How can we combine the 1s atomic orbitals from two atoms to obtain two molecular orbitals? Recall that the electron density or probability clouds that we have been using are the squares of wave functions, which came out of quantum theory. It is these wave functions, not the probability clouds themselves, that are combined into molecular orbitals. The probability clouds always are positive (probabilities for anything only can be positive or zero), but different parts of the wave functions can have positive or negative signs. These signs are important in deciding whether and how a given pair of AO's can be combined. There are two ways of combining two 1s atomic orbitals in the hydrogenlike molecules: with the same sign on the two wave functions, or with opposite signs. This amounts to adding the two wave functions or subtracting one from the other, which leads to the electron densities shown at the right. If the wave functions are added, the resulting molecular orbital has a pileup of electron density between the nuclei. When a pair of electrons is placed in this orbital, the negative charge on the electrons attracts both nuclei, and shields each nucleus from repulsion by the other. This is the electron- pair bond introduced in Chapter 4. This (ls~ + Is) MO is called a bonding orbital because electrons placed in it help to hold the nuclei together. Two electrons in such a bonding orbital are more stable (lower energy) than one electron in each of the two isolated atomic orbitals.