AO Basis Set

For all calculations, the choice of AO basis set must be made carefully, keeping in mind the scaling of the two-electron integral evaluation step and the scaling of the two-electron integral transfonuation step. Of course, basis fiinctions that describe the essence of the states to be studied are essential (e.g. Rydberg or anion states require diffuse functions and strained rings require polarization fiinctions). 

Extended Hiickel calculations are performed with a nonorthogonalized AO basis set therefore, the spin densities are to be evaluated by gross atomic populations and not simply by squares of expansion coefficients. 

The results of the above cited applications [18-28,45] have clearly shown that CS INDO method is fairly successful in combining equally satisfactory predictions of electronic spectra and potential surfaces (especially along internal rotation pathways) of conjugated molecules, a goal never reached by other NDO-type procedures. CS INDO shares, at least partly, the interpretative advantages of the CIPSI-PCILO-CNDO procedure [32,33,36,37], coming from using the same hybrid AO basis sets, but improves its predictive capabilities as far as spectroscopic and photochemical properties are concerned. 

With reference to the individual AO basis sets

fragment density matrices P t((p (Kt)) obtained from parent molecules Ms of nuclear configurations Kt, on the one hand, and the macromolecular AO basis set cp (K) of the macromolecular density matrix P (cp (K)) associated with the macromolecular nuclear configuration K, on the other hand, the following mutual compatibility conditions are assumed ... 

It is not possible to use normal AO basis sets in relativistic calculations The relativistic contraction of the inner shells makes it necessary to design new basis sets to account for this effect. Specially designed basis sets have therefore been constructed using the DKH Flamiltonian. These basis sets are of the atomic natural orbital (ANO) type and are constructed such that semi-core electrons can also be correlated. They have been given the name ANO-RCC (relativistic with core correlation) and cover all atoms of the Periodic Table.36-38 They have been used in most applications presented in this review. ANO-RCC are all-electron basis sets. Deep core orbitals are described by a minimal basis set and are kept frozen in the wave function calculations. The extra cost compared with using effective core potentials (ECPs) is therefore limited. ECPs, however, have been used in some studies, and more details will be given in connection with the specific application. The ANO-RCC basis sets can be downloaded from the home page of the MOLCAS quantum chemistry software (http //www.teokem.lu.se/molcas). 

Figure 6.7 Transformation of the minimal water AO basis set to one appropriate for the C2 point group. The effect on the form of the Fock matrix is also illustrated...

The MCSCF optimization process is only the last step in the computational procedure that leads to the MCSCF wave function. Normally the calculation starts with the selection of an atomic orbital (AO) basis set, in which the molecular orbitals are expanded. The first computational step is then to calculate and save the one- and two-electron integrals. These integrals are commonly processed in different ways. Most MCSCF programs use a supermatrix (as defined in the closed shell HF operator) in order to simplify the evaluation of the energy and different matrix elements. The second step is then the construction of this super-matrix from the list of two-electron integrals. The MCSCF optimization procedure includes a step, where these AO integrals are transformed to MO basis. This transformation is most effectively performed with a symmetry blocked and ordered list of AO integrals. Step... 

If we transform the MO s such that condition (5 11) is fulfilled, the resulting transition density matrix will be obtained in a mixed basis, and can subsequently be transformed to any preferred basis The generators Epq of course have to be redefined in terms of the bi-orthonormal basis, but this is a technical detail which we do not have to worry about as long as we understand the relation between (5 9) and the Slater rules. How can a transformation to a bi-orthonormal basis be carried out We assume that the two sets of MO s are expanded in the same AO basis set. We also assume that the two CASSCF wave functions have been obtained with the same number of inactive and active orbitals, that is, the same configurational space is used. Let us call the two matrices that transform the original non-orthonormal MO s [Pg.242]

The first problem is to choose an adequate AO basis set for the calculation. As always in this situation we have to make a compromise between accuracy (large basis set) and economy (small basis set). The system is not so big, so we should be able to afford to use a reasonably good basis set, at least for the final calculations. On the other hand, it is clear that we have to optimize the geometry of both electronic states of the system. This we may have to do using a smaller basis set. 

Here the subscript i refers to the state that is chosen as the origin of energies, (e.g., the HL state). The final features of some interest are the three states that result from diagonalization of the VB Hamiltonian in the structure set and the AO basis set. It is seen that there are three roots the lowest is the ground state representing the H H bond (see Eq. 2.2) while the other two represent excited... 

Slater functions The general arguments concerning the physically sound form of the states to be included in the AOs basis sets given above have been implemented in the Slater type AOs ... 

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