Explicitly correlated potential energy surface of H3+, including relativistic and adiabatic corrections

Investigation of Nonadiabatic Effects for the Vibrational Spectrum of a Triatomic Molecule: The Use of a Single Potential Energy Surface with Distance-Dependent Masses for H3. J Phys Chem A 2017;121:7016-7030. [PMID: 28820589 DOI: 10.1021/acs.jpca.7b04703]

On the basis of first-principles, the influence of nonadiabatic effects on the vibrational bound states of H₃⁺ has been investigated using distance-dependent reduced masses and only one single potential energy surface. For these new vibrational calculations, potentials based on explicitly correlated wave functions are used where, in addition, adiabatic corrections and relativistic contributions are taken into account. For the first time, several different fully distance-dependent reduced mass surfaces in three dimensions have been incorporated in the vibrational calculations.

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.

A systematic investigation of the ground state potential energy surface of H3+

Based on different ab initio electronic structure calculations (CI-R12 and Gaussian Geminals) of the Born-Oppenheimer electronic energy E(BO) of H(3)(+) from high to highest quality, we build up a potential energy surface which represents a highly reliable form of the topology of the whole potential region, locally and globally. We use the CI-R12 method in order to get within reasonable CPU-time a relatively dense grid of energy points. We demonstrate that CI-R12 is good enough to give an accurate surface, i.e., Gaussian Geminals are not absolutely necessary. For different types of potential energy surface fits, we performed variational calculations of all bound vibrational states, including resonances above the dissociation limit, for total angular momentum J = 0. We clarify the differences between different fits of the energy to various functional forms of the potential surface. Small rms-values (<1 cm(-1)) of the fit do not provide precise information about the interpolatory behaviour of the fit functions.

The H(3) (+) rovibrational spectrum revisited with a global electronic potential energy surface

In this paper, we have computed the rovibrational spectrum of the H(3) (+) molecule using a new global potential energy surface, invariant under all permutations of the nuclei, that includes the long range electrostatic interactions analytically. The energy levels are obtained by a variational calculation using hyperspherical coordinates. From the comparison with available experimental results for low lying levels, we conclude that our accuracy is of the order of 0.1 cm(-1) for states localized in the vicinity of equilateral triangular configurations of the nuclei, and changes to the order of 1 cm(-1) when the system is distorted away from equilateral configurations. Full rovibrational spectra up to the H(+)+H(2) dissociation energy limit have been computed. The statistical properties of this spectrum (nearest neighbor distribution and spectral rigidity) show the quantum signature of classical chaos and are consistent with random matrix theory. On the other hand, the correlation function, even when convoluted with a smoothing function, exhibits oscillations which are not described by random matrix theory. We discuss a possible similarity between these oscillations and the ones observed experimentally.

Accurate ab initio based multisheeted double many-body expansion potential energy surface for the three lowest electronic singlet states of H3+

The authors present diabatic and adiabatic potential energy surfaces for the three lowest electronic singlet states of H3+. The modeling of the surfaces is based on the multi-sheeted double many-body expansion method which consists of dressing the various matrix elements of the diatomics-in-molecules potential matrix with three-body terms. The avoided crossing between the two lowest states and the conical intersection between the second and the third state are accurately represented by construction.

Rotation-vibrational states of H3+ and the adiabatic approximation

We discuss recent progress in the calculation and identification of rotation-vibrational states of H3+ at intermediate energies up to 13,000 cm(-1). Our calculations are based on the potential energy surface of Cencek et al. which is of sub-microhartree accuracy. As this surface includes diagonal adiabatic and relativistic corrections to the fixed nuclei electronic energies, the remaining discrepancies between our calculated and experimental data should be due to the neglect of non-adiabatic coupling to excited electronic states in the calculations. To account for this, our calculated energy values were adjusted empirically by a simple correction formula. Based on our understanding of the adiabatic approximation, we suggest two new approaches to account for the off-diagonal adiabatic correction, which should work; however, they have not been tested yet for H3+. Theoretical predictions made for the above-barrier energy region of recent experimental interest are accurate to 0.35 cm(-1) or better.

Physics, chemistry and astronomy of H3+. Introductory remarks

The inspiring developments in astronomy, physics and chemistry of since 2000, which led to this Royal Society Discussion Meeting, are reviewed.