Interaction of formaldehyde with water - The Journal of Physical

Molecular Dynamics Simulation of the Reaction of Hydration of Formaldehyde Using a Potential Based on Solute−Solvent Interaction Energy Components...
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4478

J . Phys. Chem. 1989, 93, 4478-4486

Interaction of Formaldehyde with Water Robert A. Kumpf and James R. Damewood, Jr.* Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716 (Received: September 19, 1988)

The interaction of water with formaldehyde (1) (hydration) is investigated at high levels of ab initio theory. Results of calculations performed at the 6-31G**//6-31G**, MP2/6-31G**//6-31G**, 6-31l+G**//6-31G**, MP2/6-31 l+G**//6-31G**, MP3/6-3 1 1+G**//6-31G**, MP4DQ/6-311 +G**//6-3 1G**, and MP4SDQ/6-3 1 l+G**//6-3 IC** levels are discussed and compared with results obtained from previous studies.

Introduction Water is one of the most abundant substances on Earth and its interaction with organic molecules (hydration) in chemical and biochemical systems is ubiquitous. Understanding these interactions is key to uncovering the factors responsible for reactivity and chemical properties in aqueous environments. Formaldehyde (1) plays a central role in molecular hydration studies since it is the simplest representative of carbonyl-containing compounds. It therefore serves as a particularly good model system for a variety of molecules of chemical and biochemical interest. In the present study we employ ab initio methods at levels of theory as high as MP4SDQ/6-31 l+G**//6-31G** in order to investigate the interaction of 1 with water. Other computational studies of the hydration of 1 in the ground state have been reported;] however, ( I ) For previous computational studies of I-water interaction (caption letters to Figure 2 are parenthesized after references), see: (a) Schuster, P. Int. J. Quantum Chem. 1969,3,851 (g, cc, gg, hh). (b) Schuster, P. Theor. Chim. Acta 1970, 19,212 (h, bb). (c) De Jeu, W. H. Chem. Phys. Lett. 1970, 7, 153 (2). (d) Rao, C. N. R.; Murthy, A. S. N. Theor. Chim. Acta 1971, 22, 392 (i). (e) Rao, C. N. R.; Goel, A,; Rao, K. G.; Murthy, A. S. N. J . Phys. Chem. 1971, 75, 1744 (d, y). (f) Morokuma, K. J. Chem. Phys. 1971, 55. 1236 (I, ee, nn, ww, yy). (9) Johansson, A.; Kollman, P. A. J . Am. Chem. SOC.1972.94,6196 (n). (h) Del Bene, J. E. J . Chem. Phys. 1973,58,3139 (0). (i) Del Bene, J. E. J . Am. Chem. SOC.1973, 95, 6517. 6)Cremaschi, P.; Gamba, A.; Simonetta, M. Theor. Chim. Acta 1973, 31, 155 (dd). (k) Iwata, S.; Morokuma, K. Chem. Phys. Lett. 1973, 19, 94. (I) Del Bene, J. E. Chem. Phys. Lett. 1974, 24, 203 (22). (m) Johansson, A,; Kollman, P.; Rothenberg, S.; McKelvey, J . J . Am. Chem. SOC.1974, 96, 3794 (t). (n) Tapia, 0.;Nogales, A.; Campano, P. Chem. Phys. Lett. 1974, 24, 401 (e, aa). (0)Kollman, P.; McKelvey, J.; Johaansson, A,; Rothenberg, S . J . Am. Chem. Soc. 1975,97,955 (u,v). (p) Yamabe, S.; Morokuma, K. J . Am. Chem. SOC. 1975,97,4458. (q) Lathan, W. A.; Pack, G. R.; Morokuma, K. J . Am. Chem. SOC.1975,97, 6624 (m). (r) Murthy, A. S. N.; Saini, G. R.; Kamla, D.; Shah, S . B. Adu. Mol. Relax. Processes 1975, 7, 255 (j,w). (s) Swaminathan, S.; Whitehead, R. J.; Guth, E.; Beveridge, D. L. J . Am. Chem. SOC.1977, 99, 7817 (a). (t) Vishveshwara, S. Chem. Phys. Lett. 1978, 59, 26 (00). (u) Gordon, M. S.;Morris, M. L. Adu. Mol. Relax. Interact, Processes 1978, 13, 95 (k). (v) Thang, N. D.; Hobza, P.; Pancii, J.; Zahradnik, R. Collect. Czech. Chem. Commun. 1978, 43, 1366 (f, mm. xx). (w) Ahlstrom, M.; Jonsson, B.; Karlstrom, G. Mol. Phys. 1979.38, 1051 (r, kk, pp, rr, uu). (x) Mehrotra, P. K.; Beveridge, D. L. J . Am. Chem. SOC.1980, 102, 4287. (y) Williams, I . H.; Spangler, D.; Femec, D. A,; Maggiora, G. M.; Schowen, R. L. J . Am. Chem. SOC.1980, 102, 6619. (z) Williams, I. H.; Maggiora, G. M.; Schowen. R. L. J . Am. Chem. SOC.1980, 102, 7831 Gj, 11, tt). (aa) Peinel, G.; Frischleder, H.; Birnstock, F. Theor. CWm. Acta 1980, 57, 245. (bb) Butler, L. G.;Brown, T.L. J. Am. Chem. SOC.1981, 103, 6541. (cc) Maggiora, G. M.; Williams, I. H . J . Mol. Struct. 1982, 88, 23 (q, ii, qq, ss). (dd) Gresh, N.; Claverie, P.; Pullman, A. f n t . J . Quantum Chem. 1982, 22, 199. (ee) Taylor, P. R. J . Am. Chem. SOC.1982, 104, 5248. (ff) Marchese, F. T.; Mehrotra, P. K.; Beveridge, D. L. J . Phys. Chem. 1982,86, 2592 (b). (gg) Gussoni, M.; Castiglioni, C.; Zerbi, G. Chem. Phys. Lett. 1983, 99, 101. (hh) Williams, I . H.; Spangler, D.; Femec, D. A,; Maggiora, G. M.; Schowen, R. L. J . Am. Chem. SOC.1983, 105, 31 (p). (ii) Dewar, M. J . S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC.1985, 107, 3902. (jj) Ray, N. K.; Shibata, M.; Bolis, G.; Rein, R. Int. J . Quantum Chem. 1985, 27, 427 (c). (kk) Chin, S.;Ford, T. A. J . Mol. Struct. (THEOCHEM) 1985, 133, 193 (s). (11) Madura, J. D.; Jorgensen, W. L. J . Am. Chem. SOC.1986,108, 2517 (ff). (mm) Williams, I . H. J . A m . Chem. SOC.1987, 109, 6299. We have included the results of a b initio calculations presented in this paper in order to allow for comparison with 3-21 G level energetic calculations (x). For experimental studies, see: Schneider, W. G . ; Bernstein, H . J. Trans. Faraday Soc. 1956, 52, 1 3 . Nelander, B. Ber. Bunsen-Ges. Phys. Chem. 1978, 82, 61. Nelander, B. J . Chem. Phys. 1980, 72, 7 7 . It is our attempt in this study to be as complete as possible in reporting previous computational studies of the interaction of water and 1 in the ground state. If any studies were missed, their omission is inadvertent.

0022-3654/89/2093-4478$01.50/0

either lower levels of theory were employed or less complete searches of possible water-1 configurations were performed. The present study therefore serves as the most complete offered to date at high levels of ab initio theory. As such, it allows for a critical analysis of previous and current computational results on the interaction of 1 with water. In addition, since the structure and energy of these 1:1, water-molecule complexes are employed in the derivation of potential functions for the description of bulk water-molecule interactions,2 a detailed study such as the current investigation should assist in the development of accurate intermolecular potentials.

