &(CHI) A” u(C=O) A’
1364.2 1386.7 1355.6 1624.0 1613.7 1596.3 1586.8 1589.0 1553.9 1537.2 1534.9 1492.3 (14.0) 1509.7 1371.7 1385.8 1363.1 1630.0 1619.6 1604.0 1594.9 1597.7 1550.4 1538.9 1539.3 1493.0 (9.9) 1510.4 2087.7 1981.6 1998.0 1925.4 2040.6 2038.6 2002.2 2014.3 1720.7 1862.0 1862.7 1826.2 (302.9) 1826.0
u1(CH3) A’
3153.0 3176.0 2968.7 3223.4 3231.8 3211.4 3193.6 3219.9 3091.2 3132.3 3156.8 3107.3 (1.7)
3140.0
ua(CH3) A“ u,’(CH3) A‘ u(O-H) A‘
3058.4 3083.6 2899.3 3294.4 3295.4 3279.0 3256.9 3294.2 3174.8 3218.0 3249.9 3192.8 (2.4) 3069.4 3091.1 2906.9 3341.5 3345.1 3327.8 3303.0 3340.9 3207.1 3257.4 3289.1 3232.5 (3.1) 3431.2 3854.1 3397.2 3992.2 4054.3 4129.9 4117.4 4132.4 3596.8 3696.4 3818.7 3812.5 (73.7)
3241.6 3280.9 3814.4
936s 5346 5816 448.06 6426 642b 8476 850.9d 989b 988e 10486 1075‘ 11826 117V 12646 1280’ 13826 139Y 14306 14306 17M6 178P 29446 2954.1d 29966 30516 35836 3583.
1081.0
For the best ab initio calculation (MP2/6-31 l++G(d,p)), the calculated IR intensities are in parentheses. Frequencies are in cm-I and intensities in km/mol. Basis sets: I, 6-31G; II,6-31G(d); 111,6-31G(d,p); IV, 6-31 l++G(d,p); V, D95++(d,p). Reference 44. Calculated value from ref 44. Reference 46. e Reference 45.
In an infinite one-dimensional aggregate similar t o t h e crystalline arrangement, each acetic acid molecule forms two pairs (one OH--O a n d one CH-0) of H-bonds (see Figure 1). On the other hand, each carboxylic acid in a crystal constructed from dimers analogous to I can only form one pair (two OH-0) of H-bonds. If t h e H-bonding energy of I1 be more than half t h a t of I, this would be sufficient to suggest t h a t infinite chains of I1 be enthalpically preferred before cooperativity or interactions in the second a n d third dimensions are considered. If one assumes t h a t each OH-.O interaction energy is the same in both dimers, then the additional stabilization (before cooperativity is considered) is d u e to t h e two CH-0 (in addition to t h e two OH-0) interactions t h a t occur in infinite chains of dimer 11. T h e data of Table I11 indicate t h a t this condition is not met for all a b initio calculations, indicating that cooperativity will probably play an important role in determining t h e crystal s t r u a u r e . This subject will be further developed in a subsequent paper. T h e semiempirical calculations appear to suggest t h a t t h e cooperativity is not necessary to achieve the preference of infinite chains with interactions similar to 11. This c a n easily be seen a s a n artifact
d u e t o the underestimation of the stability of I by all three semiempirical methods. From Table 11, one can see that the calculatedgeometrical parameters for I1 a r e significantly different from those taken from the crystal data. This observation is consistent with our assessment t h a t cooperativity is important to determining t h e crystal structure. W e can estimate t h e energy of t h e CH-0 interaction in several different ways. First, again assuming that each OH-0 interaction is energetically equivalent in both dimers, t h e CH-0 interaction energy should be t h e difference between t h e stabilization of I1 less half that of I. Using the results for t h e highest-level calculation [MP2/6-3 l G ( d ) ] , t h e CH-0 interaction becomes -1.54,4.56, -1.17, -0.10, a n d +0.22 kcal/mol for uncorrected, CP corrected, ZPVE corrected, both corrections, and enthalpy at 298 K, respectively. Thus, the stabilization d u e t o the CH-0 interaction, which is apparent in t h e original calculation, becomes attenuated a n d eventually disappears upon application of all corrections. While acetic acid is liquid at 298 K, we do not attribute this to an enthalpically repulsive CH..-Ointeraction. Rather, we believe
M O Study of Acetic Acid Aggregation I
H
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12201
i
Figure 1. Orientation of acetic acid molecules in the hydrogen-bonded chains of the crystal structure.
