J. Phys. Chem. 1984,88, 6231-6233 Summary and Conclusions We have presented the results of some initial investigations into the nature of the metal alloy clusters which are produced from the laser vaporization/molecular beam cluster source. For both the systems investigated, Ni/Cr and Ni/Al, the cluster distributions displayed abundances of alloy clusters which could be relatively well interpreted by using a simple statistical model. This model assumes that the cluster growth rates are completely independent of chemical species and therefore that the final cluster distribution can be calculated from the initial atomic abundances. The agreement between model predictions of neutral cluster abundances and observed PI/TOF mass spectral distributions is especially good for clusters larger than about six atoms. In the nickel/chromium system, this conclusion is reached with the caveat that the chromium-rich clusters exist as singly oxidized species. The Ni/Al clusters were formed from an alloy with an exact stoichiometry, Ni3A1; however, the mixed clusters show no preference (other than can be accounted for statistically) to adopt this bulk property to form an intermetallic compound (Le. ion peaks for Ni,Al, Ni6A12, etc. do not stand out). Among the smaller clusters of both alloys, there are instances in which the PI/TOF ion signals do not agree with the relative intensities predicted by the statistical calculation of neutral cluster abundances. It is impossible to make quantitative statements about
6231
the possible nature of these discrepancies without an intimate knowledge of the photoionization efficiency of each cluster. We suspect, however, that much of the discrepancy could be explained by IP effects, since our work on pure metals indicated that clusters of from one to six or so atoms show the most dramatic variations in ionization p ~ t e n t i a l . ~Photoionization .~ studies on both systems would provide more insight into this question, as well as providing information on the IPS of clusters from alloys, a subject of interest in its own right. Further studies of the production of alloy cluster beams should concentrate on binary mixtures, since these are most readily interpreted. It would also be informative to examine the cluster distribution as a function of binary alloy composition. This would provide a more stringent test of the conclusion of purely statistical cluster distributions for the larger clusters and also probe the effects of chemical bonding in small clusters. Finally, both binary metal systems studies here form alloys in the bulk. Hence, the tendency to also produce a seemingly statistical composition of mixed clusters should not be surprising. As an opposite extreme, a binary system in which the metals do not form an alloy would be interesting to examine to see which, if any, mixed clusters are formed. Registry No. Ni, 7440-02-0; AI, 7429-90-5; Cr, 7440-47-3; AINi,, 12609-41-5; Nio,,Cr0.,,37379-76-3. 12003-81-5; Nio.7sAlo.2s,
Intermolecular Potentials from Crystal Data. 6. Determination of Empirical Potentials for O-H***O=C Hydrogen Bonds from Packing Conflguratlons' Manfred J. Sippl? George NCmethy, and Harold A. Scheraga* Baker Laboratory of Chemistry, Cornell University, Ithaca, New York 14853 (Received: July 10, 1984)
Crystal packing computations were used to determine the values of the parameters for the potential energy of the O-H4.. .O1, hydrogen bond where OI7refers to the double-bonded carbonyl or carboxylic acid oxygen. These are to be used in a self-consistent set of potential energy parameters in peptide conformational energy computations. The computed lattice constants are in good agreement with the experimental values.
Introduction An empirical potential program for the computation of conformational energies of polypeptides and proteins (ECEPP)has been developed in this l a b o r a t ~ r y . ~ This - ~ potential is defined as the sum over all pairwise interactions between the atoms of a molecule. The pairwise interaction energy is partitioned into electrostatic and nonbonded (Lennard-Jones type) contributions. Hydrogen bonds are represented by a general hydrogen bond (GHB) potential. The various empirical parameters of this potential function have been determined by optimization on suitably chosen crystals. Recently, the GHB parameters for the C-0-He. .O(H)C hydrogen bond have been revisedS6 This bond is denoted as an (1) This work was supported by grants from the National Institute of General Medical Sciences (GM-14312), and from the National Institute on Aging (AG-00322) of the National Institutes of Health, and from the National Science Foundation (PCM79-20279). (2) Postdoctoral fellow of the Max Kade Foundation. (3) Momany, F. A.; McGuire, R. F.; Burgess, A. W.; Scheraga, H. A. J. Phvs. Chem. 1975. 79. 2361. -(4) NBmethy, 6.;Pottle, M. S.; Scheraga, H. A. J. Phys. Chem. 1983,87, 1883. ( 5 ) Momany, F. A.; Carruthers, L. M.; McGuire, R. F.; Scheraga, H. A. J . Phys. Chem. 1974, 78, 1595.
