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Concerning weak interactions between groups, comparable in energies (or enthalpies) to van der Waals interactions, experimental studies have extensively been made. These include dipole-induced dipole interaction between the 1,3-dioxane and phenyl rings [11], an alkyl-phenyl interaction [12], an alkyl-alkyl interaction [13] including that between two

We have been studying factors controlling such precise molecular recognition as occurs in living systems, by use of a pair of acylurea derivatives [open chain analogues of pyrimidine bases (e.g., uracil and thymine)] which can associate strongly with each other as well as with themselves [18]. As a result, it has been clarified that (i) intermolecular association is the first requirement for molecular recognition [19], (ii) three-dimensional shape similarity between interacting groups in reacting molecules is responsible for more specific and precise molecular recognition than would otherwise be achieved [20].

These findings led us to investigate weak interactions between interacting groups. Using GLPC, it has been demonstrated that (i) enthalpies of weak interactions of a phenyl group (DD

The above-mentioned experimental enthalpies of the interactions [21] can only be determined with a phenyl group as one component, because of limitation of stationary liquids available in GLPC. Thus, some theoretical approaches to evaluate

Ab initio calculations seem not to be suitable for this purpose; they require enormous time and resources of the computer because of complicated calculations of configuration interactions (CI) using a large number of basis sets, the calculation methods being still a subject of theoretical chemists even for the intermolecular interaction of a methane dimer [25]. There appear to have been no calculation methods available for electron correlation which enable calculations of interactions between benzene and substituted benzenes to be precise enough within a realistic time. On the other hand, for semi-empirical methods such as PM3 in MOPAC where (i) CI calculations are not implemented explicitly and (ii) the effect corresponding to electron correlation is supposed to be incorporated implicitly in the set of adjustable parameters, the use of which is characteristic of semi-empirical calculations. This is evident from the fact that heats of formation for various organic compounds can be evaluated with considerable accuracy by means of MOPAC [26].

With this situation in mind, MOPAC was used to evaluate enthalpies of intermolecular interactions, and the effectiveness and limitations of the semi-empirical method were examined. In this paper, we wish to report that the calculated enthalpies of weak interactions between benzene and various substituted benzenes have close correlation with the corresponding experimental enthalpies determined by GLPC.

As monosubstituted benzenes (PhX), anisole (PhOMe), benzene (PhH), chlorobenzene (PhCl), N,N-dimethylaniline (PhNMe

As

Figure 1. (*a*) Schematic drawings of initial arrangements (**P**, **V _{r}** ,

In the case of **V** arrangements, an *intermolecular distance* is defined as the distance between the centroid of a benzene ring lying on a plane and the lowest atom (H or X) of the other PhH or PhX molecule located above the centroid of the former benzene ring (Figure 1). With **P** arrangement, an intermolecular distance is defined as the distance between the facing "above" and "below" carbon atoms of two benzene rings of parallel orientation.

Setting up of an *initial intermolecular distance* (*r*_{I}) was performed using Chem3D (CambridgeSoft Corp.) ver. 3.5 by geometrical calculation so that the *r*_{I} may become the desired value (e.g., 2.60, 2.75, 3.05, 3.20, or 3.40 A). In the case of **V _{b}** arrangement, setting up of the

In general,

DD

molecule, and D

Evaluation of interaction enthalpies (DD

r_{I} /A | DDH_{f} / kcal mol^{-1}
| |||
---|---|---|---|---|

MNDO ( V) | AM1 ( V) | PM3 ( P) | PM3 ( V)
| |

2.60 | -4.29 | -2.96 | 0.06 | -0.52 |

2.75 | -4.30 | -2.94 | 0.06 | -0.52 |

3.05 | -4.29 | -2.95 | 0.06 | -0.52 |

3.20 | -4.29 | -2.96 | 0.06 | -0.52 |

It is also evident from the data in Table 1 that the DD*H*_{f} values by PM3 method for **V** and **P** arrangements (X = H) are -0.52 and 0.06 kcal mol^{-1}, respectively, regardless of the *r*_{I}. Since the experimental interaction enthalpy (DD*H*^{t}) for X = H is -1.32 kcal mol^{-1}, **V** arrangement appears to be more suitable as an initial arrangement of the system than **P** arrangement.

An *optimized intermolecular distance* for the benzene dimer was shown to be 5.0 A between their centroids (d_{cb-cb}) by ab initio calculations [16, 29], molecular dynamics simulations [30], and Monte Carlo simulations [31]. In the present work, the d_{cb-cb} becomes 4.978 A [32], the distance practically equal to that obtained by the previous work mentioned above.

