Orbital properties

expandConfig(config::String; Err=true)

Expand configuration into Array of shell configurations.

Example

julia> expandConfig("[Ar]4s¹") == ["1s²", "2s²", "2p⁶", "3s²", "3p⁶", "4s¹"]
true

formatConfig(config::String)

format configuration in hydrogenic ordering

Example

julia> formatConfig("[Ar]4s¹")
"1s²2s²2p⁶3s²3p⁶"

splitConfig(config::String; Err=true)

Expand configuration into Array of shell configurations.

Example

julia> splitConfig("[Ar]4s¹") == (["1s²", "2s²", "2p⁶", "3s²", "3p⁶"], ["4s¹"])
true

collectConfig(config::String)

Example:

julia> collectConfig("[Be]2p¹") == ["1s↓0", "1s↑0", "2s↓0", "2s↑0", "2p↓-1"]
true

julia> collectConfig("1s²2p¹") == ["1s↓0", "1s↑0", "2p↓-1"]
true

listConfigurations(Z1::Int, Z2::Int; Q=0)

List of groundstate configurations of atoms with atomic charge Q.

Example

julia> listConfigurations(1:4; Q=0)
(1, " 1s¹", "1s¹")
(2, "1s² ", "[He]")
(3, "1s² 2s¹", "[He]2s¹")
(4, "1s²2s² ", "[Be]")

dictAtomicOrbital

Example:

julia> dictAtomicOrbital
Dict{String, Tuple{Int64, Int64}} with 15 entries:
  "4d" => (4, 2)
  "5f" => (5, 3)
  "3p" => (3, 1)
  "4p" => (4, 1)
  "5d" => (5, 2)
    ⋮  =>  ⋮

julia> n, l = get(dictAtomicOrbital, "3d", nothing)
(3, 2)

Orbit(name, n, n′, ℓ, mℓ)

Type for specification of atomic orbitals with fields:

• .name: name
• .n: principal quantum number
• .n′: radial quantum number (number of nodes in radial wavefunction)
• .ℓ: orbital angular momentum valence electron
• .mℓ: orbital angular momentum projection valence electron

The type Orbit is best created with the function castOrbit.

castOrbit(;n=1, ℓ=0, mℓ=0, msg=true)

Create Orbit with fields:

• .name: name
• .n: principal quantum number
• .n′: radial quantum number (number of nodes in radial wavefunction)
• .ℓ: orbital angular momentum valence electron
• .mℓ: orbital angular momentum projection valence electron

Example:

julia> castOrbit(n=1, ℓ=0; msg=true)
Orbital: 1s
    principal quantum number: n = 1
    radial quantum number: n′ = 0 (number of nodes in radial wavefunction)
    orbital angular momentum of valence electron: ℓ = 0
    orbital angular momentum projection of valence electron: mℓ = 0
Orbit("1s", 1, 0, 0, 0)

castOrbit(strOrbit::String; mℓ=0, msg=false)

Example:

julia> castOrbit("2p"; mℓ=-1, msg=true)
Orbital: 2p
    principal quantum number: n = 2
    radial quantum number: n′ = 0 (number of nodes in radial wavefunction)
    orbital angular momentum of valence electron: ℓ = 1
    orbital angular momentum projection of valence electron: mℓ = -1
Orbit("2p", 2, 0, 1, -1)

Spinorbit

Type for specification of atomic Spinorbitals with fields:

• .name: spinorbital name (string)
• .n: principal quantum number
• .n′: radial quantum number (number of nodes in radial wavefunction)
• .ℓ: orbital angular momentum valence electron
• .mℓ: orbital angular momentum projection valence electron
• .ms: spin magnetic quantum number (Rational{Int})

The type Spinorbit is best created with the function castSpinorbit.

castSpinorbit(;n=1, ℓ=0, mℓ=0, up=true, msg=false)

Create Spinorbit with fields:

• .name: spinorbital name (string)
• .n: principal quantum number
• .n′: radial quantum number (number of nodes in radial wavefunction)
• .ℓ: orbital angular momentum valence electron
• .mℓ: orbital angular momentum projection valence electron
• .ms: spin magnetic quantum number (Rational{Int})

Example:

julia> castSpinorbit(n=1, ℓ=0, msg=true)
Spinorbital: 1s↑
    principal quantum number: n = 1
    radial quantum number: n′ = 0 (number of nodes in radial wavefunction)
    orbital angular momentum of valence electron: ℓ = 0
    orbital angular momentum projection of valence electron: mℓ = 0
    spin magnetic quantum number: ms = 1/2
Spinorbit("1s↑", 1, 0, 0, 0, 1//2)

castSpinorbit(config::String; msg=false)

Example:

julia> castSpinorbit1("2p"; msg=true)
Spinorbital: 2p↓
    principal quantum number: n = 2
    radial quantum number: n′ = 0 (number of nodes in radial wavefunction)
    orbital angular momentum of valence electron: ℓ = 1
    orbital angular momentum projection of valence electron: mℓ = 1
    spin magnetic quantum number: ms = -1/2
Spinorbit("2p↓", 2, 0, 1, 1, -1//2)

julia> castSpinorbit1("2p↑-1"; msg=true)
Spinorbital: 2p↑
    principal quantum number: n = 2
    radial quantum number: n′ = 0 (number of nodes in radial wavefunction)
    orbital angular momentum of valence electron: ℓ = 1
    orbital angular momentum projection of valence electron: mℓ = -1
    spin magnetic quantum number: ms = 1/2
Spinorbit("2p↑", 2, 0, 1, -1, 1//2)

collectSpinorbit(config::String; msg=false)

Collect the spinobitals specified by config (in standard configuration notation) into an array of spinorbitals.

