CASPT2 method

Intensities for electronic transitions are computed as transition dipole moments between states. This is most accurate if the states are orthogonal. Some of the best results are obtained from the CIS, MCSCF, and ZINDO methods. The CASPT2 method can be very accurate, but it often requires some manual manipulation in order to obtain the correct configurations in the reference space. 

A more balanced description requires MCSCF based methods where the orbitals are optimized for each particular state, or optimized for a suitable average of the desired states (state averaged MCSCF). It should be noted that such excited state MCSCF solutions correspond to saddle points in the parameter space for the wave function, and second-order optimization techniques are therefore almost mandatory. In order to obtain accurate excitation energies it is normally necessarily to also include dynamical Correlation, for example by using the CASPT2 method. 

Finley J, Malmqvist PA, Roos BO, Serrano-Andres L (1998) The multi-state CASPT2 method. Chem Phys Lett 288 299... 

Luckily, this impasse was removed through the recent introduction of the CASPT2 model, which combines a powerful procedure for treating cases of strong non-dynamic correlation (CASSCF) with a very economical one for treating dynamic correlation296. As will be shown below, the CASPT2 method works very well for polyene radical cations. 

In the ring expansions of both la and lb, the first step is predicted to be rate-determining. If one accounts for the deficiencies of the CASPT2 method, the best estimate is that phenylcarbene (la) has a barrier to intramolecular... 

The reference (zeroth-order) function in the CASPT2 method is a predetermined CASSCF wave function. The coefficients in the CAS function are thus fixed and are not affected by the perturbation operator. This choice of the reference function often works well when the other solutions to the CAS Hamiltonian are well separated in energy, but there may be a problem when two or more electronic states of the same symmetry are close in energy. Such situations are common for excited states. One can then expect the dynamic correlation to also affect the reference function. This problem can be handled by extending the perturbation treatment to include electronic states that are close in energy. This extension, called the Multi-State CASPT2 method, has been implemented by Finley and coworkers.24 We will briefly summarize the main aspects of the Multi-State CASPT2 method. 

We have studied several triatomic compounds of general formula XUY, where X, Y = C, N, O, and U is the uranium atom in the formal oxidation state 4+, 5+, or 6+. We have determined the vibrational frequencies for the electronic ground state of NUN, NUO+, NUO, 0U02+, and OUO+61 and have compared them with the experimental measurements performed by Zhou and coworkers.62 The CASSCF/CASPT2 method has proven to be able to reproduce experimental results with satisfactory agreement for all these systems. 

In this chapter we illustrated how the CASSCF/CASPT2 method can be used to explore the nature of such chemical bonds. Classic cases are the Re-Re multiple bond in Re2Cl, and the Cr-Cr bond ranging from the quadruply bonded Cr(II)-Cr(II) moiety to the formal hextuple bond between two neutral chromium atoms. The bonding between the 3d5 electrons is weak and should be considered as an intermediate between two pairs of antiferromagnetically... 

In the study of Cu202, the CASSCF/CASPT2 method is unsatisfactory. This and related problems motivate the extension of the CASSCF/CASPT2 method to handle larger active spaces. 

All calculations were carried out with the software MOLCAS-6.0 [16]. Scalar relativistic effects were included using a DKH Hamiltonian [14,15]. Specially designed basis sets of the atomic natural orbital type were used. These basis sets have been optimized with the scalar DKH Hamiltonian. They were generated using the CASSCF/CASPT2 method. The semi-core electrons (ns, np, n — 3,4, 5) were included in the correlation treatment. More details can be found in Refs. [17-19]. The size of the basis sets is presented in Table 1. All atoms have been computed with basis sets including up to g-type function. For the first row TMs we also studied the effect of adding two h-type functions. 

The calculated barrier for the cyclization of 33t to 29 is 6 kcal/mol after taking into consideration that the CASPT2 method overestimates the energy difference between open- and closed-shell states by 3 kcaFmol. The correspondingly adjusted predicted 6 kcal/mol barrier is in nearly exact agreement with the experimental value (5.6 0.3 kcal/mol). " ... 

Several different versions of second-order perturbation theory for multireference wave functions have been implemented but the one currently in widest use is probably the CASPT2 method. This method was developed by Roos and co-workers in Lund, Sweden, and it is available in their MOLCAS package of computer programs. 

Although relatively expensive and difficult to use, CASSCF/ CASPT2 methods often provide meaningful chemical descriptions. This, coupled with the continuing increase in computational power, suggests that the study of properties and reactions involving metalloporphyrins should be pursued with these accurate methods. 

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