# Enhanced effect of CP-violating nuclear magnetic quadrupole moment in HfF$^+$ molecule

## TL;DR

This paper presents the first accurate relativistic calculations of the nuclear magnetic quadrupole moment (MQM) interaction in HfF$^+$, aiding experimental searches for T,P-odd effects related to fundamental symmetry violations.

## Contribution

It introduces a highly precise ab initio computational approach to determine the molecular parameter $W_M$ for HfF$^+$, crucial for interpreting MQM experimental data.

## Key findings

- Calculated $W_M$=0.494 $rac{10^{33} ext{Hz}}{e~ ext{cm}^2}$ for HfF$^+$
- Implemented advanced relativistic coupled cluster methods including CCSDT(Q)
- Provided interpretation framework linking MQM effects to fundamental physics constants

## Abstract

HfF$^+$ cation is a very promising system to search for the electron electric dipole moment (EDM), and corresponding experiment is carried out by E. Cornell group. Here we theoretically investigate the cation to search for another T,P-odd effect -- the nuclear magnetic quadrpole moment (MQM) interaction with electrons. We report the first accurate ab initio relativistic electronic structure calculations of the molecular parameter $W_M$=0.494 $\frac{10^{33}\mathrm{Hz}}{e~{\rm cm}^2}$ that is required to interpret the experimental data in terms of the MQM of Hf nucleus. For this we have implemented and applied the combined Dirac-Coulomb(-Gaunt) and relativistic effective core potential approaches to treat electron correlation effects from all of the electrons and to take into account high-order correlation effects using the coupled cluster method with single, double, triple and noniterative quadruple cluster amplitudes, CCSDT(Q). We discuss interpretation of the MQM effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $\theta$ and quark chromo-EDM.