Polarization moments, quantum table

Since the density matrix is Hermitian, we obtain the property of polarization moments which is analogous to the classical relation (2.15) fq = (—1 ) (f-q) and tp = (—l) 3( g). The adopted normalization of the tensor operators (5.19) yields the most lucid physical meaning of quantum mechanical polarization moments fq and p% which coincides, with accuracy up to a normalizing coefficient that is equal for polarization moments of all ranks, with the physical meaning of classical polarization moments pq, as discussed in Chapter 2. For a comparison between classical and quantum mechanical polarization moments of the lower ranks see Table 5.1. 

Table 5.1. Comparison between classical pq and quantum mechanical fq polarization moments...

There are three broad types of intermolecular forces of adhesion and cohesion (7) quantum mechanical forces, pure electrostatic forces, and polarization forces. Quantum mechanical forces account for covalent bonding. Pure electrostatic interactions include Coulomb forces between charged ions, permanent dipoles, and quadrupoles. Polarization forces arise from dipole moments induced by the electric fields of nearby charges and other permanent and induced dipoles. Ideally, the forces involved in the interaction at a release interface must be the weakest possible. These are the polarization forces known as London or dispersion forces that arise from interactions of temporary dipoles caused by fluctuations in electron density. They are common to all matter and their energies range from 0.1 to 40 kJ/mol. Solid surfaces with the lowest dispersion-force interactions are those that comprise aliphatic hydrocarbons, and fluorocarbons, and that is why such materials dominate the classification table (Table 1) and the surface energy table (Table 2). 

Another factor that influences the reactivity of two polar reactants, acylperoxyl radical with aldehyde, is the polar interaction of carbonyl group with reaction center in the transition state. Aldehydes are polar compounds, their dipole moments are higher than 2.5 Debye (see Section 8.1.1). The dipole moment of the acylperoxyl radical is about 4 Debye (/jl = 3.87 Debye for PhC(0)00 according to the quantum-chemical calculation [54]). Due to this, one can expect a strong polar effect in the reaction of peroxyl radicals with aldehydes. The IPM helps to evaluate the increment Ain the activation energy Ee of the chosen reaction using experimental data [1], The results of Acalculation are presented in Table 8.10. 

The dipole moments of some pseudoazulenes were determined by dielectric measurements. They are listed in Table II. The high values obtained (for comparison 6,6-dihydroindeno[2,1-b]quinoline has a dipole moment of 1.66 D whereas the corresponding 6-oxo compound has a value of approximately 1.6 D) are in accordance with quantum chemical calculations (see Section IV,B). The relatively high values of the dipole moments of unsubstituted pseudoazulenes and their derivatives show that some of the polar structures contribute to the resonance hybrid (Eq. 7). But in all cases the ring heteroatoms are localized at the positive end of the dipole. 

In /-band metals, the induced orbital moments dominate the induced spin moments (Table 2) due to the large angular momentum quantum number, Z = 3, and due to the correlation enhancement of the orbital polarization. There are two interesting points to note in connection with the presented data. At first, the parallel orientation of spin and orbital moments in a less than... 

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