Singlet and triplet

The ground state wave function is assumed to be a Slater determinant (indicated by bars) and is written as 

The replacement of cf) by t[)j in a Slater determinant can be done either in a spin-up or in a spin-down spin orbital. The orbitals that are the same in the ground state and excited state are denoted as (occ). Two different Slater determinants are obtained and, subsequently, linear combinations may be formed between the two possible Slater determinants. We obtain new electronic states  

Additionally, there are two excited triplet states with spin flip  

In Equations 3.58 and 3.59, we change the order between the last two MOs and obtain 

It is easy to show that Equations 3.60, 3.61, and 3.63 are triplet states and that Equation 3.62 is a singlet state. 

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The perturbations in this case are between a singlet and a triplet state. The perturbation Hamiltonian, H, of the second-order perturbation theory is spin-orbital coupling, which has the effect of mixing singlet and triplet states. 

Similar to the fullerene ground state the singlet and triplet excited state properties of the carbon network are best discussed with respect to the tliree-dimensional symmetry. SurjDrisingly, the singlet excited state gives rise to a low emission fluorescence quantum yield of 1.0 x 10 [143]. Despite the highly constrained carbon network,... 

Figure 2-55. Singlet and triplet carbenes are easily distinguished in RAMSES notation.

We substitute these expressions into the Slater determinants that form the singlet and triplet states and eolleet terms and throw out terms for whieh the determinants vanish. 

This then gives the singlet and triplet states in terms of atomie-orbital oeeupaneies where it is easier to see the energy equivalenees and differenees. 

To generate the proper A, A2, and E wavefunetions of singlet and triplet spin symmetry (thus far, it is not elear whieh spin ean arise for eaeh of the three above spatial symmetries however, only singlet and triplet spin funetions ean arise for this two-eleetron example), one ean apply the following (un-normalized) symmetry projeetion operators (see Appendix E where these projeetors are introdueed) to all determinental wavefunetions arising from the e eonfiguration ... 

To simplify the analysis of the above CSFs, the familiar homonuelear ease in whieh z = 1.0 will be examined first. The proeess of substituting the above expressions for a and a into the Slater determinants that define the singlet and triplet CSFs ean be illustrated as follows ... 

The latter rule is rigidly obeyed in the observed spectrum of helium. From the accurately known energy levels it is known precisely where to look for transitions between singlet and triplet states but none has been found. 

Previous expositions of photochemical laws have distinguished ptominentiy between states of singlet and triplet multiplicity (1). This distinction continues to be important with respect to photophysics of smaH organic molecules, but among inorganic and organometaHic compounds, states of other multiplicities, eg, doublet and quartet states (23), play an important role. Spin conservation characterizes electronic molecular excitations and localized... 

The isomerization of alkenes is believed to take place via an excited state in which the two sp carbons are twisted 90° with respect to one another. This state is referred to as the p (perpendicular) state. This geometry is believed to be the minimum-energy geometry for both the singlet and triplet excited states. 

CIS=50-50 Predicts both singlet and triplet excited states (by default,... 

Figure 4.9 Mixing of pure singlet and triplet states may generate artificial minima on the UHF energy surface...

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