Ground state of the H3(+) molecular ion: physics behind

Five physics mechanisms of interaction leading to the binding of the H3(+) molecular ion are identified. They are realized in a form of variational trial functions, and their respective total energies are calculated. Each of them provides subsequently the most accurate approximation for the Born–Oppenheimer (BO) ground state energy among (two–three–seven)-parametric trial functions being, correspondingly, H2-molecule plus proton (two variational parameters), H2(+)-ion plus H-atom (three variational parameters), and generalized Guillemin–Zener (seven variational parameters). These trial functions are chosen following a criterion of physical adequacy. They include the electronic correlation in the exponential form, exp(γr12), where γ is a variational parameter. Superpositions of two different mechanisms of binding are investigated, and a particular one, which is a generalized Guillemin–Zener plus H2-molecule plus proton (ten variational parameters), provides the total energy at the equilibrium of E = −1.3432 au. The superposition of three mechanisms, generalized Guillemin–Zener plus (H2-molecule plus proton) plus (H2(+)-ion plus H) (14 parameters) leads to the total energy, which deviates from the best known BO energy to 0.0004 au, it reproduces two–three significant digits in exact, non-BO total energy. In general, our variational energy agrees in two–three–four significant digits with the most accurate results available at present as well as major expectation values.