add licence, Shells.jl and ShellGen.jl

LICENSE.md

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+MIT License
+
+Copyright (c) 2023 Astrid Klipfel, Bastien Casier and Olivier Peltre
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

generation/ShellGen.jl

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+include("Shells.jl")
+
+#--- Sample Basis sets --- 
+
+"""
+    PairParams(atom, normalize=false[, logdev_rate, logdev_max])
+
+Sampling parameters for 2-center 2-shell basis sets.
+
+# Note
+
+When called as `PairParams(normalize::Bool)`, will sample random atomic numbers 
+within `1:10`.
+
+# Arguments
+- `atom::Vector{Int64}`: length-2 vector of atomic numbers 
+- `normalize::Bool`: whether to normalize integral outputs (if used?)
+- `logdev_rate::Real`: exponential decay rate of the wavelength logarithm distribution
+- `logdev_max::Real`: logarithm of the greatest wavelength
+"""
+struct PairParams 
+    atom::Vector{Int64}
+    normalize::Bool
+    logdev_rate::Real  
+    logdev_max::Real 
+end
+function PairParams(atom::Vector{Int64}, norm::Bool = false)
+    PairParams(atom, norm, 2, .6)
+end
+function PairParams(normalize::Bool = false)  
+    Z = rand(1:10, 2)
+    return PairParams(Z, normalize)
+end
+
+"""
+    randPair(l1, l2[, params])
+
+Sample a random 2-shell `Basis`.
+"""
+function randPair(l1::Int, l2::Int, params::PairParams)::Basis
+    # sample exponents 
+    exps = begin
+        max, rate = params.logdev_max, params.logdev_rate
+        log_devs = max .- rand(Exponential(rate), 2)
+        devs = exp.(log_devs)
+        1 ./ (2 .* devs .^ 2)
+    end
+    exp_1 = SVector{1, Float64}(exps[1])
+    exp_2 = SVector{1, Float64}(exps[2])
+    # sample 2nd atomic position
+    xyz = begin
+        exp_12 = exps[1] * exps[2] / (exps[1] + exps[2])
+        dev_12 = 1 / sqrt(2exp_12)
+        SVector{3, Float64}(dev_12 * randn((3)))
+    end
+    # atom charges
+    origin = SVector{3, Float64}(0., 0., 0.)
+    pos = (origin, xyz)
+    mol = map(zip(params.atom, pos)) do A
+        Za, ra = A
+        move(atom(Za), ra)
+    end
+    # basis sets 
+    coef :: SMatrix{2, 1, Float64} = 
+        params.normalize ? 
+            vcat(exp_1, exp_2) ./ 2pi .^ (3 / 4 ) :
+            [1., 1.]
+    shells = [BasisFunction(l1, coef[1,:], exp_1, mol[1]),
+              BasisFunction(l2, coef[2,:], exp_2, mol[2])]
+    return (mol, shells)::Basis
+    return basis
+end
+randPair(l1::Int, l2::Int, atom::Vector{Int64}) = randPair(l1, l2, PairParams(atom))
+randPair(l1::Int, l2::Int) = begin p = PairParams(); randPair(l1, l2, p); end
+randPair(l::Int, params::PairParams) = randPair(l, l, params)
+randPair(l::Int) = randPair(l, l)
+
+"""
+    QuadParams(r12_dev[, pair])
+
+Sampling parameters for 4-center basis sets.
+
+# Arguments
+- `r12_dev::Float64`: typical distance between pairwise barycenters
+- `pair::Vector{PairParams}`: sampling parameters for center pairs
+"""
+struct QuadParams
+    r12_dev::Float64 
+    pair::Vector{PairParams}
+end
+QuadParams(r12_dev::Float64) = begin
+    p = PairParams([1, 1])
+    QuadParams(r12_dev, [p, p])
+end
+QuadParams() = QuadParams(.05)
+
+"""
+    randQuadruple(l1, l2, l3, l4[, params, shuflle=false)
+
+Sample a random quadruple of shells.
+"""
+function randQuadruple(l1::Int, l2::Int, l3::Int, l4::Int, params::QuadParams, shuffle::Bool=false)
+    if shuffle
+        p = randperm(4)
+        p_1 = sortperm(p)
+        mol, shells = randQuadruple([l1, l2, l3, l4][p]..., params, false)
+        return mol[p_1], shells[p_1]
+    end
+    # sample offset between the two R³ factors
+    r12 = SVector{3, Float64}(params.r12_dev * randn(3))
+    # sample pairs and move them
+    AB, shells_AB = randPair(l1, l2, params.pair[1])
+    CD, shells_CD = randPair(l3, l4, params.pair[2])
+    ABCD = append!(center(AB), center(CD, r12))
+    shells = append!(shells_AB, shells_CD)
+    shells_ABCD = map(zip(ABCD, shells)) do pair
+        atom, shell = pair
+        BasisFunction(shell.l, shell.coef, shell.exp, atom)
+    end
+    return ABCD, shells_ABCD
+end
+function randQuadruple(l1::Int, l2::Int, l3::Int, l4::Int, ps...)
+    p = QuadParams(ps...)
+    randQuadruple(l1, l2, l3, l4, p)
+end

