Linear Stark effect

Stark effect in diatomic, linear and symmetric rotor molecules... 

A permanent EDM of a stable atomic or molecular state can arise only when both P and T invariance are broken (see Fig.l). It is often said that polar molecules possess permanent EDMs and exhibit a linear Stark effect. However, the Stark effect exhibited by the polar molecule is not really linear for sufficiently small E at zero temperature, and moreover, it violates neither P nor T symmetry [10]. We emphasize that a permanent EDM that exhibits a linear Stark effect even for an infinitesimally weak is a genuine signature of P and T violation or CP violation... 

Determination of noncentrosymmetric molecular orientation in LB films by the linear Stark effect measurement... 

For the establishment of a preparation method for LB films with well-defined noncentrosymmetric structure, quantitative evaluation of noncentrosymmetric molecular orientation is essential. The linear Stark effect, which is observed only in noncentrosymmetric materials, is expected to be helpful for the characterization of noncentrosymmetric molecular orientation in LB films [5], In this section, we describe the quantitative evaluation of noncentrosymmetric molecular orientation in LB films by the linear Stark effect measurement. 

The Stark effect is electric-field-induced change in optical transition energy of materials, and the effect is observed as spectral change in absorption due to the energy shift. In the linear Stark effect, energy shift of optical transition Av in proportion to the electric field F is presented by... 

We used two types of LB films obtained by Z- and hetero Y-type deposition which were assumed to possess noncentrosymmetric molecular orientation. For comparison, an LB film with symmetrical structure obtained by Y-type deposition was also used. On these three types of LB films, the molecular orientation were determined by the linear Stark effect measurement [6]. 

The samples for the linear Stark effect measurement were prepared as follows. First, 9 monolayers of cadmium arachidate were deposited on fused quartz plates with semitransparent A1 electrodes. Next, test layers which contained 30 layers of compound C180AZ0SN were deposited. Then, further 10 layers of cadmium arachidate were deposited. Finally, the semitransparent top A1 electrodes were vacuum-deposited. 

In the Z-type deposition film, however, the long spacing of 7.2 nm did not agree with the predicted value of 3.9 nm rather, it was the same value as that of the Y-type deposition film. This result demonstrates that the Z-type film does not possess the Z-type layer structure but the Y-type layer structure. It should be assumed that the molecules were turned over in the deposition process and formed the Y-type layer structure, since the Z-type layer structure in which a hydrophilic group touches on a hydrophobic group is unstable. The conclusion from the examination of long spacings well supports molecular orientations in the LB films determined from the linear Stark effect measurements. From the linear Stark effect and the X-ray diffraction measurements, it is demonstrated that the hetero Y-type deposition method is useful for fabrication of stable noncentrosymmetric LB films. 

As mentioned in this section, the linear Stark effect measurement provides detailed information on noncentrosymmetric molecular orientation. This technique is very helpful for the advanced molecular design of noncentrosymmetric LB films for electro-optic and nonlinear optic applications. 

The ab initio SCF cluster wavefunction has been used to investigate the bonding of CO and CN- on Cu,0 (5,4,1), (5 surface layer, 4 second layer and 1 bottom layer atoms), and to calculate their field dependent vibrational frequency shifts in fields up to 5.2 x 107 V/cm(46). A schematic view of the Cu10 (5,4,l)CO cluster is shown in Figure 8. In order to assess the significance of Lambert s proposal, that the linear Stark effect is the dominant factor in the field dependent frequency shift, the effect of the field was calculated by three methods. One is by a fully variational approach (i.e., the adsorbate is allowed to relax under the influence of the applied field) in which the Hamiltonian for the cluster in a uniform electric field, F, is given by... 

The solvent Stark term developed by Baur and Nicols 9) reflects the same qualitative interactions as the reaction field term, however, it concerns the situation when the solute is less polar (in the ideal case non-polar) than the surrounding solvent. Correlations with Stark effects are usually recognized as linear relations to the term... 

