CASSCF-CISD

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. 

Cl methods [21] add a certain number of excited Slater determinants, usually selected by the excitation type (e.g. single, double, triple excitations), which were initially not present in the CASSCF wave function, and treat them in a non-perturbative way. Inclusion of additional configurations allows for more degrees of freedom in the total wave function, thus improving its overall description. These methods are extremely costly and therefore, are only applicable to small systems. Among this class of methods, DDCI (difference-dedicated configuration interaction) [22] and CISD (single- and double excitations) [21] are the most popular. 

Let s compare these CASSCF results with those for a method that is not size-consistent, Cl with no complete aspect. We ll use CISD (configuration interaction singles and doubles Section 5.4.3). Here are the results for CISD/6-31G ... 

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...

Semi-empirical calculations involving the QCFF/PI -f CISD method and ab initio calculations using the CASSCF and HF/6-31G methods have been used to calculate vibrational frequencies of the in-plane modes for thiophene derivatives <1994JCP(100)2571, 1991JCP(94)957, 1991JCP(94)965, 1991JCP(95)4783>. 

One important conclusion from the full Cl benchmark studies of Bauschlicher, Taylor, Langhoif, and others in the 1980 s is that the MR-CISD method based on CASSCF orbitals provides potential energy surfaces which accurately parallel the full Cl surfaces.14,15 234,238-240 242 254 For example, the CASSCF MR-CISD method predicts singlet-triplet energy separations in CH2 and SiH2 within 0.01 kcal mol-1 and 0.03 kcal mol-1, respectively, of the full Cl results.236,238 The best results are obtained when no threshold is used for reference selection that is, when all CSFs in the CASSCF wavefunction are used as references. This CAS-ref MR-CISD procedure is intimately related107 to second-order configuration interaction (SOCI), which distributes electrons in... 

The reliability of SOCI, coupled with its essentially a priori selection of the Cl space, makes it an attractive alternative to full Cl. Unfortunately, for reasonable active spaces the dimension of the SOCI grows very rapidly with system size and thus the method is applicable only to small molecules. Nevertheless, for quite a few molecules it is possible to use the SOCI method in conjunction with large one-particle basis sets and hence to obtain wavefunctions very close to the exact nonrelativistic Born-Oppenheimer limit. Below, we will attempt to give the reader a sense of the types of problems to which the SOCI method has been applied. Bauschlicher, Langhoff, and Taylor have already given15 an excellent review of the related CASSCF MR-CISD method, and we refer the reader to their article for a discussion of additional important studies. 

The list of unsuccessful computational methods for the calculation of vibrational wave numbers for N2 and SiN2 (la) was extended from HF, CASSCF, and CISD to MP2. Density functional theory (DFT) in the B3LYP framework yielded vibrational wave numbers 5% above experimental values throughout. Only CCSD(T) results are closer to the experiment (6), but the B3LYP method is a better candidate for the investigation of larger systems. 

---