Karplus diagram

Karplus diagram. A plot showing the Karplus relationship. 

Strong HMBC cross peaks are often observed between H s and C s that are two and three bonds distant, provided that the geminal and vicinal (dihedral) hond angles are not such that the coupling is at or near zero (recall the Karplus diagrams presented in Sections 6.4 and... 

Karplus diagram. A plot showing the Karplus reiationship. Karpius reiationship. A mathematicai function based on orbital overlap that relates the magnitude of J-coupling as a function of the geminai bond angie or the vicinal dihedral angle. 

More recently, Caves and Karplus have used diagrammatic techniques to investigate Hartree-Fock perturbation theory. They developed a double perturbation expansion in the perturbing held and the difference between the true electron repulsion potential and the Hartree-Fock potential, V. This is compared with a solution of the coupled Hartree-Fock equations. In their interesting analysis they show that the CPHF equations include all terms first order in V and some types of terms up to infinite order. They propose an alternative iteration procedure which sums an additional set of diagrams and thus should give results more accurate than the CPHF scheme. Calculations on H and Be confirmed these conclusions. 

Fig. 20. Top stereogram of the three-dimensional structure of spinach Fd NADP reductase (FNR) with the p-strands shown as arrows, the o-helices as spirals, and FAD and 2 -phospho-5 -AMP as ball-and-stick models Bottom topological diagram for FNR, with the p-strands shown as arrows, and the a-helices as rectangles. Figure source Karplus and Bruns (1994) Structure-function relations for ferredoxin reductase. J Bioenerg Biomembr 26 92 and Karplus, Daniels and Herriotf (1991) Atomic structure of ferredoxin-NADP reductase Prototype for a structurally novel flavoenzyme family. Science 251 62.

Color Plate 13. Ribbon diagram of the pea ferredoxin-NADP reductase (Tyr308->Ser)-NADP complex. The N-terminal FAD domain and the C-terminal NADP domain are coiored in teai and red, respectively FAD in yellow and NADP in green. (Courtesy of Dr. P. A. Karplus). [See Chapter 34, Fig. 21.]... 

Detailed analyses of the density distributions and chemical bindings were also given by Kern and Karplus (1964) for HF and by Ransil and Sinai (1967) for Li2, N2, F2, HF, and LiF. Politzer et al. gave a force analysis for CO (Politzer, 1965) and NO (Politzer and Harris, 1970) molecules, and compared (Politzer, 1966) the forces for the H2 molecule calculated from various wave functions. Clinton and Hamilton (1960) examined force curves for the excited and ionized states of 02, 02+, and NO in relation to the Clinton-Rice reformulation (Clinton and Rice, 1959) of the Jahn-Teller effect (Jahn and Teller, 1937). Curtiss et al. (1975) studied ionic binding (see also, Bader and Henneker, 1965) in a series of alkali halides using the density distribution and the Berlin diagram (Berlin, 1951). 

Unfortunately, the computational studies differ in quantitative detail regarding the importance of the mechanisms that involve either Glu 165 or His 95 as the acid-base catalysts to catalyze interconversion of the tautomeric enediolate intermediates. Friesner and coworkers concluded that the transition state for proton abstraction from DHAP is the highest point on the energy diagram after formation of the enediolate anion intermediate, the calculations predict that the barrier for the criss-cross mechanism catalyzed by Glu 165 is - 3 kcal moU lower than that for classical mechanism involving catalysis of tautomerization of the enediolate intermediates by His 95, so the criss-cross mechanism is predicted to be the favored mechanism. In contrast, Cui and Karplus concluded that transition state energies for tautomerization of the enediolate anion intermediates via an enediol intermediate are isoenergetic for both the classical and criss-cross mechanisms. 

Fig. 2. Energy diagram for the H + Hg system, showing energies for linear collisions (classical calculations of Karplus et al.).

Karplus, M. 1990. Three-dimensional Pople diagram. Journal of Physical Chemistry 94 5435-5436. 

Fig. 25. Contour diagram of the Porter-Karplus potential energy surface for the collinear H 4- H2 system in Delves coordinates The solid curves are equipotentials whose energies (with respect to the bottom of the isolated H2 well) are indicated at the lower right side of the figure. The dashed line is the minimum energy path and the cross along it is the saddle point. The polar coordinates p,a of a general point P in this configuration space are also indicated. The circular arcs centered at the origin are lines of constant p.

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