Ab initio calculated coordinate and internal valence coordinate coefficients for each of the four spin-spin coupling surfaces of the acetylene molecule-(1)J(C, H), (1)J(C, C), (2)J(C, H), and (3)J(H, H) are presented. Calculations were carried out at the SOPPA(CCSD) level using a large basis set. Couplings were calculated at 35 geometries (including equilibrium) giving 35 distinct sites on the (1)J(C, C) and (3)J(H, H) surfaces and 53 distinct sites on the (1)J(C, H) and (2)J(C, H) surfaces. The results were fitted to fourth order in Taylor series expansions and are presented to second order in the coordinates. All couplings are sensitive to geometry with the principal features being (a) an even steeper increase of J(C-1, H-1) with CC bond stretching than with CH bond stretching-an example of "unexpected differential sensitivity" (or UDS), (b) very opposite variations of (2)J(C-1, H-2) with variations of the CC and C2H2 bond lengths, (c) very opposite variations of (1)J(C, C) with a CC stretch and a CH stretch and (d) very opposite variations of (1)J(C-1, H-1) with variations of the H1C1C2 and C1C2H2 angles with the latter variation being three times more effective (another example of UDS). The surfaces are averaged over a very accurate force field to give values of all couplings in 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. The dominant nuclear motion effect comes from bending at the carbon atoms with stretching being of greater importance only for (1)J(C, H). Agreement with recent experimental data both for the absolute values of the couplings and for isotope effects on them is generally very good although there are some disappointments for (1)J(C, H). Values of the reduced coupling constants and their derivatives for the carbon-carbon and the one-bond carbon-proton coupling in acetylene are compared with recent results for some other molecules. (C) 2000 American Institute of Physics. [S0021-9606(00)30207-0].