Methods A wide variety of configurations may, in principle, be important for the accurate description of the interaction of 1 with water (see, e.g., Figure 1, la-m). The set of configurations for 1:l complexes considered in this work includes well-defined geometries reported in previous water-1 studies' in order to allow for a critical comparison among previous and current computational methods. In addition, we considered configurations that we would predict to be of importance based on their analogy to potential energy minima that have been located for other, related molecular syst e m ~ .Finally, ~ since we have demonstrated that nonprejudicial searches of the potential energy surface for molecular hydration are necessary in order to ensure the location of all potential energy minima of i n t e r e ~ tthe , ~ water-1 hypersurface was searched by employing our solvent driver program (SOLDRIS). This program rigorously searches a grid of possible 1 :1 configurations and, in combination with modified molecular mechanics methods (MM2),5 allows for a preliminary search of the potential energy hypersurface for molecular hydration. This hybrid intuitive/ SOLDRI configurational search technique provides a rigorous, nonprejudicial approach to probing the potential energy hypersurface for the hydration of 1. Idealized schematics of input configurations for the 1-water complexes generated by using these approaches are shown in Figure 1 (la-m). For all molecules and complexes considered, initial geometries were obtained by geometry optimization at the 3-21G level of sophistication using the program Gaussian 82 (G82).6 These 3-21G calculations were used only as a starting point in the computational study since our previous has indicated the inadequacy (both quantitative and qualitative) of this basis set (2) For references to simulations of bulk water-I interactions, see: ref 1 x, Iff, and 111 and references cited therein. (3) (a) Damewood, J. R., Jr.; Kumpf, R. A. J . Phys. Chem. 1987,91,3449. (b) Kumpf. R. A.; Damewood, J. R.. Jr. J . Chem. SOC.,Chem. Commun. 1988. 62i. (4) Miihlbauer. W. C. F.; Damewood, J. R., Jr. J . Phys. Chem. 1988, 92, 3693. ( 5 ) SOLDRI, a SOLvent DRIver program. Miihlbauer, W. C. F.; Damewood, J. R., Jr.4 (6) Gaussian 82 (G82). Binkley, J. S.;Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, M. J.; Pople, J. A . A copy of the program may be obtained from Carnegie-Mellon University. For an introduction to basis set descriptors and MP corrections, see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. A b Initio Molecular Orbital Theory; Wiley: New York, 1986.

0 1989 American Chemical Society

Interaction of Formaldehyde with Water

The Journal of Physical Chemistry, Vol. 93, No. 11, 1989 4479

TABLE I: Calculated Absolute Energies for 1, Water, and la-k" MP2b structure 6-31G** 6-311+GZ* 1 -114.188918 -1 13.869 743 -1 13.902753 -190.419 617 -189.962 347 la -1 89.900 634 lb -190.421 395 -189.962 333 -189.901 716 -190.417 236 IC -189.961 621 -1 89.899 004 -190.416818 -189.960887 Id -189.898640 -190.415866 le -189.897 997 -189.960 393 -190.418914 If -189.959 863 -1 89.899 688 -190.41 7 05 1 -1 89.898 41 3 -189.959 542 Ig lh -189.959 082 -1 89.897 345 -190.415667 li -189.959747 -189.897628 -190.415462 -1 90.41 5 75 1 -189.959 871 -189.897 890 li lk -189.960479 -189.898 582 -190.416853 water -76.221 787 -76.023 61 5 -76.053 295

MP2C

MP3'

MP4DQC

MP4SDQc

-1 14.240 107 -190.521 672 -190.522238 -190.520087 -190.5 19 748 -1 90.5 19 046 -190.519346 -190.518627 -190.5 17 91 3 -190.518 375 -190.518506 -1 90.5 19 557 -76.274 117

-1 14.244 804 -190.529 101 -190.529636 -190.527641

-1 14.248 499 -190.534484 -190.534945 -190.533 102

-1 14.253 733 -190.541 583 -190.542 087 -190.540 166

-190.526 948 -1 90.526 061 -190.525485

-190.532 31 1 -190.531 480 -1 90.530 966

-1 90.539 410 -190.538 630 -190.538033

-76.277 026

-76.278 924

-76.280 692

In hartrees/molecule. Merller-Plesset corrections to 6-31G**//6-31G** energies a t the MP2 level. G**//6-31G** energies at the indicated level.

Merller-Plesset corrections to 6-31 I+-

TABLE 11: Calculated Complexation Energies for la-ka structure

6-31G**'

MP2c

6-31 l + G * * d

MP2C

MP3f

MP4DQ8

MP4SDQh

la lb IC

-4.6 -5.2 -3.5 -3.3 -2.9 -4.0 -3.2 -2.5 -2.7 -2.8 -3.3

-5.6 -6.7 -4.1 -3.8 -3.2 -5.2 -4.0 -3.1 -3.0 -3.2 -3.9

-4.0 -3.9 -3.5 -3.0 -2.7 -2.4 -2.2 -1.9 -2.3 -2.4 -2.8

-4.7 -5.0 -3.7 -3.5 -3.0 -3.2 -2.8 -2.3 -2.6 -2.7 -3.3

-4.6 -4.9 -3.6

-4.4 -4.7 -3.6

-4.5 -4.8 -3.6

-3.2 -2.7 -2.3

-3.1 -2.5 -2.2

-3.1 -2.6 -2.3

Id le If 1g

lh li

li lk

ZPEf 6-31G8*'

Z P E f MP2/ 6-31G8*i

-2.9 -3.0 -2.4 -2.2 -2.1 -2.3 -1.9 -1.5 -2.0 -2.0 -2.1

-3.9 -4.6 -3.0 -2.7 -2.4 -3.5 -2.7 -2.1 -2.3 -2.4 -2.1

"In kcal/mol. b6-31G**//6-31G**. CMP2/6-31G**//6-31G**. d6-31 1+G**//6-31G**. cMP2/6-311+G**//6-31G**. fMP3/6-311+G**//6-3 1G**. gMP4DQ/6-3 1 1+G**//6-31G**. MP4SDQ/6-31 l+G**//6-3 1G**. Z P E corrected 6-3 1G**//6-3 1G**. J Z P E corrected MP2/6-3lG**//6-3lG**.

