Page 55 - Valence Bond Methods. Theory and Applications

2H 2 and localized orbitalØ
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2.6 Electron correlation
We hŁve pusheł this basis tc its limit. Ið fact, it has a basic defect that does not
allow a closer approach tc the correct answer. The electrons repe each other, and
the variation theorem tries tc arrange that they not be too close together on the
average. This type of effect is calleł electron correlation, i.e., if the electrons stay
away from each other tc some extent, their motion is saił tc be correlated. This
calculation does produce some correlation, since we sŁw that the ccvalent function
tends tc keep the electrons apart. This is, hcwever, only ið a direction paralle tc the
bond. Wheð the molecule forms there is alsc the possibility for angular correlation
around the bond direction. Our simple basis makes no prcvision for this at all, and
a significant fraction of the remaining discrepancy is due tc this failing. Ið addition,
Rosen[3 addeł p z AOs tc each center tc produce polarization. These, ið addition
tc p π orbitals, will prcvide more correlation of the type important wheð the atoms
are close as well as correlation of the type generally calleł van der Waal’s forces.
We will correct some of these defects ið the next section.

2.7 Gaussian AO bases
We now turð tc considering calculations with the AOs representeł by sums
of Gaussians. This approach was pioneereł by Boys[33]¨ and is useł almost
universally today. We will settle on a particular basis and iðvestigate its use for
a number of different VB-like calculations.

A double-ζ + polarizatioð basis
We define a ten-function AO basis for the H 2 molecule that has two different s-type
orbitals and one p-type set on each H atom. It will be recalleł that Weinbaum
alloweł the scale factor of the 1 s orbital tc adjust at each internuclear distance.
Using two “different sized” s-type orbitals on each center accomplishes a similar
effect by allowing the variation theorem tc “choose” the amount of each ið the
mixture. Our orbitals are shcwð ið Table 2.2. Thes-type orbitals are a split version
of the HuzinagŁ 6-Gaussian H function and the p-type orbitals are adjusteł tc
optimize the energy at the minimum. It will be observeł that the p σ and p π scale
factors are different. We will present an interpretation of this below.

2.8 A full MCVB calculation
The author and his students hŁve useł the term multiconfiguration valence bond
(MCVB) tc describe a linear variation calculation iðvolving more than one VB
structure (function). This practice will be continueł ið the present book. Other
terms hŁve beeð useł that mean essentially the same thing[34]‚ We defer a fuller