Calculated nuclear shielding surfaces in the water molecule; prediction and analysis of σ(O), σ(H) and σ(D) in water isotopomers

Abstract

Ab initio, internal valence coordinate oxygen and hydrogen nuclear shielding surfaces for the water molecule are presented. Calculations have been performed at the MCSCF level of theory using gauge-including atomic orbitals and a large basis set. The shielding at each of 37 points on the oxygen surface and 49 points on the hydrogen surface was calculated. The results were fitted to Taylor series expansions and are reported to second order in the coordinates. The correlated proton surface is little different from a coupled Hartree-Fock surface calculated some time ago but the oxygen surface is changed considerably by the inclusion of electron correlation. The surfaces have been averaged over the nuclear motion using a very recent, highly accurate force field to give values of σ(O), σ(H) and σ(D) for selected isotopomers over a range of temperature. For the oxygen shielding the dominant nuclear motion contribution comes from the first order stretching term which is deshielding as is normally the case. Important contributions are also made by the second order stretching term (also deshielding) and the second order bending term (which gives greater shielding). For low density H2 17O vapour at 300 K the calculated oxygen shielding of 333.723 ppm is in good agreement with an experimental value of 344 (±17) ppm. The 17O-isotope shifts of HD17O and D2 17O relative to H2 17O are calculated to be 1.356 ppm and 2.697 ppm which are in excellent agreement with recently observed liquid-phase values of 1.4203(1) ppm and 2.8324(1) ppm. The very slight non-additivity in these figures comes predominantly from the second order bending contribution. Expressions for the temperature dependence of the absolute oxygen and proton shielding in low density water vapour are proposed in the absence of experimentally determined ones. The calculated proton shielding at 300 K is 30.232 ppm which is in very good agreement with the experimental value of 30.052(15) ppm. The negative nuclear motion corrections to the proton shielding are almost entirely governed by the stretching of the OH bond containing the proton with the second order term partially cancelling the first order term. The proton isotope shift of HD16O with respect to H2 16O is calculated to be 0.039 ppm at 300 K; this is close to the value of 0.0304(1) ppm observed in solution. A recent experimental value for the temperature dependence of the H2 16O/H2 18O proton isotope shift occurring in the sixth significant figure of shielding is too small to be calculated with the present level of accuracy.