Karplus Equation Research Articles

The relationship between proton–proton NMR coupling constants and substituent electronegativities. II—conformational analysis of the sugar ring in nucleosides and nucleotides in solution using a generalized Karplus equation

AbstractThe relationship between vicinal NMR proton–proton coupling constants and the pseudorotational properties of the sugar ring in nucleosides and nucleotides is reinvestigated. Compared with our earlier study several important improvements are introduced: first, a new empirical generalization of the classical Karplus equation is utilized, which allows an accurate correction for the effects of electronegativity and orientation of substituents on 3J(HH); second, empirical correlations between the parameters governing the conformation of β‐D‐furanosides (taken from an analysis of 178 crystal structures) were used to define proton–proton torsion angles as a function of the pseudorotation parameters P and Φm; and, third an iterative least‐squares computer program was devised to obtain the best fit of the conformational parameters to the experimental coupling constants. NMR data for the sugar ring in the following compounds were taken from the literature and analysed: 3′,5′‐cyclic nucleotides, a base‐stacked ribonucleotide, 2′‐anhydroarabinonucleosides, α‐D‐2′,2‐O‐cyclouridine, 2′‐ and 3′‐aminosubstituted ribonucleosides, 2′‐ and 3′‐deoxyribonucleosides. The present results confirm that the conformational properties found in the solid state are, on the whole, preserved in solution.

Conformational analysis of ribonucleosides from proton-proton coupling constants

A graphical method is described which permits the determination in solution of conformational equilibria and parameters of ribonucleosides from proton-proton coupling constants. The method is based on the pseudorotational concept and the use of the Karplus equation. Using a large number of 1H-NMR data on ribonucleosides from the literature, an optimal set of Karplus constants, A = 10.0, B = −1.2, was obtained. It is shown that this set of Karplus constants, in connection with the pseudorotational treatment, describes satisfactorily the nucleoside conformations, especially the pucker amplitude. The solution results are compared with X-ray data and the differences are discussed. The method can be used either graphically or by direct computer treatment of the data.

Phosphorus-31 and carbon-13 NMR spectra of 2-norbornyl phosphorus compounds. Karplus equations for 3JPC in several phosphorus(III) and phosphorus(IV) derivatives

Phosphorus-31 and carbon-13 NMR spectra of 2-norbornyl phosphorus compounds. Karplus equations for 3JPC in several phosphorus(III) and phosphorus(IV) derivatives

Conformational analysis of 1,2:3,4-di- O-isopropylidene-α- d- galacto-octopyranose derivatives: a 1H- and 13C-N.M.R.-spectral and x-ray comparative study

The pyranoid conformations of 7-acetamido-6,7,8-trideoxy-1,2:3,4-di- O-isopropylidene- d- glycero-α- d- galacto-octopyranose ( 3) and 7-acetamido-7,8-dideoxy-1,2:3,4-di- O-isopropylidene- l- threo-α- d- galacto-octopyranose ( 4) in solution have been determined by calculation of the dihedral angles from the vicinal, proton-proton coupling-constants, using three modifications of the Karplus equation. Of these, only the equation 3 J(HCCH)(φ)  (7.48  0.74 -ΣδE x)  (2.03  0.17 ΣE x)cos φ + (4.60  0.23 ΣδE x)cos 2φ + 0.06 (Σ ± ΔE x)sin φ + 0.62 (Σ ± ΔE x)sin 2φ indicates that the pyranoid part of 3 and 4 has the ° S 2 conformation, very slightly distorted towards ° H 5, in agreement with the conformations determined for the crystalline state. Analysis of the 1H-n.m.r. data for a series of 1,2:3,4-di- O-isopropyl-idene-α- d- galacto-octopyranose derivatives shows that the pyranoid parts of these compounds adopt the same conformation as that found for 3 and 4.

The relationship between proton-proton NMR coupling constants and substituent electronegativities—I : An empirical generalization of the karplus equation

A new coupling constant-torsion angle relation for the three-bond 1H- 1H spin-spin coupling constant is formulated. The relation includes a correction for the electronegativity of substituents. The correction term is written as a function of the electronegativity, the H-C-C-H torsion angle, and the orientation of each substituent relative to the coupled protons. A dataset consisting of 315 experimental coupling constants was used to derive six empirical parameters by means of an iterative least-squares minimization procedure. The precision of the proposed equation, expressed as the root-mean-square deviation (0.48 Hz), is superior to any hitherto reported. It is shown that separate treatment of CH 2CH 2, CH 2CH and CHCH fragments even improves this precision. An application in the field of monosubstituted cyclohexanes is given.

