243
J. Phys. Chem. 1984, 88, 243-248 in Table X. In the majority of the listed reactions, the ss value is the smallest for eq 24. However, the standard deviation for AVO*tends to be larger and in some cases it gives, probably unreasonably, large activation volumes. For example, in the aquation of C O ( N H ~ ) ~ Cthe ~ ~average +, activation volume for 0.001 and P kbar changes as follows, -1 1.77 (0.5 kbar), -9.73 (1 kbar), -8.44 (1.5 kbar) mL/mol and the AVO*obtained by eq 24 is -18.37 mL/mol. The same tendency is observed in the hydrolysis of Pt(dien)Br' [-18.91 (0.125 kbar) mL/mol and AVO* = -25.16 mL/mol], These results indicate the difficulty in the estimation of AVO*.This problem may be avoided if we choose to use A P under pressure, e.g., at 0.5 kbar, but it would result in another experimental difficulty, Le., the partial molar volume measurements at high pressure in order to construct a volume profile of a reaction. Therefore, the most practical solution would be to use several equations in the estimation of AVO' and compare the obtained results.
Experimental Section The rate constants for the Z-E isomerization of NMe2-N02-AB were measured by the high-pressure flash spectroscopic technique described before.8 The optical pressure vessel was slightly modified and its cross section is shown in Figure 3. The inner sample cell consists of a transparent glass cylinder and a hypodermic syringe and they are connected together with a Teflon coupler. Since the pressure is transmitted to the sample solution by means of the syringe, the possibility of a reduction in pressure by friction is eliminated. The pgessure-transmitting fluid was hexane. The on-line calculations of the rate constants based on the Guggenheim method were performed by a SORD M200 Mark I1 computer. The least-squares calculations of the activation and reaction volumes were done by the Gauss-Newton method and/or by the Marquardt method. The program used was MULTIdeveloped by Yama~ka.~~ Registry No. (Z)-4-(Dimethylamino)-4'-nitroazobenzene,738 15-07-3. ~~
(22) We are grateful to one of the referees for the suggestion of this
equation.
(23) Tanaka, Y.; Yamaoka, K. "Micro Computer Guide for Chemists"; Nankodo: Tokyo, 1981; pp 114-9.
Conformational Polymorphism. 5. Crystal Energetics of an Isomorphic System Including Disorder I. Bart and J. Bernstein* Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva 841 20, Israel (Received: January 18, 1982; In Final Form: May 17, 1983)
The methodology for investigating the influence of crystal forces on molecular conformation has been extended to an isomorphous system, involving chemically similar species which crystallize in essentially identical structures. The model systems chosen for this study are p-methyl-N-(p-chlorobenzy1idene)aniline (CLME) and p-chloro-N-(p-methylbenzy1idene)aniline (MECL), which crystallize in the monoclinic space group P2,/a with two molecules in the cell. Calculationsinvolving the lattice energy minimization of the two structures were carried out to understand why the unstable planar conformation is stabilized by the lattice, although there are dimethyl- (MEME) and dichloro-substituted(CLCL) N-benzylideneanilines (BA) that contain lower energy molecular conformations. Furthermore, lattice energy calculations have been applied to hypothetical structures which are based on computationally substituting MEME and CLCL molecules into the CLME and MECL structures to determine whether it is possible that these analogues will pack as isomorphs of the system studied here, and to reveal the role of the substituents on disorder. Two different potential functions were applied (6-12 and 6-exp), both of them yielding lower energies for MECL than for the hypothetical structures and the lowest energies in comparison with minimized lattice energies of all BA compounds investigated to date. Analysis of the partitioned partial atomic energies was carried out to examine the similarities and differences in packing between the two isomorphs and the hypothetical structures. The relative stability of MECL arises from the favorable energetic environment of the ring, especially due to methyl and chlorine substituents.
Introduction A number of earlier have demonstrated the utility of employing conformational polymorphism to investigate the role of crystal forces in influencing molecular conformation. The system employed in the first of those was the dimorphic p chloro-N-(pchlorobenzy1idene)aniline (CLCL) which adopts
planar one present in the orthorhombic polymorph.6 In the second example2 we asked why CLCL does not pack in a crystal in which the intramolecular energy is minimal. This was investigated computationally by substituting the CLCL molecule into the structure of form I1 of M E M E in which the molecule
MEME
different conformations in the two polymorph^.^^^ The analysis of the energetics of CLCL' revealed a favorable energy for the triclinic structure, which accounts for the stabilization of the more highly energetic planar conformation in this form over the non'In partial fulfillment of the requirements for the Ph.D. degree, Ben-Gurion University of the Negev.
