Complete active space methods

The CAS SCF (Complete Active Space) method is a special case of the MC SCF approach and relies on selection of a set of spinorbitals (usually separated energetically from others) and on construction from them of all possible Slater determinants within the MC SCF scheme. Usually low energy spinorbitals are inactive during this procedure, i.e. they are doubly occupied in each Slater determinant (and are either frozen or allowed to vary). Most important active spinorbitals correspond to HOMO and LUMO. 

Additionally, one needs to remember that for a powerful tool such as pertnrbation theory, there is no obstacle to applying the multi-determinant reference function as the unperturbed function in perturbation calculus. Thus, similar to the SCF-HF and MP2 approaches, CASPT2 would be the second-order perturbation theory complete active space method - the perturbationaUy corrected CASSCF. 

FIGURE 17.10 Excited states of BH calculated using a multi-configurational-self-consistent-field (MCSCF) complete-active-space method using the MOLPRO program, the state-of-the-art ... 

So-called complete active space (CAS) methods fomi all CSFs that... 

Roos B O, Taylor P R and Siegbahn P E M 1980 A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach Chem. Phys. 48 157-73... 

Roos B O 1987 The complete active space self-consistent field method and its applications in electronic structure calculations Adv. Chem. Phys. 69 399-445... 

So-ealled complete-active-space (CAS) methods form all CSFs that ean be ereated by distributing N valenee eleetrons among P valenee orbitals. For example, the eight non-eore eleetrons of H2O might be distributed, in a manner that gives Ms = 0, among six... 

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. 

In this exercise, we will introduce the Complete Active Space Multiconfiguration SCF (CASSCF) method, using it to compute the excitation energy for the first excited state of acrolein (a singlet). The CIS job we ran in Exercise 9.3 predicted an excitation energy of 4.437 eV, which is rather for from the experimental value of 3.72 eV. We ll try to improve this prediction here. 

When the HF wave function gives a very poor description of the system, i.e. when nondynamical electron correlation is important, the multiconfigurational SCF (MCSCF) method is used. This method is based on a Cl expansion of the wave function in which both the coefficients of the Cl and those of the molecular orbitals are variationally determined. The most common approach is the Complete Active Space SCF (CASSCF) scheme, where the user selects the chemically important molecular orbitals (active space), within which a full Cl is done. 

K. P. Lawley, Ed., chapter 69,399. John Wiley Sons Ltd., Chichester, England, 1987. The Complete Active Space Self-Consistent Field Method and its Applications in Electronic Structure Calculations. 

Nickel Atom Studied With the Complete Active Space SCF Method and Second-Order Perturbation Theory. 

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