CNDO approximation

Charge diagrams for 2-aminothiazole and 2-imino-4-thiazoline, calculated using HMO. PPP, and CNDO approximations, are illustrated in Fig. VI-1. When compared to Table 1-2 for thiazole itself it appears that the... 

The CNDO/INDO, MINDO/3, Z3NDO/1, and ZINDO/S methods might be expected to imply an even simpler equation for the electron density than the above. For example, a rigorous complete neglect of CNDO approximation, suggests that equations (87) and (88) should be replaced by expressions with a sum only over diagonal elements of the density matrix. This would represent a molecular charge density that is the exact sum of atomic densities. Alter-... 

The most complete discussion of the electrophilic substitution in pyrazole, which experimentally always takes place at the 4-position in both the neutral pyrazole and the cation (Section 4.04.2.1.1), is to be found in (70JCS(B)1692). The results reported in Table 2 show that for (29), (30) and (31) both tt- and total (tt cr)-electron densities predict electrophilic substitution at the 4-position, with the exception of an older publication that should be considered no further (60AJC49). More elaborate models, within the CNDO approximation, have been used by Burton and Finar (70JCS(B)1692) to study the electrophilic substitution in (29) and (31). Considering the substrate plus the properties of the attacking species (H", Cl" ), they predict the correct orientation only for perpendicular attack on a planar site. For the neutral molecule (the cation is symmetrical) the second most reactive position towards H" and Cl" is the 5-position. The activation energies (kJmoF ) relative to the 4-position are H ", C-3, 28.3 C-5, 7.13 Cr, C-3, 34.4 C-5, 16.9. 

In the Complete Neglect of Differential Overlap (CNDO) approximation only the Coulomb one-centre and two-centre two-electron integrals remain (eq. (3.78)). 

The integrals are again parameterized as in eq. (3.79). The approximations for the one-electron integrals in CNDO are the same as for INDO. The Pariser-Pople-Parr (PPP) method can be considered as a CNDO approximation where only 7r-electrons are treated. 

There are three methods that can be used for transforming the NDDO/INDO/CNDO approximations into working computational models. 

In the Roothaan method, within the CNDO approximation the elements of the F matrix and of various matrices contributing to the F matrix are (68) ... 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

Fig. 12 shows that, within the CNDO approximation, the X-ray conformation is no longer adopted in solution. In fact, the complex oscillates around the S conformation (Fig. 13) from the gauche C to the symmetrical C conformation (Fig. 14). A close look at this motion indicates that it may be decomposed into a simultaneous...

Upon optimizing the full set of geometrical parameters for H2N—PH2 within the CNDO approximation, we observed (92) that Csizmadia s assumption actually leads to a planar N structure with HPH = HPN = 90° (in agreement with the 97° value provided by ab-initio calculation). If, on the other hand, the assumption in question... 

When starting from the X-ray structure of SOAz(I), we computed the total energy upon the rotation through 360° of the Az group linked to S around the S—Nexo bond (Fig. 65) within CNDO approximation. This figure calls for the following remarks. 

The next step to reach to our aims is to determine the localized molecular orbitals of the anionic group. Of course, there are many methods available for the calculations of molecular orbitals in our theory, such as the various approximation methods and even the recently developed Dv-Xa method discussed in quantum chemistry. But, in view of the nature of the basic assumptions in our theory, the CNDO approximation seems to be suitable for calculations of SHG coefficients when the anionic groups consist of elements from the first, second and third families in the periodic table. EHMO type approximations are suitable for other elements, particularly if transition metal elements take part in the ionic groups or molecules. It is not necessary to use higher approximations. 

Finally it may be shown that under the CNDO approximation, the total energy of a molecule can be expressed as a sum of one- and two-atom terms... 

Both terms, however, are dependent on the total charge density of the atom. It is not surprising, therefore, that 13C shifts of atoms in conjugated molecules vary approximately linearly with the jr-electron density at the atoms (<513C= 160 Aq71). Of the available all-valence electron methods, chemical shifts have been calculated only by the CNDO approximation. 

The third fundamental hypothesis of the CNDO approximation concerns the core matrix elements H. These correspond to the and parameters of the Pariser-Parr-Pople method, the core including here only the Is electrons and the nuclei. 

So far we were concerned with the electronic (quantum) part of the energy in the CNDO approximation. The classical part of the energy describing the interactions between the cores, which are not treated explicitly in the CNDO methods, takes the form ... 

The atomic quantities ShA are equal to the perturbations Shaa of the corresponding core Hamiltonian matrix elements in the ligand AO basis. This is so because within the CNDO approximation [74] accepted in [58], for the description of the /-system, the quantities 6haa are the same for all aeA. 

There is a zero first-order contribution to the energy. The use of the CNDO approximation considerably simplifies the terms arising in these expansions and gives terms with a clear physical significance. These may be summarized as follows ... 

The CNDO approximation limits these terms to only two. 

Each term leads to a simple contribution to the energy.151 The whole scheme is therefore fairly compact and, since there is no diagonalization, it is faster than the usual SCF approach using the CNDO approximations. It must be noted that even a simple extension from CNDO to INDO integrals increases the number of contribut- ... 

A recent report (62). using CNDO approximations, describes and interprets the photoelectronic spectra of A-4-thiazoline-2-thione and other thiocarbonyl heterocvcles. The results are given in Table VII-3. The major feature is the clean separation between the two highest MOs and the others. The highest MO of tt symmetry (7.74 eV) is essentially localized on the dithiocarbamic part of the structure. The second one (8.12 eV) is highly localized on the exocvclic sulfur atom. This peculiarity... 

Weider, D., and U. Sherz (1985). Self-consistent-field cluster calculations of nickel (2 -I-) centers in cubic zinc sulfide, cadmium sulfide, and zinc sele-nide in the CNDO approximation. Phys. Rev. B32, 5273-79. 

PPP) method can be considered as a CNDO approximation where only rr-electrons are... 

Quantum mechanical calculations of molcular orbitals have been performed on five examples (8-azapurine, -hypoxanthine, -guanine, -adenine, and -xanthine) by two methods (a) a semiempirical approximation, which included contributions from the a electrons of the skeleton, and (b) the CNDO approximation, which included contributions from all the valence electrons of the molecule. The results were tabulated in parallel for each of the three possible positions of the triazole proton. In all 15 entries, the highest occupied and the lowest unoccupied molecular orbitals were calculated and also the dipole moment, the molecular energy, and the UV absorption maxima (the last-named showed only a modest agreement with experimental results). It was concluded that both types of calculation indicated that relative stabilities for the three tautomers (in each of the five sets) should decrease in the order HN-9, HN-7, and HN-8, and that the HN-8 tautomers should be 85 to 125 kJ (20-30 kcal) per mol less stable than the other two. However, it had to be admitted that, in all sets of three isomers examined experimentally, the HN-8 member has never been found inferior in stability. ... 

---