Ionic contributions to the wave function

The first two terms on the right-hand side have both eleetrons on the same eentre, they describe ionic contributions to the wave function, H+H . The later two terms describe covalent contributions to the wave function, H H. The HF wave function thus contains equal amounts of ionic and covalent contributions. The full Cl wave function may be written in terms of AOs as... 

The first two terms on the right-hand side have both electrons on the same centre, they describe ionic contributions to the wave function, The later two terms describe... 

There are many canonical covalent VB structures for methane, as well as ionic structures however, chemical intuition suggests that the main contribution to the wave function is from the following covalent structure ... 

The existence of many ionic structures in MCVB wave functions has often been criticized by some workers as being unphysical. This has been the case particularly when a covalent bond between like atoms is being represented. Nevertheless, we have seen in Chapter 2 that ionic structures contribute to electron delocalization in the H2 molecule and would be expected to do likewise in all cases. Later in this chapter we will see that they can also be interpreted as contributions from ionic states of the constituent atoms. When the bond is between unlike atoms, it is to be expected that ionic stmctures in the wave function will also contribute to various electric moments, the dipole moment being the simplest. The amounts of these ionic structures in the wave functions will be determined by a sort of balancing act in the variation principle between the diagonal effects of the ionic state energies and the off-diagonal effect of the delocalization. 

MC VB The principal function is completely open-shell, in that it involves no electron paired in a single orbital. As ionic functions are added to the wave function, these, in many but not all cases, involve electrons paired in a single orbital and begin to contribute a closed-shell nature to the description of the system. (These ionic stmctures also cause delocalization, as we have seen.)... 

Here the first two determinants are the determinantal form of the Heitler-London function (eq 1), and represent a purely covalent interaction between the atoms. The remaining determinants represent zwitterionic structures, H-H+ and H+H, and contribute 50% to the wave function. The same constitution holds for any interatomic distance. This weight of the ionic structures is clearly too much at equilibrium distance, and becomes absurd at infinite separation where the ionic component is expected to drop to zero. Qualitatively, this can be corrected by including a second configuration where both electrons occupy the antibonding orbital, Gu, i.e. the doubly excited configuration. The more elaborate wave function T ci is shown in eq. 4, where C and C2 are coefficients of the two MO configurations ... 

Our comparison shows that the LCAO method includes an ionic contribution to the bond, but the VB method does not. In fact, the simple MO approach suggests that the bond in H2 is 50% covalent and 50% ionic, which is contrary both to experience and intuition. Because the electronegativities of the two atoms in a homonuclear diatomic molecule are the same, there is no reason to expect any ionic contribution to the bond, much less such a large one. The complete absence of ionic contributions in the VB wave function suggests this method is not well suited for polar molecules such as HR Thus, the truth in describing the chemical bond and molecular structure appears to lie somewhere between the LCAO and... 

II is mainly ionic in character and function IV completely so, representing the interaction of H+ and H-. Of these IV corresponds to a known state, the first electronically excited state of the molecule. As might have been anticipated from the ionic character of the wave function, the state differs in its properties from the other known excited states, having r, = 1.29 A and v, = 1358 cm-1, whereas the others have values of rt and v, close to those for the normal hydrogen molecule-ion, 1.06 A and 2250 cm-1. The calculations of Zener and Guillemin and of Hylleraas have shown that at the equilibrium distance the wave function for this state involves some contribution from wave functions for one normal and one excited atom (with n = 2,1 = 1), and with increase in Tab this contribution increases, the molecule in this state dissociating into a normal and an excited atom. 

How can we remedy this Since H2 is nonpolar, chemical intuition tells us that ionic terms should contribute substantially less to the wave function than covalent terms. The simplest procedure is to omit the ionic terms of the MO function (13.108). This gives... 

The squares of the coefficients in a wave function are related to probability. Therefore, the total contribution from the two structures is l2 + A2 while the contribution from the ionic structure is given by A2. As a result, A2/(12 + A2) gives the fraction of ionic character to the bond and... 

Having shown that the weighting coefficient (A) of the term giving the contribution of an ionic structure to the molecular wave function is related to the dipole moment of the molecule, it is logical to expect that equations could be developed that relate the ionic character of a bond to the electronegativities of the atoms. Two such equations that give the percent ionic character of the bond in terms of the electronegativities of the atoms are... 

Ionic The function, in each case, with the next highest weight, 3 %, is ionic and involves a single excitation into the 2s AO. This contributes to adjusting the electron correlation and also contributes to adjusting the size of the wave function along the lines of the scale adjustment of the Weinbaum treatment. As we have shown, it also contributes to delocalization. 

There are two rather different questions that arise when considering ionic structures in VB wave functions. The first of these we discuss is the contribution to electric dipole moments. LiH is considered as an example. In the next section we take up ionic structures and curve crossings, using LiF to illustrate the points. 

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