# 7.8.4 EOM-DIP-CCSD

Double-ionization potential (DIP) is another non-electron-conserving variant of EOM-CCSD.998, 507, 508 In DIP, target states are reached by detaching two electrons from the reference state:

 $\Psi_{k}=R_{N-2}\Psi_{0}(N+2),$ (7.48)

and the excitation operator $R$ has the following form:

 $\displaystyle R$ $\displaystyle=$ $\displaystyle R_{1}+R_{2},$ (7.49) $\displaystyle R_{1}$ $\displaystyle=$ $\displaystyle 1/2\sum_{ij}r_{ij}ji,$ (7.50) $\displaystyle R_{2}$ $\displaystyle=$ $\displaystyle 1/6\sum_{ijka}r_{ijk}^{a}a^{\dagger}kji.$ (7.51)

As a reference state in the EOM-DIP calculations one usually takes a well-behaved closed-shell state. EOM-DIP is a useful tool for describing molecules with electronic degeneracies of the type “$2n-2$ electrons on $n$ degenerate orbitals”. The simplest examples of such systems are diradicals with two-electrons-on-two-orbitals pattern. Moreover, DIP is a preferred method for four-electrons-on-three-orbitals wave functions.

Accuracy of the EOM-DIP-CCSD method is similar to accuracy of other EOM-CCSD models, i.e., 0.1–0.3 eV. The scaling of EOM-DIP-CCSD is ${\cal{O}}({N^{6}})$, analogous to that of other EOM-CCSD methods. However, its computational cost is less compared to, e.g., EOM-EE-CCSD, and it increases more slowly with the basis set size. An EOM-DIP calculation is invoked by using DIP_STATES, or DIP_SINGLETS and DIP_TRIPLETS.