Coupled cluster singles

Photo Credit: Regina Valluzzi - Transition to Chaos

Coupled cluster singles

According to the previous notes the coupled cluster single (CCS) wavefunction has the form

where the single excitation operator replaces spinorbital \( I \) in determinant \( \Phi \) (an occupied) with an orbital \( A \) which does not occur in \( \Phi \) (an unoccupied or virtual spoinorbital) i.e.

\( t_I^A \) is the amplitude associated with the singly excited determinant \( \Phi_I^A \).

The CCS wavefunction is just a determinent wavefunction

We can carry out further simplifications to the equations above:

The second and third lines follows from the definition of the exponential function. The final line follows from the fact that

i.e. it is not possible to substitute spinorbital \( I \) more than once in determinant \( \Phi \).

In fact, the final line can be written as an unnormalized single determinant \( \Phi’ \) made from new spinorbitals \( \phi’\sub{I} \) like this,

This follows from the column expansion rule for determinants. Therefore the \( T_1 \) operator in the coupled cluster wavefunction causes a mixture of unoccupied spinorbitals into the reference orbitals,

The CCS wavefunction for a HF reference has zero amplitudes