Mar 302011

I just finished reading a new article by Musial, Perera, and Bartlett on multireference coupled cluster theory. This is an interesting paper that considers a simple but ingenious MRCC approach based on the equation of motion formalism.
For a CAS(2,2) problem, the reference wave function is taken to be a closed shell determinant \Phi^{+2} with the active orbitals either fully occupied or empty.  One then solves for the coupled-cluster wave function for this double anion state to get an intermediate wave function \exp(\hat{T}^{+2})\Phi^{+2}.  The MR ansatz used by Musial et al. is \Psi_\mathrm{easy} = \hat{S} \, \hat{r} \, \exp(\hat{T}^{+2})\Phi^{+2}, where \hat{r} removes a pair of electrons among all the occupied orbitals in \Phi^{+2}

    \[ \hat{r} = \sum_{mn} r_{mn} \hat{a}_m \hat{a}_n, \]

while \hat{S} is an operator that relaxes the wave function via ordinary excitations truncated at a give excitation level n

    \[ \hat{S} = 1 + \hat{S}_1  + \ldots + \hat{S}_n. \]

As the authors claim, the theory is simple, and simple in a multireference many-body approach is good. However, there is one problem with this approach. The energy is very sensitive to the choice of the original orbitals. In my experience, state-specific approaches based on the Jeziorski-Monkhorst ansatz tend to be a bit less sensitive. It would be great if the theory could also determine some optimal set of MOs (Bruckner, NOs, …).

 March 30, 2011  Articles

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