Vibrational states of the triplet electronic state of H3+. The role of non-adiabatic coupling and geometrical phase

Vibrational energies and wave functions of the triplet state of the H3+ ion have been determined. In the calculations, the ground and first excited triplet electronic states are included as well as the non-Born-Oppenheimer coupling between them. A diabatization procedure transforming the two adiabatic ab initio potential energy surfaces of the triplet-H3+ state into a 2x2 matrix is employed. The diabatization takes into account the non-Born-Oppenheimer coupling and the effect of the geometrical phase due to the conical intersection between the two adiabatic potential surfaces. The results are compared to the calculation involving only the lowest adiabatic potential energy surface of the triplet-H3+ ion and neglecting the geometrical phase. The energy difference between results with and without the non-adiabatic coupling and the geometrical phase is about a wave number for the lowest vibrational levels

QED correction for H3+_3^+

A quantum electrodynamics (QED) correction surface for the simplest polyatomic and polyelectronic system H$_3^+$ is computed using an approximate procedure. This surface is used to calculate the shifts to vibration-rotation energy levels due to QED; such shifts have a magnitude of up to 0.25 cm$^{-1}$ for vibrational levels up to 15~000 cm$^{-1}$ and are expected to have an accuracy of about 0.02 cm$^{-1}$. Combining the new H$_3^+$ QED correction surface with existing highly accurate Born-Oppenheimer (BO), relativistic and adiabatic components suggests that deviations of the resulting {\it ab initio} energy levels from observed ones are largely due to non-adiabatic effects

High accuracy calculations of the rotation-vibration spectrum of H3+_3^+

Calculation of the rotation-vibration spectrum of H3+, as well as of its deuterated isotopologues, with near-spectroscopic accuracy requires the development of sophisticated theoretical models, methods, and codes. The present paper reviews the state-of-the-art in these fields. Computation of rovibrational states on a given potential energy surface (PES) has now become standard for triatomic molecules, at least up to intermediate energies, due to developments achieved by the present authors and others. However, highly accurate Born--Oppenheimer energies leading to highly accurate PESs are not accessible even for this two-electron system using conventional electronic structure procedures e.g., configuration-interaction or coupled-cluster techniques with extrapolation to the complete basis set limit). For this purpose highly specialized techniques must be used, e.g., those employing explicitly correlated Gaussians and nonlinear parameter optimizations. It has also become evident that a very dense grid of \ai\ points is required to obtain reliable representations of the computed points extending from the minimum to the asymptotic limits. Furthermore, adiabatic, relativistic, and QED correction terms need to be considered to achieve near-spectroscopic accuracy during calculation of the rotation-vibration spectrum of H3+. The remaining and most intractable problem is then the treatment of the effects of non-adiabatic coupling on the rovibrational energies, which, in the worst cases, may lead to corrections on the order of several \cm. A promising way of handling this difficulty is the further development of effective, motion- or even coordinate-dependent, masses and mass surfaces. Finally, the unresolved challenge of how to describe and elucidate the experimental pre-dissociation spectra of H$_3^+$ and its isotopologues is discussed.Comment: Topical review to be published in J Phys B: At Mol Opt Phy

Ro-Vibrational States of Triplet H2D

We present rotational term values for J ≤ 3 of the vibrational states with up to twofold excitation of H2D+ in the lowest electronic triplet state (a3 ). The calculations were performed using the method of hyperspherical harmonics and our recent accurate double many-body expansion potential energy surface

Applying Value-Focused Thinking to a Make Versus Buy Decision

The United States Army placed emphasis on decreasing the load an individual Soldier carries by reducing the weight of ammunition through the use of polymer-cased ammunition.  This paradigm shift from brass to polymer raises concerns over the implementation aspect of this new procedure into the US Army’s current ammunition production process.  Our client, Project Manager Maneuver Ammunition Systems (PM-MAS) sponsored our team to analyze various candidate solutions using a methodology grounded in value-focused thinking, and recommend an implementation method to produce 7.62 mm polymer-cased ammunition at the Lake City Army Ammunition Plant (LCAAP) in Lake City, Missouri.  This paper outlines the application of systems thinking concepts, various problem definition techniques and value modeling in order to effectively compare three given scenarios using a total value score versus cost analysis for each candidate solution.  Our final recommendation is to implement the Buy scenario because of its total score of 63.5 and estimated cost of $14.62 million. 

