Ionic VB structures

Another interesting problem coneems the case of a weak resonance between two ionic VB structures as occurs in the singlet nn state of ethylene (and longer polyenes). This state (the allowed By state) is of ionic VB content... 

Of course, Schemes 4.1 and 4.2 focus only on the covalent structures. However, Rumer diagrams for ionic VB structures can be generated in the same manner. Negative and positive charges are first assigned to some specific atoms,... 

Ionic VB Structures Valence bond structures that involve oppositely charged centers. For example, the description of an electron pair bond A—B requires a covalent HL structure, A - B, and two ionic structures, A+ B and A - B +. ... 

Another optional improvement concerns the description of the ionic VB structures. At the simplest level, the active ionic orbital is just a unique doubly occupied orbital as in 10 or 11. However this description can be improved by taking care of the radial correlation (also called "in-out" correlation) of the two active electrons, and this can be achieved most simply by splitting the active orbital into a pair of singly occupied orbitals accommodating a spin-pair, much as in GVB theory. This is pictorially represented in 12 and 13 which represent improved descriptions of 10 and 11. 

Finally, a few remarks are in order concerning the non dynamic correlation of the inactive electrons. Normally, these electrons are left uncorrelated (except in the extended SD-BOVB calculation for H-F, above) in the molecule as well as in the dissociated fragments or in any conformation of a molecular system throughout a potential surface. However, since the inactive orbitals are somewhat different in the HL and ionic VB structures, it is impossible to avoid... 

The carbon-fluorine bond is a polar covalent bond in the sense that it exhibits a not negligible ionic character. This polarity is reflected in the weight of the ionic VB structure, Fj0n(H3C+F-), which is calculated to... 

This object is traditionally achieved in VB theory by taking into consideration ionic VB structures in which the electrons are redistributed amongst the valence orbitals, some of these now being doubly occupied. The simplest example is, of course, the H2 molecule, where one adds to the Heitler-London covalent function... 

Such a VB function is known as a Coulson-Fischer (CF) type. The c constant is fairly small (for H2 c 0.04), but by allowing the VB orbitals to adopt the optimum shape, the need for ionic VB structures is strongly reduced. Note that the two VB orbitals in eq. (7.8) are not orthogonal, the overlap is given by... 

Allowing all excitations in the minimal basis valence space and performing the full optimization corresponds to a [8,8]-CASSCF wave function (Section 4.6). Similarly, the SCVB wave function in eq. (7.10) may be improved by adding ionic VB structures like and CH /H this corresponds to exciting an electron from one of the singly -occupied VB orbitals into another VB orbital, thereby making it doubly occupied. The ... 

The initial work of Warshel, Hwang and Aqvist [50a] for PT in water and in carbonic anhydrase (a zinc metalloenzyme) reported FERs simulated in two ways. First, the autodissociation in water catalysed by a metal ion was studied using explicit Zn +, Mg +, Ca + and Na+ cations. Second, the energy of the product diabatic curve (for the ionic VB structure) was shifted vertically in order to change... 

Any two-state VBSCD can be transformed into a VBCMD where the Heitler-London (HL) and ionic VB structures are plotted explicitly as independent curves, instead of being combined into state curves [11]. As a rule, ionic structures, which are the secondary VB configurations of polar-covalent bonds, lie above the covalent Heitler-London (HL) stmctures at the reactant and product geometries, and generally they cross the two HL stmctures above their own crossing point. In many cases, the ionic curve is low enough in... 

Peterson and Pfeiffer did an ab initio all-electron VB calculation on H2O [C. Peterson and G. V. Pfeiffer, Theor. Chim. Acta, 26,321 (1972)]. They included 10 covalent and 39 ionic VB structures in their wave function. The large number of structures arises because they considered structures arising from such oxygen configurations as ls 2s2p and ls 2p, as well as The contribution of the ionic structures, as... 

A less trivial example is H2O. Although the H2O ionic VB structures D and E are very important, it is traditional to ignore the ionic structures and find the oxygen valence state in H2O from the perfect-pairing covalent function (15.149) corresponding to structure A. Removal of the H atoms from (15.149) gives... 

The mixing energy is given by the product of the number of excited covalent and ionic VB structures by the dose-neighbor term Thus, the becomes ... 

There is thus little hope, in our opinion, for a rigorous definition of valence minimal basis set effective Hamiltonians. To build them, the use of the diatomic effective Hamiltonian may be useful, but some supplementary assumptions should be made, along a physically grounded model, to define for instance three-body polarization energies and the energies of highly hybridized or multi-ionic VB structures. One should realize the physical origin of these numerous troubles they essentially come from the inclusion of the ionic determinants in the model space. This inclusion first resulted in intruder state problems for the diatom it also leads to the appearance of multiply ionic structures in the valence minimal basis set space of the cluster. It seems that, even for H, the definition of a full valence space is too ambitious. 

The VBSCF method [J. H. van Lenthe and G. G. BaUnt-Kurti, J. Chem. Phys., 78, 5699 (1983)] writes the molecular VB wave function as a linear combination of covalent and ionic VB structures and simultaneously optimizes the coefficients in the linear combination and the orbitals (which are expressed using a set of basis functions). The orbitals might be localized on individual atoms (as in the classical VB method of the last section) or they might be taken as sanidelocaUzed (as in the GVB method). 

A diabatic state curve made of the Lewis bond-wave function of the reactants or products. The Lewis structure is a mixture of the covalent and ionic VB structures of a bond, Each reaction possesses two Lewis curves. 

---