Starting Orbitals

The alternative strategy is to start by inspecting the MOs obtained from a ground-state self-consistent field (SCF) computation. The major difficulty here is that the virtual orbitals of an extended basis SCF computation are completely unsuitable for the representation of an excited state. Thus, one should start from an SCF computation with a one-electron basis that does not have diffuse components (STO-3G or 3-21G), from which the orbitals can be visually inspected and an active space chosen. When the active space is correct, the reduced basis-set computation may be used as a starting point for an extended basis-set computation. 

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Run a preliminary UHF/ST0-3G Pop=NahjralOrbi1al job on triplet acrolein to generate and examine the starting orbitals and their symmetries. Select those that will make up the active space you will want to create an active... 

More sophisticated procedures involve taking the start MO coefficients from a semi-empirical calculation, such as Extended HUckel Theory (EHT) or Intermediate Neglect of Differential Overlap (INDO) (Sections 3.12 and 3.9). The EHT method has the advantage that it is readily parameterized for all elements, and it can provide start orbitals for systems involving elements from essentially the whole periodic table. An INDO calculation normally provides better start orbitals, but at a price. The INDO... 

We have thus established the basis set to use and the active space for the CASSCF calculations. To perform the CASSCF calculations we need in addition a set of starting orbitals. These are most easily obtained from an SCF calculation. If we have access only to a closed shell SCF program we can... 

The six Walsh orbitals of 1 are formed f rom the (radial) spta and (tangential) p starting orbitals. They may be denoted as co0, cos, oja (CC bonding) and m0, (os, coA orbital (CC antibonding). Two important improvements of the original Walsh orbitals w are indicated in Figure 5 ... 

The classical choice of the starting orbitals is based on the following idea. Suppose that we deal with a chemical bond formed between two monovalent atoms A and B by the pairing of their valence electrons, one on A, the other on B. It is natural to assume that when one electron in the molecule is close to nucleus A, its molecular orbital will resemble the atomic orbital that it would occupy in A, and a similar situation would occur in the vicinity of B. This leads to the idea that the molecular orbital may be approximated by a linear combination... 

Atomic orbitals can combine and overlap to give more complex standing waves. We can add and subtract their wave functions to give the wave functions of new orbitals. This process is called the linear combination of atomic orbitals (LCAO). The number of new orbitals generated always equals the number of starting orbitals. 

Active space 2a-6a, In-Zir, la, 2a orbitals frozen. The starting orbitals were canonical SCF orbitals for the state in all cases. R = 2.1 bohr. Basis set ... 

In a straightforward application of the Newton-Raphson approach, Eq. (32) is solved iteratively for S and T until the convergence criteria (26) are fulfilled to the desired accuracy. This process converges nicely if the initial choice of the orbitals and the Cl coefficients are close to the final result. The energy is then in the local region where the second-order approximation is valid. Obviously such situations will not be very common in actual applications. In practice the starting orbitals are often obtained from a preceding SCF calculation, or even estimated from atomic densities , while the Cl... 

Although the primary emphasis of this chapter is on NBO analysis of existing wave functions, it is important to realize that these orbitals may also be useful in constructing new wave functions for photochemical phenomena. An important example is the CASNBO method, which uses NBOs as starting orbitals in multiconfigurational CAS (complete active space) wave functions. The CASNBO method allows the active space to be defined in the most specific and physically relevant way for a given chemical application (such as, e.g., the two-dimensional a B and space for a localized A-B bond-break-... 

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