The vibration spectrum of H3+

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.

Ab initio rotation-vibration energy levels of triatomics to spectroscopic accuracy

The factors that need to be taken into account to achieve spectroscopic accuracy for triatomic molecules are considered focusing on H3+ and water as examples. The magnitude of the adiabatic and non-adiabatic corrections to the Born-Oppenheimer approximation is illustrated for both molecules, and methods of including them ab initio are discussed. Electronic relativistic effects are not important for H3+, but are for water for which the magnitude of the various effects is discussed. For H3+ inclusion of rotational non-adiabatic effects means that levels can be generated to an accuracy approaching 0.01 cm(-1); for water the error is still dominated by the error in the correlation energy in the electronic structure calculation. Prospects for improving this aspect of the calculation are discussed.

First-principles rovibrational analysis of the H3+-molecule

The fitting of highly accurate potential energy points and of the diagonal adiabatic coupling for H3+ using different functional forms is presented. A recently derived analytical potential based on 69 points has been extended to give a highly reliable form of the topology of the surface far beyond the barrier to linearity. Rovibrational frequencies have been derived and are compared with experiment. Detailed information about the experimentally observed rovibrational transitions near 1.25 microm will be given. The computed transition frequencies reproduce experimental transitions within a tenth up to a few hundredths of a wavenumber, if a simulation of non-adiabatic effects is taken into account.