Proton conpling constants -

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17 apri11999 1 Lecture 8 (l) Psendorotational Analysis of Vicinal Proton Proton conpling constants - (n) Application of PSEUROT program to the confonnational analysis of the pentofuranose moiety

aims of the lecture : I -What is Pseudorotation?

comparison with cyclopentane; w hy do pentofuranose moieties pucker?

1 17 apri Lecture 8 (l) Psendorotational Analysis of Vicinal Proton Proton conpling constants - (n) Application of PSEUROT program to the confonnational analysis of the pentofuranose moiety in nucleosides and nucleotides " (III) The quantification of stereoelectronic effects from the measurement of coupling constants -An example in the case of nucleosides and nucleotides. f"'.aims of the lecture : I -What is Pseudorotation? r (a) -Description of the concept of pseudorotation introduced for cyclopentane (b) -Influence of the endocyclic oxygen atom in pentofuranose moiety on its pseudorotation: Thermodynamic aspect; comparison with cyclopentane; w hy do pentofuranose moieties pucker? The preferred conforinations in the crystal structures of nucleosides and nucleotides; Their two-state North (N) South (S) equilibrium in solution II. Qualitative and quantitative prediction of the conforrnatiodal space described by the pentofuranose moiety in Ducleosides and nucleotides on the basis of experimentally measured 3JHH (PSEUROT PROGRAM): (a) -Information given by the experimentally measured 3JHH in the pentofuranose moiety of nucleosides and nucleotides

17 april 1999 2 Translation of proton-proton torsion angles into 3JHH (Karplus equation); The correction for the Barfield effect Principle of the calculation performed by PSEUROT program ; The

.i""' Lirnitatiofis of the scopes of applicatiofi of the pseudofotatiofial analysis; (' III- Stereoelectronic effects (a) -What are the stereoelectronic effects?

2 17 april Translation of proton-proton torsion angles into 3JHH (Karplus equation); The correction for the Barfield effect Principle of the calculation performed by PSEUROT program ; The thermodynamic properties of the two-state N S equilibrium of Ducleosides and nucleotides in solution from a PSEUROT analysis. How accurate is a pseudorotatiodal analysis?.i""' Lirnitatiofis of the scopes of applicatiofi of the pseudofotatiofial analysis; (' III- Stereoelectronic effects (a) -What are the stereoelectronic effects? --> the anomeric and gauche effects : origins, confomlational consequences. (b) The influence of the gauche and anomeric effects on the pseudorotational behaviour of nucleosides and nucleotides ---> the quantification of the gauche and anomeric effects in nucleosides and nucleotides from the measurement of vicinal proton-proton coupling constants r

17 april 1999 4 (b) Pseudorotation of the pentofuranose moiety in nucleosides and nucleotides.endo versus exo substituents on the pentofuranose moiety H5',-.

$2'-deoxyribonucleoside.Definition of sugar puckering modes : I'"""\ C5' \ C4.$

3 17 april (b) Pseudorotation of the pentofuranose moiety in nucleosides and nucleotides.endo versus exo substituents on the pentofuranose moiety H5',-./ H H5' " Endocyclic torsion angles : vihl' vo: [C4'-04'-Cl'-C2'] VI: [04'-Cl'-C2'-C3'] V2: [Cl'-C2'-C3'-C4'] V3: [C2'-C3'-C4'-04'] V4: [C3'-C4'-04'-Cl'] V2 R OH R = OH, ribonucleoside R = H, 2'-deoxyribonucleoside.Definition of sugar puckering modes : I'"""\ C5' \ C4.CI C3' 2T 3 C2' / N N C2' 3T 2 2T 3 Largest deviation from planarity -major puckering Lesser deviation from plannarity -minor puckering 3T2 represented twist in major C3' and minor C2' puckering and 23T represented twist in symmetrical form In cyclopentane canfarmatianal changes -nat via a planner intermediate hut maximum pucker ratates virtually without potential energy barrier giving rise ta infinite number af canfarmatians.

17 april 1999 5 In furanose with unsyffietrical substitution a potential energy thresholds are created which limits the pseudorotation and lead to preferred puckering ffiodes w(t (W) H {:H j1t!

