INDO MO method

Total charge densities for the pyrylium cation have been calculated by the INDO MO method and show an increase of positive charge at the 2-, 4- and 6-positions. A linear relationship with 13C chemical shifts was shown to exist (770MR(9)l6). 

The naturally occurring isotopes of boron,, 0B (19-58%) and UB (80-42%) have spin quantum numbers of 3 and 3/2, respectively. Experimental V(C-UB) values and those calculated using an INDO-MO method, assuming only the Fermi contact mechanism, are given in Table II. (24-27) It is apparent that the calculations account for the major patterns of substituent effects on /(C-B) and that, if the orbital and dipolar mechanisms are important for these coupling constants,... 

Furthermore, Gunther et al (14) found a result similar to Sojka s (15) when correlating coumarin shifts with n charge densities calculated by the Hiickel MO method (63). This, however, fails for methoxylated coumarins (14) demonstrating that simple charge density - shift relationships are not generally applicable reliably. Ernst (20) reported a linear relationship between fi-methyl substituent effects in unhindered methylated coumarins and the it bond order, P , of the C-a—C-f) bond calculated by the INDO MO method (64) ... 

As has been shown by Ernst (71, 72) for naphthalene derivatives, para SCS can amount up to +10 ppm, and can be correlated linearly with total charge density changes calculated by INDO MO methods. This also seems to hold for 6- and 7-substituted coumarins, because fairly good correlations exist between respective para effects in both molecular systems. Exceptions only occur for 3-carboxycoumarin and 3-hydroxycoumarin, which are probably due to intramolecular hydrogen bridging. Analogous observations are noted in connection with ortho effects. 

A number of MO calculations has been carried out, and these have had mixed success in predicting chemical reactivity or spectroscopic parameters such as NMR chemical shifts and coupling constants. Most early calculations did not take into account the contribution of the sulfur 3d-orbitals to the ground state, and this accounts for some of the discrepancies between calculations and experimental observations. Of the MO methods used, CNDO/2 and CNDO/S have been most successful the INDO approximation cannot be used because of the presence of the sulfur atom. 

Computer programs for the HMO, EH, PPP, CNDO, INDO, MINDO, and ab initio SCF MO methods can be obtained from the Quantum Chemistry Program Exchange, Chemistry Department, Indiana University, Bloomington, Indiana, 47401. 

Several approaches have been made to calculate 13C chemical shifts of coumarins by MO methods. Good correlations were found between the 13C chemical shift values of coumarin (also protonated) and the n charge densities calculated by the CNDO/2 method [962], and of coumarins with it charge densities calculated by the Hiickel MO method (which, however, fails for methoxylated coumarins) [965]. Chemical shifts of mono- and dimethoxycoumarins have been correlated with parameters determined by refined INDO MO calculations, in which n bond orders, atom-atom polarizabilities, excitation energies and electron-nucleus distances were taken into consideration [966], In 3-substituted 4-hydroxy and 4-hydroxy-7-methoxycoumarins chemical shifts were found to be related to Swain and Lupton s parameters iF and M [388], according to equation 5.4 (SE = Substitution Effect) ... 

The non-bonded, through-space transmission of spin information, known as the Barfield transmission effect, has been investigated theoretically for five-membered rings by the FPT-INDO-SCF-MO method.50 An early observation of this effect was the non-equivalence of /endo-endo and exo-exo in norbomanes,51,52 which was also... 

A theoretical calculation of the 15N-13C coupling has been carried out (157) by the sum-over-excited states approach using INDO-MO data. The calculation included the Fermi contact, spin-dipolar, and orbital interactions. For the one-bond coupling, the contact term is shown to be dominant, but there are appreciable contributions from the other terms especially when multiple bonding occurs which explains the lack of a reasonable correlation between /(N-C) and the s-electron contribution to the C-N bond. Calculations using the finite perturbation method, together with INDO data, point to a similar conclusion. (212-214)... 

The original parametrization of these all-valence-electron MO methods was designed to reproduce ab initio Hartree-Fock (HF) results obtained with a minimal basis set. This gives rise to approximate MO treatments which can at best reach the accuracy of the target ab initio HF methods. Prominent examples are the CNDO/2 [13] and INDO [14] methods. 

Numerous semiempirical methods have been used to calculate dipole moments (e g, PPP, CNDO/2, CNDO/S, other CNDO variations, INDO, INDO/S, MNDO, MINDO/3, AMI, HAM3, etc ). They can be divided into 7t-electron and all-valence-electron methods. In u-electron methods such as, e g., the PPP (LCI-SCF-MO) method, only the 7i-component of the dipole moment is obtained and the o-component has to be computed separately. As in the case of empirical methods, one possibility is to calculate the o-component as a vector sum of the individual o-bond and group moments. These values are readily available from several sources [4-6,11,18,19,85] The resulting total (overall) dipole moment is then computed as a vector sum of the TT-moment and the o-moment. 

Summarizing this section, there are a number of semiempirical valence-electron SCF-MO methods that are currently accepted and widely used. A closer inspection of the underlying theoretical models reveals a much smaller variety The MNDO model forms the common basis of several popular methods (MNDO, AMI, PM3, etc.) which are often applied in studies of ground-state potential surfaces (with SINDOl as a possible alternative). Electronic spectra are usually calculated with semiempirical Cl methods specifically designed for this purpose (most notably INDO/S). 

In (16.83), vai is the number of valence electrons in the molecule, V(i) is the potential energy of valence electron i in the field of the nuclei and the inner-shell (core) electrons, and Hvai (0 is the one-electron part of Hyai-TTie CNDO and INDO methods are SCF MO methods that iteratively solve the Roothaan equations using approximations for the integrals in the Fock matrix elements. 

Purely theoretically derived values for ap of and H were obtained by ab initio (UHF) [14 to 16] and semiempirical (INDO) [14] MO methods. Values without spin annihilation seem to agree better with the experimental data [14, 15]. 

The INDO/SDCI method, in which all single excitations over the electronic ir-levels and a limited number of double excitations (more than 16 MOs) were involved. 

Most of the semiempirical MO methods currently used are based on SCF theory and differ in the approximations that are made so as to simplify the evaluation of the two-electron repulsion integrals. The approximations are then corrected for by parametrization, wherein parameters are included in the fundamental protocol to make the results match ab initio calculations on known systems. Examples of these semiempirical methods are CNDO (complete neglect of differential overlap), INDO (intermediate neglect of differential overlap), and NDDO (neglect of diatomic differential overlap). An alternative approach is to parameterize the calculations to optimize agreement with measured molecular properties, such as thermochemical, structural, or spectral data. 

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