that the calculated enthalpies are too low due to the overcorrection discussed above. Another method of estimating the strength of the CH-0 bond involves comparison of I1 with 111, where the CH--O interaction is absent. In 111,a cis monomer hydrogen bonds to a trans-acetic
cH3y?H o
\
“O
Yo-
I11
acid with one 0-H-0 H-bond. (Using two cis acids would have resulted in an additional attractive interaction between the acidic hydrogen and the oxygen atom of the OH group.) The hydrogenbonding energies and enthalpies of dimer 111 are collected in Table IV. The ab initio calculations predict a consistent H-bonding enthalpy of -4.4 to -4.8 kcal/mol. The difference in the stabilizations for 111 and I1 (AEIII- MII) should correspond to the C-H-.O stabilization. The MP2/6-31G(d) values are 3.16,1.75,2.73, 1.32, and 1.01 kcal/mol depending on the extent of correction. A third method of estimating the CH-.O interactions involves consideration of dimer IV, a cyclic complex with two C-Ha-0
IV hydrogen bonds. Half the interaction energy should represent the stabilization due to one CH.-O H-bond. Its H-bonding energies and enthalpies are presented in Table IV. These data suggest the H-bonding enthalpy of one C-H--0 interaction to be
in the range of -0.40 to -0.53 kcal/mol. These, presumably underestimated values (see the discussion above about the overcorrection of ZPVE and C P corrections) are smaller than those determined by the semiempirical methods. Although these approximations give slightly different estimates of the C-Ha-0 interaction energy, they suggest a value of slightly less than 1 kcal/mol (considering the overcorrection when CP and ZPVE corrections are both applied), which is in agreement with previous estimates of other C-H-0 interactions.9 The sum of the H-bonding energy of 111 and the half of the interaction energy of IV can be compared to the H-bonding of 11. Since I1 contains one OH-0 and one CH-0 interaction, this provides a test of the additivity of the individually determined OH-0 (from 111) and CH-0 (from IV) interaction energies. At the best a b initio level, the interaction energy of dimer I1 is greater than the sum by 0.55,0.51,0.55,0.51, and 0.48 kcal/mol for the uncorrected, CP corrected, ZPVE corrected, C P corrected, and ZPVE corrected energies and enthalpy at 298 K, respectively. Thus, the interaction energy of I1 is consistently 0.5 kcal/mol stronger than the sum of the estimated individual OH-.O and CH-0 interactions independent of the extent of correction. In all calculations the interaction energies of 111 are less than half of that of I. At the MP2/6-31G(d) level the difference ( h E 1 - 2AE111) is -3.06, -2.38, -3.14, -2.46, and -2.46 kcal/mol for uncorrected, C P corrected, ZPVE corrected, CP, and ZPVE corrected energies and enthalpy at 298 K, respectively. Thevalues for the CP corrected interactions are about 0.6 kcal/mol lower, indicating larger BSSE in I than 111. The observations that I is stabilized by 2.4-3.1 kcal/mol, more than twice the OH-0 stabilization of 111, while I1 is stabilized by 0.5 kcal/mol more than expected from the CH--O and OH-0 interactions determined from 111 and IV suggest that there might be a cooperative interaction inherent in the cyclic H-bonding structures of I and 11. This suggestion is reinforced by comparison of the structures