Aims. In this work we rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken.
Methods. Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H$_2$ . Both equilibrium and normal hydrogen was taken into consideration.
Results. Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hydrogen are calculated and thermodynamic quantities are reported for the temperature range 1 - 20000 K. Our results are compared to previous estimates in the literature. The calculations are not limited to the ground electronic state, but include all bound and quasi-bound levels of excited electronic states. Dunham coefficients of these states of H$_2$ are also reported.
Conclusions. For most of the relevant astrophysical cases it is strongly advised to avoid using simplifications, such as a harmonic oscillator and rigid rotor or ad hoc summation limits of the eigenstates to estimate accurate partition functions and to be particularly careful when using polynomial fits to the computed values. Reported internal partition functions and thermodynamic quantities in the present work are shown to be more accurate than previously available data.
The radiative ortho-para transition in the molecular hydrogen is studied. This highly forbidden transition is very sensitive to relativistic and subtle nonadiabatic effects. Our result for the transition rate in the ground vibrational level $Γ(J=1\to J=0) = 6.20(62)\cdot 10^{-14} \iyr$ is significantly lower in comparison to all the previous approximate calculations. Experimental detection of such a weak line by observation of, for example, the cold interstellar molecular hydrogen is at present unlikely.
We report extensive theoretical calculations on the rotation-inversion excitation of interstellar ammonia (NH3) due to collisions with atomic and molecular hydrogen (both para- and ortho-H2). Close-coupling calculations are performed for total energies in the range 1-2000 cm-1 and rotational cross sections are obtained for all transitions among the lowest 17 and 34 rotation-inversion levels of ortho- and para-NH3, respectively. Rate coefficients are deduced for kinetic temperatures up to 200 K. Propensity rules for the three colliding partners are discussed and we also compare the new results …
Rates of conversions of molecular internal energy to and from kinetic energy by means of molecular collision allows to compute collisional line shapes and transport properties of gases. Knowledge of ro-vibrational quenching rates is necessary to connect spectral observations to physical properties of warm astrophysical gasses, including exo-atmospheres. For a system of paramount importance in this context, the vibrational bending mode quenching of H2O by H2, we show here that exchange of vibrational to rotational and kinetic energy remains a quantum process, despite the large numbers of quantu…
We present a new computational method to calculate arbitrary pair correlation functions of an orthorombic system in the most efficient way. The algorithm is demonstrated by the calculation of the radial distribution function of shock compressed liquid hydrogen.
The present high-resolution inelastic neutron scattering experiment on ice XVII, containing molecular hydrogen with different ortho/para ratio, allows to assign the H$_2$ motion spectral bands to rotational and center-of-mass translational transitions of either {\it para}- or {\it ortho}-H$_2$. Due to its structure, ice XVII confines H$_2$ molecules to move in spiral channels of molecular size. Reported data demonstrate that H$_2$ molecules rotate almost freely in these nanometric channels, though showing larger perturbation than in clathrate hydrates, and perform a translational motion exhibi…
Theoretical cross sections for the pressure broadening by hydrogen of rotational transitions of water are compared to the latest available measurements in the temperature range 65-220 K. A high accuracy interaction potential is employed in a full close coupling calculation. A good agreement with experiment is observed above ~80 K while the sharp drop observed experimentally at lower temperatures is not predicted by our calculations. Possible explanations for this discrepancy include the failure of the impact approximation and the possible role of ortho-to-para conversion of H2.
