Fe XVII and Ni XIX
The following instructions assume familiarity with the main programs of the pCI package.
In this section, we describe a method used to construct basis sets for the cases of Fe XVII and Ni XIX. In this example, we run the hfd program in 3 sequential stages to construct the DF orbitals, then run the bass program to form virtual orbitals to account for correlations. The following is a list of the input files used in this example.
h_m_1.inp- In the first stage, we construct the \(1s, 2s, 2p, 3s, 3p, 3d\) orbitals with the \(1s^2 2s^2 2p^5 3d\) configuration.QQis0for \(3s`\) and \(3p\), but the orbital is still formed. DF is solved with 0 occupation number for these orbitals, but they won’t be very good orbitals. We can think of \(3s0\) and \(3p0\) as placeholders to keep the order of orbitals, and re-construct them in the next step.h_m_2.inp- In the second stage, we freeze the \(1s, 2s, 2p, 3d\) orbitals and re-construct the \(3s, 3p\) orbitals from the \(1s^2 2s^2 2p^5 3s\) and \(1s^2 2s^2 2p^5 3p\) configurations. Note thatNSis unchanged here, since we do not add any additional orbitals.The following code block shows
h_m_1.inpon the left andh_m_2.inpon the right of the partition. The head of both input files are identical.Fe XVII & Ni XIX KL = 0 # (0 - new calculation, 1 - continue) NS = 9 # number of orbitals NSO= 2 # number of closed orbitals (in this case only 1s2, 2s2) Z = 26.0 # atomic number AM = 56.000 # atomic mass JM = -2.0 # default parameter (do not change) R2 = 20.0 # radius of cavity kbr= 2 # key for Breit (0 - Coulomb, 1 - Gaunt, 2 - Full Breit) NL J QQ KP NC | NL J QQ KP NC | 1 1S (1/2) 2.0000 0 0 | 1 1S (1/2) 2.0000 1 0 2 2S (1/2) 2.0000 0 0 | 2 2S (1/2) 2.0000 1 0 3 2P (1/2) 2.0000 0 0 | 3 2P (1/2) 2.0000 1 0 4 2P (3/2) 3.0000 0 0 | 4 2P (3/2) 3.0000 1 0 5 3S (1/2) 0.0000 0 0 | 5 3S (1/2) 1.0000 0 1 6 3P (1/2) 0.0000 0 0 | 6 3P (1/2) 1.0000 0 2 7 3P (3/2) 0.0000 0 0 | 7 3P (3/2) 0.0000 0 2 8 3D (3/2) 1.0000 0 0 | 8 3D (3/2) 0.0000 1 3 9 3D (5/2) 0.0000 0 0 | 9 3D (5/2) 0.0000 1 3
h_m_3.inp- At the third stage, we freeze the \(1s, 2s, 2p, 3s, 3p, 3d\) orbitals, then construct the \(4s, 4p, 4d, 4f, 5g\) orbitals from the \(1s^2 2s^2 2p^5 4s, 1s^2 2s^2 2p^5 4p, \dots, 1s^2 2s^2 2p^5 5g\) configurations. Note that the number of orbitalsNshas changed from 9 to 18, since we are adding 9 additional orbitals.Fe XVII & Ni XIX KL = 0 # NS = 18 # number of orbitals NSO= 2 # number of closed orbitals (in this case only 1s2, 2s2) Z = 26.0 # atomic number AM = 56.000 # atomic mass JM = -2.0 # R2 = 20.0 # radius of cavity kbr= 2 # key for Breit (0 - Coulomb, 1 - Gaunt, 2 - Full Breit) NL J QQ KP NC 1 1S (1/2) 2.0000 1 0 2 2S (1/2) 2.0000 1 0 3 2P (1/2) 2.0000 1 0 4 2P (3/2) 3.0000 1 0 5 3S (1/2) 0.0000 1 0 6 3P (1/2) 0.0000 1 0 7 3P (3/2) 0.0000 1 0 8 3D (3/2) 0.0000 1 0 9 3D (5/2) 0.0000 1 0 10 4S (1/2) 1.0000 0 1 11 4P (1/2) 1.0000 0 2 12 4P (3/2) 0.0000 0 2 13 4D (3/2) 1.0000 0 3 14 4D (5/2) 0.0000 0 3 15 4F (5/2) 1.0000 0 4 16 4F (7/2) 0.0000 0 4 17 5G (7/2) 1.0000 0 5 18 5G (9/2) 0.0000 0 5
b_m_2.inp- Finally, we run thebassprogram to add virtual orbitals toHFD.DATto account for correlations. Here, we are constructing the \(24spdfg\) basis set, where the designation \(24spdfg\) means that all orbitals up to \(n=24\) are included for the \(spdfg\) partial waves. Therefore, the list of orbitals included here extends to \(24g\), designated by-2.4401and2.4401. The digital format here is represented assn.nlqq, wherennrepresents the principal quantum number,lis the orbital angular momentum quantum number,lis the orbital angular momentum quantum number, andqqis the occupation number of the orbital. The signscorresponds to the total angular momentum, represeented by-for \(j=l-1/2\), or an empty space for \(j=l+1/2\). For brevity, not all orbitals are displayed.Fe XVII & Ni XIX Z = 26.0 Am = 52.0 Nso= 4 # number of core orbitals (defines DF operator) Nv = 194 # number of valence & virtual orbitals Ksg= 1 # defines Hamiltonian: 1-DF, 3-DF+Breit Kdg= 0 # diagonalization of Hamiltonian (0=no,1,2=yes) orb= 4s 1 # first orbital for diagonalization Kkin 1 # kinetic balance (0,1,or 2) orb= 5s 1 # first orbital to apply kin.bal. orb= 2p 3 # last frozen orbital orb= 0p 3 # last orbital in basis set kout= 0 # detail rate in the output kbrt= 2 # 0,1,2 - Coulomb, Gaunt, Breit ---------------------------------------------------------- 0.1002 0.2002 -0.2102 0.2104 1 0.3001 # 2 -0.3101 # These orbitals are in HFD.DAT already run by hfd 3 0.3101 # 4 -0.3201 # 5 0.3201 # 6 0.4001 3 0.4001 # reading 4s from 4s from HFD.DAT 7 -0.4101 3 -0.4101 # key '3' means 'read in from HFD.DAT' 8 0.4101 3 0.4101 # HFD.DAT is h_m_3.inp in this case 9 -0.4201 3 -0.4201 10 0.4201 3 0.4201 11 -0.4301 3 -0.4301 12 0.4301 3 0.4301 13 0.5001 # key '0' or ' ' means 'build nl from (n-1)l' 14 -0.5101 # e.g. 5s is built from 4s, 5p from 4p 15 0.5101 # 5d from 4d, ... 16 -0.5201 17 0.5201 18 -0.5301 19 0.5301 20 -0.5401 3 -0.5401 # since key '3' is present, 5f is read in from HFD.DAT 21 0.5401 3 0.5401 22 -0.6401 23 0.6401 : : : 193 -2.4401 194 2.4401
The following bash script utilizes the above input files and forms the final \(24spdfg\) basis set for Fe XVII and Ni XIX.
#! /bin/bash
#####################################################################
# script to form basis set for Fe 16+ and Ni 18+
cp h_m_1.inp HFD.INP
./hfd
cp h_m_2.inp HFD.INP
./hfd
cp HFD.DAT h0.dat
cp h_m_3.inp HFD.INP
./hfd
mv HFD.DAT h_m.dat
mv h0.dat HFD.DAT
cp b_m_2.inp BASS.INP
./bass <b.in
./bass
echo " End of script"