Valency, electronic theory

Sern i-em pirical qtiari turn m ech an ics m ethods h ave evolved over the last three decades. Using today s microcomputers, they can produce rn can in gful, often quart tilalive, results for large molecular systems. The roots of the methods lie in the theory of 7 electrons, now largely superseded by all-valence electron theories. 

It is generally believed that it was Ingold [1] in the early 1930s who proposed the first global electrophilicity scale to describe electron-deficient (electrophile) and electron-rich (nucleophile) species based on the valence electron theory of Lewis. Much has been accomplished since then. One of the widely used electrophilicity scales derived from experimental data was proposed by Mayr et al. [5-12] ... 

To initiate the process we need an initial guess of the coefficients, to calculate the density matrix values Ptu. The guess can come from a simple Hiickel calculation (for a 7i electron theory like the PPP method) or from an extended Hiickel calculation (for an all-valence-electron theory, like CNDO and its descendants). The Fock matrix of Frs elements is diagonalized repeatedly to refine energy levels and coefficients. 

Molecular geometries may be calculated by means of quantum-chemical semi-empirical valence electron theories, such as Dewar s MINDO/3 , MNDO " or AMl procedures, or by classical molecular force-field methods, such as Allinger s MM2 procedure. Alternatively, inirio Hartree-Fock SCF MO methods allow, by virtue of analytical gradient evaluations , the determination of molecular geometries independent of experimentally adjusted integral values. 

I Valency, electronic theory of. 22 electrons and electrical coii-... 

Theorem and All-Valence Electrons Theory. An Approximate LCAO Theory for the Electronic Absorption and MCD Spectra of Conjugated Organic Compounds, Part 2. 

The first reliable energy band theories were based on a powerfiil approximation, call the pseudopotential approximation. Within this approximation, the all-electron potential corresponding to interaction of a valence electron with the iimer, core electrons and the nucleus is replaced by a pseudopotential. The pseudopotential reproduces only the properties of the outer electrons. There are rigorous theorems such as the Phillips-Kleinman cancellation theorem that can be used to justify the pseudopotential model [2, 3, 26]. The Phillips-Kleimnan cancellation theorem states that the orthogonality requirement of the valence states to the core states can be described by an effective repulsive... 

To date there is no evidence that sodium forms any chloride other than NaCl indeed the electronic theory of valency predicts that Na" and CU, with their noble gas configurations, are likely to be the most stable ionic species. However, since some noble gas atoms can lose electrons to form cations (p. 354) we cannot rely fully on this theory. We therefore need to examine the evidence provided by energetic data. Let us consider the formation of a number of possible ionic compounds and first, the formation of sodium dichloride , NaCl2. The energy diagram for the formation of this hypothetical compound follows the pattern of that for NaCl but an additional endothermic step is added for the second ionisation energy of sodium. The lattice energy is calculated on the assumption that the compound is ionic and that Na is comparable in size with Mg ". The data are summarised below (standard enthalpies in kJ) ... 

Oxygen is a colourless gas which condenses to a pale blue liquid, b.p. 90 K, which is markedly paramagnetic indicating the presence of unpaired electrons (p. 229). Simple valence bond theory (as used in this book) would indicate the structure... 

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

Chemists were quick to appreciate Bohr s model because it provided an extremely clear and simple interpretation of chemistry. It explained the reason behind Mendeleev s table, that the position of each element in the table is nothing other than the number of electrons in the atom of the element, which, of course, represents an equal number of periodic changes in the nucleus. Each subsequent atom has one more electron, and the periodic valence changes reflect the successive filling of the orbital. Bohr s model also provided a simple basis for the electronic theory of valence. 

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

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 ... 

Because of the general validity of Koopmans theorem for closed-shell molecules ionization energies and, as we shall see, the associated vibrational sttucture represent a vivid illustration of the validity of quite simple-minded MO theory of valence electrons. 

The valence theory (4) includes both types of three-center bonds shown as well as normal two-center, B—B and B—H, bonds. For example, one resonance stmcture of pentaborane(9) is given in projection in Figure 6. An octet of electrons about each boron atom is attained only if three-center bonds are used in addition to two-center bonds. In many cases involving boron hydrides the valence stmcture can be deduced. First, the total number of orbitals and valence electrons available for bonding are determined. Next, the B—H and B—H—B bonds are accounted for. Finally, the remaining orbitals and valence electrons are used in framework bonding. Alternative placements of hydrogen atoms require different valence stmctures. 

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