Molecular Mechanics in Crystalline Media

Inorganic Chemistry

Volumn 37, Issue 10, 1998, Pages 2563-2569

  Mercandelli, Pierluigi ^a   Moret, Massimo ^a   Sironi, Angelo ^a  

^a Dipto Chim Strutturale S   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000681074     PISSN: 00201669     EISSN: None     Source Type: Journal    
DOI: 10.1021/ic9713339     Document Type: Article

References (42)

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4. In a conventional MM study, the connectivity of the atoms is exactly defined (and is not allowed to change during the minimization), and, as a consequence, the number of valence electrons of each atom is also strictly controlled. However, within the EPS formalism, which allows variable connectivity of the metals, we lose control of the local number of valence electrons on each metal center.
5. Sironi, A. Inorg. Chem. 1995, 34, 1432.
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15. Note that, to deal with space group symmetry, the usual MM3 symmetry operation has been augmented with a translational component.
16. Actually, PACKMM encodes all the symmetry information needed to obtain the SMs atoms from the RM ones as a list of integers (one for each atom). This allows, using the proper decoding routine, to periodically update (during the minimization process) the SMs on the base of the actual RM. The underlying assumption for these procedure is that relatively small deformations of the RM do not lead any "new" molecule to join or any "old" one to leave the actual SMs cluster. This assumption can be checked by verifying that the minimized coordinates fed into PACKMM afford the same SMs cluster (in term of symmetry operator) of the starting coordinates.
17. This is not true if the electrostatic energy is approximated by the dipolc interaction energy computed throughout bond dipoles (since we would also need to memorize the bonding pattern of the SMs). For this reason we have restored an older option (available in MM2), and we compute the charge interaction energy instead.
18. Note that this weighting scheme must be used only to compute the weighted intramolecular energy but not to compute the forces acting on each atom. Indeed, it is possible to demonstrate that these unweighted forces are the derivatives of the weighted intramolecular energy.
19. To obtain the energy per RM, the normalization factor is the reciprocal of the maximum crystallographic site occupancy (CSO) within the RM. For instance, in the following example of cubic diamond, where the RM is constituted by just one C atom with CSO = 1/24, the normalization factor will be 24 and mult(C) will be 1.
20. Note that, when an atom of the RM lies on a special position even its intermolecular interaction energy must be weighted with its normalized crystallographic site occupancy.
21. For instance, OPEC by A. Gavezzotti.
22. If there is cooperation, however, we must also take into account the ES reorganization energy.
23. Gavezzotti, A.; Filippini, G. In Theoretical Aspects and Computer Modeling of the Molecular Solid State; Gavezzotti, A., Ed.; Wiley: Chichester, 1997; p 61.
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25. -1) for that radius. The problem would be more serious if Coulombic interactions were also considered (but this is not the case for carbon lattices) since they converge much slower.
26. Note that the relative instability of the HD lattice with respect to the CD one is due to 1,4 interactions, which are however differently parametrized in MM2 and MM3. Indeed, with MM3 the instability arises from torsional terms while with MM2 it arises from 1,4 vdW interactions.
27. Namely, iceane-and bicyclo[2.2.2]octane-like cages, in a 1:1 ratio, the former being almost unstrained while the latter heavily strained.
28. Possibly for reasons analogous to those discussed above, but now the correct sampling does not refer any more to cages (which are all equivalent in BC-8) but to rings. Indeed, in the BC-8 structure there are two differently strained kind of rings: one moderately unstrained, a six-membered twist-boat, the other heavily strained, an eight-membered chair with a very short next-nearest-neighbor contact.
29. MM2 is substantially similar to MM3 whenever the geometrical aspects alone are concerned.
30. Fahy, S.; Louie, S. G. Phys. Rev. 1987, B36, 3373.
31. Bondi, A. J. Phys. Chem. 1964, 68, 441.
32. Dunitz, J. D. The Crystal as a Supramolecular Entity. Perspectives in Supramolecular Chemistry; Wiley: Chichester, 1996; Vol. 2, p 1.
33. The recognition of these weak, directional, intermolecular forces has, indeed, greatly contributed to the thought of crystals as Supramolecular entities.
34. Edwards, A. J.; Burke, N. J.; Dobson, C. M.; Prout, K.; Heyes, S. J. J. Am. Chem. Soc. 1995, 117, 4637.
35. 1/a); a = 24.70 Å and c = 14.37 Å for the iodine derivative (rhombohedral, R3c).
36. i is the vector passing through the atom i and perpendicular to n.
37. Zimmerman, H. E.; Zhu, Z. J. Am. Chem. Soc. 1994, 116, 9757.
38. This request is not as stringent as it could appear at a first sight. Indeed, since anomalous contacts normally arises from atoms on the surface of the molecule (mainly hydrogens), it is often enough to drop all the H-H "bonds" from the connectivity table generated on the base of covalent radii, to lower the criteria for a well-behaved AU. Accordingly, it is possible to instruct PACKMM to refuse (or to accept) anomalously short (or long) contacts between selected atoms or atom types, to deal with rough AUs (or with supramolecular contacts).
39. Masciocchi, N.; Moret, M.; Cairati, P.; Sironi, A.; Ardizzoia, G. A.; La Monica, G. J. Am. Chem. Soc. 1994, 116, 7768.
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41. Gavezzotti, A.; Filippini, G. J. Am. Chem. Soc. 1996, 118, 7153.
42. Giacovazzo, C. In Fundamentals of Crystallography; Giacovazzo, C., Ed.; IUCr, Oxford University Press: Oxford, 1992; p 68.