# Expression for an expanded configuration interaction wave function

I am trying to write down an expanded expression for the configuration interaction wave function. We know that the wave function $\Psi$ is a linear combination (LC) of configuration state functions (CSF), each CSF is a LC of Slater determinants, each determinant is an antisymmetrized product of molecular orbitals (MO's), and each MO is a LC of basis functions (BF). Without saying anything about the antisymmetrizer operator $\mathcal{A}$, are the equations below in general correct? What would the expanded wave function $\Psi$ look like? I have trouble putting the expression for the MO's into the expression for the determinants.

\begin{align} \Psi &= \sum\limits_{i} c_i ( \text{csf} )_i \\ \text{csf} &= \sum\limits_{j} d_j ( \text{det} )_j \\ \text{det} &= \mathcal{A} \prod\limits_k (\text{mo})_k \\ \text{mo} &= \sum\limits_{l} e_l (\text{bf})_l \\ \end{align}

• What about simply doing $\Psi=\sum_i c_i \mathcal{A} \prod_k (\text{mo})_k$ ? Your equations are fine, but 2 remarks: 1. CSF: Unless you want to go into details about how spin is treated, you can skip the CSF step. It is just a way to couple certain CI coefficients together. $\Psi=\sum_i d_j (\text{det})_j$ is true as well. 2. indices: Since you usually have more than one MO/Determinant (or wave functions in case of excited states) it is common write these equations with one more index, e.g. $\text{mo}_j=\sum_i c_{ij}(\text{bf}_i$ – Feodoran May 29 '17 at 20:57