We developed the ab initio linear combination of Gaussian type orbital program with a generalized Hartree–Fock–Slater (GHFS) functional and calculated the four hydrogen clusters as models of the noncollinear magnetic clusters. We found that the GHFS solutions with the three-dimensional noncollinear spin structure is the ground state near the Td conformation. Computational results are compared with those of the ab initio generalized Hartree–Fock functional and the differences between them are discussed. Implications of the calculated results are discussed in relation to the electronic structures of Fe4S4 and Mn4O4 clusters. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 664–671, 2000