Periodic Reporting for period 1 - ezEmbedMagnet (Quantum Chemical Design of Molecular Magnets)
Okres sprawozdawczy: 2022-11-01 do 2024-10-31
This project aims to design efficient molecular magnets for quantum technologies by introducing a new quantum chemical approach that combines the accuracy of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with the efficiency of density functional theory (DFT). Our focus is on two types of systems: linear single-molecule magnets with a twofold-coordinated cobalt(II) magnetic center and cobalt atoms adsorbed on MgO(001) and (111) metallic surfaces.
These systems exhibit high spin-reversal energy barriers (i.e. slow magnetic relaxation), which is key to designing efficient molecular magnets. However, a comprehensive understanding of the origins of such magnetic behavior is still lacking.
One standard strategy to tackle molecular magnets is to use a multireference method and extract magnetic properties from phenomenological spin Hamiltonians. This approach often yields accurate results; however, outcomes are sensitive to the choice of active-orbital space, and achieving high accuracy requires including dynamic correlation through additional and costly computational steps. For surface-bound metal atoms, DFT+U (i.e. Hubbard correction to DFT) methods are commonly used. However, DFT+U is not parameter-free, and results depend on the functional choice. In contrast, EOM-CCSD offers significant advantages: it does not introduce empirical parameters nor requires active-space selection and accounts for both dynamic and non-dynamic correlation. However, the high computational cost of EOM-CCSD restricts its applications to small molecules. To address this, we present a new embedding approach that applies EOM-CCSD to the magnetic center while using DFT for the remainder, namely EOM-CCSD-in-DFT. Furthermore, embedded EOM-CCSD can be combined with post-processing tools available in the ezMagnet software to predict the spin-reversal barrier, magnetic anisotropy, magnetization, and susceptibility. Equipped with these new tools, our objectives are: (i) to establish new design rules for maximizing spin-reversal barriers in Co(II) complexes, (ii) to identify the preferred adsorption structures of Co atoms on various substrates, and (iii) to assess the influence of the substrate on the Co magnetic behavior. These findings will impact a range of scientific fields, including molecular magnetism, solid-state physics, and quantum chemistry.
Furthermore, this project provides a predictive tool for the design of efficient molecular magnets, which will be beneficial to major industry players in developing next-generation molecular quantum devices. The outcomes of this project will also be used to develop additional methods, such as periodic embedding theories for strongly correlated materials, and to describe other complex chemical systems with easily localized active sites, with implications for catalysis and electronics.
These systems exhibit high spin-reversal energy barriers (i.e. slow magnetic relaxation), which is key to designing efficient molecular magnets. However, a comprehensive understanding of the origins of such magnetic behavior is still lacking.
One standard strategy to tackle molecular magnets is to use a multireference method and extract magnetic properties from phenomenological spin Hamiltonians. This approach often yields accurate results; however, outcomes are sensitive to the choice of active-orbital space, and achieving high accuracy requires including dynamic correlation through additional and costly computational steps. For surface-bound metal atoms, DFT+U (i.e. Hubbard correction to DFT) methods are commonly used. However, DFT+U is not parameter-free, and results depend on the functional choice. In contrast, EOM-CCSD offers significant advantages: it does not introduce empirical parameters nor requires active-space selection and accounts for both dynamic and non-dynamic correlation. However, the high computational cost of EOM-CCSD restricts its applications to small molecules. To address this, we present a new embedding approach that applies EOM-CCSD to the magnetic center while using DFT for the remainder, namely EOM-CCSD-in-DFT. Furthermore, embedded EOM-CCSD can be combined with post-processing tools available in the ezMagnet software to predict the spin-reversal barrier, magnetic anisotropy, magnetization, and susceptibility. Equipped with these new tools, our objectives are: (i) to establish new design rules for maximizing spin-reversal barriers in Co(II) complexes, (ii) to identify the preferred adsorption structures of Co atoms on various substrates, and (iii) to assess the influence of the substrate on the Co magnetic behavior. These findings will impact a range of scientific fields, including molecular magnetism, solid-state physics, and quantum chemistry.
