Hydrogen-like orbitals computation

T vo main streams of computational techniques branch out fiom this point. These are referred to as ab initio and semiempirical calculations. In both ab initio and semiempirical treatments, mathematical formulations of the wave functions which describe hydrogen-like orbitals are used. Examples of wave functions that are commonly used are Slater-type orbitals (abbreviated STO) and Gaussian-type orbitals (GTO). There are additional variations which are designated by additions to the abbreviations. Both ab initio and semiempirical calculations treat the linear combination of orbitals by iterative computations that establish a self-consistent electrical field (SCF) and minimize the energy of the system. The minimum-energy combination is taken to describe the molecule. 

Now we will calculate one by one aU die integrals fliat appear in the Dirac matrix equation. The integral y ) = because die scalar product leads to the nuclear attraction integral with a hydrogen-like atomic orbital, and diis gives the result above (see Appendix H available at booksite.elsevier.com/978-0-444-59436-5, p. e91). The next integral can be computed as follows ... 

It should be apparent that the most obvious basis set to use for an ab initio calculation is the set of hydrogen-like atomic orbitals Is, 2s, 2p, and so on that we are all familiar with from atomic structure and bonding theory. Unfortunately, these "actual" orbitals present computational difficulties because they have radial nodes... 

Orbital Surfaces. Molecular orbitals provide important clues about chemical reactivity, but before we can use this information we first need to understand what molecular orbitals look like. The following figure shows two representations, a drawing and a computer-generated picture, of a relatively high-energy, unoccupied molecular orbital of hydrogen molecule, H2. 

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