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,