Dipole moment nuclear

There have been numerous applications of continuum models to equilibria and reactions in solution surveys of these and extensive listings are provided by Cramer and Truhlar.16 Other studies have focused upon the effects of solvents upon solute molecular properties, such as electronic and vibrational spectra,16 dipole moments, nuclear quadrupole and spin-spin coupling constants and circular dichroism.12... 

Nuclear magnetic dipole moment (nuclear magnetons) nuclear quadrupole moment (barns nonzero if I > 1)... 

Since the vibrational eigenstates of the ground electronic state constitute an orthonomial basis set, tire off-diagonal matrix elements in equation (B 1.3.14) will vanish unless the ground state electronic polarizability depends on nuclear coordinates. (This is the Raman analogue of the requirement in infrared spectroscopy that, to observe a transition, the electronic dipole moment in the ground electronic state must properly vary with nuclear displacements from... 

Laser Raman diagnostic teclmiques offer remote, nonintnisive, nonperturbing measurements with high spatial and temporal resolution [158], This is particularly advantageous in the area of combustion chemistry. Physical probes for temperature and concentration measurements can be debatable in many combustion systems, such as furnaces, internal combustors etc., since they may disturb the medium or, even worse, not withstand the hostile enviromnents [159]. Laser Raman techniques are employed since two of the dominant molecules associated with air-fed combustion are O2 and N2. Flomonuclear diatomic molecules unable to have a nuclear coordinate-dependent dipole moment caimot be diagnosed by infrared spectroscopy. Other combustion species include CFl, CO2, FI2O and FI2 [160]. These molecules are probed by Raman spectroscopy to detenuine the temperature profile and species concentration m various combustion processes. 

The interaction of the electron spin s magnetic dipole moment with the magnetic dipole moments of nearby nuclear spins provides another contribution to the state energies and the number of energy levels, between which transitions may occur. This gives rise to the hyperfme structure in the EPR spectrum. The so-called hyperfme interaction (HFI) is described by the Hamiltonian... 

There are other important properties tliat can be measured from microwave and radiofrequency spectra of complexes. In particular, tire dipole moments and nuclear quadmpole coupling constants of complexes may contain useful infonnation on tire stmcture or potential energy surface. This is most easily seen in tire case of tire dipole moment. The dipole moment of tire complex is a vector, which may have components along all tire principal inertial axes. 

Using the Condon approximation, the transition dipole moment is taken to be a constant with respect to the nuclear coordinates. Equation (26) then reduces to the familiar expression... 

It is interesting to note that the acyclic analog, nitroguanidine, exists in the symmetrical form 288 rather than as 289. Structure 288 has been established by ultraviolet and proton nuclear magnetic resonance spectroscopy. X-ray crystallography, dipole moments, and ipK measurements (see reference 367 and references therein). 

In order to compare calculated and observed dipole moments, we should replace the classical expression of the dipole moment by its quantum analogue jx = f F x1Ir dr where /I is the dipole moment operator (given by jx = —eri + . eZ-Blj with i and j running over the electronic and nuclear coordinates, respectively, and — e the electron charge). The actual calculation of a VB dipole moment is described below. 

A nucleus in a state with spin quantum number 7 > 0 will interact with a magnetic field by means of its magnetic dipole moment p. This magnetic dipole interaction or nuclear Zeeman effect may be described by the Hamiltonian... 

Nuclear magnetic dipole moment of ground (g) and excited (e) state (in nuclear magnetons, n.m.)... 

Fig. 7.3 Effect of magnetic dipole interaction (7/m), electric quadmpole interaction (Hq), and combined interaction// = Hu + //q, Em> q on the Mossbauernuclear levels of Ni. The larger spacings between the sublevels of the ground state are due to the somewhat larger magnetic dipole moment of the nuclear ground state as compared to the excited state. The relative transition probabilities for a powder sample as well as the relative positions of the transition lines are indicated by the stick spectra below...

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