J. theor. Biol. (1978) 72, 751-756



An Ab Initiu Reinvestigation of PC and PH Coupling Constants in Phosphates In a previous study (Giessner-Prettre & Pullman, 1974), we have calculated, by the finite perturbation method within the INDO approximations, the conformational dependence of PC and PH spin-spin coupling constants in ethylphosphate taken as a model compound for these couplings in nucleotides. Some of the results obtained were surprising. The calculated values of the three-bond vicinal POCC and POCH coupling constants were negative for the trans-planar arrangement of the four atoms concerned while there is, to our knowledge, no experimental evidence of negative vicinal coupling constants between two atoms having positive nuclear moments. In addition we found a strong dependence of the two-bond POC coupling constants upon the rotation angle about the PO bond [angle o in Sundaralingam’s notation (1973)]. Since the experimental values reported in the literature for this type of coupling constants in nucleotides, polynucleotides and related compounds are all within the range of 4.3-5-4 Hz (Man&h & Smith, 1972; Smith, Mantsch, Lapper & Schleich, 1973; Kotowycz & Hayamizu, 1973; Schleich, Cross, Blackburn & Smith, 1975; Schleich, Cross & Smith, 1976; Alderfer & Ts’o, 1977; Morr, Kula & Ernst, 1975) with the only exception of the cyclic nucleotides in which the variation can be attributed to particular structural and geometrical reasons (Smith et al., 1973; Lapper, Mantsch & Smith, 1973; Lapper & Smith, 1973) our result implies a remarkable constancy of the values of o and o’ in solution for the different non-cyclic nucleotides and polynucleotides studied. We felt that because of the strong implication that they have on the interpretation of the experimental data these results needed a reinvestigation. Thus we undertook the computation of 2Jpoc, 3Jwcc and 3JpocH in few model cases by an ab initio SCF method which does not present the possible artefacts that can appear in a semiempirical procedure like INDO. The contact contribution to the coupling constant is calculated by the double perturbation method developed by Barbier, Gagnaire, Berthier & Levy (1971). In this method the third order term which takes into account the first order of the electronic correlation is added to the second order 751


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perturbation term which is obtained from the LCAO SCF MO’s. The coupling constant between nuclei A and B is given by: with

+ c



(olQoIw(~l L

q~xJqw)lo) -___.(EN-Eo)(EL-Eo)


where 8(A) is the contact term of the theoretical development of Ramsey, V is the two electron interaction operator, N and L are triplet singly excited states and M singlet doubly excited states. The computations have been carried out with the ST0 3G basis set. As the calculated values of coupling constants are quite sensitive to the basis set utilized (Barbier et al., 1975; Giessner-Prettre & Pullman, unpubl.) we report in Table 1 the values of the different coupling constants in ethane, ethylene, PH, and PH:. They illustrate on classical examples the order of magnitude of the results obtained by this type of computation. In every case the calculated value of the coupling constant is smaller than the experimental one. With the exception of the ‘JHH in ethylene the ratio JcdJexp. is greater than two but the comparison of the calculated and TABLE 1

Coupling constants (in Hz) in small reference molecules

Ethane Ethylene Ph+ PI-L

talc [email protected]) talc expcbj talc exp”) talc exp”)





3Jmtrans ‘JHH

12.7 34.6 28.3 67.6

55.8 124.9 71.4 156.2 203.3’@ 548-O”’ 76.0”’ 182*0’“’

-1.5 -4.5 -0.3 -2.4


5.9 g .(y”’ 8.6 19.1

2.4 2.5

1 .(p 3.5’0 11.5(d)

(a) gauche vicinal coupling; (b) from Lynden-Bell & Sheppard (1962) and Graham & Halloway (1963); (c) average of the trans and gauche values; (d) cis vicinal coupling; (e) ‘JpH coupling constant; (f) from Sheldrick (1967).






experimental values shows that the theory is able to reproduce qualitatively all the variations measured between the different coupling constants. The calculated values of the PC and PH coupling constants in the gg (w = w’ = 60”) and the gt (o = 60”, w’ = 180”) conformations of dimethyl phosphate, a typical model compound for phosphodiester linkages, reported in Table 2 show that 2Jpo, is much larger in magnitude for w = 60” than for w = 180”. The variation reported here is similar to the one that we obtained with the semiempirical method but the range of the variation is greatly reduced. The calculated values are smaller than the experimental ones which are of about 5 Hz, as in the examples of Table 1. The calculated variations show that there is a conformational dependence of the two-bond POC coupling constants upon the torsion angle about the PO bond and that the values of o and o’ in non-cyclic nucleotides in solutions are constant at least as a time average since there seems to be experimental evidence about the flexibility of conformations of nucleotides in solution (Evans & Sarma, 1976). Previously the conformational dependence of the two-bond coupling constants has been studied mainly on geminal proton-proton couplings (Maciel, McIver, Ostlund & Pople, 1970; Renaud, Bovenkamp, Fraser & Capoor, 1977; Aminova & Samitov, 1974; Barfield, Hruby & Meraldi, 1976); the present results tend to show that this behaviour is most probably valid for all two-bond coupling constants although the conformational parameter which determines this behaviour is not for the moment as clearly established as in the case of vicinal couplings. The present calculations confirm the negative sign that we have found previously for ‘Jpoc (GiessnerPrettre & Pullman, 1974). The conformation of the methyl groups of the dimethylphosphate molecule has been chosen such that one of hydrogens and the phosphorus are trans with respect to the CO bond; consequently the two other hydrogens of the methyls are gauche to phosphorus. The values reported in Table 2 show that for q = 180” 3JpocH are by an order of magnitude smaller than those obtained semiempirically, and that presently the calculated trans coupling constant is positive and no more negative as in the semi‘JPOCH empirical treatment. In this case also the computed value is smaller than the experimental ones which lie in the range 4-10 Hz (Singh, Herbut, Lee & Sarma, 1976). In order to determine if the discrepancy of sign between the two methods is specific for 3JpocH, we undertook the calculation of the coupling constants of ethyl phosphate which presents a 3Jpocc coupling constant. For this anion we have chosen the conformation with o = 60” about the PO bond and cp = 180” about the CO bond. As in the case of 3JpocH of dimethylphosphate, the present results indicate a positive value for the trans three-bond




Calculated .Ipc and JpHcoupling constants(in Hz) itI dimethylphosphate(DMP-) and ethylphosphate anions 2JPOC =JPoc 3JKlCH 3Ji=OCH (0=6oo,(o) (w=1309(a’c*=18cl’,((L)

An ab initio reinvestigation of PC and PH coupling constants in phosphates.

J. theor. Biol. (1978) 72, 751-756 LETTERS TO THE EDITOR An Ab Initiu Reinvestigation of PC and PH Coupling Constants in Phosphates In a previous s...
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