CASPT

The other half of the isomerization takes place directly bypassing a trappable intermediate, as recently confirmed by extensive theoretical calculations [B3LYP, CASPT 2, (8/8)CASSCF] [145],... 

Although not rigorously size-extensive, CASPT behaves better than MRSDCI theory for systems of many electrons. The CASPT and other MRPT methods are important in the sense that they are the only generally applicable methods for ab initio calculations of dynamical correlation of open-shell and closed-shell multiconfigura-... 

CASSCF CASPT2(v) CASPT(c-v) INDO/S CASSI INDO/S... 

To avoid long perturbation vectors, we impose a diagonal block structure on Ho- This is accomplished by defining the zero-order CASPT operator as [25]... 

To set up a size-extensive perturbation theory, the zero-order Hamiltonian must be additively separable. We shall here show that, for multiplicatively separable zero-order wave functions, the CASSCF Fock operator and the zero-order energy are both additively separable but that the presence of projection operators nevertheless makes the zero-order CASPT Hamiltonian H ... 

Fig. 14.12. The block-diagonal structure of the zero-order CASPT Hamiltonian matrix.

Comparing (14.7.15) and (14.7.16), we find that Hqab is not equal to Hoa + Hob- A similar argument would show that the zero-order CASPT Hamiltonian (14.7.8) is not additively separable. 

For a single-determinant closed-shell Hartree-Fock state, the zero-order CASPT operator (14.7.8) reduces to the closed-shell Fock operator. In this limit, the operators /a and /b have 0a) and 0b) as eigenfunctions ... 

The nonseparable contributions to the zero-order CASPT Hamiltonian (14.7.15) then vanish and Hoab becomes separable ... 

In this subsection, we consider the first-order CASPT (CASPTl) wave-function correction and the second-order CASPT (CASPTl energy correction. We adopt the internally contracted scheme, in which the CASPTl correction is written as a linear combination of all single and double excitations from 0) [26] ... 

In Table 14.8, we have listed the CASPT and MPPT energies calculated up to order 10 for the water molecule at the geometries / ref and 2/ ref- The CASPT results have been calculated using the uncontracted, determinantal scheme. In the CASPT calculations, a (3.0.1.2) valence CAS reference state is employed, with the inactive ai CAS orbital frozen in the MPPT calculations, the canonical lot Hartree-Fock orbital has been kept frozen. 

Table 14.8 The convergence of the CASPT and MPPT series for the water molecule in the cc-pVDZ basis at the reference geometries / ref and 2/ ref. The listed energies are the errors (in Eh) relative to the rci energy (in the same basis and with the same frozen orbitals)...

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