generation/Shells.jl

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+using Random
+using Distributions
+using StaticArrays
+using GaussianBasis
+using Molecules
+using PeriodicTable
+using Printf
+
+"""Type of `GaussianBasis.BasisSet` parameters"""
+const Basis = Tuple{Atom, Vector{BasisFunction}}
+
+""" 
+    atom([Z, [xyz]])
+
+Return a `Molecules.Atom` instance at specified position. 
+
+When called with no arguments, `atom()` will return a mass 1 ghost
+atom with zero electric charge.
+
+# Arguments
+- `Z::Union{Integer, String}=0` atomic number or symbol. 
+- `xyz::SVector{3, Float64}` atom position, defaults to zero.
+
+# Examples
+```jldoctest
+julia> H = atom("H");   # hydrogen atom at 0
+julia> He = atom(2, SVector(0.76, 0., 0.)) # Helium-like center
+julia> ghost = atom();  # ghost center at 0
+```
+"""
+atom(Z::Integer) = Molecules.Atom(Z, Float64(Z), SVector(0., 0., 0.))
+atom(symbol::String) = GaussianBasis.parse_string(symbol * " 0 0 0")[1]
+atom() = Molecules.Atom(0, 1.0, SVector(0., 0., 0.))
+atom(symbol::Union{Integer, String}, xyz::SVector{3, Float64}) = move(atom(symbol), xyz)
+atom(xyz::SVector{3, Float64}) = move(atom(), xyz)
+
+"""
+Move an atom to a new position.
+"""
+move(atom::Molecules.Atom, xyz::SVector{3, Float64})::Molecules.Atom = 
+    Molecules.Atom(atom.Z, atom.mass, xyz)
+
+"""
+    center(atoms[, offset])
+
+Move a vector of atoms to a desired barycenter.
+
+All atoms are treated as mass 1.
+"""
+function center(atoms::Vector{Molecules.Atom{T, X}}) where T<:Real where X<:Real
+    center(atoms, SVector{3, X}([0, 0, 0]))
+end
+
+#--- Parse H atom once for all
+HYDROGEN = atom("H")
+
+"""
+Patch `string_repr(A::Atom)` to accept ghost centers.
+"""
+Molecules.string_repr(A::Atom) = begin
+    name = haskey(elements, A.Z) ? elements[A.Z].symbol * " " : "∅ "
+    out = name * "(Z = $(A.Z))"
+    out = out * @sprintf " : %.2f %.2f %.2f" A.xyz...
+end
+Base.show(io::IO, ::MIME"text/plain", at::Atom) = begin
+    show(io, Molecules.string_repr(at))
+end
+
+