in describing the geometry and energy of intermolecular interactions. These initial 3-21G geometries were then used as input configurations for subsequent complete or symmetry constrained (as noted below) geometry optimization at the 6-31G** (double { valence with polarization functions on heavy atoms and hydrogens) level (Le., 6-31G**//6-31G**). The 6-31G** basis set was chosen for these geometry calculations because of its proven ability to accurately describe intermolecular hydrogen bonded complexes.' Single point calculations correcting for electron correlation were performed for all configurations at the MP2/ 6-3 lG**//6-3 1G** and MP2/6-311+G**//6-31G** levels. In order to check the effects of higher order perturbative corrections, in several cases the MP4SDQ/6-31 l+G**//6-31G** level of theory was employed. Zero point energy (ZPE) correction calculations were performed at the 6-31G** level for all structures considered. ZPE corrected 6-31G**//6-31G** and MP2/631G**//6-31G** energies are reported in Table 11. We note that, due to the anharmonic nature of the intermolecular potentials and the harmonic approximations employed by the computational method! the ZPE corrections can be expected to be overestimated. For isolated molecule calculations, it has been suggesteds that scaling the calculated. ZPE corrections (by a factor of ca. 0.9) leads to more accurate results by comparison to experiment. We are hesitant to apply this scale factor to the current intermolecular calculations, however, since it has not been established if this scale factor is also appropriate for calculating ZPE corrections to in(7) The 6-31G**//6-31G** basis set obtains a binding energy of 5.54 kcal/mol for the water dimer compared to 5.4 f 0.7 kcal/mol determined experimentally. Del Bene, J. E. J. Chem. Phys. 1987, 86, 21 10. See: Curtis, L. A.; Frurip, D. J.; Blander, M. J. Chem. Phys. 1979, 71, 2703 (5.4 f 0.7 kcal/mol), and Reimers, J.; Watts, R.; Klein, M . Chem. Phys. 1982, 64, 95 (5.4 f 0.2 kcal/mol) for experimental information. See also: Curtiss, L. A,; Blander, M. Chem. Rev. 1988.88, 827. (8) Hout, R. F.; Levi, B. A.; Hehre, W. J. J. Comput. Chem. 1982.3, 234. See also: Koch, W.; Frenking, G.; Gauss, J.; Cremer, D.; Collins, J. R. J. Am. Chem. SOC.1987, 109, 5917.

TABLE III: Selected 6-31G** Calculated Structural Parameters for 1 and Water Bond Length"

C-0

1.184 1.093 0.943

C-H 0-H Bond Angleb H-C-0 H-C-H H-0-H a

In angstroms.

122.1 115.7 106.0

In degrees.

TABLE I V Selected 6-31C** Calculated Structural Parameters for

la C=O C-Hb C-H 0-H

Distance" 1.188 1.091 1.091 2.096

Hb-C-0 H-C-0 H-C-H

122.1 121.7 116.2

H-O-*C-H*

Torsion Angled 158.3

0.-0 0-HE 0-H

3.042 0.946 0.943

C-0-H 0-Ha-0 H-0-HC

117.4 176.7 105.6

Angled

"In angstroms. b T h e hydrogen proximal to water. cThe water hydrogen oriented toward the carbonyl oxygen. In degrees. e Parameter for water.

termolecular potentials. For symmetry-constrained structures, imaginary frequencies are ignored in the calculation of the ZPE correction. This may lead to higher error levels for these values. Because the harmonic approximation is also employed in the entropic correction calculations of G82: the values calculated for the complexes considered in this work must also, to some degree,

4480

The Journal of Physical Chemistry, Vol. 93, No. 11, 1989

TABLE V: Selected 6-31C** Calculated Structural Parameters for lb

Kumpf and Damewood TABLE I X Selected 6-31G** Calculated Structural Parameters for If

Distance"

c=o

0.-0

1.189 1.090 1.092 2.107

C-Hb C-H 0.-H

(C)Hb-O 0-HC 0-H

121.7 121.5 116.8 100.9

C-H-0 0-H-0 H-0-H'

C-O-*H-O

Torsion Angled 10.0

106.5 146.7 106.1

'In angstroms. b T h e hydrogen proximal to water. c T h e water hydrogen oriented toward t h e carbonyl oxygen. In degrees. (Parameters for water.

C-Hb C-H

1.188 1.082 1.090

(C)O*-H (C)H--O 0-H'

2.698 2.646 0.944

Hb-C=O H-CEO H-C-H C=O. ..H

121.6 122.0 116.7 94.9

C-H-0 0-H-0 H-0-He

110.9 96.6 104.0

H-O***C-H

Torsion Angled 123.9

Angled

Angled Hb-C-0 H-C-0 H-C-H C-O-*H(O)

Distance'

c=o

2.945 2.708 0.947 0.943

"In angstroms. b T h e hydrogen oriented toward water. cThe water hydrogen. degrees. eParameters for water. TABLE X: Selected 6-31G** Calculated Structural Parameters for

le TABLE VI: Selected 6-31G** Calculated Structural Parameters for IC

Distance'

C=O C-H O-.H(O)

0.-0 0-Hb 0-H

1.186 1.092 2.166

3.109 0.945 0.943

122.0 116.1 166.2

0-H-0 H-0-Hd

H-C-0-H

Torsion AngleC 95.5

1.186 1.092 2.917

H-CEO H-C-H

122.3 115.4

Angleb

Anglec H-C-0 H-C-H C=O...H

Distance'

c=o C-H c-*o

175.1 105.5

In angstroms.

Distance'

c=o C-Hb C-H

1.188 1.090 1.095

Distance'

122.0 116.0

2.567 0.943

AngleC

'In angstroms.

O-.O-H H-0-Hd

51.8 103.7

b T h e water hydrogen. C I ndegrees. dParameter for

water.

H-CEO H-C=O* H-C-H

121.5 122.4 116.0

C-H (C)O***O H-C=O H-C-H

122.0 116.0

(C)O*-Hb 0-Hb

2.61 1 0.943

O I n

51.9 103.8

angstroms. b T h e water hydrogen. c I n degrees. dParameter for

water.

be in error and, therefore, will not be reported

Results and Discussion Absolute energies obtained for configurations la-k in this work at levels of theory of 6-31G** or higher are reported in Table I. Binding energies and ZPE corrected binding energies are reported in Table 11. Selected calculated bonding parameters for 1, water, and la-k are reported in Tables 111-XIV. In order to facilitate discussion, results for individual water-1 configurations will be considered in the subsections below. To allow for comparison with other theoretical results, the computational methods, binding energies, and information on intermolecular geometries employed

177.8 106.8 106.0

H-0.-C-0

Torsion Angled 56.3

Distance'

c=o C-H c--0

1.186 1.091 3.222

H-C=O H-C-H

o=c ...o

122.5 115.1 169.7

H-C*-0-H

Torsion AngleC 10.9

0-Hb (C)H*-O

0.943 2.804

C-H-.O

102.6 I 06.1

AngleC

AngleC 0.-0-H H-O-Hd

C-H-*O He-0-H H-0-He

TABLE XII: Selected 6-31G** Calculated Structural Parameters for li

Distance' 1.186 1.092 3.086

0-He

2.507 3.597 0.944

"In angstroms. b T h e hydrogen oriented toward the water oxygen. C T h e water hydrogen. degrees. 'Parameter for water.

TABLE VIII: Selected 6-31G** Calculated Structural Parameters for l e

c=o

(C)Hb*-O

c.-0 Angled

Id

H-C=O H-C-H

102.5 105.5

H-0-He

In degrees. CParameters for water.

TABLE VII: Selected 6-316** Calculated Structural Parameters for

(C)O-Hb 0-Hb

o=c...o

lh

b T h e water hydrogen oriented toward the carbonyl oxygen. 'In degrees. "Parameter for water.

1.186 1.092 3.041

2.998 0.944

TABLE XI: Selected 6-31G** Calculated Structural Parameters for

'In angstroms.

C=O C-H (C)O*-O

(C)H-.O 0-H

'In angstroms.

H-0-~d

b T h e water hydrogen. c I n degrees. dParameters for

water. TABLE XIII: Selected 6-31G** Calculated Structural Parameters for l j Distance' c=o 1.187 (C)H*-O 2.802 C-H 1.091 0-Hb 0.943 c.-o 3.232 Angle' H-CEO H-C-H

'In angstroms. "he water.

122.5 115.1

C-He-0 H-0-Hd

103.3 106.1

water hydrogen. c I n degrees. dParameters for

The Journal of Physical Chemistry, Vol. 93, No. 11, 1989 4481

Interaction of Formaldehyde with Water H

' 0 H'

lb

la H

Id

IC

H

4

Hd C = O

H

>O

lh

le H H

>.

