Electronic energy curves

The discussion of electronic energy curves also throws light on such questions as the structure of the carbon monoxide molecule. The empirical study of potential curves obtained from band spectral data has shown18 that for atoms in the first row of the periodic system a double bond leads 18 An account of this work will be published at some future time. 

The electronic energy curve reaches a minimum in therefore the first... 

Electronic and nuclear energy in H2. a. Values for non-interacling electrons. 6, Coulomb energy of nuclear repulsion, c, Approximate electronic energy curve for interacting electrons. Units ordinates, 1 = Rydberg constant, abscissas, 1 = radius of first Bohr orbit in hydrogen atom. 

Electronic Energy Curves The Morse Function.—Born and Oppen-heimer1 carried out a quantum-mechanical treatment of molecules, making use of the fact that the nuclei in a molecule are several thou-... 

Fig. VII-1.—A curve representing the electronic energy of a diatomic molecule as a function of the distance between the nuclei. The zero for energy is the energy of the separated atoms. The minimum of the curve corresponds to the equilibrium value of the internuclear distance. The curve shown, which approximates closely the observed electronic energy curves for many states of diatomic molecules, corresponds to the Morse function.

A. simple function that gives a close approximation to the electronic energy curve for many states of diatomic molecules is the Morse function. This function is... 

Fig. VII-2.—Some vibrational energy levels for an idealised diatomic molecule. The electronic energy curve has been approximated by a parabola, corresponding to a Qooke s-law interaction between the two atoms. The firat five vibrational states are represented. They are separated by the energy difference hv. The lowest vibrational state, with v 0, has the zero-point vibrational energy...

The reference point for energy in the energy scale is the minimum of the electronic energy curve for the lowest electronic state. 

The harmonic approximation is typically a good approximation for low vibrational levels. The adiabatic approximation is often valid for high vibrational levels and even energies in the continuum above the dissociation limit. Both harmonic and adiabatic approximations are expected to fail when the separation between electronic energy curves is small compared to differences between vibrational levels. 

The electron impact results for carbon monoxide will now be discussed in some detail, as an illustration of the method applied to a diatomic molecule. The ion current against electron energy curves for C " from CO and for O from GO are given in Figure 5.2A.L It will be seen that the initial appearance potential of G + is well defined at 20-9 0 2 eV, and that the appearance potential of 0 is at almost exactly the same voltage, given by Hagstrum... 

Total (Epnai) and electronic energy curve of Th 73+ with the point-like (Epn) and finite (Ejn) nuclei charge distributions (38). The total energy is the sum of the electronic energy and Z, h/R term. All energies are in Hartree. 

Figure 3. Typical cross section vs. electron energy curves...

Hie harmonic-oscillator force constant k in Eq. (4.28) is obtained ask = cPV/dx, and the harmonic-oscillator curve essentially coincides with the U R) curve aX.R = Rt, so the molecular force constant is k = d lJ/dR n=n (see also Problem 4.28). Differences in nuclear mass have virtually no effect on the electronic-energy curve U(R), so different isotopic species of the same molecule have essentially the same force constant k. 

As noted in Section 4.3, isotopic species such as H Cl and tf Cl have virtually the same electronic energy curve U(R) and so have virtually the same equilibrium bond distance. However, the different isotopic masses produce different moments of inertia and hence different rotational absorption frequencies. 

One way to improve the result is obviously to modify the U-like basis functions to include an adjustable f parameter as indicated in (7.17) When the energy is calculated and f varied to give the lowest energy for each R, one obtains an electronic energy curve with a minimum at 73 pm (1 pm shorter than the experimental bond distance) and a dissociation energy of 335 kJmoP ... 

The characteristic emission has a distinct energy threshold (appearance potential), which occurs at E = Ep (i.e., for 1 = 2 = 0). This results in the transfer of both the incident and core electrons to Ep, as shown in Figure 2. This event is signaled by the appearance of a small bump in the total emission versus incident electron energy curve. The excitation process is the same for all APS spectra. It seems that differences in the decay step are responsible for the spectral differences between SXAPS, AEAPS, and DAPS. In terms of this model DAPS provides information directly about the excitation process and is free of the relaxation complications. SXAPS and AEAPS include additional information dependent on the different decay (relaxation) steps. 

In section 2 we describe the method employed and in sections 3 and 4 we comment upon the electronic energy curves and wavefunctions. 

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