When constructing molecular orbitals from atomic orbitals, the consideration of only fully in-phase (+ and +) or fully out-of-phase (+ and -) combinations is a simplification based on the concept of constructive and destructive interference.
In molecular orbital theory, atomic orbitals combine to form molecular orbitals through a process called linear combination of atomic orbitals (LCAO). When two atomic orbitals overlap, their wave functions combine, resulting in the formation of molecular orbitals. The combination can either be constructive or destructive, depending on the relative phase of the wave functions.
Constructive interference occurs when the wave functions of the atomic orbitals have the same sign (+ and +) and align in-phase. In this case, the resulting molecular orbital has a higher electron density between the nuclei, making it stable and called a bonding molecular orbital (σ or π bond).
Destructive interference occurs when the wave functions of the atomic orbitals have opposite signs (+ and -) and align out of phase. In this case, the resulting molecular orbital has a node, or a region of zero electron density, between the nuclei. This molecular orbital is less stable and referred to as an antibonding molecular orbital (σ* or π* antibond).
The consideration of other smaller phase shifts, such as partial constructive or partial destructive interference, would introduce additional variations in electron density and energy distribution, making the analysis more complex. The simpler approach of considering only fully in-phase or fully out-of-phase combinations is sufficient to explain the general behavior of molecular orbitals and their effects on chemical bonding.
It is worth noting that the concepts of bonding and antibonding molecular orbitals are derived from the mathematical treatment of wave functions and the resulting electron density distributions. These concepts provide a useful framework for understanding molecular properties and reactivity but should not be interpreted as physical entities with localized positions in space.