Julia code for the optimization of basis in quantum chemistry on a toy model. This code is used in our paper On basis set optimization in quantum chemistry, available on arXiv.

Requirements:

Julia 1.7 with the libraries:

• Optim, Polynomials, SpecialPolynomials, KrylovKit for the computations;
• JSON3 for saving results;
• PGFPlots, LaTeXStrings, DataFrames for plotting results.

Usage

This code runs the computations to perform the numerical experiments from [1]. Each section with numerical results is associated with a .jl file which runs the computations, saves them in the associated folder (in .json files) and then automatically plots the results in these folders (in .pdf files).

To perform the computations, first open the Julia shell with julia --project from the location of this repository and then run

using Pkg
Pkg.instantiate()

Then, you can run all the computations at once with include("run_all_computations.jl"). Running all the computations takes around 30 minutes. You can also run computations for each section individually by include("file.jl") to perform the simulations for the associated section.

The .jl file and folder are associated to the following sections:

• naive_approach.jl runs simulations from Section 2.
• optimize_basis.jl runs simulations from Section 4.1.
• optimize_basis_random_start.jl runs simulations from Section 4.2.1.
• optimize_basis_extrapolate_a.jl runs simulations from Section 4.2.2.
• optimize_basis_compare_sampling.jl runs simulations from Section 4.2.3.
• optimize_basis_N5.jl runs simulations from Section 4.2.4.

Contact

This is research code, not necessarily user-friendly, actively maintened or extremely robust. If you have questions or encounter problems, get in touch!