Synthesis and pharmacological evaluation of cis-3,4,4a,9a-tetrahydro-1H-pyrano[3,4-b]benzofuran-1-ones. Tricyclic analogues related to the antilipidemic drug clofibrate.

The chemistry and pharmacology of two delta-lactones, cis-6-chloro-9a-methyl-3,4,4a,9a-tetrahydro-1H-pyrano[3,4-b]benzofuran-1-one (2) and the 9a-demethyl analogue 3, are reported. Lactones were prepared from dihydrobenzofuran precursors possessing geometrical configurations confirmed both by synthesis and 1H NMR spectroscopy. All cis-dihydrobenzofurans exhibited Jvic = 9.0-10.8 Hz, whereas their trans isomers exhibited Jvic = 5.0--6.0 Hz in agreement with predictions based on the Karplus equation. The pharmacological profiles for 2 and 3 were compared to that of clofibrate (1) in normal male Sprague-Dawley rats. Using equimolar doses (0.4 mmol/kg, po, twice daily for 7 days), 1 exhibited both anticholesterolemic and antitriglyceridemic activity, lactone 2 exhibited only antitriglyceridemic activity, and 3 was inactive as an antilipidemic agent. No correlation was observed for inhibition of hepatic HMG-CoA reductase activity and serum cholesterol lowering.

Synthesis and 13C N.M.R. Studies of Some Polycyclic Hydrocarbons with Trimethyltin at the Bridgehead

The synthesis of (adamantan-1-yl)trimethylstannane (1), (bicyclo[2,2,2]oct-1-yl)trimethylstannane (2), (bicyclo[2,2,1]hept-1-yl)trimethylstannane (3), (cubanyl)trimethylstannane(4) and tricyco[[4,1,1,02,7]- hept-1-yl)trimethylstannane (5) is described and the carbon-13 nuclear magnetic resonance spectra of these compounds are reported. In particular, it is found that the coupling constant of the directly bonded tin bridgehead carbon atoms is not greatly dependent on the degree of s character of the carbon exocyclic bonding orbital and that vicinal coupling between tin and carbon is observed to fit a Karplus equation. A linear relationship occurs between 1J(117,119Sn,13CMe) and 2J(117,119Sn,13HMe).

Arithmetic manipulation of coupling constants to obtain torsional angles

AbstractVarious arithmetic combinations of Jtrans and Jcis from the AA′BB′ analysis of CH2—CH2– fragments in 6‐membered rings have been examined for their relationship to the internal torsional angle Ψ. The simple ratio R (Jtrans/Jcis) appears to offer the most complete removal of substituent electronegativity effects and hence the best values of Ψ. The Karplus equation is very inaccurate when the substituents are highly polar. The simple difference D (Jtrans–Jcis) overcompensates for electronegativity effects and thus also gives relatively inaccurate torsional angles. An alternative, artificial linear combination of the coupling constants, such as D′ (Jtrans–2Jcis), appears to be able to provide torsional angles that are almost as good as those from the R value, although the Karplus A value must be evaluated. Adjustment of the simple difference D for electronegativity is possible by including a function of the AA′ and BB′ chemical shifts. These results are fairly good, and the parameter A need not be evaluated. This approach may fail, however, with particularly anisotropic substituents, since the chemical shift may depend on factors other than electronegativity. Although all five methods give reasonably good results, the R value appears to offer the most reliable results for the full range of substituents.

Analysis of the Vorontsova equation for calculation of vicinal coupling constants: Criticism of the criticism of the Karplus equation

AbstractAnalysis of the Vorontsova calculation of vicinal coupling constants in terms of angular and chemical shift dependence indicates some serious inconsistencies in this equation.

Structural studies on 2-acetamido-1-N-(4-L-aspartyl)-2-deoxy-beta-D-glucopyranosylamine and 2-acetamido-6-O-(alpha-L-fucopyranosyl)-1-N-(4-L-aspartyl)-2-deoxy-beta-D-glucopyranosylamine by 360-MHz proton-magnetic-resonance spectroscopy.

The 360-MHz proton magnetic resonance spectra of 2-acetamido-1-N-(4-L-aspartyl)-2-deoxy-beta-D-glucopyranosylamine (GlcNAcbeta1 leads to Asn) and 2-acetamido-6-O-(alpha-L-fucopyranosyl)-1-N-(4-L-aspartyl)-2-deoxy-beta-D-glucopyranosylamine (Fucalpha1 leads to 6GlcNAcbeta1 leads to Asn) in deuterium oxide were completely interpreted. The chemical shifts and coupling constants were refined by simulation of the spectra. By means of an adapted Karplus equation the pyranose ring conformation of the sugars was calculated. The change of the geminal coupling constant J6a,6b in the N-acetylglucosamine residue of Fucalpha1 leads to 6GlcNAcbeta1 leads to Asn with respect to GlcNAcbeta1 leads to Asn is proposed to be characteristic for the (1 leads to 6) glycosidic linkage.