0022-3654/84/2088-0243$01.50/0
T. Hagler, J . Am. Chem. SOC.,100, 673 (1978). (2) A. T. Hagler and J. Bernstein, J. Am. Chem. SOC.,100, 6349 (1978). (3) I. Bar and J. Bernstein, J . Phys. Chem., 86, 3223 (1982). (4) J. Bernstein and G. M. J. Schmidt, J . Chew. SOC.,Perkin Trans. 2, 951 (1972). ( 5 ) J. Bernstein and I. Izak, J . Chem. SOC., Perkin Trans. 2, 429 (1976). (6) J. Bernstein, Y . M. Engel, and A. T. Hagler, J . Chem. Phys., 75, 2346 (198 1). (1) J. Bernstein and A.
0 1984 American Chemical Society
244
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984 071
Bar and Bernstein
011
rm
Figure 2. Stereo packing diagram of the isomorphous structures MECL and CLME. The view is on the best plane of the four bridge atoms of M2
on J
mi
H30
071
Figure 1. Numbering of atoms and assignment of partial charges (as fraction of an electron) in MECL and CLME. Chhrges are given for the unique atoms only; those in parentheses are for MECL. The meaning of X is given in the text.
adopts very nearly the energetically preferred free-molecule conformation.6 The results showed that the structure of the dichloro analogue in the MEME structure is less stable than either of the polymorphs of CLCL, thus accounting for the nonexistence of the tested structure. A third study3 treated the trimorphic MEME system for which lattice energy calculations demonstrated the relative stability of forms I and 111, in which the unstable planar conformation is adopted7v8with respect to form 11, which exhibits a nonplanar conformationg that is close to the free-molecule energy minimum? Furthermore, it was shown that the stability of the polymorphs I and I11 is enhanced by the relatively favorable environment of the disordered bridge atoms, demonstrating the influence of disorder on the stabilization of the energetically less favorable planar conformation. Although the size of the methyl group does not differ greatly from that of a chlorine atom,1° there is no isomorphism between the trimorphic M E M E system and the dimorphic CLCL system. Substitution of one of the methyl groups in MEME by a chlorine atom, or alternatively one of the chlorine atoms in CLCL by a methyl group, leads to two compounds which are chemically different (MECL and CLME). These two structures are crys-
,,
H3c+yN
Cl-JC---
MECL
C1+VNq7&
CH3
CLME tallographically isomorphous" but are not isomorphous with any member of the CLCL4*5or MEME7-9 systems. These structural relationships suggest that the molecular lattice energies of heterodisubstituted MECL and CLME are similar but that they differ from those of the homodisubstituted analogues. The two isomorphous compounds crystallize in the monoclinic space group P z J a with two molecules in the unit cell. The structures are disordered in a fairly complex fashion and for the purposes of the present discussion we distinguish among three different types of disorder discussed in detail elsewhere." For orientational disorder the molecule at any one crystallographic site may be oriented in different ways but in the two or more dispositions each atom is essentially superimposed on another; the disorder is due to the fact that dissimilar atoms (e.g., C and N) may occupy the same site. This is the disorder which requires the use of X in place of C and N at the bridge atoms (Figure 1). For positional disorder the C and N, for example, may occupy different positions (approximately 0.6 8, from each other) while (7) I. Bar and J. Bernstein, Acta Crystallogr., Sect. B, 38, 121 (1982). (8) J. Bernstein, I. Bar, and A. Christensen, Acta Crystallogr.,Sect. B, 32, 1609 (1976). (9) I. Bar and J. Bernstein, Acta Crystallogr.,Sect. B, 33, 1738 (1977). (10) L. Pauiing, "The Nature of the Chemical Bond", Cornell University Press, Ithaca, NY, 1960, pp 260. (11) I. Bar and J. Bernstein, Acta Crystallogr.,Sect. B, 39,266 (1983).
the reference molecule, which is darkened. the atoms of the rings are nearly superimposed (maximum displacement 0.35 A). The situation is represented by the positional disorder between X2-X3 and X2I-X23 in Figure 1. For substitutional the atoms of the parent molecule occupy constant positions but the substituents may be interchanged due to their similar steric properties and bond lengths with the parent molecule. The first two types of disorder appear separately or in combination in the homo-para-disubstituted benzylideneanilines." With hetero para disubstitution as in the present case, an additional variable is present, which can lead to the third type of disorder, substitutional. This disorder involves the random occupation at a given crystallographic site by two or more types of atoms, in particular substituents, and an example similar to that encountered here has been given by Dunitz,lZaciting Clews and Cochran.lzb The simple exchange of Me and C1 substituents in this case would of course interchange MECL with CLME and would imply the existence of mixed crystals, which is not the case here. While there is an intimate relationship between orientational and substitutional disorder, we believe that the additional definition of the latter term is required to account for cases of unsymmetric substitution. The structures studied here represent a combination of these three different modes. In both structures the molecule adopts an energetically unfavorable conformation6 in which the exocyclic torsion angle are 1lo and 9O for MECL and CLME, respectively, with the rings rotated in the same direction with respect to the plane of the atoms in the central bridge. While the molecules are chemically distinct, the crystal structures are very similar with respect to the substitutional disorder which was not possible in previously studied homodisubstituted BA's. Hence, a computational investigation of the energetics of this system is a logical extension of previous studies to further test the utility and limits of this technique in investigating crystal forces, polymorphism, isomorphism, and disorder. The structures of MECL and CLME also provide an opportunity for investigating the question of whether it is energetically favorable for M E M E and CLCL to pack in a structure isomorphous with the two heterosubstituted compounds. This investigation,then, includes a study of the crystal energetics of both isomorphs MECL and CLME, as well as computational substitution of M E M E and CLCL into the MECL, C L M E structures. Partitioning of the final overall lattice energy is carried out to obtain individual atomic contributions to the total energy. Finally, we attempt to analyze the molecular and crystal energetics of the systems studied and to evaluate the potential functions by comparing the results for the two functions employed.
