Optimized basis functions provided by the database Ver. 2019

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.

Table 1: A set of choices for the PAO basis functions from E to Kr.

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

Table 2: A set of choices for the PAO basis functions from Rb to Bi.

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