General Symmetry Stuff

Question 1

What’s the equation that calculates how many of each irreducible representations are in a reducible representation?

Answer 1

n(irreducible)= (1/h) x sum of: character in reducible representation, character in irreducible representation, and number of symmetry operations in a given class

Question 2

What does LCAO stand for?

Answer 2

Linear combinations of atomic orbitals

Question 3

Why could energies of bonding orbitals be lowered and energies of anti bonding orbitals be raised more than expected?

Answer 3

S-P mixing. Essentially the S and P orbitals on different atoms interfere with each other either constructively or destructively.

Question 4

What does SALC stand for?

Answer 4

Symmetry adapted linear combination

Question 5

What is the equation for finding a SALC using the projection operator method?

Answer 5

(1/root(a^2 + b^2 + c^2))×(asigma1 + bsigma2 + csigma3)

Question 6

If asked to find the SALC of a particular sort of orbital in a molecule according to a particular irreducible representation, how would you go about doing so?

Answer 6

Assign each orbital to sigma1, sigma2 etc and draw a table that shows where sigma1 would end up in each case under the given symmetry operations decided by the point group of the molecule. Multiply each sigma value by the corresponding numbers of the irreducible representation and plug into the projection operator method.

Question 7

For the SALC equation, what do the coefficients of each sigma value mean and also what do the signs in front of them mean?

Answer 7

The coefficients give relative sizes of the corresponding orbitals
The signs show whether the orbitals are in phase or out of phase.