21.15109/ARP/O4CEI6Thiering, GergőGergőThiering0000-0003-3357-5583Wigner Research Centre for PhysicsGali, ÁdámÁdámGali0000-0002-3339-5470Wigner Research Centre for PhysicsARP2025PhysicsVASPJahn-Teller effectDiamondNV center(D) Zero-field splitting(A) Hyperfine coupling(P) Nuclear quadropular couplingPoint defectRabi oscillationFermi's Golden Ruleab-initiofirst principlesDFTluminescencequbitspin coherencespin relaxationThiering, GergőGergőThieringWigner Research Centre for Physics2025-08-012025-08-07VASP INCAR, OUTCAR, vasprun.xml, POSCAR etc. input/output files.10.48550/arXiv.2402.19418458567548456443631443476170439737190464280117601767284719918246108036269application/gzipapplication/gzipapplication/gzipapplication/gzipapplication/gziptext/markdowntext/csvapplication/vnd.oasis.opendocument.spreadsheetapplication/vnd.openxmlformats-officedocument.spreadsheetml.sheetapplication/gzip1.0CC BY 4.0Optically accessible solid state defect spins serve as a primary platform for quantum information processing, where precise control of the electron spin and ancillary nuclear spins is essential for operation. Using the nitrogen-vacancy (NV) color center in diamond as an example, we employ a combined group theory and density functional theory study to demonstrate that spin-lattice relaxation of the $^{14}$N nuclear spin is significantly enhanced due to strong entanglement with orbital degrees of freedom in the $|^3E\rangle$ optical excited state of the defect. This mechanism is common to other solid-state defect nuclear spins with similar optical excited states. Additionally, we propose a straightforward and versatile \textit{ab initio} scheme for predicting orbital-dependent spin Hamiltonians for trigonal defects exhibiting orbital degeneracy.See the Readme.md file for instructions.