Molecular orbitals occupancy

Molecular orbital occupancies in such diatomic molecules predict bond orders and magnetic properties. High bond orders correspond to large dissociation energies and short bond lengths. 

Fig. 1.13 Electron correlation diagrams and ground state molecular orbital occupation for a hydrogen (H2) and b oxygen (O2) molecules. For oxygen, the li orbitals are so low in energy, i.e. so tightly held by their respective nuclei, that they do not contribute significantly to bonding...

In Figure 4-3, the molecular orbital occupancies that arise from the presence of two antibonding 71 electrons are displayed, together with a more complete formulation of the wave-functions for these two electrons. 

FIGURE 11-26 Molecular orbital occupancy diagrams for the homonuclear diatomic molecules of the second-period elements... 

Molecular orbital theory helps us understand some of the previously unexplained features of the O2 molecule. Each O atom brings six valence electrons to the diatomic molecule, O2. In the molecular orbital occupancy diagram... 

EXAMPLE 11-6 Writing a Molecular Orbital Occupancy Diagram and Determining Bond Order... 

Represent bonding in 2 with a molecular orbital occupancy diagram, and determine the bond order in this ion. 

PRACTICE EXAMPLE A Refer to Figure 11-26. Write a molecular orbital occupancy diagram, determine the bond order, and write the electronic configurations of (a) N2 (b) Ne2 (c) 2 . 

PRACTICE EXAMPLE B The bond lengths for 2, O2, 2 , and are 112,121,128, and 149 pm, respectively. Are these bond lengths consistent with the bond order determined from the molecular orbital occupancy diagram Explain. 

Write plausible molecular orbital occupancy diagrams for the following heteronuclear diatomic species (a) NO ... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

The 2 s and the 1 are called occupation numbers. In standard molecular orbital theory, occupation numbers are 0, 1 or 2 and they tell us the occupancy of a given orbital. 

The relative energies of the molecular orbitals available for occupancy by the valence electrons of the second period elements are shown in Figure 3. This order applies at least through N2- ... 

For molecular systems with up to thirty valence electrons, an amplitude of =t0.1 a.u. was chosen for the contour level. For systems with more than thirty valence electrons it was necessary to reduce this value to 0.08 a.u. to maintain the orbital size at a comfortable visual level. The molecular orbitals were normalized to an occupancy... 

FIGURE 3.37 The molecular orbital energy-level diagram for methane and the occupation of the orbitals by the eight valence electrons of the atoms. 

FIGURE 3.40 The molecular orbital energy-level diagram for SFf, and the occupation of the orbitals by the 12 valence electrons of the atoms. Note that no antibonding orbitals are occupied and that there is a net bonding interaction even though no d-orbitals are involved. 

Li, Liu and Lu investigated the electronic structures and the possible aromaticity of some 10 r-electron systems, including the dication, at the HF/6-31G level [118]. The optimised S-S bond length of is 210 pm. Based on the analysis of the bonding characteristics in terms of the canonical molecular orbital and the Foster-Boys localized molecular orbital, they concluded that is of weak aromaticity. This is due to the occupation of the weak antibonding MOs. As a consequence, the bond strengths of the 10 r-electron systems decrease with respect to their 6 r-electron counterparts. 

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