of the monomer and the various dimers. The shortening of the C-0 bonds and the O--O distances and the lengthening of the C=O and 0-H bonds are all more pronounced in the structure of dimer I than II.42 One should note that IV is also cyclic. Therefore, there may already be some cooperativity in the estimate of the CH-0 interactions derived from it. (We were unable to find a conformationally stable structure with only one CH-0 interaction.) Thus, the 0.5 kcal/mol for the cooperativity in I1 might be slightly low. The C-H bond distances have been included in Table I1 upon the suggestion of a referee. The in-plane are consistently shorter than the out-of-plane C-H bond lengths, in accord with previous reports.j9a>43The difference between the two distinct C-H bond types for acetic acid has been reported to be constant (0.00520.0053 b;) for HF/4-21G and HF/5-31G** optimization^.^^ The present data suggest that these values to be 0.0044-0.0046 8,for H F and 0.0033-0.0041 b; for MP2 calculations, in conflict with the earlier findings. Vibrational Analysis. Tables V and VI contain the calculated and the experimental vibrational frequencies of cis-acetic acid and dimer I, while Table VI1 presents statistical analyses of comparisons to experimental frequencies. Previous ab initio (43 1G) frequency calculations have been reported for monomeric acetic acid.’“ In Table V, the calculated frequencies are listed corresponding to the observations of Haurie and Novak,44 Mar6chal,45 Bertie and M i ~ h a e l i a nand , ~ ~Zelsmann et al.47 All of the assignments are straightforward except for 6(0-H), the 0-H in-plane bend, and v(C-0), the C-0 stretch, which are strongly coupled. We assign the lower frequency to the C-0 stretching vibration as it is predicted to have the higher intensity by all a b initio methods in accord with expectations for a C-0 stretch and MarCchal’s as~ignment.~5 All ab initio methods predict the same order with one exception: a t the MP2/6-31G level the asymmetric appears at higher frequency than the symmetric methyl deformation. All
Turi and Dannenberg
12202 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
TABLE VI: Calculated a d Experimental Frequencies (cm-1) of Acetic Acid Dimer I* HF vib modes AM1 PM3 SAM1 I I1 I11 Intermolecular Frequencies 73.2 53.7 61.5 84.3 72.9 43.8 y(twist) A, ~ ( 0 - H - 0 ) A, r(O-H*.O) B, b(O-H..O) A, v(O-H*.O) A, b(0-H-0) &
21.0 50.9 68.5 141.2 128.3
41.3 82.7 135.0 285.5 220.3
30.9 82.5 120.1 204.7 182.9
19.6 22.2 422.0 447.5 539.8 538.4 582.1 567.6 1101.1 1100.6 602.0 629.7 1041.1 1041.2 1072.7 1073.2 1569.1 1575.0 1410.6 1409.7 1422.9 1424.0 1364.6 1364.7 1372.1 1372.1 2062.7 2077.4 3153.7 3153.6 3059.6 3059.7 3070.0 3070.0 3373.9 3385.6
34.5 33.5 421.1 557.5 563.8 562.9 572.5 497.7 988.4 974.5 647.7 679.7 983.5 987.0 1007.6 1008.5 1491.9 1497.1 1361.2 1360.4 1291.0 1272.1 1389.4 1388.8 1385.5 1385.5 1918.5 1948.2 3176.2 3176.0 3083.0 3083.0 3091.4 309 1.4 3735.5 3771.6
40.8 35.2 419.1 472.6 542.7 542.4 595.7 584.3 1034.0 1034.9 682.2 703.0 1009.5 1009.8 1044.6 1045.4 1479.2 1482.6 1348.6 1348.0 1295.7 1289.2 1358.2 1358.3 1364.6 1364.6 1928.9 1964.3 2967.5 2967.4 2896.9 2896.9 2904.7 2904.8 3120.9 3155.7
55.4 120.8 162.2 180.0 168.2
48.9 117.7 154.1 165.2 157.8
MP2
I
I1
expt 48.56 56.P 98.9' 120.w 155.W 171.P
49.7 118.1 153.9 159.6 153.9
