Molecular orbital method overlap

Qualitatively, the resonance picture is often used to describe the structure of molecules, but quantitative valence-bond calculations become much more difficult as the structures become more complicated (e.g., naphthalene, pyridine, etc.). Therefore the molecular-orbital method is used much more often for the solution of wave equations.5 If we look at benzene by this method (qualitatively), we see that each carbon atom, being connected to three other atoms, uses sp1 orbitals to form a bonds, so that all 12 atoms are in one plane. Each carbon has a p orbital (containing one electron) remaining and each of these can overlap equally with the two adjacent p orbitals. This overlap of six orbitals (see Figure 2.1) produces six new orbitals, three of which (shown) are bonding. These three (called it orbitals) all occupy approximately the same space.6 One of the three is of lower energy than... 

A promising semi-rigorous molecular orbital method, PRDDO, partial retention of diatomic differential overlap has been reported in the interim [186]. Also, the method of diatomics-in-molecules has been revived and the derivations extended to include p orbitals appropriately [187]. 

Mention should be made here of a series of recent papers by Pople and coworkers on self-consistent molecular-orbital methods in which they use mainly small optimized sets of Gaussian orbitals as fits to STOs or energy-optimized atomic orbitals to study a wide variety of molecules, including triatomics [123-130]. (One of the papers [124] also discusses a variant of a semirigorous technique, PDDO (projection of diatomic differential overlap).)1... 

An approximate (non-SCF) molecular-orbital method involving extensive parametrization of the required integrals and with the overlap integral represented as a simple product of radial and angular terms... 

In the molecular-orbital method, bonding is considered to arise from the overlap of atomic orbitals. When any number of atomic orbitals overlap, they combine to... 

The first of the zero differential overlap (ZDO) methods was the simple tt-electron method due to Htickel. Historically this method was very important in that it showed rather quickly that molecular orbital methods that... 

M. D. Newton, N. S. Ostiund, and J. A. Pople, /. Chem. Phys., 49, 5192 (1968), Projection of Diatomic Differential Overlap Least-Squares Projection of Two-Center Distributions onto One-Center Functions. M. D. Newton, /. Chem. Phys., 51, 3917 (1969). Self-Consistent Molecular-Orbital Methods. 11. Projection of Diatomic Differential Overlap (PDDO). M. D. Newton, W. A. Lanthan, W, J. Hehre, and. . A. Pople,/. Chem. Phys., 51, 3927 (1969). Self-Consistent Molecular-Orbital. Methods. 111. Comparison of Gaussian Expansion and PDDO Methods Using Minimal STO Basis Sets. 

In order to estimate actual bond energies by using the overlap criterion one usually uses the molecular-orbital method. Hence, we shall return to this matter again after the molecular-orbital method has been introduced. 

Robert S. Mulliken (United States) for his fundamental work concerning chemical bonds and the electronic structure of molecules by the molecular orbital method. Mulliken received the Nobel Prize in recognition of his work studying that nature of how electrons behaving in molecules, in particular for the molecular orbital approach that he developed. Molecular orbitals are formed by the overlap of the orbitals on individual atoms, and these can be used to rationalize whether bonds will exist between pairs of atoms, how strongly the pairs will be bonded, and what type of reactivity the molecule may be expected to undergo. 

The molecular orbital method is a very flexible and often successful tool for analyzing electronic structure-dependent properties. Its deficiencies are intimately connected with the treatment of superpositions of configurations. In particular, the molecular orbital model is not satisfactory when the overlap between relevant valence orbitals on adjacent atoms is smaller than 1/2. This result was particularly well illustrated by Coulson and Fischer in their well-known study of the hydrogen molecule, and it is relevant for the molecular orbital treatment of TT-electron systems, where the typical overlap is in the range 1/3-1/4. Evidence has also been presented for the insufficiency of the PPP-model when... 

EHT, extended Huckel theory CNDO, complete neglect of differential overlap INDO, intermediate neglect of differential overlap NNDO, neglect of diatomic differential overlap SCF, self-consistent field MINDO, modified INDO ab initio, without the use of independently derived parameters. For an independent assessment of the different molecular orbital methods applied to carbocations, see Ref. 3. 

An alternative strategy was to develop methods wherein the two-electron integrals are parameterized to reproduce experimental heats of formation. As such, these are semi-empirical molecular orbital methods—they make use of experimental data. Beginning first with modified INDO (MINDO/1, MlNDO/2, and MINDO/3, early methods that are now little used), the methodological development moved on to modified neglect of diatomic differential overlap (MNDO). A second MNDO parameterization was created by Dewar and termed Austin method 1 (AMI), and finally, an "optimized" parametrization termed PM3 (for MNDO, parametric method 3) was formulated. These methods include very efficient and fairly accurate geometry optimization. The results they produce are in many respects comparable to low-level ab initio calculations (such as HF and STO-3G), but the calculations are much less expensive. 

The mechanism of Si-O chemical bonding was analyzed for covalent and ionic bond orders in p- and Y-C2S. Each bond order was evaluated by an overlapping population calculated by the DV-Xa molecular orbital method (Xiuji et al. 1994). There are slight differences in computed covalent and ionic bond orders obtained for both dicalcium silicates. However, Xiuji et al. (1994) demonstrated that the differences in hydraulic activity between p- and Y-C2S do not arise from the difference of Si-O chemical bonding. Further investigation will be required to establish the relationship between these differences in the crystal structure to hydraulic activity of belite. 

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