Numerical and Theoretical Aspects of the DMRG-TCC Method
Exemplified by the Nitrogen Dimer [2]
FABIAN M. FAULSTICH1, MIHÁLY MÁTÉ2, ANDRE LAESTADIUS1, MIHÁLY ANDRÁS CSIRIK3, LIBOR VEIS4, ANDREJ ANTALIK4, JIŘÍ BRABEC4, REINHOLD SCHNEIDER5, JIŘÍ PITTNER4, SIMEN KVAAL1, and ÖRS LEGEZA3
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo,
P.O. Box 1033 Blindern, N-0315 Oslo, Norway
Email: f.m.faulstich@kjemi.uio.no
We investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. This multi-reference formalism combines the single-reference coupled-cluster (CC) approach with a full configuration interaction (FCI) solution covering the static correlation [3]. This keeps the computational costs low as the full configuration interaction solution is calculated for a subsystem and guarantees the high accuracy of the CC method for the dynamical correlation. In the presented approach the FCI solution is approximated by matrix-product states [4]. The computational results presented in [4, 5] show that the precession of the DMRG-TCC method outruns traditional high accuracy CC methods like CCSD(T) and even CCSDTQ. The outstanding performance of the young DMRG-TCC method makes it an extremely promising candidate for the computation of strongly correlated systems. We here extend the mathematical analysis performed in [1] by numerical investigations of the error behavior. Since error studies require high precision calculations, we restrict the investigations on bond dissociation of the Nitrogen dimer, which is due to its size computationally accessible. The main focus of this error study lies on the CAS choice by means of the quantum information theory properties: single site entropy and mutual information profile. We here elaborate on the robustness of the CAS choice with respect to the bond dimension and furthermore compare the exact error behavior to the analytically predicted error bound. This reveals interesting features of the tailored coupled cluster method.
REFERENCES
[1] F. M. Faulstich, A. Laestadius, S. Kvaal, O. Legeza, and R. Schneider, Analysis of the coupled-cluster method tailored by tensor-network states in quantum chemistry, arXiv preprint arXiv:1802.05699, (2018).
[2] F. M. Faulstich, M. Máté, A. Laestadius, M. A. Csirik, L. Veis, A. Antalik, J. Brabec, R. Schneider, J. Pittner, S. Kvaal, et al., Numerical and theoretical aspects of the dmrg-tcc method exemplified by the nitrogen dimer, arXiv preprint arXiv:1809.07732, (2018).
[3] T. Kinoshita, O. Hino, and R. J. Bartlett, Coupled-cluster method tailored by configuration interaction, The Journal of chemical physics, 123 (2005), p. 074106, https://doi.org/10.1063/1.2000251
[4] L. Veis, A. Antalík, J. Brabec, F. Neese, O. Legeza, and J. Pittner, Correction to coupled cluster method with single and double excitations tailored by matrix product state wave functions, The Journal of Physical Chemistry Letters, 8 (2016), pp. 291–291, https://doi.org/10.1021/acs.jpclett.6b01908.
[5] L. Veis, A. Antalík, O. Legeza, A. Alavi, and J. Pittner, The intricate case of tetramethyleneethane: A full configuration interaction quantum monte carlo benchmark and multireference coupled cluster studies, Journal of Chemical Theory and Computation, 14 (2018), pp. 2439– 2445, https://doi.org/10.1021/acs.jctc.8b00022.
1 Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
2 Department of Physics of Complex Systems, Eötvös Loránd University, Pf. 32, H-1518 Budapest, Hungary.
3 Strongly Correlated Systems “Lendület” Research Group, Wigner Research Center for Physics, H-1525, Budapest, Hungary.
4 J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
5 Modeling, Simulation and Optimization in Science, Department of Mathematics, Technische Universität Berlin, Sekretariat MA 5-3, Straße des 17. Juni 136, 10623 Berlin,Germany