First excited state configuration

Table 1. Ground state and first excited state configurations, and their energy difference, for lanthanides and actinides...

An important property of determinants is that a multiple of any column can be added to another column without altering the value of the determinant. This means that the spin orbitals are not unique other linear combinations give the same energy. To illustrate this, consider the first excited state configuration of the helium atom (ls 2s ), which can be written as the following 2x2 determinant ... 

The coefficients indicate the composition of the electronic state in terms of a linear combination of the various electronic configurations defined earlier in the output. Here is an example from a 4,4 CAS showing the first two excited state configurations ... 

Inspection of Table 2 reveals that all those molecules that suffer a molecular-symmetry reduction in the ground state possess (E2 — E1) values considerably larger than the critical value, so that they should have a fully-symmetrical nuclear configuration in their first excited states. On the other hand, there are cases where a molecule has an ( , — Eg) value significantly higher than the critical value, but has a relatively smaller (Ej— i) value. The ( 2 i) value of the pentalene dianion (I ) is of the same order of magnitude as the critical value and those for the peri-condensed nonalternant hydrocarbon, XVII, the fulvalenes, XXI, XXII and XXIII, and the dianions, IVand VII are significantly smaller than the critical value ( 0.6eV). 

Fig. 13 Qualitative molecular orbital energy level diagram of the dimer d orbitals with the 14 electrons showing the electronic configuration 525 27i47i 4o2 (singlet) and the first excited state 828 2it4it 4a1CT 1 (triplet)...

In a recent comprehensive study at the CASSCF level of ab initio theory, Cave and lohnson have carried out calculations for all six rotamers of the hexatriene radical cation. In agreement with experiment they found that the first excited state is hardly affected by the additional interactions which prevail in partially cA-configurated rotamers, whereas the energy of the second excited states decreases as the number of those cA-interactions increases. On this basis, they were able to confirm some of the original assignments of the observed spectra305 but proposed revisions for some of the others. 

Figure 9.16 Schematic representation of the excitation of an electron from a vibrational level in a ground-state configuration to vibrational levels in the first excited state. The ground-state electron can have any vibrational sub-state (a) v" = 0 (b) v" = 1 (c) v" = 2 (d) v" = 3...

The configuration of six n elections in the ground and the first excited state is as follows ... 

Next, we assume that this expansion can be safely limited to the first two terms for the ground state vl/j and the first excited state 2- For the nuclear configuration where the energy difference ... 

Write the electron configuration and draw an orbital diagram to show the first excited state of a sodium atom. Assume that the outermost electron is excited. 

The geometric limitation for migration with retention of configuration should be lifted in the first excited state of the homotropenylium ions. Childs and Rogerson showed that this was indeed the case and reported a number of examples where photochemically induced circumambulations take place. An example is given in Scheme 27164. 

The fact that these HOMOs and LUMOs have a two-fold degeneracy implies that there are four isoenergetic one-electron transitions to yield the first excited states this complication is however resolved by the interaction of these one-electron excitations, and this is known as configuration interaction. The concept of configuration interaction (Cl) is somewhat similar to that of the interaction of atomic orbitals to form molecular orbitals. An electron configuration defines the distribution of electrons in the available orbitals, and an actual state is a combination of any number of such electron configurations, the state wavefunction being... 

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