Hydrogen molecule vibrational levels

The optimized structures of the first water substitution are shown in Fig. 4.5. The initial reactant complex (RC1) is symmetric with the two water molecules located on the same side of the plane formed by the nonaquated cisplatin, the syn arrangement. The oxygen atoms of each water molecule are hydrogen bonded to one of the amine groups, at a distance of 1.7 A. The lowest vibrational level (31.9 cm 1) corresponds to the reaction coordinate for water substitution. An alternative complex with... 

Fermi resonance physchem In a polyatomic molecule, the relationship of two vibrational levels that have In zero approximation nearly the same energy they repel each other, and the eigenfunctions of the two states mix. fer-me, rez-3n-3ns fermium chem Asynthetic radioactive element, symbol Fm, with atomic number 100 discovered in debris of the 1952 hydrogen bomb explosion, and now made in nuclear reactors. fer-me-3m )... 

Figure 23-2 The potential energy of the hydrogen molecule as a function of internuclear distance, and the position of its vibrational energy levels. AE values are energy differences between successive levels v designates vibrational quantum numbers. Adapted from Calvert and Pitts,2 p. 135.

The spectroscopic dissociation energy D is the dissociation energy of an ideal gas molecule at absolute zero, where all the gas molecules are in the zero potential energy level, h is Planck s constant (6.62 x lO Vrg second), and iv, is the frequency of vibration of the nuclei at the lowest vibrational level, which is above the point of zero potential energy at the equilibrium intemuclear separation. Thus, for the hydrogen molecule. D — 4.476 electron volts, l o = 1.3185 x IO 1 sec1, and since I electron volt = 23.06 kilocalories per mole wc calculate I) using Hq.(21) as... 

Figure 1.1 Morse curve characterizing the energy of the molecule as a function of the distance R that separates the atoms of a diatomic molecule such as hydrogen. At a distance equal to Re, which corresponds to point 0, the molecule is in its most stable position, and so its energy is called the molecular equilibrium energy and expressed as Ee. Stretching or compressing the bond yields an increase in energy. The number of bound levels is finite. Dq is the dissociation energy and De the dissociation minimum energy. The horizontal lines correspond to the vibrational levels.

In this section we have concentrated on calculations for H-T only, which have particular relevance to the fine and hyperfine constants determined from Jefferts experiments. Many other papers deal with calculations of the vibration-rotation level energies, for which there is much less experimental data. There are also many papers dealing with the heteronuclear molecule, HD+, which is really a special case because the Bom Oppenheimer approximation collapses, particularly for the highest vibrational levels of the ground electronic state. Even the homonuclear species H and D exhibit some fascinating and unusual effects in their near-dissociation vibration rotation levels. Finally we note that in order to match the accuracy of the experimental measurements for all the hydrogen molecular ion isotopomers, it is necessary to include radiative and relativistic effects. 

The radiation of a vibrational band is directly correlated to the vibrational population in the excited state I(v — v") = n(v ) x Av>v . Av>v is the transition probability. Thus, several vibrational bands which originate from different vibrational levels yield the corresponding vibrational population. In case of hydrogen or deuterium molecules the population of the first four or five vibrational levels, respectively, is accessible. Higher vibrational levels are disturbed by pre-dissociation processes. For further analysis, it is very convenient to use the relative vibrational population n(v )/n(v = 0). 

While these investigations succeeded in a better qualitative understanding of the role of molecules in a divertor, it has to be kept in mind that quantitative predictions may be different for hydrogen and deuterium. Concerning deuterium, the vibrational levels and some selected rate coefficients have to be replaced in the codes and in addition the application of isotopic relations has to be critically reviewed. Another aspect is the influence of surfaces (particularly carbon material) on the vibrational population of the molecule (see Sect. 4.4.2). 

Besides volume processes wall collisions of hydrogen particles can contribute to the vibrational population. A direct process is the interaction of already vi-brationally excited molecules with the surface (v) +wall —> ff2(w) mostly depopulating the vibrational levels. Further fundamental mechanisms are the Langmuir-Hinshelwood and the Eley-Rideal mechanism. They are based on recombining hydrogen atoms or ions Hads/gas + Hads —> H2(v). In the first case an adsorbed particle at the surface recombines with another adsorbed particle (Langmuir-Hinshelwood mechanism). In the second case one particle from the gas phase recombines with an adsorbed particle (Eley-Rideal mechanism). For these processes the data base is scarce and often not determined from plasma material interaction experiments. A dependence on particle densities, surface material and surface treatment as well as surface temperature can be expected. 

The saturated vapors of many elements contain moderately high concentrations of dimer molecules some vapors or gases even consist only of dimer molecules. The longest known and widely used lasers involving diatomic molecules are obviously the hydrogen and nitrogen lasers (20,21), which can be excited by short pulsed discharges. The laser transitions in dimer molecules are transitions between rotational-vibrational levels of different electronic states. 

Figure 2 Schematic potential energy curve for the hydrogen molecules with scale at bottom of the curve exaggerated to show relation between n = 0 vibrational energy levels of the four isotopic forms of the molecules. Note that molecules containing a heavy isotope are more stable (have higher dissociation energies) than molecules with a light isotope. Isotope fractionations between molecules are explained by differences in their zero-point energies...

Figure. 90. Potential energy curve and vibrational energy levels for the hydrogen molecule. The vertical scale gives the differences in energy between adjacent vibrational levels...

---