QMol-grid

QMol-grid provides a MATLAB suite of routines for performing quantum-mechanical simulations in atomic and molecular systems.

QMol-grid: A MATLAB package for quantum-mechanical simulations in atomic and molecular systems

The QMol-grid package provides a suite of routines for performing quantum-mechanical simulations in atomic and molecular systems in one spatial dimension. All simulations use an underlying Cartesian-grid discretization scheme. The QMol-grid package is written using MATLAB's object-oriented features and handle classes.

The QMol-grid package provides support for the following types of computations:

• DFT Ground- and excited-state density-functional theory, both using a Cartesian grid or basis-set discretization
• HF Ground- and excited-state Hartree Fock, both using a Cartesian grid or basis-set discretization
• CI Ground- and excited-state configuration interaction, both using a Cartesian grid or basis-set discretization
• SE Ground- and excited-state Schrödinger equation, both using a Cartesian grid or basis-set discretization
• TDDFT Real-time time-dependent density-functional theory, using a Cartesian grid
• TDHF Time-dependent Hartree Fock, using a Cartesian grid
• TDSE Time-dependent Schrödinger equation, using a Cartesian grid
• TDCI Time-dependent configuration interaction, using a Cartesian grid

The time-propagators are computed using symplectic-split operators (2nd, 4th, and 6th order in time, and spectral in space). They support field-free and laser-driven simulations (in the dipole approximation) with the following on-the-fly features, each specifying their own time sampling

• Checkpointing, with the creation of a restart MATLAB file that can be used to resume a calculation that was stopped before it was finished
• Calculation and storage of the dipole, dipole velocity, and dipole acceleration signals
• Calculation and storage of the wave function(s)/Kohn-Sham orbitals and Hamiltonian-component energies
• Storage of the wave function(s) (Schrödinger), and Kohn-Sham orbitals and one-body density (DFT)
• Calculation and storage of the ionization signal, keeping track of how much electronic density is absorbed at the domain boundaries
• Calculation and storage of the results of installable output functions of the wave function(s) (Schrödinger), and Kohn-Sham orbitals or one-body density (DFT)
• Saving the intermediate Schrödinger- or DFT-model objects in separate MATLAB files (.mat)

Installation

The QMol-grid package can be installed directly from MATLAB (preferred) or its GitHub repository.

From MALAB (preferred):

• In the Add-Ons explorer, search for "QMol-grid" and the add the package to MATLAB. This will install the latest release version of QMol-grid. The package documentation will then be accessible in MATLAB's, in the "Supplemental Software" section

From the GitHub repository:

• include the entire content of the folder /src/, including all its subfolders, in a folder of the type <user>/Documents/MATLAB/QMol-grid (see the instructions on GitHub for getting a specific release or development version)
• add permanently the folder <user>/Documents/MATLAB/QMol-grid (without its subfolders) to MATLAB path
• after successful installation, the package documentation will be accessible in MATLAB's, in the "Supplemental Software" section

Tests

Display the list of components in the QMol-grid package

QMol_doc.showComponents;

The QMol-grid package provides a suite of tests that performs low-level checks on the various properties that are defined throughout its components. The test suite can be used to check basic functions after installing the package or modifying its components.

Run all available unit tests using

QMol_test.test;

Limitations

• The current release only supports one-dimensional computations
• Time propagation on basis sets is currently not available

Documentation

A full description of the QMol-grid package, including all possible input parameters and calculation features is included in the MATLAB documentation provided with the package. After installation, the package documentation is accessible in MATLAB, in the "Supplemental Software" section. The documentation includes a series of tutorials, starting with SE ground-state calculations, and going through TDSE, DFT, and TDDFT calculations to help new users getting familiarized with setting up calculations, input parameters, and output variables. Throughout, the documentation also includes many script samples illustrating how one can use the various features. Finally, the documentation discusses the required class structure for advanced users who wish to add their own functionalities to the package and inherit common interface methods to the QMol-grid package.

A copy of the QMol-grid package documentation is also available on the GitHub wiki.

See the GitHub page and documentation tutorials for illustrative examples of how to use QMol-grid.

Reference

• F. Mauger and C. Chandre, "QMol-grid: A MATLAB package for quantum-mechanical simulations in atomic and molecular systems," SoftwareX 28, 101968 (2024)

Acknowledgments

The original development of the QMol-grid package, and its (TD)DFT features, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-SC0012462.

Addition of the (TD)SE, (TD)CI, and extended TDDFT features was supported by the National Science Foundation under Grant No. PHY-2207656.