Atomic dipoles

The reason for this difference was first pointed out by Mott (17) and Is based upon atomic dipole selection rules (4J =0+1). In a Ft atom the empty 5d state has J = 5/2 symmetry, hence a transition Is expected at the edge (J = 3/2)... 

An important addition to the model was the inclusion of virtual particles representative of lone pairs on hydrogen bond acceptors [60], Their inclusion was motivated by the inability of the atom-based electrostatic model to treat interactions with water as a function of orientation. By distributing the atomic charges on to lone pairs it was possible to reproduce QM interaction energies as a function of orientation. The addition of lone pairs may be considered analogous to the use of atomic dipoles on such atoms. In the model, the polarizability is still maintained on the parent atom. In addition, anisotropic atomic polarizability, as described in Eq. (9-28), is included on hydrogen bond acceptors [65], Its inclusion allows for reproduction of QM polarization response as a function of orientation around S, O and N atoms and it facilitates reproduction of QM interaction energies with ions as a function of orientation. 

Applequist J, Carl JR, Fung K-K (1972) Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities. J Am Chem Soc... 

Figure 2.5 (a) Hypothetical ionic molecule with spherical ions and the corresponding charge transfer moment, (b) In a real molecule the ions are polarized leading atomic dipoles in each atom that oppose the charge transfer moment. 

Figure 2.6 The dipole moment of the water molecule can be resolved into two OH bond moments. This does not give the true value of the bond moments because this procedure ignores the atomic dipoles.

Figure 2.9 The dipole moment of NH3 is much larger than that of NF3 because a large atomic dipole adds to the vector sum of the NH bond dipoles, whereas a large atomic dipole opposes the vector sum of the large NF atomic dipoles.

It has often been assumed that atomic charges can be calculated from the measured dipole moment of a diatomic molecule and the bond length. For this assumption to hold, however, the center of negative charge of an atom would have to be situated at the nucleus, in other words, atoms would have to be spherical. But we have seen that atoms in molecules are not spherical, and so the center of negative charge is not centered at the nucleus. Each atom therefore has a dipole moment called the atomic dipole moment (Chapter 2). 

The atomic dipole moment can be obtained by integrating the moment of a volume element prfidr over the atomic basin. The atomic dipole moment M(fl), where is a vector centered on the nucleus of the atom, is then... 

This moment measures the extent and direction of the shift of an atom s electronic charge cloud with respect to the nucleus. The quantity M(fi) can effectively be regarded as an intra-atomic dipole moment. The intra-atomic dipole moment of each atom contributes to the... 

As mentioned above and discussed in Chapter 2, atomic charges were often obtained in the past from dipole moments of diatomic molecules, assuming that the measured dipole moment equal to the bond length times the atomic charge. This method assumes that the molecular electron density is composed of spherically symmetric electron density distributions, each centered on its own nucleus. That is, the dipole moment is assumed to be due only to the charge transfer moment Mct. and the atomic dipoles Malom are ignored. 

Another example of the importance of atomic dipoles appeared in Chapter 2, where we attributed the small dipole moment of NF3 to the moment produced by the lone pair on nitrogen, which makes an important contribution to the atomic dipole on nitrogen and opposes the charge transfer moment due to the electronegativity difference between nitrogen and fluorine. 

As its name implies, AIM enables us to calculate such properties of atoms in a molecule as atomic charge, atomic volume, and atomic dipole. Indeed it shows us that the classical picture of a bond as an entity that is apparently independent of the atoms, like a Lewis bond line or a stick in a ball-and-stick model, is misleading. There are no bonds in molecules that are independent of the atoms. AIM identifies a bond as the line between two nuclei. 

The term molecular crystal refers to crystals consisting of neutral atomic particles. Thus they include the rare gases He, Ne, Ar, Kr, Xe, and Rn. However, most of them consist of molecules with up to about 100 atoms bound internally by covalent bonds. The dipole interactions that bond them is discussed briefly in Chapter 3, and at length in books such as Parsegian (2006). This book also discusses the Lifshitz-Casimir effect which causes macroscopic solids to attract one another weakly as a result of fluctuating atomic dipoles. Since dipole-dipole forces are almost always positive (unlike monopole forces) they add up to create measurable attractions between macroscopic bodies. However, they decrease rapidly as any two molecules are separated. A detailed history of intermolecular forces is given by Rowlinson (2002). 

Anti-Stokes broadening, 101 Atomic dipole phases, 68... 

General properties and definitions of polarizabilities can be introduced without invoking the complete DFT formalism by considering first an elementary model the dipole of an isolated, spherical atom induced by a uniform electric field. The variation of the electronic density is represented by a simple scalar the induced atomic dipole moment. This coarse-grained (CG) model of the electronic density permits to derive a useful explicit energy functional where the functional derivatives are formulated in terms of polarizabilities and dipole hardnesses. 

The physical meaning of Equation 24.28 is clear the local held felt by an atom is not the bare applied held but a held screened by M 1, which is the inverse of a molecular nonlocal held response. The bare nonlocal polarizability a(L,J) describing the response of the atom (dipole induced at) L to the bare held E applied at the atom J is also related toM 1 by... 

The atomic dipole moment can be attributed to the preferential population of specific nonspherical atomic orbitals. In particular, this is the case for atoms with doubly-filled nonbonding lone-pair orbitals, such as the oxygen atoms in C—O—H and H—O—H, or oxygen in a terminal position as it is in the carbonyl group. An early demonstration of the bias introduced in X-ray positions of non-hydrogen atoms was the combined X-ray and neutron study of oxalic acid dihydrate (Coppens et al. 1969), which showed the X-ray positions of the oxygen atoms to be systematically displaced by small amounts into the direction of the lone pair density. 

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