Methods The energy minimizations were carried out with techniques applied earlier.' The lattice energy for both isomorphs was calculated by employing two different potential functions: 6-1 2 and Williams' 6-exponential functions, both including a 1/ r Coulombic term.' The 6-9 potential was not applied, since we have noted previously that this function has consistently yielded minimized lattice energies for the BA's which are experimentally approximately twice the expected values.'-3 Parameters employed for the atoms are unchanged from those previously used, except for the charges (Figure 1) which are assigned average values (for the ring and substituent atoms) of the charges in previous work (12) (a) J. D. Dunitz, "X-ray Analysis and the Structure of Oragnic Molecules", Cornell University Press, Ithaca, NY, 1979, p 55; (b) C. J. B. Clews and W .Cochran, Acta Crystallogr.,1, 4 (1948).
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984 245
Conformational Polymorphism TABLE I: Comparison of Experimental and Minimized Crystal Structures of CLME and MECL 6-12 exptlu
exP A
calcd
6.298 7.295 13.616 101.41 613.18 306.59
0.329 -0.117 -0.131 2.29 12.67 6.34
6.363 6.912 13.624 101.10 587.97 293.99
-0.123 1.98 -12.54 -6.27
MECL 6.190 7.305 13.681 99.14 610.83 305.42
0.230 -0.105 -0.012 -0.06 13.88 6.94
6.180 6.961 13.782 97.93 587.23 293.62
0.220 -0.449 0.089 -1.27 -9.73 -4.87
calcd
A
CLME a, A
b C
P, deg vol, A 3
vol/molecule,A'
5.969 (2) 7.412 (2) 13.747 (4) 99.12(2) 600.51 300.26
5.960(1) b 7.410 ( 1 ) C 13.693 (3) P , deg 99.20 (2) vol, A3 596.95 vol/molecule, A3 298.48 a, A
0.394 -0.500
Figures in parentheses are esd's of least significant digit.
TABLE 11: Summary of Lattice Energy Calculations crystal energy, kcal/mol 6-12 CLME initial Etot -36.62 Enb -37.28 Eelec 0.66 final Etot -39.65 -40.26 Enb Eelec 0.6 1 MECL initial Etot -38.76 -38.56 Enb -0.20 Eelec final Etot -41.06 -40.98 Enb Eelec -0.07 AE(MECL-CLME) -1.41
exP -37.67 -38.33 0.66 -39.88 -40.55 0.67 -39.89 -39.69 -0.20 -41.08 -41.02 -0.06 -1.20
to account for the disorder in these structures. Furthermore, the crystallographic molecular site symmetry in both structures is (C,) (Figure 2 ) , which requires orientational disorder, due to the lack of a molecular center of symmetry. Positional disorder exists as well for the bridge atoms and is nonstatistical as in M E M E
form III* leading to two nonequivalent positions with occupancy 0.714 and 0.286 (f0.008) in MECL and 0.80 and 0.20 (fO.O1) in CLME." The charges given for the bridge atoms in Figure 1 proportionally account for the differences in occupancy of the two positions. Hydrogen atom coordinates were generated with a C-H bond length of 1.08 A with sp2 and sp3 hybridization for the carbon atoms in the ring and methyl group, respectively. Parameters were kept constant for all the lattice energy calculations. The presence of the methyl and chloro substitutent groups with half-occupancy allowed us to test why MEME and CLCL do not pack as isomorphs of this system. The starting point for these calculations was a model molecule obtained by excluding one of the statistically disordered substitutents, e.g., Me in MECL, and assigning full occupancy to the remaining one (C1 in this case); disorder on the bridge and crystallographically determined molecular conformation were retained in this model, in which the charges were adjusted to maintain neutrality over the entire molecule. The charges for these hypothetical molecules were assigned the same values as for the calculation on the monodisubstituted compounds MEME3 and CLCL.'.
