7.8.4 EOM-DIP-CCSD

Double-ionization potential (DIP) is another non-electron-conserving variant of EOM-CCSD.^{1009, 511, 512} 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:

$R$

$=$

$1/2{\displaystyle \sum _{ij}}{r}_{ij}ji+1/6{\displaystyle \sum _{ijka}}{r}_{ijk}^a{a}^{†}kji.$

(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 $𝒪(N^6)$, 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 7.8.8 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.