Operators permutation

However, to construct the appropriate linear combinations of the n orbitals, it is sufficient to choose a subgroup of > whose symmetry operations permute all... 

Invariant operators, permutational symmetry, conical intersection, adiabatic state, 735-737... 

The regular orbit of a point symmetry group is the set of positions for which the only operation that leaves each vertex label invariant is the identity all other operations permute... 

To maintain full antisymmetry of an amplitude, the algebraic expression for a diagram should be preceded by a permutation operator permuting the open lines in all distinct ways, 2P(— )pP. 

When we apply permutations (or other symmetry operations) successively (this is commonly referred to as multiplying the operations so that (31) is the product of (123) and (12)), we write the operation to be applied first to the right in the manner done for general quantum mechanical operators. Permutations do not necessarily commute. For example. 

Since each methane symmetry operator permutes the hydrogen Is orbitals among themselves, (15.42) is sent into itself by each symmetry operation and belongs to the totally symmetric species Aj. We need three more symmetry functions. The construction of these is not obvious without the use of group theory, and we shall simply write down the results. The remaining three orthogonal (unnormalized) symmetry-adapted basis functions can be taken as... 

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