4 17 april In furanose with unsyffietrical substitution a potential energy thresholds are created which limits the pseudorotation and lead to preferred puckering ffiodes w(t (W) H {:H j1t!o H r-- Preference of the pentofuranose rings in X-ray crystal structures ofnucleos(t)ides for N- and S-type conformations -nucleides [de Leeuw, Haasnoot & Altona lsr. J. Chem.1980, 20, 108] -1 < PN < 34,137 < Ps < 194 with 30 < 'l'm (N or S) < 46 a-nucleides [Swarna Latha & Yathindra Biopolymers 1992,32, 249] -18 < PN < 19,168 < Ps < 224 with 28 < 'l'm (N or S) < 49.The geometry of each individual pseudorotamer can be defined using two parameters:

5 17 apri > the Phase Angle of Pseudorotation P, which represents the part of the pentofuranose ring which is mostly puckered --> the Maximum Puckering Amplitude, \Jl m, which describes the extent of the puckering..p can be calculated from the sugar endocyclic torsion angles Vo -V4 :,,-..As far as the pentofuranose ring must be closed, the sum of endocyclic torsion angles defining its geometry is zero. Vo + VI + V2 + V3 + V4 = O.p and 'I' ffi can also be calculated from t wo known endocyclic torsions: rms error of the relation: structures) Vi = 'P ro cos [P + 47t(i-2)/5] therefore V2 = 'P ro cos(p) (1) (from 178 X-ray crystal r- - o '-' > - > - C";j > - - > - o > vo -.-V3 40 o p (.) Bach endocyclic torsion angle Vo...V 4 has been calculated assuming \.{1 m =35 constant over the whole range of Phase angles v 1 V2 v4.preferred hyperspace of conforinations in X-ray crystal structures of nucleosides and nucleotides : North (N) region: 00 < PN < 36 ; N sugars in A-type ONA

17 apri11999 7 South (S) region: 144 < Ps < 1800; S sugars in B-type ONA Only a few crystal structures in the East region of the Pseudorotation wheel, NONE in the West region; Average maximum

-Relative order of magnitude for the energy barriers in East and West regions : (OLSON, 1982) : ---> ribose : 3.8 kcal/mol and 7.5 kcal/mol respectively ---> 2'-deoxyribose : 1.8 kcal/mol and 5.

6 17 apri South (S) region: 144 < Ps < 1800; S sugars in B-type ONA Only a few crystal structures in the East region of the Pseudorotation wheel, NONE in the West region; Average maximum puckering amplitude : 'Pm = 38 :t4 I"--' Potential energy barriers created by the presence of heterocyclic nucleobase, OH and CH2OH substituents in the West and East regions W hy do pentoforanose moieties pocker? -Substituents ful ly eclipsed if the five-membered ring were planar (all torsions = D); -The energy barrler to the rotation around C-Q bond is smaller than that of a rotation around C-C bond; -Relative order of magnitude for the energy barriers in East and West regions : (OLSON, 1982) : ---> ribose : 3.8 kcal/mol and 7.5 kcal/mol respectively ---> 2'-deoxyribose : 1.8 kcal/mol and 5.8 kcal/mol, respectively -The East and West energy barriers can be explained by stereochemical considerations: --> C2' and C3' substituents fully eclipsed; --> The energy barrler in the West region is larger than that in the East region due to the steric hindrance generated by the relative positions of the nucleobase and 5'CH20H in the former. 2 state North (N) South (S) equilibrium experimentally evidenced by NMR observations of two distinctly identifiable and dynarnically interconverting N and S conformations (i.e. t wo sets of chemical shifts and 3JHH) of the constituent sugar moieties in oligonucleotides. I -Qualitative and quantitative prediction of the position of the conformational equilibrium in solution of five-membered rings AD applicatiod to Ducleosides (PSEUROT program)

the torsion an gles relevant for the prediction of the values of vicinal 3 J HH

projections : l'"-" NH2 OH rn N NH2 N OH l{ I N N OH H OH OH r- in

$vicinal 3 J HH H2' N(base) P4' V 1 \ C -IJ2" "1' View along C2'-Cl' H1 <1>1'2"$

7 17 april Vicinal3JHH couplings can be extracted from the lh spectra of nucleosides.the torsion an gles relevant for the prediction of the values of vicinal 3 J HH in the pentafuranose moiety of nucleosides can be represented using Newman projections : l'"-" NH2 OH rn N NH2 N OH l{ I N N OH H OH OH r- in 2'-deoxyadenosine : 5 vicina13jhh ( case of a S conformation) in Adenosine 3 vicinal 3 J HH H2' N(base) P4' V 1 \ C -IJ2" "1' View along C2'-Cl' H1 <1>1'2" Hi' View along C2'-C 1, r" <1>2'3' ci» 2.3( H2' n2" HO r V2 "'l' H2" HO View along C2'-C3' View along C2'-C3' <1>3'4' {;"3' C5' H4' H C2' 04'V3 View along C3'-C4' View along C2'-C I'

17 apri11999 9.The endocyclic torsion angles and the proton-proton torsion angles in the pentofuranose moiety are linearly related (from 178 X-ray crystal structures) : In 2'-deoxyribonucleosides <!

