Software

OPSOLDE

On Polynomial Solutions of Ordinary Linear Differential Equations. This Mathematica script (and accompanying GUI) can generate analytical polynomial solutions to ordinary linear differential equations provided they have polynomial-form coefficients. Notable applications exist, such as application to the Heun and (2+1)-dimensional Dirac equations, both of which are built into the GUI as defaults.

Published Alongside: Algorithms, 13(11), 286 (2020). doi: 10.3390/a13110286.

Oscallot

This Mathematica script models interacting isotropic quantum harmonic oscillator systems from first principles. The code first positions 2, 3, or 4 oscillators along the z-axis, generates the appropriate Hamiltonian elements, and considers a trial interaction wavefunction in the form of linear combinations of single-oscillator wavefunctions. The energy contributions are solved for, and the expansion coefficients are variationally optimized using the method of Lagrange multipliers. Post-calculation, each Oscillator’s electron density is obtained and used to compare and contrast various post-SCF dispersion coefficients that are commonly employed in density-functional theory.

Published Alongside: J. Chem. Phys. 158, 204110 (2023). doi: 10.1063/5.0142465.