using AtomicLevels
The ground state of hydrogen and helium:
c"1s",(c"1s2",c"[He]")
(1s, (1s², [He]ᶜ))
The ground state configuration of xenon, in relativistic notation:
Xe = rc"[Kr] 5s2 5p6"
[Kr]ᶜ 5s² 5p-² 5p⁴
As we see above, by default, the krypton core is declared
“closed”. This is useful for calculations when the core should be
frozen. We can “open” it by affixing *
:
Xe = c"[Kr]* 5s2 5p6"
1s² 2s² 2p-² 2p⁴ 3s² 3p-² 3p⁴ 3d-⁴ 3d⁶ 4s² 4p-² 4p⁴ 5s² 5p-² 5p⁴
Note that the 5p shell was broken up into 2 5p- electrons and 4 5p electrons. If we are not filling the shell, occupancy of the spin-up and spin-down electrons has to be given separately:
Xe⁺ = rc"[Kr] 5s2 5p-2 5p3"
[Kr]ᶜ 5s² 5p-² 5p³
It is also possible to work with “continuum orbitals”, where the
main quantum number is replaced by a Symbol
:
Xe⁺e = rc"[Kr] 5s2 5p-2 5p3 ks"
[Kr]ᶜ 5s² 5p-² 5p³ ks
A single orbital is constructed this way:
o"2s",ro"5f-"
(2s, 5f-)
Their parities and degeneracies are given by
(parity(ro"2s"),degeneracy(ro"2s")),(parity(ro"5f-"),degeneracy(ro"5f-"))
((even, 2), (odd, 6))
It is possible to generate a range of orbitals quickly:
os"5[d] 6[s-p] k[7-10]"
7-element Array{Orbital,1}: 5d 6s 6p kk kl km kn
ros"5[d] 6[s-p] k[7-10]"
13-element Array{RelativisticOrbital,1}: 5d- 5d 6s 6p- 6p kk- kk kl- kl km- km kn- kn
We can easily generate all possible excitations from a reference configuration. If no extra orbitals are specified, only those that are “open” within the reference set will be considered:
excited_configurations(rc"[Kr] 5s2 5p-2 5p3")
2-element Array{Configuration{RelativisticOrbital{Int64}},1}: [Kr]ᶜ 5s² 5p-² 5p³c [Kr]ᶜ 5s² 5p- 5p⁴
By appending virtual orbitals, we can generate excitations to configurations beyond those spanned by the reference set:
excited_configurations(rc"[Kr] 5s2 5p-2 5p3", ros"5[d] 6[s-p]"...)