8 17 apri The endocyclic torsion angles and the proton-proton torsion angles in the pentofuranose moiety are linearly related (from 178 X-ray crystal structures) : In 2'-deoxyribonucleosides <!>1'2' = 1.03 VI <!>1'2" = 1.02 VI In ribonucleosides <!>1'21 = 1.10 VI (f)2'3' = 1.06 V (f)2"3' = 1.06 V <1>213'= 1.09 V <!>3'4' = 1.09 V3-124 <1>3'4' = 1.09 V The proton-proton torsion angles in the pentafuranose moiety of nucleosides depend on the Phase Angle of Pseudorotation as follows : ('Pm (N) = 'Pm(S) = 35 ) ---> for ribonucleosides x <1>1'2' = f (P) o l 50 J e o --50 N e -150,.<1>3'4' = f (P).I, I, I, I, I, N... N.N.., N.., N.,..... N ' -200 I I. I' I' I' I, o p (O). The proton-proton torsion angles can subsequently be transiated in 3JHH vicinai coupling constants using the EOS Karplus equation or the new Karplus equation developed later which is based on the A, substituent effect scale :

9 17 apri > EOS equation :, Dxj i=l- n (13 substituent) (3) ---> "A" substituents parameters as a basis of the latest Karplus equation : (4) Influence of the electronegativity of the substituents incorporated in the Ci and Si parameters as weil as the interactions between the substituents ---> The vicinal proton-proton coupling constants in 2'-deoxynucleosides and ribonucleosides are function of the Phase Angle of Pseudorotation at a fixed Puckering

17 apri11999 11 ribonucleosides : N conformers: as 'lim is increased, 312'3' becomes smaller, 313'4' becomes larger and 3 J 1 '2' is not affected.

. Assumption that the pentofuranose ring in nucleosides and nucleotides is involved in a two-state N S equilibrium.

$time scale): (5).The experimentally measured 3JHaHb(exp) are therefore function of the pseudorotatiodal parameters defining each of the N [i.e. PN and \}I m(n)] and S conformers [i.$

10 17 apri ribonucleosides : N conformers: as 'lim is increased, 312'3' becomes smaller, 313'4' becomes larger and 3 J 1 '2' is not affected. S conformers: 3 J 1 '2' becomes larger as 'II m is increased, 3 J 2'3' becomes smaller, whereas 313'4' remains unchanged.. Assumption that the pentofuranose ring in nucleosides and nucleotides is involved in a two-state N S equilibrium..the experimentally measured vicinal proton-proton coupling constants are time-average couplings retated to the couplings in each of the N and S conformers and their relative populations (on the NMR time scale): (5).The experimentally measured 3JHaHb(exp) are therefore function of the pseudorotatiodal parameters defining each of the N [i.e. PN and \}I m(n)] and S conformers [i.e Ps and \}I m(s)] and the molar fraction of olle of them: [the full expression can be obtained using the combination of equations (1), (2), (3) (or (4) in the second version of the program) and (5)].PSEUROT calclllates the best fit between the experimentai3jhahb(exp) (i.e. 5 for 2'deoxy, 3 for ribonllcleosides) and starting vallles provided by the llser as estirnates for the PN, 'P m(n), PS, 'P m(s) and xs pararneters. ---> Newton-Raphson rninirnization procedure including second derivatives.