Values of /rc and /iceq were obtained from the linear Stark effects, and, making the assumption that the total dipole moment of both conformers is the same, then nf /paeq was estimated. Substitution in the equation gave AE = 245 + 150 cal mol 1 corresponding to 60% N-Heq conformer at 20°C.144 The validity of the assumption of equal overall dipole moments of the two conformers has been challenged.9... 

The eigenvalue problem for the simple cos y potential of Eq. (4) can be solved easily by matrix diagonalization using a basis of free-rotor wave functions. For practical purposes, however, it is also useful to have approximate analytical expressions for the channel potentials V,(r). The latter can be constructed by suitable interpolation between perturbed free-rotor and perturbed harmonic oscillator eigenvalues in the anisotropic potential for large and small distances r, respectively. Analogous to the weak-field limit of the Stark effect, for linear closed-shell dipoles at large r, one has [7]... 

The rotational quantum numbers of the free linear dipole are j and m (with m S j), and the rotational constant is denoted by B. Analogous to the strong-field limit of the Stark effect, for linear dipoles at small r, one has... 

In addition to the orbitals shown in Fig. 1 there are hybrid orbitals that are not stationary states for the electron in an isolated atom. They can be obtained by taking a linear combination of the standard orbitals in Fig. 1. Since the electron distribution is off center they are useful only for atoms that are perturbed by an electric field (Stark-effect) or by the approach of other atoms as occurs in chemical-bond formation. 

The three curves into which the entry channel V (R) branches as the distance decreases dissociate into He+ (/i = 2) + Hg+(5distance between the charge at Hg+ and He+ (n = 2), the nearly degenerate helium states are split by the linear Stark effect, which leads to... 

An equivalent form is given by Englefield.11 It is possible to find quite a variety of phases for the transformation coefficients of Eq. (6.18).10-13 The phase depends on the phase conventions established for the spherical and parabolic states. The choice of phase in Eq. (6.18) is for spherical functions with an /, as opposed to (-r)e, dependence at the origin and the spherical harmonic functions of Bethe and Salpeter. A few examples of the spherical harmonics are given in Table 2.2. The parabolic functions are assumed to have an ( n) ml/2 behavior at the origin and an e m angular dependence. This convention means, for example, that for all Stark states with the quantum number m, the transformation coefficient (nni>i2m nmm) is positive. To the extent that the Stark effect is linear, i.e. to the extent that the wavefunctions are the zero field parabolic wavefunctions, the transformation of Eqs. (6.17) and (6.18) allows us to decompose a parabolic Stark state in a field into its zero field components, or vice versa. 

For the extreme red Stark state of high n Eq. (6.38) reduces to Eq. (6.35) since Z2 1. For this Stark state the Stark shift increases the binding energy, and for an m = 0 state the energy is adequately given using the linear Stark effect as... 

The system of equations obtained, (5.22) and (5.23), in broad line approximation in many cases allows us to carry out the analysis of non-linear optical pumping of both atoms and molecules in an external magnetic field. Some examples will be considered in Section 5.5, among them the comparatively unexplored problem of transition from alignment to orientation under the influence of the dynamic Stark effect. But before that we will return to the weak excitation and present, as examples, some cases of the simultaneous application of density matrix equations (5.7) and expansion over state multipoles (5.20). 

The prerequisite for the creation of orientation in the aligned state can also be formulated in terms of the time reversal properties of a Hamiltonian operator which represents the perturbation. As is shown in [276, 277] the alignment-orientation conversion may only take place if the time invariant Hamiltonian is involved. For instance, the Hamiltonian operator of the linear Zeeman effect is odd under time reversal and is thus not able to effect the conversion, whilst the operator of the quadratic Stark effect is even under time reversal and, as a consequence, the quadratic Stark effect can produce alignment-orientation conversion. 

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