64-element Array{Configuration{RelativisticOrbital{Int64}},1}: [Kr]ᶜ 5s² 5p-² 5p³ [Kr]ᶜ 5s 5p-² 5p³ 5d- [Kr]ᶜ 5s 5p-² 5p³ 5d [Kr]ᶜ 5s 5p-² 5p³ 6s [Kr]ᶜ 5s² 5p- 5p⁴ [Kr]ᶜ 5s² 5p- 5p³ 6p- [Kr]ᶜ 5s² 5p- 5p³ 6p [Kr]ᶜ 5s² 5p-² 5p² 6p- [Kr]ᶜ 5s² 5p-² 5p² 6p [Kr]ᶜ 5p-² 5p⁴ 6p- [Kr]ᶜ 5p-² 5p⁴ 6p [Kr]ᶜ 5s 5p- 5p⁴ 5d- [Kr]ᶜ 5s 5p- 5p⁴ 5d [Kr]ᶜ 5s 5p- 5p⁴ 6s [Kr]ᶜ 5p-² 5p³ 5d-² [Kr]ᶜ 5p-² 5p³ 5d- 5d [Kr]ᶜ 5p-² 5p³ 5d- 6s [Kr]ᶜ 5s 5p- 5p³ 5d- 6p- [Kr]ᶜ 5s 5p- 5p³ 5d- 6p [Kr]ᶜ 5s 5p-² 5p² 5d- 6p- [Kr]ᶜ 5s 5p-² 5p² 5d- 6p [Kr]ᶜ 5p-² 5p³ 5d² [Kr]ᶜ 5p-² 5p³ 5d 6s [Kr]ᶜ 5s 5p- 5p³ 5d 6p- [Kr]ᶜ 5s 5p- 5p³ 5d 6p [Kr]ᶜ 5s 5p-² 5p² 5d 6p- [Kr]ᶜ 5s 5p-² 5p² 5d 6p [Kr]ᶜ 5p-² 5p³ 6s² [Kr]ᶜ 5s 5p- 5p³ 6s 6p- [Kr]ᶜ 5s 5p- 5p³ 6s 6p [Kr]ᶜ 5s 5p-² 5p² 6s 6p- [Kr]ᶜ 5s 5p-² 5p² 6s 6p [Kr]ᶜ 5p-² 5p³ 6p-² [Kr]ᶜ 5p-² 5p³ 6p- 6p [Kr]ᶜ 5p-² 5p³ 6p² [Kr]ᶜ 5s² 5p⁴ 6p- [Kr]ᶜ 5s² 5p⁴ 6p [Kr]ᶜ 5s² 5p³ 5d-² [Kr]ᶜ 5s² 5p³ 5d- 5d [Kr]ᶜ 5s² 5p³ 5d- 6s [Kr]ᶜ 5s² 5p- 5p² 5d-² [Kr]ᶜ 5s² 5p- 5p² 5d- 5d [Kr]ᶜ 5s² 5p- 5p² 5d- 6s [Kr]ᶜ 5s² 5p³ 5d² [Kr]ᶜ 5s² 5p³ 5d 6s [Kr]ᶜ 5s² 5p- 5p² 5d² [Kr]ᶜ 5s² 5p- 5p² 5d 6s [Kr]ᶜ 5s² 5p³ 6s² [Kr]ᶜ 5s² 5p- 5p² 6s² [Kr]ᶜ 5s² 5p³ 6p-² [Kr]ᶜ 5s² 5p³ 6p- 6p [Kr]ᶜ 5s² 5p- 5p² 6p-² [Kr]ᶜ 5s² 5p- 5p² 6p- 6p [Kr]ᶜ 5s² 5p³ 6p² [Kr]ᶜ 5s² 5p- 5p² 6p² [Kr]ᶜ 5s² 5p-² 5p 5d-² [Kr]ᶜ 5s² 5p-² 5p 5d- 5d [Kr]ᶜ 5s² 5p-² 5p 5d- 6s [Kr]ᶜ 5s² 5p-² 5p 5d² [Kr]ᶜ 5s² 5p-² 5p 5d 6s [Kr]ᶜ 5s² 5p-² 5p 6s² [Kr]ᶜ 5s² 5p-² 5p 6p-² [Kr]ᶜ 5s² 5p-² 5p 6p- 6p [Kr]ᶜ 5s² 5p-² 5p 6p²
Again, using the “continuum orbitals”, it is possible to generate the state space accessible via one-photon transitions from the ground state:
Xe⁺e = excited_configurations(rc"[Kr] 5s2 5p6", ros"k[s-d]"...,
max_excitations=:singles,
keep_parity=false)
16-element Array{Configuration,1}: [Kr]ᶜ 5s² 5p-² 5p⁴ [Kr]ᶜ 5s 5p-² 5p⁴ ks [Kr]ᶜ 5s 5p-² 5p⁴ kp- [Kr]ᶜ 5s 5p-² 5p⁴ kp [Kr]ᶜ 5s 5p-² 5p⁴ kd- [Kr]ᶜ 5s 5p-² 5p⁴ kd [Kr]ᶜ 5s² 5p- 5p⁴ ks [Kr]ᶜ 5s² 5p- 5p⁴ kp- [Kr]ᶜ 5s² 5p- 5p⁴ kp [Kr]ᶜ 5s² 5p- 5p⁴ kd- [Kr]ᶜ 5s² 5p- 5p⁴ kd [Kr]ᶜ 5s² 5p-² 5p³ ks [Kr]ᶜ 5s² 5p-² 5p³ kp- [Kr]ᶜ 5s² 5p-² 5p³ kp [Kr]ᶜ 5s² 5p-² 5p³ kd- [Kr]ᶜ 5s² 5p-² 5p³ kd
We can then query for the bound and continuum orbitals thus:
map(Xe⁺e) do c
b = bound(c)
num_electrons(b) => b
end
