Completely Neglected Differential Orbital

Based on the idea of orbital electronegativity introduced by Hinze-Whitehead-Jaffe, in 1981 Ponec had introduced the orbital electronegativity based on the semiempirical approximation CNDO ( complete neglecting differential overlapping , the complete neglect of the differential-orbital overlap even for the orbitals belonging to the same atom) (Ponec, 1981). 

Ihc complete neglect of differential overlap (CNDO) approach of Pople, Santry and Segal u as the first method to implement the zero-differential overlap approximation in a practical fashion [Pople et al. 1965]. To overcome the problems of rotational invariance, the two-clectron integrals (/c/c AA), where fi and A are on different atoms A and B, were set equal to. 1 parameter which depends only on the nature of the atoms A and B and the ii ilcniuclear distance, and not on the type of orbital. The parameter can be considered 1.0 be the average electrostatic repulsion between an electron on atom A and an electron on atom B. When both atomic orbitals are on the same atom the parameter is written , A tiiid represents the average electron-electron repulsion between two electrons on an aiom A. 

Invariant Procedures. Journal of Chemical Physics 43 S129-S135. pie J A and G A Segal 1965. Approximate Self-Consistent Molecular Orbital Theory. II. Calculations with Complete Neglect of Differential Overlap. The Journal of Chemical Physics 43 S136-S149. iple J A and G A Segal 1966. Approximate Self-Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 systems. Journal of Chemical Physics 44 3289-3296. 

The complete neglect of differential overlap (CNDO) method is the simplest of the neglect of differential overlap (NDO) methods. This method models valence orbitals only using a minimal basis set of Slater type orbitals. The CNDO method has proven useful for some hydrocarbon results but little else. CNDO is still sometimes used to generate the initial guess for ah initio calculations on hydrocarbons. 

Pople JA, Segal GA. Approximate self-consistent molecular orbital theory. II. Calculations with complete neglect of differential overlap. J Chem Phys 1965 43 S136-49. 

A method which is similar to the Pariser-Parr-Pople method for the n electron system and is applicable to common, saturated molecules has been proposed by Pople 28>. This method is called the CNDO complete neglect of differential overlap) SCF calculation. Katagiri and Sandorfy 29> and Imamura et al. °) have used hybridized orbitals as basis of the Pariser-Parr-Pople type semiempirical SCF calculation. 

The simplest theory that is consistent with these requirements employs the complete neglect of differential overlap (CNDO)29. This semi-empirical approach will be discussed in some detail, albeit without extensive mathematical justification, as it illustrates the type of approximations that are made in more advanced theories. In addition to the assumptions outlined above, the remaining Coulomb-type integrals are reduced to a single value -yAB that depends only on the nature of atoms A and B with which < > and t are associated, respectively, and not on the actual type of orbitals that overlap. This is equivalent to stating ... 

Various theoretical methods (self-consistent field molecular orbital (SCF-MO) modified neglect of diatomic overlap (MNDO), complete neglect of differential overlap (CNDO/2), intermediate neglect of differential overlap/screened approximation (INDO/S), and STO-3G ab initio) have been used to calculate the electron distribution, structural parameters, dipole moments, ionization potentials, and data relating to ultraviolet (UV), nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), photoelectron (PE), and microwave spectra of 1,3,4-oxadiazole and its derivatives <1984CHEC(6)427, 1996CHEC-II(4)268>. 

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

The CNDO procedure proposed and developed by Pople and his co-workers 5 61), as well as a number of its variants, are characterized by the assumption of vanishing overlap between basis set orbitals (CNDO = Complete Neglect of Differential Overlap), which reduces the number of non-zero two electron integrals drastically. Various other approximations and modifications had to be introduced... 

Complete neglect of differential overlap Constrained space orbital variation (analysis)... 

On the basis of complete neglect of differential overlap (CNDO/2) calculations which include silicon p and d orbitals in the basis set, the effect of the trimethylsilyl substituent is due to electron withdrawal by the interaction of both the silicon p and d orbitals with the aromatic ir-system (85). In as much as the silicon p orbitals are primarily involved in the cr and cr orbitals of the trimethylsilyl group, interaction of the silicon p orbitals with the ir-system amounts to a hyperconjugative, v — cr, electron withdrawl (85). 

Polarizability-Kow Relationships Molar polarizabilities can be derived from molecular orbital (MO) calculations by the complete neglect of differential overlap (CNDO) method [42]. The following correlation has been found for polar compounds that contain either hydrogen-bond-accepting or hydrogen-bond-donating groups (alkanols, alkanones, dialkyl ethers, alkanenitriles) ... 

Baetzold used extended Hiickel and complete neglect of differential overlap (CNDO) procedures for computing electronic properties of Pd clusters (102, 103). It appeared that Pd aggregates up to 10 atoms have electronic properties that are different than those of bulk palladium. d-Holes are present in small-size clusters such as Pd2 (atomic configuration 4dw) because the diffuse s atomic orbitals overlap strongly and form a low-energy symmetric orbital. In consequence, electrons occupy this molecular orbital, leaving a vacant d orbital. For a catalytic chemist the most important aspect of these theoretical studies is that the electron affinity calculated for a 10-atom Pd cluster is 8.1 eV. This value, compared to the experimental work function of bulk Pd (4.5 eV), means that small Pd clusters would be better than bulk metal as electron acceptors. 

HOMO = highest occupied molecular orbital. 6LUMO = lowest unoccupied molecular orbital. CEH = extended Huckel (calculations). dCNDO = complete neglect of differential overlap. efcc = face-centered cubic. 

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