H

H

\O H/

>C=O

H

,O H

H/*,

i i '

Hdc=o

C

H4

0-H

H+*.

H . H H

li

lk

-H

H

i

dC=O 11

lm Figure 1. Idealized schematics of complexes between 1 and water. la: the conventional hydrogen-bonded form. Ib: the ringlike configuration. IC: bifurcated hydrogen bond. Id: head-to-tail configuration. le: perpendicular head-to-tailconfiguration. 1E side-by-sideconfiguration. lg: face-to-face, side-by-side configuration. Ih: C-H-0 hydrogen-bonded structure. li: alternate head-to-tail configuration. Ij: perpendicular alternate head-to-tail configuration. Ik: perpendicular alternate side-by-side configuration. 11 and Im: previously reported minima.

TABLE XIV Selected 6-31C** Calculated Structural Parameters for lk

Distancea

c=o C-H c-so

1.187 1.092 2.873 2.705

H-C=O H-C-H

O...Hb

(C)H-.O 0-Hb 0-H

3.058 0.944 0.943

122.2

C4-H

115.7 91.8

H-O-H~

82.6 106.5

AngleC O=C.-O

a In angstroms. bThe water hydrogen oriented toward the carbonyl oxygen. CIndegrees. dParameters for water.

in previous calculations are reported graphically in Figure 2. Structure la: The Conventional Hydrogen-Bonded Form The configuration that is most often considered for the interaction of 1 and water is the structure in which water is hydrogen bonded to one of the carbonyl oxygen lone pairs ( l a , Figure 1). At the 6-31G**//6-31G** level of theory we find a C1structure for l a and calculate a binding energy of 4.6 kcal/mol for this configuration. This binding energy is not substantially altered, even at levels of theory as high as MP4SDQ/6-311+G**//631G**, where a binding energy of 4.5 kcal/mol is obtained. While 6-31 1+G** shows a somewhat lower complexation energy of 4.0 kcal/mol, and MP2/6-31G**//6-31G** a somewhat higher complexation energy of 5.6 kcal/mol (see below), all other intermediate levels of theory provide binding energies that are within 0.2 kcal/mol of the 6-31G**//6-31G** and MP4SDQ/6-311+G**//6-31G** values.

It is instructive to compare the results of these calculations with those reported previously for la. Computational methods including EHT, CNDO/2, INDO, heuristic modeling (method A), QPEN (method B), electrostatics (method C), and ab initio calculations employing basis sets ranging from STO-3G to the MP4SDQ/6311+G**//6-31G** level employed in this work (as well as selected other basis sets: basis A, B, and C) have been used in the study of configuration l a (see references, Figure 2). Binding energies obtained by these previous computational studies are reported graphically in Figure 2. While one must be cautious in making comparisons between the results of these computational methods since different geometries and optimization levels were employed (see notes to Figure 2), many of the results obtained for higher levels of ab initio theory (6-31G**//6-31G** and MP2/6-3 11+G**//6-3 1G**-MP4SDQ/6-3 1 l+G**//6-31G**) as well as two of the calculations at the 4-31G level,I0 method A,ISmethod C,Ij and basis B1"are in reasonable agreement. The largest deviations are observed for ab initio basis A,IWCNDO/ 2,1a*b*d9esJJ INDO,lfsUmethod B,lffone STO-3G study,l= and some 4-3 1G applications.lm~q~kk Perhaps somewhat surprisingly, in some cases ST0-3G,1g*hsq-hh basis C," and EHTICprovide remarkably good estimates of the binding energy for this configuration at the geometries employed by these authors. The structure that we calculate at the 6-31G** level (Table IV) is typical of that obtained for hydrogen-bonded structure^.^ (9) For reviews of hydrogen bonding, see: Scheiner, S. in Aggregation Processes in Solution. Studies in Physical and Theoretical Chemistry; Wyn-Jones, E., Gormally, J., Eds.; Elsevier Scientific: New York, 1983. Joesten, M. D.; Schaad, L. J. Hydrogen Bonding, Marcel Dekker: New York, 1974. Kollman, P. A,; Allen, L. C. Chem. Reu. 1972, 72, 283. Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; W. H. Freeman: San Francisco,

1960.

Kumpf and Damewood

4482 The Journal of Physical Chemistry, Vol. 93, No. 11 1989 I

P

I

Interaction of Formaldehyde with Water

The Journal of Physical Chemistry, Vol. 93, No. 11, 1989 4483 The O.-O separation is 3.042 A, and the O-.H(O) separation is 2.096 A. This, coupled with the near linear 0.-H-0 angle (176.7'), provides supportive evidence for the formation of an 0-H-0 hydrogen bond.

Structure Ib: Ringlike Configuration As part of our configurational search of the water-I potential energy hypersurface, we were able to locate another low-energy complex with CI symmetry (lb). This complex adopts an unusual ringlike configuration in which one of the water hydrogens points toward the carbonyl oxygen while the water oxygen points toward one of the C-H groups (see Figure 1). At all levels of theory, Ib is calculated to be very stable in terms of relative energy. Binding energies for this configuration range from 5.2 kcal/mol at the 6-31G** level to 4.8 kcal/mol at MP4SDQ/6-311+G**//6-31G**. As observed in calculations for la, the predicted binding energy for l b is substantially greater at the MP2/631G**//6-31G** level (6.7 kcal/mol) and significantly smaller (3.9 kcal/mol) at the 6-311+G**//6-31G** level (see below for discussion of basis sets). While detailed structural information has not been reported previously for lb, one recent study'" has graphically reported a configuration that is similar to I b . Insufficient computational details were provided for this 3-21G structure to allow for complete comparison with our results; however, since the bonding parameters reported compare well with ours, we assume that this and our structure are closely related and include relevant data in Figure 2. Another recent computational study"' has also reported a configuration that we are unable to classify as configuration l a or Ib, and we have therefore not included these data in Figure 2. The previous binding energy obtained for l b a t the 631G*//3-21G levell" is relatively close to the values obtained in the present investigation. The MP2/6-31G*//3-21G results,l" like our MP2/6-31G**//6-31G** calculations, seem to somewhat overestimate the binding energy by comparison to higher levels of theory. As noted previously,[" the basis set superposition error (BSSE)l0 inherent at the 3-21G//3-21G level of sophistication results in a significant overestimation of the binding energy for l b (Figure 2). The structure of complex Ib is of particular interest (Table V). The (C=)O-.H and (C)H.-O distances are 2.107 and 2.708 A, respectively, placing both the carbonyl oxygen and C-H bond of formaldehyde at distances that allow for potential interaction with water, although the C-0 distance is significantly longer than that typically observed for C-H--0 hydrogen bonds." In addition, the O=C-H fragment of 1 and the 0-H bond of water form a near planar five-membered ring, with internal bond angles that range between 100.9' and 146.7'.

