Electric field, internuclear

The polarlsablllty of a molecule will vary during vibrations which change the Internuclear separations. Thus the vibrations of a molecule sitting In an electrical field will be coupled to the field via the polarlsablllty. This should be particularly noticeable for a molecule adsorbed on an electrode surface where the field strength Is typically In the range 10 -10 V cm, The dipole, perpendicular to the surface, Induced In the molecule by the static electric field will fluctuate In step with the normal mode vibrations of the molecule. 

Thus, we observe that when applying a finite electric field to a molecule, in addition to the instability with respect to the internuclear distance R, one obtains an instability connected to a change of the electric field strentgh F, as intuitively explained previously. In a more general way, the possible instabilities can be rationalized as follows at some... 

Figure SCF-MO density difference map for LiF in uniform electric field along internuclear axis minus electron density of field-free molecule.11 Contours are drawn corresponding to values of the electron density as follows A= — 0.800, B= -0.400, C= -0.200, D= -0.080,..., J=0,... S=0.800 electrons...

It should be stressed that this is a purely hypothetical concept which involves splitting the nucleus of the atom into two nuclei [2]. As for the true case of separated atoms, these two hypothetical new nuclei produce an inhomogeneous electric field in the direction of the internuclear axis. L and S... 

The calculated moment thus considerably exceeds the experimental value and furthermore represents the dipole as acting in the opposite direction the chlorine is represented as positive and the hydrogen negative. This result is clearly incorrect and Debye has shown that the error is due to the fact that the Lorentz-Lorenz equation is not valid at the small distances considered owing to the non-uniform character of the field. If the internuclear distances were of the order of 5 A, this type of calculation would be permissible. Attempts have been made to calculate the polarizability in a non-uniform electric field by the methods of wave mechanics , but have not yet been successful in producing a theory of the intermediate type of bond. 

POLY ATOM programs and elsewhere the less obvious ones are tr, diamagnetic shielding F and FG, the electric field and field gradient at the nucleus x the diamagnetic susceptibility. Z is the internuclear axis. All properties are relative to the carbon atom origin and the values are in the global co-ordinate system and atomic units. 

In the dipole approximation, the interaction between molecules and a laser light is given by (r, / ) = — E t). where TJ(l) is the electric field and p(r) is the dipole moment. Here, we will consider only one-dimensional systems, i. e., diatomic molecules, with the coordinate x denoting the internuclear distance between the two atoms. In first order perturbation theory, the probability for a transition between the initial state vibrational eigenstate excited potential U ix) is proportional to... 

Figure 23 Energy diagram for Rydberg diatomic levels, (a) fixed internuclear distance R = Ro. (b) Fixed electric field. The spacing between the +) and the levels at reson-nance is AW (R).

FIGURE 7. Left - Potential curves for the ground state of the Hj molecule in longitudinal electric field F (a.u.). Right - The equilibrium internuclear distance of the molecule Hj as a function of the applied electric field strength. 

When the laser field becomes comparable to the internuclear binding field of a molecule, which clearly depends on the orientation of the internuclear axis with respect to the electric field vector of the radiation, the molecular potential is deformed potential wells become more shallow and, as a consequence, the number of vibrational states which are observable is reduced. This effect is called molecular bond softening [503]. 

When atom-1 approaches atom-2, the axial electric field created by atom-1 lifts the 2L + 1 Ml-degeneracy of atom-2 and vice-versa. Here Ml is the projection of L into the internuclear axis and is related to the molecular A quantum number as... 

The dependence of the dipolar couplings on the orientation of the internuclear vector in the principle axis system of the electric field gradient has Inherent information about the molecular geometry of the relevant and sites. For example, in a peptide bond, where two carbons are bound to the same nitrogen, the dipolar coupling of each depends on the orientation of its respective internuclear vector with respect to the common coordinate system of the nitrogen electric field gradient principle axis system. Thus, the NMR spectrum is analyzed in terms of the relative orientation of the internuclear vectors, In principle, this can lead to an independent determination of the conformation of the peptide bond. 

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