What is meant by 'linear combinations of atomic orbitals' in molecular orbital theory?

In molecular orbital theory, the concept of 'linear combinations of atomic orbitals' refers specifically to the process of combining the wave functions of atomic orbitals from the same atom to create molecular orbitals. This is fundamentally accomplished by taking similar types of atomic orbitals, such as s, p, or d orbitals, and mathematically combining them through the use of coefficients.

The resulting molecular orbitals can be classified as bonding or antibonding, depending on how the atomic orbitals interfere with each other. When the wave functions are added constructively, this leads to lower-energy bonding molecular orbitals. Conversely, destructive interference results in higher-energy antibonding molecular orbitals. This method allows for the prediction of the electronic structure and properties of molecules based on the combination of their constituent atomic orbitals.

The other options do not fully capture the essence of the concept. For example, combining orbitals from different atoms is involved in molecular orbital formation, but it is the linear combination of atomic orbitals from the same type that primarily determines the resulting molecular orbitals. Thus, focusing on similar types of atomic orbitals and their coefficients is the accurate depiction of what 'linear combinations of atomic orbitals' entails in molecular orbital theory.