Structure optimizations for excited states with correlated second-order methods: CC2, CIS(D), and ADC(2)

Christof Hättiga
a Forschungszentrum Karlsruhe, Institute of Nanotechnology, P.O. Box 3640, D-76021 Karlsruhe, Germany

Adv. Quant. Chem., 50, 37-60 (2005).
Available online 15 November 2005

The performance of the second-order methods for excitation energies CC2 and ADC(2) is investigated and compared with the more approximate CIS and CIS(D) methods as well as with the coupled-cluster models CCSD, CCSDR(3) and CC3. As a by-product of this investigation the first implementation of analytic excited state gradients for ADC(2) and CIS(D,,) is reported.
It is found that for equilibrium structures and vibrational frequencies the second-order models CIS(D), ADC(2) and CC2 give often results close to those obtained with CCSD. The main advantage of CCSD lies in its robustness with respect to strong correlation effects. For adiabatic excitation energies CC2 is found to give from all second-order methods for excitation energies (including CCSD) the smallest mean absolute errors. ADC(2) and CIS(D 0) are found to give almost identical results.
An advantage of ADC(2) compared to CC2 is that the excitation energies are obtained as eigenvalues of a Hermitian secular matrix, while in coupled-cluster response the excitation energies are obtained as eigenvalues of a non-Hermitian Jacobi matrix. It is shown that, as a consequence of the lack of Hermitian symmetry, the latter methods will in general not give a physically correct description of conical intersections between states of the same symmetry. This problem does not appear in ADC(2).

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