H2 potential curves

Figure 5-1. H2 potential curves computed within the restricted and unrestricted Hartree-Fock (RHF and UHF) and Kohn-Sham (RKS and UKS) formalisms. 

Fig. 1.5 The H2 bond potential (solid) with a Morse potential fitted to it (dashed curve). Reference H2 potential curve from [351]...

Some novel aspects of our PES concern the various configurations. For the asymptotic system H2—H2, we reproduce the accurate H2 potential curve including... 

Fig. 1.2. Potential energy curves of H2 and Hj showing ionization and dressed states in a laser field. The dressed curves lead to bond softening and a distortion of the potential curve of the ground state of the ion, as will be discussed in Sect. 1.2.3...

The bond energy given above has been obtained by subtracting from the RHF energy for H2 the energy of two separated hydrogen atoms (-627 kcal/mol). Suppose instead that we would use the RHF model to compute the potential curve for the dissociation of H2. The first thing to notice is that the form of the molecular orbital (2 3) is independent of the intemuclear distance. The same form of the wave function (2 4) is thus obtained also for the separated atoms. Let us expand this wave function as products of the atomic orbitals lsA and lsB ... 

Figure 2.1 Potential curves for H2 showing the erratic behaviour of the SCF curve as a function of the internuclear distance. For comparison the MCSCF curve which dissociates correctly is also given.

A very important aspect of the results described above for De is that the error obtained at a certain level of approximation is systematic. This fact combined with the fact that the results improve as the method improves are aspects of ab initio methods which are at least as important as the final accuracy of the results. So far the only property discussed is De. It is clear that the most important chemical information, such as reaction pathways and thermochemistry, is obtained from relative energies, but the accuracy of other properties is also of interest. If we look at the equilibrium bond distance Re and the harmonic vibrational frequency we, these properties also display a systematic behaviour depending on the method chosen and this systematic behaviour is easy to understand. Since the RHF method dissociates incorrectly, the potential curves tend to rise too fast as the bond distance is increased. At the RHF level this leads to too short equilibrium bond distances and vibrational frequencies that are too high. When proper dissociation is included at the MCSCF level, the opposite trend appears. Since the dissociation energies are too small at this level the potential curves rise too slowly as the bond distance increases. This leads to too long bond distances and too low frequencies. These systematic trends are nicely illustrated by the results for three of the previously discussed diatomic molecules. For H2 the experimental value for Re is 1.40 ao and for uje it is 4400 cm-1. At the RHF level Re becomes too short, 1.39 ao, and we becomes too high, 4561 cm-1. At the two configuration MCSCF level Re becomes... 

Figure 28.5 Current-potential curves for p-GaP under low- to moderate-intensity illumination a 1 M NaCl (pH = 1) electrolyte is employed. Illumination is from a 200-W high-pressure mercury lamp filtered with neutral density filter. Intensity is relative to the full lamp output. The H2/H+ redox potential is -0.3 V vs. SCE in this cell. Thus, this cell yields approximately 400 mV of open-circuit photovoltage. Note that increased illumination increases both the saturation photocurrent and the onset potential. Although the photocurrent is increased at higher light intensities, a calculation of the quantum yield for electron flow indicates that this parameter decreases with increased light intensity.

Figure 63. Potential curves of ground states of H2 and H2", drawn with same asymptote, showing a crossing at 2.5 atomic units.2... 

Figure 64. Contour plot of potential-energy surface for ground state of linear H3+. Values for / , and R2 are in atomic units, and energies are in electron volts. Indicated energies are with respect to dissociated particles. Cut through surface at large / , coincides with potential curve of H2 at small R2 and with curve of at large R2 (see Fig. 63).2...

H-H and the H-H+ potential curves are only negligibly perturbed by He and He, respectively. This means, of course, that no reactions in which reactions products containing helium are formed occur prior to the ionization. On the other hand, it is found in mass-spectrometric studies that, in addition to H2+, the products HeH and HeH+ are formed.9,87,88 These products can only arise from reactions, in the second half of the (Pl)-colli-sion, between the vibrationally excited H and He. We may indicate these conditions by the following scheme ... 

Figure 1.13 The ground (lower solid line) and excited (dashed line) potential energy curves of the molecular ion H2+.The upper potential curve represents the ground electronic potential curve shifted by the energy ha> of one photon of the electromagnetic radiation. The ground vibrational wavefunction in the ground electronic state is coupled to the continuum of scattering states of the excited electronic potential depicted here by dense set of energy levels.

To illustrate this phenomenon, we return to the molecular hydrogen ion H2+. The ground vibrational state of the system is bound in the potential depicted in Figure 1.13. Suppose now that we expose the system to a monochromatic electromagnetic radiation with a frequency radiation field now couples between the ground electronic state and the excited electronic state of the system. The excited electronic state of the hydrogen molecular ion is a dissociative potential curve, which is well approximated by [48] ... 

Fig. 15.5. Calculated potential energy curves for the lB and lA states of H2S in C -symmetry, i.e., the two H-S bond distances are varied symmetrically. The HSH bending angles are o=85°, 92°, and 100°. Note the different vertical axes for the three pairs of potential curves. Adapted from Heumann, Diiren, and Schinke (1991).

Fib. 9. Potential curves relating to the dissociative chemisorption of a molecule M (H2) on a metal Me without an activation energy. 

In all cases where an activation energy is already present at 0 = 0 (N2 on iron, H2 on contaminated metal surfaces see Sec. V,9) it increases with increasing 0 values. The increase of the activation energy is slower than the decrease of the heat of chemisorption. An examination of Fig. 37 shows that this should be so. The maxima in the potential curves are shifted to the left and the minima of the curves are either at the same distance from the surface—as we have assumed in our figure—... 

FIGURE 9.2 Current density vs. electrode potential curves for the H2-02 and the CH30H-02 fuel cells showing the reaction overvoltages T a and T c at different catalytic electrodes (Pt, Pt-Ru,...). 

Figure 3.16 Potential curves for the lscr and 2pa states of HD+. In the homonuclear (H2+), the two states are asymptotically degenerate the degeneracy is lifted in the he nuclear case by 29.8 cm-1 (inset). (Taken from Fig. 1, Ref. [83].)...

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