Dipolar term

Prop = cavity term + dipolar term + hydrogen-bonding terms... 

The electron-electron dipolar term, Ho, equals S1.D.S2. The tensor D is completely anisotropic and only mixes T-states with one another. It is therefore dropped. The nuclear Zeeman term, tlzi =... 

The complete Hamiltonian of the molecular system can be wrihen as H +H or H =H +H for the commutator being linear, where is the Hamiltonian corresponding to the spin contribution(s) such as, Fermi contact term, dipolar term, spin-orbit coupling, etc. (5). As a result, H ° would correspond to the spin free part of the Hamiltonian, which is usually employed in the electron propagator implementation. Accordingly, the k -th pole associated with the complete Hamiltonian H is , so that El is the A -th pole of the electron propagator for the spin free Hamiltonian H . 

Fig. 12. Effect of a strong exchange interaction on the shape of the EPR spectrum displayed by a pair of centers A and B having identical g vEilues, = 1.89, g, = 1.96, g = 2.07, and rotated magnetic axes according to xjly, yglx, zJIzy,. (a) 9 GHz spectrum calculated with J = 0 (b) and (c) spectra calculated with J = 25 X 10 cm at 9 and 35 GHz, respectively. The spectra were calculated as described in Ref. 192) without including any dipolar terms, with the linewidths ui = cr, = oi = 0.01.

If the interface is in the zero charge state, named also the point of zero charge (pzc), the Galvani potential should be equal to the dipolar term [19-21] ... 

The first two terms in (5) are called D-terms or dipolar terms, which are nonzero only if Ape =/= 0. The two-photon resonance denominator, ( leg — 2hco), indicates that an electron is excited into the lower excited state e. If we consider a near resonance condition hco = %imaginary part of the D-terms can be written in SI units as ... 

Now 2a or 2/3 for an unpaired electron in a pure 2p orbital is equal to /7n/3nr, (1/r3), where (1/r3) is defined by Eq. (5D). The symbol Bo is used to denote the dipolar term for a pure 2p orbital. Theoretical calculations indicate a value of 34 G for I4N as shown in Table II. The ratio of 2a and 2d with respect to Ba gives the fractional p character of the unpaired electron in the two orthogonal p orbitals. A positive value of B0 confirms that our choice of signs in Eq. (12) was correct. 

For nuclei other than protons the dipolar term is smaller, due to the smaller value of yjv, a.nd the contact term may be larger, in case of directly coordinated nuclei. Therefore, contact relaxation may more often be the dominant contribution to nuclear relaxation. 

The dipolar terms contribute to the electric field. With the density deformation functions of the multipole model (chapter 3) and Eq. (8.36), one obtains... 

The main purpose of the sequences is to obtain an averaged Hamiltonian H in which the dipolar term is very small compared with the chemical shift term. The zeroth-order of the average dipolar Hamiltonian term is given by the following equation ... 

Solvatochromic Approach The solvatochromic approach describes a solvent-dependent property, XYZ, as a function of a cavity term, a dipolar term, and terms that account for hydrogen bonding [21] ... 

LSER Model of Leahy In the LSER model of Leahy [22], the cavity term is substituted by the molar volume, Vm, at 25°C in g cm-3 or by the intrinsic molecular volume, V), in mLmoL1. The dipolar term and the hydrogen-bonding terms are represented by the dipole moment, n, and the HBA basicity, (3, respectively. Group contribution schemes have been developed to calculate the solvatochromic parameters from molecular structure input [23]. Leahy [22] gives the following equation derived with a diverse set of monofunctional liquids ... 

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