# Analytical Gradient Theory for Strongly Contracted (SC-) and Partially Contracted (PC-) N-Electron Valence State Perturbation Theory (NEVPT2)

## TL;DR

This paper develops an analytical gradient theory for NEVPT2, enabling accurate molecular geometry optimization using strongly and partially contracted schemes, with PC-NEVPT2 showing promising results comparable to CASPT2.

## Contribution

The paper introduces an analytical gradient algorithm for NEVPT2 with both contraction schemes, improving geometry optimization capabilities for correlated systems.

## Key findings

- PC-NEVPT2 yields geometries comparable to CASPT2.
- SC-NEVPT2 gradients show numerical instability.
- The developed method facilitates future molecular dynamics simulations.

## Abstract

An analytical gradient theory for single-state N-electron valence state perturbation theory (NEVPT2), using both strongly contracted (SC) and partially contracted (PC) internal contraction schemes, is developed. We demonstrate the utility of the developed algorithm in the optimization of the single-state molecular geometry of acrolein, benzyne, benzene, the retinal chromophore PSB3, the GFP chromophore pHBI, and porphine, with the cc-pVTZ basis sets. The SC-NEVPT2 analytical gradients exhibit numerical instability due to the lack of invariance with respect to the rotations among the inactive orbitals. On the other hand, PC-NEVPT2 gives molecular geometries comparable to CASPT2 in any tested cases. We discuss possible future developments that will make the NEVPT2 gradient algorithm a powerful tool for optimizing the molecular geometries and conducting molecular dynamics simulations of correlated systems.

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Source: https://tomesphere.com/paper/1907.10180