Electron quadratic

From an all-electron (quadratic configuration interaction with all single and double excitations) potential [22]. — For gaseous ND2 derived [23] from LMR [24] and lODR frequencies [25]. For NHD in a nitrogen matrix from an IR spectrum [20]. — For gaseous ND2 from an LMR spectrum [24]. 

More accurately, as the inverse problem process computes a quadratic error with every point of a local area around a flaw, we shall limit the sensor surface so that the quadratic error induced by the integration lets us separate two close flaws and remains negligible in comparison with other noises or errors. An inevitable noise is the electronic noise due to the coil resistance, that we can estimate from geometrical and physical properties of the sensor. Here are the main conclusions ... 

Figure B3.2.11. Total energy versus lattice constant of gallium arsenide from a VMC calculation including 256 valence electrons [118] the curve is a quadratic fit. The error bars reflect the uncertainties of individual values. The experimental lattice constant is 10.68 au, the QMC result is 10.69 (+ 0.1) an (Figure by Professor W Schattke).

The symmetry argument actually goes beyond the above deterniination of the symmetries of Jahn-Teller active modes, the coefficients of the matrix element expansions in different coordinates are also symmetry determined. Consider, for simplicity, an electronic state of symmetiy in an even-electron molecule with a single threefold axis of symmetry, and choose a representation in which two complex electronic components, e ) = 1/v ( ca) i cb)), and two degenerate complex nuclear coordinate combinations Q = re " each have character T under the C3 operation, where x — The bras e have character x. Since the Hamiltonian operator is totally symmetric, the diagonal matrix elements e H e ) are totally symmetric, while the characters of the off-diagonal elements ezf H e ) are x. Since x = 1, it follows that an expansion of the complex Hamiltonian matrix to quadratic terms in Q. takes the form... 

Stueckelberg derived a similar fomiula, but assumed that the energy gap is quadratic. As a result, electronic coherence effects enter the picture, and the transition probability oscillates (known as Stueckelberg oscillations) as the particle passes through the non-adiabatic region (see [204] for details). 

Determination of the paiameters entering the model Hamiltonian for handling the R-T effect (quadratic force constant for the mean potential and the Renner paiameters) was carried out by fitting special forms of the functions [Eqs. (75) and (77)], as described above, and using not more than 10 electronic energies for each of the X H component states, computed at cis- and toans-planai geometries. This procedure led to the above mentioned six parameters... 

For vei y small vibronic coupling, the quadratic terms in the power series expansion of the electronic Hamiltonian in normal coordinates (see Appendix E) may be considered to be negligible, and hence the potential energy surface has rotational symmetry but shows no separate minima at the bottom of the moat. In this case, the pair of vibronic levels Aj and A2 in < 3 become degenerate by accident, and the D3/, quantum numbers (vi,V2,/2) may be used to label the vibronic levels of the X3 molecule. When the coupling of the... 

The speed of an electric motor can be changed by altering the frequency of the electric current. This is because the ratio is the same as 60 or 50 f/p (f = the frequency of the current, p = the number of poles in the stator). Frequency converters are built of electronic components, frequently combined with microprocessors. They provide good motor protection and are superior to the traditional bimetal protection. The characteristic curve for a pump and fan motor is also quadratic, making lower demands to the frequency converters When the frequency of the electrical current is changed in the frequency converter, the main AC supply is transformed into DC. The DC is then treated... 

Quadratic Configuration Interaction. A general technique for determining electron correlation energies... 

The techniques for calculating the electronic states of an impurity in a metal from first principles are well understood and have already been implemented. An approximate method that leads to much simpler calculations has been proposed recently. We investigate this method within the framework of the quadratic Korringa-Kohn-Rostoker formalism, and show that it produces surprisingly good predictions for the charge on the impurity. 

The matrix elements of the inactive electrons and the interaction between the active and inactive electrons can be approximated by expressing the corresponding potential surfaces as a quadratic expansion around the equilibrium values of the various internal coordinates, and by nonbonded potential functions for the interaction between atoms not bonded to each other or to a common atom ... 

The dependence of the currents of m/e 16 and m/e 30 upon sample pressure, using an electron energy of 2.3 e.v., is shown in Figure 8. The linear variation of m/e 16 and the quadratic variation of m/e 30 with pressure, together with the results shown in Figure 7, indicate the occurrence of Reaction 14. 

In this volume dedicated to Yngve Ohm we feel it is particularly appropriate to extend his ideas and merge them with the powerful practical and conceptual tools of Density Functional Theory (6). We extend the formalism used in the TDVP to mixed states and consider the states to be labeled by the densities of electronic space and spin coordinates. (In the treatment presented here we do not explicitly consider the nuclei but consider them to be fixed. Elsewhere we shall show that it is indeed straightforward to extend our treatment in the same way as Ohm et al. and obtain equations that avoid the Bom-Oppenheimer Approximation.) In this article we obtain a formulation of exact equations for the evolution of electronic space-spin densities, which are equivalent to the Heisenberg equation of motion for the electtons in the system. Using the observation that densities can be expressed as quadratic expansions of functions, we also obtain exact equations for Aese one-particle functions. 

Figure 37. Electronic excitation of the NaK wavepacket from the inner turning point of the ground X state. The X A transition is considered. The initial wave packet is prepared by two quadratically chirped pulses within the pump-dump mechanism. Taken from Ref. [37].

Vilkas, M.J., Ishikawa, Y. and Koc, K. (1998) Quadratically convergent multiconfiguration Dirac-Fock and multireference relativistic configuration-interaction calculations for many-electron systems. Physical Review E, 58, 5096-5110. 

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