Finite-size effects in periodic coupled cluster calculations
Here, we provide the first rigorous study of the finite-size error in the simplest and representative coupled cluster theory, namely the coupled cluster doubles (CCD) theory, for gapped periodic systems. Given exact Hartree-Fock orbitals and their corresponding orbital energies, we demonstrate that the correlation energy obtained from the approximate CCD method, after a finite number of fixed-point iterations over the amplitude equation, exhibits a finite-size error scaling as $$\mathcal{O}(N^{-\frac{1}{3}}_k)$$. Here $$N_k$$ is the number of discretization points in the Brillouin zone and characterizes the system size. Under additional assumptions ensuring the convergence of the fixed-point iterations, we demonstrate that the CCD correlation energy also exhibits a finite-size error scaling as $$\mathcal{O}(N^{-\frac{1}{3}}_k)$$. Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculation can be boosted to $$\mathcal{O}(N^{-1}_k)$$ with accurate amplitudes. This also provides the first proof of the scaling of the finite-size error in the third order Møller-Plesset perturbation theory (MP3) for periodic systems.
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES)
- Grant/Contract Number:
- AC02-05CH11231; SC0022364
- OSTI ID:
- 2438077
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 500; ISSN 0021-9991
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Similar Records
Open-Shell Tensor Hypercontraction
Tensor decomposition in post-Hartree–Fock methods. II. CCD implementation