Results The energy, lattice parameters, and partitioned energies resulting from the lattice energy minimizations are summarized in Tables 1-111. Analysis of the data in these tables leads to the following observations: Heterodisubstituted Compounds MECL, CLME. (1) The molecular volumes of the experimental cells suggest that MECL is slightly more efficiently packed them CLME (Table I). This is reflected as well in the minimized structures with the 6-12 potential, while for the exponential potential the calculated molecular volumes are virtually identical for the two structures. (2) There is a correlation between the lowest molecular volume and the lowest minimized energy (Tables I and 11) leading to a more stable lattice for MECL with respect to CLME by 1.4 and 1.2 kcal/mol, for the 6-1 2 and 6-exponential potentials, respectively. We note that roughly half of the stabilization of MECL over C L M E is due to the unfavorable electrostatic contribution to the total energy in the latter and points up one of the principal energetic differences between the two structures. (3) Detailed analysis of the energetic distinctions between the two isomorphs is assisted by partitioning of the minimized total lattice energy into its individual atomic contributions (Table 111). As in previous studies2g3it is convenient to compare the contribution
TABLE 111: Partition of the Minimized Crystal Energy into Individual Atomic Contributions, ei (kcal/mol)' CLME MECL Aei(MECL-CLME) 6-12 exP 6-12 -0.83 (12) -0.90 (10) -0.21 (2) -1.95 (3) -1.62 (4) 0 (11) -0.34 (17) -0.43 (15) -0.01 (10) -1.57 (4) -1.85 (3) +0.14 (16) -1.24 (6) -1.55 (5) +O.lS (17) - 1.3 1 (5) - 1.43 (7) +0.02 (13) c10 -1.20 (7) -1.40 (8) +0.01 (12) c11 -1.16 (8) -1.49 (6) +0.20 (19) H12 -0.29 (19) -0.04 (19) -0.21 (3) H13 -0.42 (16) -0.26 (18) -0.13 (6) H14 -0.83 (11) -0.69 (13) +0.02 (14) H15 -0.44 (15) -0.30 (17) -0.05 (9) C16 -1.12 (9) -1.30 (9) -0.12 (7) H17 -0.80 (13) -0.72 (12) +0.05 (15) H18 -0.86 (10) -0.78 (11) -0.20 (4) H19 -0.77 (14) -0.68 (14) -0.19 (5) c120 -2.95 (1) -2.94 (1) -0.23 (1) x21 -2.11 (2) -1.82 (2) +0.19 (18) H22 -0.30 (18) -0.37 (16) -0.08 (8) bridge -4.70 -8.24 +0.10 ring -9.26 -9.91 -0.03 substituents -6.50 -6.42 -0.69 Owing to symmetry only half of the atoms in the molecule are given. The number in parentheses gives the ranking of contribution in increasing energy. atom
c1 x2 H5 c7 C8 c9
6-12 -0.62 (13) -1.95 (3) -0.33 (16) -1.71 (4) -1.39 (5) -1.33 (7) -1.21 (8) -1.36 (6) -0.08 (19) -0.29 (17) -0.85 (10) -0.39 (15) -1.00 (9) -0.85 (11) -0.66 (12) -0.58 (14) -2.72 (1) -2.30 (2) -0.22 (18) -4.80 -9.23 -5.81
exP -0.69 (11) -1.62 (6) -0.43 (15) -2.00 (3) -1.73 (4) -1.47 (7) -1.38 (8) -1.65 (5) +0.20 (19) -0.09 (18) -0.67 (12) -0.26 (17) -1.19 (9) -0.78 (10) -0.61 (13) -0.51 (14) -2.75 (1) -2.02 (2) -0.29 (16) -4.36 -9.74 -5.84
exP -0.2 (2) 0 (12) o (13) +0.15 (16) +0.18 (18) +0.04 (14) -0.02 (11) +0.16 (17) -0.24 (1) -0.17 (6) -0.02 (10) -0.04 (9) -0.11 (7) +0.06 (15) -0.17 (4) -0.17 (5) -0.19 (3) +0.20 (19) -0.08 (8) +0.12 -0.17 - 0.5 8 the atomic
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984
246
Bar and Bernstein
TABLE IV: Comparison of Experimental and Minimized Hypothetical Crystal Structures CLME without Cla 6-12 a, A
b C
P , deg vol, A3 vol/molecule, A 3
exptl 5.969 7.412 13.747 99.12 600.51 300.26
calcd 6.358 7.41 1 13.266 102.19 610.96 305.48
exP calcd 0.389 6.483 -0.001 7.020 -0.481 13.078 3.07 102.28 10.45 581.57 5.23 290.79 MECL without Cla A
6-12 5.960 b 7.410 C 13.693 P, deg 99.20 vol, A3 596.95 vol/molecule, A3 298.48 See end of Methods section. a, A
a
CLME without Mea 6-1 2
A
0.5 14 -0.392 -0.669 3.16 -18.94 -9.47
calcd 6.495 7.299 13.391 101.31 622.57 311.29
exP
calcd 0.526 7.588 6.471 -0.113 -0.356 12.484 2.19 103.20 22.06 596.72 11.03 298.36 MECL without Mea 6-12
exP
A
A
1.619 -0.941 -1.263 4.08 -3.79 1.90 exP
calcd
A
calcd
A
calcd
A
calcd
A
6.191 7.495 13.520 99.25 619.18 309.59
0.23 1 0.085 -0.173 0.05 22.22 11.11
6.167 7.137 13.630 97.65 594.64 297 32
0.207 -0.273 -0.063 -1.55 -2.31 -1.16
6.444 7.343 13.407 100.90 622.91 311.46
0.484 -0.067 0.286 1.70 25.961 12.98
7.609 6.463 12.460 102.97 597.11 298.56
1.649 -0.947 -1.233 3.77 0.16 0.08
