Karplus parameters constants

Structural properties of two macrocyclic derivatives 42 (R = H, Ts) have been studied by molecular mechanics and 111 NMR spectroscopy, and new sets of Karplus parameters for calculation of the vicinal coupling constants of the butyrolactone moieties have been determined <2002EJ0351>. 

In his calculations, Karplus assumed that both of the carbon atoms to which the hydrogen atoms are attached are sp -hybridized, and he pointed out that evidence was available to show that the actual value of the relationship was dependent on the other substituents attached to the carbon atoms. The empirical modifications of the Karplus parameters which were developed to obtain meaningful results from carbohydrates are discussed in detail in Section 11,2 (p. 71). Williamson has since obtained some rather elegant results which largely justify these empirical assumptions. From derivatives of hexachloronorbornene, he obtained a linear relationship between 1,3-coupling constants and substituent electronegativities which show unequivocally that allowance has to be made for substituent effects in the Karplus relationship. 

Hruska (12) developed a procedure to determine the rotamer populations of the 3 GH20H-group from the coupling constants between H(3 A), H0 B) and H(A ). With the Karplus parameters given in eq. (1) the equations used are ... 

This equation was predicted on theoretical grounds, but the constants, A, B, and C are empirical.450 Other forms of the equation, some of them simplified, have also been proposed.451 The Karplus relationship is often used to estimate time-averaged torsion angles in peptides. For a CaH - NH torsion angle the parameters A, B and C of Eq. 3-52 are 6.4,1.4, and 1.9, respectively. For a CaH - CpH they are 9.5,1.6, and... 

Laurie s studies of the heteronuclear NMR parameters of sugars and other molecules did much to extend the experimental generality of the Karplus dependence of vicinal coupling constants on the dihedral angles and other properties of the coupled nuclei. 

The combination of MD and NMR is standard in stmctural studies of proteins and other biomolecular systems. In this method, called the restrained MD (rMD) [1,2], nuclear Over-hauser enhancement (NOE) data from NMR are used as limits for inter-proton distances, incorporated into the force field. Other NMR parameters, namely vicinal nuclear spin-spin, i.e. J coupling constants can also be used in the same way to restrict torsional angles to certain intervals (after being fitted to Karplus type of relationships [3]). In these particular investigations, MD simulations are used as an aid in structure refinement. This chapter will not deal with these aspects, however. 

Coefficients0 in Selected Three-Parameter Karplus Equations, 3J = A cos2

Coupling Constants, Ranked According to the Magnitude of A... 

ACD/H-NMR from Advanced Chemistry Development (ACD) Labs calculates H-NMR spectra under any basic frequency. The system uses 3D molecular structure minimization and Karplus relationships to predict proton-proton coupling constants. The software recognizes spectral differences among diastereotopic protons, cis-trans isomers of alkenes, syn-anti isomers of amides, oximes, hydrazones, and nitrosa-mines. The base data set includes more than 1,000,000 experimental chemical shifts and 250,000 experimental coupling constants. To quantify intramolecular interactions in new organic structures and to predict their chemical shifts, ACD/HNMR uses an algorithm based on intramolecular interaction parameters to quantify intramolecular interactions in new organic structures and to predict their chemical shifts. 

Therefore, the harmonic force constant k2 is expressed in terms of molecular charge distribution and its variation with R, i.e., we have the expression relating k2 with the nuclear quadrupole coupling constants obtained experimentally, which is of great importance to the theoretical study of diatomics. Equation (12) is valid not only for exact wave functions but for any functions in which all parameters involved are optimized with respect to R (see Section VII). The Hartree-Fock wave functions belong to this class (Kern and Karplus, 1964 Cade et al., 1966). 

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. 

The most commonly used NMR parameter in conformational studies is the three-bond coupling constant 3Jnm in the fragment N-A-B-M (see ref. [119] and refs, cited therein). The connection between three-bond coupling constant (vicinal coupling) and the dihedral angle N-A-B-M are expressed in the well known Karplus type [120,121] relations... 

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