Wave function molecular orbital

The coefficients indicate the contribution of each atomic orbital to the molecular orbital. This method of representing the molecular orbital wave function in terms of combinations of atomic orbital wave functions is known as the linear combination of atomic orbitals approximation (LCAO). The combination of atomic orbitals chosen is called the basis set. 

The following presentation is limited to closed-shell molecular orbital wave-functions. The first section discusses the unique ability of molecular orbital theory to make chemical comparisons. The second section contains a discussion of the underlying basic concepts. The next two sections describe characteristics of canonical and localized orbitals. The fifth section examines illustrative examples from the field of diatomic molecules, and the last section demonstrates how the approach can be valuable even for the delocalized electrons in aromatic ir-systems. All localized orbitals considered here are based on the self-energy criterion, since only for these do the authors possess detailed information of the type illustrated. We plan to give elsewhere a survey of work involving other types of localization criteria. 

The equations for the bonding and anti-bonding molecular orbital wave functions for the linear combinations of the two Is atomic orbitals of the two hydrogen atoms may now be written in the forms ... 

It has not proved mathematically feasible to calculate the electron-electron repulsion that causes this change in orbital-energies for many-electron molecules. It is even difficult to rationalize the qualitative changes in sequence on the basis of the shapes of the 11orbitals. Greater success has been achieved by an approximate method which begins with orbitals characteristic of the isolated atoms present in the molecule, and assumes that molecular orbital wave functions can be obtained by taking linear combinations of atomic orbital wave functions (abbreviated L.C.A.O.). For... 

Contribution /x of ionic terms calculated with best screening constant of — curve 1 a molecular orbital wave function curve 2 a Heitler-London wave function curve 3 atomic orbitals. 

P. C. Hiberty, C. Leforestier, J. Am. Chem. Soc. 100, 2012 (1978). Expansion of Molecular Orbital Wave Functions into Valence Bond Wave Functions. A Simplified Procedure. 

Descriptors Based on Molecular Orbital Wave Functions and Energies (Section IV.F)... 

Mulliken, R.S., Criteria for the construction of good self-consistent-field molecular orbital wave functions, and the significance of L.A.A.O.M.O. population analysis, J. Chem. Phys., 36, 3428-3439, 1962. 

Just as atomic orbitals are solutions to the quantum mechanical treatment of atoms, molecular orbitals (MOs) are solutions to the molecular problem. MOs have many of the same characteristics as atomic orbitals. Two of the most important are (1) they can hold two electrons with opposite spins and (2) the square of the molecular orbital wave function indicates the electron probability. 

It will be recalled that the transformation to localized orbitals leaves the molecular orbital wave function, charge density and all other ground state properties completely unchanged. The relationship between LMOs, which are convenient for describing bonding and the CMOs, which give a zeroth order description of the one-electron ion states, was described in the last section. 

We wish to compare the valence band density of states (DOS) of f.c.c. and h.c.p. metals with and without stacking faults. We therefore adopt a mixture of the f.c.c. and h.c.p. structures as a representative of the stacking fault structure of either of these structures. To calculate the DOS we summed up the squares of the coefficients of molecular orbital wave functions and convoluted the summed squares with the Gaussian of full width 0.5 eV at half maximum. For these DOS calculations we chose the metals Mg, Ti, Co, Cu and Zn. The model clusters employed here for both the f.c.c. and the h.c.p. structures were made of 13 atoms i.e., a central atom and 12 equidistant neighbor atoms. These structures are shown in Fig. 1. We reproduced the typical electronic structures in bulk materials by extracting the molecular orbitals localized only on the central atom from all the molecular orbitals which contributed - those localized on ligand atoms as well as on the central atom. To perform calculations we take the symmetry of the cluster as C3, and the number... 

If H denotes the total Hamiltonian of the H2 molecule, CF found A as a function of the internuclear distance R by minimizing < H > with respect to the wave function (24). Their findings were (a) for R <. 6Requiiibrium, A = 1 (b) for R > 1.6 Requilibriums A falls quite rapidly to zero as the H2 molecule is stretched further. For A = 1, Eq. (24) is the molecular orbital wave function built as a linear combination of atomic orbitals, whereas for R > 1.6 ReqUiiibrium one sees that electrons quickly go back on to their own atoms . 

The most-favored positions and orientations of water molecules around a solute can be determined by the use of electrostatic potentials. The electrostatic potential, evaluated from some molecular orbital wave function, is used to estimate the electrostatic interaction energy (e,) be-... 

Spin-Orbit Matrix and Electric Field Gradient Tensor Derived from Many-Electron Molecular Orbital Wave Functions... 

A molecular orbital wave function for the bond between H and Cl in HCl, constructed, assuming that the bond is formed from the Is electron of H atom and a 3p electron of Cl atom ... 

The molecular orbital wave function for II2- molecule anion ... 

Where y 1V2. .. are one electron molecular orbital wave functions. according to equation (1) we have... 

Atomic orbitals Molecular orbitals Wave function Symbol... 

Nitrogen-14 nuclear quadrupole coupling constants in oxazole have been calculated by using the complete neglect of differential overlap method (CNDO/2) including all the valence electrons,232 and from ab initio molecular-orbital wave functions using Gaussian basis sets.234... 

What is a molecular orbital wave function How does it differ from a valence bond wave function ... 

The author of [73] deduced a physical model of the hydrogen bond from ah initio molecular orbital wave functions. The characteristic of the model are as follows the dipole moment of the A-H bond /Ta-h ) the difference between the first ionization potential of the electron donor and the noble gas in its row of the Mendeleev Table A / the length R of the hydrogen bonding lone pair. A number of characteristic of the intermolecular strength can be described in terms of these quantities. 

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