Atomic orbitals electron assignment

MOLECULAR ORBITAL and valence bond calculations of the IT—electron energies of unsaturated molecules customarily start with models in which appropriate atomic orbitals are assigned to each nucleus to provide a framework for -notions of the binding electrons. Atomic orbital representations of organic molecules are now very commonly used in the teaching of elementary organic chemistry, although there often seems to be confusion between atomic orbital and molecular orbital representations. 

Population anaiysis methods of assigning charges rely on the LCAO approximation and express the numbers of electrons assigned to an atom as the sum of the populations of the AOs centered at its nucleus. The simplest of these methods is the Coulson analysis usually used in semi-empirical MO theory. This analysis assumes that the orbitals are orthogonal, which leads to the very simple expression for the electronic population of atom i that is given by Eq. (53), where Natomic orbitals centered... 

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.

To describe atoms with several electrons, one has to consider the interaction between the electrons, adding to the Hamiltonian a term of the form Ei< . Despite this complication it is common to use an approximate wave function which is a product of hydrogen-like atomic orbitals. This is done by taking the orbitals in order of increasing energy and assigning no more than two electrons per orbital. 

STRATEGY Because sulfur is in Period 3 and has empty 3d-orbitals available, it can expand its valence shell to accept additional electrons. After assigning all the valence electrons to bonds and lone pairs to give each atom an octet, assign any remaining electrons to the sulfur atom. 

The Lewis structure shows that methyl methaciylate has the formula C5 Hg O2, with 40 valence electrons. You should be able to verily that the two CH3 groups have. s -hybridized carbons, the inner oxygen atom is s hybridized, the outer oxygen atom uses 2 p atomic orbitals, and the three double-bonded carbons are s p hybridized. These assignments lead to the following inventory of a bonds and inner-atom lone pairs ... 

The valence electron for the cesium atom is in the 6s orbital. In assigning quantum numbers, n = principal energy level = 6. The quantum number l represents the angular momentum (type of orbital) with s orbitals = 0, p orbitals = 1, d orbitals = 2, and so forth. In this case, l = 0. The quantum number m is known as the magnetic quantum number and describes the orientation of the orbital in space. For, v orbitals (as in this case), mt always equals 0. For p orbitals, mt can take on the values of -1, 0, and +1. For d orbitals, can take on the values -2, -1, 0, +1, and +2. The quantum number ms is known as the electron spin quantum number and can take only two values, +1/2 and -1/2, depending on the spin of the electron. 

Equation (11.8) reads The average of the expectation values of r — for the various valence AOs of atom I, weighted by the rations of the orbital populations to the total atomic population of atom I equals the inverse of the — / distance. For all their their simplicity, Eqs. (11.7) and (11.8) cannot be tested numerically by direct calculation. The reason is linked to the difficulty of partitioning the total electron density into atomic contributions, in spite of an important conceptual step forward due to Parr [219]. A practical step in the same direction is in the construction of suitable in situ valence atomic orbitals (VAO) from accurate ab initio computations [143], as advocated long ago by Mulliken [220] and discussed by Del Re [221]. As will be seen, such in situ VAOs do provide useful information, but they are of no help in solving the additional problem of assigning suitable populations to the orbitals and of dividing overlap populations into atomic contributions. In view of this situation, we take Eqs. (11.5) and (11.8) as statements whose validity rests on experimental evidence, at least for saturated hydrocarbons. 

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