Line internuclear distance

Fig. 2. Energy as a function of internuclear distance the full line refers...

Figure 4.4 Data in Fig. 4.3 when plotted di (h , - hfi versus time. The slope of the lines represents the internuclear distance r that corresponds to the rate of nOe buildup, which is directly proportional to r . (Reprinted from D. H. Williams et al.,J. Am. Chem. Soc. 105,1332, copyright (1983), with permission from The American Chemical Society, 1155 16th Street, N.W. Washington, D.C. 20036, U.S.A.). 

Fig. 9.1 The internuclear transfer of magnetization via NOE cross-relaxation in an isolated spin-pair. (A) Build-up curves for the cross-peak intensity in a 2D NOESY experiment for various internuclear distances r. The dashed line indicates a typical mixing time tm = 300rns used for drug-like molecules.

There are three internuclear distances rAB, rBC and rAC and a plot of the PE as a function of three independent variables requires four dimensional space. Therefore, we can consider that three atoms lie along a straight line. A plot of PE as a function or rAB and rBC results in a PES as shown in Fig. 9.11. 

Fig. 4. Calculated energies (solid lines with filled symbols) and first-order non-adiabatic coupling matrix elements (NACME) (dotted lines with empty symbols) of the first three excited states in as a function of internuclear distance R.

From precise wavelength measurements of the fluorescence spectrum (which may be performed e. g. by interferometric methods accurate values for the molecular constants can be obtained since the wavelength differences of subsequent lines in the fluorescence progression yield the energy separation of adjacent vibrational and rotational levels as a function of v . From these spectroscopically deduced molecular constants, the internuclear distance can be calculated A special computer programm developed by Zare ) allows the potential curve to be constructed from the measured constants and, if the observed fluorescence progression... 

As was discussed qualitatively in Section II,A,2, the local magnetic fields produced at a nucleus in a solid by the magnetic dipole moments of nuclei around it are often responsible for the observed line widths. Van Vleck (73) has derived, in a rigorous manner, an expression for the second moment of the absorption curve of the nuclei in terms of the magnetic moments, spins, and internuclear distances of the nuclei. The second moment ((AH )) of the shape function g(H — Ho) normalized to unit area is... 

Pure rotational spectroscopy in the microwave or far IR regions joins electron diffraction as one of the two principal methods for the accurate determination of structural parameters of molecules in the gas phase. The relative merits of the two techniques should therefore be summarised. Microwave spectroscopy usually requires sample partial pressures some two orders of magnitude greater than those needed for electron diffraction, which limits its applicability where substances of low volatility are under scrutiny. Compared with electron diffraction, microwave spectra yield fewer experimental parameters more parameters can be obtained by resort to isotopic substitution, because the replacement of, say, 160 by lsO will affect the rotational constants (unless the O atom is at the centre of the molecule, where the rotational axes coincide) without significantly changing the structural parameters. The microwave spectrum of a very complex molecule of low symmetry may defy complete analysis. But the microwave lines are much sharper than the peaks in the radial distribution function obtained by electron diffraction, so that for a fairly simple molecule whose structure can be determined completely, microwave spectroscopy yields more accurate parameters. Thus internuclear distances can often be measured with uncertainties of the order of 0.001 pm, compared with (at best) 0.1 pm with electron diffraction. If the sample is a mixture of gaseous species (perhaps two or more isomers in equilibrium), it may be possible to unravel the lines due to the different components in the microwave spectrum, but such resolution is more difficult to accomplish with electron diffraction. 

Figure 1-1. Dispersion energy for the He-K+ ion as a function of the internuclear distance R represented by its multipole expansion (large dashed line), damped multipole expansion (small dashed line), and by the nonexpanded results (full line)...

Figure 1.13 Examples of potential surfaces for collinear reactions of the type A + BC - AB + C. Energies are expressed in eV relative to separated A + BC at zero energy, and the dotted lines indicate the equilibrium internuclear distances of BC and AB.

Calculate 1, the moment of inertia, and r, the internuclear distance, for both HCI and DCI. The masses (in atomic mass units) are H = 1.007825, D = 2.014102, Cl = 34.968853, and Cl = 36.965903. If HBr and DBr are examined, it is unlikely that the two nearly equal Br and Br spectral lines will be resolved, and it is appropriate to use the average atomic mass (79.904) in similar calculations. Tabulate all of your results, along with your estimates of the experimental uncertainty. Compare your results with literature values, which can be found in Ref. 2. 

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