# Pair Natural Orbitals for Coupled Cluster Quadratic Response Theory

## TL;DR

This paper explores how using pair natural orbitals can improve the efficiency of quantum chemistry calculations for large molecules.

## Contribution

The paper introduces and evaluates new methods combining pair natural orbitals with response property optimizations for coupled cluster calculations.

## Key findings

- PNO++ methods improve accuracy in response properties compared to standard PNOs.
- Combined-PNO++ maintains CCSD correlation energy accuracy while reducing computational cost.
- Truncation errors were analyzed using electric dipole hyperpolarizability metrics.

## Abstract

Reduced-scaling approaches have yielded significant improvements
in the computational efficiency of coupled cluster methods, making
them more feasible for studying large molecules. In this work, we
extend the use of pair natural orbitals (PNOs) to frequency-dependent
quadratic response properties. We evaluate the performance of PNOs
alongside methods optimized for response properties that derive from
an approximate field-perturbed density matrix known as perturbation-aware
PNOs (PNO++). Additionally, we concatenate the PNO and PNO++ spaces
to obtain the combined-PNO++ method, which is tailored to simultaneously
maintain the accuracy of the CCSD correlation energies and response
properties. We analyze the truncation errors associated with these
methods using first electric dipole hyperpolarizability – specifically
the average second-harmonic generation and optical refractivity, using
canonical coupled cluster singles and doubles (CCSD) as a reference.
The performance analysis of the PNO family provides valuable insights
into the viability of implementing CCSD quadratic response properties
at a full-production level, highlighting which techniques may yield
the most successful results.