Example:

julia> config = "1s²2s²2p⁶";

julia> collectSpinorbit(config; msg=true)
10-element Vector{Spinorbit}:
 Spinorbit("1s↓", 1, 0, 0, 0, -1//2)
 Spinorbit("1s↑", 1, 0, 0, 0, 1//2)
 Spinorbit("2s↓", 2, 1, 0, 0, -1//2)
 Spinorbit("2s↑", 2, 1, 0, 0, 1//2)
 Spinorbit("2p↓", 2, 0, 1, -1, -1//2)
 Spinorbit("2p↓", 2, 0, 1, 0, -1//2)
 Spinorbit("2p↓", 2, 0, 1, 1, -1//2)
 Spinorbit("2p↑", 2, 0, 1, -1, 1//2)
 Spinorbit("2p↑", 2, 0, 1, 0, 1//2)
 Spinorbit("2p↑", 2, 0, 1, 1, 1//2)

Shell(name, spinorbitals)

Type for specification of closed electron shells with fields:

• .name: shell configuration (::String)
• .spinorbit: Array of spinorbitals (::Vector{Spinorbit})

The type Shell is best created with the function castShell.

castShell(;n=1, ℓ=0, msg=false)

Create closed electron Shell with fields:

• .name: shell configuration (::String)
• .spinorbit: Array of Spinorbitals (::Vector{Spinorbit})

Example:

julia> castShell(n=3, ℓ=0, msg=true)
Shell configuration: 3s²
    shell occupation: wl = 2 electrons
    principal quantum number: n = 3
    orbital angular momentum of electrons: ℓ = 0
Shell("3s²", Spinorbit[Spinorbit("3s↓", 3, 2, 0, 0, -1//2), Spinorbit("3s↑", 3, 2, 0, 0, 1//2)])

castShell(strShell::String; msg=false)

Example:

julia> castShell("3s", msg=false)
Shell("3s²", Spinorbit[Spinorbit("3s↓", Orbit("3s", 3, 2, 0, 0), -1//2), Spinorbit("3s↑", Orbit("3s", 3, 2, 0, 0), 1//2)])

Shells(name, shells)

Type for specification of closed electron Shells with fields:

• .name: shell configuration (::String)
• .count: number of shells (::Int)
• .n: array of shell principal quantum numers (Vector{Int})
• .ℓ: array of shell angular momenta (::Vector{Int})
• .shell: Array of Shells (::Vector{Shell})

The type Shells is best created with the function castShells.

castShells(strShells::String; msg=false)

Create configuration of closed electron Shells with fields:

• .name: shell configuration (::String)
• .count: number of shells (::Int)
• .n: array of shell principal quantum numers (Vector{Int})
• .ℓ: array of shell angular momenta (::Vector{Int})
• .shell: Array of Shells (::Vector{Shell})

Example:

julia> castShells("1s2s",msg=true);
Shell: 1s²
    number of shell electrons: N = 2
    principal quantum number: n = 1
    orbital angular momentum of electrons: ℓ = 0
Shell: 2s²
    number of shell electrons: N = 2
    principal quantum number: n = 2
    orbital angular momentum of electrons: ℓ = 0

Term(name::String, n::Int, ℓ::Int, S::Real, L::Int, J::Real)

Type for specification of atomic fine-structure Terms with fields:

• name: name
• .n: principal quantum number
• .n′: radial quantum number (number of nodes in wavefunction)
• .ℓ: orbital angular momentum valence electron
• .S: total electron spin in units of ħ
• .L: total orbital angular momentum in units of ħ
• .J: total electronic angular momentum in units of ħ

The type Term is best created with the function castTerm.

castTerm(n::Int; ℓ=0, S=1//2, L=0, J=1//2, msg=false)

Specify Term in the Term notatation with fields:

• .n: principal quantum number
• .n′: radial quantum number (number of nodes - autogenerated)
• .ℓ: orbital angular momentum valence electron
• .S: total electron spin
• .L: total orbital angular momentum
• .J: total electronic angular momentum

Examples:

julia> castTerm(1; ℓ=0, S=1//2, L=0, J=1//2, msg=true)
Term created: 1s ²S₁⸝₂; n = 1,  n′ = 0, ℓ = 0, S = 1//2, L = 0, J = 1//2
Term("1s ²S₁⸝₂", 1, 0, 0, 1//2, 0, 1//2)