Atomic orbital molecular orbitals from

The origins of the Finnis-Sinclair potential [Finnis and Sinclair 1984] lie in the density of states and the moments theorem. Recall that the density of states D(E) (see Section 3.8.5) describes the distribution of electronic states in the system. D(E) gives the number of states between E and E - - 8E. Such a distribution can be described in terms of its moments. The moments are usually defined relative to the energy of the atomic orbital from which the molecular orbitals are formed. The mth moment, fi", is given by ... 

Antibonding MO (Section 1.11) A molecular orbital that is higher in energy than the atomic orbitals from which it is formed. 

The molecular orbitals are labelled a and ir depending on whether they are symmetrical about the internuclear axis or have a nodal plane passing through the nuclei. The m.o. s are numbered in sequence of increasing energy, independent of the numbering of the atomic orbitals. This numbering serves to avoid any confusion in cases where atomic orbitals from different levels are combined, as in... 

The trigonal bond orbitals in the ten valence electron system as well as the two sets of trigonal lone pair orbitals in the 14 valence electron system are superpositions of it orbitals and o orbitals. The formation of such trigonally symmetric molecular orbitals from a-type and w-type molecular orbitals is entirely analogous in character to the formation of the three (sp2) hybrid atomic orbitals from one (s) and two ip) atomic orbitals which was discussed in the preceding section. This can be visualized by looking at the diatomic molecule... 

The distribution of the molecular orbitals can be derived from the patterns of symmetry of the atomic orbitals from which the molecular orbitals are constructed. The orbitals occupied by valence electrons form a basis for a representation of the symmetry group of the molecule. Linear combination of these basis orbitals into molecular orbitals of definite symmetry species is equivalent to reduction of this representation. Therefore analysis of the character vector of the valence-orbital representation reveals the numbers of molecular orbitals... 

Figure 1.5 The shape of selected molecular orbitals formed from the overlap of two atomic orbitals. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Figure 4.2 is a diagram of the relative energies of the molecular orbitals of the E2 molecules, together with those of the atomic orbitals from which they were constructed. The sideways overlap involved in the production of k orbitals is not as effective as the end-on overlap which characterizes the production of o orbitals. For a given interatomic dis-... 

A sigma bond is a molecular orbital that looks like an s-type atomic orbital when viewed down its axis and has cylindrical symmetry. A tt bond looks like a p-type of atomic orbital from the same... 

The essence of the model is to build up any reaction profile through the qualitative mixing of appropriate electronic configurations. Thus, just as the properties of molecular orbitals (energy, geometry) may be readily appreciated by analysis of the atomic orbitals from which they are derived, the essence of a reaction profile may be more readily comprehended by understanding the building blocks from which it is constructed. 

The number of molecular / V I orbitals equals the number of atomic orbitals from which... 

A molecular orbit lower in energy than any of the atomic orbitals from which it is derived lends stability to a molecule or ion when populated with electron Bonding Pair... 

For ethylene (H2C=CH2>, the simplest tt system, there are two ways that we can combine the two p atomic orbitals from the two carbon atoms so that we get two TT molecular orbitals. 

In electronic structure problems, we would normally be interested in bonding interactions of s, p and d-atomic orbitals from atoms sited on the vertices of a molecular stmcture and hence only Fcr, F r and F. In vibrational problems, the mechanical representation is Fcoordinates = Fff X Fxyz = Fcr + F r for an empty cluster and F + F r + Fxyz for a cluster with a centrally placed atom. For the cases of interest in molecular problems, equations 3.5 to 3.7, which follow from a knowledge of the permutation characters alone, can be used to generate, once and for all, the foil set of reducible characters for the orbits of the molecular point groups. 

Molecular Orbitals of H2. The simplest example of a diatomic molecule is H2. For this molecule, the only atomic orbitals available are the Is orbitals of the hydrogens. These orbitals interact to yield bonding als and antibonding als molecular orbitals the molecular orbital energy level diagram is shown in Figure 2-3. (Subscripts are often used to designate the atomic orbitals from which the molecular orbitals are derived.)... 

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