Valence Bond Output for the H2 Molecule

The first output for H2 was calculated with the program TURTLE (4), and is presented in Output 2.1. The relevant output information begins with the section called vb-symbolic , which specifies the multiplicity of the molecule, the number of electrons, and the number of VB configurations (i.e., structures). This process is followed by a symbolic representation of the VB structures, namely, the VB basis set of structures for the problem, or in short, the VB structure-set. Here, the numbers 1 and 2 designate the atomic orbitals (AOs) in which the VB program distributes the bonding electrons. The number 1 is the Is AO of one of the hydrogen atoms, say H1 and 2 is the AO of the other atom, H2. Thus, structure 1, represented as 1 2 , is the covalent (HL) structure, where each atom possesses one electron, while structures 2 and 

A Chemist s Guide to Valence Bond Theory, by Sason Shaik and Philippe C. Hiberty Copyright 2008 John Wiley Sons, Inc. 

written as 1 1 and 2 2 , represent the ionic structures where one of the atoms (Hi or H2) possesses two electrons and the other none. 

The structure representation is followed by a symbolic representation of the wave functions, along with a coarse normalization, in the section entitled list of configurations . As can be seen, the wave function of the HL structure (structure 1) involves two determinants. In the description of the determinants, the letters a and b stand for a and p spins, respectively. By convention, the orbitals are written in the same orders in both determinants, irrespective of their spins. If we represent our AOs by the symbols lsi and ls2, these two determinants are the ones shown in Equation 2.1, 

The next section entitled, final YBSCF results..gives the total energy ( vb-energy ) and the wave function ( vb-vector ), the latter is expressed in the usual manner in terms of the coefficient of the structure-set, as follows  

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