Electron configuration theory

F. Mansfeld and H.H. Uhlig, Passivity in Copper-Nickel-Aluminum Alloys-A Confirmation of the Electron Configuration Theory, J. Electrochem. Soc., Vol 115, 1968, p 900-904... 

In the most connnonly employed mean-field models [25] of electronic structure theory, the configuration specified for study plays a central role in defining the mean-field potential. For example, the mean-field... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

To provide further insight why the SCF mean-field model in electronic structure theory is of limited accuracy, it can be noted that the average value of the kinetic energy plus the attraction to the Be nucleus plus the SCF interaction potential for one of the 2s orbitals of Be with the three remaining electrons in the s 2s configuration is ... 

A vexing puzzle m the early days of valence bond theory concerned the fact that methane is CH4 and that the four bonds to carbon are directed toward the corners of a tetrahedron Valence bond theory is based on the overlap of half filled orbitals of the connected atoms but with an electron configuration of s 2s 2p 2py carbon has only two half filled orbitals (Figure 2 8a) How can it have bonds to four hydrogens ... 

Nowadays there is a tendency to use the word term to describe that which arises from an approximate treatment of an electron configuration, whereas the word state is used to describe something that is observable experimentally. For example, we can say that the s 2s 2p 3d configuration of C gives rise to a term which, when spin-orbit coupling is taken into account, splits into Pi, 2 Pj, states. Since spin-orbit coupling can be excluded only in theory but never in practice there can be no experimental observation associated with the P term. ... 

Here the a, are the LCAO coefficients, which have to be determined. The formulation of HF theory where we use the LCAO approximation is usually attributed to Roothaan (1951a). His formulation applies only to electronic configurations of the type 1/ 3,...,. Following the discussion of Chapter 5, the charge... 

This reactivity pattern can be rationalized in terms of a diabatic model which is based upon the principle of spin re-coupling in valence (VB) bond theory [86]. In this analysis the total wavefunction is represented as a combination of two electronic configurations arising from the reactant (reaction coordinate. At the outset of the reaction, is lower in energy than [Pg.141]

A mark of the success of this theory lies in the fact that no low lying superfluous / levels have been found which defy classification according to a plausible electronic configuration for the atom in question. On the other hand, there are sometimes predicted levels which have not yet been observed as in the case of three of the six terms for the s2p3 configuration in carbon (Moore [1949]). 

Figure 5. Niels Bohr came up with the idea that the energy of orbiting electrons would be in discrete amounts, or quanta. This enabled him to successfully describe the hydrogen atom, with its single electron, In developing the remainder of his first table of electron configurations, however, Bohr clearly relied on chemical properties, rather than quantum theory, to assign electrons to shells. In this segment of his configuration table, one can see that Bohr adjusted the number of electrons in nitrogen s inner shell in order to make the outer shell, or the reactive shell, reflect the element s known trivalency.

This is a crudal and frequently overlooked point about electronic configurations. They are far from being based in quantum mechanics it is precisely this theory that shows them to be an inadequate concept The notion that electron orbits and configurations really exist or "refer" is a relic of the old quantum theory and of Pauli s introduction of the exclusion prind-ple in its original and now strictly incorrect... 

The origin of electronic configuration Is frequently and inaccurately attributed to Niels Bohr, who introduced quantum theory to tire study of the atom. But Bohr essentially tidied up Thomson s pre-quantum configurations and took advantage of a more accurate knowledge erf the number of electrons each of the elements actually possessed. Furtlrer developments in quantum theory, including Pauli s occlusion principle and Schrodjtiger s equation. 

What Do We Need to Know Already This chapter draws on many of the principles introduced in the preceding chapters. In particular, it makes use of the electron configurations of atoms and ions (Sections 1.13 and 2.1) and the classification of species as Lewis acids and bases (Section 10.2). Molecular orbital theory (Sections 3.8 through 3.12) plays an important role in Section 16.12. 

Molecules have some occupied and some unoccupied orbitals. There occur diverse interactions (Scheme 1) when molecules undergo reactions. According to the frontier orbital theory (Sect 3 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume), the HOMO d) of an electron donor (D) and the LUMO (fl ) of an electron acceptor (A) play a predominant role in the chemical reactions (delocalization band in Scheme 2). The electron configuration D A where one electron transfers from dio a significantly mixes into the ground configuration DA where... 

The orbital phase theory is applicable to the singlet diradicals [20]. The electron configuration of the singlet states of the cross- (TMM) and linear (BD) conjugate diradicals is shown in Scheme 9, where the mechanism of the delocalization of a and P spins between the radical centers through the double bond are separately illustrated by the arrows. The cyclic [-a-Tr-b-T -] interaction is readily seen to occur for the spin delocalizations. The p orbital a) in one radical center and the n orbital are occupied by a spins, and therefore, electron-donating orbitals. The p orbital (b) in the other radical center and the ii orbital are not occupied by a spins. 

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