11 17 apri ribonucleosides : N conformers: as 'lim is increased, 312'3' becomes smaller, 313'4' becomes larger and 3 J 1 '2' is not affected. S conformers: 3 J 1 '2' becomes larger as 'II m is increased, 3 J 2'3' becomes smaller, whereas 313'4' remains unchanged.. Assumption that the pentofuranose ring in nucleosides and nucleotides is involved in a two-state N S equilibrium..the experimentally measured vicinal proton-proton coupling constants are time-average couplings retated to the couplings in each of the N and S conformers and their relative populations (on the NMR time scale): (5).The experimentally measured 3JHaHb(exp) are therefore function of the pseudorotatiodal parameters defining each of the N [i.e. PN and \}I m(n)] and S conformers [i.e Ps and \}I m(s)] and the molar fraction of olle of them: [the full expression can be obtained using the combination of equations (1), (2), (3) (or (4) in the second version of the program) and (5)].PSEUROT calclllates the best fit between the experimentai3jhahb(exp) (i.e. 5 for 2'deoxy, 3 for ribonllcleosides) and starting vallles provided by the llser as estirnates for the PN, 'P m(n), PS, 'P m(s) and xs pararneters. ---> Newton-Raphson rninirnization procedure including second derivatives.

17 april 1999 12 program then recalculates 3JHaHb(calc) coupling constants and compares theffi to the experimental 3 J HaHb( exp ) to gi ve the rms of the pseudorotational analysis: I PSEUROT I

(2) IProton-Proton Torsion Angles f - Karplus-Altona Equation (3) ( 4) Two-state model I Theoretical time-averaged 3JIrn I (S) Comparison NO YES (6) Converged?

12 17 april program then recalculates 3JHaHb(calc) coupling constants and compares theffi to the experimental 3 J HaHb( exp ) to gi ve the rms of the pseudorotational analysis: I PSEUROT I Estirnates for P(N,S) 'I' m(n,s), Xsi Pseudorotation Concept (I) IEndocyclic Torsion Angles (vo- v =.- - AH & BH from ah initio calc. (2) IProton-Proton Torsion Angles f - Karplus-Altona Equation (3) ( 4) Two-state model I Theoretical time-averaged 3JIrn I (S) Comparison NO YES (6) Converged? Optirnized PN' Ps, 'I' m(n), 'I' m(s) and Xs values from multilinear lit c -How accurate is a pseudorotational analysis? 2'-deoxyribonucleosides : 1: 1 fit; ribonucleosides : 3 knowns, 5 unknowns, underdetermined system, at least two parameters used as initial estirnates for the optimization need

17 april 1999 13 to be fixed during the calculation.

random errors in the measured coupling constants tend to cancel each other; The N S equilibrium of the pentofuranose moiety in Ducleosides and nucleotides is shifted towards more N or S

13 17 april to be fixed during the calculation. 2) Variable-dependent 3JHaHb(exp) -Determination of the thermodynamic properties of the two-state N p S equilibrium of nucleosides and nucleotides in solution from a PSEUROT analysis. random errors in the measured coupling constants tend to cancel each other; The N S equilibrium of the pentofuranose moiety in Ducleosides and nucleotides is shifted towards more N or S conforinations as the temperature is lowered or increased which is obvious from their temperature dependent 1 H NMR spectra. exarnple lh spectrum of adenosine recorded at 500 Mhz at 75 C (pd = 6.5, 20 mm in D20) : 3) A unique or several possible solutions for one PSEUROT minimization? The selection of the starting estirnated vallles for PN, 'P m(n), PS, 'P m(s) parameters has a strong inflllence on : ---> the rms of the pseudorotatiodal analysis ---> Exarnple : Dependence of the rms of the analysis on the values selected for PN and Ps at t wo different puckered amplitudes for the N and S conformers : (a) \I' m (N) = \I' m(s) = 35, kept fixed during the optimization procedure; (b) \l'm(n) = \l'm(s) procedure; = 39.5, kept fixed during the optimization ---> Optimal geometries and calculated proton-proton coupling constants for the N and S conformers for the t wo optima determined from the calculations (b ):

17 april 1999 14 ---> Comparison of the experimental (3JHaHb(exp») and recalcnlated (3JHaHb(calc») vicinal conpling constants for the t wo optimal resnlting from

e < 20% ), it is advisable to constrain its Phase Angle and Puckering Amplitude to different values during several optimizations which will therefore mimic the

From this set of PSEUROT analyses, one can then extract ranges of acceptable values for the Phase Angle and the Puckering Amplitude of the major conformer.

