# Developers Manual:ABINIT

## .hgh file format

The format number 3 for ABINIT pseudopotentials allows the use of the pseudopotentials from the Hartwigsen et al. 1998 article with a few extra header lines added to the file. The local part of the pseudopotential is given by: $V_{loc}(r)=-\frac{Z_{ion}}{r}\mathrm{erf}\left(\frac{r}{\sqrt{2}r_{loc}}\right)+\exp{\left[-\frac{1}{2}\left(\frac{r}{r_{loc}}\right)^2\right]\left[C_1+C_2\left(\frac{r}{r_{loc}}\right)^2+C_3\left(\frac{r}{r_{loc}}\right)^4+C_4\left(\frac{r}{r_{loc}}\right)^6\right]},$ where $\mathrm{erf}{()}$ is the error function.

The nonlocal contribution to the pseudopotential is given by: $\Delta{}V_l(r)=\sum_{i=1}^{3}\sum_{j=1}^{3}p_i^l(r)h_{i,j}^lp_j^l(r)$ where the projectors $p_i^l(r)$ are Gaussians of the form: $p_i^l(r)=\frac{\sqrt{2}r^{l+2(i-1)}\exp{\left[-\frac{1}{2}\left(\frac{r}{r_{loc}}\right)^2\right]}}{r_l^{l+(4i-1)/2}\sqrt{\Gamma\left(l+(4i-1)/2\right)}}$ satisfying the normalization condition $\int_0^{\infty}p_i^l(r)p_i^l(r)r^2dr=1$

Line Column Descritpion 1 title line will be printed without modification in the output of ABINIT 2 1 $Z$ the atomic number 2 $Z^{ion}$ number of valence electrons. 3 981030 the date of generation. 3 1 3 the pseudopotential format, always 3 for format 3 ;-) 2 $i^{XC}$ the exchange and correlation functional used to generate the pseudopotential 3 $l_{max}$ maximum angular momentum of the wavefunctions 4 0 angular momentum, not used 5 2001 number of radial mesh points, not used 6 0 prefactor of a harmonic well, not used 4 1 $r_{loc}$ radius 2 $C_1$ 3 $C_2$ 4 $C_3$ 5 $C_4$

## .fhi file format

The format number 6 for ABINIT pseudopotentials allows the use of pseudopotentials generated from by the fhi98PP code with a few extra header lines added to the file.

Line Column Descritpion 1 title line will be printed without modification in the output of ABINIT 2 1 $Z$ the atomic number 2 $Z^{ion}$ number of valence electrons. 3 981030 the date of generation. 3 1 6 the pseudopotential format, always 6 for format 6 ;-) 2 $i^{XC}$ the exchange and correlation functional used to generate the pseudopotential 3 $l_{max}$ maximum angular momentum of the wavefunctions 4 $l_{loc}$ angular momentum of the potential to be used as local pseudopotential 5 $m_{max}$ number of radial mesh points 6 $r_{well}^2$ prefactor of a harmonic well, not used 4 1 $r_{chrg}$ radius at which the core charge vanish (in a.u.) 2 $f_{chrg}$ amplitude of core charge, has no physical meaning in fhi98PP scheme of core correction 3 $q_{chrg}$ integrated model core charge, not actually used by ABINIT 5 to 7 unused

## Exchange and Correlation

ABINIT uses the Pseudopotentials generated by the fhi98PP program with a few extra header lines added to the file. But the Exchange and Correlation Code differs.

Code Exchange Correlation Correction 0 - - - 1 TeterPade1993 TeterPade1993 - 2 PerdewZunger1981 PerdewZunger1981 - 3 Teter1991 Teter1991 - 4 Wigner1934 Wigner1934 - 5 HedinLundqvist1971 HedinLundqvist1971 - 6 Slater - - 7 PerdewWang1992 PerdewWang1992 - 8 PerdewWang1992 - - 9 PerdewWang1992 GellMannBrueckner1957 - 10 - GellMannBrueckner1957 - 11 PerdewBurkeErnzerhof1996 PerdewBurkeErnzerhof1996 - 12 PerdewBurkeErnzerhof1996 - - 13 PerdewWang1992 PerdewWang1992 LeeuwenBaerends1994 14 ZhangYang1998 ZhangYang1998 - 15 HammerHansenNorskov1999 HammerHansenNorskov1999 - 16 Hamprecht1998 Hamprecht1998 - 20 FermiAmaldi1934 FermiAmaldi1934 - 21 FermiAmaldi1934 FermiAmaldi1934 - 22 FermiAmaldi1934 FermiAmaldi1934 - 30 Slater - - 31 Slater VoskoWilkNusair1980 - 32 Slater PerdewZunger1981 - 33 Slater PerdewWang1992 - 34 Slater Attaccalite2002 -