Optimisation of the CASSCF Wavefunction

The discussion in this section follows closely that in Roos [19]. In analogy to equation 5.12, we define the CASSCF state as a linear combination of configurations  

The K) are expanded in the same basis as 0) with the Cl coefficients defined such that an orthonormal set is obtained, (K L) = (5kl- A variational parameter 5ko can be assigned to each of the K) and the variation of our CASSCF state can be considered as a unitary 

The optimisation of the MO coefficients is implemented differently. Using second quantisation, a substitution operator, E, can be defined  

a and a are creation and annihilation operators, respectively. therefore has the effect of substituting an electron in state i for one in state j. As was done for the Cl coefficients, we now define an anti-hermitian operator, T in terms of the variational parameters Tif. 

We can now use the two exponential operators defined above to express a variation in the Cl and MO coefficients of our CASSCF state 0)  

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