Linear Response Selected Configuration Interaction

TL;DR

This work extends selected configuration interaction (SCI) to molecular response properties by introducing a linear-response (LR) framework for SCI wave functions. By adding two LR-inspired determinant-selection criteria, the authors present four LR-SCI models (GS, GS+V, GS+X, GS+V+X) that enable robust convergence of response properties toward the near-FCI limit, including static polarizabilities, damped X-ray absorption spectra, and NMR spin-spin coupling constants. The approach demonstrates near-FCI accuracy for polarizabilities in water and ammonia, accurately reproduces water’s K-edge XAS spectra with damped LR, and achieves CCSDT-like accuracy for J-couplings in small bases, with improvements in basis-set quality yielding closer agreement to experiment and higher-level methods. The results establish LR-SCI as a promising, systematically improvable route for computing molecular response properties beyond the reach of exact FCI, while noting current computational limits and potential avenues for scaling. Overall, LR-SCI broadens the diagnostic power of SCI by enabling accurate, benchmark-quality treatment of response observables across challenging systems and spectroscopic observables.

Abstract

In this work, we extend selected configuration interaction (SCI) methods beyond energies and expectation values by introducing a linear response (LR) framework for molecular response properties. Existing SCI approaches are capable of approximating the energy of the full configuration interaction (FCI) wave function with high accuracy but at a much lower cost. However, conventional determinant selection will, by design, mainly select determinants that are expected to improve energies, and this can lead to the omission of many determinants that are important for wave function response. We address this by introducing two new selection criteria motivated by linear response theory. Using these extended determinant selection criteria, we demonstrate that LR-SCI can systematically converge toward the FCI limit for static polarizabilities. Using a damped LR formulation, we compute the water K-edge X-ray absorption spectrum in active spaces up to (10e, 58o). Finally, we use LR-SCI to compute NMR spin-spin coupling constants for water, where we find that accuracy beyond that offered by CCSDT can be achieved. Overall, LR-SCI offers a promising route to compute response properties with near-FCI accuracy to systems beyond the reach of exact FCI.

Figures (7)

• Figure 1: Schematic overview of the LR-SCI calculation. The upper box shows the ground-state HCI iterations, where the ground-state CI problem is solved and the determinant space $\mathcal{D}_k$ is iteratively expanded by adding determinants $\Delta \mathcal{D}$ that satisfy the criterion in Eq. \ref{['eq:hci_criterion']} until convergence. The middle box shows the additional property-gradient determinant addition step, which is included with the +V coupling (Eq. \ref{['eq:hci_prop_criterion']}). The lower box shows the formation of the property gradient and the solution of the linear response equations. If the +X coupling (Eq. \ref{['eq:hci_rsp_criterion']}) is used, an iterative determinant-addition step is included to identify determinants that couple strongly to the response vector. Finally, the converged response vectors are used to evaluate molecular properties, such as polarizabilities or NMR spin-spin coupling constants.
• Figure 2: The left panels show the $\alpha_{xx}$, $\alpha_{yy}$, and $\alpha_{zz}$ components of the static polarizability of the water molecule in a cc-pVDZ basis (8e, 23o). The middle panel shows the RMSD between the SCI polarizability and the reference FCI result. The right panel shows the error in $\alpha_{zz}$ relative to the frozen-core FCI reference.
• Figure 3: The left panels show the $\alpha_{xx}$, $\alpha_{yy}$, and $\alpha_{zz}$ components of the static polarizability of the ammonia molecule in a cc-pVDZ basis (8e, 28o). The middle panel shows the RMSD between the SCI polarizability and the reference FCI result. The right panel shows the error in $\alpha_{zz}$ relative to the frozen-core FCI reference.
• Figure 4: Water/cc-pVDZ K-edge X-ray absorption spectrum. A (10e, 14o) active space is used. The spectrum is computed from the isotropically averaged imaginary part of damped polarizability, with $\gamma=0.4$ eV. The damped polarizability is computed with a 0.005 a.u. frequency resolution. The left panels show the computed absorption spectrum, while the right panels show the number of determinants included in the CI expansion (log scale) at a given threshold $\varepsilon$. Different SCI coupling models are tested (see panel titles). CASCI (black lines) results serve as the reference result.
• Figure 5: RMSD in the isotropically averaged imaginary part of damped polarizability, with $\gamma=0.4$ eV (see Figure \ref{['fig:water_xas_calibration']}) against the maximum number of determinants required across the frequency grid.