Heitler-London HL wave function

This simple wave function, so called the Heitler-London (HL) wave function, was able to account for about 66% of the bonding energy of H2, and performed a little better than the rival MO method that appeared almost at the same time. 

This section aims to illustrate the origin of the quantum mechanical exchange-overlap densities and their different behaviour in the case of the chemical bond in ground state H2 and the Pauli repulsion in He2. We choose as starting point for the 1Xg+ ground state of the systems the normalized Heitler-London (HL) wave functions (Magnasco, 2008) ... 

The classical VB wave function, on the other hand, is build from the atomic fragments by coupling the unpaired electrons to form a bond. In the H2 case, the two electrons are coupled into a singlet pair, properly antisymmetrized. The simplest VB description, known as a Heitler-London (HL) function, includes only the two covalent terms in the HF wave function. 

We focus on the three-body forces in Fig. 5.21 where the SCF portion is compared with its components extracted before (Heitler-London, HL) and after (deformation, def) the wave functions of the monomers are perturbed by one another. It is apparent that the latter SCF-def forces are largely responsible for the anisotropy of the SCF three-body terms. The Heitler-London component is weaker, and resembles a mirror of SCF-def, with a maximum where SCF-def contains a minimum. The extremum at 20° corresponds to a configuration... 

Figure 4.3 Comparision of EDA frozen energies in kcal/mol along an angle for water dimer [upper] and formamide dimer [lower] with DEDA [blue curves] and MO-EDA [red curves] The MO-EDA employs the Heitler-London [HL] antisymmetrization of two fragments wave functions to represent the frozen density state. Reprinted with permission from Lu, Z., Zhou, N., Wu, Q. and Zhang, Y. Directional dependence of hydrogen bonds A density-based energy decomposition analysis and its implications on force field development./Chem Theory Comput 7, 4038-4049 [2011]. Copyright [2011] American Chemical Society.

HmA=BH 2-electron n bonds can most simply be described as a resonance mixture of the three structures shown in 13 the covalent Heitler—London (HL) structure. 13a, hereafter referred to as hl, and the ionic structures 13b and 13c designated and 3>a+b - The total wave function for the n bond then becomes... 

HL Heitler—London. The term corresponds to the wave function used by Heitler and London to calculate the bonding energy of the H2 molecule in 1927, and is used as a generic name to describe a covalent many-electron wave function. 

It should be remarked that, while the Heitler-London function (1.93) for H2 is a two-determinant wave function, the Heitler-London function (1.94) for He2 is a single determinant wave function, so that in this case HL and MO approaches coincide. 

If a and b are the respective AOs of two hydrogen atoms, I hl in Eq. [3] is just the historical wave function used in 1927 by Heitler and London to treat the bonding in the H2 molecule, hence the subscript descriptor HL. This wave function displays a purely covalent bond in which the two hydrogen atoms remain neutral and exchange their spins (the singlet pairing is represented, henceforth by the two dots connected by a line as shown in 7 in Scheme 3). 

Inspection of Eqa (6) for T2(MO) shows that it corresponds to the Heitler-London function obtained when the + of Eqn. (2) is replaced by a - this is a result that we have obtained previously in section 3-5. We may also obtain T3(M0) (= (ionic)) from T3 (HL) by exciting an electron from one atomic orbital into the other and changing the sign of the linear combination. (The sign change is necessary in order to satisfy the spectroscopic rule that an even — odd excitation is allowed, whereas toth even — even and odd —> odd excitations are forbidden. The even and odd characters of T (HL) and T (ionic) refer to the behaviour of the wave-functions with respect to inversion through the centre of symmetry of the molecule. Thus T (HL) and T. (ionic) are synunetric (even) and T (HL) and T (ionic) are antisymmetric (odd).)... 

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