aR Y

Structure IC: Bifurcated C=O.-H(OH) Hydrogen Bond For configuration IC,the lone pairs from the carbonyl oxygen form a bifurcated arrangement with one of the hydrogens of water, resulting in a complex of C, symmetry. Binding energies obtained after geometry optimization under this symmetry constraint are smaller than those observed for l a and Ib and range between 3.5 kcal/mol at 6-31G**//6-31G** and 4.1 kcal/mol at MP2/6(IO) See: Latajka, Z.; Scheiner, S. J . Chem. Phys. 1987, 87, 1194. (1 1) For reviews of C-Ha-0 hydrogen bonding, see: (a) Green, R . D. Hydrogen Bonding by C-H Groups; Wiley: New York, 1974. (b) Meot-Ner (Mautner), M. Acc. Chem. Res. 1984, 17, 186. (c) Deakyne, C. A. Ionic Hydrogen Bonds. Part 11. Theoretical Calculations. In Molecular Structure and Energetics Vol. I& Liebman, J. F.,Greenberg, A,, Eds.; VCH Publishers: New York, 1985; Chapter 4 and references cited therein. See also: (d) Taylor, R.;Kennard, 0. J . Am. Chem. SOC.1982, 104, 5063. (e) Sarma, J. A. R. P.; Desiraju, G. R . Acc. Chem. Res. 1986, 19, 222. (f) Tamura, Y.; Yamamoto, G.; Oki, M. Chem. Lett. 1986, 1619. (12) In ref 7b, data on hydrogen bond energies calculated for several complexes using MP4SDQ and MP4SDTQ corrections at a variety of levels of theory (56 calculations for each) are provided. MP4SDTQ consistently calculates hydrogen bond energies that are, on average, 0.2 kcal/mol more stable than MP4SDQ in this s t ~ d y . ' ~We do not feel that ca. 0.2 kcal/mol would make a meaningful difference in the conclusions or binding energies reported here and therefore have not performed calculations at this level in this work.

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The Journal of Physical Chemistry, Vol. 93, No. 11, 1989

