Complete active-space SCF

CAS SCF complete active space self-consistent field... 

CAS-SCF. CAS-SCF (complete active space self-consistent field) calculations select the chemically most significant electrons and orbitals and apply configuration interactions to this set. 

CAS SCF Complete Active Space Self-Consistent Field An iterative and variational method of solving the Schrddinger equation with the variational wave fune-tion in the form of a linear combination of aU the Slater determinants (eoef-ficients and spinorbitals are determined variationaUy) that ean be built from a limited set of the spinorbitals (forming the active space). 

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. 

QDMBPT = quasi-degenerate many-body perturbation theory, (POL-) Cl = (polarization-) configuration interaction, MC SCF = multiconfiguration SCF, CAS SCF = complete active space SCF, MRD Cl = multireference double-excitation Cl, UHF = unrestricted Hartree-Fock, UMP2 = unrestricted Moller-Plesset perturbation method of second order. - An analytical, combined polynomial-exponential form for E(x) with x = (r-rg)/r and a figure for x= —0.98 to +0.04. 

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... 

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. 

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

With regard to the former, one would like to include as many important configurations as possible. Unfortunately, the definition of an important configuration is often debatable. One popular remedy is the full-valence complete active space SCF (CASSCF) approach in which configurations arising from all excitations from valence-occupied to valence-virtual orbitals are chosen. [29] Since this is equivalent to performing a full Cl within the valence space, the full-valence CASSCF method is limited to small systems. Nevertheless, the CASSCF approach using a well-chosen (often chemically motivated) subspace of the valence orbitals has been shown to yield a much improved depiction of the wave function at all points on a potential surface. Furthermore, the choice of an active space can be adjusted to describe excited state wave functions. 

For the sake of completeness, we recall that the idea of the single-root formalism exploiting the Hilbert space approach was also proposed by Banerjee and Simons [31] and Laidig and Bartlett [34,35]. In both approaches they start from the complete active space MC SCF wave function, however, in order to eliminate redundant cluster amplitudes they approximate the wave operator by... 

In an MCSCF calculation, not only the coefficients of the multiple configurations in the MC wave function, but also the orbitals in them, are simultaneously optimized. An (n/m)MCSCF calculation, in which the n active electrons and m active orbitals are chosen in the manner described in the preceding paragraph, is called a complete active space (CAS)SCF calculation. ... 

We shall not perform the somewhat elaborous calculation of the MC wave function in detail. A somewhat simpler example is the dissociation of a double bond and it is given as an exercise (exercise 2). Here we only note that the number of configuration state functions (CSF s) will increase very quickly with the number of active orbitals. In most cases we do not have to worry about the exact construction of the MC wave function that leads to correct dissociation. We simply use all CSFs that can be constructed by distributing the electrons among die active orbitals. This is the idea behind the Complete Active Space SCF (CASSCF) method. The total number of such CSFs is for N2 175 for a singlet wave function. A further reduction is obtained by imposing spatial symmetry. All these CSFs are not included in a wave... 

A diatomic silylene of astrophysical interest, silicon sulfide S=Si , was treated by a three-stage calculation221. MOs from an HF-SCF treatment were employed in a complete active space SCF calculation whose optimized MOs were in turn used for a Cl calculation that included as many as three million configurations Comparison of various spectroscopic constants with those from experiment revealed fair agreement221. 

Some molecular species are not calculated properly by straightforward model chemistries these include singlet diradicals and some excited state species. For these the standard method is the complete active space approach, CAS (CASSCF, complete active space SCF). This is a limited version of configuration interaction, in which electrons are promoted from and to a carefully chosen set of molecular orbitals. 

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