0022-3654/84/2088-6231$01.50/0
H4.--OI8hydrogen bond, because hydroxyl or carboxylic acid hydrogen and hydroxyl or carboxylic acid (C-0-H) oxygen are designated' in ECEPP as atom types 4 and 18, respectively. In this paper, we present a revision of the GHB parameters for the closely related C-O-H.-O=C or H4--0,, hydrogen bond, where the carbonyl (O=C) oxygen is designatedSas atom type 17. In our earlier ~ t u d i e s the , ~ parameters for this hydrogen bond had been derived from carboxylic acid crystals, where the H4-O17 interaction exists in a symmetric pair of hydrogen bonds linking two carboxyl groups. In the present study we used crystals with isolated H4--Ol7 hydrogen bonds (Figure 1 ) . We find that the H4--01,interaction is significantly weaker for an isolated hydrogen bond than for the hydrogen-bonded pairs in carboxylic acids. This difference is probably due to the unique configuration of the antiparallel hydrogen bonds in carboxylic acid dimers, which may result in resonance stabilization. Methods The general hydrogen bond potential (GHB) is represented in the forms*7
(6) NBmethy, G.; Scheraga, H. A. J. Phys. Chern. 1977, 80,928.
0 1 9 8 4 American Chemical Society
6232 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
Sippl et al.
where X is the acceptor atom, which is a carbonyl oxygen, 0 1 7 , in the present study. The depth and position (Urninand rrnin, respectively) of this potential are given as urnin
= (@/A’5)[(10/,2)6 - (‘?‘lA5I
(2)
rmin= (12Af/10B)1/2
(3)
UGH, is only part of the total energy of the hydrogen bond. The total energy of interaction includes electrostatic as well as nonbonded interactions involving neighboring atoms attached to H and X. The parameter B H - X = 5783 kcal AIo/mol of the attractive part of the hydrogen bond and the parameters for the other nonbonded interactions are those reported in the previous st~dies.4~ The partial charges on the atoms, required for the evaluation of the electrostatic interaction, were determined by the molecular orbital C N D 0 / 2 (ON) method8 and are all shown in Figure 1 . With these parameters fixed, the GHB for the H4”’017 bond is a function of the repulsive coefficient of the potential. The optimal value of A’H...xwas determined by minimizing the binding energy of crystals, as was done previou~ly.~The coordinates of the heavy atoms of the crystals were generated from the X-ray fractional coordinates by standard technique^.^ Since the covalent bonds formed between hydrogens and heavy atoms tend to appear too short in the X-ray investigations, we generated the positions of the hydrogen atoms by using the ECEPP standard ge0metr9~which is based on neutron diffraction data,I0 even when coordinates for the hydrogens were reported in the X-ray investigation. Prior to the minimization of the crystal lattice energy, the hydroxyl groups participating in the H4”’017hydrogen bond were rotated into a position in which the interaction energy of the H atom with surrounding atoms is the lowest, in order to start from a unique and reasonable conformation. The crystal lattice energy was then minimized as a function of the cell parameters a, b, c and a,@, y. In order to preserve the space groups of the crystals, the angles a,@, y between the cell axes were allowed to vary only if they were not equal to 90’. The repulsive parameter of the GHB was determined as that value which minimizes the root-mean-square deviation of the calculated and observed cell parameters, i.e. n
u = [ ( l / n ) C ( l i m l d- lrbsd)2]1/2 i= 1
(4)
where 1, = a, b, c, a,@, y and n = 4 or 6, depending on the space group of the crystal. Every crystal was treated independently by this procedure. The final value of A’H..,X is the one which minimized the sum of the u’s for all three crystals.