Kumpf and Damewood

CHART I (a) Reference 1s. Configurations minimized with respect t o water-1 orientation by using method A. The energies reported here are estimated from isoenergy contour maps to within 0.6 kcal/mol. Binding energy = 5.4 kcal/mol (la). 5.4 kcal/mol (IC), 2.4 kcal/mol ( l b ) , and 3.6 kcal/mol ( l j ) . (b) Reference Iff. Binding energy = 6.2 kcal/mol (la), 2.8 kcal/mol (li). Structures were assigned on the basis of inspection of Figure 8 in this reference. (c) Reference Ijj. Monomer geometries were not specified explicitly. The 0-0 distance is 2.88 A. The C=O-.O and 0 - H - 0 angles are 119' and 179O, respectively. Binding energy = 4.9 kcal/mol. (d) Reference le. Experimental structural parameters employed for 1. Parameters for water are 1.03 and 1.04 8, for free and hydrogen-bonded 0 - H bonds, respectively. H-0-H angle = 107". C=O-H angle = 120.0"; 0-He-0 angle = 180°. Binding energy = 4.1 kcal/mol (EHT); 7.2 kcal/mol (CNDO/2). ( e ) Reference In. Calculations include second-order perturbation corrections. The complex was planar with a O-.O distance of 2.55 A and a C=O-H angle of 125". Binding energy was obtained from inspection of the potential energy curve. Binding energy = 9.0 kcal/mol. A structure corresponding to the 180' degree rotation of the water molecule was also reported (not shown in this figure). Binding energy = 8.9 kcal/mol. (f) Reference Iv. Complete CNDO/2 optimization was performed for the hydrogen-bonded complex resulting in a nearly planar structure. Binding energy = 8.2 kcal/mol. A related structure (not shown in this figure) was also reported with the water molecule rotated 180.0". Binding energy = 7.7 kcal/mol. (9) Reference la. For 1: C-H = 1.12 A, C - 0 = 1.21 A, H-C-H and H-C=O angles = 120". For water: 0-H = 1.04 A, H-0-H angle = 105". Water molecule is coplanar with 1 at an 0-0 distance of 2.55 A and a C-0-H angle of 120'. Binding energy = 7.6 kcal/mol. (h) Reference lb. Water geometry optimized by CNDO/2. The experimental geometry of 1 was employed. The hydrogen-bonded complex was obtained by varying the Ha-0 and 0-0 distances (1.04 and 2.55 A, respectively) and C=O-H angle (ca. 125'). Binding energy = 7.5 kcal/mol. (i) Reference Id. Potential energy minimum located as a function of the O-.O distance. Geometry of 1 obtained from CNDO/2 minimization. Free and hydrogen-bonded 0-H distances in water are 1.03 and 1.04 A, respectively. The 0 - H of water was oriented along a lone air of the carbonyl group. Binding energy = 7.1 kcal/mol. ti) Reference Ir. Monomer geometries were held fixed. For 1: C=O = 1.21 A, C-H = 1.12 H-C-H = 120'. For water: 0-H = 0.96 A, H-0-H = 104.52'. The Ha-0 distance was optimized to 2.6 A. Binding ener y 6.5 kcal/mol. (k) Reference lu. Water was oriented in the opposite direction from that shown for l a (Figure I ) . For 1: C-H = 1.12 A, C - 0 = 1.25 G-C-H (distal to water) = 122.2", 0-C-H (proximal to water) = 122.3'. For water the 0 - H distances for free and hydrogen-bonded 0-H bonds are 1.03 and 1.05 A; the H-0-H angle = 105.6'; C-O-.H angle = 132.6"; O-.H-O angle = 173.9'; He-0 distance = 1.44 A. Binding energy = 12.1 kcal/mol. (I) Reference If. Structural parameters for 1: H-C = 1.120 A, C=O = 1.210 A, H-C-H = 118.0°. Water: 0-H = 0.982 A, H-0-H = 101.07°. These geometries were maintained in the complex with a C(0)-H distance of 1.890 A (INDO = 1.80 A) and a C=O-O angle of 116' (INDO = 120'). Binding energy = 6.3 kcal/mol (INDO); 3.5 kcal/mol (Basis C). (m) Reference Iq. Experimental structural parameters were employed for 1. Complex geometry as in (1). Energy includes dispersive corrections. Binding energy = 3.9 kcal/mol (STO-3G); 7.0 kcal/mol (4-31G). (n) Reference Ig. Structural parameters as in (I). Binding energy = 3.4 kcal/mol. (0) Reference Ih. Structure of monomers from STO-3G optimizations for C,, symmetry. These geometries were maintained in the complex with an 0-0 distance of 2.88 A, a C=O-O angle of 119O, and an 0.-H-0 angle of 179". Binding energy = 3.3 kcal/mol. (p) Reference Ihh. During optimization of the complex, monomer geometries were held fixed with the following parameters: for water, the 0-H bond length was 0.989 A and the H-0-H angle was 100': for 1, the C-0 and C-H bond lengths were 1.217 and 1.101 A, respectively. The H-C-H angle was 114.5'. Complex geometry as in (0). Binding energy = 3.3 kcal/mol. (4) Reference ICC. Geometries as in (0). Energy includes counterpoise and dispersive corrections. Binding energy = 0.4 kcal/mol. (r) Reference 1w. Monomer geometries were optimized using basis set B and these geometries were maintained in the calculation of the complex. the 0-0 separation was 2.95 8, and the H-O-.X angle was 62' (X = point on C=O vector). Binding energy = 6.9 kcal/mol (basis A); 4.1 kcal/mol (basis B). (s) Reference lkk. Calculations were performed at the 4-31G//4-31G level. Binding energy = 7.1 kcal/mol. (t) Reference Im. Monomers were held fixed at experimental geometries. The O.-O distance = 3.05 A. The C=O-H angle = 120O. Binding energy = 6.3 kcal/mol. (u) Reference lo. Predicted hydrogen bond strength was obtained from 4-31G calculations where AE(X-H-Y) = AH-Y) g(X). Although explicit geometric information was unavailable, this entry was included for comparative purposes. Binding energy = 5.5 kcal/mol. (v) Reference lo. Hydrogen bond strength calculated as in (u) and subsequently scaled. Binding energy = 3.4 kcal/mol. (w) Present work. Geometries obtained by optimization at the 6-31G** level. (x) Reference Imm. Calculations performed with 3-21G optimized parameters. Binding energy = 9.1 kcal/mol (3-21G), 4.6 kcal/mol (6-31G*), 6.6 kcal/mol (MP2/6-31G*) (lb), 5.3 kcal/mol (3-21G), 2.8 kcal/mol (6-31G*), 3.8 kcal/mol (MP2/6-31G*) (lg). AH information reported at the 3-21G level but not included here for reasons discussed in the Methods section. Geometries for AMI calculations did not allow for structural classification. (y) Reference le. Structural parameters for 1 are experimental. Parameters for water are 1.03 and 1.04 8, for free and hydrogen-bonded 0 - H groups and 107' for the H-0-H angle. Both the C=O-H and 0.-H-0 angle are 180'. Binding energy = 3.2 kcal/mol (EHT), 7.5 kcal/mol (CNDO/2). (z) Reference IC. The binding energy was estimated from graphed data. Experimental bond lengths were employed for the monomers with an H-C-H angle of 120" for 1 and an H-O-H angle of 105' for water. The 1:l complex had a fixed C=O.-H angle of 180° The geometry of this complex was optimized by first varying the 0-0 separation, followed by optimization of the 0 - H distance. Binding energy = 14.1 kcal/mol. (aa) Reference In. Structure reported as a saddle point. 0--0 distance = 2.55 A, C=O.-H angle = 180'. Second-order perturbation corrected energies. Binding energy = 8.3 kcal/mol. (bb) Reference lb. Water geometry optimized by CNDO/2. Experimental geometry used for 1. Calculations for the complex employed fixed monomer geometries with 0-0 and 0.-H distances = 2.55 and 1.04 A, respectively. The C=O-H angle is 180°. Binding energy = 7.2 kcal/mol. (cc) Reference la. Structural parameters for 1 and water as in (9) with an O-.H-O angle of 180' and an 0-0 distance of 2.55 8,. Binding energy = 7.2 kcal/mol. (dd) Reference Ij. Monomer geometries were C N D 0 / 2 optimized with a C=O distance of 1.247 A, an ( 0 ) H - 0 distance of 1.1 14 A, and an H-C-H angle of I 15.7". The minimization was performed for different 0 - H values which were varied from 1.4 to 2.4 8, in 0.2-A increments. Binding energy = 7.1 kcal/mol. (ee) Reference If. Geometries optimized using INDO. Binding energy = 9.6 kcal/mol. (ff) Reference 111. Calculations were performed at the 6-31+G*//6-31+G1 level. Binding energ 3.8 kcal/mol (lc), 3.4 kcal/mol (Id), 2.5 kcal/mol (lj). (gg) Reference la. Structural parameters for monomers as in (9) with O.-O distance ca. 2.4 and = the 0-0-H angle ca. 52.5O. The binding energy is estimated from potential energy curves. Binding energy = 2.9 kcal/mol. (hh) Reference la. Structural parameters for monomers as in (g). 0-0 separation ca. 2.4 8,. The binding energy is estimated from potential energy curves. Binding energy = 3.0 kcal/mol. (ii) Reference lcc. Monomer geometries were STO-3G optimized with a C-0 distance = 2.93 A and C-O-X angle (where X = bisector of H-0-H angle) is 110.8°. Energy includes counterpoise and dispersive corrections. Binding energy = 1.6 kcal/mol. (jj) Reference lz. Structural parameters from STO-3G optimization under C, symmetry. C.-O distance = 2.94 8,. Binding energy = I .1 kcal/mol. (kk) Reference Iw. Monomer geometries optimized using basis B and these geometries were maintained in calculations for the complex. C-0 distance = 2.75 A, C.-O-X angle = 90' (X = bisector of water hydrogens). Binding energy = 5 . 1 and 4.1 kcal/mol (basis A) (two values were reported for the same structure); 2.4 kcal/mol (basis B). (11) Reference lz. Structural parameters obtained from 4-31G optimizations for C,symmetry. Binding energy = 3.9 kcal/mol. (mm)Reference Iv. Complete CNDO/2 optimization was performed for the C-H.-0 hydrogen-bonded complex with the water molecule rotated 90' out of the plane of formaldehyde. Binding energy = 2.2 kcal/mol. A related structure was also reported (not shown in this figure) in which the water molecule was rotated 90". resulting in a nearly planar complex. Binding energy = 2.2 kcal/mol. (nn) Reference If. Structural parameters as in (I) with a (C)H-.O distance of 1.946 A and He-0-X angle (where X is the H-O-H bisector) of 116'. Binding energy = 0.6 kcal/mol. (00)Reference It. Structural parameters for the monomers optimized for STO-3G. The C-Ha-0 angle is 180.0'. The C.-0 distance is 3.186 A. Binding energy = 1.9 kcal/mol. (pp) Reference Iw. Monomer geometries optimized using basis B and maintained in the complex. C-0 distance = 2.99 A. Binding energy = 4.3 kcal/mol. (qq) Reference ICC. Structural parameters as in (ii) with a C-0 distance of 3.33 A. Energy includes counterpoise and dispersive corrections. Binding energy = 1.1 kcal/mol. (rr) Reference Iw. Monomer geometries optimized using basis B and these geometries were maintained in the complex. C - 0 distance = 3.0 A. Binding energy = 4.8 kcal/mol (basis A), 2.2 kcal/mol (basis B). (ss) Reference lcc. Structural parameters for monomers as in (ii). The C - 0 distance is 2.96 8, and the C.-O-X angle is 144.5' (X = bisector of the H-0-H angle). Energy includes counterpoise and dispersive corrections. Binding energy = I .5 kcal/mol. (tt) Reference lz. Structural parameters as in (jj) with water constrained to the symmetry plane. Binding energy = 1.1 kcal/mol. (uu) Reference lw. Monomer geometries were optimized using basis B and maintained in calculations for the complex. C-0 distance = 2.72 8, and the C-0-X angle = 44O (X = bisector of the H-0-H angle). Binding energy = 4.8 kcal/mol. (w) Reference Ir. Geometries as for (j) with the 0-H-r distance optimized to 3.0 A. Binding energy = 1.3 kcal/mol. (ww) Reference If. Structural parameters for monomers as in (I). C=O-H distance = 2.3 A. C=O.-O-H torsion angle = 180.0". Binding energy = 0.7 kcal/mol. (xx) Reference Iv. Complete CNDO/2 optimization was performed. C=O-O-H torsion angle = 180.0°. Binding energy = 9.6 kcal/mol. A related structure (not shown in this figure) was also reported, where the H a - H plane was rotated 60° toward the oxygen lone pair. Binding energy = 8.4 kcal/mol. (yy) Reference If. Structural parameters for monomers as in (I). He-0 distance = 1.796 A. C=O-.O-H torsion angle = 180.0". Binding energy = 2.5 kcal/mol. (zz) Reference 11. Structural parameters were obtained from STO-3G optimization with monomer geometries held fixed. Binding energy = 0.7 kcal/mol.

1

1,

1

3 1G**//6-3 IG**. Binding energy estimates at the higher levels of theory considered are consistently 3.6 kcal/mol (Table 11). Previous studies of configuration IC employing CND0/2,'anqeJe INDO," and method AIs obtained binding energies that are

substantially larger than those calculated in the present work. By contrast, previous EHTle and 6-31 +G*"l calculations provide a binding energy in good agreement with higher levels of theory (Figure 2).

