Active space orbitals

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

R. D. Harcourt, in Valence Bond Theory, D. L. Cooper, Ed., Elsevier, Amsterdam, The Netherlands, 2002, pp. 349-378. Valence Bond Structures for Some Molecules with Four Singly-Occupied Active-Space Orbitals Electronic Structures, Reaction Mechanisms, Metallic Orbitals. 

Valence bond structures for some molecules with four singly-occupied active-space orbitals electronic structures, reaction mechanisms, metallic orbitals... 

Qualitative valence-bond (VB) descriptions of the electronic structures of molecules are often able to provide "primitive patterns of understanding" [1] of the origin of various molecular properties. In this chapter, we shall give consideration to VB structures for some molecular systems that involve four active-space orbitals. The discussion will include VB formulations of the electronic structures of isolated molecules, reaction mechanisms, and types of "metallic orbitals" that can be used in VB representations for electron conduction in metallic lithium. For the latter topic, the results of STO-6G VB calculations are reported in order to make a provisional comparison of two conduction mechanisms. 

SINGLET AND TRIPLET SPIN WAVEFUNCTIONS FOR FOUR SINGLY-OCCUPIED ACTIVE SPACE ORBITALS... 

The phenomenon of four singly-occupied active-space orbitals (AO or MO) arises in many seemingly-unrelated molecular situations. The singlet spin (S = 0) Rumer diagrams for these orbitals indicate that there are two linearly-independent or canonical spin-pairings schemes. These spin-pairings are well-exemplified by the 7i-electrons of butadiene, for which two canonical Lewis VB structures with different 7i-electron spin pairings are those of 1 and 2. 

Figure 4.7 Representation of the active space orbitals for the Cope rearrangemenL See insert for color representation of this figure.)...

Figure 4.7 Representation of the active space orbitals for the Cope rearrangement.

The FCI wavefunction, while being completely impractical, still serves well for illustrative purposes. For the discussion, it is necessary that a single CSF or a class of CSFs dominates the many particle ground state wavefunction Tofxi,..., x,ld) -these are the configurations with nd electrons in the active space orbitals. If it possible to identify such a class, then na is fixed and one can cleanly divide the CSFs in the FCI space into two categories (a) the model space ( a space) CSFs. These are all CSFs with exactly na electrons in the active, metal-d-based orbitals and (b) the outer space that contains all other CSFs. 

As the accuracy of electron correlation methods is Hmited by the choice of the dimension of the active orbital space, the convergence behavior of the spin density with respect to the size of the active space must be studied to ensure that accurate ah initio spin densities are obtained. Although the CASSCF spin densities were quantitatively converged for medium-sized active orbital spaces, larger active spaces (more than 13 electrons correlated in 13 orbitals) were found to be unstable, that is, active space orbitals have been rotated out of the active space during the MCSCF procedure, while the spin densities started to diverge compared to the smaller sized CASSCF results. 

In these instances the multireference Cl energy (but not the SA-MCSCF energy) is dependent on the definition of the individual orbitals. In this situation the orbitals in these spaces must be uniquely defined. These definitions result in new antisymmetric contributions to Ug. These new contributions to U (X) are obtained by differentiating the equations used to uniquely define these orbital spaces. The approach for the determination of these antisymmetric contributions from a core/virtual orbital space rotation and from an active space orbital rotation are presented in Appendices B and D of Ref. 41 respectively. 

There are many factors governing the choice of active space. An important consideration is the nature of the chemical problem that is to be addressed. For example, if a chemical reaction is to be studied, then all orbitals involved in bond breaking/formation must be considered. If, instead, excited state properties are of interest, for example in the simulation of absorption processes, then orbitals whose occupations differ significantly between the ground and excited state must be included. This can be particularly important in coordination complexes, where excitation processes may involve a change in the oxidation state of the metal ion. However, some general points with regard to the choice of active space orbitals can be made ... 

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