Diatomic molecule heteronuclear

Figure Bl.2.1. Schematic representation of the dependence of the dipole moment on the vibrational coordinate for a heteronuclear diatomic molecule. It can couple with electromagnetic radiation of the same frequency as the vibration, but at other frequencies the interaction will average to zero.

Figure 1.11 (a) Rotation of a heteronuclear diatomic molecule about axes perpendicular to the... 

Rule 1 shows that transitions are allowed in heteronuclear diatomic molecules such as CO,... 

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

Figure 6.1 Variation of dipole moment fi with intemuclear distance r in a heteronuclear diatomic molecule...

Some heteronuclear diatomic molecules, such as nitric oxide (NO), carbon monoxide (CO) and the short-lived CN molecule, contain atoms which are sufficiently similar that the MOs resemble quite closely those of homonuclear diatomics. In nitric oxide the 15 electrons can be fed into MOs, in the order relevant to O2 and F2, to give the ground configuration... 

It is important to realize that electronic spectroscopy provides the fifth method, for heteronuclear diatomic molecules, of obtaining the intemuclear distance in the ground electronic state. The other four arise through the techniques of rotational spectroscopy (microwave, millimetre wave or far-infrared, and Raman) and vibration-rotation spectroscopy (infrared and Raman). In homonuclear diatomics, only the Raman techniques may be used. However, if the molecule is short-lived, as is the case, for example, with CuH and C2, electronic spectroscopy, because of its high sensitivity, is often the only means of determining the ground state intemuclear distance. 

Since the vacancy in the nip orbital behaves, in this respect, like a single electron, the states arising are the same as those from nlp) n 2p), since we can ignore electrons in filled orbitals. Equation (7.77), dropping the g and u subscripts for a heteronuclear diatomic molecule, gives... 

All heteronuclear diatomic molecules, in their ground electronic state, dissociate into neutral atoms, however strongly polar they may be. The simple explanation for this is that dissociation into a positive and a negative ion is much less likely because of the attractive force between the ions even at a relatively large separation. The highly polar Nal molecule is no exception. The lowest energy dissociation process is... 

The symmetry index heteronuclear diatomic molecule. 

Recently, a quantitative lateral interaction model for desorption kinetics has been suggested (103). It is based on a statistical derivation of a kinetic equation for the associative desorption of a heteronuclear diatomic molecule, taking into account lateral interactions between nearest-neighbor adatoms in the adsorbed layer. Thereby a link between structural and kinetic studies of chemisorption has been suggested. 

The bond in a heteronuclear diatomic molecule, a diatomic molecule built from atoms of two different elements, is polar, with the electrons shared unequally by the two atoms. We therefore rewrite Eq. I as... 

FIGURE 3.33 A typical d molecular orbital energy-level diagram for a heteronuclear diatomic molecule AB the relative contributions of the atomic orbitals to the molecular orbitals are represented by the relative sizes of the spheres and the horizontal position of the boxes. In this case, A is the more electronegative of the two elements. 

The molecular orbital energy-level diagrams of heteronuclear diatomic molecules are much harder to predict qualitatitvely and we have to calculate each one explicitly because the atomic orbitals contribute differently to each one. Figure 3.35 shows the calculated scheme typically found for CO and NO. We can use this diagram to state the electron configuration by using the same procedure as for homonuclear diatomic molecules. 

EXAMPLE 3.8 Sample exercise Writing the configuration of a heteronuclear diatomic molecule or ion... 

Nitrogen oxide (NO) is an example of heteronuclear diatomic molecules, those composed of different atoms. This interesting molecule has been in the news several times in recent years, because of important discoveries about the role of NO as a biological messenger, as we describe in our introduction to Chapter 21. 

In the heteronuclear diatomic molecule we have a system where at. We assume that the difference between the two atomic levels d = at - > 0 is much larger than... 

The limitation of the above analysis to the case of homonuclear diatomic molecules was made by imposing the relation Haa = Hbb> as in this case the two nuclei are identical. More generally, Haa and for heteronuclear diatomic molecules Eq. (134) cannot be simplified (see problem 25). However, the polarity of the bond can be estimated in this case. The reader is referred to specialized texts on molecular orbital theory for a development of this application. 

Figure 6.1 Binding and antibinding regions for a heteronuclear diatomic molecule consisting of two nuclei A and B with ZA = ZB. The coordinate system is superimposed. The distance from a point with coordinates (x,y,z) to nucleus A is rA and to nucleus B is rB. the distance between the nuclei is RAb To obtain the 3D binding and antibinding regions rotate the figure about the intemuclear axis.

An HC1 molecule is a heteronuclear diatomic molecule composed of H (EN = 2.1) and Cl (EN = 3.0). Because the electronegativities of the elements are different, the pull on the electrons in the covalent bond between them is unequal. Hence HC1 is a polar molecule. 

This type of spectra is given by diatomic molecules with permanent dipole moments, i.e. in heteronuclear diatomic molecules and polyatomic molecules with and without permanent dipole moment. 

For practical purposes the rules for diatomic molecules concerning even and odd J reduce to the statement that for homonuclear diatomic molecules the molecular partition function must be divided by two (s = 2), while for heteronuclear diatomic molecules no division is necessary (s = 1). The idea of the symmetry number, s,... 

This presents a problem when we discuss the dipole moment of a polar heteronuclear diatomic molecule, AX, where X will be the more electronegative. In the chemical picmre, it is quite common to say that in the ground state the molecule lies along some axis and that it has a definite dipole moment. In the physical picmre, we say that the molecule has no measurable dipole moment in the ground state. 

Up to now we have been discussing the local properties of the exchange-correlation potential as a function of the spatial coordinate r. However there are also important proi rtira of the exchange-correlation potential as a function of the particle number. In fact there are close connections between the properties as a function of the particle number and the local properties of the exchange-correlation potential. For instance the bumps in the exchange-correlation potential are closely related to the discontinuity properties of the potential as a function of the orbital occupation number [38]. For heteronuclear diatomic molecules for example there are also similar connections between the bond midpoint shape of the potential and the behavior of the potential as a function of the number of electrons transferred from one atomic fragment to another when... 

Problem 7-8. Consider the case of a heteronuclear diatomic molecule constrained to move in one dimension. Let the masses of the nuclei be denoted by m and M, and the force constant by k. Set up and solve the secular equation determine that the allowed modes of motion are the overall translation and vibration. Determine the vibrational frequency in terms of m, M and k. 

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