For many-electron systems such as atoms and molecules, it is obviously important that approximate wavefiinctions obey the same boundary conditions and symmetry properties as the exact solutions. Therefore, they should be antisynnnetric with respect to interchange of each pair of electrons. Such states can always be constmcted as linear combinations of products such as [Pg.31]

Electronic Connectors. The complexity and size of many electronic systems necessitate constmction from relatively small building blocks which ate then assembled with connectors. An electronic connector is a separable electrical connector used in telecommunications apparatus, computers, and in signal transmission and current transmission <5 A. Separable connectors ate favored over permanent or hard-wired connections because the former facilitate the manufacture of electronic systems also, connectors permit assemblies to be easily demounted and reconnected when inspection, replacement, or addition of new parts is called for. [Pg.23]

Hamiltonian operator, 2,4 for many-electron systems, 27 for many valence electron molecules, 8 semi-empirical parametrization of, 18-22 for Sn2 reactions, 61-62 for solution reactions, 57, 83-86 for transition states, 92 Hammond, and linear free energy relationships, 95 [Pg.232]

Note on an Approximate Treatment for Many-Electron Systems Chr. Mpller and M. S. Plesset Physical Review 46 (1934) 618 [Pg.199]

Petersson and coworkers have extended this two-electron formulation of asymptotic convergence to many-electron atoms. They note that the second-order MoUer-Plesset correlation energy for a many-electron system may be written as a sum of pair energies, each describing the energetic effect of the electron correlation between that pair of electrons [Pg.278]

Dirac, P. A. M. 1929 Quantum mechanics of many-electron systems. Proc. R. Soc. Land A 123, 714-733. [Pg.57]

APPENDIX A-MOLECULAR ORBITAL TREATMENT OF MANY-ELECTRON SYSTEMS [Pg.27]

The main difficulty in solving the Schrodinger equation (Eq. II. 1) for a many-electron system comes from the two-electron interaction terms [Pg.216]

This completes the discussion of the theory for many-electron systems from which we believe we have elucidated the reason for the failure of earlier approximate formulas for London forces. Many approximations remain and we summarize a few that seem most. important. [Pg.68]

The main method so far for treating correlation in many-electron systems is based on an expansion of configurations of the type III.18 [Pg.316]

Magnetic heat capacity of nickel, 133 Magnetic susceptibility, 25 Maleic anhydride, 168 Many electron system, correlations in, 304, 305, 318, 319, 323 Melting temperature and critical temperature for disordering correlation, 129 [Pg.409]

QMC teclmiques provide highly accurate calculations of many-electron systems. In variational QMC (VMC) [112, 113 and 114], the total energy of the many-electron system is calculated as the expectation value of the Hamiltonian. Parameters in a trial wavefiinction are optimized so as to find the lowest-energy state (modem [Pg.2220]

In a recent paper Ostrovsky has criticized my claiming that electrons cannot strictly have quantum numbers assigned to them in a many-electron system (Ostrovsky, 2001). His point is that the Hartree-Fock procedure assigns all the quantum numbers to all the electrons because of the permutation procedure. However this procedure still fails to overcome the basic fact that quantum numbers for individual electrons such as t in a many-electron system fail to commute with the Hamiltonian of the system. As aresult the assignment is approximate. In reality only the atom as a whole can be said to have associated quantum numbers, whereas individual electrons cannot. [Pg.107]

Kryachko E. S., Ludena E. V., "Energy Density Functional Theory of Many-Electron Systems" Kluwer, Dordrecht, 1990. [Pg.243]

Table II shows clearly the large differences between various theories for many-electron systems. The Kirkwood-Muller equation always yields somewhat too large coefficients for the atoms which are the only spherical systems but the London equation deviates by a greater amount on the low side. The Slater-Kirkwood equation gives a high value for He but yields coefficients smaller than the empirical ones for all other cases. |

The main advantage of the method with correlation factor, based on Eq. III. 128 or Eq. III. 129, lies in the fact that it may be applied to any many-electron system. The practical calculation of the energy integrals involved may be fairly cumbersome, but the approach is nevertheless straightforward. [Pg.305]

M0LLER, Chr., and Plesset, M. S., Phys. Rev. 46, 618, Note on an approximation treatment for many-electron systems." [Pg.326]

Perdew J P and Zunger A 1981 Self-interaction correction to density-functional approximations for many-electron systems Phys. Rev. B 23 5048 [Pg.2230]

Perdew J P and A Zunger 1981. Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems. Physical Review B23 5048-5079. [Pg.181]

Our earlier discussion of off-diagonal s, however, indicated that 2Q would substantially exceed in many-electron systems. Consequently, if Eq. 34 is used with N an empirical factor,31 we may expect the N values to exceed substantially the actual number of electrons of the outer subshell. [Pg.67]

A sum-over-states expression for the coefficient A for the expansion of the diagonal components faaaa was derived by Bishop and De Kee [20] and calculations were reported for the atoms H and He. However, the usual approach to calculate dispersion coefficients for many-electron systems by means of ab initio response methods is still to extract these coefficients from a polynomial fit to pointwise calculated frequency-dependent hyperpolarizabiiities. Despite the inefficiency and the numerical difficulties of such an approach [16,21], no ab initio implementation has yet been reported for analytic dispersion coefficients for frequency-dependent second hyperpolarizabiiities which is applicable to many-electron systems. [Pg.113]

See also in sourсe #XX -- [ Pg.86 , Pg.87 ]

See also in sourсe #XX -- [ Pg.9 ]

See also in sourсe #XX -- [ Pg.5 , Pg.3207 ]

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