How to generate a pseudopotential 1 40 AE wfn l=0 PS wfn l=0 0.8 0.6 0 0.4 -20 0.2 -40 0 -60 -0.2 -80 -0.4 0 0.5 1 0 1.5 2 2.5 3 AE logder l=0 PS logder l=0 20 3.5 4 -100 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.6 l=0 Pseudopot r 0.5 1 l=0 Pseudopot q 0.4 -2 0 0.2 -4 0 -6 -0.2 -8 -0.4 -10 -0.6 -12 -14 -0.8 0 0.5 1 1.5 2 2.5 3 3.5 4 -1 0 5 10 15 20 Objectives Generate a norm-conserving pseudopotential using ATOM Description of the input file of the ATOM code for a pseudopotential generation A title for the job N 1s2 2s2 2p3 3d0 4f0 pg ≡ PseudopotentialI. generation ENERGY FUNCTIONAL FOR A DIELECTRIC INSIDE AN ELECTRIC FIELD. core Chemical symbol of the atom Principal quantum number pg n=N 1 2 2 3 4 Nitrogen tm2 2.0 c=ca 0.0 0.0 4 0 2.00 1 3.00 2 0.00 3 0.00 1.15 1.15 Angular quantum number Cutoff radii for the Occupation different shells (in bohrs) (spin up) (spin down) 0.0 0.0 0.00 0.00 0.00 0.00 1.15 1.50 0.0 0.0 valence Number of core and valence orbitals Exchange-and correlation functional ca ≡ Ceperley-Alder (LDA) wi ≡ Wigner (LDA) hl ≡ Hedin-Lundqvist (LDA) bh ≡ von-Barth-Hedin (LDA) gl ≡ Gunnarson-Lundqvist (LDA) pb ≡ Perdew-Burke-Ernzerhof, PBE (GGA) rv ≡ revPBE (GGA) rp ≡ RPBE, Hammer, Hansen, Norvskov (GGA) ps ≡ PBEsol (GGA) wc ≡ Wu-Cohen (GGA) +s if spin (no relativistic) +r if relativistic bl ≡ BLYP Becke-Lee-Yang-Parr (GGA) am≡ AM05 by Armiento and Mattson (GGA) vw ≡ van der Waals functional How to run a pseudopotential generation with ATOM 2 I. ENERGY FUNCTIONAL FOR A DIELECTRIC INSIDE AN ELECTRIC FIELD. $ ../../Utils/pg.sh N.tm2.inp ==> Output data in directory N.tm2 ==> Pseudopotential in N.tm2.vps and N.tm2.psf (and maybe in N.tm2.xml) $ ls N.test.inp N.tm2.inp N.tm2.vps N.tm2 N.tm2.psf N.tm2.xml $ cd N.tm2 $ ls AECHARGE INP PSPOTR1 RHO pots.gplot AELOGD0 OUT PSPOTR2 SCRPSPOTR0 pots.gps AELOGD1 PSCHARGE PSPOTR3 SCRPSPOTR1 pseudo.gplot AELOGD2 PSLOGD0 PSWFFMT SCRPSPOTR2 pseudo.gps AELOGD3 PSLOGD1 PSWFNQ0 SCRPSPOTR3 scrpots.gplot AEWFNR0 PSLOGD2 PSWFNQ1 VPSFMT scrpots.gps AEWFNR1 PSLOGD3 PSWFNQ2 VPSOUT subps.gplot AEWFNR2 PSPOTQ0 PSWFNQ3 VPSXML subps.gps AEWFNR3 PSPOTQ1 PSWFNR0 charge.gplot vcharge.gplot CHARGE PSPOTQ2 PSWFNR1 charge.gps vcharge.gps FOURIER_AREA PSPOTQ3 PSWFNR2 coreq.gplot vspin.gplot FOURIER_QMAX PSPOTR0 PSWFNR3 coreq.gps vspin.gps $ Run the script The pseudopotentials will be on the same parent directory: .vps (unformatted) .psf (formatted) .xml (in XML format) Different output files in a new directory (same name as the input file without the .inp extension) An explanation of the different files can be found in the ATOM User’s Guide (page 6) Plotting the all electron and pseudo charge densities $ gnuplot –persist charge.gplot (To generate a figure on the screen using gnuplot) $ gnuplot charge.gps (To generate a postscript file with the figure) The