Torsion/torsional parameters

For each combination of four atom types, A, B, C and D, there are generally three torsional parameters to be determined, yABCo... 

One way of reducing the number of parameters is to reduce the dependence on atom types. Torsional parameters, for example, can be taken to depend only on the types of the two central atoms. All C-C single bonds would then have the same set of torsional parameters. This does not mean that the rotational barriers for all C-C bonds are identical, since van der Waals and/or electrostatic tenns also contribute. Such a reduction replaces all tetra-atomic parameters with diatomic constants, i.e. 

Much controversy is found in the literature regarding the conformational preference of the six-membered ring piperidine (5)4 5. However, most experimental evidence is consistent with a predominance of the H-equatorial conformer by 0.25-0.74 kealmol-1. As noted above, the C—C—N—H and C—C—N—lp torsional parameters were adjusted to reproduce an intermediate value of 0.30 kcal mol-1. MM2 calculations of this system have revealed, perhaps contrary to chemical intuition, that most of the energy difference between the H-axial and H-equatorial conformers results from torsional energy while the 1,3-diaxial interactions have only a negligible contribution5. 

Most of the data for these parameterization studies came from ah initio calculations although other sources were also used, in particular, to validate the resulting force field. Thus a set of small model molecules with different conformations of the R—N—C—N—R moiety was calculated at various levels of theory and the results used to derive torsional parameters, hydrogen bond parameters and conformationally dependent correction terms for natural bond lengths and angles, as described below ... 

Torsional parameters. These (in conjunction with hydrogen bonding parameters, see below) were chosen to reproduce the ab initio conformational energies of the model compounds. 

Torsional parameters and VdW parameters for internal hydrogen bonds in the N—C—N moiety were obtained by fitting the ab initio rotational profiles of methylenediamine (MDA, 15) and /V-methylmelliylenediamine (NMMDA, 16). A comparison of relative conformational energies between ab initio and MM2 results for 15 and 16 is provided in Table 6. Bond length correction terms for inner and outer C—N bonds (K, K2 and... 

As in the case of the MM2 force field, parameterization of MM3 for amines was based mainly on experimental data with occasional references to ab initio calculations, mainly to evaluate relative conformational energies and derive appropriate torsional parameters. As mentioned above, one notable difference between the two force fields is the removal of lp on sp3 nitrogens from MM3. This simplifies the treatment of vibrational spectra and allows for a realistic treatment of nitrogen inversion which could not be handled by MM2. As usual with MM3, parameterization was aimed at reproducing a variety of molecular properties such as structure, steric energy, dipole moments, moments of inertia, heat of formation and vibrational spectra. A complete list of MM3 parameters for amines is provided in Reference 6. 

Maxwell, D. S., Tirado-Rives, J., and Jorgensen, W. L. (1995) A comprehensive study of the rotational energy profiles of organic systems by ab initio MO theory, forming a basis for peptide torsional parameters. J. Comput. Chem. 16, 984-1010. 

The principle aim of the reported studies was to model structures, conformational equilibria, and fluxionality. Parameters for the model involving interactionless dummy atoms were fitted to infrared spectra and allowed for the structures of metallocenes (M = Fe(H), Ru(II), Os(II), V(U), Cr(II), Cofll), Co(ni), Fe(III), Ni(II)) and analogues with substituted cyclopentadienyl rings (Fig. 13.3) to be accurately reproduced 981. The preferred conformation and the calculated barrier for cyclopentadienyl ring rotation in ferrocene were also found to agree well with the experimentally determined data (Table 13.1). This is not surprising since the relevant experimental data were used in the parameterization procedure. However, the parameters were shown to be self-consistent and transferable (except for the torsional parameters which are dependent on the metal center). An important conclusion was that the preference for an eclipsed conformation of metallocenes is the result of electronic effects. Van der Waals and electrostatic terms were similar for the eclipsed and staggered conformation and the van der Waals interactions were attractive 981. It is important to note, however, that these conclusions are to some extent dependent on the parameterization scheme, and particularly on the parameters used for the nonbonded interactions. 

Torsional potential function. The torsional parameters were adjusted to give the best representation of the methyl and nitro group rotation in DMNA. 

Another problem directly related to the number of atomic types involved is that of actual construction of the parameters system, provided some guess concerning the form of the force fields is accepted. A simple estimate given in [199] on the example of the MM2 type of parametrization specifying 71 atomic types shows the number of van der Waals parameters to be 142, the number of different stretching parameters to be about 900, and that for the bending parameters, about 27000. Finally the number of the torsion parameters tends to exceed one million. This clearly indicates that the amount of available experimental data of the accuracy required to obtain... 

The conformational analysis of oligothiophenes by use of a combined molecular dynamics (MD)/NMR spectroscopic protocol has been carried out. A series of MD simulations were performed for 2-(2-thienyl)-3-hexylthiophene 173, 2,5-bis(3 -hexyl-2 -thienyl)thiophene 176, and 2,5-bis(4 -hexyl-2 -thienyl)-thiophene 177, with a new MM2 torsional parameter set developed earlier for unsubstituted and methyl-substituted 2,2 -bithiophene. 

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