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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2506.08744 |
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| _version_ | 1866918077626580992 |
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| author | Wesolowski, Tomasz Adam |
| author_facet | Wesolowski, Tomasz Adam |
| contents | Frozen Density Embedding Theory (FDET) [Wesolowski {\it Phys. Rev. A} {\bf 77}, 012504 (2008)] provides the interpretation of the eigenvalue equations for an embedded $N'$-electron wavefunction, in which the embedding operator is multiplicative, as the Euler-Lagrange equation corresponding to the constrained minimisation of the Hohenberg-Kohn energy functional. The constraint is given by a non-negative function integrating to an integer $N-N'>0$ with $N$ being the total number of electrons in the whole system ($\min_{ρ\rightarrow\forall_{\mathbf{r}}\big(ρ({\mathbf r})\ge ρ_2({\mathbf r}\big)} E^{HK}_v[ρ]=E^{HK}_v[ρ_1^{FDET}+ρ_2]\ge E^{HK}[ρ_v^{o}]=E^o_v$). The exact FDET eigenvalue equations are analysed for $ρ_2$ such that it is equal to the exact ground-state density $ρ_v^{o}({\mathbf r})$ in some measurable volume. It is shown that, the stationary ($ρ_1^{FDET}$) obtained from the FDET eigenvalue equations - if it exists - differs from $ρ_1^o=ρ_v^{o}-ρ_2$ leading to the sharp inequality $E^{HK}[ρ_1^{FDET}+ρ_2]> E^o_v$ for such densities $ρ_2$.
The result is discussed in the context of subsystem DFT, pseudopotential theory, and exact density-dependent embedding potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08744 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density dependent embedding potentials for piecewise exact densities Wesolowski, Tomasz Adam Chemical Physics Frozen Density Embedding Theory (FDET) [Wesolowski {\it Phys. Rev. A} {\bf 77}, 012504 (2008)] provides the interpretation of the eigenvalue equations for an embedded $N'$-electron wavefunction, in which the embedding operator is multiplicative, as the Euler-Lagrange equation corresponding to the constrained minimisation of the Hohenberg-Kohn energy functional. The constraint is given by a non-negative function integrating to an integer $N-N'>0$ with $N$ being the total number of electrons in the whole system ($\min_{ρ\rightarrow\forall_{\mathbf{r}}\big(ρ({\mathbf r})\ge ρ_2({\mathbf r}\big)} E^{HK}_v[ρ]=E^{HK}_v[ρ_1^{FDET}+ρ_2]\ge E^{HK}[ρ_v^{o}]=E^o_v$). The exact FDET eigenvalue equations are analysed for $ρ_2$ such that it is equal to the exact ground-state density $ρ_v^{o}({\mathbf r})$ in some measurable volume. It is shown that, the stationary ($ρ_1^{FDET}$) obtained from the FDET eigenvalue equations - if it exists - differs from $ρ_1^o=ρ_v^{o}-ρ_2$ leading to the sharp inequality $E^{HK}[ρ_1^{FDET}+ρ_2]> E^o_v$ for such densities $ρ_2$. The result is discussed in the context of subsystem DFT, pseudopotential theory, and exact density-dependent embedding potentials. |
| title | Density dependent embedding potentials for piecewise exact densities |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2506.08744 |