Results and Discussion Optimal fitting of the minimized crystal parameters to the observed parameters was obtained with A’H...X= 16583 kcal A12/mol. This corresponds to rmin= 1.855 A and Urnin= -2.00 kcal/mol for the H4”’017 GHB. This value of A’H...Xdiffers considerably from the previous one of 13 344 kcal AI2/mol derived from carboxylic acid interaction^.^*^ Quantum-mechanical effects such as resonance may account for this difference between carboxylic acid double hydrogen bonds and isolated hydrogen bonds, so that two different repulsive parameters should be used for H4*.*017hydrogen bonds, viz., A’H ...X = 16583 kcal Alz/mol for isolated H4”’017 bonds and A’H...~ = 13344 kcal AI2/mol for each H4--Ol7pair in carboxylic acid dimers. To our knowledge, no carboxylic acid type double hydrogen bonds have been reported in X-ray structures of proteins, but individual HpO17 interactions (7) McGuire, R.F.;Momany, F. A.; Scheraga, H. A. J. Phys. Chern. 1972, 76,315. (8) Yan, Y. F.; Momany, F. A.; Scheraga, H. A. J . Phys. Chem. 1970, 74, 420. (9) Megaw, H. D. “Crystal Structures: A Working Approach”; W. B. Saunders Co.: Philadelphia, PA, 1973. (10) Koetzle, T. F.; Hamilton, W. C. Acta Crystallogr., Sect. B 1972, 28, 2083.
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Intermolecular Potentials from Crystal Data
A
H8B II\
The Journal of Physical Chemistry, Vol. 88, No. 25, I984 6233
B
C
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H4;
'
C3 c2 I54
173
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H39
01/c'$02
\ -366
-370
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HI
H3 Figure 1. Structures and CNDO/2 (ON) partial charges indicated near the atomic symbols in electronic units (XlOOO) used to determine the repulsive parameter A'+x: (A) 1-hydroxy-cis-bicycle[5.3.0]dec-9-en-8-0ne,'~(B) dihydroxyacetic acid (glyoxylic acid monohydrate),'* (C) a-hydroxyisobuytric acid.') The numbering scheme follows that reported in the respective X-ray analyses.
occur quite frequently. Therefore, we replace the value of derived from carboxylic acid double hydrogen bonds by our new estimate, keeping in mind that, for carboxylic acid type double hydrogen bonds, the previously established value is appropriate. In Table I we compare the computed crystal parameters with the experimental ones. The l-hydroxy-cis-bicyclo[5.3.0]dec-9en-8-one molecule has a double bond between carbon atoms C3 and C4 (Figure 1). Since we do not have parameters for olefinic double-bonded carbon atoms in the ECEPP potential set, we used the parameters of aromatic carbons for these two atoms and those of aromatic hydrogens for the attached hydrogens. In the crystal, the molecules form a linear pattern of hydrogen bonds between 02-H2 and 0 1 of neighboring molecules, along t h e y direction of the crystal. After optimization, the deviation = 0.00496 is very small for this crystal, with no large differences among the values of the deviations Aa, Ab, and Ac; Le., there was no large displacement of the molecules in any direction. This indicates that the assignment of aromatic nonbonded parameters to the double-bonded C and H atoms is a good approximation, at least for this crystal. Otherwise, we would have observed larger de(1 l) Rafalko, P. w.;Davis, R. E. Acta Crystallogr. Sect. B 1978, 34, 290. (12) Lis, T. Acta Crystallogr. Sect. C Cryst. Struct. Commun. 1983, C39, 1082. (13) Gaykema, W. P. J.; Kanters, J. A.; Roelofsen, G. Cryst. Struct. Commun. 1978, 7 , 463.
viations between calculated and observed crystal parameters, especially in the direction of interaction of the double-bonded carbons with other atoms. Interestingly, the two carboxylic acids studied, viz., dihydroxyacetic acid and a-isobutyric acid, do not form carboxylic acid type dimers in their crystals. This is probably due to packing constraints imposed by the particular structures of the molecules. Two of the three 0-H groups of dihydroxyacetic acid form H4-O18hydrogen bonds (01-H1.-03 and 03-H3-04), and one 0-H group is involved in an HyO17 hydrogen bond (04-H4. -02). In a-isobutyric acid, one hydroxyl group forms an H p O l 8 hydrogen bond (01-H1-.03) while the second forms an H4-017 hydrogen bond (03-H3.-02). Thus, both molecules have both types of O-H-.O hydrogen bonds. The values of A'H-.X obtained from these two molecules, after varying the cell parameters, are close to that obtained for l-hydroxy-cis-bicyclo[5.3.0]dec-9-en%one. The repulsive parameter A'H-X for the H4-O18interactions has been recalculated recently.6 The revised value was used for the H4--Ol8interactions in the present study. Since the estimate of the H4"'017 repulsive parameter of these two molecules is close to the estimate obtained from l-hydroxy-cis-bicyclo[5.3.0]dec9-en-8-one, we conclude that our estimates of the repulsive parameters for both hydrogen bonds are self-consistent. Acknowledgment. We are indebted to S. Rumsey for assistance with the computer programs.
