Abstract The any particle molecular orbital (APMO) approach extends regular electronic structure methods to study atomic and molecular systems in which electrons and other particles are treated simultaneously as quantum waves. A number of electronic structure methodologies have been extended under the APMO framework and applied to investigate nuclear quantum effects including isotope effects and nuclear delocalization and to calculate proton binding energies and affinities. In addition, APMO methodologies have been employed to analyze physical and chemical properties of atomic and molecular systems containing exotic subatomic particles.