Interaction of Formaldehyde with Water The geometry of IC is normal (Table VI), with O-.O and ( 0 ) H - 0 separations of 3.109 and 2.166 A, respectively. The 0.-H-0 angle is also relatively close to being linear at 175.1'.

Structure Id: "Head-to-Tail" Configuration In structure Id, water and the carbonyl oxygen of 1 are proximal and the dipoles of the two molecules are aligned in a complementary head-to-tail fashion. This represents one of the configurations that allows for very favorable electrostatic interactions between water and 1. Binding energies calculated for this C2, structure range between 3.0 and 3.8 kcal/mol. These binding energies are in good agreement with the previously reported 631+G* result of 3.4 kcal/mol'l' and the 2.9 kcal/mol obtained by CND0/2.Ia Calculations were not performed for this structure by us beyond the MP2/6-31 l+G**//6-31G** level of sophistication since our experiences with other structures (see above and below) revealed that higher levels of perturbative correction had little effect on computational results. The 0-0 separation in complex Id is 3.041 A (Table VII) and the C=O bond length of 1.186 A is not significantly different than the 1.184 A calculated for 1. The 0.-H distances of 2.567 A are substantially longer than those calculated for l a and ICand the H-0-0 angle of 5 1.8' clearly shows the nonlinear nature of this arrangement for Id. Structure le: Perpendicular "Head-to-Tail" Configuration Configuration l e is similar to Id except for the arrangement of the water plane with respect to the H-C-H plane of 1. For l e , those two planes are nearly perpendicular and this C, configuration has, in general, a somewhat lower binding energy than Id. At the 6-31G**//6-31G** level the value is 2.9 kcal/mol while at the MP2/6-31 l+G**//6-31G** level it is 3.0 kcal/mol. As for other configurations, the MP2/6-31G**//6-31G** level obtains a binding energy that is somewhat higher than these values at 3.2 kcal/mol while 6-31 l+G**//6-31G** obtains a lower value of 2.7 kcal/mol. The one previous C N D 0 / 2 studyla of configuration l e obtained a binding energy (3.0 kcal/mol) in excellent agreement with our 6-31G**//6-31G** and MP2/6-311+G**//6-31G** values. The structure of configuration l e is very similar to that calculated for Id except for those parameters that reflect the relative torsional orientation of 1 and water (see Tables VI1 and VIII). Structure If: "Side-by-Side" Configuration In our previous studies of molecular hydration? we investigated the interaction of acetonitrile and nitromethane with water and found that a structure that we referred to as the "side-by-side" configuration was very stable in terms of relative binding energy. In this configuration, the dipoles of water and the organic molecule are oriented in a complementary "side-by-side" manner. Configuration If is the analogous, C, configuration for the 1-water complex. Our calculated binding energies range from 4.0 kcal/mol a t the 6-31G**//6-31G** level to 3.1 kcal/mol at MP4SDQ/ 6-31 I+G**//6-31G** for this configuration. The 6-31 1+G**//6-3 1G** level obtains a binding energy of 2.4 kcal/mol, and the MP2/6-31G**//6-31G** level obtains 5.2 kcal/mol. No previous studies have reported detailed information on this structure. The structure of complex If (Table IX) is typical of the "side-by-side" structures that we have observed previously. The 0--0 distance is 3.031 A and the C.-0 separation is 3.201 A. The C=O-H and 0-H-0 angles of 94.9' and 96.6O, respectively clearly indicate the lack of linear hydrogen bonding arrangements in this complex. Structure lg: "Face-to-Face, Side-by-Side" Configuration Configuration l g is most easily viewed as a 90' rotation of 1 in the side-by-side configuration If. For l g we calculate a binding energy of 3.2 kcal/mol at the 6-31G**//6-31G** level and 2.6 kcal/mol at MP4SDQ/6-31 l+G**//6-31G** level. The MP2/6-31G**//6-31G** level obtains a binding energy of 4.0 kcal/mol while 6-31 l+G**//6-31G** provides, as usual, a substzdally lower estimate of 2.2 kcal/mol. Basis B,IW 6-

The Journal of Physical Chemistry, VOI. 93. NO. 11, I989 4485 31G*,'" and MP2/6-31G*//3-21G1" all provide reasonable estimates of this binding energy. Basis AI" and 3-21G'" significantly overestimate the binding energies while both STO-3G studieslz,ccsignificantly underestimate the binding efficiency. The structure of l g is reported in Table X. The C.-O separation of 2.917 A and O=C-O angle of 102.5' are typical of a sideby-side s t r ~ c t u r e . ~

Structure l h C-H.-0 Hydrogen Bond The extent to which aldehydes are capable of forming C-H.-0 hydrogen bonds]' with simple, neutral oxygen donors has been a subject of debate for a considerable period of time."*'*" We investigated this C, configuration and find that the near linear C-Ha-0 arrangement is a potential energy minimum with binding energies ranging between 2.3 and 2.5 kcal/mol for the MP4SDQ/6-3 1 1+G**//6-3 1G** and 6-3 1G**//6-3 1G** levels. For MP2/6-31G**//6-31G** and 6-31 l+G**//6-31G** the calculated binding energies are 3.1 kcal/mol and 1.9 kcal/mol, respectively. These values are in good agreement with one of the ab initio studies reported previously" which employed the STO-3G basis set, the C N D 0 / 2 study'", and with the results obtained from method AIs (Figure 2). The structure of l h (Table XI) is, as mentioned above, entirely consistent with the formation of a C-H-0 hydrogen bond. The (C)H-0 separation of 2.507 A is longer than the 2.204 A we observed for the C-H-0 hydrogen bond in the malononitrilewater complex.3b This longer bond length may be a reflection of the weaker C-H-0 hydrogen-bonding interaction in the case of 1. Despite the long (C)H--O separation, the C-H-.O angle of 177.8' is nearly linear and strongly suggestive of hydrogen bond formation. Structure li: Alternate "Head-to-Tail" Configuration li is, like Id, a head-to-tail configuration in which the dipoles of water and 1 are aligned in a complementary way. For li, however, water is oriented so that it is proximal to the carbonyl carbon of 1 while in Id it was proximal to the carbonyl oxygen. In addition, for this C, structure, the water and H-C-H planes are nearly coincident. We calculate binding energies of 2.7 and 2.6 kcal/mol at the 6-31G**//6-31G** and MP2/631 l+G**//6-31G** levels of sophistication. As has been observed for other configurations (see above), calculations at the 6-31 1+G**//6-31G** level provide a binding energy that is somewhat lower than these estimates (2.3 kcal/mol) and MP2/6-31G**/ /6-31G** provides an estimate that is slightly higher at 3.0 kcal/mol. One previous study'" employing basis A considered configuration li and obtained a binding energy that was higher than those obtained in this work (4.3 kcal/mol) while method B'" is in good agreement. The C.e.0 separation in li is significant at 3.222 A as is the (C)H-O separation of 2.804 A (see Table XU). The H-C-0-H torsion angle of 10.9' shows that this structure is only moderately distorted from a C2, configuration. Structure lj: Perpendicular Alternate "Head-to-Tail" Structure Ij is similar to li except for the relative orientations of water and 1. In this C, structure (Ij), the H-O-H and H-C-H planes are perpendicular, a configuration that potentially allows for favorable interaction between the oxygen of water and the C-H groups of 1. For this configuration we calculate somewhat more favorable binding energies relative to l h of 2.8 and 2.7 kcal/mol at the 6-31G**//6-31G** and MP2/6-31 l+G**//6-31G** levels, respectively. At the 6-31 l+G**//6-31G** level the binding energy is again somewhat lower at 2.4 kcal/mol and somewhat higher at MP2/6-31G**//6-31G** which obtains a binding energy of 3.2 kcal/mol. Method A,ISbasis B,IWand 6-31+G*l1' all obtain binding energies for l j that are in reasonable agreement with the present results while basis A found1" a much higher and STO-3GICCa significantly lower binding energy (Figure 2). The structural features of l j (Table XIII) are normal with a C-0 and (C)H-O separation of 3.232 and 2.802 A, respectively,

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The Journal of Physical Chemistry, Vol. 93, No. I I, 1989

and a C-H-0

angle of 103.3'.

