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The optimized PAO functions are provided on the website (http://www.openmx-square.org/) as the database Ver. 2019. This should be the first choice by general users, since they were generated by the orbital optimization method [41], and tested well through a series of benchmark calculations. For most elements in the database Ver. 2019, three systems are chosen as training sets of chemical environment, and the PAO functions were optimized by the orbital optimization method for the chosen systems [41]. Then, those optimized ones are unified to form a single PAO file through a combination scheme of a subspace rotation method and Gram-Schmidt orthogonalization. Thus, the optimized PAO functions have been already optimized for a set of different chemical environments, which may increase the transferability of the optimized PAO functions. In fact, the series of benchmark calculations shown in the website of the database are in good agreement with corresponding all electron calculations. From the benchmark calculations one may find a proper cutoff radius and the number of basis functions for each element. The input files used for the benchmark calculations are also available on the website, which may be useful for users to get used to the OpenMX calculations at the initial stage. The accuracy of the database (2019) was validated by the delta gauge [40]. The mean delta factor of 71 elements is 1.774 meV/atom with the standard deviation of 1.702 meV/atom, which implies high accuracy of the database (2019). Users are strongly encouraged to use the new database due to the high accuracy. See also the section 'Calculation of Energy vs. lattice constant'.
For user's convenience, a set of proper choices for the basis functions is provided in Tables 1 and 2. For each pseudopotential, three choices: Quick, Standard, and Precise are given in the Tables. Quick allows us a quick calculation, but with a reasonably accuracy. Standard can be a proper choice for the most of users, which balances the accuracy and efficiency. Precise almost reaches to convergent results in most of cases. The tables give a guideline in choosing the basis functions, while of course, basis functions should be properly selected depending on your purpose.
| VPS | Valence electrons | Quick | Standard | Precise |
| E | 0.0 | Kr10.0-s1p1 | Kr10.0-s2p1d1 | Kr10.0-s2p2d1f1 |
| H_PBE19 | 1.0 | H5.0-s2 | H6.0-s2p1 | H7.0-s2p2d1 |
| He_PBE19 | 2.0 | He8.0-s1p1 | He8.0-s2p1 | He10.0-s2p2d1 |
| Li_PBE19 | 3.0 | Li8.0-s3p1 | Li8.0-s3p2 | Li8.0-s3p2d1 |
| Be_PBE19 | 2.0 | Be7.0-s2p1 | Be7.0-s2p2 | Be7.0-s3p2d1 |