Furthermore, this project provides a predictive tool for the design of efficient molecular magnets, which will be beneficial to major industry players in developing next-generation molecular quantum devices. The outcomes of this project will also be used to develop additional methods, such as periodic embedding theories for strongly correlated materials, and to describe other complex chemical systems with easily localized active sites, with implications for catalysis and electronics.
For the Co-based systems under study, we explored the performance of embedded EOM-CCSD for computing spin-state energetics and spin-related properties, e.g. orbital angular momentum and spin-orbit coupling (SOC). Our findings reveal that the Co(II) molecular magnet exhibits a non-Aufbau doubly-degenerate ground state characterized by maximal orbital angular momentum and large SOC. These features, driven by the undelying axial ligand field, result in strong axial magnetic anisotropy and a high spin-reversal barrier. For Co adatoms, we performed periodic DFT calculations to determine the most favorable coordination geometry. Our results indicate that Co preferentially adsorbs on the oxygen site of MgO(001), while on Pt(111) and Cu(111) surfaces, it occupies hollow sites. The density of states (DOS) of Co/MgO(001) demonstrates strong axial hybridization between the cobalt and oxygen atoms. In contrast, axial hybridization was significantly reduced for Co on Pt(111) and Cu(111). For Co/MgO(001), we built a cluster model consisting of Co atoms on a two-layer cluster representing MgO(001). EOM-CCSD-in-DFT calculations showed that Co adatoms on MgO(001) exhibit an axial ligand field similar to that of the Co(II) complex, also leading to a non-Aufbau doubly-degenerate ground state with maximal orbital angular momentum and large SOC. For these states, we computed a large spin-reversal barrier comparable to that calculated for the Co(II) complex. The susceptibility plots for both the Co(II) molecular magnet and Co/MgO(001) significantly deviate from the Curie behavior, which indicates a significant orbital angular momentum contributing to their magnetic behavior. The computed spin-reversal barrier and susceptibility curves closely matched experimental values, confirming the reliability of the embedding approach. These results were further analyzed using a natural orbital picture. For both the Co(II) complex and Co/MgO(001), the spin-orbit coupled states of the doubly-degenerate ground states are related by a substantial orbital inversion. Such orbital torque is essential for generating large orbital angular momentum, consistent with El-Sayed's rule. In summary, our findings highlight how the linear coordination environment in both the Co(II) molecular magnets and Co/MgO(001) plays a pivotal role in enabling robust molecular magnetism characterized by large spin-reversal barriers. Conversely, the disruption of the axial ligand field in Co on hollow sites of Pt(111) and Cu(111) explains the experimentally observed smaller spin-reversal barriers of Co on metals. These results will drive major players in quantum information science to build a new era of molecular quantum technology with applications in data storage, computing, sensing, and spintronics. This project also highlights that finite models for metals are limited in their ability to capture long-range interactions, potentially introducing artifacts. Consequently, enhancing this approach by incorporating surface periodicity is essential for advancing the application of embedded EOM-CC methods in surface science, motivating and inspiring further research in this area.
Molecular magnets are often large and complex molecules or solids, not accessible to standalone EOM-CCSD. This work represents the first application of EOM-CCSD, implemented through an embedding formalism, to investigate such systems. By integrating this embedding framework with the functionalities of the ezMagnet software, we successfully computed macroscopic magnetic properties, enabling direct comparisons with experimental results. This quantum chemical approach bypasses the spin-Hamiltonian formalism and avoids reliance on approximate expressions of the susceptibility. Furthermore, this approach pioneers the study of magnetic adsorbates using many-body correlated methods. Therefore, ezMagnetEmbedd marks a significant advancement over the current state of the art, which typically relies on multireference or DFT+U calculations coupled with spin Hamiltonians. Crucially, this project has validated the significant role of linear coordination environments in shaping molecular magnetism, both in metallic complexes and metal adatoms. Additionally, it opens promising new avenues for studying how environmental factors influence the magnetic behavior of spins on surfaces, which is a critical step toward the practical development of next-generation molecular quantum devices.