Electric field, geometry

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

Fig. 25. Reflection geometry for irras showing the s andp components of the electric fields of the incident (U ) and reflected (S ) beams (41).

At low voltages, i.e., below the onset of the corona discharge, the electric field EfrJ depends on the voltage and the geometry of the system only. The electric field is given by... 

FIGURE 13.10 Electric field as a function of radial distance (tubular geometry). 

The change in the dipole moment with respect to a geometry displacement along a normal coordinate is approximately proportional to the intensity of an IR absorption. In the so-called double harmonic approximation (terminating the expansion at first order in the electric field and geometry), the intensity is (except for some constants)... 

Figure 3. Different geometries for microwave conductivity measurements, (a) Sample (black square) at end of microwave guide, (b) sample in microwave resonator, and (c) sample above dielectric microwave spiral. The electrical field E of the microwave is shown schematically.

In deriving the kinetic equation describing the arrival of various ionic species at the cathode, it is assumed that the primary species N2 + is formed at the central wire at a constant rate, and during its passage in the direction x perpendicular to the axis its concentration is modified by various reactions. In this treatment both ion diffusion and ion-ion or electron-ion recombination processes are neglected because the geometry of the discharge tube and the presence of an electric field would... 

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

The foregoing equations are coupled and are generally nonlinear no general solution exists. However, these equations serve as a starting point for most of the analysis that is relevant to electrophoretic transport in solutions and gels. Of course, the specific geometry and boundary conditions must be specified in order to solve a given problem. Boundary conditions for the electric field include specification of either (1) constant potential, (2) constant current, or (3) constant power. 

Henry [ 157] solved the steady-flow continuity and Navier-Stokes equations in spherical geometry, neglecting inertial terms but including pressure and electrical force terms, coupled with Poisson s equation. The electrical force term in Henry s analysis consisted of the sum of the externally applied electric field and the field due to the double layers. His major assumptions are low surface potential (i.e., potentials less than approximately 25 mV) and undistorted double layers. The additional parameter ku appearing in the Henry... 

The adiabatic electronic potential energy surfaces (a function of both nuclear geometry and electric field) are obtained by solving the following electronic eigenvalue equation... 

Equation (28) is the set of exact coupled differential equations that must be solved for the nuclear wave functions in the presence of the time-varying electric field. In the spirit of the Born-Oppenheimer approximation, the ENBO approximation assumes that the electronic wave functions can respond immediately to changes in the nuclear geometry and to changes in the electric field and that we can consequently ignore the coupling terms containing... 

Time steps of about 60 s between switching on and off were realized. The performance of the MSE structures depends on their geometry, the electric field strength and the gas pressure. 

The theoretical method, as developed before, concerns a molecule whose nuclei are fixed in a given geometry and whose wavefimctions are the eigenfunctions of the electronic Hamiltonian. Actually, the molecular structure is vibrating and rotating and the electric field is acting on the vibration itself. Thus, in a companion work, we have evaluated the vibronic corrections (5) in order to correct and to compare our results with experimental values. 

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