Multipole moments permanent

Eo and E (Afi(i)) are respectively the electric fields generated by the permanent and induced multipoles moments. a(i) represents the polarisability tensor and Afi(i) is the induced dipole at a center i. This computation is performed iteratively, as Epoi generally converges in 5-6 iterations. It is important to note that in order to avoid problems at the short-range, the so-called polarization catastrophe, it is necessary to reduce the polarization energy when two centers are at close contact distance. In SIBFA, the electric fields equations are dressed by a Gaussian function reducing their value to avoid such problems. 

For a determination of the permanent multipole moments, Eq. 2.42 must be averaged over the ground state nuclear vibrational wavefunction transition elements are also often of interest which are matrix elements between initial and final rotovibrational states. For example, for a diatomic molecule with rotovibrational states vJM), the transition matrix elements (v J M Q(m vJM) will be of interest a prime designates final states. 

Equation (1-239) relates the interaction-induced part of the dipole moment of the complex AB to the distortion of the electron density associated with the electrostatic, exchange, induction, and dispersion interactions between the monomers. The polarization contributions to the dipole moment through the second-order of perturbation theory (A/a, A/a, and A/a ) have an appealing, partly classical, partly quantum, physical interpretation. The first-order multipole-expanded polarization contribution (F) is due to the interactions of permanent multipole moments on A with moments induced on B by the external field F, and vice versa. The terms... 

The fourth term, the electrostatic interaction, was omitted since one monomer, the Ar atom, has no permanent multipole moments. 

Energy of Induced Multipole Interaction.—Interaction between a Multipolar System and External Fields. We calculated above the potential energy of electrostatic interaction between a multipole system and external fields, or thefirst-orderenergyduetothefirstpowerofthefield. Besides that energy, which took account only of the reoriratation of permanent multipoles, we have to take into consideration contributions due to the drcum-stance that an external electric field induces higher-order multipole moments given by the expressions (72) and (79). 

Knowing the molecular permanent multipole moments and transition moments (or closure moments derived from sum rules, such as (36)), the computation of the fust and second order interaction energies in the multipole expansion becomes very easy. One just substitutes all these multipole properties into the expressions (16), (20), (21) and (22), together with the algebraic coefficients (24) (tabulated up to terms inclusive in ref. in a somewhat different form ), and one calculates the angular functions (lb) for given orientations of the molecules. 

A standard question in spectroscopy is does a given molecule have a permanent dipole moment This can usually be decided immediately by inspection, but the formal group-theoretical answer is that a molecule can exhibit a component of permanent dipole for each occurrence of the totally symmetric To in the dipole character T (/u.) = xyz = Ft- Similar reasoning can be extended to other multipole moments, polarisabilities and corresponding magnetic properties. 

A. D. Buckingham, Adv. Chem. Phys., 12, 107 (1967). Permanent and Induced Multipole Moments and Long-Range Intermolecular Forces. 

As an example, explicit expressions of /3 can be given in the case of the dipole polarizability of the H atom and for a few simple VdW interactions which depend on the electrical properties of the molecules such as electric dipole moments and polarizabilities (Stone, 1996). As we have already said, these dipole moments, and the higher ones known generally as multipole moments, can be permanent (when they persist in absence of any external field) or induced (when due, temporarily, to the action of an external field and disappear when the field is removed). 

In this chapter, we shall examine two different approaches to explain the nature of the hydrogen bond and the structure of H-bonded dimers. First, a qualitative MO model where H-bonding is assumed to stem from electron transfer from an electron-rich donor MO1 on one partner to an electron acceptor MO2 centred at the H atom of the partner molecule. Second, a quantitative electrostatic approach, where the H-bond and the shape resulting therefrom for the dimers, can be understood in terms of the long-range interactions between the first few permanent multipole moments of the interacting molecules, yielding the electrostatic model. 

In the first case, the hydrogen bond and the shape resulting therefrom for these dimers can be understood in terms of the long-range interactions between the first few permanent multipole moments of the interacting molecules (Magnasco et al., 1989b). 

As in the Rayleigh case, the pair polarizability results as well from nonlinear light scattering mechanisms (induced by hyperpolarizabilities and permanent multipole moments). For tetrahedral molecules nonlinear mechanisms contribute to some correlation functions listed in Table V—only those related to the depolarized spectrum and governed by double rotational transitions (QQ, QO, and 00). The nonlinear origin corrections Atp j7"1 j2 which must be added to the linear origin terms cp 1 °f Table V for a tetrahedral molecule are successively [17]... 

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