14 17 april > Comparison of the experimental (3JHaHb(exp») and recalcnlated (3JHaHb(calc») vicinal conpling constants for the t wo optimal resnlting from the procedure (b): ---> If the population of one of the pseudorotalners is reduced (i.e < 20% ), it is advisable to constrain its Phase Angle and Puckering Amplitude to different values during several optimizations which will therefore mimic the influence of the ill defined geometry of this conformer on the calculation. From this set of PSEUROT analyses, one can then extract ranges of acceptable values for the Phase Angle and the Puckering Amplitude of the major conformer. ---> In the case where the t wo pseudorotamers are similarly populated, it can be envisaged to constrain their puckering amplitudes to the same value in a certain range which can be defined on the basis of other structural methods (i.e. for instance X-ray data) and to let the Phase Allgles of the t wo conformers being optimized

15 17 april during the calculation. The process can then be repeated by incrementing the values of both puckering amplitudes by 1 or a few degrees. D -Limitations of the scopes of application of the pseudorotational analysis; "' > Problem of the complexity of the 1 H spectra of oligonucleotides; the simplification of the 1 H spectrum can be achieved by partial isotope labelling of the oligomer; (see Lecture 19b ) f" III -Anomeric and Gauche effects : A) The definition of anomeric effect 1) The Edward- Lemieux effect In the pyranose ring, conformations in which the alkoxy groups at Cl are axial are generally more stable than those with equatorial substituents, although purely steric considerations would predict an opposite conformational preference. --- OCH3

17 april 1999 16 OCH3 f' f' Scheme 1 : The axial preference of exocyclic 1-methoxy substituent in 1- methoxypyranose (A) resulting from the O-C-O anomeric effect is the preponderant factor in the

16 17 april OCH3 f' f' Scheme 1 : The axial preference of exocyclic 1-methoxy substituent in 1- methoxypyranose (A) resulting from the O-C-O anomeric effect is the preponderant factor in the drive of the conformational equilibrium of this compound although purely steric interactions would predict an equatorial orientation of the exocyclic substituent as depicted for methoxycyc1ohexane in (B)..The Generalized anomeric effect. r The previous phenomenon is not restricted to six-membered rings or to carbohydrates: it can also be extended to the so-called "generalized anomeric effect" which defines the preference for the synclinal (gauche) over the antiperiplanar (trans) orientation in a R-X-A- y fragment, where A is an element of intermediate electronegativity (such as C, P, S), y denotes an atom more electronegative than A (such as O, Halogen or N), X is an element which possesses lone pairs, R is a substituent containing C or H.,, I y

17 april 1999 17 I y anti gauche > The extent of the anomeric preference increases as the electronegativity of the substituent increases and decrases as the steric effect of the y substituent

17 17 april I y anti gauche > The extent of the anomeric preference increases as the electronegativity of the substituent increases and decrases as the steric effect of the y substituent increases. 2) The Origin of the Anomeric Effect : (in R-X-A-Y fragment) Several explanations effect: have been advanced for the origin of the allomeric (a) Higher electrostatic repulsions resulting from unfavorable dipole-dipole interactions between the ring dipole generated by the unshared lone pairs of electrons on the endocyclic X element and the dipole oriented along the exocyclic A- y bond may destabilize the pseudoequatorial orientation of the y substituent and thereby favour conformations where it is pseudoaxially oriented; (b) Favorable overlap between a filled n electron pair of the X element and the vacant antibonding 0"* orbital of the A- y bond would result in the direct stabilization of the pseudoaxially oriented y substituent in terros of molecular orbital theory. This second alternative corresponds to the hyperconjugation of the X lone pairs to the exocyclic A- y bond in valence bond theory; of olle > The extent of stereoelectronic preference for axial conformations increases as the donating ability of the lone pair of the endocyclic X atom increases and as the exocyclic A- y bond becomes better acceptor.

18 17 april (a) Destabilization of equatorial substituents due to dipole-dipole repulsions in S confonnation " /""' " " N HO. - N North (N) sugar South (S) sug ar (bl) Stabilization of anomeric effect due to stabilizing n(o) O'*Cl'-N overlap - Hok"::J (b2) Stabilization of anomeric effect due to hyperconjugation effect () \\ N N- ),'. 0- HO -V. HO v' B) The gauche effect: 1) Definition The gauche effect describes the stabilization of the gauche over the trans orientation in X-C-C- Yfragments upon substitution of X and Y by electronegative groups. >. 5 aj > 'i "Q o Jt y o zy l-y A.E l' jf :.: ; ; ; ; : ;..,,, [X-C-C- Y] torsion angle f/' y

