Intemuclear distance

Consider the collision of an atom (denoted A) with a diatomic molecule (denoted BC), with motion of the atoms constrained to occur along a line. In this case there are two important degrees of freedom, the distance R between the atom and the centre of mass of the diatomic, and the diatomic intemuclear distance r. The Flamiltonian in tenns of these coordinates is given by ... 

NOE-difFerence spectroscopy is particularly valuable for distinguishing stereoisomers, for it relies solely on intemuclear distances, and thus avoids any problems of ambiguity or absence associated with couplings. With smallish molecules, it is best carried out in the above 1D maimer, because 2 s are necessary for tire transmission of the NOE. The transmission process becomes more efficient with large molecules and is almost optimal for proteins. However, problems can occur with molecules of intemiediate size [3f]. A 2D version of the NOE-difference experiment exists, called NOESY. 

Figure B3.1.1. Energy as a fimction of intemuclear distance for a typical bound diatomic molecule or ion.

Two colliding atoms approach on tire molecular ground-state potential. During tire molasses cycle witli tire optical fields detuned only about one line widtli to tire red of atomic resonance, tire initial excitation occurs at very long range, around a Condon point at 1800 a. A second Condon point at 1000 takes tire population to a 1 doubly excited potential tliat, at shorter intemuclear distance, joins adiabatically to a 3 potential, drought to be die... 

We assume that the nuclei are so slow moving relative to electrons that we may regard them as fixed masses. This amounts to separation of the Schroedinger equation into two parts, one for nuclei and one for electrons. We then drop the nuclear kinetic energy operator, but we retain the intemuclear repulsion terms, which we know from the nuclear charges and the intemuclear distances. We retain all terms that involve electrons, including the potential energy terms due to attractive forces between nuclei and electrons and those due to repulsive forces... 

Plot the curve of the bond energy of H2 vs. intemuclear distance for the H2 molecule using the STO-3G, double zeta valence (DZV), and triple zeta valence (TZV) basis sets in the GAMESS implementation. 

The fact that the separated-atom and united-atom limits involve several crossings in the OCD can be used to explain barriers in the potential energy curves of such diatomic molecules which occur at short intemuclear distances. It should be noted that the Silicon... 

When heterolytic bond cleavage is favored, the configuration energies as functions of intemuclear distance vary as shown below. 

Since depends on nuclear coordinates, because of the term, so do and but, in the Bom-Oppenheimer approximation proposed in 1927, it is assumed that vibrating nuclei move so slowly compared with electrons that J/ and involve the nuclear coordinates as parameters only. The result for a diatomic molecule is that a curve (such as that in Figure 1.13, p. 24) of potential energy against intemuclear distance r (or the displacement from equilibrium) can be drawn for a particular electronic state in which and are constant. 

The use of the symbols F J) and B for quantities which may have dimensions of frequency or wavenumber is unfortunate, but the symbolism is used so commonly that there seems little prospect of change. In Equations (5.11) and (5.12) the quantity B is known as the rotational constant. Its determination by spectroscopic means results in determination of intemuclear distances and represents a very powerful structural technique. 

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...

From the following wavenumbers of the P and R branches of the 1-0 infrared vibrational band of H Cl obtain values for the rotational constants Bq, Bi and B, the band centre coq, the vibration-rotation interaction constant a and the intemuclear distance r. Given that the band centre of the 2-0 band is at 4128.6 cm determine cOg and, using this value, the force constant k. 

The approach adopted in the MO method is to consider the two nuclei, without their electrons, a distance apart equal to the equilibrium intemuclear distance and to construct... 

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. 

Sketch potential energy curves for the following states of CdH, Br/ and CH, given their intemuclear distances r, and suggest qualitative intensity distributions in the v" = 0 progressions for transitions between the states observed in absorption ... 

The much greater convergence in the R branch in the 1o3q band is due to a very much larger decrease of B in the upper state it is 75.69 x 10 cm less than the value of 1.478 221 834 cm in the lower state. This decrease is characteristic of vibrational overtone levels and is due, mostly, to anharmonicity which results in the molecule spending most of its time at much larger intemuclear distances than in the u = 0 level. 

This general technique has been applied also to the direct observation of vibrational motion in bound electronic states. Although no transition states as such are involved in vibrational motion there is, again, a transitory change of intemuclear distance. 

Dipole-dipole (homonuclear) Afjfhomo) (mean-squared local field) Spin-echo NMR Intemuclear distances, number of surrounding nuclei... 

Fig. 3.2. Energy as a function of intemuclear distance for nonbonded atoms.

If we were to calculate the potential energy V of the diatomic molecule AB as a function of the distance tab between the centers of the atoms, the result would be a curve having a shape like that seen in Fig. 5-1. This is a bond dissociation curve, the path from the minimum (the equilibrium intemuclear distance in the diatomic molecule) to increasing values of tab describing the dissociation of the molecule. It is conventional to take as the zero of energy the infinitely separated species. 

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