78.2 51.7 123.0 154.8 172.2 167.6
72.0 (0.0) 50.7 (4.3) 128.2 157.1 178.4 174.3 (23.1)
84.0 91.9 468.6 493.1 654.9 645.3 668.4 670.1 967.6 968.7 913.3 966.9 1123.8 1125.9 1177.7 1179.0 1436.9 1436.1 1527.8 1510.1 1586.8 1587.6 1612.1 1603.1 1604.0 1604.0 1951.1 1989.5 3212.2 3212.1 3280.2 3280.2 3328.2 3328.3 3805.3 3854.2
83.3 88.9 441 .O 475.5 586.5 582.1 607.8 611.6 887.3 882.4 930.1 972.7 1072.9 1078.6 1126.9 1128.3 1280.0 1285.8 1460.1 1455.2 1485.6 1488.5 1554.2 1551.5 1550.0 1550.0 1687.6 1694.8 3091.2 3091.2 3174.4 3 174.4 3207.8 3209.1 3215.0 3295.2
79.9 86.6 (0.4) 446.1 483.3 (34.3) 609.9 601.4 (0.3) 627.1 632.4 (53.5) 925.0 923.8 (3.8) 941.1 987.4 (254.2) 1063.8 1066.3 (37.2) 1106.8 1107.5 (11.3) 1342.1 1349.9 (365.2) 1447.6 1435.9 (1.4) 1516.2 1505.4 (208.6) 1540.3 1535.5 (52.2) 1538.1 1538.1 (19.5) 1789.4 1825.1 (625.2) 3131.4 3131.5 (1.3) 3217.4 3217.4 (3.5) 3256.2 3257.0 (10.3) 3275.6 3357.3 (2338.3)
Intramolecular Frequencies
a
90.9 99.5 467.0 499.8 646.0 639.8 655.4 655.7 960.7 959.6 978.0 1032.2 1153.1 1156.8 1207.4 1209.0 1405.7 1396.9 1559.1 1551.2 1592.1 1596.4 1626.6 1622.0 1629.1 1629.7 1852.3 1871.6 3223.5 3223.5 3294.2 3294.2 3343.9 3343.9 3580.9 3647.4
83.6 91.6 467.6 494.4 655.9 646.4 668.1 668.0 967.1 968.2 909.3 963.1 1131.3 1133.6 1185.9 1187.1 1436.8 1436.4 1539.9 1521.7 1599.2 1598.6 1620.2 1614.6 1619.6 1619.6 1955.8 1993.3 3232.5 3232.5 3296.8 3296.8 3344.7 3344.8 3166.9 38 13.6
438.7C 616.2' 616.2c 623.06 89 1.7' 896.06 942.06 1007.W 1014.06 1065.W 1066.06 1285.W 1290.06 1370.2C 1428.3' 1430.06 1428.3' 1430.06 1681.5' 1737.06 2954. l e
3035.W 2965.06
For the best ab initio calculation (MP2/6-31G(d)), the calculated IR intensities are in parentheses. Frequencies are in cm-I and IR intensities Reference 47. Reference 46. Reference 45. *Calculated value from ref 47/The
in km/mol. Basis sets: I, 6 3 1 G ; II,631G(d); III,6-31G(d,p). methyl and hydroxyl bends are strongly coupled.
MO methods (both a b initio and semiempirical) predict the 6the semiempirical have smaller errors than the HF calculations, though thestandarddeviations aresimilar. The MP2 calculations (C-(2-0) in-plane torsion to appear a t lower frequency than the r(O-H), the wagging motion of the 0-H hydrogen. S v e r d l o ~ ~ ~ provide the best results. The corrected assignment of S(C-C-O) assigned a band at 452 cm-1 to the S(C-C-0) vibration, but his provides an improvement in the error analysis (about 15 cm-1 or proposal was ignored for about 25 years. Raman studieslq.M 2 4 %in standard deviation). The analyses for the frequencies reopended the assignment of the sharp monomer band found at of dimer I show somewhat larger error. The assignment of the experimental frequencies is complicated by the somewhat broad 448 cm-I. As all of our calculations agree with Sverdlov and the Raman studies, we assign the S(C-(2-0) vibration to the band peaks in the spectra. All MO calculations predict the two lowest at 448 cm-1. The qualitative order of the semiempirical intermolecular vibrations to be in the reverse order to the frequencies is not the same as that of the a b initio calculations. experimental assignments. Since they both have the same symmetry (A,,) and the predicted IR intensity of one of them is The stretching vibrations are generally overestimated, while the frequencies of