Multireference calculations

In 1986, Schaefer et al. reported the first extensive ab initio calculations of S3 [61]. SCF and CISD calculations indicated that the global minimum is the ring D3h form. The more sophisticated CASSCF and MR-CISD calculations, on the other hand, favoured the open bent structure of 2 symmetry. The preference of the open form was subsequently confirmed by several other theoretical investigations [62-65]. The I>3h structure is calculated to be 31-44 kj mol less stable than the open C2V structure, depending on the method of calculation and the level of theory applied [56, 59-65]. The best estimate of the S-S bond length of the Czv form is 193.2 pm (CCSD(T)) [65] and the bond angle is 117°. Compared with the multireference calculations, DFT methods adequately describe the structure and PES of S3. 

Gordon and Truhlar (1986) have emphasized that variations on the theme of Eq. (7.60) can be useful in different circumstances. For instance, one might imagine carrying out multireference calculations and assuming two different scale factors, one applying to the non-dynamical... 

The formation of an intermediate ONOO (69) species in Figure 8 has been claimed in a spectroscopic study but was later questioned due to multireference calculations. NO3 reacts with NO2 to form dinitrogen pentoxide. ... 

The fact that the two preceding series are equivalent is by no means surprising. Indeed, the nephelauxetic effect is related directly to covalency the reduction of B by complex formation is caused by delocalization of the d-electron cloud on the ligands, which is in turn caused by the formation of covalent bonds. Even if not complete, the nephelauxetic series can come in handy when having to constmct the reference space of a multireference calculation, since it helps to... 

Figure 4.1 Important features of ground- and excited-state PESs for ethylene photodynamics and demonstration of the inadequacy of TDDFT and CIS methods for this problem, (a) Sq and PESs for ethylene in the pyramidalization and torsion coordinates (defined in the inset) that dominate the photodynamics. This surface was calculated using multireference perturbation theory — CAS(2/2) PT2. The global minimum on Si occurs at twisted and pyramidalized geometries. (b-d) A quantitative comparison of the Si PES obtained with CAS(2/2) PT2, TDDFT/B3LYP, and CIS, respectively. All calculations use the 6-3IG basis set. The TDDFT and CIS calculations are performed in a spin-unrestricted formalism. Contour values are given in eV, and in all cases the energies are referenced to the Sq equilibrium geometry at the corresponding level of theory. Only the multireference calculation captures the Si minimum correctly.

The results for this model considered at the minimum basis set (MBS) and double zeta (DZ) levels are given in Tables 2 and 3, respectively. In both cases, the (2,2) model space is used in multireference calculations. Again, both AL-RMR-CCSD-1 and AL-RMR-CCSD-2 represent a good approximation to the full RMR CCSD (both differing by only a few /lihartree at the MBS level and by 10-60 /ihartree at the DZ level). In turn, RMR CCSD represents a significant improvement over the standard CCSD (by more than 7 mhartree for a 0 for a DZ model). 

Number of reference states used in the multireference calculations. 

Most users prefer to avoid multireference calculations, since they are more complex, require more judgment, and are more difficult to execute than single-reference calculations. However, as in the example of singlet O2, above, some molecules have important non-dynamical correlation and require a multireference calculation. Fortunately, there are some simple ways to predict when such effects will be important. 

Columbus is also a multipurpose multifunction electronic structure code, developed mainly by the Shavitt and Pitzer groups at Ohio State University. The strength of Columbus is in multireference calculations, which include MRCI and MRCC approaches. A specialized and modified program, called CIDBG, is capable of performing spin-orbit Cl using relativistic ECP. This program has been implemented for massively parallel environments. ... 

COLUMBUS originated in 1980 at the Ohio State University and was developed by I. Shavitt, H. Lischka (University of Vienna), and R. Shepard (Battelle Columbus Laboratories). The program was designed to carry out a variety of multireference calculations on ground and excited states of molecules (Lischka et al. 2006). Specific features include ... 

Yet another criterion, known in various guises among people who carry out multireference calculations, is the... 

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