Ab initio calculations of the benzene dimer indicated that interplanar angles (dihedral angles) between interacting benzene molecules approaching 90°, the "T-stacked" arrangement, are enthalpically favorable [16]. Moreover, when they adopt edge-to-face stacked orientation [17], electrostatic interaction between two benzene rings is reported to be attractive (-1.4 kcal mol^{-1}). These findings agree with our result that the optimized geometry, which leads to close relationship between the DD*H*_{f} and DD*H*^{t} , is similar to the initial arrangement of vertical type (**V**). The T-shaped orientation of two benzene molecules is well recognized in four kinds of studies: (i) crystal structures of benzene [33], peptides (and proteins) [15], and organic compounds [34], (ii) molecular beam electric deflection studies [35], (iii) NMR studies [36], and (iv) theoretical calculations [30, 31, 37].

As to *interaction energy*, ab initio calculations of the benzene dimer for various orientations [16] revealed that the interaction energy minimum was ca. -2.4 kcal mol^{-1}; a similar result was obtained by more recent calculations that the interaction energy for the T-shaped structure was -2.64 kcal mol^{-1} [29, 38, 39]. Moreover, NMR studies showed the enthalpy (D*H* ) of the benzene-benzene interaction to be ca. -2.0 kcal mol^{-1} [40], the D*H* value corresponding to theDD*H*^{t} of -1.32 kcal mol^{-1} for X = H; transfer of a benzene molecule from an environment of saturated hydrocarbon molecules into an environment of benzene molecules is energetically favorable to an extent ranging to ca. -l kcal mol^{-1} [41]. These theoretical and experimental results suggest the enthalpy of PhH-PhH interaction to be ca. -l to -2 kcal mol^{-1}. Accordingly, the calculated enthalpy (DD*H*_{f}) of the PhH-PhH interaction by PM3 method might be more positive by ca. 0.5 kcal mol^{-1} or more.

*PhH-PhX Interactions*

As mentioned above, the calculated enthalpy (DD*H*_{f}) of the PhH-PhH interaction was satisfactory in comparison with interaction energies (or enthalpy) obtained with ab initio calculations and with the experiment. Thus, the DD*H*_{f} values were further calculated for various PhH-PhX systems in the case of the five initial arrangements. As the *r*_{I}, 2.75 A was chosen, because the *optimized intermolecular distance* ( *r*_{o} ) for X = H has been shown to be all 2.5 A except for **P** arrangement *r*_{o} =5.41A), regardless of the *r*_{I} [42], and because the sum -- (a half of thickness of a benzene ring) + (van der Waals radius of a H atom) -- is 2.9 A.

Figure 2 depicts a plot of the DD*H*_{f} against the DD*H*^{t} for initial arrangement **P** ( *r*_{I} = 2.75 A). Arrangements after geometry optimization (*optimized geometries*) have been found to resemble the initial arrangement **P**. For most pairs, the PhH-PhX interactions are slightly repulsive. Optimized intermolecular distances ( *r*_{o} ) change from 4.7 to 5.5 A. There exists no appreciable relationship between the DD*H*_{f} and DD*H*^{t}.

In the case of initial arrangement **V _{r}** (

For initial arrangement

The DD

Table 2 Initial arrangements **V**^{a}, optimized intermolecular distances ( *r*_{o} ), The DD*H*_{f} (*r*_{I} = 2.75 A), and the DD*H*^{t} [21]

