Configuration excited

Let us consider another example. In describmg the n electron pair of an olefin, it is important to mix in doubly excited configurations of the fomi (n ). The physical importance of such configurations can again be made clear by using the identity... 

For /2(Ar)i7, an extensive CI-CSP simulation was carried out, and the results were compared with those of the simple CSP approximation. Both calculations are for the ultrafast dynamics following excitation of the I2 into the B state. We found that the CI-CSP calculation, including doubly excited configurations , is close to converged for times up to t 500 fs, when 1500 configurations are included. Fig. 2 shows co(t)p, the coefficient of the CSP term and the doubly excited terms in the full CI-CSP wavefunction,... 

A single-excitation configuration interaction (CIS) calculation is probably the most common way to obtain excited-state energies. This is because it is one of the easiest calculations to perform. 

The amount of computation for MP2 is determined by the partial transformation of the two-electron integrals, what can be done in a time proportionally to m (m is the number of basis functions), which is comparable to computations involved in one step of CID (doubly-excited configuration interaction) calculation. To save some computer time and space, the core orbitals are frequently omitted from MP calculations. For more details on perturbation theory please see A. Szabo and N. Ostlund, Modem Quantum Chemistry, Macmillan, New York, 1985. 

It follows from this that the excited configurations of C and Si in Equation (7.10) give P, P, D, D, and terms. It follows also that the noble gases, in which all occupied orbitals are filled, have only 5 terms arising from their ground configurations. 

Some excited configurations of the lithium atom, involving promotion of only the valence electron, are given in Table 7.4, which also lists the states arising from these configurations. Similar states can easily be derived for other alkali metals. 

For hydrogen and the alkali metal atoms in their ground configurations, or excited configurations involving promotion of the valence electron, there is only one electron with an unpaired spin. For this electron = - - or — and the corresponding electron spin part... 

Question. From the ground electron configuration of zirconium derive the ground state (i.e. the values of L, S and J) explaining which rules enable you to do this. Then derive the states arising from the excited configuration... 

Just as for atoms, excited configurations of molecules are likely to give rise to more than one state. For example the excited configuration... 

The analogy is even closer when the situation in oxygen is compared with that in excited configurations of the helium atom summarized in Equations (7.28) and (7.29). According to the Pauli principle for electrons the total wave function must be antisymmetric to electron exchange. 

Table 7.8 Ground and excited configurations of some AH2 molecules...

The first excited configuration is obtained by promoting an electron from an e g to an 62 orbital, resulting in... 

The states can be obtained in a similar way to those for the excited configuration of N2 in Equation (7.76). The symmetry species of the orbital part of the electronic wave... 

Including triply excited configurations is often needed in order to obtain very accurate results with MP4, QCISD or CCSD (see Appendix A for some of the computational details). The following example illustrates this effect. 

Table 4.2 Weights of excited configurations for the Neon atom...

It can clearly be seen that the CISD curve is worse than either of the other two, which are essentially identical out to a AR of 1.3 A. The size inconsistency of the CISD method also has consequences for the energy curve when the bond is only half broken. Figure 11.11 illustrates why the use of Cl methods has declined over the years, it normally gives less accurate results compared with MP or CC methods, but at a similar or Irigher computational cost. Furthermore, it is difficult to include the important triply excited configurations in Cl methods (CISDT scales as M ), but it is relatively easy to include them in MP or CC methods (MP4 and CCSD(T) scales as M ). 

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