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--- howto:xas_tdp [2021/08/02 15:17] – [Simple examples] abussy
+++ howto:xas_tdp [2021/08/02 15:39] – [Simple examples] abussy
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-where $\varepsilon_a$ is the orbital energy of a virtual MO and $\varepsilon_I$ the energy of the donor core MO. Under Koopman's condition, these energies are interpreted as the electron affinity and and the ionization potential (IP). However, DFT is notoriously bad at prediction accurate absolute orbital eigenvalues. Therefore, and because $|\varepsilon_I| >> |\varepsilon_a|$, excitation energies are expected to be widely improved if the DFT energy $\varepsilon_I$ were to be replace by an accurate value of the IP.
+where $\varepsilon_a$ is the orbital energy of a virtual MO and $\varepsilon_I$ the energy of the donor core MO. Under Koopman's condition, these energies are interpreted as the electron affinity and and the ionization potential (IP). However, DFT is notoriously bad at predicting accurate absolute orbital eigenvalues. Therefore, and because $|\varepsilon_I| >> |\varepsilon_a|$, excitation energies are expected to be widely improved if the DFT energy $\varepsilon_I$ were to be replace by an accurate value of the IP.
 The IP can be accurately calculated using the second-order electron propagator equation:
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 The only difference between the above input file and that of a standard XAS LR-TDDFT calculation is the addition of the ''&GW2X'' subsection. In this case, only default parameters are used, which corresponds to the original GW2X scheme with a convergence threshold of 0.01 eV. Note that the core specific all-electron aug-pcX-2 basis set is used (triple zeta quality). This inputs corresponds to an entry of table II in the [[https://doi.org/10.1063/5.0058124|reference paper]], although slacker parameters are used here (in order to make this tutorial cheap and easy to run, this particular calculations takes ~2 minutes on 4 cores).
-In the output file, the correction for each S $2p$ is displayed. Note that the correction amounts to a shift of 1.9 eV compared to standard XAS LR-TDDFT, leading to a first singlet excitation energy of 164.4 eV (at the L$_3$ edge). This fits [[https://doi.org/10.1016/s0301-0104(97)00111-0|experimental results]] within 0.1 eV. thus clearly improving the XAS LR-TDDFT result. Note that the core IPs, including spin-orbit coupling effects, are also provided. These can be directly used to produce a XPS spectrum. The content of the OCS.spectrum yields the corrected spectrum directly.
+In the output file, the correction for each S $2p$ is displayed. Note that the correction amounts to a shift of 1.9 eV compared to standard XAS LR-TDDFT, leading to a first singlet excitation energy of 164.4 eV (at the L$_3$ edge). This fits [[https://doi.org/10.1016/s0301-0104(97)00111-0|experimental results]] within 0.1 eV. thus clearly improving the XAS LR-TDDFT result. Note that the core IPs, including spin-orbit coupling effects, are also provided. These can be directly used to produce a XPS spectrum. The content of the ''OCS.spectrum'' file yields the corrected spectrum directly.
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 === How can I make the GW2X correction run faster ?===
+The GW2X correction scheme scales cubically with the number of MOs in the system. Therefore, the best way to improve performance is to reduce that number. Because an accurate description of the core region is only necessary for the exited atoms, all other atoms can be described with pseudopotentials. This drastically reduces the number of MOs since only valence states are kept. In the solid NH3 example above, all nitrogen atoms are equivalent under symmetry. Therefore, their individual contribution to the XAS spectrum is bound to be the same. This allows for the description of a single nitrogen atom at the all-electron level, while all others (and the hydrogens) use pseudopotentials. Note that the ADMM approximation is also utilized. This greatly reduces the cost of the underlying hybrid DFT calculation, as well as the evaluation of the generalized Fock matrix as required by GW2X.
 === Why don't I get the absolute core IP in periodic systems ? ===
 For molecules in non-periodic boundary conditions, the potential is such that it is zero far away. In the periodic case, the zero is ill defined. As a consequence, all Kohn-Sham eigenvalues end up shifted by some unknown, constant amount. Therefore, their absolute values and that of the calculated IP cannot be interpreted in a physical manner. However, the correction scheme depends on the difference $|\varepsilon_a-\varepsilon_I|$, where the shift cancels out.
+=== Why is the LOCALIZE keyword required ? ===
+In order to efficiently evaluate the antisymmetric integrals of the type $\langle Ia | jk \rangle$, the same local RI scheme as XAS_TDP is used. Therefore, the core state $I$ needs to be local in space. However, the rotation required to get the pseudocanonical orbitals needed for the original GW2X scheme may break this localization, provided that there are other equivalent atoms in the system. To prevent that from happening, all core states localized on other atoms are ignored for the rotation and the subsequent IP calculation. This has negligible impact since core states belonging to different atoms only weakly interact. It is however important to keep the value of the LOCALIZE keyword to a minimum to insure that only core states are ignored.