Virtual dipole

Turning to molecular physics, we note first papers by Ya.B. which are close to the problem of phase transition. We begin with the theory of interaction of an atom with a metal (11). By applying quantum-mechanical perturbation theory to the interaction of the virtual dipole moment of an atom with conducting electrons of the metal, the dependence on distance of the attractive force of the atom to the surface is obtained. The calculation led to a slow, r2, law for the potential energy decay with distance. This paper was published in 1935, and for many years remained essentially the only one devoted to the subject. 

Nonlinear optics is a scattering process. As each photon "arrives" or "leaves", it induces a virtual dipole allowed transition frequently abbreviated... 

The derivation of these equations is described elsewhere in this volume. is the average value of the angle between real and virtual dipole when no external field is present. 

The size of the U matrix is the number of occupied orbitals times the number of virtual dipole moment, from the derivative formula (10.21) is given as (since an HF wave ... 

The polarisation potential is complex and nonlocal. The imaginary part is due to on-shell amplitudes for the excitation of Q space from P space. At long range the potential is real. We will show its relationship for large r, where it is due to virtual dipole excitations, to the classical dipole potential where a is the polarisability. 

In the homogeneous metal, there are no real" charge fluctuations, just as in the Helium atom there is no real" dipole moment. Van der Waals attraction between two Helium atoms comes about as the result of the correlated quantum fluctuations of a virtual dipole moment induced in each atom by the other. Similarly, an attractive force comes about from correlated, virtual, charge fluctuations In the two planes. I eliminate H from the Hamiltonian to leading order in W. using the operator generalization of second-order perturbation theory for the energy levels. This yields ... 

Here we have to sum over all states connected to the ground state by dipole radiation these are the p-states. Each of these p-states (we can neglect the spin) is threefold-degenerate, corresponding to the three main directions in which the virtual dipole can be oriented mi = 1,0). For a fixed value of the main quantum numbers n and n" and therefore of the /in and /in" we obtain in total nine different orientation possibilities. Elementary trigonometry yields the number 6 for the sum over the corresponding cosine factors. Therefore... 

Molecules initially in the J = 0 state encounter intense, monochromatic radiation of wavenumber v. Provided the energy hcv does not correspond to the difference in energy between J = 0 and any other state (electronic, vibrational or rotational) of the molecule it is not absorbed but produces an induced dipole in the molecule, as expressed by Equation (5.43). The molecule is said to be in a virtual state which, in the case shown in Figure 5.16, is Vq. When scattering occurs the molecule may return, according to the selection mles, to J = 0 (Rayleigh) or J = 2 (Stokes). Similarly a molecule initially in the J = 2 state goes to... 

Reactions offluorinated dipoles. In recent years, much effort has been devoted to the preparation of tnfluoromethyl-substituted 1,3-dipoles with the goal of using them to introduce trifluoromethyl groups into five-membered nng heterocycles Fluorinated diazoalkanes were the first such 1,3-dipoles to be prepared and used in synthesis A number of reports of cycloadditions of mono- and bis(tnfluo-romethyl)diazomethane appeared prior to 1972 [9] Other types of fluonne-substi-tuted 1,3-dipoles were virtually unknown until only recently However, largely because of the efforts of Tanaka s group, a broad knowledge of the chemistry of tnfluoromethyl-substituted nitrile oxides, nitnle imines, nitnle ylides, and nitrones has been accumulated recently... 

In this equation, AG°CS is taken to be negligible for p- and y-cyclodextrin systems and to be constant, if there is any, for the a-cyclodextrin system. The AG W term is virtually independent of the kind of guest molecules, though it is dependent on the size of the cyclodextrin cavity. The AG dw term is divided into two terms, AG°,ec and AGs°ter, which correspond to polar (dipole-dipole or dipole-induced dipole) interactions and London dispersion forces, respectively. The former is mainly governed by the electronic factor, the latter by the steric factor, of a guest molecule. Thus, Eq. 2 is converted to Eq. 3 for the complexation of a particular cyclodextrin with a homogeneous series of guest molecules ... 

Fig. 1.7 Correlation between virtual log P (calculated with the molecular lipophilicity potential) and the dipole moment (f = 0.76) as obtained from MD simulation of acetylcholine in water. Reproduced from Ref [16] with kind permission of American Chemical Society 2005.

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. 

The Raman effect arises when a photon is incident on a molecule and interacts with the electric dipole of the molecule. In classical terms, the interaction can be viewed as a perturbation of the molecule s electric field. In quantum mechanics the scattering is described as an excitation to a virtual state lower in energy than a real electronic transition with nearly coincident de-excitation and a change in vibrational energy. The scattering event occurs in 10 14 seconds or less. The virtual state description of scattering is shown in Figure 1. 

For many years, investigations on the electronic structure of organic radical cations in general, and of polyenes in particular, were dominated by PE spectroscopy which represented by far the most copious source of data on this subject. Consequently, attention was focussed mainly on those excited states of radical ions which can be formed by direct photoionization. However, promotion of electrons into virtual MOs of radical cations is also possible, but as the corresponding excited states cannot be attained by a one-photon process from the neutral molecule they do not manifest themselves in PE spectra. On the other hand, they can be reached by electronic excitation of the radical cations, provided that the corresponding transitions are allowed by electric-dipole selection rules. As will be shown in Section III.C, the description of such states requires an extension of the simple models used in Section n, but before going into this, we would like to discuss them in a qualitative way and give a brief account of experimental techniques used to study them. 

Figure 7.4b shows PT for the aluminum film case. There is a dramatic increase in PT for both dipole orientations at small distances. Virtually all of that energy is converted into heat in the metal, thereby accounting for the strong fluorescence quenching on metal surfaces. For dipoles oriented parallel,... 

In the metal film case, the intensity is virtually zero for distances less than 5 nm. This quenching effect occurs at all angles, not just supercritical ones. The excitation energy is almost entirely converted into heat in the metal film. At larger distances, the dipole near field couples with surface plasmons whose emission into the glass is centered around 0 = 0P. At even larger distances, the near field is too weak to interact with the surface, and the supercritical intensity drops toward zero. 

---