Physics, chemistry and astronomy of H3+. Introductory remarks

A nearly complete treatment of the effect of non-adiabaticity on rovibrational energies of H3+ (Part III)

In this article, significant contributions of non-adiabaticity for the rovibrational bound states up to 25 000 cm-1 and total angular momentum J = 0-20 of H3+ are investigated. A coupled-perturbed full configuration interaction (CP-FCI) treatment is applied to calculate all couplings between electronic states caused by the nuclear motion. These derivative couplings were evaluated up to the second order by means of a perturbation treatment and include all nuclear Cartesian first and second derivatives of the electronic wavefunctions. In particular, the coupling of special derivatives with respect to r and R in the Jacobi coordinate representation is more significant than thought. The perturbation approach is especially optimal for the treatment of weak non-adiabaticity in case of rovibrational energies in H3+ and had not been available before for H3+ or other triatomics. Using exclusively Gaussian basis functions for CP-FCI appears to be sufficient, because explicit correlated wavefunctions are already used for all other potential energy contributions. Our work is an extension of earlier non-adiabatic investigations based on first derivative couplings of electronic states that led to the concept of geometry-dependent effective nuclear masses and which needs only a single potential energy surface for the dynamics. The implementation allows us to include all non-adiabatic effects up to the order of O(μ-2), μ being the reduced nuclear mass. Our treatment works for any isotopologue and for the whole potential energy curve or surface. By this treatment, a further reduction in deviations to experimental data for most rovibrational levels to less than 0.1 cm-1 is possible. For the related transition frequencies, 1366 of 1720 known rovibrational transitions in H3+ have deviations less than 0.1 cm-1 without using any empirically adjustable parameters or optimizing the nuclear mass for a specific transition. For many questionable assignments (deviations >0.3 cm-1) of observed transitions in H3+, a new labeling is proposed.

Structure, energetics, and spectroscopy of the chromophores of HHe+n, H2He+n, and He+n clusters and their deuterated isotopologues

The linear molecular ions H₂He⁺, HHe+2, and He+3 are the central units (chromophores) of certain He-solvated complexes of the H₂He+n, HHe+n, and He+n families, respectively. These are complexes which do exist, according to mass-spectrometry studies, up to very high n values. Apparently, for some of the H₂He+n and He+n complexes, the linear symmetric tetratomic H₂He+2 and the diatomic He+2 cations, respectively, may also be the central units. In this study, definitive structures, relative energies, zero-point vibrational energies, and (an)harmonic vibrational fundamentals, and, in some cases, overtones and combination bands, are established mostly for the triatomic chromophores. The study is also extended to the deuterated isotopologues D₂He⁺, DHe+2, and D₂He+2. To facilitate and improve the electronic-structure computations performed, new atom-centered, fixed-exponent, Gaussian-type basis sets called MAX, with X = T(3), Q(4), P(5), and H(6), are designed for the H and He atoms. The focal-point-analysis (FPA) technique is employed to determine definitive relative energies with tight uncertainties for reactions involving the molecular ions. The FPA results determined include the 0 K proton and deuteron affinities of the ⁴He atom, 14 875(9) cm^-1 [177.95(11) kJ mol^-1] and 15 229(8) cm^-1 [182.18(10) kJ mol^-1], respectively, the dissociation energies of the He+2 → He⁺ + He, HHe+2 → HHe⁺ + He, and He+3 → He+2 + He reactions, 19 099(13) cm^-1 [228.48(16) kJ mol^-1], 3948(7) cm^-1 [47.23(8) kJ mol^-1], and 1401(12) cm^-1 [16.76(14) kJ mol^-1], respectively, the dissociation energy of the DHe+2 → DHe⁺ + He reaction, 4033(6) cm^-1 [48.25(7) kJ mol^-1], the isomerization energy between the two linear isomers of the [H, He, He]⁺ system, 3828(40) cm^-1 [45.79(48) kJ mol^-1], and the dissociation energies of the H₂He⁺ → H+2 + He and the H₂He+2 → H₂He⁺ + He reactions, 1789(4) cm^-1 [21.40(5) kJ mol^-1] and 435(6) cm^-1 [5.20(7) kJ mol^-1], respectively. The FPA estimates of the first dissociation energy of D₂He⁺ and D₂He+2 are 1986(4) cm^-1 [23.76(5) kJ mol^-1] and 474(5) cm^-1 [5.67(6) kJ mol^-1], respectively. Determining the vibrational fundamentals of the triatomic chromophores with second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) techniques, both built around the Eckart-Watson Hamiltonian, proved unusually challenging. For the species studied, VPT2 has difficulties yielding dependable results, in some cases even for the fundamentals of the H-containing molecular cations, while carefully executed VCI computations yield considerably improved spectroscopic results. In a few cases unusually large anharmonic corrections to the fundamentals, on the order of 15% of the harmonic value, have been observed.

Analysis of QED and non-adiabaticity effects on the rovibrational spectrum of H3 + using geometry-dependent effective nuclear masses

The influence of QED effects (including one- and two-electron Lamb-shift, Araki-Sucher term, one-loop self-energy, and finite nuclear size correction) together with non-adiabatic effects on the rovibrational bound states of H₃ ⁺ has been investigated. Non-adiabaticity is modeled by using geometry-dependent effective nuclear masses together with only one single potential energy surface. In conclusion, for rovibrational states below 20 000 cm^-1, QED and relativistic effects do nearly compensate, and a potential energy surface based on Born-Oppenheimer energies and diagonal adiabatic corrections has nearly the same quality as the one including relativity with QED; the deviations between the two approaches for individual rovibrational states are mostly below 0.02 cm^-1. The inclusion of non-adiabatic effects is important, and it reduces deviations from experiments mostly below 0.1 cm^-1.

