I N T R O D U C T I O NThat nuclear spin-spin coupling constants are often very dependent on interbond angles has been known for many years.' Attention has been largely devoted to vicinal coupling constants and there is still lively interest in this area., However, the angle dependence of geminal coupling constants has also been of interest. In this paper we report the results of accurate calculations of the dependence of the coupling constant 2J(H,, H2) of the methane molecule on the interbond angle HI-C-H,.Our primary aim was to carry out a definitive calculation of the angle dependence of this coupling, subsequently denoted J ( 1, 2), which would lead to a simple equation from which J(1, 2) could be predicted for any angle not only for methane but, hopefully to a high degree of accuracy, for any methylene group involving an sp3-hybridized carbon atom. In the process of calculation, however, we also obtained all other coupling constants of the methane molecule for a set of variations of the HI-C--H, angle which leaves the molecule with C,, symmetry. They are the carbonproton coupling constants J(C, 1) = J(C, 2) and J(C, 3) = J(C, 4) and the other two proton-proton coupling constants J(1, 3) = J(1, 4) = 4 2 , 3) = 4 2 , 4) and 4 3 , 4).