| B_PBE19 | 3.0 | B7.0-s2p2 | B7.0-s2p2d1 | B7.0-s3p2d2 |
| C_PBE19 | 4.0 | C6.0-s2p2 | C6.0-s2p2d1 | C6.0-s3p2d2 |
| N_PBE19 | 5.0 | N6.0-s2p2 | N6.0-s2p2d1 | N6.0-s3p2d2 |
| O_PBE19 | 6.0 | O6.0-s2p2 | O6.0-s2p2d1 | O6.0-s3p2d2 |
| F_PBE19 | 7.0 | F6.0-s2p2 | F6.0-s2p2d1 | F6.0-s3p3d2f1 |
| Ne_PBE19 | 8.0 | Ne9.0-s2p2 | Ne9.0-s2p2d1 | Ne9.0-s3p2d2 |
| Na_PBE19 | 9.0 | Na9.0-s3p2 | Na9.0-s3p2d1 | Na9.0-s3p2d2 |
| Mg_PBE19 | 8.0 | Mg9.0-s2p2 | Mg9.0-s3p2d1 | Mg9.0-s3p2d2 |
| Al_PBE19 | 3.0 | Al7.0-s2p1d1 | Al7.0-s2p2d1 | Al7.0-s3p2d2 |
| Si_PBE19 | 4.0 | Si7.0-s2p1d1 | Si7.0-s2p2d1 | Si7.0-s3p3d2 |
| P_PBE19 | 5.0 | P7.0-s2p2d1 | P7.0-s2p2d1f1 | P7.0-s3p2d2f1 |
| S_PBE19 | 6.0 | S7.0-s2p2d1 | S7.0-s2p2d1f1 | S7.0-s3p2d2f1 |
| Cl_PBE19 | 7.0 | Cl7.0-s2p2d1 | Cl7.0-s2p2d1f1 | Cl7.0-s3p2d2f1 |
| Ar_PBE19 | 8.0 | Ar9.0-s2p2d1 | Ar9.0-s2p2d1f1 | Ar9.0-s3p2d2f1 |
| K_PBE19 | 9.0 | K10.0-s3p2 | K10.0-s3p2d1 | K10.0-s3p2d2 |
| Ca_PBE19 | 10.0 | Ca9.0-s3p2 | Ca9.0-s3p2d1 | Ca9.0-s3p2d2 |
| Sc_PBE19 | 11.0 | Sc9.0-s2p2d1 | Sc9.0-s3p2d1 | Sc9.0-s3p2d2 |
| Ti_PBE19 | 12.0 | Ti7.0-s2p2d1 | Ti7.0-s3p2d1 | Ti7.0-s3p2d2f1 |
| V_PBE19 | 13.0 | V6.0-s2p2d1 | V6.0-s3p2d1 | V6.0-s3p2d2f1 |
| Cr_PBE19 | 14.0 | Cr6.0-s2p2d1 | Cr6.0-s3p2d1 | Cr6.0-s3p2d2f1 |
| Mn_PBE19 | 15.0 | Mn6.0-s2p2d1 | Mn6.0-s3p2d1 | Mn6.0-s3p2d2f1 |
| Fe_PBE19H | 16.0 | Fe5.5H-s2p2d1 | Fe5.5H-s3p2d1 | Fe5.5H-s3p2d2f1 |
| Fe_PBE19S | 14.0 | Fe6.0S-s2p2d1 | Fe6.0S-s3p2d1 | Fe6.0S-s3p2d2f1 |
| Co_PBE19H | 17.0 | Co6.0H-s2p2d1 | Co6.0H-s3p2d1 | Co6.0H-s3p2d2f1 |
| Co_PBE19S | 15.0 | Co6.0S-s2p2d1 | Co6.0S-s3p2d1 | Co6.0S-s3p2d2f1 |
| Ni_PBE19H | 18.0 | Ni6.0H-s2p2d1 | Ni6.0H-s3p2d1 | Ni6.0H-s3p2d2f1 |
| Ni_PBE19S | 16.0 | Ni6.0S-s2p2d1 | Ni6.0S-s3p2d1 | Ni6.0S-s3p2d2f1 |
| Cu_PBE19H | 19.0 | Cu6.0H-s2p2d1 | Cu6.0H-s3p2d1 | Cu6.0H-s3p2d2f1 |
| Cu_PBE19S | 11.0 | Cu6.0S-s2p1d1 | Cu6.0S-s3p2d1 | Cu6.0S-s3p2d2f1 |
| Zn_PBE19H | 20.0 | Zn6.0H-s2p2d1 | Zn6.0H-s3p2d1 | Zn6.0H-s3p2d2f1 |
| Zn_PBE19S | 12.0 | Zn6.0S-s2p1d1 | Zn6.0S-s3p2d1 | Zn6.0S-s3p2d2f1 |
| Ga_PBE19 | 13.0 | Ga7.0-s2p2d1 | Ga7.0-s3p2d2 | Ga7.0-s3p2d2f1 |
| Ge_PBE19 | 4.0 | Ge7.0-s2p1d1 | Ge7.0-s3p2d2 | Ge7.0-s3p2d2f1 |
| As_PBE19 | 15.0 | As7.0-s3p2d1 | As7.0-s3p2d2 | As7.0-s3p2d2f1 |
| Se_PBE19 | 6.0 | Se7.0-s3p2d1 | Se7.0-s3p2d2 | Se7.0-s3p2d2f1 |
| Br_PBE19 | 7.0 | Br7.0-s3p2d1 | Br7.0-s3p2d2 | Br7.0-s3p2d2f1 |
| Kr_PBE19 | 8.0 | Kr10.0-s2p2d1 | Kr10.0-s3p2d2 | Kr10.0-s3p2d2f1 |
| VPS | Valence electrons | Quick | Standard | Precise |
| Rb_PBE19 | 9.0 | Rb11.0-s2p2d1 | Rb11.0-s3p2d2 | Rb11.0-s3p2d2f1 |
| Sr_PBE19 | 10.0 | Sr10.0-s2p2d1 | Sr10.0-s3p2d2 | Sr10.0-s3p3d2f1 |
