Heitler-London structures

BEP = Bell-Evans-Polanyi BOVB = breathing orbital VB FMVB = fragments in molecules based VB HL structure = Heitler-London structure PRS = perfectly resonating state VBCM = VB configuration mixing VBSCD = VB state correlation diagram VBSCF = self-consistent field VB. 

Heitler-London wave function, 15-16 Helium atom, wave function for, 3 Heterolytic bond cleavage, 46, 51, 47,53 Histidine, structure of, 110 Huckel approximation, 8,9,10,13 Hydrocarbons, force field parameters for, 112... 

LD model, see Langevin dipoles model (LD) Linear free-energy relationships, see Free energy relationships, linear Linear response approximation, 92,215 London, see Heitler-London model Lysine, structure of, 110 Lysozyme, (hen egg white), 153-169,154. See also Oligosaccharide hydrolysis active site of, 157-159, 167-169, 181 calibration of EVB surfaces, 162,162-166, 166... 

These results are confirmed by the corresponding VB calculations using the full Cl of three singlets from two orbitals (Heitler-London plus two ionic structures). 

Just before returning to Europe in 1929, Slater generalized into an N-electron system the wave function used by Pauling in the treatment of helium in the 1928 Chemical Reviews essay. The title of Slater s paper, "The Self-Consistent Field and the Structure of Atoms," shows his debt to Hartree, although Slater s method turned out to be a great deal more practical than Hartree s, as well as consistent with the methods of Heitler, London, and Pauling.70... 

The reader will recall that in Chapter 2 we gave examples of H2 calculations in which the orbitals were restricted to one or the other of the atomic centers and in Chapter 3 the examples used orbitals that range over more than one nuclear center. The genealogies of these two general sorts of wave functions can be traced back to the original Heitler-London approach and the Coulson-Fisher[15] approach, respectively. For the purposes of discussion in this chapter we will say the former approach uses local orbitals and the latter, nonlocal orbitals. One of the principal differences between these approaches revolves around the occurrence of the so-called ionic structures in the local orbital approach. We will describe the two methods in some detail and then return to the question of ionic stmctures in Chapter 8. 

The second method of discussing the electronic structure of molecules, usually called the valence-bond method, involves the use of a wave function of such a nature that the two electrons of the electron-pair bond between, two atoms tend to remain on the two different atoms. The prototype of this method is the Heitler-London treatment of the hydrogen a olecule, which we shall now discuss. 

Shortly after quantum mechanics evolved Heitler and London[l] applied the then new ideas to the problem of molecule formation and chemical valence. Their treatment of the H2 molecule was qualitatively very successful, and this led to numerous studies by various workers applying the same ideas to other substances. Many of these involved refinements of the original Heitler-London procedure, and within three or four years, a group of ideas and procedures had become reasonably well codified in what was called the valence bond (VB) method for molecular structure. 

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 ... 

When Heitler-London AO-type wavefunctions (i.e.. ..aabP +. ..baaP in which a and b are AOs) are used to represent electron-pair 7i c(CN) and 7i y(CN) bonds, it can be deduced [2,4,16, cf. also Eq.(ll) below] that VB structure 7 is equivalent to resonance between the Kekule Lewis structure 3 and the Dewar or "long-bond" Lewis structures 11-13. Only nearest-neighbour spin-pairing is indicated in increased-valence structures [2-5,10]. When the "long" or formal bonds are omitted from structures 11-13, these structures are designated as singlet diradical structures [2-4]. 

In the Kekule structure 3 there are four singly-occupied carbon and nitrogen 2p% and 2p7ty AOs. Labelling these orbitals as px(Q, Px(N), p (C) and py(N), the primary 5 = 0 Heitler-London wavefunction for the n electrons which occupy these orbitals is given by Eq.(8),... 

Because structures 11-13 do not involve C-N triple bonds, Eq.(ll) shows that in Eq.(9), the Px(C)-px(N) and py(C)-py(N) spin-pairings form fractional 7ix(CN) and Jty(CN) electron-pair n-bonds via Heitler-London AO formulations of the bond wavefunctions. 

Shifted ST0-6G electronic energies ( = -E - 36.0 a.u.), and VB structural weights for resonance between VB structures I-IX. Structures VII-IX involve (2s)1(2p)1, (2s)1(2p)1 and (2p)2 configurations for the LiW. The wavefunctions for the electron-pair bonds involve Heitler-London AO formulations. 

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... 

This chapter begins a series of chapters devoted to electronic structure and transport properties. In the present chapter, the foundation for understanding band structures of crystalline solids is laid. The presumption is, of course, that said electronic structures are more appropriately described from the standpoint of an MO (or Bloch)-type approach, rather than the Heitler-London valence-bond approach. This chapter will start with the many-body Schrodinger equation and the independent-electron (Hartree-Fock) approximation. This is followed with Bloch s theorem for wave functions in a periodic potential and an introduction to reciprocal space. Two general approaches are then described for solving the extended electronic structure problem, the free-electron model and the LCAO method, both of which rely on the independent-electron approximation. Finally, the consequences of the independent-electron approximation are examined. Chapter 5 studies the tight-binding method in detail. Chapter 6 focuses on electron and atomic dynamics (i.e. transport properties), and the metal-nonmetal transition is discussed in Chapter 7. 

---