from three atomic groups and the hydrogens bonded to them. The groups are as follows: (1) bridge (X2, X21); (2) ring (C4, C7, C8, C9, C10, C l l ) ; (3) substitutents C16, C120. For consideration of the entire molecule symmetry-related atoms must also be included. The environment of the bridge atoms is clearly an important factor in the total energy and also appears to be the most sensitive to a change in potential function. The largest single atom contributor is C120 although the methyl group makes a larger contribution. The major contribution for the stabilization of MECL over C L M E is seen to be due to the substituents as a whole, and individually both contribute to this stabilization, with a much smaller contribution from the ring atoms. The bridge atoms are destabilizing. MECL is more nearly statistically disordered than C L M E which, as suggested earlier, on the average results in a larger number of Coulombically repulsive interactions (Table 11). Homodisubstituted MEME and CLCL in Hetero Crystal Structures. In Tables IV-VI we present the results for the hypothetical structures as described in the Methods section. The following points are significant. (1) For the minimized hypothetical structures the differences between the volume/molecule in the hypothetical structures based on the MECL structure and those based on the C L M E structure are small, again emphasizing the fact that the structures are very similar. We note, however, that the values for the MECL structure are consistently higher. Furthermoore, the molecular volumes for the molecules minimized with the 6-12 potential are higher than the experimental value, while those minimized with the 6-exp potential are lower. (2) Comparison of Tables I1 and V shows that the minimized energies of the experimental structures, including the disorder in the region of the substituents, is significantly more negative than the energy of all the hypothetical structures for both potentials. (3) The hypothetical structures including only methyl groups are more negative in energy than the equivalent structures with only chlorine as substituent. When both substituents are chlorines, the electrostatic contribution is again destabilizing, with a significantly higher contribution to the total energy than in the C L M E heterodisubstituted case. This indicates that these hypothetical structures are quite unfavorable for CLCL molecules with this conformation, but also suggests the possibility of an overestimated value for the charge assigned to the chlorine substituent. (4) The atomic group contributions (Table IV) are all consistently lower for the hypothetical structures than the experimental ones. As might be expected the largest proportional change in group contribution is for the substituents. For all the hypothetical structures methyl groups contribute more to stabilization than chlorines.
TABLE V: Summary of Lattice Energy Calculations of Hypothetical Crystal Structures crystal energy, kcal/mol CLME without C P CLME without Mea initial Etot Enb Eelec final Etot Enb
Eelec
a
6-12 -27.95 -27.46 -0.49 -30.87 -30.33 -0.54
exP 6-1 2 exP -29.52 -24.55 -25.99 -29.03 -27.00 -28.44 -0.49 2.45 2.45 -31.32 -27.18 -27.76 -30.66 -29.04 -28.84 -0.66 1.86 1.08 crystal energy, kcal/mol
MECL without Cla 6-12 exp initialEtot -28.52 -30.28 -29.60 Enb -27.84 -0.68 Eelec -0.68 final Etot -30.78 -30.84 -30.26 -30.31 Enb -0.53 Eelec -0.52 See end of Methods section.
MECL without Mea 6-12 exp -24.26 -26.67 2.41 -27.05 -28.96 1.91
-25.97 -28.38 2.41 -27.70 -28.78 1.08
Discussion Close Phcking. The principle of close packing suggests that the most densely packed arrangements have the most negative lattice energy.’3a This generalization is preserved by the isomorphs; Le., we expect the relative stability to be MECL > CLME since the density of MECL is slightly higher than that of CLME. The structures of the trimorphic M E M E and the hypothetical structures of MECL and CLME containing only Me as substituent appear to obey this rule as well, leading to a relatively more stable structure for the hypothetical structures than for the trimorphic system (Table VII). However, the dimorphs of CLCL and the hypothetical structures of C L M E and MECL with C1 as substituent appear to be an exception to the density rule.13 The energy calculations indicate a more stable structure for the hypothetical structures relative to the dimorphs of CLCL, although the volume molecule of the latter is smaller. Burger has noted13 that exceptions to the density rule are most often to be found among polymorphs which are disordered, since the “average molecules” are more extended than the ordered structure leading to a lower packing coefficient. In the CLCL system4a5only orientational disorder is present, while (13) (a) A. Burger and R.Ramberger, Mikrochim. A m . , II, 259 (1979); (b) ibid., 11, 273 (1979).
The Journal of Physical Chemistry, Vol. 88, No. 2, 1984 241
Conformational Polymorphism
TABLE VI: Partitioning of the Minimized Crystal Energy of Hypothetical Crystal Structures into Individual Atomic Contributions, ei (kcal/mol)a CLME without C1 CLME without Meb MECL without Clb MECL without Meb
c1 x2 H5 c7 C8
c9 c10 c11
H12 H13 H14 H15 C16 H17 H18 H19 c120 x21 H22 bridge ring substituents
6-1 2 -0.88 (8) -1.78 (2) -0.34 (17) -1.41 (3) -1.18 (4) -1.12 (6) -1.04 (7) -1.16 (5) -0.37 (16) -0.50 (13) -0.45 (15) -0.56 (12) -0.60 (10) -0.74 (9) -0.58 (11) -0.49 (14)
exP -0.97 (8) -1.47 (4) -0.45 (13) -1.66 (1) -1.49 (3) -1.25 (6) -1.17 ( 7 ) - 1.40 (5) -0.11 (18) -0.34 (17) -0.50 (12) -0.37 (16) -0.80 (9) -0.66 (10) -0.54 (11) -0.44 (14)
6-12 -0.14 (12) -1.86 (2) -0.29 (10) -1.74 (3) -1.45 (5) -1.01 (7) -1.01 (8) -1.22 (6) +0.35 (15) -0.03 (14) -0.82 (9) -0.22 (11)
exP - 0.43 (11) - 1.49 (5) -0.34 (12) - 1.78 (3) -1.73 (4) -1.14 (7) -1.13 (8) -1.27 (6) +0.45 (15) +0.11 (14) -0.62 (9) - 0.44 (10)
exP -1.45 (1) - 1.36 (2) -0.55 (13) -1.28 (5) -1.13 (7) -1.16 (6) -1.12 (8) -1.04 (9) -0.57 (12) -0.61 (10) -0.31 (17) -0.58 (11) -1.33 (3) -0.18 (18) -0.53 (14) -0.43 (16)
6-12 -0.13 (12) -1.95 (2) -0.11 (13) -1.75 (3) -1.45 (5) -1.01 (7) - 1.00 (8) -1.21 (6) +0.35 (15) -0.03 (14) -0.83 (9) -0.20 (11)
-2.08 (1) -1.67 (4) -2.28 (1) - 1.90 (2) -1.61 (2) - 1.32 (4) -0.42 (15) -0.12 (13) -0.39 (17) -0.48 (15) -0.25 (10) -7.96 -8.26 -7.42 -7.70 -9.18 -9.26 -8.71 -9.25 -7.98 -7.26 -2.44 - 1.67 -2.55 -2.47 -2.08 Owing to symmetry only half of the atoms in the molecule are given. The number in parentheses gives the ranking of atomic contribution in increasing energy. See end of Methods section. -1.92 (1) -0.32 (18) -8.72 -8.67 -2.41
- 1.64 (2)
-1.70 (4) -2.37 (1) -0.07 (13) -9.18 -7.29 - 1.70
6-12 -1.35 (3) -1.68 (1) -0.45 (15) -1.06 (6) -0.88 (8) -1.07 (5) -0.98 (7) -0.79 (9) -0.77 (10) -0.74 (11) -0.40 (16) -0.67 (12) -1.12 (4) -0.29 (18) -0.59 (13) -0.55 (14)
TABLE VII: Volume/Molecule for Experimental and Minimized Crystal Structure and Summary of Lattice Energy Calculations voumolecule, A3 potential function structure exptl 6-12 exP CLCL triclinic 284.3 300.1 284.1 CLCL orthorhombic 284.3 307.4 292.8 CLME without M e 31 1.3 298.4 MECL without Mea 311.5 298.6 MEME I 307.5 312.8 299.5 MEME I1 302.9 318.9 305.4 MEME I11 289.9 314.5 295.2 CLME without Cla 305.5 290.8 MECL without Cia 309.6 297.3 lattice energy, kcal/mol
a
CLCL triclinic CLCL orthorhombic CLME without Mea MECL without Mea MEME I MEME I1 MEME 111 CLME without Cla MECL without Cla See end of Methods section.