PhX | V_{p} | V
_{m} | |||
---|---|---|---|---|---|

r_{o} /A | DDH_{f} | r_{o} /A | DDH_{f} | DDH^{t}
| |

kcal mol^{-1} | kcal mol^{-1} | kcal mol^{-1}
| |||

PhEt | 2.51 | -0.49 | 2.51 | -0.50 | -1.09 |

PhMe | 2.51 | -0.50 | 2.51 | -0.50 | -1.18 |

PhF | 2.48 | -0.64 | 2.48 | -0.67 | -1.26 |

PhCl | 2.49 | -0.61 | 2.48 | -0.63 | -1.29 |

PhH | 2.50 | -0.52 | 2.50 | -0.52 | -1.32 |

PhOMe | 2.45 | -0.80 | 2.50 | -0.53 | -1.51 |

PhNMe_{2} | 2.43 | -0.80 | 2.51 | -0.48 | -1.58 |

PhNO_{2} | 2.45 | -0.91 | 2.54 | -1.24 | -1.84 |

In the case of initial arrangement **V _{m}** (

The DD

Figure 2. A plot of the DD*H*_{f} optimized from initial arrangement **P** (*r*_{I} = 2.75 A) against the DD*H*^{t}. The numbers show substituents X of PhX: 1, ethyl; 2, methyl; 3, fluoro; 4, chloro; 5, H; 6, methoxy; 7, dimethylamino; 8, nitro group. All optimized geometries are similar to **P** arrangement (). In the case of *r*_{I} = 3.40 A, (1) the DD*H*_{f} values are equal to those for *r*_{I} = 2.75 A except for (i) X = NMe_{2} (more positive by 0.07 kcal mol^{-1}) and (ii) X = Et (more negative by 2.07 kcal mol^{-1}) and (2) optimized geometries are similar to **P** arrangement except for X = Et (an arrangement similar to **V _{r}**).

Figure 3. A plot of the DD*H*_{f} optimized from initial arrangement **V _{p}** (

Figure 4. A plot of the DD*H*_{f} optimized from initial arrangement **V _{m}** (

Figure 5. A plot of the DD*H*_{f} optimized from initial arrangement **V _{m}** or

The results described here demonstrate that it is the initial arrangement **V _{p}** or

Evaluation of intermolecular interactions by means of ab initio MO method requires incorporation of electron correlation, for which calculations of considerably large configuration interactions (CI) are necessary. On the other hand, in the case of MOPAC methods such as PM3, it would not be unreasonable to consider that the DD

This is the first example in which theoretical enthalpies of the weak interactions between various pairs of aromatic molecules bear close correlation with the experimental enthalpies. The results presented here encourage us to evaluate enthalpies of weak interactions between benzene and a variety of molecules such as other substituted benzenes and alkenes by semi-empirical MO methods.

We thank Mr. Mitsuru Koike for valuable assistance.

Dixon, M., Webb, E. C., Thorne, C. J. R. and Tipton, K. F.,

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[ 21] Ito, M. M., Kato, J., Takagi, S., Nakashiro, E., Sato, T., Yamada, Y., Saito, H., Namiki, T., Takamura, I., Wakatsuki, K., Suzuki, T. and Endo, T.,

[ 22] Endo, T., Ito, M. M., Yamada, Y., Saito, H., Miyazawa, K. and Nishio, M.,

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[ 24] Endo, T., Tajima, K., Yamashita, M., Ito, M. M., Nishida, J. and Ogikubo, T.,

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[ 26] Kihara, H., Uchida, N. and Ikuta, S.,

[ 27] Stewart, J. J. P.,

[ 28] The DD

[ 29] Hobza, P., Selzle, H. L. and Schlag, E. W.,

[ 30] Linse, P.,

[ 31] Jorgensen, W. L. and Severance, D. L.,

[ 32] d

[ 33] Cox, E. G., Cruickshank, D. W. J. and Smith, J. A. S.,

[ 34] Slawin, A. M. Z., Spencer, N., Stoddart, J. F. and Williams, D. J.,

[ 35] Steed, J. M., Dixon, T. A. and Klemperer, W.,

[ 36] Laatikainen, R., Ratilainen, J., Sebastian, R. and Santa, H.,

[ 37] Price, S. L. and Stone, A. J.,

Chipot, C., Jaffe, R., Maigret, B., Pearlman, D. A. and Kollman, P. A.,

[ 38] An ab inito study [29] of interaction energies of the benzene dimer, however, showed that the parallel-displaced structure is slightly more stable than the above-mentioned T-shaped one by 0.88 kcal mol

[ 39] It has been suggested that the interaction energy for the benzene dimer calculated with ab initio method depends significantly upon the basis set implemented and the method for electron correlation calculation applied [Hobza, P., Selzle, H. L. and Schlag, E. W.,

[ 40] Slejko, F. L., Drago, R. S. and Brown, D. G.,

[ 41] Jencks, W. P.,

[ 42] Optimized intermolecular distances (

[ 43] The PM3 MOPAC calculations have revealed that PhH-PhX pairs sometimes adopt irrational structures (e.g., CP and CP*) in which a pair of closest H atoms in the interacting benzene rings are located within the van der Waals spheres. It should be noted that these unreasonable structures are occasionally more "stable", namely, have apparently more negative heats of formation than the realistic ones. Thus, when optimized geometries and/or energetics are studied using the MOPAC program for intra- or intermolecular systems composed of two (or more) aromatic rings, one had better examine whether a non-realistic structure having such an irrationally close contact of the rings is "stabilized" or not.

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