core and the charge densities are angularly integrated (multiplied by Charge densities (electrons/bohr) 7 The PS and AE valence charge densities are equal beyond the cutoff radii AE core charge AE valence charge PS core charge PS valence charge 6 ) 5 Small peak in the AE valence charge density due to orthogonality with AE core 4 3 2 1 0 0 0.5 1 1.5 r (bohr) 2 2.5 3 Plotting the all pseudopotenial information $ gnuplot –persist pseudo.gplot (To generate a figure on the screen using gnuplot) $ gnuplot pseudo.gps (To generate a postscript file with the figure) 1 40 AE wfn l=0 PS wfn l=0 0.8 0.6 0 0.4 -20 0.2 -40 0 -60 AE and PS wavefunctions -0.2 -0.4 0 0.5 1 0 1.5 2 2.5 3 AE logder l=0 PS logder l=0 20 AE and PS logarithmic derivatives -80 3.5 4 -100 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.6 l=0 Pseudopot r 0.5 1 l=0 Pseudopot q 0.4 -2 0 0.2 -4 The more Fourier components, the harder the pseudopotential 0 -6 -0.2 -8 -0.4 Real space pseudopotential -10 -12 Fourier transformed pseudopotential -0.6 -0.8 -14 -1 0 0.5 1 1.5 2 2.5 3 3.5 4 0 5 10 15 20 A figure like this for each angular momentum shell in the valence Plotting the real-space pseudopotentials $ gnuplot –persist pots.gplot (To generate a figure on the screen using gnuplot) $ gnuplot pots.gps (To generate a postscript file with the figure) 0 Vs Vp Vd Vf Pseudopotential (Ry) -5 -10 Beyond the largest cutoff radius, the pseudopotential -15 -20 tends to -25 -30 -35 0 0.5 1 1.5 2 r (bohr) 2.5 3 3.5 4 Plotting the unscreened and screened pseudopoten $ gnuplot –persist scrpots.gplot (To generate a figure on the screen using gnuplot) $ gnuplot scrpots.gps (To generate a postscript file with the figure) 4 0 Vs Vs(scr) 2 0 -10 Pseudopotential (Ry) -2 -4 -15 -6 -20 -8 -25 -10 -30 -12 -14 Vp Vp(scr) -5 0 2 4 0 6 8 10 0 2 4 0 Vd Vd(scr) -5 -35 6 8 10 8 10 Vf Vf(scr) -2 -4 -6 -10 -8 -10 -15 -12 -14 -20 -16 -25 0 2 4 6 8 10 -18 r (bohr) 0 2 4 6 Exploring the output file $ vi OUT 2 I. ENERGY FUNCTIONAL FOR A DIELECTRIC INSIDE AN ELECTRIC FIELD. ATM Version 3.3 (2008/09/13) ATM3.3 28-MAR-12 Nitrogen ------------------------------------------------------------ &v&d N pseudopotential generation ----------------------------correlation = ca nonspin-polarized nuclear charge number of core orbitals number of valence orbitals electronic charge ionic charge = = = = = 7.000000 1 4 7.000000 0.000000 $ grep ’&v’ OUT ATM3.3 28-MAR-12 Nitrogen 2s 0.0 2.0000 -1.35223895 2p 0.0 3.0000 -0.53262229 3d 0.0 0.0000 0.00000000 4f 0.0 0.0000 0.00000000 ---------------------------- &v 2s 0.0 2.0000 -1.35223253 2p 0.0 3.0000 -0.53261661 3d 0.0 0.0000 0.00000000 4f 0.0 0.0000 0.00000000 ---------------------------- &v 4.72576386 3.67454481 0.00142446 0.00246771 -15.36854475 -13.16757601 -0.13826878 -0.13367744 1.17006869 3.50294491 0.00142446 0.00246771 -8.02041578 -9.33629169 -0.09876341 -0.09548389 &v&d &v &v &v &v &v &v &v &v ATM Version 3.3 (2008/09/13) ATM3.3 28-MAR-12 Nitrogen ------------------------------------------------------------ Comparing AE and PS eigenvalues N pseudopotential generation $ grep ----------------------------correlation = ca &v&d ‘&v’ OUT nonspin-polarized nuclear charge number of core orbitals number of valence orbitals electronic charge ionic charge = = = = 7.000000 1 4 7.000000 $ grep ’&v’ OUT ATM3.3 28-MAR-12 Nitrogen 2s 0.0 2.0000 -1.35223895 2p 0.0 3.0000 -0.53262229 3d 0.0 0.0000 0.00000000 4f 0.0 0.0000 0.00000000 ---------------------------- &v 2s 0.0 2.0000 -1.35223253 2p 0.0 3.0000 -0.53261661 3d 0.0 0.0000 0.00000000 4f 0.0 0.0000 0.00000000 ---------------------------- &v Eigenvalues (in Ry) 4.72576386 3.67454481 0.00142446 0.00246771 -15.36854475 -13.16757601 -0.13826878 -0.13367744 1.17006869 3.50294491 0.00142446 0.00246771 -8.02041578 -9.33629169 -0.09876341 -0.09548389 &v&d &v &v &v &v &v &v &v &v The AE and PS eigenvalues are not exactly identical because the pseudopotentials are changed slightly to make them approach their limit tails faster I. ENERGY FUNCTIONAL FOR A DIELECTRIC INSIDE AN ELECTRIC FIELD. Cite1,2 . If the cutoff radii are negative un!k (!r ) = ! ! ! ! cnµ (!k)eik·(!rµ +R−!r) φµ (!r − !rµ − R), (1) ! Rµ pe No semicore tm2 Ti pb 0.000 0.000 0.000 0.000 0.000 0.000 5 4 4 0 2.000 0.000 #4s 4 1 0.000 0.000 #4p ENERGY FUNCTIONAL INSIDE #3d AN ELECTRIC FIELD. 3 FOR 2 A DIELECTRIC 2.000 0.000 4 3 0.000 0.000 #4f -1.20 -1.20000 -1.30000 2.48000 1.00000 -1.00000 #23456789012345678901234567890123456789012345678901234567890 ! ! r) i! k·(! +R−! ! nr )==4 lcnµ = (0!k)es =rµ0.0 un!k (! φµ (!r − !rµ − R), a extr 0.087 -0.154 0.259 -0.585 ! Rµ r extr 0.035 0.220 0.752 2.943 No semicore r zero 0.092 0.393 1.252 r 90/99 % 5.320 7.740 Cite1,2 . pe tm2 Ti pb 0.000 0.000 0.000 0.000 0.000 0.000 5 4 4 0 2.000 0.000 #4s 4 1 0.000 0.000 #4p 3 2 2.000 0.000 #3d 4 3 0.000 0.000 #4f -1.20 -1.20000 -1.30000 2.48000 1.00000 -1.00000 I. ENERGY FUNCTIONAL FOR A #23456789012345678901234567890123456789012345678901234567890 In the OUT file, these radii are written in n = 4 l = 0 Citea1,2extr . r extr r zero r 90/99 % -0.154 0.220 0.393 7.740 0.259 0.752 1.252 un!k (!r ) = = 0 s = 0.0 extr 0.087 extr 0.035 zero 0.092 position of the last node: 1.252 Bohr -0,2 0,0 -0.154 0.220 0.393 0.259 0.752 1.252 -0.585 2.943 (1) 2 rc set to 3.28 Core radius ( 3.28) outside wfn extremum ( 2.94) l a r r 0,2 ! ! ! cnµ (!k)eik·(!rµ +R−!r) φµ (!r −0,0 !rµ − R), ! Rµ n = 4 0,4 DIELECTRIC INSIDE AN ELECTRIC FIELD. Ruler -0.585 2.943 ! (1) position of the last peak: 2.943 Bohr s = 0.0 0.087 0.035 0.092 5.320 Ruler 0,6 radial part of the 4s orbital I. 10,0 5,0 15,0 distance to nuclei (Bohr) 20,0
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