Title: Summary Linear Combination of Atomic Orbitals (LCAO)

Choose the correct statement.

- The energy levels of molecular orbitals can be calculated from the linear combination of atomic orbitals. (correct)
- The energy levels of crystal orbitals can be calculated from the linear combination of atomic orbitals.

- In the variation method, one guesses an initial trial wavefunction and then varies its adjustable parameters to minimize the expectation value of the energy. (correct)
- In the variation method, one guesses an initial trial wavefunction and then varies its adjustable parameters to minimize the expectation value of the position.

- ß gives a measure of the interactions (overlap) between two atomic orbitals in the environment of a molecule, and therefore it is 0 for orthogonal orbitals. (correct)
- ß gives a measure of the interactions (overlap) between two atomic orbitals in the environment of a molecule, and therefore it is maximum for orthogonal orbitals.

- By solving the secular equations, one can find the energies for the combination of atomic orbitals. (correct)
- By solving the secular equations, one can find the energy for the bonding case as a result of the linear combination of atomic orbitals.

- The molecular orbitals formed from the combination of s orbitals are called σ orbitals (bonding and anti-bonding). (correct)
- The molecular orbitals formed from the combination of s orbitals are called π orbitals (bonding and anti-bonding).

- Interactions between p orbitals are more complicated. The p orbitals that point directly towards each other along the bond direction interact strongly with each other and form a strong σ orbital. The interaction between the p orbitals oriented perpendicular to the bond direction is weaker. The molecular orbitals formed from these orbitals are the π orbitals. (correct)
- Interactions between p orbitals are more complicated. The p orbitals that point directly towards each other along the bond direction interact strongly with each other and form a strong π orbital. The interaction between the p orbitals oriented perpendicular to the bond direction is weaker. The molecular orbitals formed from these orbitals are the σ orbitals.

- When the two atoms in a covalent bond are not the same, their on-site integrals (α) are not the same. As a result, their contribution to the bonding and anti-bonding molecular orbitals are no longer equal. The bonding molecular orbital will mostly present the character of the more electronegative atom. (correct)
- When the two atoms in a covalent bond are not the same, their on-site integrals (α) are not the same. As a result, their contribution to the bonding and anti-bonding molecular orbitals are no longer equal. The bonding molecular orbital will mostly present the character of the less electronegative atom.

- When extending LCAO theory to bands in solids, the band is then described by a Bloch function, which consists of the cell function multiplied by a complex exponential. (correct)
- When extending LCAO theory to bands in solids, the band is then described by a Dirac function, which consists of the cell function multiplied by a complex exponential.

- The band structure shows the energy as a function of k. The bandwidth is then calculated as the difference in energy between the two extreme k values. (correct)
- The band structure shows the density of states as a function of energy. The bandwidth corresponds to the difference between the maximum and the minimum energy.