Application of the GOLDSTONE Program

To illustrate the use of the Goldstone program, let us consider the wave operator and correlation energies of some atom or molecule. For close-shell systems, of course, we can choose always a 1-dimensional model space, 0c), which coincides with the reference state P). In this case, the total energy of the system up to first order is equal to the vacuum expectation value of the normal-ordered Hamiltonian 

For all higher-order correlation energies (of closed-shell systems), moreover, we can follow similar lines and evaluate the vacuum expectation values EI I = (0c HX2 0c). This results in the standard Moeller-Plesset expressions for the energy corrections. 

For open-shell atoms and molecules, in contrast, the computation of the total energies requires to evaluate first the individual terms of the wave operator and the energy E I successively order-by-order up to an given order n. Having 

2 Evaluation of the second- and third-order correlation energies for closed-shell atoms 

Not much need to be said here to understand the Maple dialog below once, the Goldstone program has been loaded by executing the command 

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