Double-ionization potential (DIP) is another non-electron-conserving variant of
EOM-CCSD.^{Wladyslawski:2002, Kus:2011, Kus:2012}
In DIP, target states are reached by detaching two electrons from the reference state:

$${\mathrm{\Psi}}_{k}={R}_{N-2}{\mathrm{\Psi}}_{0}(N+2),$$ | (7.48) |

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

$R$ | $=$ | $1/2{\displaystyle \sum _{ij}}{r}_{ij}ji+1/6{\displaystyle \sum _{ijka}}{r}_{ijk}^{a}{a}^{\u2020}kji.$ | (7.49) |

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 $\mathcal{O}({N}^{6})$,
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.

Note: The performance of EOM-DIP may be poor if the reference state is unstable with respect to electron detachment. See Section 7.10.8 for details.

Note: In some applications of EOM-DIP-CCSD, only 2$h$ operators were included in the EOM part. These calculations correspond to energies obtained from EOM_PRECONV_DOUBLES=TRUE calculation.