Electric moment second

ECP (Effective Core Potential) 171 Effective pair potential 68 EHMO (Extended Huckel Molecular Orbital Model) 130 Eigenvalue 17 Eigenvector 17 Einstein relation 253 Electric dipole moment 100, 265, 282 Electric field gradient 278 Electric moments 184 Electric quadrupole moment 268, 269 Electric second moment 268 Electric susceptibility 256 Electron affinity 147 Electron correlation 186, 273 Electron density 100, 218, 222 Electron relaxation 118 Electron spin 91, 95, 99, 277, 305 Electronic Schrodinger equation 74 Electrostatic field 14 Electrostatic field gradient 271... 

The first process is due to Schottky barriers [30], which are electrical dipole moments that form at the metal I molecule interfaces, as discussed above [34,40]. The second process arises if the electrically-active portion of the molecule is placed asymmetrically within the metal I molecule I metal sandwich. This geometry is common, because a long alkyl tail is often needed to make the molecule amphiphilic so that it will form well-ordered Langmuir-Blodgett monolayers [76-78]. 

If the hfs of the nucleus under consideration is not resolved in the EPR spectrum, all nuclear spin states are simultaneously saturated and a sign determination using ENDOR line intensities is not possible. In this case the relative signs may sometimes be determined from second order hf contributions. This method has been applied by DuVarney and Spaeth74) to determine the sign of the 41K electric quadrupole moment using F centres in KC1. 

Including the spherical component, the electric field gradient can be interpreted as the second-moment tensor of the distribution p(r)/ r — r 5. 

At temperatures above absolute zero, all atoms in molecules are in continuous vibration with respect to each other [26]. Infrared spectroscopy is an absorption spectroscopy. Two primary conditions must be fulfilled for infrared absorption to occur. First, the energy of the radiation must coincide with the energy difference between excited and ground states of the molecule, i.e., it is quantized (Fig. 14.2). Radiant energy will then be absorbed by the molecule, increasing its natural vibration. Second, the vibration must entail a change in the electrical dipole moment (Fig. 14.3). 

Note that since both /z and E are vector quantities, a is a second-rank tensor. The elements of a can be computed through differentiation of Eqs. (9.1) and (9.2). The difference between die permanent electric dipole moment and that measured in the presence of an electric field is referred to as the induced dipole moment. 

Second-order perturbation sums are a second example in which one is interested in an average or integral over a spectral density. For example, the dynamic polarizability a of a system at a frequency co0 is related to the spectral density /(co) of the electric dipole moment of the system by... 

The first term in the square bracket in this equation is the electric monopole moment, which is equal to the nuclear charge, Ze. The second term in the square bracket is the electric dipole moment while the third term in the square bracket is the electric quadmpole moment. For a quantum mechanical system in a well-defined quantum state, the charge density p is an even function, and because the dipole moment involves the product of an even and an odd function, the corresponding integral is identically zero. Therefore, there should be no electric dipole moment or any other odd electric moment for nuclei. For spherical nuclei, the charge density p does not depend on 0, and thus the quadmpole moment Q is given by... 

The energy of the emitted y ray is determined by the energy difference between the nuclear excited and ground states. This energy difference is not altered by the first term, eZU, since this term equally affects the nuclear excited and ground states in both the source and absorber. In addition, atomic nuclei do not possess electric dipole moments, and therefore the second term in Eq. (9) must be equal to zero. Thus, when considering the Mossbauer effect, Ee can be written in the form... 

P is the macroscopic polarization. It consists of a lattice polarization b21 w originating from the electric dipole moment arising from the mutual displacement of the two sublattices, and of a second term b22 P originating from the pure electron polarization. According to definition, P and E are connected by... 

Among the molecular properties introduced above are the permanent electric dipole moment /xa and traceless electric quadrupole moment a(8, the electric dipole polarizability aajg(—w to) [aiso(to) = aaa(—or, o>)], the magnetizability a(8, the dc Kerr first electric dipole hyperpolarizability jBapy(—(o a>, 0) and the dc Kerr second electric-dipole hyperpolarizability yapys(— ( >, 0,0). The more exotic mixed hypersusceptibilities are defined, with the formalism of modern response theory [9]... 

The predominant interaction for a 2H spin system is the quadrupolar interaction, which couples the electric quadrupole moment of the 2H nucleus to its electronic surrounding. This interaction is a second-rank tensor Hq which lies approximately along the C-2H bond in organic molecules. Thus, in practice, 2H nuclei may be considered to be isolated. It shows that the 2H NMR formalism is similar to that of an isolated proton pair [8] ... 

Electron correlation introduces basically two effects into ab initio calculations on intermolecular forces. Hartree-Fock calculations do not account for dispersion forces and hence the dispersion energy is included only in Cl calculations. A second contribution comes from a correction of monomer properties through electron correlation effects. Again, the correlation correction of the electric dipole moment is the most important contribution. In the case of (HF)2 these two effects are of opposite sign and hence the influence of electron correlation on the calculated results is rather small (Table 3). 

The spacing of the different energy levels studied by NQR is due to the interaction of the nuclear quadrupole moment and the electric field gradient at the site of the nucleus considered. Usually the electric quadrupole moment of the nucleus is written eQ, where e is the elementary charge Q has the dimension of an area and is of the order of 10 24 cm2. More exactly, the electric quadrupole moment of the nucleus is described by a second order tensor. However, because of its symmetry and the validity of the Laplace equation, the scalar quantity eQ is sufficient to describe this tensor. 

This second effect will be computed first. A molecule of permanent electric dipole moment m (C m), when put into an external electric field E (V m a), assumes an angle 6 with respect to E its energy All (J) is then... 

Since a second-rank cartesian tensor Tap transforms in the same way as the set of products uaVfj, it can also be expressed in terms of a scalar (which is the trace T,y(y), a vector (the three components of the antisymmetric tensor (1 /2 ) Tap — Tpaj), and a second-rank spherical tensor (the five components of the traceless, symmetric tensor, (I /2)(Ta/= + Tpa) - (1/3)J2Taa). The explicit irreducible spherical tensor components can be obtained from equations (5.114) to (5.118) simply by replacing u vp by T,/ . These results are collected in table 5.2. It often happens that these three spherical tensors with k = 0, 1 and 2 occur in real, physical situations. In any given situation, one or more of them may vanish for example, all the components of T1 are zero if the tensor is symmetric, Yap = Tpa. A well-known example of a second-rank spherical tensor is the electric quadrupole moment. Its components are defined by... 

In the second line of (6.319) we have used the fact that the permanent electric dipole moment of the molecule lies along the internuclear axis (q = 0). The matrix elements of (6.319) in a case (a) basis are... 

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