Aufbau method

At the start of the 1960s, priorities centred on postulating and testing new structural principles for polymers. One approach, other than the classical polymerization methods, was that of oxidative coupling. By this technique, copper chloride and aluminium chloride were used to make an oligobenzene from benzene [Ic]. This reaction was systematically extended and became established as the general aufbau method of synthesizing polyaro-matics and polyheterocycles [la]. 

In an Extended Hiickel calculation, the Aufbau population of molecular orbitals is unambiguous. The calculation method is non-iterative and the total energy is proportional to the sum of the energies of occupied orbitals. The Aufbau guarantees the lowest energy wave function. 

Figure 7-2 One method of remembering the pattern for filling the atomic orbitals (Aufbau principle)...

Standard wavefunction methods (i.e., other than DFT), which have been extensively applied both to the computation of vertical (i.e., at ground state equilibrium geometry) excitation energies and excited state reaction paths are the current preferred method for applications in this field. Wavefunction methods that are used in studying photochemical mechanisms are limited to those that can describe excited states correctly. Unfortunately, standard methods for the evaluation of the ground state PES such as SCF and DFT cannot describe excited states because they are restricted to the aufbau principle. 

All three methods require knowledge of the subshells occupied by electrons in a certain atom. The Aufbau principle or building-up rule states that electrons at ground state fill orbitals starting at the lowest available energy levels. 

The second method uses what is often called the Aufbau chart. You can easily produce this from memory by constructing it as follows ... 

Abb. 5-6 Emissions-Probenahmeapparatur nach der LAGA-Methode (Aufbau Beheizter Filter, Kiihler, Impinger) [Liitzke 1987]... 

Although the aufbau approach of MO theory is adequate in all that follows, it may be useful for the sake of completeness to mention the rather more complicated method developed by Heitler, London, Slater, Pauling and others, and to stress that the two theories do not conflict. Both lead to approximations to the same charge density the difference is superficial and the same Fcynman-Hellman interpretation applies in each case. To appreciate this, it is sufficient to consider the molecule Hg. From the MO standpoint, the full two-electron wave function would be the product... 

We can combine the LCAO method for with an aufbau principle, analogous to that developed for atoms, to describe the electron configuration of more complex molecules. Electrons available from the two atoms are fed into the MOs, starting with the MO of lowest energy. At most, two electrons can occupy each MO. The ground-state H2 molecule, therefore, accommodates two electrons with opposite spins in a a-gu bonding MO (Fig. 6.10). The diatomic molecule is more stable than the isolated atoms by the energy difference — 2AE. 

In our own work,33 that we here shall discuss briefly, we used the embedded-atom potential together with the Aufbau/Abbau method of Section 2.8 in optimizing the structure. The stability function, A2E(N), Eq. (50), is shown in Figure 18. It shows a set of peaks that correspond to particularly stable clusters. It is interesting to notice that if one instead studies the total-energy difference... 

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