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30.2 Wave function Ansätze

The so called ''ansatz'' determines the definition of the explicitly correlated wave function. This is to be distinguished from the various approximations that can be used to approximate the Hamiltonian matrix elements. Generally, we use ansatz 3 (cf. I), for which the projector has the form

$$\hat Q_{12} = (1-\hat o_1) (1 - \hat o_2) (1 - \hat v_1 \hat v_2),$$

where $\hat o_i$ is a one-electron projector for electron $i$ onto the occupied space, and $\hat v_i$ projects onto the virtual orbital space. In the case that domain approximations are used in local explicitly correlated wave functions, the operators $\hat v$ are replaced by operators $\hat d^{ij}$ that project just onto the domain for the orbital pair $ij$.

In MOLPRO the following wave function ansätze can be used: