9638
J. Phys. Chem. 1996, 100, 9638-9648
Molecular Orbital Studies of Crystalline Nitroanilines La´ szlo´ Turi† and J. J. Dannenberg* Department of Chemistry, City UniVersity of New YorksHunter College and The Graduate School, 695 Park AVenue, New York, New York 10021 ReceiVed: January 3, 1996; In Final Form: March 20, 1996X
The intermolecular interactions leading to crystals of m- and p-nitroaniline have been studied to better understand the interactions that lead to significantly differing crystal structures. Molecular orbital calculations using three semiempirical (AM1, PM3, and SAM1) Hamiltonians are presented for many aggregates containing up to 10 molecules of both m- and p-nitroaniline. The differences in the capacities for hydrogen bonding, both N-H‚‚‚O and C-H‚‚‚O, caused by the differing geometries of the monomeric units dictate the different crystal structures. p-Nitroaniline forms H-bonded chains with three-centered H-bonds that allow identical H-bonding on each side to adjacent chains. Thus, they form layers, which then stack (head-to-tail) to form centrosymmetric microcrystals. m-Nitroaniline, on the other hand, forms chains which can form much stronger H-bonds on one side than on the other. Thus, these chains combine in pairs to form “strands” comprised of two chains. These chains then stack in a head-to-head manner. The resulting “stacks” of strands then combine through C-H‚‚‚O H-bonds to others that are approximately perpendicular (104°). While the head-to-head orientation of the stacks is somewhat unfavorable, it favors the combination of the stacks by properly positioning the C-H‚‚‚O interactions. Thus, a repulsive interaction is tolerated to allow for a more attractive one.
The manner in which molecules nucleate and crystallize remains a very important problem in solid state organic chemistry. Crystal engineering, the ability to predict (and eventually direct) the structures of crystalline materials, can have important implications for the development of new materials. Theoretical study of various sized aggregates of molecules allows us to better understand the kinds and magnitudes of the intermolecular interactions that bind the growing aggregates and (eventually) crystals. Understanding these interactions and their cooperative effects can also have important consequences for studies of molecular recognition. We have previously studied aggregates of acetic acid1 and 1,3-cyclohexanedione2 using molecular orbital (MO) theory. In this paper we turn our attention to the meta and para isomers of nitroaniline, for which we had previously studied H-bonding dimers.3 Etter et al. investigated the crystal structures of various nitroanilines and related compounds.4 They found that the primary structure determinants of these crystals are intermolecular hydrogen bonds. The crystals of these isomers of nitroaniline are particularly interesting as potential nonlinear optical materials.5 Of the two isomeric molecules, p-nitroaniline, with its effective push/pull conjugated interaction between the two substituents, might be expected to have the greater second-order hyperpolarizability. However, while crystals of the meta isomer show frequency doubling, those of para do not. The simple reason for this observation is that the para isomer (unlike the meta) crystallizes in a centrosymmetric manner. All centrosymmetric materials have no even-ordered hyperpolarizabilities due to symmetrydictated cancellation effects.6 Thus, the nitroanilines illustrate the importance of designing properly constructed materials (crystals, in this case) as well as molecules. In this paper, we present semiempirical MO calculations on various sized aggregates of m- and p-nitroaniline. In previous work we have used both ab initio and semiempirical calcula† Present address: Eo ¨ tvo¨s Lora´nd University, Physical Chemistry Department, Budapest 112, P.O. Box 32, Hungary H-1518. X Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(96)00034-2 CCC: $12.00
tions.1,2 However, the size of the molecules and the aggregates studied put proper ab initio calculations beyond the realm of what is today practical. Furthermore, we have learned from our previous comparisons of ab initio and MO semiempirical calculations what are the likely errors in the latter. The one small complex (CH3NO2/NH3) studied using ab initio calculations gave a surprising result that indicated that it is not prototypical. Those results are described elsewhere.7 Methods We performed semiempirical AM1,8 SAM1,9 and PM310 calculations on various aggregates of p- and m-nitroaniline. The optimization procedure was similar to that employed for 1,3diones and acetic acid.1,2 The aggregates were completely optimized with the geometric constraints used in a previous work:2 (a) the individual molecules were kept superimposable, and (b) the appropriate translational vectors characterizing the ordered crystal structure were kept parallel. In addition to these two constraints, all 10 heavy atoms (except the amino nitrogen for m-nitroaniline which was allowed to move out of the aromatic plane) and the aromatic hydrogens of the nitroaniline molecule were constrained in a common plane. Due to the size of the nitroaniline molecules, the largest aggregate contained only 10 individual monomers (still enough to model the threedimensional crystal structures). Results and Discussion p-Nitroaniline. The four orientations that we considered for the interaction of two p-nitroaniline molecules are shown in Figure 1. Previous work indicated that the H-bonding pattern at the AM1 global minimum corresponds to I, characterized by two equivalent N-O‚‚‚H interactions between each amino hydrogen of one molecule and a nitro oxygen of the other. II has an almost symmetric three-centered H-bond between an amino hydrogen and two nitro oxygens. This pattern is different from both the orientation found in the crystal structure (III and Figure 2) and the most stable arrangement (I). Nevertheless, II is a local minimum on the AM1 potential surface.3 III (not © 1996 American Chemical Society
MO Studies of Crystalline Nitroanilines
J. Phys. Chem., Vol. 100, No. 23, 1996 9639
Figure 4. p-Nitroaniline 2/2/2 microcrystal (AM1-optimized structure).
TABLE 1: Incremental Hydrogen-Bonding Energies (kcal/mol) for p-Nitroaniline Chainsa aggregateb dimer trimer tetramer pentamer hexamer extrapolated
Figure 1. Four possible H-bonding orientations (I-IV) of p-nitroaniline dimer.
Figure 2. H-bonding patterns in p-nitroaniline chains.
Figure 3. Schematic illustration of the layer structure of p-nitroaniline chains. Note the numbering of the atoms and the unit cell parameters.
a local minimum), which corresponds to the crystal structure, has a rather asymmetric, three-centered H-bond with an additional C-H‚‚‚O interaction between a nitro oxygen and an aromatic proton meta to the nitro group. Dimer IV is the least stable of the four dimers, nevertheless important for determining the two-dimensional layer structure (Figure 3). We shall consider the aggregation of p-nitroaniline in all three directions. The first direction that we consider contains the strongest H-bonding interactions between the nitro and the amino groups of two p-nitroaniline molecules (Figure 2). The H-bonded chains form two-dimensional layers involving ad-
AM1
PM3c
SAM1
-5.81 (-6.84) -6.75 (-7.88) -7.06 (-8.18) -7.16 (-8.30) -7.23 (-8.33) -7.29 (-8.34)
-2.97 (-3.01) -2.69 (-2.67) -3.45 (-3.15) -3.40 (-3.60) -3.56 (-3.35) -3.85
-4.11 (-4.61) -5.14 (-4.80) -5.45 (-5.57) -5.59 (-5.43) -5.66 (-5.72) -5.72 (-5.75)
a Heats of formation of the monomer: 21.55 (AM1), 10.69 (PM3), and 11.83 kcal/mol (SAM1). b Numbers in parentheses correspond to H-bonding chains with two equivalent N-H‚‚‚O H-bonds (I). c No PM3 extrapolation for chains I, due to noncooperative trends.
ditional N-H‚‚‚O interactions (Figure 3). The three-dimensional crystal structure is formed from stacked layers with opposite (head-to-tail, or ht) directionality of the neighboring layers (Figure 4). The unit cell contains four nitroaniline molecules. The cell parameters a and c translate every second layer into each other. The angle between these two vectors, β, is 91.45°.11 Figure 3 illustrates the relation between the other two parameters, b and d. The diagonal (d) of the parallelogram determined by a and c superimposes every second molecule in the first H-bonded direction defined above. The second H-bonding direction (to form layers) corresponds to b (perpendicular to d). We define an aggregate as a microcrystal comprised of chains of linearly H-bonded molecules, which interact to form layers, which stack to form the microcrystals. We use the notation (L/C/M) for the microcrystals, where L, C, and M denote the number of layers, chains, and monomers in each of the three main directions.12 The Hydrogen Bonded Network: Chains and Layers. Figure 2 illustrates the geometries of the H-bonded chains of the crystal structure, while Tables 1 and 2 collect the energetic and geometric data. All three methods predict two distinct minima. At the global minimum the H-bonding orientation of the chains resembles the H-bonded pattern of I, while the other resembles that of II (Figure 1). The only exception involves the dimer structure. Using PM3, II is not a minimum but collapses to I (Figure 1). We begin by considering the chains containing the motif, II, closest to the observed crystal structure:
En ) E∞ - a(1 - e-b(n-1))
(1)
All three methods indicate cooperativity (Table 1). The strongest H-bonds are predicted by AM1 and the weakest by PM3. PM3 also shows cooperativity after three molecules are aggregated. The H-bonding strength in an infinite chain is estimated by fitting an exponential function for the incremental
9640 J. Phys. Chem., Vol. 100, No. 23, 1996
Turi and Dannenberg
TABLE 2: Calculated and Experimental Geometries for p-Nitroaniline Chainsa aggregates
N-O
N2-O1
N2-C4
C1-N1
N1-H6
N1-H5
monomer dimer trimer
1.206 1.206 1.207
1.204 1.206 1.207
1.474 1.471 1.469
1.370 1.366 1.364
0.990 0.989 0.990
0.989 0.987 0.987
tetramer
1.207
1.207
1.468
1.363
0.991
0.987
pentamer
1.208
1.208
1.468
1.363
0.991
0.988
hexamer
1.208
1.208
1.466
1.362
0.992
0.988
monomer dimer trimer
1.216 1.218 1.219
1.216 1.218 1.219
1.490 1.483 1.481
1.416 1.412 1.410
0.994 0.994 0.994
0.994 0.994 0.994
tetramer
1.219
1.219
1.479
1.409
0.994
0.994
pentamer
1.219
1.220
1.478
1.408
0.994
0.994
hexamer
1.220
1.220
1.477
1.407
0.994
0.994
monomer dimer trimer
1.231 1.234 1.235
1.231 1.231 1.231
1.484 1.480 1.478
1.379 1.371 1.369
0.991 0.994 0.996
0.991 0.989 0.990
tetramer
1.235
1.231
1.477
1.368
0.997
0.990
pentamer
1.236
1.231
1.476
1.367
0.998
0.990
hexamer
1.236
1.231
1.476
1.366
0.999
0.990
exptl11
1.247
1.246
1.460
1.371
N1‚O2c
N1‚O1c
H6‚O2c
H6‚O1c
Rb
βb
H4‚O1c
AM1 7.9 0.3 3.180 0.3 3.163 3.157 0.1 3.154 3.144 0.1 3.147 3.144 0.3 3.145 3.138
3.257 3.239 3.263 3.247 3.243 3.238 3.250 3.244 3.239
2.271 2.259 2.246 2.247 2.237 2.241 2.235 2.237 2.230
2.341 2.317 2.347 2.328 2.325 2.317 2.331 2.324 2.320
139.8 140.5 139.6 140.2 140.1 140.4 140.0 140.2 140.2
19.5 20.1 19.3 19.8 19.8 20.1 19.6 19.8 19.8
2.434 2.443 2.424 2.435 2.424 2.434 2.425 2.427 2.420
PM3 27.7 24.6 3.398 22.7 3.578 3.555 22.4 3.556 3.527 22.0 3.546 3.528 21.9 3.541 3.508
3.466 3.707 3.831 3.785 3.651 3.734 3.698 3.760 3.662
3.267 2.655 2.621 2.610 2.695 2.611 2.650 2.599 2.661
2.762 2.769 2.887 2.865 2.699 2.807 2.737 2.837 2.708
112.4 132.4 130.5 128.9 137.2 130.8 135.5 129.7 136.8
74.0 18.6 17.1 15.3 28.5 16.9 23.9 15.9 27.1
4.295 2.750 2.868 2.729 3.243 2.724 3.078 2.727 3.190
SAM1 11.6 0.0 2.898 0.0 2.875 2.890 0.0 2.879 2.868 0.0 2.868 2.875 0.0 2.872 2.863
4.059 4.015 4.043 4.012 4.005 3.990 4.006 3.992 3.986
1.946 1.922 1.933 1.922 1.910 1.910 1.915 1.912 1.903
3.125 3.082 3.112 3.082 3.075 3.061 3.078 3.064 3.059
135.6 135.9 135.3 135.5 135.4 135.6 135.2 135.3 135.3
13.6 13.7 13.1 13.2 13.1 13.2 12.9 13.0 12.9
3.114 3.066 3.075 3.041 3.029 3.015 3.019 3.005 2.995
120.6
12.0
τb
3.07
3.76
d
16.187 16.180 16.179 16.169
16.586 16.728 16.701 16.720
16.556 16.518 16.501 16.483 15.211
Distances in angstroms, angles in degrees. b R, C1-N1‚‚‚O2B angle; β, H6-N1‚‚‚O2B angle; τ, H6-N1-C1-C6 torsional angle. c H-bond is between molecules A and B (Figure 3). a
part of the H-bonding interaction. In eq 1, the incremental interaction energy of the nth monomer with the H-bonding system, En, is expressed in terms of the H-bonding energy for adding a monomer to an infinite chain, E∞. The values for a, b, and En are obtained by fitting calculated values for several En’s. Since E1 ) E∞ - a, a represents the cooperative (including, but not restricted to, the nonadditive) part of the interaction for an infinite chain. According to the extrapolated values the cooperativity corresponds to 25% or 39% of the dimer interactions for the AM1 and SAM1 methods and 36% for PM3 compared to the half of the total trimeric interaction (see the different dimer interactions in PM3). The geometries predicted by three different methods differ only in slight details (Table 2). Of the four possible H-bonding patterns (Figure 1) in the previous study,3 AM1 and PM3 prefer an almost symmetric three-centered H-bond between an amino hydrogen and two nitro oxygens, similar to that in II. SAM1 gives a very nonsymmetric three-centered H-bond with shorter N1‚‚‚O2 and longer N1‚‚‚O1 (see numbering of Figure 3) distances between the H-bonded nitro and amino groups than those reported experimentally.11 The intramolecular geometric parameters provide additional information on the structural changes upon aggregation (Table 2). All methods predict, for example, the C4-N2 distance to be within 0.02 Å to the experimental value. The other C-N distance involving the amino group (C1-N1) is very well reproduced in AM1 and SAM1, while PM3 overestimates it significantly. Generally all three methods reproduce the intramolecular parameters reasonably well. Although AM1 and PM3 predict N-O bond lengths that are too short, they seem
to be converging toward the experimental value. An interesting point involves the nonplanarity of the amino group. Similar to a previous work3 for dimer formation at the AM1 level, aggregation results in complete planarization of the amino group at both AM1 and SAM1 levels. Although the H-bonded chain formation slightly decreases the nonplanarity in PM3, the 21.9° out-of-plane torsional angle (or 0.34 Å deviation from the plane of the aromatic ring) of the H-bonded hydrogen in the hexamer remains significant. Despite the fact that hydrogen atom positions determined experimentally by X-ray diffraction are not very reliable, the observed 0.2 Å deviation from the plane of the aromatic ring also suggests some nonplanarity. The intermolecular geometries are also worth attention. Interestingly, while AM1 reproduces the shorter O‚‚‚N contact (N1‚‚‚O2) better, PM3 gives a better estimate for the longer one (N1‚‚‚O1). As mentioned earlier, SAM1 poorly predicts both. Increasing aggregation decreases the N‚‚‚O distances, consistent with cooperativity. The unit cell dimension, d, is overestimated by all three methods, primarily because H-bonding patterns of the optimized chains differ from that of the crystal. While AM1 (closest to experiment) and SAM1 distances converge toward the experimental value upon aggregation, those for PM3 oscillate. The H-bonding energies of the most stable H-bonding chains (I), are collected in Table 1 in parentheses. The AM1 hydrogenbonding energies for the chains corresponding to I are about 1 kcal/mol stronger than for the chains of II. For the other two methods the difference is much smaller. The optimized intermolecular distances of the H-bonded chains, which significantly differ from the experimental values,
MO Studies of Crystalline Nitroanilines
J. Phys. Chem., Vol. 100, No. 23, 1996 9641
TABLE 3: H-Bonding Enthalpies (kcal/mol) of p-Nitroaniline Layers and 2/2/2 Nonplanar and Planar Microcrystalsa AM1 aggregate 2/2 2/3 2/4 2/5 3/2 3/3 2+1b 3+2 3+2+1 4+3+2 4+3+2+1 2/2/2pc 2/2/2npc
total -10.17 (-14.06) -23.04 (-30.54) -37.55 (-48.06) -52.40 (-66.02) -14.73 -34.35 -6.82 -11.57 -20.29 -31.77 -42.13 -31.77 -30.98
PM3 incremental
-12.87 (-16.48) -14.51 (-17.52) -14.85 (-17.96) -19.62
-11.43 -10.64
total
SAM1 incremental
-9.29 (-9.63) -18.42 (-18.56) -28.43 (-28.26) -38.63 (-38.80) -15.89 -31.09 -5.73 -12.22 -17.23 -30.05 -35.72 -21.52 -26.02
-9.13 (-8.93) -10.01 (-9.70) -10.20 (-10.54) -15.20
-2.94 -7.44
total -6.77 (-6.76) -17.52 (-19.94) -29.33 (-27.02) -41.78 (-43.02) -9.42 -25.53 -5.06 -7.93 -15.05 -23.68 -31.90 -33.70 -33.10
incremental
-10.75 (-13.18) -11.81 (-7.08) -12.45 (-16.00) -16.09
-20.16 -19.56
a Numbers in parentheses correspond to interaction energies for the layers constructed from chains I. b See text for explanation. c Total enthalpies and enthalpies between layers are listed for 2/2/2 planar (p) and nonplanar (np) aggregates.
and the preference for chains with interaction I indicate that aggregation in one direction is insufficient for determining the interactions within a crystalline chain. Thus, interactions between neighboring chains should have an important role in determining the overall structure. Figures 2 and 3 show that the amino hydrogens which do not participate in H-bonding within the chains can form H-bonds to nitro oxygens of the adjacent chains as in IV. The absence of this interaction in one-dimensional chains explains why individual chains favor I. The layer structure of three tetramer chains (a 1/3/4 aggregate) is depicted in Figure 3. In this structure, a nitro oxygen (O2) participates in a strong N-H‚‚‚O interaction with an amino hydrogen (H6) (see molecules A and B in Figure 3). The other oxygen (O1) forms two intrachain H-bonds, one to the same amino hydrogen as does O2 (H6) and another to an aromatic (H4) hydrogen, plus an interchain H-bond to an amino hydrogen, as in IV (see Figure 1 and molecules A and C in Figure 3). The energetic and geometrical data for the optimized layer structures are collected in Tables 3 and 4. Even in the smallest two-dimensional aggregate considered, comprised of two interacting dimers (1/2/2), the two-dimensional H-bonding network is apparent. All three MO methods predict layer structures that differ considerably from those of the individually optimized chains and also from motif II. The interchain N-H‚‚‚O interaction favors formation of a two-dimensional H-bonding network that is more characteristic of the crystal structure (III and Figure 3). Table 3 indicates that adding two units of p-nitroaniline to the end of a 1/2/M aggregate results in increasing incremental H-bonding energies. These incremental values for formation of 1/2/3, 1/2/4, and 1/2/5 aggregates are -12.87, -14.51, and -14.85 kcal/mol for AM1, -10.75, -11.81, and -12.45 kcal/mol for SAM1, and -9.13, -10.01, and -10.20 kcal/mol for PM3. As it can be seen from Figure 3, addition of two monomers to the end of a 1/2/M aggregate creates two H-bonding intrachain interactions and one N-H‚‚‚O H-bond between the chains. As the comparable incremental H-bonding energies increase as the aggregate grows, they appear to be cooperative. Table 4, collects the geometrical data for the layers. The agreement between the experimentally observed11 and the calculated geometries is excellent, particularly for AM1 and SAM1 nonbonding distances (O‚‚‚N). Both AM1 and SAM1 accurately predict two of the three H-bonding N‚‚‚O distances,
while PM3 predicts all three O‚‚‚N distances to be too long by a consistent 0.4-0.6 Å. This observation indicates that PM3 underestimates the strength of the N-H‚‚‚O interactions (see also Table 1). The unit cell parameters are quite sensitive to small geometric errors in the H-bonding geometries. For example, AM1 predicts a short d, and long b mainly because of deviations from the observed nonbonding angles R, and β, which characterize the directionality of the H-bonds. If the minor inconsistencies in geometries are put aside, all three methods model the H-bonded network rather well. The N‚‚‚O and H‚‚‚O H-bonding distances generally decrease with increasing M in 1/2/M aggregates consistent with two-dimensional cooperative effects. Table 3 also contains interaction energies for 1/C/M aggregates formed from chains with the H-bonding motif, I (in parentheses). The data indicate that PM3 and SAM1 predict similar interaction energies for layers with the I and III motifs. AM1 predicts layers of I to be preferred enthalpically. Careful inspection of the 1/C/M aggregates with motif III (Figure 3) reveals that (except for the nitro groups at the end of a chain) both nitro oxygens are completely H-bonded only in every second molecule within the chains at the upper or lower edges of the two-dimensional aggregate. The unsatistified hydrogenbonding potential of those molecules not participating in all of their possible H-bonds favors the growth of the aggregates containing motif III over those of I. The uncoordinated H-bonding sites create large end effects, which explains why calculations on small 1/C/M layers cannot fully account for the energetic preference of III. We need to consider complexes with completely H-bonded nitro groups, like those shown in Figure 5. In these triangular aggregates all H-bonding sites of the nitro groups are H-bonded except those at the end of the chains. Tables 3 and 4 contain the data for three of these, denoted by 2+1, 3+2+1 and 4+3+2+1. Removal of a molecule from the top of the triangle leads to complexes such as 3+2 and 4+3+2. The total interaction energy of a 2+1 aggregate only approximately corresponds to the interaction energy of a fully H-bonded nitro group due to a presumably slightly repulsive interaction between the two molecules that do not H-bond (at the bottom of the triangle). The interaction energies for adding a monomer to a 3+2 aggregate are -8.72, -5.01, and -7.12 kcal/mol for AM1, PM3, and SAM1, respectively. These values are all larger than the extrapolated incremental H-bonding energies for chains of I. The differences
9642 J. Phys. Chem., Vol. 100, No. 23, 1996
Turi and Dannenberg
TABLE 4: Calculated and Experimental Geometries of p-Nitroaniline Layers and 2/2/2 Nonplanar and Planar Microcrystalsa aggregates N2-O2 N2-O1 N2-C4 C1-N1 2/2 2/3
1.205 1.207
1.205 1.204
1.472 1.472
1.368 1.366
2/4
1.207
1.205
1.470
1.365
2/5
1.208
1.205
1.469
1.364
3/2 3/3
1.206 1.207
1.204 1.204
1.475 1.472
1.373 1.366
2+1 3+2+1
1.206 1.206
1.204 1.205
1.474 1.473
1.368 1.366
4+3+2+1 1.206
1.205
1.471
1.366
2/2/2p 2/2/2np
1.207 1.207
1.205 1.205
1.471 1.471
1.367 1.365
exptl11
1.247
1.246
1.460
1.371
2/2 2/3
1.219 1.220
1.216 1.217
1.485 1.482
2/4
1.220
1.218
1.480
2/5
1.220
1.218
1.479
3/2 3/3
1.219 1.220
1.216 1.217
1.485 1.482
2+1 3+2+1
1.218 1.219
1.217 1.217
1.485 1.483
4+3+2+1 1.219
1.218
1.481
2/2/2p 2/2/2np
1.220 1.220
1.218 1.218
exptl11
1.247
1.246
N1‚O2c N1‚O1c H6‚O2c H6‚O1c
5.0 3.091 0.0 3.158 3.164 0.1 3.147 3.155 0.1 3.143 3.147 10.3 3.123 0.1 3.176 3.176 3.6 3.377 1.3 3.186 3.171 0.5 3.178 3.166 7.8 3.146 1.3 3.145 3.07
3.804 4.349 4.356 4.291 4.391 4.339 4.351 4.098 4.394 4.372 4.827 4.416 4.377 4.419 4.375 4.348 4.327
1.481 1.480 1.460
1.371
3.76
1.233 1.234
1.231 1.231
1.480 1.478
1.373 1.370
2/4
1.235
1.232
1.477
1.369
2/5
1.236
1.232
1.476
1.368
3/2 3/3
1.233 1.234
1.231 1.231
1.481 1.479
1.374 1.371
2+1 3+2+1
1.233 1.234
1.231 1.231
1.481 1.480
1.373 1.371
4+3+2+1 1.234
1.231
1.479
1.370
2/2/2p 2/2/2np
1.234 1.234
1.233 1.233
1.477 1.477
1.371 1.369
exptl11
1.247
1.246
1.460
1.371
0.0 3.005 0.0 2.942 2.971 0.0 2.946 2.929 0.0 2.921 2.936 0.0 3.039 0.0 2.962 3.001 0.0 2.944 0.0 2.988 2.987 0.0 2.978 2.979 5.0 2.928 1.5 2.928 3.07
R1b 125.9 110.1 110.1 112.2 108.5 110.4 110.1 116.7 108.9 109.8 97.8 108.4 109.6 108.4 109.8 109.9 110.5
β1b H4‚O1c 17.6 9.9 10.0 7.8 11.5 9.7 10.0 18.6 11.1 10.2 22.2 11.6 10.5 11.6 10.2 11.9 10.0
2.401 2.369 2.374 2.375 2.363 2.368 2.370 2.355 2.377 2.382 2.537 2.393 2.385 2.395 2.391 2.362 2.366
120.6 12
4.334 4.409 4.428 4.391 4.446 4.410 4.427 4.463 4.470 4.467 5.243 4.566 4.534 4.561 4.498 4.329 4.269
3.07
AM1 2.168 2.980 2.190 3.607 2.196 3.613 2.171 3.532 2.194 3.660 2.172 3.593 2.178 3.607 2.206 3.331 2.213 3.660 2.209 3.631 2.491 4.172 2.226 3.685 2.206 3.637 2.218 3.686 2.199 3.632 2.185 3.609 2.177 3.581
3.76
1.414 24.7 3.705 1.412 23.6 3.628 3.641 1.410 23.2 3.620 3.602 1.409 22.9 3.594 3.600 1.415 25.3 3.796 1.412 24.2 3.680 3.692 1.413 24.9 3.662 1.412 25.2 3.737 3.700 1.411 25.0 3.717 3.687 1.407 21.2 3.674 1.412 23.4 3.605
2/2 2/3
PM3 2.736 3.495 2.641 3.575 2.650 3.588 2.632 3.557 2.608 3.610 2.607 3.579 2.607 3.587 2.803 3.643 2.695 3.649 2.704 3.638 2.730 4.444 2.756 3.763 2.714 3.698 2.736 3.760 2.699 3.679 2.755 3.536 2.647 3.431
109.3 114.6 114.2 115.0 112.9 114.5 114.0 111.0 112.9 113.2 96.7 110.5 111.4 110.6 112.0 117.8 118.6
11.0 6.2 4.1 5.6 1.6 6.0 2.5 2.5 6.8 5.8 17.6 8.2 6.6 8.1 5.8 19.3 13.3
3.847 3.876 3.898 3.880 3.879 3.878 3.891 3.829 3.861 3.886 4.101 3.905 3.908 3.915 3.901 3.735 3.732 3.76
127.9 129.2 129.3 129.3 128.8 129.3 129.3 126.8 128.1 128.3 127.7 126.5 126.4 126.5 127.0 123.7 124.3
6.1 7.3 7.3 7.3 6.8 7.3 7.3 5.0 6.2 6.4 6.1 4.8 4.7 4.8 5.3 4.9 2.8
120.6 12
N1‚O1d H5‚O1d
3.224 14.888 3.208 3.193 14.895 3.208 3.166 14.882 3.180 3.171 3.203 14.844 3.188 3.189 3.047 14.835 3.148 3.146 14.839 3.143 3.151 3.198 3.214
2.304 2.298 2.280 2.278 2.275 2.265 2.257 2.291 2.280 2.269 2.407 2.246 2.225 2.238 2.227 2.282 2.286
15.211 3.14 2.670 2.670 2.710 2.664 2.722 2.662 2.716 2.668 2.673 2.698 3.339 2.689 2.690 2.686 2.703 2.616 2.621
120.6 12 SAM1 2.020 3.007 1.958 3.017 1.988 3.037 1.961 3.019 1.943 3.023 1.936 3.016 1.950 3.028 2.052 3.004 1.976 3.016 2.015 3.036 1.961 3.225 1.999 3.070 1.999 3.074 1.988 3.078 1.991 3.060 1.938 2.954 1.935 2.946
d
3.610 15.727 3.510 3.468 15.678 3.469 3.470 15.705 3.455 3.459 3.486 15.653 3.458 3.438 3.390 15.511 3.383 3.370 15.535 3.374 3.388 3.460 3.538
2.776 2.758 2.684 2.696 2.678 2.691 2.661 2.716 2.715 2.671 2.699 2.653 2.596 2.642 2.606 2.793 2.827
15.211 3.14 2.440 2.542 2.572 2.548 2.528 2.552 2.566 2.363 2.467 2.507 2.785 2.451 2.450 2.464 2.471 2.101 2.127
3.851 15.989 3.887 3.710 15.946 3.765 3.745 15.968 3.797 3.700 3.884 15.902 3.869 3.746 4.189 15.795 3.797 3.651 15.748 3.773 3.662 3.842 3.863 15.211 3.14
2.940 2.982 2.772 2.843 2.822 2.881 2.767 2.981 2.965 2.818 3.364 2.897 2.721 2.871 2.730 2.943 2.955
R2b
β2b
b
126.6 139.4 139.1 136.9 141.7 138.9 139.2 131.0 139.7 138.3 162.1 140.4 138.0 140.1 137.8 136.8 136.7
18.0 19.2 18.8 16.6 21.4 18.5 18.8 19.2 19.4 17.9 42.1 20.1 17.7 19.8 17.4 18.5 16.7
6.554 7.053 7.025 7.026 6.879 7.089 6.910 7.060 7.064 7.107 7.093
146.1 29
6.07
139.8 148.2 145.3 146.4 144.3 147.3 144.0 145.0 148.3 146.3 137.5 147.7 144.8 147.7 144.2 153.2 151.0
6.689 6.688
28.4 35.2 32.6 33.5 31.9 34.2 31.4 33.8 35.9 33.9 39.6 36.7 33.3 36.6 32.6 41.4 38.4
6.680 6.677 6.695 6.692 6.690 6.685 6.683 6.692 6.685
146.1 29
6.07
141.2 142.0 137.3 139.7 139.5 140.5 138.1 142.2 142.1 138.8 151.1 142.7 138.5 142.4 138.4 141.8 141.8
6.831 6.805
19.9 20.7 16.0 18.4 18.2 19.3 16.8 20.8 20.8 17.5 29.6 21.3 17.1 21.0 17.0 21.5 30.3
146.1 29
6.772 6.768 6.856 6.817 6.869 6.808 6.799 6.866 6.866 6.07
Distances in angstroms, angles in degrees. R1, C1-N1‚‚‚O2 angle; β1, H6-N1‚‚‚O2 angle; R2, C1-N1‚‚‚O1 angle; β2, H5-N1‚‚‚O1 angle. H-bond is between molecules A and B (Figure 3). d H-bond is between molecules A and C (Figure 3). a
c
τb
b
B
are still greater for adding a monomer to the 4+3+2 aggregate to form 4+3+2+1. Here the interaction energies are -10.36, -5.67, and -8.22 kcal/mol for AM1, PM3, and SAM1, respectively. Let us compare the average stabilization of individual molecules within layers of I and III. For I, we approximate the stabilization as the sum of (a) the extrapolated incremental H-bonding energy of chain I and (b) an estimated stabilization between the chains. The extrapolated incremental energies (Table 1) for chain I are -8.3, -3.6, and -5.8 kcal/mol for
B
C
C
AM1, PM3, and SAM1, respectively (for PM3 where the extrapolation failed, we used the largest incremental energy). We estimate the interchain interactions as -1.5, -3.0, and -1.5 kcal/mol for AM1, PM3, and SAM1 from the interchain stabilization of 1/2/M aggregates of I (Table 4, in parentheses) divided by M. Thus, the interaction energies per molecule of an infinite two-dimensional layer with interaction I become -9.9, -6.6, and -7.3 kcal/mol for the three MO methods. Without taking into account further cooperative effects or other weaker interactions between the chains (for example, repulsions
MO Studies of Crystalline Nitroanilines
Figure 5. 2+1, 3+2+1, and 4+3+2+1 aggregates of p-nitroaniline.
originating from the proximity of aromatic hydrogens or neighboring chains), the last stabilization energies for the 4+3+2+1 aggregate (H-bonding pattern III) in AM1 and SAM1 (-10.4 and -8.2 kcal/mol) are greater than the stabilization estimated for infinite layers of I. Thus, both AM1 and SAM1 predict the two-dimensional H-bonding network of III within the chains, combined with IV, between the chains, to be enthalpically preferred. PM3 reverses the order of the stabilities of I and III. However, the PM3 values (-6.6 kcal/mol for I, -5.7 kcal/mol for III) might be appropriate if inclusion of cooperativity reverses this energetic order. The geometries of the aggregates 2+1, 3+2+1, and 4+3+2+1 collected in Table 4 parallel the trends observed for 1/C/M aggregates. Only small changes in the unit cell parameters occur when considering the fully H-bonded nitro groups. Aggregation in the Third Direction. The crystal growth in the third direction involves stacking of the infinite twodimensional layers (Figure 4). The layers are bound by weak interactions. The large number of molecules in meaningful three-dimensional microcrystals limits the extent of the calculations. A 2/2/2 microcrystal is the largest structure that we could readily consider. Tables 3 and 4 contain the results for the microcrystals. The simplest model microcrystal consists of two stacked monomers (2/1/1). All three methods predict the head-to-tail, ht, to be preferred over the head-to-head, hh, orientation of the molecules. In fact, all three methods predict the hh complex
J. Phys. Chem., Vol. 100, No. 23, 1996 9643 to be repulsive. The ht orientation is stabilized by -2.80, -2.36, and -3.70 kcal/mol in AM1, PM3, and SAM1, respectively. The ht dimer is roughly centrosymmetric. This orientation seems to be consistent with optimizing the electrostatic attractions between the electron-rich nitro groups and the relatively positive amino protons. Stepwise stacking of two additional pairs of molecules to the 2/1/1 complex forms the 4/1/1 and 6/1/1 aggregates (four and six stacked molecules, respectively). The repeating unit in this direction also consists of two molecules. New 1-3 pairwise repulsions occur between nitroaniline molecules of every second row (which have the hh orientation with respect to each other). The interaction energies for this step (adding a 2/1/1 to a 2/1/1 forming a 4/1/1 complex) are -0.50 and -0.32 kcal/mol for AM1 and PM3, while no suitable minimum was found in SAM1. The addition of another 2/1/1 aggregate to 4/1/1 lowers the enthalpy by -0.52 and -0.34 kcal/mol (AM1 and PM3), slightly more than in the previous step. The translation vectors connecting every second stacked monomer are related to the unit cell parameter c. The AM1 translations are 9.129 and 9.106 Å for 4/1/1 and 6/1/1, while PM3 predicts 9.305 and 9.306 Å. Despite the simplicity of the model, these values are surprisingly close to the experimental 8.592 Å, indicating that both PM3 and AM1 describe the mostly electrostatic interlayer interactions reasonably well. A somewhat better model for stacking contains a H-bonded dimer with a monomer stacked parallel to one of the molecules of the dimer (1/1/2+1). Consideration of this complex is instructive despite the fact that the H-bonding interactions within the H-bonded single chains (II) differ from those of the crystal (III). As in the 2/1/1 case we conclude that the hh orientation is predicted to be repulsive and not a minimum on the potential surface, while ht is stable by -2.64, -1.89, and -5.88 kcal/ mol by AM1, PM3, and SAM1, respectively. The 2/2/2 microcrystal is a more appropriate model of the crystal structure as it contains all relevant interactions: the H-bonding interactions and other intermolecular forces (Figure 4). This microcrystal consists of two stacked layers of two dimers each. We studied both the ht and hh orientations with and without the constraint that all heavy atoms within a layer be coplanar. While none of the three MO methods could locate a minimum for the hh orientation, all found stable minima for ht microcrystals. These are approximately centrosymmetric. AM1 and SAM1 predict the structures consisting of planar layers to be more stable, while PM3 favored nonplanar layers. The SAM1 stabilization is larger, -20.16 kcal/mol (-5.04 (kcal/ mol)/stacked molecule pair); AM1 and PM3 give smaller interactions, -11.43 kcal/mol (-2.86 (kcal/mol)/stacked molecule pair) and -7.44 kcal/mol (-1.86 (kcal/mol)/stacked molecule pair). One can estimate the average stabilization per molecule within the crystal lattice as the sum of the intralayer stabilization (from 4+3+2+1 aggregate: -10.36, -5.67, and -8.22 kcal/mol in AM1, PM3, and SAM1) plus the interlayer interaction for a molecule pair. This leads to calculated heats of sublimation for crystalline p-nitroaniline of -13.3, -7.6, and -13.2 kcal/mol for AM1, PM3, and SAM1, respectively. While the AM1 and SAM1 values are closer to the experimental value of 26.1 kcal/mol13 than that for PM3, all three values are low. This discrepancy might be due to limited size of the microcrystals studied (too small to have major cooperative interactions) or to calculational problems. The 2/2/2 structure is nearly centrosymmetric. The geometries of the H-bonding aggregates do not significantly differ from those of the individually optimized layers (Table 4). All methods predict d to be longer than in the corresponding 1/2/2
9644 J. Phys. Chem., Vol. 100, No. 23, 1996
Turi and Dannenberg
Figure 8. Interactions between stacked strands of m-nitroaniline in the direction of the unit cell vector b.
Figure 6. H-bonded chains (b) and strands (c) of m-nitroaniline crystals. The calculated structure is shown at the bottom (d). Note the numbering (a) and the unit cell parameter d (c). Figure 9. Approximately perpendicularly stacked (second stacking direction) m-nitroaniline chains.
TABLE 5: Incremental Hydrogen-Bonding Energies (kcal/mol) for m-Nitroaniline Chainsa
Figure 7. A 2/2/2 m-nitroaniline microcrystal illustrating the stacking of the strands.
layer. Thus, the difference between the observed and the calculated unit cell parameters increases. m-Nitroaniline. The crystal structure of m-nitroaniline14 differs significantly from that of p-nitroaniline.11 The H-bonded chains of m-nitroaniline follow H-bonding pattern II in Figure 1 (see also Figure 6). Instead of forming infinite layers, two H-bonded chains form a strand (Figure 6) via stronger interchain H-bonding interactions than in the para isomer. Parallel strands stack with all the nitro groups pointing in the same direction (hh) as illustrated in Figure 7. The stacked strands are superimposable by the translation vectors a and c. The third edge (d) of the right triangle of a and c translates every nitroaniline molecule within the H-bonded chains (see Figures 6 and 8). The resulting stacked structures interact with two other stacks oriented almost perpendicularly (104°) via C-H‚‚‚O H-bonds involving aromatic C-H’s (Figures 8 and 9). These interactions determine the crystal structure. The longest of the
aggregate
AM1
PM3
SAM1
dimer trimer tetramer pentamer hexamer extrapolated
-4.77 -5.42 -5.62 -5.70 -5.74 -5.76
-2.46 -2.89 -3.02 -3.07 -3.10 -3.12
-3.18 -3.81 -4.02 -4.09 -4.14 -4.18
a Heats of formation of the monomer: 24.02 (AM1), 12.55 (PM3), and 14.46 kcal/mol (SAM1).
three unit cell parameters, b, (perpendicular to the plane of a, c, and d) translates the three-dimensional microcrystal. The four types of interactions will be examined separately. The first and second include H-bonding interactions within the H-bonded chains and strands of m-nitroaniline. The notation of these structures is similar to that defined earlier; 1/M will denote single H-bonded chains, while 2/M stands for the H-bonded strands containing two chains from M monomers. L/1/M and L/2/M will be used to denote the stacks of L chains and strands, respectively, for consideration of the first stacking direction. The fourth interaction is the stacking in the b direction: the interactions between L/2/M aggregates that result in microcrystals. Hydrogen-Bonded Chains and Strands. Figure 6 illustrates the hydrogen-bonding orientation both within and between the H-bonded m-nitroaniline chains. Tables 5 and 6 contain the
MO Studies of Crystalline Nitroanilines
J. Phys. Chem., Vol. 100, No. 23, 1996 9645
TABLE 6: Calculated and Experimental Geometries for m-Nitroaniline Chainsa aggregates
N2-O2
N2-O1
N2-C3
C1-N1
N1-H5
N1-H6
τb
N1‚O2c
N1‚O1c
H5‚O2c
H5‚O1c
C6‚O2c
H4‚O2c
d
3.316 3.308 3.306 3.303 3.300
3.227 3.217 3.212 3.208 3.206
2.401 2.392 2.390 2.387 2.383
2.306 2.295 2.289 2.285 2.284
3.334 3.326 3.322 3.319 3.318
2.386 2.375 2.369 2.366 2.364
8.235 8.230 8.228 8.226 8.225
monomer dimer trimer tetramer pentamer hexamer
1.202 1.204 1.204 1.205 1.205 1.205
1.202 1.203 1.204 1.204 1.204 1.204
1.490 1.487 1.486 1.481 1.484 1.484
1.394 1.395 1.389 1.388 1.387 1.387
0.995 0.995 0.995 0.996 0.996 0.996
AM1 0.995 25.4 0.994 22.9 0.994 21.9 0.993 21.2 0.993 20.9 0.993 20.6
monomer dimer trimer tetramer pentamer hexamer
1.215 1.217 1.217 1.218 1.218 1.218
1.216 1.217 1.217 1.218 1.218 1.218
1.499 1.494 1.492 1.495 1.490 1.490
1.427 1.426 1.426 1.425 1.425 1.425
0.995 0.995 0.996 0.996 0.996 0.996
PM3 0.995 30.9 0.995 28.2 0.995 27.3 0.995 26.8 0.995 26.5 0.995 26.3
4.116 4.108 4.096 4.090 4.088
3.883 3.663 3.654 3.648 3.645
3.226 3.218 3.205 3.199 3.196
2.703 2.681 2.672 2.667 2.663
3.706 3.685 3.677 3.672 3.668
2.687 2.665 2.655 2.651 2.648
8.629 8.609 8.603 8.598 8.594
monomer dimer trimer tetramer pentamer hexamer
1.228 1.230 1.231 1.231 1.232 1.232
1.229 1.228 1.228 1.228 1.228 1.228
1.498 1.497 1.497 1.497 1.497 1.497
1.391 1.385 1.382 1.381 1.380 1.379
0.994 0.996 0.997 0.998 0.998 0.998
SAM1 0.994 21.5 0.993 18.7 0.993 17.2 0.992 16.1 0.992 15.3 0.992 14.8
2.964 2.952 2.975 2.941 2.938
3.890 3.861 3.843 3.832 3.825
1.979 1.964 1.955 1.949 1.946
3.196 3.160 3.137 3.125 3.116
4.054 4.027 4.009 4.000 3.994
3.400 3.363 3.339 3.325 3.316
8.656 8.646 8.641 8.638 8.636
exptl13a
1.223
1.222
1.467
1.391
3.459
3.270
a
3.372
8.251
Distances in angstroms, angles in degrees. τ, H5-N1-C1-C6 torsional angle. H-bond is between molecules A and B (Figure 6). b
energetic and geometric information for the appropriate aggregates. One can see from Figure 6 that the H-bonds within the chains resemble pattern II of Figure 1. This structure contains an almost symmetrical three-centered H-bond between an amino hydrogen (H5) and two nitro oxygens (O1 and O2). One of the nitro oxygens (O2) participates in an additional C-H hydrogen bond with an aromatic hydrogen (H2) to the nitro group. The energies for the aggregation in this first direction are collected in Table 5. The trends are similar to those for p-nitroaniline. AM1 predicts the strongest interactions, and PM3, the weakest. The H-bonds are weaker than for p-nitroaniline aggregates (Tables 1, and 5). The cooperativity (using the extrapolated values of Table 5) is also less, 21%, 27%, and 31% (compared to the dimer interactions) in AM1, PM3, and SAM1. The smaller cooperative interactions probably result from the less favorable conjugation between the nitro and amino groups (thereby smaller polarizability) compared to p-nitroaniline. The geometrical data of Table 6 demonstrate that AM1 predicts the H-bonding pattern extremely well, while the PM3 and SAM1 structures seriously deviate from the crystal structure. PM3 predicts a structure similar to III of Figure 1 (containing a rather asymmetric three-centered H-bond between the nitro and the amino group) and overestimates the H-bonding distances. SAM1 optimization results in a structure with only one H-bond (between O2 and H5). It also overestimates the C-H‚‚‚O distances. AM1 correctly estimates the translation vector d, while the other two methods predict d to be too long. The geometrical data also reflect the strong influence of aggregation and cooperativity. The H-bonding distances and translational vectors become shorter with increasing aggregate size, suggestive of cooperative interactions. Tables 7 and 8 present the energetic and geometric data for selected m-nitroaniline strands (2/M aggregates, M ) 2, 3, 4). One of the nitro oxygens, O1, can form additional H-bonds to an adjacent chain. In the crystal structure O1 forms such a bond to an amino group on the adjacent chain as part of an almost symmetric three-centered H-bonding pattern (see the interaction between molecules A and D in Figure 6). An aromatic hydrogen (H1) forms a C-H‚‚‚O H-bond to the nitro group of a molecule of the adjacent chain (interaction between molecules A and C).
c
TABLE 7: H-Bonding Enthalpies (kcal/mol) of m-Nitroaniline 2/M Strands (M ) 2, 3, 4), L/1/M Stacks (L, M ) 2, 3), and a 2/2/2 hh Microcrystal (See Text for Explanation) AM1 aggregate
total
between chains
2/2 2/3 2/4 2/1/2a 2/1/3 2/1/4 3/1/2 3/1/3 2/2/2
-14.08 -28.23 -43.14 -8.03 -17.79 -28.19 -11.67 -25.35 -21.77
-4.54 -7.85 -11.52 1.51 2.59 3.43 2.64 5.22 6.39
PM3
SAM1
total
between chains
total
between chains
-7.68 -14.02 -21.34 -4.51 -9.85 -15.65 -7.09 -14.59
-2.76 -3.32 -4.60 0.41 0.85 1.09 0.29 1.46
-6.43 -14.38 -23.41 -3.78 -9.30 -15.61 -4.68 -11.31
-0.07 -0.40 -1.39 2.58 4.68 6.41 4.86 9.66
a Total enthalpies and enthalpies between layers are listed for L/C/M aggregates.
The sides of the chains which contain the better H-donor and acceptor groups interact to form a strand; the substituents on neighboring chains are directed toward each other. Interestingly, only the nitro groups of one chain of a strand (upper chain on Figure 6) form two three-centered H-bonding interactions (one intrachain, the other interchain). The nitro groups of the other chain (lower chain in Figure 6) participate in only one intrachain three-centered H-bond and one interchain C-H‚‚‚O interaction to the ortho H1 of the first chain. The three methods predict distinctly different interchain H-bonding stabilization (Table 7). AM1 predicts strong interaction (-11.52 kcal for 2/4); PM3 calculates less than half of the AM1 stabilization (-4.60 kcal/ mol for 2/4), while SAM1 barely predicts any attraction (-1.39 kcal/mol for 2/4). Both AM1 and SAM1 results indicate twodimensional cooperativity as the interchain interaction per molecule pair (interchain interaction divided by M for aggregate 2/M) becomes stronger with increasing M. All three methods prefer similar orientations for H-bonded strands, slightly different from the experiment (Figure 6d and Table 8). They favor structures with O1 of a nitro group H-bonding to only one amino hydrogen (H6) on the corresponding molecule of the adjacent chain. Thus, one chain of the strand is shifted by about 2 Å relative to the other in the d direction (Figure 6). In this geometry, each molecule partici-
9646 J. Phys. Chem., Vol. 100, No. 23, 1996
Turi and Dannenberg
TABLE 8: Calculated and Experimental Geometries of m-Nitroaniline Layersa aggregates N2-O2 N2-O1 N2-C3 C1-N1 τb N1-O2c N1‚O1c H5‚O2c H5‚O1c C6‚O2c H4‚O2c 2/2
1.202 1.205 1.487 1.390 23.0 3.251
2/3
1.203 1.205 1.486 1.387 20.9 3.250
2/4
1.203 1.206 1.485 1.385 19.6 3.243
2/2
1.216 1.218 1.494 1.425 28.7 4.035
2/3
1.216 1.218 1.492 1.424 28.1 3.978
2/4
1.216 1.219 1.491 1.424 27.6 4.032
2/2
1.229 1.229 1.498 1.381 14.4 3.115
2/3
1.230 1.229 1.498 1.376
8.2 3.026
2/4
1.230 1.229 1.497 1.373
3.5 3.002
exptl13a
1.223 1.222 1.467 1.391
3.459
d
N1‚O1d H6‚O1d H5‚O1d C2‚O1d H1‚O1d O1‚O1d
AM1 3.241 2.365 2.381 3.380 2.426 8.301 3.156 3.186 3.231 2.353 2.357 3.371 2.414 8.293 3.157 3.170 3.226 2.341 2.347 3.367 2.412 8.289 3.159 3.166
2.169 2.226 2.171 2.208 2.172 2.195
3.669 3.832 3.697 3.811 3.719 3.805
3.847 3.803 3.825 3.807 3.815 3.807
3.110 2.963 3.076 2.974 3.052 2.078
5.115 4.990 5.121 5.015 5.099 5.027
PM3 3.756 3.200 2.885 3.835 2.784 8.836 3.386 3.831 3.772 3.116 2.867 3.833 2.790 8.834 3.451 3.584 3.713 3.179 2.810 3.779 2.721 8.783 3.483 3.588
2.658 2.942 2.636 2.678 2.620 2.654
3.270 4.886 3.492 4.248 3.586 4.206
4.989 3.808 4.571 4.093 4.587 4.186
4.617 2.785 4.151 3.179 4.108 3.296
6.896 4.380 6.251 5.067 6.209 5.222
SAM1 4.020 2.140 3.310 4.183 3.477 8.860 3.049 3.285 3.931 2.042 3.215 4.096 3.400 8.768 3.071 3.174 3.902 2.013 3.181 4.068 3.373 8.741 3.074 3.146
2.068 2.352 2.080 2.217 2.086 2.180
3.506 3.997 3.651 3.873 3.690 3.841
4.019 3.458 3.834 3.541 3.767 3.579
3.346 2.574 3.067 2.676 2.793 2.718
5.406 4.416 5.133 4.615 5.025 4.686
3.270
3.372
8.251 4.539 3.336
3.393 5.355
3.337 7.306
a Distances in angstroms, angles in degrees. b τ, H -N -C -C torsional angle. c H-bond is between molecules A and B (Figure 6). d H-bond 5 1 1 6 is between molecules A and C for the first number and between molecules D and A for the second (Figure 6).
TABLE 9: Calculated and Experimental Geometries of m-Nitroaniline L/C/M Stacked Layersa N2-O2
N2-O1
N2-C3
C1-N1
τb
N1‚O2c
N1‚O1c
H5‚O2c
H5‚O1c
C6‚O2c
H4‚O2c
d
a
c
2/1/2 2/1/3 2/1/4 3/1/2 3/1/3 2/2/2
1.203 1.204 1.205 1.203 1.204 1.202
1.203 1.204 1.204 1.203 1.204 1.204
1.488 1.487 1.486 1.488 1.487 1.488
1.392 1.391 1.390 1.394 1.392 1.391
22.3 22.0 21.8 22.9 22.4 24.1
3.308 3.295 3.288 3.299 3.288 3.250
AM1 3.264 3.251 3.243 3.278 3.266 3.311
2.431 2.371 2.363 2.378 2.362 2.366
2.363 2.345 2.335 2.387 2.367 2.475
3.386 3.371 3.365 3.403 3.389 3.459
2.431 2.420 2.416 2.449 2.439 2.520
8.301 8.282 8.273 8.319 8.300 8.368
6.400 6.043 5.888 6.409 6.064 6.367
5.286 5.663 5.812 6.240 5.667 5.429
2/1/2 2/1/3 2/1/4 3/1/2 3/1/3
1.216 1.217 1.218 1.216 1.217
1.217 1.217 1.217 1.217 1.217
1.495 1.493 1.492 1.494 1.493
1.427 1.427 1.426 1.427 1.427
28.0 27.2 26.7 27.5 27.1
4.149 4.069 4.043 4.351 4.106
PM3 3.775 3.722 3.700 3.934 3.761
3.269 3.174 3.144 3.516 3.217
2.829 2.768 2.744 3.035 2.817
3.821 3.771 3.751 3.984 3.814
2.763 2.726 2.708 2.906 2.759
8.809 8.751 8.729 8.982 8.804
6.875 6.599 6.519 7.454 6.743
5.507 5.747 5.804 5.011 5.660
2/1/2 2/1/3 2/1/4 3/1/2 3/1/3
1.229 1.230 1.231 1.229 1.230
1.228 1.228 1.228 1.228 1.228
1.498 1.497 1.497 1.498 1.498
1.386 1.383 1.381 1.387 1.384
18.1 16.0 14.5 17.9 16.1
3.004 2.978 2.966 3.031 2.993
SAM1 3.985 3.940 3.915 4.027 3.972
2.028 1.995 1.980 2.065 2.015
3.306 3.251 3.221 3.357 3.289
4.158 4.112 4.088 4.204 4.147
3.495 3.447 3.418 3.537 3.480
8.771 8.733 8.717 8.822 8.767
6.813 6.518 6.387 7.018 6.635
5.524 5.813 5.932 5.346 5.731
exptl13a
1.223
1.222
1.467
1.391
3.459
3.270
8.251
6.499
5.084
aggregates
a
3.372
Distances in angstroms, angles in degrees. b τ, H5-N1-C1-C6 torsional angle. c H-bond is between molecules A and B (Figure 6).
pates in two, almost equivalent H-bonds between the chains of a strand: the nitro group of every monomer H-bonds to an amino hydrogen on the adjacent chain, while the amino group of the same monomer H-bonds to a nitro group of a molecule of the other chain. Thus, both O‚‚‚N interchain distances to the same molecule are approximately the same. This prediction differs from the experimental observation of one short 3.336 Å and one long 5.355 Å O‚‚‚N contact.13a The trends for the calculated unit cell parameters follow those for single chains. The gradual strengthening of H-bonding interactions shortens d and the H-bonding distances, as well. The unit cell parameter d lengthens upon forming strands from chains improving the agreement between AM1 predictions and experiment. The amino groups become more coplanar with the rings upon aggregation. The larger out-of-plane torsional angle (τ in Tables 6 and 8) compared to the p-nitroaniline case is due
to the fact that the amino nitrogens in m-nitroaniline optimizations were not confined to the aromatic plane. Stacking of the Strands: InVerse or Parallel? Stacking of the strands can occur in two different ways. In the first (corresponding to the crystal structure) the nitro groups point in the same direction (hh orientation), while in the second they point in opposite directions (ht). Calculations for m-nitroaniline stacks give a similar result to those of the p-nitroaniline investigation. We optimized stacks of 2/1/2, 2/1/3, 2/1/4, 3/1/2, 3/1/3 (two or three stacked chains), and 2/2/2 (two stacked strands) in the hh orientation both with vectors a and c constrained perpendicular (β ) 90°) and with optimized β. Tables 7 and 9 summarize the results of these calculations. Calculations with all three MO methods failed to find stable minima for the stacked structures when β was optimized. While the geometrical constraint of β ) 90° keeps
MO Studies of Crystalline Nitroanilines
J. Phys. Chem., Vol. 100, No. 23, 1996 9647
TABLE 10: Stacking Interaction Energies (kcal/mol) and H-bonding Distances (Å) interaction energy total
stackinga
O2‚C5b
O2‚H3b
O2‚C4b
a
1+1 2+1
-2.17 -3.24
-2.17 -3.24
-13.44
-3.90
AM1 2.346 2.324 2.322 2.339 2.334
4.174 4.171 4.032 4.022
5.927
4+2
3.350 3.362 3.385 3.353 3.350
2+1
-1.55
-1.55
-9.90
-4.98
PM3 1.879 1.878 2.604 2.613
3.771 3.769 4.445 4.455
6.154
4+2
2.967 2.966 3.600 3.605
2+1
-2.65
-2.65
3.296 3.100
SAM1 2.302 2.057
4.259 4.026
7.759
3.375
6.499
exptl6a a
geometry
aggregate
3.456
6.040
6.850
c
d
5.753
8.341
6.022
9.120
5.084
8.251
b
Interactions not including H-bonding energies within chains. The first number corresponds to the interaction for molecules A and F (Figure 8) and the second for A and E.
the chains (except for 2/2/2 aggregates in PM3 and SAM1) stacked, the interstrand interaction energy is repulsive (Table 7). Nonetheless, these structures are minima on the constrained potential surface. These results parallel those for p-nitroaniline. Although these structures are unstable, the unit cell dimensions a and c are reasonably reproduced by all three methods (Table 9). As before, AM1 provides better geometrical results than the other two methods. We found the best agreement for a 2/1/2 aggregate at the AM1 level, where the differences are e0.2 Å. As the 2/2/2 AM1 aggregate accurately reproduces the unit cell parameters, we conclude that the error in the interchain (within a strand) H-bonding distances does not significantly affect the unit cell parameters. We also performed calculations on aggregates with ht chain orientations. In the simplest case, for two stacked monomers, 2/1/1 with opposite directionality, we found -1.83 and -2.72 kcal/mol stabilization for AM1 and SAM1 methods, while PM3 does not locate stable minimum on the potential surface. Calculations for an ht aggregate containing eight monomers (a 2/2/2 aggregate) predict strong stabilization between the strands: -7.39, -7.62, and -13.37 kcal/mol for AM1, PM3, and SAM1. Additional potential surface calculations for different aggregates all underscore these observations: the hh orientation is repulsive in all single cases, while the optimal ht arrangement is always stabilized. Thus, the evident contradiction between the experimentally observed hh directionality and the stabilized ht orientation suggests that interactions between the stacked strands might be of great importance in determining the crystal structure. ObserVed hh Orientation Results from C-H‚‚‚O Interactions. The interactions between stacks of strands might provide the stabilization necessary to overcome the unfavorable interactions between the hh-oriented stacked strands. The angle between the directions of the H-bonded chains (that is, the angle between two diagonals, d, of a rectangle with sides a and c (Figure 8) of this second stacking interaction is approximately 104°. The only possible H-bond acceptor in this interaction (O2) is hindered by the aromatic rings. The planar benzene rings (especially its C5 and H3 atoms) if rotated appropriately, however, can make close contact with these O2 atoms. Figures 8 and 9 depict structures illustrating this kind of interaction. Of the three methods only AM1 predicts a minimum for the simplest case, the interaction of only two molecules (1+1, molecules A and E in Figure 8). The interaction energy (Table 10) is surprisingly strong, -2.17 kcal/mol. An aromatic hydrogen of a nitroaniline
molecule, H3, forms a C-H‚‚‚O H-bond to the nitro group of a molecule of the other stack. AM1 predicts the distance between C5 and O2 to be 3.350 Å, in good agreement with the experimental 3.456 Å. In another complex (2+1), two stacked hh monomers (molecules E and F in Figure 8) interact with an additional monomer in the second stacking direction (molecule A in Figure 8). This simple complex contains hh-oriented parallel molecules (molecules E and F) in the first stacking direction. The complex contains both the attraction of two C-H‚‚‚O H-bonds (between molecules A and E and between molecules A and F) and the repulsion between the unfavorably oriented, stacked m-nitroaniline molecules. (The repulsion between the hh-oriented parallel molecules is +0.76 kcal/mol with AM1, for example.) The overall stabilization of the 2+1 complex, -3.24, -1.55, and -2.65 kcal/mol by AM1, PM3, and SAM1 respectively, indicates that the attractive C-H‚‚‚O interactions are sufficient to hold the complex together despite the unfavorable electrostatic interactions between the stacked monomers. The largest aggregate (containing two stacked chains, 2/1/2, interacting with two monomers from the second stacking direction: 4+2; see also Figures 8 and 9) is stabilized by -13.44 and -9.90 kcal/mol by AM1 and PM3 (SAM1 did not predict a minimum). The total stabilization less the interaction energy of two H-bonded dimers indicates that the stabilizing C-H‚‚‚O interaction overcomes the hh repulsion by 3.90 and 4.98 kcal/ mol. In the crystal structure every molecule participates in two such C-H‚‚‚O H-bonds. This is illustrated in Figure 8, where the nitro oxygen (O2) of molecule A is the H-bond acceptor (to F), while C5 of the same molecule is a H-bond donor (to E). Table 10 also collects the relevant geometrical parameters. Again, AM1 is especially good at predicting the H-bonding geometries between C2 and O2 (3.35-3.38 Å calculated vs 3.456 Å experimental C‚‚‚O distance), while all methods overestimate the C4‚‚‚O2 distance. Our attempts to find stacked aggregates with ht-oriented chains stabilized via two C-H‚‚‚O interactions per monomer failed. When the C-H‚‚‚O H-bonds from the second stacking direction are similar in geometry to those in the hh complex, the ht-oriented stacked monomers must distort from their electrostatically most favorable arrangement. In fact, their interaction becomes slightly repulsive. If the stacked ht monomers keep their favorable electrostatic orientation (-1.86 kcal/mol between two stacked monomers in AM1), the C-H‚‚‚O
9648 J. Phys. Chem., Vol. 100, No. 23, 1996 interactions distort from their optimal geometry, becoming only minimally attractive. This fact indicates that the ht orientation in the most favorable electrostatic orientation probably cannot accommodate a monomer from the second stacking direction using both possible C-H‚‚‚O H-bonds. On the other hand, in the 2+1 hh aggregate adjacent strands are shifted with respect to each other (Figure 9) lowering the head-to-head repulsions between the strands (only +0.76 kcal/mol with AM1) while ensuring a favorable geometry for the C-H‚‚‚O H-bonds between stacks. The ht alignment would not permit such favorable orientation for these C-H‚‚‚O interactions. Conclusions Semiempirical AM1, PM3, and SAM1 calculations have been performed for p- and m-nitroaniline aggregates. The results of these calculations give sound reasons for understanding the different crystal structures of these two compounds. p-Nitroaniline forms infinite two-dimensional layers from interconnected H-bonded chains. The presence of H-bonds (the combination of patterns III and IV of Figure 1) between the chains suggest the stability and preference of the observed H-bonded network over the structure (I) that would have been expected to be most stable by considering only H-bonded chains. The two-dimensional layer structures then stack with ht orientation that is stabilized by dipole-dipole interactions giving rise to the crystal structure. The most important difference in the nucleation of m-nitroaniline is the formation of H-bonded strands consisting of two chains. The H-bonded pattern (three-centered H-bonds) is similar to that of p-nitroaniline, but due to the different relative orientation of the substituents, this pattern leads to the association of only two chains to form linear strands. Stacking of the strands takes place in an hh manner (nitro groups pointing to the same direction). Although this orientation in itself would be destabilized by the forementioned dipole-dipole interactions, additional C-H‚‚‚O H-bonds between the almost perpendicularly interacting stacks reverse this tendency, overcome the weak repulsion between the strands, and ultimately dictate the final arrangement of the crystal structure. The ht orientation in p-nitroaniline results in a centrosymmetric crystal structure, while m-nitroaniline owing to the hh orientation of the stacked strands crystallizes in a non-centrosymmetric manner. As a very important consequence, m-nitroaniline crystals exhibit second-order nonlinear optical properties, while those of p-nitroaniline do not. These studies also illustrated the significance of both the cooperative effects (for example, geometry changes upon aggregation) and the C-H‚‚‚O interactions (m-nitroaniline crystallization). In fact, these crystal structures also exemplify the existence of aromatic C-H‚‚‚O H-bonds.
Turi and Dannenberg Among the applied methods, AM1 performed very well at predicting both relative energies and geometries. Especially its H-bonding geometries and unit cell parameters are impressive. In addition, its heat of sublimation estimates were closest to the experimental data. PM3 and SAM1 methods could reproduce the main trends; their predictions of smaller details, however, are not as good. PM3 tends to underestimate the strength of N-O‚‚‚H interactions and thus overestimates their bond lengths. Its H-bonding energies are always lower than those of the other two methods. The greatest problem with SAM1 is its difficulties in finding suitable minima on the potential surface, even in such regions where the other two methods clearly suggest stable alignments. It also appears to overestimate the significance of electrostatic interactions such as the dipole-dipole interactions in the stacking phenomenon. Acknowledgment. The inspiration for this work came from Margaret Etter, to whom we are most grateful and whose memory we honor. This work was supported in part by the PSC-BHE, NSF, and IBM Corporation. L.T. gratefully acknowledges the financial support of the Foundation for the Hungarian Research and Higher Education and the Soros Foundation at the last stages of the project. References and Notes (1) Turi, L.; Dannenberg, J. J. J. Am. Chem. Soc. 1994, 116, 8714. (2) Turi, L.; Dannenberg, J. J. Chem. Mater. 1994, 6, 1313. Turi, L.; Dannenberg, J. J. J. Phys. Chem. 1992, 96, 5819. (3) Vinson, L. K.; Dannenberg, J. J. J. Am. Chem. Soc. 1989, 111, 2777. (4) Panunto, T. W.; Urbanczyk-Lipkowska, Z.; Johnson, R.; Etter, M. C. J. Am. Chem. Soc. 1987, 109, 7786. (5) Dannenberg, J. J. In Materials for Nonlinear Optics; Marder, S. R., Sohn, J. E., Stucky, G. D., Eds.; ACS Symposium Series 455; American Chemical Society: Washington, DC, 1991; p 457. (6) Zyss, J.; Oudar, J. L. Phys. ReV. A 1982, 26, 2028. (7) Turi, L.; Dannenberg, J. J. J. Phys. Chem. 1995, 99, 639. (8) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902. (9) Dewar, M. J. S.; Jie, C.; Yu, J. Tetrahedron 1993, 49, 5003. (10) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209. (11) Trueblood, K. N.; Goldish, E.; Donohue, J. Acta Crystallogr. 1961, 14, 1009. (12) A referee has pointed out the similarities between our calculational treatment of molecular crystals in this paper (as well as in our previous work) to the aufbau principle described by Kitaigorodoskii. This principle (Kitaigorodskii, A. I. Organic Chemical Crystallography; Consultants Bureau: New York, 1961) has been more recently discussed: Perlstein, A. J. Am. Chem. Soc. 1994, 116, 455. (13) Hoyer, H.; Peperle, W. Z. Electrochemistry 1958, 62, 61. Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; London: Academic Press, 1970; p 334. (14) (a) Dhaneshwar, N. N.; Tavale, S. S.; Pant, L. M. Acta Crystallogr. 1978, B34, 2507. (b) Skapski, A. C.; Stevenson, J. L. J. Chem. Soc., Perkin Trans. 2 1973, 1197.
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