17 apri11999 19 The proportion of the preference for gauche orientations increases regularly in XCH2CH2Y (X, Y=halogen) when X and Y are changed from I to F, so that in the gas phase

19 17 apri The proportion of the preference for gauche orientations increases regularly in XCH2CH2Y (X, Y=halogen) when X and Y are changed from I to F, so that in the gas phase gauche-l,2-difluoroethane clearly predominates : The relative energy of the trans compared to the gauche conformer fo11ows a linear relationship : r where x represedts the electrodegativity scale. of X substituedt in the HuggiDS 2) Origins of the gauche effect : The gauche effect overcomes both unfavorable steric and dipolar repulsion interactions. Various explanations have been proposed for its origin : (a) Wolfe (1972) : nuclear-electron attraction between X and Y, which predominates over nuclear-nuclear and electron-electron repulsive temls. (b) stabilizing overlap between bonding and anti-bonding orbitals, as an extension of the hyperconjugation theory propos ed for the origin of the anomeric effect (Brunck and Weinhold, 1979): (a) Competitive 0'-0'* interactions FH H F) trans H H H H H -- - H+H F- H. F H gauche,.. O' C3'H3' O'* A 0"* x... x 0" C3'H3' (C) 1,2-difluoroethane : the gauche preference is due to the relative

. ;., 17 april 1999 20 destabilization of the trans form owing to more severely bent bonds and reduced bond overlap.

20 . ;., 17 april destabilization of the trans form owing to more severely bent bonds and reduced bond overlap. Bond-bending in 1,2-difluoroethane fragments is directly proportional to the electronegativity of X and y substituents. (Wiberg, 1990). III -The influence of the anomeric and gauche effects on the conformational equilibrium of nucleosides and nucleotides : A) Predictioll of the illfluellce of the allomeric effect of the Ducleobase Oll the bias of the two-state North (N) South (S) equilibrium of the pelltofurallose moiety ill Ducleosides : f' The anomeric effect in nucleosides is induced by the presence of the nucleobase at Cl' and it is maxiffiallyachieved when the conformation of the pentafuranbose moiety belongs to the East portion of the pseudorotational wheel, as in this situation one of the lone pairs of the endocyclic oxygen of the pentafuranose moiety is fully antiperiplanar to the exocyclic glycosidic C- N bond. However, due to the large steric hindrance generated by the relative positions of the exocyclic S'CH20H and nucleobase substituents in the se conformations, the existence of E-type sugar pseudorotaffiers are prevented. The anomeric effect therefore acts with is maximal strength in N- type pseudorotamers. B) The influence of various gauche effects on the pseudorotation of the sugar moiety in nucleosides and nucleotides : r ;-.. In 2'-deoxynucleosides: GE [03'-C3'-C4'-04'] favours S-type conformation In ribonucleosides: GE [03'-C3'-C4'-04'] favours S-type conformation and GE [02'-C3'-C4'- 04'] favours N-type conformation GE [02'-C3'-C4'-N] favours S-type conformation C) The quantification of the relative strengths of various stereoelectronic effects driving the pseudorotation of the sugar moiety in Ducleosides and nucleotides : The previous stereoelectronic effects can be quantified by (i) The temperature-dependent ffieasurement of proton-proton endocyclic coupling constants for the sugar moiety, which can be ultimately successfully transiated in the relative populations of the N- and S-type pseudorotaffiers using the PSEUROT program [see Lecture 8(1) & (II)]. (ii) The thermodynamics of the two-state N p S equilibrium can then be determined through van't Hoff plots of the molar fractions of the N and S

'. 17 apri11999 21 pseudorotaffiers as a function of the inverse of the temperature, which gives both the enthalpy and entropy contributions to the free-energy of this equilibriuffi as the latter

21 '. 17 apri pseudorotaffiers as a function of the inverse of the temperature, which gives both the enthalpy and entropy contributions to the free-energy of this equilibriuffi as the latter parameter can be derived from the Gibbs relation : (iii) Therefore, the comparisoll of the thermodyllamic properties of the sugar moieties of various Ducleosides and Ducleotides hearing olle, t wo or more exocyclic suhstituents ellahles to calculate the illdividual stereoelectronic contrihutions to the free-energy of the pseudorotatiodal equili hri um. (\ r-" "'

Stereochemical Considerations in Planning Synthesis

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