INDO/CI method

Zhou. Y.-F., Wang, X.-M, Zhao, X., Jiang, M,-H, A quantum-chemical INDO/CI method for calculating two-photon cross sections. J. Phys, Chem. Sol. 62, 1075—1079 (2001)... 

The geometries, electronic structures and electronic spectra of stilbene derivatives and chromophores based on dithienothiophenes are systematically studied by AMI and INDO/CI method. On the basis of correct UV-Vis spectra, the position and strength of the two-photon absorption can be predicted (2001MI1). 

Micron- and submicron-scale lateral structures of optically nonlinear organic films comprised of substituted trons-stilbene derivatives (Ri = OCH3, R2 = CN) was characterized [45]. Second harmonic generation (SHG), optical microscopy, and atomic force microscopy (AFM) were used in this investigation. The third-order nonlinear optical properties and two-photon absorption ofdifferent types of stilbene derivatives (D-tt-D, A-7t-A, D-7t-A) were investigated [46]. Using the INDO/CI method, the UV-vis spectra were explored and the position and strength of the two-photon absorption were predicted by sum-over-states expression. Relationships of the structures, spectra, and nonlinear optical properties have been examined. Two-photon absorption spectra (650-1000 nm) of a series of asymmetrically substituted stilbenoid chromophores... 

There are several other semi-empirical methods such as the relativistic extended Hiickel method formulated by Pyykko and co-workers. The Dirac-Slater multiple Xa method (Case 1982) has also been employed to include relativistic effects approximately. Zerner and co-workers use the INDO/CI method to study lathanide compounds. We will discuss these in section 3.2. 

The ionization potentials, singlet and triplet excited states, and frontier molecular orbitals of 1,4-, 1,8-, and 4,5-diazafluorenones were investigated by the all-valence-electrons INDO/S-CI method. Calculated molecular properties were found to be in accordance with experimental results... 

Good test cases would be the solvent effects on the UV-vis absorption spectra of formaldehyde and acetone that have been the subject of innumerous theoretical studies. Innovative theoretical methods have been applied to formaldehyde (see also the compilation of results in [20,32,113,114,115,116]). Unfortunately the experimental result for formaldehyde in water is not clear because of chemical problems mostly associated to the aggregation and formation of oligomers. Therefore a better test case is the UV-vis spectra of acetone, because reliable experimental solvent shifts and several theoretical results are available (see the compilation of results in [117]). The Stokes shift of the n-rr transition of acetone has been critically discussed by Ohrn and Karlstrom [118], Grozema and van Duijnen [17] studied the solvatochromic shift of the absorption band of acetone in as much as eight different solvents. Acetone is known to shift the maximum of the n-rr band by 1500-1700 cm 1 when immersed in water [119,120,121], Using the conventional HF/6-31 G(d) point charges, Coutinho and Canuto [54] simulated acetone in water and performed INDO/CIS... 

Onsager s SCRF is the simplest method for taking dielectric medium effects into account and more accurate approaches have been developed such as polarizable continuum modes, " continuum dielectric solvation models, - explicit-solvent dynamic-dielectric screening model, - and conductor-like screening model (COSMO). Extensive refinements of the SCRF method (spherical, elliptical, multicavity models) in conjunction with INDO/CIS were introduced by Zerner and co-workers ° as well. 

Kotzian et al. (1991) and Kotzian and Rosch (1992) applied their INDO/1 and INDO/S-CI methods to hydrated cerium(III), i.e. model complexes [Ce(H20) ] (n=8,9), in order to rationalize the electronic structure and the electronic spectrum of these species. Besides the scalar relativistic effects spin-orbit coupling was also included in the INDO/S-CI studies. The spin-orbit splitting of the 4f F and 5d states of the free Ce " ion was calculated as 2175cm" and 2320cm in excellent agreement with the experimental values of 2253 cm and 2489 cm" , respectively. The calculated energy separation between the F and states of approximately 44000cm" (estimated fi-om fig. 5 in Kotzian and Rosch 1992) is somewhat lower than the experimental value of 49943 cm" (Martin et al. 1978). 

There are several theoretical studies on LaO and related lanthanide oxides. We have already mentioned the ligand-field theory model calculations of Field (1982) as well as Carette and Hocquet (1988). More recently, Kotzian et al. (1991a,b) have applied the INDO technique (Pople et al. (1967) extended to include spin-orbit coupling [see also Kotzian et al. (1989a, b)] to lanthanide oxides (LaO, CeO, GdO and LuO). The authors call it INDO/S-CI method. The INDO parameters were derived from atomic spectra, model Dirac Fock calculations on lanthanide atoms and ions to derive ionization potentials, Slater-Condon factors and basis sets. The spin-orbit parameter is derived from atomic spectra in this method. 

Table 52, reproduced from Kotzian et al. s work, compares the INDO/SCI energy separations with experiment for several electronic states of LaO. It is evident from table 52 that the INDO/S-CI method predicts the energy separations for these compounds reasonably well. Kotzian et al. also computed the transition moments for the observed A<->C, B<- X, C<- X, D<- X and F<- X systems. 

Kotzian et al. (1991a, b) as well as Kotzian and Rosch (1991a, b) have applied the INDO/S-CI method extended to include spin-orbit coupling on the diatomic CeO. They have studied 16 electronic states of CeO arising from the 4f6s configuration of Ce" at the experimental of 1.820A. The results of their computations are shown in... 

SCF/CISD methods in conjuction with quasi-relativistic ECPs. More recently, Kotzian et al. (1991a,b) have used the INDO/S-CI method to compute the energy separations of 45 12 electronic states of GdO. We use the Kotzian et al. (1991a, b) and the Dolg et al. (1990a,b) works as the basis for discussion on the electronic states of GdO. 

Kotzian et al. (1991b) have considered several structures of 03, D3, 3 and C3 symmetries. They noted that the agreement with the experimental spectrum could be obtained for a geometry with low symmetry, (i.e., with the three-fold axis removed) although for simplicity, Kotzian et al. (1991a, b) considered [Ce(H20)9] complex as if it had point-group symmetry. The INDO/S-CI method confirmed the previous... 

Two other types of basis set that have been used successfully in hfs calculations are Chipman s contracted [3s,2p] bases, and basis sets based on Slater type orbitals (STOs). The former of these is mainly used in single excitation configuration interaction (CIS) calculations, and are based on a very fortuitous cancellation of errors between method and basis set. The performance of the CIS/[3s,2p] approach lies within 20-25% of experiment. One should recall, though, that once we go to larger molecular systems, the CIS method becomes computationally very demanding, STOs have mainly been used in semiempirical INDO hfcc calculations (STO-SG) and in the density functional theory (DFT) studies of Ishii and Shimitzu (STO-6G). The number of hfcc studies using these basis sets at the ab initio or DFT levels is however to date very limited. 

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