16-element Array{Pair{Int64,Configuration{RelativisticOrbital{Int64}}},1}: 44 => [Kr]ᶜ 5s² 5p-² 5p⁴ 43 => [Kr]ᶜ 5s 5p-² 5p⁴ 43 => [Kr]ᶜ 5s 5p-² 5p⁴ 43 => [Kr]ᶜ 5s 5p-² 5p⁴ 43 => [Kr]ᶜ 5s 5p-² 5p⁴ 43 => [Kr]ᶜ 5s 5p-² 5p⁴ 43 => [Kr]ᶜ 5s² 5p- 5p⁴ 43 => [Kr]ᶜ 5s² 5p- 5p⁴ 43 => [Kr]ᶜ 5s² 5p- 5p⁴ 43 => [Kr]ᶜ 5s² 5p- 5p⁴ 43 => [Kr]ᶜ 5s² 5p- 5p⁴ 43 => [Kr]ᶜ 5s² 5p-² 5p³ 43 => [Kr]ᶜ 5s² 5p-² 5p³ 43 => [Kr]ᶜ 5s² 5p-² 5p³ 43 => [Kr]ᶜ 5s² 5p-² 5p³ 43 => [Kr]ᶜ 5s² 5p-² 5p³
map(Xe⁺e) do c
b = continuum(c)
num_electrons(b) => b
end
16-element Array{Pair{Int64,_1} where _1,1}: 0 => ∅ 1 => ks 1 => kp- 1 => kp 1 => kd- 1 => kd 1 => ks 1 => kp- 1 => kp 1 => kd- 1 => kd 1 => ks 1 => kp- 1 => kp 1 => kd- 1 => kd
Angular momentum coupling overview
This is done purely non-relativistic, i.e. 2p-
is considered
equivalent to 2p
.
terms(c"1s")
1-element Array{Term{Int64},1}: ²S
terms(c"[Kr] 5s2 5p5")
1-element Array{Term{Int64},1}: ²Pᵒ
terms(c"[Kr] 5s2 5p4 6s 7g")
13-element Array{Term{Int64},1}: ¹D ¹F ¹G ¹H ¹I ³D ³F ³G ³H ³I ⁵F ⁵G ⁵H
jj coupling is implemented slightly differently, it calculates the
possible J:s resulting from coupling n
equivalent electrons in
all combinations allowed by the Pauli principle.
intermediate_terms(ro"1s", 1)
1-element Array{Rational{Int64},1}: 1//2
intermediate_terms(ro"5p", 2)
2-element Array{Rational{Int64},1}: 0//1 2//1
intermediate_terms(ro"7g", 3)
9-element Array{Rational{Int64},1}: 3//2 5//2 7//2 9//2 11//2 13//2 15//2 17//2 21//2
CSFs are formed from electronic configurations and their possible term couplings (along with intermediate terms, resulting from unfilled subshells).:
sort(vcat(csfs(rc"3s 3p2")..., csfs(rc"3s 3p- 3p")...))
7-element Array{CSF{RelativisticOrbital,Rational{Int64}},1}: 3s(1/2|1/2) 3p²(0|1/2)+ 3s(1/2|1/2) 3p-(1/2|1) 3p(3/2|1/2)+ 3s(1/2|1/2) 3p²(2|3/2)+ 3s(1/2|1/2) 3p-(1/2|0) 3p(3/2|3/2)+ 3s(1/2|1/2) 3p-(1/2|1) 3p(3/2|3/2)+ 3s(1/2|1/2) 3p²(2|5/2)+ 3s(1/2|1/2) 3p-(1/2|1) 3p(3/2|5/2)+
- [x] Generate configurations with cores; [He], [Ne], &.
- [ ] Coefficient of fractional parentage
- [ ] Seniority number
- [-] Different coupling schemes
- [X] LS-coupling
- [ ] jk-coupling, e.g., Ne I, first excited state: 1s²2s²2p⁵(²P⁰₃.₂)3s ²[³/₂]⁰₀,₁
- [x] jj-coupling