methyl distortions (which are approximately close to zero, their relative assignment is difficult. We assign the correct) are in the wrong order. lower frequency to the out-of-plane bend, rather than the twist. Table VI presents the calculated and experimental frequencies Table VI11 compares the calculated frequencies of the monofor dimer I. In the dimer, each monomer vibration is doubled, mers (cis and trans) with those of all four dimers for the MP2/ resulting in pairs of symmetric (8) and unsymmetric (u) 6-3 1G(d) calculations (the highest level used for dimer frequenfrequencies which are alternatively Raman- and IR-active. While cies). Several comparisons are particularly interesting. The 0-H the frequency shifts and splittings for most pairs are small, several stretches are both considerably weakened in I. For 11, only one large shifts and splittings are observed. They are particularly 0-H stretch is weakened as there is but one H-bond. In 111, the apparent for those vibrations that should be most affected by the H-bond involves the 0-H of the cis conformation, whose frequency H-bonding interactions, such as the0-H stretches (which weaken) decreases significantly while that of the trans barely changes. and out-of-plane deformations (which stiffen considerably). IV, which has no 0-H H-bonds, shows little change in 0-H The statistical analyses of Table VI1 indicate that the HF a b stretch. The C=O stretches are weakened in all four dimers, initio methods tend to overestimate the frequencies. Surprisingly, but particularly in I. The frequencies for the C-0 stretches and
The Journal of Physical Chemistry, Vol. 97, NO. 47, 1993 12203
M O Study of Acetic Acid Aggregation
TABLE VII: Statistical Analyses of Freauency Calculations' Hartree-Fock method AM1 PM3 SAM1 I I1 I11 IV Monomers ratio av
SD
1.037 (1.028) 0.119 (0.140)
0.995 (0.986) 0.111 (0.130)
1.099 (1.089) 0.046 (0.089)
0.998 (0.989) 0.093 (0.1 16)
1.107 (1.097) 0.044 (0.088)
1.103 (1.093) 0.043 (0.087)
1.095 (1.085) 0.038 (0.083)
~~~
V
I
I1
1.099 1.023 1.043 (1.089) (1.014) (1.033) 0.041 0.052 0.044 (0.085) (0.087) (0.084)
abs error av
SD
57.3 (53.3) 142.1 (150.7)
37.1 (32.7) 129.9 (137.0)
-8.6 (-12.6) 116.1 (122.4)
162.3 (158.3) 109.4 (125.2)
175.6 (171.6) 117.5 (132.4)
171.8 (167.8) 127.3 (140.8)
159.5 (155.5) 122.0 (135.1)
~~
MP2
169.1 (165.1) 130.0 (143.0)
50.8 (46.8) 73.6 (89.0)
80.5 (76.5) 71.8 (88.4)
I11
IV
1.044 1.023 (1.035) (1.014) 0.045 0.039 (0.085) (0.077) 90.6 (86.6) 89.3 (103.6)
61.9 (57.9) 78.5 (91.7)
V 1.030 (1.020) 0.044 (0.082) 74.3 (70.3) 90.4 (103.3)
Dimer IC ratio 1.001 1.132 1.116 1.113 0.961 1.033 av 1.061 1.077 0.132 0.206 0.198 0.095 0.076 SD 0.079 0.095 0.080 abs error av 56.7 42.8 13.1 129.4 139.3 136.1 47.1 68.7 114.4 128.5 158.5 163.1 159.3 184.1 73.4 78.2 SD Ratios are calculated over the experimentalfrequencies,while the absolute errors are the differencebetween calculated and experimentalfrquencies in cm-I. Standard deviations are relative to the average values of different types of error. Basis sets: I, 6-31G; 11, 6-31G(d); 111, 6-31G(d,p); IV, 6-31 l++G(d,p); V, D95++(d,p). Comparison made to the most recent values of refs 45 and 46 (S(C-C-0) is assigned to 448 cm-1). The values in parentheses are compared to ref 44, where S(C-C-0) is assigned to 581 cm-l. Comparison made to refs 45-47.
