Goldstone program

In the Goldstone program below [cf. Section 4], Wick s theorem is fulfilled implicitly by performing a pairwise permutation of the operators until all operators are in normal order. This ensures that all contractions are taken into account easily. Of course, this step-wise procedure gives the same results as a more sophisticated implementation of Wick s theorem which, in particular, is helpful for large operator strings. 

In the Goldstone program below, we distinguish the following six types of orbitals with the following indices ... 

In fact, the definition of the extended normal-order sequence (50) is very crucial to our implementation of the GOLDSTONE program. Therefore, in order to make this convention more transparent for the reader, let us consider the effective one-particle part of the operator (47), F = /). Using the definitions of the... 

TABLE 10.1 Main commands of the GOLDSTONE program for deriving atomic and molecular perturbation expansions within an (one-electron) orbital picture ... 

FIGURE 10,4 Part of the user manual as provided for 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 total energy of the system up to first order is equal to the vacuum expectation value of the normal-ordered Hamiltonian... 

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

We first define the rest interaction V for the case that the one-particle spectrum has obtained by means of an arbitrary potential V. In the Goldstone program, this operator can be assigned to the variable Vrest by entering... 

FIGURE 10.5 lAT output of the GOLDSTONE program for the third-order energy correction for closed-shell atoms and molecules. Only the first eight (out of (14)) terms are show in this figure. See text for further explanation. 

Suppose we have started from a Hartree-Fock spectrum, that is we have used the variable VHP in all the steps above. Then, the third-order correlation energy for closed-shell atoms is obtained with the GOLDSTONE program by typing... 

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