Hydrogen molecular ions: H3+, H5+ and beyond

Three decades after the spectroscopic detection of H3+ in space, the inspiring developments in physics, chemistry and astronomy of Hn+ (n = 3, 5, 7) systems, which led to this Royal Society Discussion Meeting, are reviewed, the present state of the art as represented by the meeting surveyed and future lines of research considered. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

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.

High-resolution sub-Doppler Lamb dips of the ν2 fundamental band of H3(+)

The high-resolution sub-Doppler Lamb dips of the ν2 fundamental band transitions of H3(+) have been observed using an extended negative glow discharge tube as an ion source and a periodically poled lithium niobate optical parametric oscillator as a radiation source. The absolute frequency of the R(1,0) transition was measured to be 81,720,371.550 MHz with an accuracy of 250 kHz using an optical frequency comb. In addition, we have investigated the linewidth of the Lamb-dip signal of the R(3,0) transition systematically and obtained its pressure-broadening parameter, which may shed some light on the reaction of H3(+) with H2. This is the first observation of the infrared saturated spectrum and the first determination of the pressure-broadening parameter of the ro-vibrational transitions of a molecular ion.

Binary recombination of para- and ortho-H3+ with electrons at low temperatures

Results of an experimental study of binary recombination of para- and ortho-H(3)(+) ions with electrons are presented. Near-infrared cavity-ring-down absorption spectroscopy was used to probe the lowest rotational states of H(3)(+) ions in the temperature range of 77-200 K in an H(3)(+)-dominated afterglow plasma. By changing the para/ortho abundance ratio, we were able to obtain the binary recombination rate coefficients for pure and para-H(3)(+) and ortho-H(3)(+). The results are in good agreement with previous theoretical predictions.

Stabilization of H+-H2 collision complexes between 11 and 28 K

Formation of H(3)(+) via association of H(+) with H(2) has been studied at low temperatures using a 22-pole radiofrequency trap. Operating at hydrogen number densities from 10(11) to 10(14) cm(-3), the contributions of radiative, k(r), and ternary, k(3), association have been extracted from the measured apparent binary rate coefficients, k*=k(r)+k(3)[H(2)]. Surprisingly, k(3) is constant between 11 and 22 K, (2.6±0.8)×10(-29) cm(6) s(-1), while radiative association decreases from k(r)(11 K)=(1.6±0.3)×10(-16) cm(3) s(-1) to k(r)(28 K)=(5±2)×10(-17) cm(3) s(-1). These results are in conflict with simple association models in which formation and stabilization of the complex are treated separately. Tentative explanations are based on the fact that, at low temperatures, only few partial waves contribute to the formation of the collision complex and that ternary association with H(2) may be quite inefficient because of the 'shared proton' structure of H(5)(+).

Dissociative recombination of H3+: 10 years in retrospect

The dissociative recombination of H(3)(+) has been an intriguing problem for more than half a century. The early experiments on H(3)(+) during the first 20 years were carried out without mass analysis in decaying plasma afterglows, and thus the measured rates pertained to an uncontrolled mixture of H(3)(+) and impurity ions. When mass analysis was used, the rate coefficient was determined to be an uneventful value of about 10(-7) cm(3) s(-1), a very common rate coefficient for many molecular ions. But this was not the end of the story, not even the beginning of the end; it marked only the end of the beginning. The story I will tell in this article started about 10 years ago, when the dissociative recombination of H(3)(+) was approaching its deepest crisis. Today, owing to an extensive experimental and theoretical effort, the state of affairs has reached a historically unique level of harmony, although there still remains many things to sort out.

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.

Benchmark measurements of H(3)(+) nonlinear dynamics in intense ultrashort laser pulses

The H(3)(+) ion is the simplest polyatomic molecule and is destined to play a central role in understanding such molecules in intense ultrashort laser pulses. We present the first measurements of the intense field dissociation and ionization of D(3)(+) using coincidence three-dimensional momentum imaging. Our results show features that are a consequence of this molecule's unique equilateral triangular geometry, providing a fundamentally new system for theoretical development.

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.

Dissociative recombination of H3+ in the ground and excited vibrational states

The article presents calculated dissociative recombination (DR) rate coefficients for H(3) (+). The previous theoretical work on H(3) (+) was performed using the adiabatic hyperspherical approximation to calculate the target ion vibrational states and it considered just a limited number of ionic rotational states. In this study, we use accurate vibrational wave functions and a larger number of possible rotational states of the H(3) (+) ground vibrational level. The DR rate coefficient obtained is found to agree better with the experimental data from storage ring experiments than the previous theoretical calculation. We present evidence that excited rotational states could be playing an important role in those experiments for collision energies above 10 meV. The DR rate coefficients calculated separately for ortho- and para-H(3) (+) are predicted to differ significantly at low energy, a result consistent with a recent experiment. We also present DR rate coefficients for vibrationally excited initial states of H(3) (+), which are found to be somewhat larger than the rate coefficient for the ground vibrational level.