Permanent multipoles

The interaction of higher multipoles (permanent as well as induced first, the octupole with the corresponding octupole polarizabilities and hyperpolarizabilities, etc.) with the higher derivatives of electric field together with the corresponding cross terms denoted as H-... 

The interaction of higher multipoles (permanent as well as induced first, the octupole with... 

A common feature of many mesogenic molecules is the presence of polar substituents and aromatic cores [3]. The electrostatic interactions between such groups can be incorporated into a molecular potential with the addition of dipolar and quadrupolar terms, respectively. Rather than represent these permanent electrostatic interactions by using a model in which a charge distribution is scattered over the surface of the molecule, it is very common to use one (or more) point multipoles [2,29]. Thus for an electrostatic Gay-Berne model, the pair potential is given by the sum... 

K. Halbach 1980, (Design of permanent multipole magnets with oriented rare earth cobalt material), Nud. Instrum. Meth. 169, 1-10. 

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. 

More recently, Ponder and co-workers [40-48] developed the AMOEBA force field based on a modification of the formulation of Applequist [49] and Thole [50], It is based on a modification of Eq. (9-3) with the static electric field due to permanent charges replaced by permanent multipoles ... 

In the AMOEBA force field the permanent atomic multipoles are determined from QM calculations [40], The prescription considers that the resulting multipoles on the atoms result from two components, the permanent and the induced moments ... 

The scaling factor Sj can take any value between 0 and 1 and is applied to site j. The superscripts p and m indicate permanent and mutual induction, respectively. Equation (9-19) can be solved iteratively using similar procedures to those used to solve Eq. (9-3). The formal permanent moments can be calculated by subtracting induced moments from moments from ab initio calculations. For any conformation of a given compound the atomic multipoles can be determined from Distributed Multipole Analysis (DMA) [51]. 

The noncovalent interactions or van der Waals forces involved in supramolecular entities may be a combination of several interactions, e.g., ion-pairing, hydrophobic, hydrogen bonding, cation-Tr, tt-tt interactions, etc. They comprise interactions between permanent multipoles, between a permanent multipole and an induced multipole, and between a time-variable multipole and an induced multipole. 

Local multipoles do not, therefore, interact with oscillating dipoles. They do, however, interact with and re-enforce permanent dipoles. The sign of the effect so generated on the infrared spectrum will depend on the particular case, and of course different modes wiU be affected differently. Particularly relevant is a study 47) carried out on Os(CO)4Br2 and Os(CO)4l2. In this, it was found that CO stretching frequencies increase, with increasing solvent multipole effect, in the order... 

Madelung term and, 1 162-171 permanent electrical multipole term Uq and, 1 176-177... 

Permanent electrical multipole term Uq, lattice energies and, 1 176-177 Pemitrous acid, 22 147 Perovskites, ordered, 35 354, 370-371 Perovskite type fluorides, 20 152-166 Peroxides, see also specific compounds fluorinated, 16 109-168 fluoroaUcyl, spectral properties of, 16 154, 155... 

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. 

One of the simplest orientational-dependent potentials that has been used for polar molecules is the Stockmayer potential.48 It consists of a spherically symmetric Lennard-Jones potential plus a term representing the interaction between two point dipoles. This latter term contains the orientational dependence. Carbon monoxide and nitrogen both have permanent quadrupole moments. Therefore, an obvious generalization of Stockmayer potential is a Lennard-Jones potential plus terms involving quadrupole-quadrupole, dipole-dipole interactions. That is, the orientational part of the potential is derived from a multipole expansion of the electrostatic interaction between the charge distributions on two different molecules and only permanent (not induced) multipoles are considered. Further, the expansion is truncated at the quadrupole-quadrupole term. In all of the simulations discussed here, we have used potentials of this type. The components of the intermolecular potentials we considered are given by ... 

One of the mechanisms responsible for the emergence of linear birefringences is the temperature (7) dependent orientational effect the fields have on the molecules of the sample, through the interaction with their permanent multipoles. On the other hand this fact alone would not explain the occurrence of birefringences also for atoms or molecules with spherical symmetry. Electronic rearrangements, involving high order responses to... 

The distribution of partial electronic charges within an amino acid gives rise to various permanent electronic dipole and higher order multipole... 

The second component to the electrostatic interaction is the polarization of the charge distribution by an external field from a permanent multipole. This interaction is always attractive, but it is not pairwise additive and it increases with the number of electrons. For example is the polarizability for water 1.5 A3, while it is 10.6 A3 for benzene. 

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... 

---