  Approximate natural orbitals are investigated as a way to improve a Monte
Carlo configuration interaction (MCCI) calculation. We introduce a way to
approximate the natural orbitals in MCCI and test these and approximate natural
orbitals from MP2 and QCISD in MCCI calculations of single-point energies. The
efficiency and accuracy of approximate natural orbitals in MCCI potential curve
calculations for the double hydrogen dissociation of water, the dissociation of
carbon monoxide and the dissociation of the nitrogen molecule are then
considered in comparison with standard MCCI when using full configuration
interaction as a benchmark. We also use the method to produce a potential curve
for water in an aug-cc-pVTZ basis. A new way to quantify the accuracy of a
potential curve is put forward that takes into account all of the points and
that the curve can be shifted by a constant. We adapt a second-order
perturbation scheme to work with MCCI (MCCIPT2) and improve the efficiency of
the removal of duplicate states in the method. MCCIPT2 is tested in the
calculation of a potential curve for the dissociation of nitrogen using both
Slater determinants and configuration state functions.
