Intemuclear distances effective

The symbols in the second column represent the electronic state in particular the first number is the total quantum number of the excited electron. We shall see later that in one case at least the symbol is probably incorrect. The third column gives the wave-number of the lowest oscillational-rotational level, the fourth the effective quantum number, the fifth and sixth the oscillational wave-number and the average intemuclear distance for the lowest oscillational-rotational level. The data for H2+ were obtained by extrapolation, except rQ, which is Burrau s theoretical value (Section Via). 

It is possible to distinguish between direct and indirect nOes from their kinetic behavior. The direct nOes grow immediately upon irradiation of the neighboring nucleus, with a first-order rate constant, and their kinetics depend initially only on the intemuclear distance r" indirect nOes are observable only after a certain time lag. We can thus suppress or enhance the indirect nOe s (e.g., at He) by short or long irradiations, respectively, of Ha- a long irradiation time of Ha allows the buildup of indirect negative nOe at He, while a short irradiation time of Ha allows only the direct positive nOe effects of Ha on He to be recorded. 

To study dipole-dipole relaxation, one must distinguish between homonuclear and heteronuclear (unlike) spin-1 pairs. The latter gives rise to the so-called 3/2 effect.29 For an isolated pair of like spin-i nuclei (/= 1) separated by an intemuclear distance r, the treatment of spin relaxation is identical to that for a spin-1 quadrupole system. The Zeeman spin-lattice relaxation time T1Z and spin-spin relaxation time T2 are given, respectively, by... 

Here, AT is a constant, f is the incoming intensity, R is the distance of the scattered wave from the molecule (in practical terms, it is the distance between the scattering center and the point of observation), i and j are the labels of atoms in the jV-atomic molecule, g contains the electron scattering amplitudes and phases of atoms, 5 is a simple function of the scattering angle and the electron wavelength, I is the mean vibrational amplitude of a pair of nuclei, r is the intemuclear distance r is the equilibrium intemuclear distance and is an effective intemuclear distance), and k is an asymmetry parameter related to anharmonicity of the vibration of a pair of nuclei. 

The fa intemuclear distance in the expression of molecular intensities (vide supra) is an effective parameter without rigorous physical meaning. It is, however, related in a good approximation to the thermal average... 

The following table summarizes the consequences of various vibrational effects on the intemuclear distance t5qies enumerated above ... 

We define a ten-function AO basis for the H2 molecule that has two different s -type orbitals and one />-type set on each H atom. It will be recalled that Weinbaum allowed the scale factor of the s orbital to adjust at each intemuclear distance. Using two different sized 5-type orbitals on each center accomplishes a similar effect by allowing the variation theorem to choose the amount of each in the mixture. Our orbitals are shown in Table 2.2. The 5-type orbitals are a split version of the Huzinaga 6-Gaussian H function and the p-type orbitals are adjusted to optimize the energy at the minimirm. It will be observed that the p and scale factors are different. We will present an interpretation of this below. 

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