6-1 2 -22.73 -21.68 -27.18 -27.05 -29.33 -22.71 -27.57 -30.87 -30.78
exP -23.99 -22.34 -27.76 -27.70 -28.21 -22.67 -29.70 -31.32 -30.84
in the hypothetical structures positional disorder was retained as well, presumably leading to a “more extended” structure and a larger cell relative to the two known polymorphs of CLCl. In form I9 of the MEME system there is positional disorder, while in form III* both positional and orientational disorder are present. In terms of disorder form I11 is similar to the hypothetical structure of MECL and C L M E with Me as substituent. The structural similarity of M E M E I11 to the hypothetical structures suggests a relationship in their packing coefficients and indeed both the minimized energies and the molecular volumes for the hypothetical structures most clearly resemble those for M E M E 111. The lattice energy calculated for the hypothetical structures thus suggests the possibility of the existence of additional polymorphic forms of CLCL and MEME isomorphic with MECL and CLME. These presumably have not been found yet due to our
exP -0.43 (11) -1.56 (5) -0.16 (13) -1.75 (3) -1.73 (4) -1.13 (8) -1.13 (7) -1.26 (6) +0.47 (15) +0.10 (14) -0.61 (9) -0.44 (10)
-2.10 (1) -1.81 (2) -0.32 (12) -7.70 -7.91 -2.10
lack of knowledge about the conditions necessary for their crystallization. Partitioned Energy. The use of partial atomic energies allows us to compare details of energetics in the two structures. The favorable energetics of MECL relative to C L M E (Table 111) is due for the most part of the contribution of the substituents (for both potentials), while the bridge atoms are destabilizing factors. In earlier s t u d i e ~ we , ~ postulated that the forces acting as the extremities of the molecules play an important role in determining the packing of these structures. If the methyl group is taken as a single substituent for comparison with the chlorine, the results obtained for this pair of isomorphic structures are consistent with this earlier postulate. In the CLCL system it was shown that the chlorine atoms are the largest contributors, and in the M E M E system the methyl group was the major ”single-atom” contributor; the same holds for this system. In contrast to the previous results, the methyl and chlorine are in different energetic environments in the two structures. The methyl contributes to the stabilization of MECL over CLME (Ae, -0.46, -0.39 kcal/mol) while the chIorine contributions are Ae, -0.23, -0.19 kcal/mol for the 6-12 and exponential potentials, respectively. The environmental difference for the two substituents can very nearly account for the energy difference between MECL and CLME. In fact, as pointed out earlier, the environmental change for the substituents may be due to a difference in the electrostatic contribution from the heterosubstitution. The latter contribution is not present in the hypothetical structures and in those cases the calculations thus lead to similar energetic environments for both compounds with both potentials. Hence, the lattice energy minimizations strongly suggest that the disorder due to the location of the heterodisubsituted BA’s on a crystallographic center of symmetry plays a significant role in the energetic preference of the experimental isomorphs over the hypothetical ones. The disorder can be shown to be important in the bridge region as well as for the substituents. As noted above, form I11 of MEME* exhibits a mode of disorder in the bridge region similar to that found in MECL and CLME, the major difference being occupancies of 0.6 and 0.4 for X and X’, respectively,in MEME 111. The differences in energy between form I11 of MEME3 and the hypothetical structures with Me as a substituent arise from a more favorable environment of the bridge atoms in the latter (Ae, -2.66, -2.20 kcal/mol) for the CLME and MECL hrpothetical structures with the 6-1 2 potential and (Ae, -1.80, -1.26 kcal/mol) for the same compounds with
248
J. Phys. Chem. 1984, 88, 248-250
the exponential potential. By comparison the differences from the rings are (Ae,-0.34, -0.48 kcal/mol) with the 6-12 potential and (Ael +0.08, +0.06 kcal/mol) with the exponential potential. Comparison between the hypothetical structure with C1 as a substituent and the triclinic polymorph of CLCL’ suggests that the stabilization of the hypothetical structure is provided by the favorable environment of the bridge atoms (Ael -5.12 kcal/mol) of both compounds over the CLCL with the 6-12 potential and -3.68 kcal/mol with the exponential potential, leading again to the conclusion that the mode of disorder in the region of the bridge is very important to the relative stability of a particular structure in this family of compounds. Potential Functions and Heat of Sublimation. The results presented above demonstrate that the computed energetic difference between the isomorphic structures M E C L and C L M E are not significantly different for the two functions employed. The nonbonded parameters for the Williams’ exponential potential of the nitrogen atom were taken as those of carbon, in order to be consistent with the calculations that were carried on the homodisubstituted molecules.’-3 Despite this, we have again obtained essentially similar results for the 6-1 2 and Williams’ potentials. The mode of disorder is similar in the two isomorphs, so that the treatment of the bridge atoms is the same, apparently leading to equivalent results. The absolute values of the minimized lattice energies with the two potentials are somewhat larger than the estimate of ca. 26 kcal/mol, based on the experimental sublimation energy of BA14 (20.5 kcal/mol) and the expected contribution from a methyl group15 (2.45 kcal/mol) and a chlorine15 (3.0 kcal/mol). This method of estimating the sublimation energy does not take into account the three modes of disorder that are present here.” Since the average molecule which we observe in the structure is obtained by superposition of four molecules, there is an additional configurational entropy contribution16 for distribution over four (14) G. E. Coates and E. Sutton, J . Chem. Soc., 1187 (1948). (15) A. Bondi, J . Chem. Eng. Data, 8, 371 (1963). (16) (a) E. F. Westrum, Jr., and J. P. McCullough, “Physics and Chemistry of the Organic Solid State”, Vol. 1, D. Fox, M. M. Labes, and A Weissberger, Eds., Interscience, New York, 1963; (b) N. G. Parsonage and L. A. K. Staveley, “Disorder in Crystals”, Clarendon Press, Oxford, 1978, Chapters 9 and 10.
