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--- howto:lrigpw [2017/05/08 08:33] – [When to use it] dgolze
+++ howto:lrigpw [2017/05/14 13:31] – [How to use it] dgolze
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 ===== Introduction =====
-Density functional theory (DFT) calculations in CP2K employ the Gaussian and plane waves (GPW) method. In GPW, the description of the total density on realspace grids is typically the computationally most expensive part. By introducing a local resolution-of-the-identity (LRI) approach, the linear scaling of the GPW approach can be retained, while reducing the prefactor for the grid operations. The combined approach, LRIGPW, is comprehensively described in [[doi>10.1021/acs.jctc.7b00148 | J. Chem. Theory Comput., 2017]].\\
+Density functional theory (DFT) calculations in CP2K employ the Gaussian and plane waves (GPW) method. In GPW, the description of the total density on realspace grids is typically the computationally most expensive part. By introducing a local resolution-of-the-identity (LRI) approach, the linear scaling of the GPW approach can be retained, while reducing the prefactor for the grid operations. The combined approach, LRIGPW, is comprehensively described in [[doi>10.1021/acs.jctc.7b00148 | J. Chem. Theory Comput., 13, 2202 (2017)]].\\
 In LRIGPW, the atomic pair densities $\rho_{\mathrm{AB}}$ are approximated by an expansion in a set of fit functions centered at atom A $\{f_i^{\mathrm{A}}(\mathbf{r})\}$ and atom B $\{f_j^{\mathrm{B}}(\mathbf{r})\}$,
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 Auxiliary basis sets are available for the MOLOPT basis sets. All auxiliary basis sets have been generated by simple geometric progression without any need for further optimization. These basis sets are available in different sizes: MEDIUM and LARGE. Using the large auxiliary basis sets, the accuracy is improved, but the computational overhead increases.\\
-The LRI auxiliary basis sets are generally quite large leading to a potentially ill-conditioned overlap matrix, Equation (10) in [[doi>10.1021/acs.jctc.7b00148 | J. Chem. Theory Comput., 2017]]. The inversion of this matrix can thus be numerical instable. If the SCF is not converging, set [[inp>FORCE_EVAL/DFT/QS/LRIGPW#LRI_OVERLAP_MATRIX|LRI_OVERLAP_MATRIX]] to AUTOSELECT. In this case, the atomic pairs are identified that have extremely large condition numbers. For these pairs, the pseudoinverse instead of the regular inverse is calculated. The threshold for the condition number can be given by  [[inp>FORCE_EVAL/DFT/QS/LRIGPW#MAX_CONDITION_NUM|MAX_CONDITION_NUM]].\\
+The LRI auxiliary basis sets are generally quite large leading to a potentially ill-conditioned overlap matrix, Equation (10) in [[doi>10.1021/acs.jctc.7b00148 | J. Chem. Theory Comput., 13, 2202 (2017)]]. The inversion of this matrix can thus be numerical instable. If the SCF is not converging, set [[inp>FORCE_EVAL/DFT/QS/LRIGPW#LRI_OVERLAP_MATRIX|LRI_OVERLAP_MATRIX]] to AUTOSELECT. In this case, the atomic pairs are identified that have extremely large condition numbers. For these pairs, the pseudoinverse instead of the regular inverse is calculated. The threshold for the condition number can be given by  [[inp>FORCE_EVAL/DFT/QS/LRIGPW#MAX_CONDITION_NUM|MAX_CONDITION_NUM]].\\
-The LRI integrals, Equations (31)-(34) in [[doi>10.1021/acs.jctc.7b00148 | J. Chem. Theory Comput., 2017]], are calculated prior to the SCF. The traditionally used Obara-Saika scheme is computationally too demanding here. Therefore, a more efficient integral scheme based on solid harmonic Gaussians (SHG) is employed and invoked by [[inp>FORCE_EVAL/DFT/QS/LRIGPW#SHG_LRI_INTEGRALS|SHG_LRI_INTEGRALS]], see [[doi> 10.1063/1.4973510| J. Chem. Phys., 146, 034105, 2017]] for details.
+The LRI integrals, Equations (31)-(34) in [[doi>10.1021/acs.jctc.7b00148 | J. Chem. Theory Comput.,13, 2202 (2017)]], are calculated prior to the SCF. The traditionally used Obara-Saika scheme is computationally too demanding here. Therefore, a more efficient integral scheme based on solid harmonic Gaussians (SHG) is employed and invoked by [[inp>FORCE_EVAL/DFT/QS/LRIGPW#SHG_LRI_INTEGRALS|SHG_LRI_INTEGRALS]], see [[doi> 10.1063/1.4973510| J. Chem. Phys., 146, 034105, 2017]] for details.
 ===== When to use it =====