| Y_PBE19 | 11.0 | Y10.0-s3p2d1 | Y10.0-s3p2d2 | Y10.0-s3p3d2f1 |
| Zr_PBE19 | 12.0 | Zr7.0-s3p2d1 | Zr7.0-s3p2d2 | Zr7.0-s3p2d2f1 |
| Nb_PBE19 | 13.0 | Nb7.0-s3p2d1 | Nb7.0-s3p2d2 | Nb7.0-s3p2d2f1 |
| Mo_PBE19 | 14.0 | Mo7.0-s3p2d1 | Mo7.0-s3p2d2 | Mo7.0-s3p2d2f1 |
| Tc_PBE19 | 15.0 | Tc7.0-s3p2d1 | Tc7.0-s3p2d2 | Tc7.0-s3p2d2f1 |
| Ru_PBE19 | 14.0 | Ru7.0-s3p2d1 | Ru7.0-s3p2d2 | Ru7.0-s3p2d2f1 |
| Rh_PBE19 | 15.0 | Rh7.0-s3p2d1 | Rh7.0-s3p2d2 | Rh7.0-s3p2d2f1 |
| Pd_PBE19 | 16.0 | Pd7.0-s3p2d1 | Pd7.0-s3p2d2 | Pd7.0-s3p2d2f1 |
| Ag_PBE19 | 17.0 | Ag7.0-s3p2d1 | Ag7.0-s3p2d2 | Ag7.0-s3p2d2f1 |
| Cd_PBE19 | 12.0 | Cd7.0-s3p2d1 | Cd7.0-s3p2d2 | Cd7.0-s3p2d2f1 |
| In_PBE19 | 13.0 | In7.0-s3p2d1 | In7.0-s3p2d2 | In7.0-s3p2d2f1 |
| Sn_PBE19 | 14.0 | Sn7.0-s3p2d1 | Sn7.0-s3p2d2 | Sn7.0-s3p2d2f1 |
| Sb_PBE19 | 15.0 | Sb7.0-s3p2d1 | Sb7.0-s3p2d2 | Sb7.0-s3p2d2f1 |
| Te_PBE19 | 16.0 | Te7.0-s3p2d2 | Te7.0-s3p2d2f1 | Te7.0-s3p3d2f1 |
| I_PBE19 | 7.0 | I7.0-s3p2d2 | I7.0-s3p2d2f1 | I7.0-s3p3d2f1 |
| Xe_PBE19 | 8.0 | Xe11.0-s3p2d1 | Xe11.0-s3p2d2 | Xe11.0-s3p2d2f1 |
| Cs_PBE19 | 9.0 | Cs12.0-s3p2d1 | Cs12.0-s3p2d2 | Cs12.0-s3p2d2f1 |
| Ba_PBE19 | 10.0 | Ba10.0-s3p2d1 | Ba10.0-s3p2d2 | Ba10.0-s3p2d2f1 |
| La_PBE19 | 11.0 | La8.0-s3p2d1f1 | La8.0-s3p2d2f1 | La8.0-s3p3d2f1 |
| Ce_PBE19 | 12.0 | Ce8.0-s3p2d1f1 | Ce8.0-s3p2d2f1 | Ce8.0-s3p3d2f1 |
| Pr_PBE19 | 13.0 | Pr8.0-s3p2d1f1 | Pr8.0-s3p2d2f1 | Pr8.0-s3p3d2f1 |
| Nd_PBE19 | 14.0 | Nd8.0-s3p2d1f1 | Nd8.0-s3p2d2f1 | Nd8.0-s3p3d2f1 |
| Pm_PBE19 | 15.0 | Pm8.0-s3p2d1f1 | Pm8.0-s3p2d2f1 | Pm8.0-s3p3d2f1 |
| Sm_PBE19 | 16.0 | Sm8.0-s3p2d1f1 | Sm8.0-s3p2d2f1 | Sm8.0-s3p3d2f1 |
| Dy_PBE19 | 20.0 | Dy8.0-s3p2d1f1 | Dy8.0-s3p2d2f1 | Dy8.0-s3p3d2f1 |
| Ho_PBE19 | 21.0 | Ho8.0-s3p2d1f1 | Ho8.0-s3p2d2f1 | Ho8.0-s3p3d2f1 |
| Lu_PBE19 | 11.0 | Lu8.0-s3p2d2 | Lu8.0-s3p2d2f1 | Lu8.0-s3p3d2f1 |
| Hf_PBE19 | 12.0 | Hf9.0-s3p2d2 | Hf9.0-s3p2d2f1 | Hf9.0-s3p3d2f1 |
| Ta_PBE19 | 13.0 | Ta7.0-s3p2d2 | Ta7.0-s3p2d2f1 | Ta7.0-s3p3d2f1 |
| W_PBE19 | 12.0 | W7.0-s3p2d2 | W7.0-s3p2d2f1 | W7.0-s3p3d2f1 |
| Re_PBE19 | 15.0 | Re7.0-s3p2d2 | Re7.0-s3p2d2f1 | Re7.0-s3p3d2f1 |
| Os_PBE19 | 14.0 | Os7.0-s3p2d2 | Os7.0-s3p2d2f1 | Os7.0-s3p3d2f1 |
| Ir_PBE19 | 15.0 | Ir7.0-s3p2d2 | Ir7.0-s3p2d2f1 | Ir7.0-s3p3d2f1 |
| Pt_PBE19 | 16.0 | Pt7.0-s3p2d2 | Pt7.0-s3p2d2f1 | Pt7.0-s3p3d2f1 |
| Au_PBE19 | 17.0 | Au7.0-s3p2d2 | Au7.0-s3p2d2f1 | Au7.0-s3p3d2f1 |
| Hg_PBE19 | 18.0 | Hg8.0-s3p2d2 | Hg8.0-s3p2d2f1 | Hg8.0-s3p3d2f1 |
| Tl_PBE19 | 19.0 | Tl8.0-s3p2d2 | Tl8.0-s3p2d2f1 | Tl8.0-s3p3d2f1 |
| Pb_PBE19 | 14.0 | Pb8.0-s3p2d2 | Pb8.0-s3p2d2f1 | Pb8.0-s3p3d2f1 |
| Bi_PBE19 | 15.0 | Bi8.0-s3p2d2 | Bi8.0-s3p2d2f1 | Bi8.0-s3p3d2f1 |