Conformational Analysis. Part XVII. A Simple Application of the Karplus Equation to Study the Preferred Conformations of the Ethyl Group in Some Alkylsubstituted 4-Ethyl-1,3-oxathiolanes.

Conformational Analysis. Part XVII. A Simple Application of the Karplus Equation to Study the Preferred Conformations of the Ethyl Group in Some Alkylsubstituted 4-Ethyl-1,3-oxathiolanes.

ChemInform Abstract: LOW‐TEMPERATURE NMR STUDIES OF THE CONFORMATIONS OF 3‐ARYL‐1,2,3‐OXATHIAZOLIDINE 2‐OXIDES

A complete iterative NMR spectral analysis has been carried out for twelve 3-aryl-1,2,3-oxathiazolidine 2-oxides at several low temperatures over a range of 111 °C. The magnitudes of the two vicinal coupling constants either increased or decreased markedly with a decrease in the temperature. On the basis of the resulting vicinal coupling constants, the correlations between the ratios of the vicinal coupling constants and the corresponding torsion angles were obtained and made it possible to assign their twist-envelope conformations. From the experimental data, the parameters of the Karplus equation could be given: Jvic=5.3-cos(135±θ)+4.3cos2(135±θ) +45°≥θ≥-45°

Low-temperature NMR Studies of the Conformations of 3-Aryl-1,2,3-oxathiazolidine 2-Oxides

Abstract A complete iterative NMR spectral analysis has been carried out for twelve 3-aryl-1,2,3-oxathiazolidine 2-oxides at several low temperatures over a range of 111 °C. The magnitudes of the two vicinal coupling constants either increased or decreased markedly with a decrease in the temperature. On the basis of the resulting vicinal coupling constants, the correlations between the ratios of the vicinal coupling constants and the corresponding torsion angles were obtained and made it possible to assign their twist-envelope conformations. From the experimental data, the parameters of the Karplus equation could be given: Jvic=5.3-cos(135±θ)+4.3cos2(135±θ) +45°≥θ≥-45°

Stereochemical aspects of proton chemical shifts. III—Configurational assignments in pentacyclic systems without recourse to a karplus equation

AbstractIt is shown that in contrast to the use of coupling constants, chemical shift criteria may lead to unambiguous structural elucidations in pseudorotational frameworks (pentacycles, heptacycles, etc.).

Conformations of Sugars: Proton Dihedral Angles from Gauche Coupling Constants

Proton coupling constants have been used in calculating dihedral angles of vicinal gauche protons in variety of pyranose derivatives of glucose, mannose, arabinose, xylose, altrose, and galactose. The calculations involve the use of a formula which was derived from a correlation of the coupling constants of ethane derivatives with the electronegativities of substituents and their orientation relative to the coupled protons.The results indicate that the formula has general applicability and gives more reasonable values than a Karplus equation in which the constants have been adjusted to fit some compounds of the series. The calculated dihedral angles indicate that an equatorial substituent generally causes little distortion of dihedral angles, whereas an axial substituent generally causes the equatorial proton on the same carbon to have a smaller than normal dihedral angle with the adjacent axial proton and a larger than normal dihedral angle with the adjacent equatorial proton.

Correlations between molecular parameters and the spin–spin coupling constants of vicinal protons: Criticism of the karplus equations

AbstractConformationally rigid systems such as xylopyranose 1,2,4‐ortho esters (1a) and (1b) and 10‐methoxy‐6‐aza‐isoadamantane (2), for which the identity of conformations both in the crystalline state and in solution can reasonably be assumed, provide good models for the study of experimental correlations between the spin–spin coupling constants (J) of the vicinal protons and the dihedral bond angles (DBA) determined from an X‐ray study in the HCCH bond system. The Karplus equations and their modifications (with and without corrections for the electronegativity of adjacent groups) were found to be unable to provide satisfactory correlations between these parameters. Optimum coefficients for the equations connecting the J and DBA values with corrections for electronegativity were calculated by the least squares method. The same procedure was used to obtain an equation connecting the J with DBA values using the sum of the chemical shifts as a measure of the electronic factors affecting the J ∝ DBA dependence. The accuracy of the equation thus obtained lies within ±18% as opposed to ±48% for the original Karplus equations. A similar correlation was obtained for the angles between the intercrossing lines formed by the directions of the vicinal CH bonds (ILA). When combined with the sum of chemical shifts, ILA provides a better correlation with the coupling constants J than the conventional parameter DBA.

