Computational study of statically confined electron systems by means of quantum chemical and machine learning techniques

Resumen

Once the state of the art concerning Wigner molecules, Hooke atoms and some machine learningtechniques has been described, in this section the main goals of the present work will be provided. Weshall now list the mains goals of this work:1. Optimize distributed gaussian basis functions for correctly describing the one- and two-dimensionallyconfined electronic systems by means of machine learning approaches (Neural Networks) for variableconfinement parameter k = ¿2 . Besides, set an optimal wavefunction based electronic structure methodfor obtaining accurate wavefunctions. Employ the settled protocole in order to study the Wigner locationfor small number of electrons n = {2, 3, 4} in the high spin state.2. Optimize one-centre even tempered basis functions using classical optimiza tion techniques (simplexand Newton-Raphson) for properly describing three dimensional spherical Hooke atoms composed byfew number of electrons n = {2, 4, 6, 8, 10} and confinement parameter k = ¿2= 1/4. Settle an optimalwavefunction based method for obtaining accurate energies for the lowest laying singlet and triplet states.3. Implement and improve machine learning methods based on semi-supervised learning and uncertaintysampling for obtaining phase diagrams efficiently and provide some chemically relevant systems.4. Calculate analytical one-body integrals corresponding to gaussian confinement potentials in terms ofgaussian basis functions and implement them in GAMESS-US. Provide some examples related to theprevious sections.