In the adiabatic approximation, when discussing the motion of the two electrons in the two H atoms we can treat the distance between the nuclei as fixed and consider only the wave functions of the motion of the two electrons. For total spin S = 1, the total spin wave function is symmetric for interchange of the two electrons and so the total space wave function is antisymmetric. Pauli's principle requires the electrons, which in this case have parallel spins, to get away from each other as far as possible. This means that the probability for the two electrons to come near each other is small and the states are repulsive states. As S = 1 there are three such states. For total spin S = 0, the space wave function is symmetric. The probability of the electrons being close together is rather large and so the state is an attractive one. As S = 0, there is only one such state.
