Atomic orbitals interaction

Each two-electron integral is the sum of all the terms arising from the charge distribution representative of the first pair of atomic orbitals interacting with the charge distribution representative of the second pair of atomic orbitals. Thus in the simplest case, the (ssiss) interaction is represented by the repulsion of two monopoles, while a (pj pjjlp jjp jj), a much more complicated interaction,... 

Atomic orbitals interact with each other to give bond orbitals (Sect. 1), which mutually interact to give molecular orbitals (Sect. 2). Here we will examine interactions of molecular orbitals, especially those of frontier orbitals important for chemical reactions. 

If each of the six n electrons in benzene occupied a single atomic n orbital and there were no interaction, each would have an energy of a. The total energy would then be 6a, which is zero if we assume, as above, that a is the zero of our energy scale. However, when the atomic orbitals interact to produce the MOs, the six electrons will now occupy these MOs according to Hund s rule and the Pauli exclusion principle. The first two will enter the A orbital, and the remaining four occupy the E orbitals. The total energy of the system is then... 

A covalent bond is formed between two atoms together in a molecular structure. It is formed when atomic orbitals overlap to produce a molecular orbital. For example, the formation of a hydrogen molecule (H2) from two hydrogen atoms. Each hydrogen atom has a half-filled Is atomic orbital and when the atoms approach each other, the atomic orbitals interact to produce two MOs (the number of resulting MOs must equal the number of original atomic orbitals) ... 

Chapter i described a covalent bond as a pair of electrons that is shared between two atoms. The purpose of this chapter is to reexamine bonding in more depth using a model that employs electron orbitals. This model will provide us with a better understanding of bonds and reactivity. The chapter begins with a review of atomic orbitals. Then a model where bonding results from atomic orbitals interacting to form molecular orbitals is discussed. Because resonance is so important in organic chemistry, considerable attention is devoted to this topic. The idea of orbitals can help us understand resonance better. Finally, a number of examples of how to use resonance and when it is important are presented. 

Let s consider the shape of the MO first. The simplest picture considers molecular orbitals as resulting from the overlap of atomic orbitals. When atoms are separated by their usual bonding distance, their AOs overlap. Where this overlap occurs, either the electron waves reinforce and the electron density increases, or the electron waves cancel and the electron density decreases. The left-hand side of Figure 3.3 shows the overlap of the Is atomic orbitals on two different hydrogens (Hu and H/ ) when these hydrogens are separated by their normal bonding distance. The two atomic orbitals interact to produce two molecular orbitals. The MOs result from a linear combination of the AOs (called the LCAO approximation). Simply, this means that the AOs are either added (lsa + lsfc) or subtracted (1 sa — lst) to get the MOs. 

At first this picture suggests that the electrons will have to climb up to the empty orbital if it is higher in energy than tire filled orbital. This is not quite true because, when atomic orbitals interact, their energies split to produce two new molecular orbitals, one above and one below the old orbitals. This is the basis for the static structure of molecules described in the last chapter and is also tire key to reactivity. In these three cases this is what will happen when the orbitals interact (the new molecular orbitals are shown in black between the old atomic orbitals). 

The easiest way of visualizing a molecular orbital is to start by picturing two isolated atoms and the electron orbitals that each would have separately. These are just the orbitals of the separate atoms, by themselves, which we already understand. We will then try to predict the manner in which these atomic orbitals interact as we gradually move the two atoms closer together. Finally, we will reach some point where the inter-nuclear distance corresponds to that of the molecule we are studying. The corresponding orbitals will then be the molecular orbitals of our new molecule. 

Recall that in the MO model for the gaseous Li2 molecule (Section 14.3), two widely spaced MO energy levels (bonding and antibonding) result when two identical atomic orbitals interact. However, when many metal atoms interact, as in a metal crystal, the large number of resulting MOs become closely spaced, forming a virtual continuum of levels, called bands (see Fig. 16.23). 

The molecular orbital energy levels produced when various numbers of atomic orbitals interact. Note that for two atomic orbitals two rather widely spaced energy levels result. (Recall the description of H2 in Section 14.2.) As more atomic orbitals become available to form MOs, the resulting energy levels become more closely spaced, finally producing a band of very closely spaced orbitals. 

So far, we have considered primarily interactions between orbitals of identical energy. However, orbitals with similar, but not equal, energies interact if they have appropriate symmetries. We will outline two approaches to analyzing this interaction, one in which the molecular orbitals interact and one in which the atomic orbitals interact directly. 

Since classical-type calculations cannot intrinsically reproduce such effects as atomic orbital interactions, it is necessary to adjust the conformational potential energy terms to accurately reproduce experimentally observed torsional barrier heights. Harmonic torsional correction functions are incorporated in the repetoire of classical potential energy terms in order to economically satisfy this requirement. These functions may be described in several ways. Sets of parameters may be given to fit a general purpose torsional correction term which includes provisions for describing cis/trans barriers. The general form of this equation is... 

The overlap interaction of two atomic orbitals, say the 3r orbitals of two sodium atoms, produces two molecular orbitals, one bonding orbital and one antibonding orbital (Ghapter 9). If N atomic orbitals interact, N molecular orbitals are formed. In a single metallic... 

The two lobes of a p orbital have opposite phases. When two in-phase atomic orbitals interact, a covalent bond is formed. When two out-of-phase atomic orbitals interact, a node is created between the two nuclei. 

Interaction of in-phase p atomic orbitals gives a bonding tt molecular orbital that is lower in energy than the p atomic orbitals. Interaction of out-of-phase tt atomic orbitals gives an antibonding v molecular orbital that is higher in energy than the p atomic orbitals. 

Six p atomic orbitals interact to give the six tt molecular orbitals of 1,3,5-hexatriene. 

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