Karplus parameters approach

The early development of the Karplus relationship has been outlined in Section 1.4 (see p. 60). The significance of this method was soon realized by Jardetzky and by Lemieux, who applied it to the determination of the conformation of the o-ribofuranose and 2-deoxy-D-eri/first time, that furanoid rings are nonplanar in solution. However, it was not realized at that time that the Karplus parameters are subject to a substituent effect, so the original parameters were used hence, the particular values obtained in these investigations may require some slight modification. All of the following empirical modifications of the Karplus parameters were based on the intuitive assumption that allowance must be made for a substituent effect, and this step has only recently been justified by Williamson, and by Laszlo and Schleyer. ... 

Hence, the set of incremental coefficients ACq is included in the fitting process. The authors used this formulation within a self-consistent fitting approach [81] to obtain very accurate amino acid-specific Karplus parameters for the six vicinal -couplings that probe the side-chain torsion angle x by making use of six additional AC parameters. In a subsequent study, the results were further improved by introducing an additional sine term to account for asymmetry effects. 

The amount of Monte Carlo selection that has been employed in different studies has varied. For example, Blais and Bunker [48, 305] used a complete Monte Carlo procedure in their studies of the K + CH3I reaction, although the distribution of one or more parameters could be suppressed, allowing them to observe how particular results depended on different features of the collisions. On the other hand, Karplus et al. [20] adopted a rather different approach in their investigation of the H + Ha system. A batch of trajectories was calculated with particular values of v, b and vibrational and rotational energies of H2. The remainder of the variables were chosen by Monte Carlo methods. The vibrational and rotational energies corresponded to individual rotational states in the zero-point vibrational level. By averaging the results... 

X-ray crystallography for detection of metalloproteins accuracy problems, 66 determination of geometric parameters DFT-the Hohenberg-Kohn theorem approach, 67 QM/S techniques, 67 QSOR approach, Karplus relationship, 67 refinement of, linear-scaling quantum chemical methods, 66-67... 

Despite the extremely wide use of multi-dimensional NMR techniques for conformational studies of biological macromolecules, at present, only a small part of the information contained in the NMR spectrum can be used for structure determination [118,119]. The reason is that there are no well-established correlations between NMR chemical shifts and the structural parameters [118] and only a few useful correlations besides Karplus relations [120,121] for nuclear spin-spin coupling constants. As a consequence, a great deal of important information about the system is not available without turning to quantum chemical approaches for the theoretical interpretation. 

Some years later, aided by considerably more rapid computers than available to Wall and co-workers, Karplus, Porter, and Sharma reinvestigated the exchange reaction between H2 and H [24]. As with the earlier work, the twelve classical equations of motion were solved. In addition, discrete quantum-mechanical vibrational and rotation states were included in the total energy so that the trajectories were examined as a function of the initial relative velocity of the atom and molecule and the rotational and vibrational quantum numbers j and v of the molecule. The more sophisticated potential energy surface of Porter and Karplus was used [7], and the impact parameter, orientation and momentum of the reactants, and vibration phase were selected at random from appropriate distribution functions. This Monte Carlo approach was used to examine 200-400 trajectories for each set of VyJ, and v. The reaction probability P can be written as... 

Nazarski et al. have studied extensively conformational equilibriums of some flexible pyrrolidin-2-ones and -thiones (Fig. 4) in solution by means of experimental NMR parameters ( H and C chemical shifts, and and their DFT predictions. Among others, the authors have calculated three-bond J(H,H) couplings applying DFT approach (B3LYP/IGLO-II// B3LYP/6-31G(d) theory levels) or using the Karplus-type relationships. The former appeared to perform better. 

Delley B (1990) An all-electron numerical method for solving the local density functional for pol) tomic molecules. J Chem Phys 92(1) 508 Delley B (2000) From molecules to solids with the DMoP approach. J Chem Phys 113(18) 7756 Delley B (2002) Hardness conserving semilocal pseudopotentials. Phys RevB 66(15) 155125 Ferre N, Assfeld X, Rivah JL (2002) Specific force field parameters determination for the hybrid ab initio QM/MM LSCF method. J Comput Chem 23(6) 610 Field MJ, Bash PA, Karplus M (1990) A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J Comput Chem 11(6) 700... 

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