Occurrence and Impact of Electric-Field-Induced Discontinuities in Correlation Energies from Localized Pair-Natural-Orbital Methods

We report an investigation of discontinuities in the correlation energy produced by external static electric fields within the local pair-natural-orbital coupled-cluster singles and doubles (LPNO-CCSD) method. Such discontinuities arise as a result of variations in both the dimensions and character of the pairwise virtual-orbital domains resulting from changes in the strength of the field. Using several small-molecule test cases – water, fluoroethylene, hypofluorous acid and cis-1,3-butadiene we observe that, although the discontinuities in the correlation energy are small (typically 1 μEh), they can yield substantial errors in higher-order electric-field-dependent properties computed using finite-difference techniques. For the static hyperpolarizability (third derivative of the energy with respect to the field) of water, for example, the discrepancies between LPNO-CCSD and canonical-MO CCSD methods can exceed 100%. Furthermore, weak-field displacements that should normally decrease errors in numerical differentiation can yield orders-of-magnitude errors due to magnification of the energy discontinuities by small field-displacement denominators. For larger molecules, such fields can produce dramatic errors in the static polarizability (second derivative of the energy with respect to the field) and hyperpolarizability even with very tight PNO cutoffs. The use of basis sets containing diffuse functions, which are essential for reliable predictions of field-dependent response properties, tend to exacerbate the observed errors. In addition, the use of fixed virtual PNO dimensions does no resolve the problem due to mixing of the PNOs relative to zero-field orbitals as a result of large condition numbers of the pair-correlation densities.