  In the noisy intermediate-scale quantum era, ab initio computation of the
electronic structure problem has become one of the major benchmarks for
identifying the boundary between classical and quantum computational power. The
single-particle basis set plays a key role in the electronic structure methods
implemented on both classical and quantum devices. To investigate the
consequences of the single-particle basis set, we propose a framework for more
customizable basis set generation and basis set optimization. This framework
allows configurations of composite Gaussian-type basis functions to go beyond
typical Gaussian-type basis set frameworks such as the atomic orbitals and
floating basis sets. Such basis set generations set the stage for more flexible
variational optimization of basis set parameters. To realize this framework, we
have developed an open-source electronic structure package named ``Quiqbox'' in
the Julia programming language. Both the Hartree--Fock procedure and
Gaussian-based electronic integral computations are implemented in this
package. We compare Quiqbox with the basis set optimization package DiffiQult
and find faster convergence of the basis set optimization with lower run time.
We also demonstrate the additional customizability Quiqbox brings for more
systematic basis set research with an example of constructing and optimizing
delocalized orbitals.
