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 C
_{1}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.

How To Perform a Calculation

How to quote

10.1 CC2 Ground-State Energy Calculations

10.2 Calculation of Excitation Energies

10.3 First-Order Properties and Gradients

10.3.1 Ground State Properties, Gradients and Geometries

10.3.2 Excited State Properties, Gradients and Geometries

10.3.3 Visualization of densities and Density analysis

10.3.4 Fast geometry optimizations with RI-SCF based gradients

10.4 Transition Moments

10.4.1 Ground to excited state transition moments

10.4.2 Transition moments between excited states

10.4.3 Ground to excited state two-photon transition moments

10.4.4 Phosphorescence lifetimes using SOC-PT-CC2

10.5 Ground State Second-order Properties with MP2 and CC2

10.6 Parallel RI-MP2 and RI-CC2 Calculations

10.7 Spin-component scaling approaches (SCS/SOS)

How to quote

10.1 CC2 Ground-State Energy Calculations

10.2 Calculation of Excitation Energies

10.3 First-Order Properties and Gradients

10.3.1 Ground State Properties, Gradients and Geometries

10.3.2 Excited State Properties, Gradients and Geometries

10.3.3 Visualization of densities and Density analysis

10.3.4 Fast geometry optimizations with RI-SCF based gradients

10.4 Transition Moments

10.4.1 Ground to excited state transition moments

10.4.2 Transition moments between excited states

10.4.3 Ground to excited state two-photon transition moments

10.4.4 Phosphorescence lifetimes using SOC-PT-CC2

10.5 Ground State Second-order Properties with MP2 and CC2

10.6 Parallel RI-MP2 and RI-CC2 Calculations

10.7 Spin-component scaling approaches (SCS/SOS)