Intemudear distance

Figure 30 (a) A view of [VO(salnpn)] molecule with some intemudear distances (in A) 723 (b) schematic... 

As described in the Introduction, it is usually possible to consider the modeling of experimental data separately from the scheme actually used to move atoms about. Ideally, the different models should be able to be used in the different minimization or dynamics schemes. Thus, the subsequent sections describe the kind of data offered by NMR and the kinds of penalty functions or pseudo-energy terms that can be used to represent them. For convenience, we use nomenclature common to force field-based approaches where one refers to a distance constraint potential Vdc r) as a function of intemudear distance. 

The phrase van der Waals radius arises as a distinction from intemudear distance radii. Thus, from the van der Waals equation for the P-Vrelation in gases (an improvement on the simple gas law PV=nRT), a quantity b can be found which refers to the space taken up out of the whole gas volume V by the molecules themselves. 

Bond Dipole moment D Intemudear distance A Weight of structure per cent ... 

Most of protein structural information from NMR is obtained in the form of nuclear Overhauser effects or NOEs between pairs of protons that are less than 6 A apart through space. An NOE between a spin pair carries distance information, but only short distances are observed because NOEs have an inverse sixth power dependence on distance. However, the distance cannot be uniquely determined given a measured NOE intensity without making some assumption about the environment of the spin pair and the motion of the vector between them. The simplest model for obtaining a distance from cross peak intensities in a nuclear Overhauser effect spectrum (NOESY) is the isolated ri d spin pair (RRNN - rigid rotor nearest neither) approximation (Jardetzky and Roberts, 1981). In this approximation the observed cross peak intensity, which is proportional to the cross relaxation rate, is related to a sini e intemudear distance, r. 

The total wavefunction li = -P is obtained from MRCISD at each value of intemudear distance. 

Buckingham asked about the status of calculations for molecules in excited states, schaefer replied that more has been done at the more accurate level of approximations and that the results are just as reliable. There are some exceptions, such as the B state of CH, which has a shallow minimum. In such a case, it obviously is difficult to establish either by experiment or by theory an accurate intemudear distance. In response to a question by Buckingham, schaefer indicated that excited states of the same symhietry as the ground state are more difficult to handle and less has been done with them. 

As long as we do not neglect to understand each of the factors in the Bom-Lande equation (4.13), we can simplify the calculations. It should be realized that the only variables in the Bom-Lande equation are the charges on the ions, the intemudear distance, the Madelung constant, and the value of n. Equation 4.13 may thus be simplified with no loss of accuracy by grouping the constants to give ... 

The intemudear distance in the fluorine molecule is 142 pm, which is shorter than the sum of two van der Waals radii. The difference obviously comes from the fact that the electron clouds of the fluorine atoms overlap extensively in the formation of the F—F bond whereas little overlap of the van der Waals radii occurs between Ihe molecules... 

There are small but important differences between the evolution of a given spin under a homonudear as opposed to a heteronuclear dipolar coupling [3—5] As a consequence, a different methodology is required for the determination of the intemudear distance between a homonudear dipolar-coupled pair of spins. 

Rotational resonance (RR) is an intriguing phenomenon which is observed when Vr is equal to a small integer multiple of the difference in the isotropic chemical shift frequencies of two resonances in the spectram [66, 67]. The most apparent effect of RR is that the normally narrow spectral peaks acquire sphttings and broadenings, the nature of which depend on the dipolar coupHng between the two spins. As a specific example, experimental spectra (together with best-fit simulations) corresponding to the = 1, 2, and 3 RR conditions for aU-E-[ll,20- C2]-retinal are shown in Fig. 9.15 [68]. In this case, it was possible to determine that the intemudear distance between the two labels is 0.301 + 0.008 run. 

A slightly different ptobkni arises when we consider the lower oxidation states of metals. We know that CaFj is stable. Why not CaF as well Assuming that CaF would crystallize in the same geometry as KF and that the intemudear distance would be about the same, we can calculate a lattice energy Ibr CaF, C/g > —795 kJ mcd The terms in the Bom-Haber cycle are... 

Rg. 4.10 Electron density contours in sodium chloride. Numbers indicaie the electron density (electrons A" = 10 electrons pm" ) along each comour line. The boundary" of each ion is defined as the minimum in electron density between the ions. The intemudear distance is 281 pm (< Z8l A). [Modified from Schoknecht, C. Z. Naturforsch. 1957, I2A, 983. Reproduced with permission.]... 

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