STO-3G minimal basis set

Optimize the geometry of this system at the Hartree-Fock level, using the STO-3G minimal basis set and the 6-31G(d) basis set (augmented as appropriate). Run a frequency calculation following each optimization in order to confirm that you have found an equilibrium structure. 

Single determinant ab initio MO with STO-3G minimal basis set. The force field used is Bartell s older version (186). 

All these calculations require a set of atomic orbitals from which MOs can be calculated (the basis set). The earliest to be used were Slater-type orbitals (STOs) but these are mathematically inconvenient, and the STO-3G minimal basis set, which uses gaussian functions to mimic Slater orbitals, is commonly used. More sophisticated gaussian basis sets, which lead to improved accuracy, carry labels such as 6-31G(d) and 6-31++G(dp). Successive increases in basis set size (STO-3G—>3-21G—>3-31G(d)—>6-311G(3df)) give improved bond-length accuracy. 

STO-3G minimal basis set <88RHA235>. The calculated structure of allene episulfide is similar to the values obtained by microwave analysis (78JA7436), as shown in Figure 2. 

Section 3.5 contains a detailed illustration of the closed-shell ab initio SCF procedure using two simple systems the minimal basis set descriptions of the homonuclear (H2) and heteronuclear (HeH" ) two-electron molecules. We first describe the STO-3G minimal basis set used in calculations on these two molecules. We then describe the application of closed-shell Hartree-Fock theory to H2. This is a very simple model system, which allows one to examine the results of calculations in explicit analytical form. Finally, we apply the Roothaan SCF procedure to HeH. Unlike H2, the final SCF wave function for minimal basis HeH is not symmetry determined and the HeH example provides the simplest possible illustration of the iterative SCF procedure. The description of the ab initio HeH calculation given in the text is based on a simple FORTRAN program and the output of a HeH calculation found in Appendix B. By following the details of this simple but, nevertheless, real calculation, the formalism of closed-shell ab initio SCF calculations is made concrete. 

To perform an SCF calculation, we first choose a geometry for the nuclei. We let the helium nucleus be nucleus 1 with position vector Ri and the hydrogen nucleus be nucleus 2 with position vector R2, so that Ri - R2I = Ri2 = R is the internuclear distance. We will use the exact internuclear distance so that R = 1.4632 a.u. We then need to specify the basis set, which in our case is the STO-3G minimal basis set consisting of a Is basis function on each of the two nuclei. 

With the STO-3G minimal basis set, the above correlation energy is -0.0258 a.u. as compared to —0.0275 a.u. obtained using spin-orbital pairs. Thus pair theory is not only variant to unitary transformations of degenerate HF... 

The first step in the parameterization requires performing valence ab initio Hartree-Fock SCF calculations on the model molecules by a theoretical pseudopotential method [64] with first an STO-3G minimal basis set and then a double-zeta basis set. For botli model molecules we take the Fock operator to be... 

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