We present quantum dynamical calculations that describe the rotational excitation of H$_2$O due to collisions with H atoms. We used a recent, high accuracy potential energy surface, and solved the collisional dynamics with the close-coupling formalism, for total energies up to 12 000 cm$^{-1}$. From these calculations, we obtained collisional rate coefficients for the first 45 energy levels of both ortho- and para-H$_2$O and for temperatures in the range T = 5-1500 K. These rate coefficients are subsequently compared to the values previously published for the H$_2$O / He and H$_2$O / H$_2$ col…
New calculations for rotational excitation of cyanoacetylene by collisions with hydrogen molecules are performed to include the lowest 38 rotational levels of HC3N and kinetic temperatures to 300 K. Calculations are based on the interaction potential of Wernli et al. A&A, 464, 1147 (2007) whose accuracy is checked against spectroscopic measurements of the HC3N-H2 complex. The quantum coupled-channel approach is employed and complemented by quasi-classical trajectory calculations. Rate coefficients for ortho-H2 are provided for the first time. Hyperfine resolved rate coefficients are also deduc…
Compositionally tunable vanadium oxyhydrides Sr2VO4-xHx (x = 0 - 1) without considerable anion vacancy were synthesized by high-pressure solid state reaction. The crystal structures and their properties were characterized by powder neutron diffraction, synchrotron X-ray diffraction, thermal desorption spectroscopy, and first-principles density functional theory (DFT) calculations. The hydrogen anions selectively replaced equatorial oxygen sites in the VO6 layers via statistical substitution of hydrogen in the low x region (x < 0.2). A new orthorhombic phase (Immm) with an almost entirely hydro…
State-to-state differential cross sections (DCSs) for rotationally inelastic scattering of H2O by H2 have been measured at 71.2 meV (574 cm-1) and 44.8 meV (361 cm-1) collision energy using crossed molecular beams combined with velocity map imaging. A molecular beam containing variable compositions of the (J = 0, 1, 2) rotational states of hydrogen collides with a molecular beam of argon seeded with water vapor that is cooled by supersonic expansion to its lowest para or ortho rotational levels (JKaKc= 000 and 101, respectively). Angular speed distributions of fully specified rotationally exci…
Water exists as two nuclear-spin isomers, para and ortho, determined by the overall spin of its two hydrogen nuclei. For isolated water molecules the conversion between these isomers is forbidden and they act as different molecular species. Yet, these species are not readily separable, and little is known about their specific physical and chemical properties, conversion mechanisms, or interactions. Here we demonstrate the production of isolated samples of both spin isomers in pure beams of para and ortho water, with both species in their respective absolute ground state. These single-quantum-s…
A theoretical description of IR spectroscopy data for a hydrogen bond (HB) is constructed on the base of trigonometric double-well potential for which an exact analytic solution of the one-dimensional Schrödinger equation (SE) is available. The wave functions (full orthogonal basis) are expressed via the spheroidal function while its spectrum of eigenvalues yields the corresponding energy levels (both special functions are implemented in {\sl {Mathematica}}). Then an approximate solution of two-dimensional SE taking into account the excitation state of heavy atoms stretching mode in HB is obta…
The impact of including the reactions of C and CH with molecular hydrogen in a gas-grain network is assessed via a sensitivity analysis. To this end, we vary 3 parameters, namely, the efficiency for the reaction \ce{C + H2 -> CH2}, and the cosmic ray ionisation rate, with the third parameter being the final density of the collapsing dark cloud. A grid of 12 models is run to investigate the effect of all parameters on the final molecular abundances of the chemical network. We find that including reactions with molecular hydrogen alters the hydrogen economy of the network; since some species are…
The ionization energy of ortho-H$_2$ has been determined to be $E^\mathrm{o}_\mathrm{I}(\mathrm{H}_2)/(hc)=124\,357.238\,062(25)$ cm$^{-1}$ from measurements of the GK(1,1)--X(0,1) interval by Doppler-free two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave near-infrared laser spectroscopy. $E^\mathrm{o}_\mathrm{I}$(H$_2$) was used to derive the dissociation energy of H$_2$, $D^{N=1}_{0}$(H$_2$), at $35\,999.582\,894(25)$ cm$^{-1}$ with a precision that is more than one order of magnitude better than all previous res…
We report in this review recent fully-quantum time-independent calculations of cross sections and rate constants for the gas phase ortho-to-para conversion of H$_2$ by H and H$^+$. Such processes are of crucial interest and importance in various astrophysical environments. The investigated temperature ranges was 10$-$1500 K for H+H$_2$ and 10$-$100 K for H$^+$+H$_2$. Calculations were based on highly accurate H$_3$ and H$_3^+$ global potential energy surfaces. Comparisons with previous calculations and with available measurements are presented and discussed. It is shown that the existence of a…
We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal functions. We adapt the gausslets to particular systems using one dimensional coordinate transformations, putting more basis functions near nuclei, while maintaining orthogonality. Three dimensional basis functions are composed out of products of the 1D functions in an efficient way called multislicing. We demonstrate the new bases with both Hartree Fock and d…