The hydrogen molecule H2\rm{H}_{2} in inclined configuration in a weak magnetic field

Highly accurate variational calculations, based on a few-parameter, physically adequate trial function, are carried out for the hydrogen molecule \hh in inclined configuration, where the molecular axis forms an angle $\theta$ with respect to the direction of a uniform constant magnetic field ${\bf B}$, for $B=0,\, 0.1,\, 0.175$ and $0.2\,$a.u. Three inclinations $\theta=0^\circ,\,45^\circ,\,90^\circ$ are studied in detail with emphasis to the ground state $1_g$. Diamagnetic and paramagnetic susceptibilities are calculated (for $\theta=45^\circ$ for the first time), they are in agreement with the experimental data and with other calculations. For $B=0,\, 0.1$ and $0.2\,$a.u. potential energy curves $E$ vs $R$ are built for each inclination, they are interpolated by simple, two-point Pad\'e approximant $Pade[2/6](R)$ with accuracy of not less than 4 significant digits. Spectra of rovibrational states are calculated for the first time. It was found that the optimal configuration of the ground state for $B \leq B_{cr}=0.178\,$a.u. corresponds always to the parallel configuration, $\theta=0$, thus, it is a $^1\Sigma_g$ state. The state $1_g$ remains bound for any magnetic field, becoming metastable for $B > B_{cr}$, while for $B_{cr} < B < 12$\,a.u. the ground state corresponds to two isolated hydrogen atoms with parallel spins.Comment: 31 pages, 11 Tables, 7 Figures (2 new), following referee's suggestions parts 4,5,6 essentially rewritten, to be published at Journal of Quantitative Spectroscopy and Radiative Transfe

ExoMol molecular line lists – XX. A comprehensive line list for H3+

H3+ is a ubiquitous and important astronomical species whose spectrum has been observed in the interstellar medium, planets and tentatively in the remnants of supernova SN1897a. Its role as a cooler is important for gas giant planets and exoplanets, and possibly the early Universe. All this makes the spectral properties, cooling function and partition function of H3+ key parameters for astronomical models and analysis. A new high-accuracy, very extensive line list for H3+ called MiZATeP was computed as part of the ExoMol project alongside a temperature-dependent cooling function and partition function as well as lifetimes for excited states. These data are made available in electronic form as supplementary data to this article and at www.exomol.com

Benchmark Rovibrational Linelists and Einstein A-coefficients for the Primordial Molecules and Isotopologues

Complete benchmark rovibrational energy linelists calculated for the primordial polar molecules of the universe, namely HD+, HD, and the HeH+ isotopologues, with accuracy up to 10(-2) cm(-1) for low-lying states, are presented. To allow for these calculations to be performed, new high-accuracy potential energy curves, which include the diagonal Born-Oppenheimer adiabatic corrections and the leading relativistic corrections, are determined. Also, a new approach for calculating non-adiabatic corrections involving an effective vibrational nuclear mass obtained based on the atoms-in-molecules theory is employed. The vibrational and rotational masses are taken as being different and dependent on the nuclear distance. Accurate dipole moment curves are calculated and used to generate lists of Einstein A-coefficients. The energy linelists and the sets of Einstein A-coefficients for HD are upgrades of previous calculations including quasibound states, while for HD+ and HeH+ and its isotopologues the present results represent significant improvement over the previous calculations. The results obtained here suggest that, with the inclusion of the non-adiabatic corrections, the accuracy limit at least for low-lying states might have been reached. Thus, further progress should involve accounting for even smaller effects such as the quantum-electrodynamics corrections. The present results represent the state-of-the-art of theoretical spectroscopy of the primordial polar molecules.CAPES; Polish National Science Centre [DEC-2013/10/E/ST4/00033]; CNPqThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]