a standard of accuracy near equilibrium separations. This introduction of higher-order OPs as variational parameters, with closure of the theory at their level, is the essential novelty of our work and is responsible for its favorable scaling with high accuracy.

OP-NOFT, general formulation
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The NSO basis
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We consider time-reversal invariant saturated systems with non-degenerate, singlet ground states. The inverse approach [@Garrod1964] starts from a set of $N$-representability conditions on the 2-DM needed for it to be derivable from a generic $N$-electron wavefunction. Instead, we take a forward approach: we introduce a specific form for the trial wavefunction and derive the 2-DM explicitly. Our starting point is that of conventional FCI, except that our one-particle basis is the complete set of NSOs of the trial function $\Psi$, $\psi_k(x) = \phi_k({{\bf{r}}}) \chi_k(\sigma)$, with ${{\bf{r}}}$ space and $\sigma$ spin coordinates. The NOs $\phi_k({{\bf{r}}})$ are real and independent of the spin function $\chi_k(\sigma)$. The complete set of $N$-electron orthonormal SDs $\Phi_{{{\bf{k}}}}(x_1,x_2,\cdots,x_N)$, ${{\bf{k}}}=k_1,k_2,\cdots,k_N$, formed from its NSOs supports representation of any trial wavefunction $\Psi(x_1,x_2,\cdots,x_N)$ as the expansion $$\Psi(x_1,\cdots,x_N) = \sum_{{{\bf{k}}}} C_{{{\bf{k}}}} \Phi_{{{\bf{k}}}}(x_1,\cdots,x_N).
\label{expansion}$$

As the ground-state wave function is real, so are the trial functions and the normalized $C_{{{\bf{k}}}}$ ($\sum_{{{\bf{k}}}} C_{{{\bf{k}}}}^2 = 1$). 