Covalent contribution 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... 

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 ... 

Some of the calculations mentioned indicate a contribution from the wave-functions corresponding to the covalent structures of 1-2 per cent. In view of the very considerable number of assumptions in the mathematical treatment, magnitudes of this order should have no significance. 

The summed weights, classified as covalent and ionic, show a consistent trend with the nature of the X atom. The value of the covalent contribution to the total VB wave function generally increases as X gets heavier from Si —> Pb for the CH3—XH3 series, and from... 

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 ... 

The unique electronic structure of these (L-A3)MoO(dithiolene) complexes arises from two basic factors. The first is the strong axial a- and Ji-donor properties of the terminal oxo ligand, which dominates the ligand field and predetermines the energy of the Mo-based dxz, dyz, and dzi acceptor orbitals. The second is the equatorial dithiolene sulfur donors, from which the low-energy LMCT transitions arise. Dithiolene covalency contributions to the electroactive C, or redox, orbital can be directly probed via the relative oscillator strengths of the / —> ixy and /fp —> (/", transitions (see above). These three wave functions may be expanded in terms of Mo- and dithiolene sulfur-based functions ... 

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... 

We are thus invited to view the H2 molecule, which as far as every chemist is concerned is quintessentially covalent, as a resonance mixture between a covalent contribution, represented by wave function (1), and an ionic part, represented by wave function (2), a physical picture which flies in the face of every chemical instinct. 

The HF wave funetion eontains equal amounts of ionie and eovalent eontributions (Section 4.3), For covalently bonded systems, like H2O, the HF wave funetion is too ionie, and the effect of electron correlation is to increase the covalent contribution. Since the ionic dissociation limit is higher in energy than the covalent, the effect is that the equiUbrium bond length increases when correlation methods are used. For dative bonds, such as metal-ligand compounds, the situation is reversed. In this case the HF wave function dissociates correctly, and bond lengths are normally too long. Inclusion of... 

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. 

Express the VB wave functions for the ground state ( B,) and first covalent excited state (2A2) of the pentadienyl radical in terms of Kekule structures. Deduce the qualitative spin distribution change upon excitation. Hints For the excited-state case, you will need to express the Kekule structures in terms of determinants. For the ground state, you may express the wave function as the spin alternant determinant, plus some minor contributions of the two determinants that exhibit a single spin frustration (two identical neighboring spins). You may consult ChemPhysChem. 5, 515 (2004). 

An important feature of the BOVB method is that the active orbitals are chosen to be strictly localized on a single atom or fragment, without any delocalization tails. If this were not the case, a so-called "covalent" structure, defined with more or less delocalized orbitals like, e.g., Coulson-Fischer orbitals, would implicitly contain some ionic contributions, which would make the interpretation of the wave function questionable [27]. The use of pure AOs is therefore a way to ensure an unambiguous correspondence between the concept of Lewis structural scheme and its mathematical formulation. Another reason for the choice of local orbitals is that the breathing orbital effect is... 

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