MR CISD

The acronym SEC refers to the case where the reference wave function is of the MCSCF type and tire correlation energy is calculated by an MR-CISD procedure. When the reference is a single determinant (HE) the SAC nomenclature is used. In the latter case the correlation energy may be calculated for example by MP2, MP4 or CCSD, producing acronyms like MP2-SAC, MP4-SAC and CCSD-SAC. In the SEC/SAC procedure the scale factor F is assumed constant over the whole surface. If more than one dissociation channel is important, a suitable average F may be used. 

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. 

The MR-CISD+Q method has been shown to yield very accurate results for energy differences between open- and closed-shell species. For example, see Matzinger, S. Fiilscher, M.P. J. Phys. Chem. 1995, 99, 10747. 

C. Comparison with MR-CISD and MR-LCCM on the Two-Configuration Reference Insertion of Be in H2 Molecule... 

MR CISD approximation taken from [69]. Missing values were not present. 

Another way to exploit the complementarity of Cl and CC approaches was explored earlier by Meissner et al. [10]. Instead of using Cl as a source of higher-than-pair clusters and correcting CCSD, it exploits the CC theory to correct the MR CISD results. In the spirit of an earlier work on Davidson-type corrections for SR CISD [10], Meissner et al. formulated a CCSD-based corrections for both SR [72] and MR [74] CISD. The latter was later extended to higher lying excited states [73]. 

It turns out that MR CISD represents again the most suitable source of the required higher-order clusters. Carefully chosen small reference space MR CISD involves a very small, yet representative, subset of such cluster amplitudes. Moreover, in this way we can also overcome the eventual intruder state problems by including such states in MR CISD, while excluding them from CMS SU CCSD. In other words, while we may have to exclude some references from Ado in order to avoid intruders, we can safely include them in the MR CISD model space Adi. In fact, we can even choose the CMS for Adi. Thus, designating the dimensions of Ado and Adi spaces by M and N, respectively, we refer to the ec SU CCSD method employing an NR-CISD as the external source by the acronym N, M)-CCSD. Thus, with this notation, we have that (N, 1)-CCSD = NR-RMR CCSD and (0, M)-CCSD = MR SU CCSD. Also, (0,1)-CCSD = SR CCSD. For details of this procedure and its applications we refer the reader to Refs. [63,64,71]. 

Let us, finally, reiterate that, similarly as the MR CISD method can serve as an external source for correcting CCSD approaches, we can conversely use CCSD to formulate Davidson-type corrections for MR CISD, both for the lowest-lying [72,74] and the higher-lying states [73]. 

Scalar quasidgenerate DC (SQDC) for MR CISD [7,60] f Scalar generalized DC (SGDC) for MR CISD [10,60]... 

In this regard, it is interesting to compare these ec results with those of Meissner et al. [72-74], which use the CC-based corrections for MR CISD. Although the absolute energy deviations are very similar for both (2,2)-CCSD (3rd column of Table IV) and (10th column of Table II), the... 

Throughout this work, several systems are discussed and the specific theoretical level is indicated in each case. The adopted notation is given as follows. CASSCF calculations including n electrons, m orbitals and averaging k states is denoted as SA-fc-C ASSCIm). If all CAS configurations are used to build the reference space for the MRCI procedure, it is referred to simply as MRCI. On the other hand, if a different space with p electrons and q orbitals is used, it is denoted MRCI(/ , q). The Cl expansion includes either all single and double excitations (MR-CISD) or... 

Figure 8-5. Minima of the crossing seam in pyrrole. Calculations were performed at (a) MR-CISD/SA-3-CASSCF(6,5)/6-31G and (b) MR-CISD/SA-3-CASSCF(6,6)/6-31G levels. Dashed lines indicate (a) the ring opening (ii,) and (b) the H-detachment...

Figure 8-6. H-detachment (left) and ring-opening (right) deactivation paths in pyrrole. Both paths start at the ground state equilibrium geometry. Calculations at MR-CISD level (see [68] for details on the calculations)...

Laidig and Bartlett/li8(a)/ have implemented the theory in its linearized form. They applied it to the symmetric dissociating potential curve for the ground state of water and the symmetric abstraction from BeH2. Each T is truncated at the two-body level. The results were compared to the corresponding MR-CISD values. To our knowledge, a quadratic extension of the formalism has not been applied computationally. A spin-adapted version of the linearized model has also been recently formu1 ated/118[Pg.332]

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