EOMCC

Equation-of-Motion Coupled-Cluster (EOMCC) methods are a class of ab initio quantum chemical techniques for calculating electronic excited states, built on a coupled-cluster description of the ground state. In EOMCC, the ground state is written as |Ψ0> = e^T |Φ0>, where |Φ0> is a reference determinant and T is a cluster operator. Excited states are represented as |Ψk> = Rk e^T |Φ0>, with Rk an excitation operator. The electronic Hamiltonian is similarity-transformed as H̄ = e^{-T} H e^{T}, and the excitation energies ωk are obtained by solving the non-Hermitian eigenvalue problem H̄ Rk |Φ0> = ωk Rk |Φ0>, typically within a chosen excitation manifold. This framework yields both energies and wavefunction information for multiple excited states in a size-extensive manner.

Common variants include EOM-CCSD, which includes singles and doubles; EOM-CCSDT, which adds triples; and various approximate triples schemes. Practical implementations often target neutral excited states with EE-EOM-CCSD, or ionized and electron-attached states with IP-EOM-CCSD and EA-EOM-CCSD, respectively. The same ground-state CC reference is used across these variants, enabling balanced treatment of ground and excited states.

Advantages and limitations:

- Strengths: provides accurate valence and many Rydberg excited states, describes relative energetics reliably, and is size-extensive with the same reference framework as CC theory.

- Limitations: states with strong double-excitation character are poorly described at the EOM-CCSD level and require higher-order methods (e.g., EOM-CCSDT) or multireference approaches; computational cost increases rapidly with higher excitations.

Applications include electronic spectra, photochemistry, and spectroscopy studies of molecules and materials.