Conformational studies on pertrimethylsilyl derivatives of some 6-deoxyaldohexopyranoses and of four less-common aldohexopyranoses by 220-MHz P.M.R. spectroscopy. Substituent and configurational effects on the chemical shifts of the ring protons

The complete interpretation of 220-MHz p.m.r. spectra and the accurate chemical shifts and coupling constants, obtained after computer simulation of the spectra, of the per- O-trimethylsilyl (Me 3Si) derivatives of a number of 6-deoxy-aldohexopyranoses and of β- D-altro-, β- D-allo-, and α- and β- D-talo-pyranose are given. By means of an adapted Karplus equation, the structure of the derivatives has been studied in detail. All of the pyranoid rings occur in the 4 C 1( D) or 1 C 4( L) chair conformation. The preferred conformation of the C-5—CH 2OSiMe 3 group in the four aldohexopyranoses was found to be dependent on the configuration at C-4. By comparison of Me 3Si-aldohexopyranoses with the corresponding 6-deoxy analogues, it was found that the 6-OSiMe 3 group has no marked effect on the conformation of thering. The influence of this group on the chemical shifts of the ring protons is discussed in terms of electric field and inductive effects. Rules are presented for the estimation of the chemical shifts of the ring protons of Me 3Si-aldohexopyranoses and Me 3Si-6-deoxyaldohexopyranoses.

Complete analysis of the proton magnetic resonance spectrum of tetrahydrofuran

A computer program incorporating symmetry has been written to carry out efficiently the complete analysis of the PMR spectra of systems [AB] 4 with C 2 v symmetry. Using this program, the PMR spectrum of tetrahydrofuran has been analyzed. The best set of coupling values (Hz, ±0.02) is: 2J A − 2J B = 3.80, 3J B c = 8.80, 3J B t= 6.10, 3J AB c = 7.63, 3J AB t = 6.09, 4J A c = −0.02, 4J A t = −0.35, 4J AB c = 0.01 , and 4 J AB t = −0.46 (A and B refer to α- and β-protons and c and t mean respectively same and opposite side of the ring.) The individual values of 2 J A and 2J B are not well-defined, their sum being ( 2J A + 2J B ) = −22 ± 4 Hz . There are 23 other equally valid sets of couplings resulting from the above by performing some concerted coupling interchanges. The above-mentioned set has been selected as physically meaningful in accordance with evaluated values for vicinal couplings ( 3J c > 3J t ) by using a generalized Karplus equation and taking into account the conformer populations obtained by assuming a barrier to pseudorotation of ∼54 cm −1.

Conformational studies of per- O-trimethylsilyl derivatives of D-fructoses and oligosaccharides containing β- D-fructofuranose residues by 220- and 300-MHz P.M.R. spectroscopy

The interpretation of 220- and 300-MHz P.M.R. spectra and the accurate chemical shifts and coupling constants of a number of per- O-trimethylsilyl-(TMS-) D-fructose derivatives and TMS-oligosaccharides containing β- D-fructofuranose residues are presented. On the basis of calculations with an adapted Karplus equation it is concluded that TMS-α- and -β- D-fructopyranose occur in the 2C 5(D) chair conformation whereas the D-glucopyranose rings in the oligosaccharides adopt the usual 4 C 1(D) chair conformation. The structure of the latter units is very similar to that of TMS-α- D-glucopyranose. The 4 E(D) envelope and 4 T 5(D) twist are the principal conformations of the D-fructofuranose rings. The conformation of the furanose ring depends on the number and kind of monosaccharide units attached thereto. The calculated, preferred conformation of the C-5-CH 2OTMS group of the D-fructofuranose moieties correlates with the time-averaged displacement of C-4 above the plane of C-2, C-3, and O-5.

The conformation of rifamycin S in solution by 1H NMR spectroscopy

The 1H NMR spectra of rifamycin S in different solvents and at different temperatures strongly suggest the existence of a dominant conformer. The nine dihedral angles of the ansa chain from C-28 to C-19, considered conformationally flexible, were obtained from the vicinal interproton coupling constants by the Karplus equation and the proper alternative for each of them compares well with the corresponding values given by X-ray analysis in solid state. All the possible conformations derivable from the intrinsic alternatives of the NMR method were calculated for the ansa chain between C-28 and C-19 and, by applying geometrical considerations, such as closure of the polygonal path of the ansa and the steric incompatibility between the various atoms of the ansa and of the chromophore, only two of them appeared real. Thus, NMR spectroscopy can be used for studying the conformation of the ansa chain of rifamycins in solution.