Treating configurations

CISD. CISD (configuration interaction, single double) are LCAO expressions that treat configuration interactions by including one or two excited states. The designations CISDT and CISDTQ expand this to three and four excitations, respectively. 

There are three types of treating configurations (Fig. 14.8) and they all consist of the same parts including an electrode, an electrical insulator or dielectric, and a return path or ground. The differences among the three configurations are in the location of the electrode. In a conventional system (Fig. 14.8a), the web passes over a roll which is covered with insulating... 

To begin a discussion of the relative advantages and disadvantages of this treating configuration, we must first review the dynamics of dielectric insulators. 

In Chapter 11, we treat configuration-interaction (Cl) theory, concentrating on the full Cl wave function and certain classes of truncated Cl wave functions. The simplicity of the Cl model allows for efficient methods of optimization, as discussed in this chapter. However, we also consider the chief shortcomings of the Cl method - namely, the lack of compactness in the description and the loss of size-extensivity that occurs upon truncation of the Cl expansion. 

In this section we concentrate on the electronic and vibrational parts of the wavefimctions. It is convenient to treat the nuclear configuration in temis of nomial coordinates describing the displacements from the equilibrium position. We call these nuclear nomial coordinates Q- and use the symbol Q without a subscript to designate the whole set. Similarly, the symbol v. designates the coordinates of the th electron and v the whole set of electronic coordinates. We also use subscripts 1 and ii to designate the lower and upper electronic states of a transition, and subscripts a and b to number the vibrational states in the respective electronic states. The total wavefiinction f can be written... 

Seetion treats the spatial, angular momentum, and spin symmetries of the many-eleetron wavefunetions that are formed as anti symmetrized produets of atomie or moleeular orbitals. Proper eoupling of angular momenta (orbital and spin) is eovered here, and atomie and moleeular term symbols are treated. The need to inelude Configuration Interaetion to aehieve qualitatively eorreet deseriptions of eertain speeies eleetronie struetures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of ehemieal reaetivity is also developed. 

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

The treatment of electronic motion is treated in detail in Sections 2, 3, and 6 where molecular orbitals and configurations and their computer evaluation is covered. The vibration/rotation motion of molecules on BO surfaces is introduced above, but should be treated in more detail in a subsequent course in molecular spectroscopy. 

If, instead of a configuration like that treated above, one had a 52 configuration, the above analysis would yield F, and symmetries (because the two 5 orbitals m values could be combined as 2 + 2, 2 - 2, -2 + 2, and -2 -2) the wavefunctions would be identical to those given above with the 7ii orbitals replaced by 82 orbitals and 71.1 replaced by 5.2. Likewise, dp- gives rise to H, and symmetries. 

Compounds in which a chirality center is part of a ring are handled in an analo gous fashion To determine for example whether the configuration of (+) 4 methyl cyclohexene is R or S treat the right and left hand paths around the nng as if they were independent substituents... 

In writing Eq. (8.41), we have clearly treated Aw as a contribution to enthalpy. This means we neglect volume changes (AHp jj. versus AUp jj.) and entropy changes beyond the configurational changes discussed in the last section (AGp jj. versus AH jj.). In a subsequent development it is... 

The states arising from this configuration are the same as those from. .. (1u2m) (I ig) 5 because a single vacancy in e g can be treated like an electron. 

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