TABLE MII: Comparison of the Calculated Frequencies (in cm-') for Acetic Acid Monomers with the Intramolecular Frequencies of Dimers I, 11,111, and IV at the MP2/6-31C(d) Level monomers dimers approxvibmodes cis trans I I1 111 IV 90.5
128.2
427.6
437.6
585.9
597.7
695.3
606.0
557.6
466.2
888.3
880.6
1035.4 1025.5 1103.8 1092.9 1239.8 1245.6 1388.1 1343.8 1469.3 1454.4 1537.2 1540.4 1538.9 1549.0 1862.0 1884.3 3132.3 3115.4 3218.0 3196.7 3257.4 3252.8 3696.4 3756.0
79.9 86.6 446.1 483.3 627.1 632.4 601.4 609.9 941.1 987.4 923.8 925.0 1063.8 1066.3 1106.8 1107.5 1342.1 1349.9 1505.4 1516.2 1435.9 1447.6 1535.5 1540.3 1538.1 1538.1 1789.4 1825.1 3131.4 3131.5 3217.4 3217.4 3256.2 3257.0 3275.6 3357.3
84.5 156.3 439.1 452.6 601.7 611.8 565.3 598.0 707.4 891.6 900.4 908.9 1053.3 1060.7 1103.4 1115.3 1255.8 1299.5 1408.1 1427.0 1480.9 1484.8 1537.5 1538.8 1539.7 1557.4 1825.7 1843.9 3128.2 3130.6 3213.4 3216.0 3254.7 3262.5 3501.6 3689.4
98.1 122.6 437.0 447.7 595.3 619.5 594.3 612.4 478.4 893.0 891.5 901.6 1036.2 1047.3 1096.3 1101.8 1249.5 1286.0 1459.2 1477.0 1359.3 1416.7 1539.4 1546.9 1537.4 1540.9 1849.6 1864.2 3117.6 3128.8 3199.7 3214.1 3251.7 3256.6 3535.4 3751.6
155.2 165.1 438.2 441.6 588.8 591.3 562.7 563.1 699.1 700.2 890.7 892.7 1045.2 1049.1 11 10.2 1112.2 1244.3 1247.0 1391.2 1397.8 1478.3 1479.0 1539.5 1544.0 1553.7 1557.9 1844.9 1852.6 3127.2 3127.4 3211.3 3211.4 3258.5 3259.8 3694.0 3694.2
0-H deformations (which are strongly coupled) increase in each dimer, particularly for I. There are apparent weakenings of two C-H stretches (at 3132 and 3218 cm-1) for one vibration in I1 and both in IV. Similarly, the methyl deformation at 1539 cm-1 increases for one vibration for I1 and both for IV. The particularly large changes in the 0-H, C=O, and C-0 vibrations for dimer I (in comparison to the other dimers) provides additional evidence for substantial cooperativity in the cyclic
structure. The smaller changes in dimers I1 and IV suggest less cooperativity for these cases. On the other hand, the changes in the methyl vibrations of I1 and IV confirm the presence of CH-0 H-bonding interactions.
Conclusions Our calculations show that HF wave functions (while they often give reasonable energies of interaction) are insufficient to correctly describe the geometries of acetic acid and its gas-phase dimer, I. Optimization at least at the MP2 level is necessary. We expect these conclusions to apply to the other dimers as well. Comparisons of the stabilization energies of the various dimers suggest that there are cooperative contributions to the stabilizations of the cyclic dimers, especially for I, where it is about 2.4-3.1 kcal/mol. Comparison of the vibrations of the dimers with those of the monomers confirms this cooperativity. We estimate the C-H-0 contribution to the stability of I1 to be about 0.5-1.0 kcal/mol. This is not sufficient to explain the preference for I1 in the crystal structure, which must involve additional cooperative effects associated with further aggregation. The vibrational frequencies of acetic acid and dimer I are in the same qualitative order for all levels of ab initio calculation. On the basis of the calculated vibrations, we suggest that Sverdlov's original assignment of 6(C-C-0) is correct and that the assignments of the two lowest intermolecular vibrations for I be reversed. The MP2/6-31G(d) calculated frequencies are reasonably accurate, while the HF frequencies are generally too high.
Acknowledgment. This work was supported in part by the PSC-BHE, NSF, and IBM Corp. References and Notes (1) (a) Turi, L.; Dannenberg, J. J. J . Phys. Chem. 1992,96,5819. (b)
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