Structure lk: Perpendicular Alternate "Side-by-Side'' Structure l k is of C, symmetry and is similar to the side-by-side structure, Ig, except the water is rotated by approximately 90' so that the oxygen atom points toward the carbonyl carbon and one of the water hydrogens points toward the carbonyl oxygen. This orientation is similar to one of the assumed transition states for nucleophilic attack of water on 1 reported previously.'YJ The binding energy calcualted for l k by both 6-31G**//6-31G** and MP2/6-31 l+G**//6-31G** is 3.3 kcal/mol, and at the 631 I+G**//6-31G** level it is somewhat lower at 2.8 kcal/mol. At MP2/6-31G**//6-31G** the binding energy is somewhat higher at 3.9 kcal/mol. These calculated binding energies agree reasonably well with the results from basis AIw and are significantly higher than the binding energy calculated previously by using STO-3G1z~CC (Figure 2). The structural parameters for l k are normal (Table XIV) with a O=C-0 angle of 91.8'. Structures 11 and Im: Previously Reported Minima Previous studies have considered structures l I i f J and Im;IF-'J however, under constraints of C, symmetry, we were unable to locate minima corresponding to these structures. For completeness, we have reported the energetic results of these previous studies in Figure 2. Configuration 11 is calculated to have a binding energy of only 0.71f and I .31r kcal/mol, while values of 0.7,", 2.5,1f and 9.6'" kcal/mol are obtained for lm. Zero Point Energy (ZPE) Corrected Binding Energies The relative energy ordering for the configurations considered in this study (la-k) obtained at the MP2/6-31 I+G**//6-31G** level of I b > l a > I C > Id > l k > If > l e > l g > l j > l i > l h is not substantially altered when ZPE corrections are applied to the 6-31G**//6-31G** energies. This ZPE correction yields a relative energy ordering of l b > l a > IC > If > Id > l e = Ik > l i E I j > l g > lh. Similarly, when these same corrections are applied to the MP2/6-31G**//6-31G** level calculations, the relative stability ordering remains essentially the same: l b > l a > If > IC > Id N l g N l k > l e N l j > l i > lh. As expected, in both cases the binding energies are significantly decreased when ZPE corrections are applied to the calculated binding energies. As mentioned in the Methods section, the harmonic approximation employed in the calculation of these ZPE corrections should lead to an overestimation of their values. Even though these ZPE corrections, therefore, represent upper limits, we are unable to conclude that the contributions of zero-point energy in the real system will not slightly alter the presented relative energy orderings since the degree of ZPE overestimation could differ for each configuration. We are confident, however, that zero-point energies in the real system will not substantially alter the presented energy orderings. Basis Set Evaluation and the Quality of Computational Results The basis sets employed in this work are the highest level reported and the geometries (la-k) the most complete considered for I-water interaction.' As such, these data allow for a critical comparison to previous work (see above) as well as among various levels of theoretical approximation. Inspection of the binding energy data reported in Figure 2 reveals that calculations performed at the 6-3 1G**//6-31G**, MP2/6-31 I+G**//6-31G**, and MP4SDQ1*/6-31l+G**//631G** levels of sophistication are all in relatively good agreement. Indeed the observation that MP2/6-3 11+G**//6-31G** and MP4SDQ/6-311+G**//6-31G** were in very good energetic agreement in the early stages of this study was taken as justification for our discontinuing single point calculations at this higher level of theory. While the good agreement between 6-31G**/ /6-31G** and higher levels of theory seems to be consistent, we

Kumpf and Damewood are hesitant to suggest that this will always be the case for the calculation of intefmolecular interactions, even in the case of the I-water system. The 6-3 lG**//6-31G** calculation undoubtedly contains some basis set superposition error (BSSE), and this basis does not consider the effects of electron correlation. We therefore feel that calculations should consistently be performed at the MP2/6-311+G**//6-31G** or higher level in order to obtain quality results for appropriate reasons. We point out that the present calculations and comparisons clearly indicate the effects of performing Merller-Plesset (MP) corrections to calculations performed with a basis set that cannot be considered complete. In all cases (la-k see above) we conclude that the MP2/6-31G**//6-31G** level provides estimates for the binding energy for 1-water configurations that are too favorable by comparison to more sophisticated levels of theory. Even though MP2/6-31G**//6-31G** would be considered a higher level of theory than 6-31G**//6-31G**, results obtained at this level are actually in poorer agreement with higher levels of theory than 6-31G**//6-31G**. In addition, we point out that our application of higher levels of theory without correction for correlation effects by M P corrections, as exemplified in our 63 1 I+G**//6-3 1G** level calculations, consistently leads to an underestimation of the binding energy. In the latter case, the observed decrease in binding energy relative to 6-3 1G**//6-3lG** can be attributed to a decrease in BSSE. Since this decrease in BSSE is not compensated for by the consideration of dispersive effects by the 6-31 1+G** basis, the binding energy is underestimated. Comments on the Formaldehyde-Water Potential Energy Hypersurface This assemblage of data on the interaction of 1 with water allows us to comment on the 1-water potential energy hypersurface. It is widely believed that the potential energy profile for hydrogen bonding is, in general, relatively shallow. The results of the present study, at all levels of theory, allow us to conclude that this clearly pertains to the case of the interaction of 1 with water. Despite sometimes large differences in complex structure, the interaction energies for this system remain relatively similar. Indeed, at almost any level of theory reported, using modest error limits for the calculations would not allow one to establish a clear energy ordering for all configurations considered. It is, however, possible to clearly state that the interaction of water with the carbonyl oxygen region of 1 is more favorable than with the C-H end of the molecule. We feel that these collective observations must be considered in the generation of any accurate model for bulk water-1 interaction^.'^ Through the application of chemical intuition and SOLDRI potential energy search techniques, we have been able to provide a very accurate picture of the hydration potential for 1. As such, the present comparative study reemphasizes4 the usefulness of a combined intuitive-SOLDRI approach when investigating 1: 1 intermolecular interaction potentials. The data presented for these 1:1 configurations contribute significantly to developing our understanding of the interaction of organic molecules such as 1 with aqueous environments and can assist in the evolutionary development2 of more accurate potentials for bulk water-1 simulations. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, the Cottrell Research Corporation, Academic Computing Services at the University of Delaware, and Cornell Theory Center for support of this research. Registry Yo

1, 50-00-0, water, 7732-18-5

( 1 3) While relying on the best data available at the time, some previous simulations''." have employed potential functions that predict configuration l b , e.g., to reside along a significant potential energy hill, rather than being a potential energy minimum as presented in this work (see also ref 4). We feel that, in order to develop the most accurate potential functions possible, data such as the appropriate nature of Ib, etc., must be considered.