Chapter 10
Second-Order Approximate Coupled-Cluster (CC2) Calculations

ricc2 is a module for the calculation of excitation energies and response properties at a correlated second-order ab initio level, in particular the second-order approximate coupled-cluster model CC2 [148], but also the MP2, CIS(D), CIS(D_∞), and ADC(2) levels. All calculations employ the resolution-of-the-identity (RI) approximation for the electron repulsion integrals used in the correlation treatment and the description of excitation processes. At present the following functionalities are implemented:

ground state energies

for MP2 and CC2 and spin-component scaled variants thereof; the MP2 results are identical with those obtained with rimp2 (but usually the calculations are somewhat faster).

excitation energies

for the models CIS/CCS, CIS(D), CIS(D_∞), ADC(2), and CC2 including spin-component scaled SCS and SOS version of of the latter four methods

transition moments

for ground state—excited and excited—excited state transitions for the models CCS and CC2; for ADC(2) only moments for ground state—excited state transitions are available

two-photon transition moments

for ground state—excited state transitions for the models CCS and CC2

induced transition moments

for ground state—excited state transitions for the models CCS and CC2 for the computation of spin-orbit induced oscillator strengths for transitions from the ground state to excited triplet states and phosphorescence lifetimes with SOC-PT

first-order properties

for the ground state with SCF (CCS), MP2, and CC2 and for excited states with CCS, CC2, ADC(2) and CIS(D_∞)

geometric gradients

for the electronic ground state at the MP2 and the CC2 level; for electronically excited states at the CIS(D_∞), ADC(2), and CC2 level

second-order properties

for the ground state with MP2 and CC2 and a closed-shell RHF reference wavefunction (currently restricted to the sequentical and SMP parallel versions)

gradients for auxiliary basis sets

for RI-MP2, -CC2, etc. calculations based on the RI-MP2 error functional

F12 corrections

to RI-MP2; MP2 ground-state energies can be computed (in C₁ symmetry) using explicitly-correlated two-electron basis functions in the framework of the MP2-F12 model [145,149].

solvent effects

for the methods and states for which (orbital–relaxed) densities are available equilibrium solvent effects can be included in the framework of the cosmomode (for details see Chapter 17.2).

All functionalities at the MP2 and CC2 level are implemented for closed-shell RHF and open-shell UHF reference wavefunctions (with the exception of induced transition moments using SOC-PT, which are only available for a closed-shell RHF reference). Ground state energies for MP2, MP2-F12 and CC2 and excited state energies for CC2 are also implemented for single determinant restricted open-shell Hartree-Fock (ROHF) reference wavefunctions (cmp. Sec. 9.3). (Note, that no gradients are available for MP2 and CC2 with ROHF reference wavefunctions.) For a two-component GHF reference wavefunction energies for the CCS, MP2/ADC(2), CIS(D_∞) and CC2 methods as well as ground state—excited state transtition moments for ADC(2) and CC2 are available.

The second-order models MP2, CIS(D), CIS(D_∞), ADC(2) and CC2 can be combined with a spin-component scaling (SCS or SOS). (Not yet available for second-order properties, two-photon and induced transition moments.) For the SOS variants one can switch to an implementation with (⁴)-scaling costs by setting the keyworkd for the numerical Laplace transformation (LT) ($laplace) .

As listed above, some functionalities are, as a side-produce, in ricc2 also implemented at the uncorrelated HF-SCF, CIS, and CCS levels. There are only made available in ricc2 for easier test calculations and comparisons, without that the code in ricc2 has optimized for them.

For calculations with CCSD, CCSD(T) and other higher-order models beyond CC2 see Chapter 11.