positions which at room temperature is 0.83 kcal/mol, Le., R T In 4). Concluding Remarks. In the present study we have extended to an isomorphic system the computational techniques previously applied to conformational polymorphs. Three different kinds of disorder have been included in the calculations, using two different potential functions. The lattice energy obtained for the two heterodisubstituted compounds MECL and CLME is lower than that obtained when the same calculation is carried out on the homodisubstituted molecules placed in the same lattice. However, the latter calculations suggest the existence of additional but as yet unreported polymorphic forms for the homodisubstituted compounds, with the higher energy planar molecular conformation. These results are consistent for two different potentials. The fact that the relative stability of MECL arises from the favorable energetic environment of the substitutents and not from the differences in occupancy as exemplified by the hypothetical structures emphasizes the importance of the role of heterodistribution in the stabilization of these structures and suggests investigating further the role of substituents in these systems. although there is a difference in the occupancy factor of the bridge atoms in MECL and CLME, it is difficult to attribute the energetic stabilization only to it. The same difference in occupancy factors was preserved by the hypothetical structures also, but they were equivalent in terms of energy, so that it seems that the substituents are the main factor which lead to the more stable structure. A simple perturbation may be achieved by substituting bromine for chlorine in these two compounds, and we have recently carried out structural studies on this pair of compound^.'^ The two compounds are isomorphous with the structures studied here. The system thus provides an additional variable to test the methods employed in these computational studies. Both the structures and the lattice energetics will be reported in due course.
Acknowledgment. The work was supported in part by a grant from the U.S.-Israel Binational Science Foundation (BSF) Jerusalem, Israel. Registry No. CLME, 15485-32-2; MECL, 29574-09-2; MEME, 16979-20-7;CLCL, 10480-32-7. (17) I. Bar and J. Bernstein, unpublished results.
Photoc>atalyticand Photoelectrochemical Reactions of Aqueous Solutions of Formic Acid, Formaldehyde, and Methanol on Platinized CdS Powder and at a CdS Electrode Michio Matsumura, Masahiro Hiramoto, Toshio Iehara, and Hiroshi Tsubomura* Laboratory f o r Chemical Conversion of Solar Energy, Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan (Received: January 24, 1983; In Final Form: June 1 , 1983)
Hydrogen evolves by illumination of suspensions of platinized CdS powder in aqueous solutions of formic acid, formaldehyde, and methanol. The organic compounds are oxidized. The reaction rate is high at low pH for formic acid and at high pH for methanol. The reactivities of these compounds on platinized CdS powder at various pHs have good correlation with their photoanodic reactions on a CdS electrode.
Introduction photocatalytic reactions of aqueous so~utionsof organic materials on semicondutor particles have attracted wide attention with regard to solar energy utilization.’-’’ Among the photo(1) (2) (3) (4)
Kraeutler, B.; Bard, A. J. J. Am. Chem. SOC.1978, 100, 2239. Izumi, I.; Fan, F. F.; Bard, A. J. J. Phys. Chem. 1981, 85, 218. Sakata, T.; Kawai, T.; Hashimoto, K. Chem. Phys. Lett. 1982,88,50. Kawai, T.; Sakata, T. J . Chem. Soc., Chem. Commun. 1979, 1047.
0022-3654/84/2088-0248$01.50/0
catalysts, platinized titanium dioxide (Pt/TiO,) shows excellent activity and has been studied extensively.’-* It can oxidize even (5) Kawai, T.; Sakata, T. Chem. Lett. 1981, 81. (6) Sakata, T.; Kawai, T. J. Synth. Org. Chem. Jpn. 1981, 39, 589. (7) Sato, S.;White, J. M. Chem. Phys. Lett. 1980, 72, 83. (8) Sato, S.; White, J. M. J. Phys. Chem. 1981, 85, 336. (9) Yanagida, S . ; Azuma, T.; Sakurai, H. Chem. Lett. 1982, 1069. (10) Fox, M. A.; Chen, C.-C. J. Am. Chem. SOC.1981, 103, 6757. (1 1) Fujihira, M.; Satoh, Y.; Osa, T. J. Electroanal. Chem. 1981,126, 277.
0 1984 American Chemical Society
