Explicit electron correlation for high accuracy coupled-cluster calculations
Final Report Abstract
The coupled-cluster expansion of the many-electron wavefunction gives very accurate results for the correlation energy already at low orders. Full treatment up to pair clusters and perturbative treatment of three-electron clusters, the well-known CCSD(T) method, leads to nearly quantitative results in many cases, high-accuracy results can be obtained if further corrections are included, typically up to four-electron clusters. Reaching fully quantitative results is hampered, however, by the need to use very large basis sets for the discrete representation of orbitals, as the coupled-cluster wavefunction is based on an expansion in terms of orbital product states (Slater determinants). The slow convergence of the correlation energy as a function of the underlying basis-set expansion can be improved by including Slater-type geminals which explicitly depend on the interelectronic distance, known as F12 theory. In this project we have contributed new ideas to coupled-cluster F12 theory and enhanced the understanding of existing approaches. To this end we have used novel techniques to provide reliable numerical implementations of new methods, namely automated term generation for derivation of working equations and general tensor contraction approaches for numerical evaluation of the latter. Using these means, we have investigated the importance of geminal terms in the complete CCSD-F12 method and extracted a rule for selecting the most important terms. In collaboration with the groups of D. P. Tew (Bristol) and Ch. Hättig (Bochum) this has lead to the development of the CCSD(F12*) model, which now is one of the standard approaches in the field. Furthermore, we have developed a general ansatz for the explicitly correlated cluster expansion based on a generalized geminal operator. We have showed that connected product terms of cluster operators and the generalized geminal lead to new wavefunction ansätze, that either allow for the accurate treatment of response properties and excited states, or for incorporating geminal corrections into higher-order connected clusters. An F12-based correction of the non-iterative triples correction was proposed and implemented subsequently. Finally, we have also successfully included F12 terms into our recently developed internally contracted multireference coupled-cluster scheme (ic-MRCC). The suggested ic-MRCCSD(F12*) is the direct analogue of the single-reference model CCSD(F12*). The method is expected to enable highly accurate calculations on complex open-shell systems (bond-breaking processes, transition metals), which cannot be treated with standard single-reference coupled-cluster methods.
Publications
- “Implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 with optimally reduced auxiliary basis dependence”, J. Chem. Phys. 129, 201103 (2008)
A. Köhn, G. W. Richings, D. P. Tew
- “A modified ansatz for explicitly correlated coupled-cluster wave functions that is suitable ¨ for response theory”, J. Chem. Phys. 130, 104104 (2009)
A. Köhn
- “Explicitly correlated triple excitations in coupled-cluster theory”, J. Chem. Phys. 130, 131101 (2009)
A. Köhn
- “Response properties with explicitly correlated coupled-cluster methods using a Slater-type ¨ correlation factor and cusp conditions”, J. Chem. Phys. 131, 124118 (2009)
M. Hanauer, A. Köhn
- “Communications: Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12”, J. Chem. Phys. 132, 231102 (2010)
C. Hättig, D. P. Tew, A. Köhn
- “Explicitly correlated internally contracted multireference coupled-cluster singles and doubles theory: ic-MRCCSD(F12*)”, Chem. Phys. Lett. 565, 122-127 (2013)
W. Liu, M. Hanauer, A. Köhn
(See online at https://doi.org/10.1016/j.cplett.2012.12.052)
