Origin of Magnetic Anisotropy in Nickelocene Molecular Magnet and Resilience of its Magnetic Behavior

Abstract

Robustness of nickelocene’s (NiCp<sup>2</sup>, Cp = cyclopentadienyl) magnetic anisotropy and addressability of its spin states make this molecular magnet attractive as a spin sensor. However, microscopic understanding of its magnetic anisotropy is still lacking, especially when NiCp<sup>2</sup> is deposited on a surface to make quantum sensing devices. Quantum chemical calculations of such molecule/solid-state systems are limited to density functional theory (DFT) or DFT+U (Hubbard correction to DFT). We investigate the magnetic behavior of NiCp<sup>2</sup> using the equation-of-motion coupled-cluster (EOM-CC) framework. Our first-principle calculations agree well with experimentally derived magnetic anisotropy and susceptibility values. The calculations show that magnetic anisotropy in NiCp<sup>2</sup> originates from a large spin-orbit coupling (SOC) between the triplet ground state and the third singlet state, whereas the coupling with lower singlet excited states is negligible. We also considered a set of six ring-substituted NiCp<sup>2</sup> derivatives and a model system of the NiCp<sup>2</sup>/MgO(001) adsorption complex. To gain insight into the electronic structure of these systems, we analyze spinless transition density matrices and their natural transition orbitals (NTOs). The NTO analysis of SOCs explains how spin states and magnetic properties are retained upon modification of the NiCp<sup>2</sup> coordination environment and upon its adsorption on a surface. Such resilience of the NiCp<sup>2</sup> magnetic behavior supports using NiCp<sup>2</sup> as a spin-probe molecule by functionalization of the tip of a scanning tunneling microscope.

Spin–orbit couplings within spin-conserving and spin-flipping time-dependent density functional theory: Implementation and benchmark calculations

“…This new implementation extends the scope of computational tools for modeling spinforbidden processes in large molecular systems, as illustrated by our recent study in which we applied this SF-TD-DFT SOC code to describe the magnetic behavior of nickelocene molecular magnet adsorbed on the MgO(001) surfaces using the state-interaction scheme. 59…”

“…The SF approach extends Kohn-Sham TD-DFT to treat certain types of strong correlation, such as bond-breaking, conical intersections, and systems with two or more unpaired electrons. 55,[57][58][59] This work describes the implementation of SOCs using TD-DFT and SF-TD-DFT within the Q-Chem electronic structure package 60,61 and presents benchmark results for molecules featuring different types of electronic structure: e.g., closed-shell organic molecules, diradicals, and a molecular magnet. We compare the results obtained with different DFT and wave-function-based methods and assess the effect of specific density functionals and basis sets on the SOC.…”

State-Interaction Approach for Evaluating g-Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks

“…This procedure is visualized in Figure 1 and implemented in a postprocessing Python script, which is now included in the ezMagnet suite 52 (see the Supporting Information (SI) for details). This approach, originally described 15 by Gerloch and McMeeking in 1975, simply follows from the mapping between the eigenstates of microscopic Hamiltonian, eq 4, and the phenomenological spin Hamiltonian, eq 1.…”