Finite-size effects in periodic coupled cluster calculations
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911764111687680 |
|---|---|
| author | Xing, Xin Lin, Lin |
| author_facet | Xing, Xin Lin, Lin |
| contents | 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. Assuming that the CCD equations are solved using exact Hartree-Fock orbitals and orbital energies, we prove that the convergence rate of finite-size error scales as $\mathscr{O}(N_\mathbf{k}^{-\frac13})$, where $N_{\mathbf{k}}$ is the number of discretization point in the Brillouin zone and characterizes the system size. Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculations can be boosted to $\mathscr{O}(N_\mathbf{k}^{-1})$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06043 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite-size effects in periodic coupled cluster calculations Xing, Xin Lin, Lin Numerical Analysis Chemical Physics Computational Physics 81Q99, 65G99, 65D32 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. Assuming that the CCD equations are solved using exact Hartree-Fock orbitals and orbital energies, we prove that the convergence rate of finite-size error scales as $\mathscr{O}(N_\mathbf{k}^{-\frac13})$, where $N_{\mathbf{k}}$ is the number of discretization point in the Brillouin zone and characterizes the system size. Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculations can be boosted to $\mathscr{O}(N_\mathbf{k}^{-1})$ 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. |
| title | Finite-size effects in periodic coupled cluster calculations |
| topic | Numerical Analysis Chemical Physics Computational Physics 81Q99, 65G99, 65D32 |
| url | https://arxiv.org/abs/2302.06043 |