Nuclear magnetic shielding in the acetylene isotopomers calculated from correlated shielding surfaces

Ab initio, symmetry-coordinate and internal valence coordinate carbon and hydrogen nuclear shielding surfaces for the acetylene molecule are presented. Calculations were performed at the correlated level of theory using gauge-including atomic orbitals and a large basis set. The shielding was calculated at equilibrium and at 34 distinct geometries corresponding to 53 distinct sites for each nucleus. The results were fitted to fourth order in Taylor series expansions and are presented to second order in the coordinates. The carbon-13 shielding is sensitive to all geometrical parameters and displays some unexpected features; most significantly, the shielding at a carbon nucleus (C-1, say) is six times more sensitive to change of the C1C2H2 angle than it is to change of the H1C1C2 angle. In addition, for small changes, sigma(C-1) is more sensitive to the C2H2 bond length than it is to the C1H1 bond length. These, and other, examples of "unexpected differential sensitivity" are discussed. The proton shielding surface is much more as expected with sigma(H-1) being most sensitive to the C1H1 bond length, less so to the CC bond length and hardly at all to the C2H2 bond length. The surfaces have been averaged over a very accurate force field to give values of sigma(C), sigma(H), and sigma(D) for the ten isotopomers containing all possible combinations of C-12, C-13, H-1, and H-2 nuclei at 0 K and at a number of selected temperatures in the range accessible to experiment. For the carbon shielding the dominant nuclear motion contribution comes from the bending at "the other" carbon atom with the combined stretching contributions being only 20% of those from bending. For the proton shielding it is the stretching of the CH bond containing the proton of interest which provides the major nuclear motion contribution. For sigma(C) in (HCCH)-C-13-C-13 at 300 K our best result is 117.59 ppm which is very close to the experimental value of 116.9 (+/- 0.9) ppm. For sigma(H) in (HCCH)-C-13-C-13 at 300 K we obtain 29.511 ppm which is also in very close agreement with the experimental value of 29.277 (+/- 0.001) ppm. Calculated values are also very close to recent, highly accurate carbon and proton isotope shifts in the ten isotopomers; carbon isotope shifts differ by no more than 10% from the measured values and proton isotope shifts are generally in even better agreement than this. The observed anomaly whereby the C-13 isotope shift in (HCCD)-C-13-C-12 is greater than that in (DCCH)-C-13-C-12 both with respect to (HCCH)-C-13-C-12 is explained in terms of the bending contribution at "the other" carbon. The observed nonadditivity of deuterium isotope effects on the carbon shielding can be traced to a cross term involving second order bending. (C) 2000 American Institute of Physics. [S0021-9606(00)30401-9].