Atoms orbital occupation

Mulliken population analysis. This treatment shows how a molecule under investigation distributes electrons according to the atomic orbital occupancy. Note that the overlap population between two atoms is divided evenly between them without consideration of possible differences in atom types, electronegativities, and so on. 

This then gives the singlet and triplet states in terms of atomic-orbital occupancies where it is easier to see the energy equivalences and differences. 

Notice that all three triplet states involve atomic orbital occupancy in which one electron is on one atom while the other is on the second carbon atom. In contrast, the singlet state places both electrons on one carbon (it contains two terms one with the two electrons on the left carbon and the other with both electrons on the right carbon). 

The first two of these atomic-orbital-based Slater determinants ( sx a sx (3 and sy a sy (3 ) are denoted "ionic" because they describe atomic orbital occupancies, which are appropriate to the R —> °° region, that correspond to X S + Y and X + Y valence bond structures, while sx a sy (3 and sy a sx (3 are called "covalent" because they correspond to X + Y structures. 

Now let us inquire into the physical meaning of the two conditions Hu -H22 and H12 (= H21) = 0. If we consider the basis (< )1 and 2) of the secular equation (Eq. [2]) as the diabatic components of the adiabatic electronic eigenfunction (a diabatic function describes the energy of a particular spin-coupling or atomic orbital occupancies,14 while the adiabatic function represents the surface of the real state), the crossing condition (real or avoided) is fulfilled when the two diabatic components and ( >2 cross each other, and this happens when H11 = H22, that is, when the energy of the two diabatic potentials (H11 is... 

Selected Natural Atomic Orbital Occupancies of re-Type Orbitals Calculated by Natural Orbital Population Analysis"... 

Mulliken-type populations are a useful tool when it comes to analysing the charge and spin distribution in a molecule or solid. However, one must bear in mind that there is rigorously no such thing as an atom in a molecule or in a crystal, and thus such analysis must be viewed somewhat critically. Especially when atomic orbitals are very diffuse, their Mulliken-type populations may not be very realistic. On the other hand, the Mulliken analysis has the advantage that individual atomic orbital occupations may be obtained. 

The first thorough examination of the population analysis problem has become the most widely used method. In 1955 Robert MuIIiken outlined the procedure for obtaining atomic and orbital populations that now bears his name—MuIIiken population analysis. - MuIIiken analysis distributes electrons according to the atomic orbital occupancy. 

Spin properties are notoriously difficult to calculate accurately57. Here, we are actually calculating spin populations, with their intrinsic uncertainties, and not the directly observed hyperfine interactions. On the other hand, analyses of the hyperfine interactions in the ESR spectra to give experimental atomic orbital occupancies for the radical electron are based on a simplistic, rigid linear combination of atomic orbitals (LCAO)-MO model with the reference electron-nuclear coupling parameters taken from the free atom. No allowance is made for radial or angular polarization of the atomic orbitals in the molecular environment. Thus agreement at these levels between calculated and experimental values can only be qualitative, at best. 

In Figure 3-2, the Is atomic orbital occupations for A -B and A- B are displayed for the helium molecule ion, Hc2. Because each of these valence-bond stmctures has only one unpaired electron, Pauling deduced that the length and... 

If a Heitler-London description of the C-0 7i-bond is used, the 5 = 0 spin ground-state configuration involves the atomic orbital occupancies of (7tc) (7to) (n)% with antiparallel spins for the and tIq electrons. When an n electron is excited, either one of the or orbitals becomes doubly-occupied to generate (7tc) (7to) (n) and (7tc) (7to) (n) configurations. Ignoring electron spins, the resulting valence-bond stmctures are... 

The ionization energy, electron affinity, and orbital occupancy determine the chemical behavior, or reactivity, of the elements. The uppermost (high-est-energy) occupied orbitals are called the valence orbitals the electrons occupying them are the valence electrons. An element s ionization energy, the energy required to remove an electron from a neutral atom, is related to its reactivity A low ionization energy means that the valence electron is readily removed, and the element is likely to become involved in... 

Figure 16-3D shows the simplified representation of the interaction of two helium atoms. This time each helium atom is crosshatched before the two atoms approach. This is to indicate there are already two electrons in the Is orbital. Our rule of orbital occupancy tells us that the Is orbital can contain only two electrons. Consequently, when the second helium atom approaches, its valence orbitals cannot overlap significantly. The helium atom valence electrons fill its valence orbitals, preventing it from approaching a second atom close enough to share electrons. The helium atom forms no chemical bonds. ... 

A fluorine atom has the orbital occupancy shown below ... 

The experimental quantities shown in (14) and (15) indicate that the F ion is more stable than a fluorine atom and an electron. Energetically, a fluorine atom wants" another electron. It is profitable to express reaction (12) in terms of orbital occupancy ... 

Remember the spatial arrangement of the p or- atom has partially filled valence orbitals. Elec-bitals Each one protrudes along one of the tron sharing can occur, placing electrons close three cartesian axes (as shown in Figure 15-9). to two nuclei simultaneously. Hence a stable If the electrons have the orbital occupancy of bond can occur. This is shown in representations 20), then two electrons occupy the p orbital (22) and (23). 

There are a number of orbital occupancies that we might consider for the carbon atom ... 

The boron atom presents the same sort of option in orbital occupancy as does carbon ... 

The analytical determination of the derivative dEtotldrir of the total energy Etot with respect to population n, of the r-th molecular orbital is a very complicated task in the case of methods like the BMV one for three reasons (a), those methods assume that the atomic orbital (AO) basis is non-orthogonal (b), they involve nonlinear expressions in the AO populations (c) the latter may have to be determined as Mulliken or Lbwdin population, if they must have a physical significance [6]. The rest of this paper is devoted to the presentation of that derivation on a scheme having the essential features of the BMV scheme, but simplified to keep control of the relation between the symbols introduced and their physical significance. Before devoting ourselves to that derivation, however, we with to mention the reason why the MO occupation should be treated in certain problems as a continuous variable. 

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