Equilibrium structures have been obtained for molecules of general type Me 3− n H n M–NXY, where the central atoms M are Ge, Sn and Pb, while XY is NN, CO and CS, and n=0 or 3, using Möller–Plessett (MP2) or density functional (B3LYP) calculations. The structures have been compared with experimental spectral and diffraction results, and with the corresponding molecules where M is C and Si. Some differences between the structural parameters between these two methodologies are discussed in relation to known rotation constants for these and related heavy atom molecules. The results show that the MP2 values for B (in C 3 V ) or B and C (in C S symmetry molecules) are always lower than the experimental ones, with the B3LYP series even lower; the reverse occurs with the A rotation constants, but there are few ‘ A values’ for comparison in this series. Thus, in cases where the equilibrium structure is determined either to assist experimental data interpretation (as in electron diffraction), or to predict the results of non-existent spectral data, the MP2 method is to be preferred over B3LYP. The effects upon individual bond lengths are relatively small, but the extra fine tuning of the MP2 results seems clear for these compounds. The variations in the ratios of NX to XY are discussed for these and related molecules, and the effects of electronegativity discussed. The basis sets used for the substituent H, C, N, O atoms were of triple zeta quality with polarisation functions. The atoms Ge, Sn and Pb were represented by new large bases, containing mainly uncontracted functions, and relatively close to the Hartree–Fock limiting energies. Most published bases for these large atoms use either effective core potentials, which cannot allow core polarisation, or highly contracted GTOs which are unsuitable for determination of molecular properties such as electric field gradients of the compounds (as described in a following paper).