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 [260], but also the MP2, CIS(D), CIS(D\(_\infty\)), 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
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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
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for the models CIS/CCS, CIS(D), CIS(D\(_\infty\)), ADC(2), and CC2 including spin-component scaled SCS and SOS version of of the latter four methods
- transition moments
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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
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for ground state—excited state transitions for the models CCS and CC2
- induced transition moments
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for ground state—excited state transitions for the models CCS and CC2 for the computation of e.g.
- first-order properties
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for the ground state with SCF (CCS), MP2, and CC2 and for excited states with CCS, CC2, ADC(2) and CIS(D\(_\infty\))
- geometric gradients
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for the electronic ground state at the MP2 and the CC2 level; for electronically excited states at the CIS(D\(_\infty\)), ADC(2), and CC2 level
- second-order properties (linear response function):
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for the ground state with MP2 and CC2 and a closed-shell RHF reference wavefunction, frequency-dependent properties are restricted to CC2
- third-order properties (quadratic response function):
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for the ground state with CC2 and a closed-shell RHF reference wavefunction
- gradients for auxiliary basis sets
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for RI-MP2, -CC2, etc. calculations based on the RI-MP2 error functional
- F12 corrections
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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 [265, 258].
- solvent effects
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can be included with COSMO (for details see Chapter 21.2 and Section 10.9).
- polarizable embeddings
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as described in Section 21.5 can be combined with single-point ground- and excited-state energies and gradients, for Details see Secs. 21.5 and 10.9.
- static embeddings
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all methods available in ricc2 can be combined with the Periodic Electrostatic Embedded Cluster Method (PEECM) (see Sec. 21.4) and non-periodic charge and multipole embeddings (see Sec. 21.1) for single-point energies, gradients, and all available properties that do not involve derivatives with respect to nuclear coordinates
- damped response
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also known as complex polarization propagator for the CC2 linear response function (currently restricted for CC2, no spin component scaling, and can not be combined with COSMO, PE, or FDE, only parallelized with OMP, not yet with MPI) [263, 266]
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\(_\infty\)) 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\(_\infty\)), 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 \({\cal O}({\cal N}^4)\)-scaling costs by setting the keyword for the numerical Laplace transformation (LT) ($laplace) .
As listed above, some functionalities are, as a by-product, in ricc2 also implemented at the uncorrelated HF-SCF, CIS, and CCS levels. They are only made available in ricc2 for test calculations and comparisons, without that the code in ricc2 has been optimized for them.
For calculations with CCSD, CCSD(T) and other higher-order models beyond CC2 see Chapter 11.