The Ansatz

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The Ansatz

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The coupled cluster wave function is given by

| $\displaystyle \Psi_{{\rm CC}}^{}$ $\displaystyle \rangle$ = e| $\displaystyle \Psi_{0}^{}$ $\displaystyle \rangle$

(12)

with $\hat{T}$ = $\hat{T}_{1}^{}$ + $\hat{T}_{2}^{}$ +... and

$\displaystyle \hat{T}_{1}^{}$	=	$\displaystyle \sum_{{ia}}^{}$ t_i^a $\displaystyle \hat{a}_{a}^{\dagger}$ $\displaystyle \hat{a}_{i}^{}$
$\displaystyle \hat{T}_{2}^{}$	=	$\displaystyle \sum_{{ijab}}^{}$ t_ij^ab $\displaystyle \hat{a}_{a}^{\dagger}$ $\displaystyle \hat{a}_{b}^{\dagger}$ $\displaystyle \hat{a}_{i}^{}$ $\displaystyle \hat{a}_{j}^{}$
	$\displaystyle \vdots$

the cluster operator. Inserting (13) into the Schrödinger equation we obtain

$\displaystyle \hat{H}$ e| $\displaystyle \Psi_{0}^{}$ $\displaystyle \rangle$ = Ee| $\displaystyle \Psi_{0}^{}$ $\displaystyle \rangle$ .

(13)

Multiplying by e^- yields

e^- $\displaystyle \hat{H}$ e| $\displaystyle \Psi_{0}^{}$ $\displaystyle \rangle$ = E| $\displaystyle \Psi_{0}^{}$ $\displaystyle \rangle$ .

(14)

Projecting (15) onto $\langle$ $\Psi_{0}^{}$ | and substituted determinants we get non-linear equations for the energy E and the amplitudes t_i^a, t_ij^ab, ... respectively.

Michael Hanrath 2008-08-13