Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets

2020 ◽  
Vol 152 (3) ◽  
pp. 034105 ◽  
Author(s):  
Pavel Pokhilko ◽  
Daniil Izmodenov ◽  
Anna I. Krylov
Keyword(s):  
Single Molecule ◽  
Open Shell ◽  
Natural Orbital ◽  
Single Molecule Magnets ◽  
Orbital Approximation

Extension of Frozen Natural Orbital Approximation to Open-Shell References: Theory, Implementation, and Application to Single-Molecule Magnets

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Daniil Izmodenov ◽  
Anna I. Krylov
Keyword(s):  
Density Matrix ◽  
Single Molecule ◽  
Open Shell ◽  
State Density ◽  
Molecular Orbitals ◽  
The State ◽  
Wave Functions ◽  
Virtual Space ◽  
Single Molecule Magnets ◽  
Natural Orbitals

Natural orbitals are often used in quantum chemistry to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual-virtual block of the state density matrix instead of the canonical Hartree-Fock molecular orbitals results in smaller errors when the same fraction of virtual orbitals is frozen. This strategy, termed frozen natural orbitals (FNO) approach, has been successfully used to reduce the cost of state-specific coupled-cluster (CC) calculations, such as ground-state CC, as well as some multi-state methods, i.e., EOM-IP-CC (equation-of-motion CC method for ionization potentials). This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip), which has been developed to describe certain multi-configurational wave-functions within the single-reference framework. In contrast to EOM-IP-CCSD, which describes open-shell target states by using a closed-shell reference, EOM-SF-CCSD relies on high-spin open-shell references (triplets, quartets, etc). Consequently, straightforward application of FNOs computed for an open-shell reference leads to an erratic behavior of the EOM-SF-CC energies and properties, which can be attributed to an inconsistent truncation of the α and β orbital spaces. A general solution to problems arising in the EOM-CC calculations utilizing open-shell references, termed OSFNO (open-shell FNO), is proposed. The OSFNO algo-rithm first identifies corresponding orbitals by means of singular value decomposition (SVD) of the overlap matrix of the α and β molecular orbitals and determines virtual orbitals corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve the spin purity of the open-shell orbital subspace to the extent allowed by the original reference thus facilitating a safe truncation of the virtual space. The performance of the OSFNO approximation in combination with different choices of reference orbitals is benchmarked for a set of diradicals and triradicals. For a set of di-copper single-molecule magnets, a conservative truncation criterion corresponding to a two-fold reduction of the virtual space in a triple-zeta basis leads to errors of 5–18 cm<sup>-1</sup> in the singlet–triplet gaps and errors of ∼2-3 cm<sup>-1</sup> in the spin–orbit coupling constants.

Extension of Frozen Natural Orbital Approximation to Open-Shell References: Theory, Implementation, and Application to Single-Molecule Magnets

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Daniil Izmodenov ◽  
Anna I. Krylov
Keyword(s):  
Density Matrix ◽  
Single Molecule ◽  
Open Shell ◽  
State Density ◽  
Molecular Orbitals ◽  
The State ◽  
Wave Functions ◽  
Virtual Space ◽  
Single Molecule Magnets ◽  
Natural Orbitals

Natural orbitals are often used in quantum chemistry to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual-virtual block of the state density matrix instead of the canonical Hartree-Fock molecular orbitals results in smaller errors when the same fraction of virtual orbitals is frozen. This strategy, termed frozen natural orbitals (FNO) approach, has been successfully used to reduce the cost of state-specific coupled-cluster (CC) calculations, such as ground-state CC, as well as some multi-state methods, i.e., EOM-IP-CC (equation-of-motion CC method for ionization potentials). This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip), which has been developed to describe certain multi-configurational wave-functions within the single-reference framework. In contrast to EOM-IP-CCSD, which describes open-shell target states by using a closed-shell reference, EOM-SF-CCSD relies on high-spin open-shell references (triplets, quartets, etc). Consequently, straightforward application of FNOs computed for an open-shell reference leads to an erratic behavior of the EOM-SF-CC energies and properties, which can be attributed to an inconsistent truncation of the α and β orbital spaces. A general solution to problems arising in the EOM-CC calculations utilizing open-shell references, termed OSFNO (open-shell FNO), is proposed. The OSFNO algo-rithm first identifies corresponding orbitals by means of singular value decomposition (SVD) of the overlap matrix of the α and β molecular orbitals and determines virtual orbitals corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve the spin purity of the open-shell orbital subspace to the extent allowed by the original reference thus facilitating a safe truncation of the virtual space. The performance of the OSFNO approximation in combination with different choices of reference orbitals is benchmarked for a set of diradicals and triradicals. For a set of di-copper single-molecule magnets, a conservative truncation criterion corresponding to a two-fold reduction of the virtual space in a triple-zeta basis leads to errors of 5–18 cm<sup>-1</sup> in the singlet–triplet gaps and errors of ∼2-3 cm<sup>-1</sup> in the spin–orbit coupling constants.

Seeking Magneto-Structural Correlations in Easily Tailored Pentagonal Bipyramid Dy(III) Single-Ion Magnets

2019 ◽  
Author(s):  
Guo-Zhang Huang ◽  
Ze-Yu Ruan ◽  
Jie-Yu Zheng ◽  
Yan-Cong Chen ◽  
Si-Guo Wu ◽  
...  
Keyword(s):  
Single Molecule ◽  
Structural Engineering ◽  
Magnetic Hysteresis ◽  
Sweep Rate ◽  
Coordination Bond ◽  
Pentagonal Bipyramid ◽  
Single Molecule Magnets ◽  
Crystal Field Theory ◽  
Bond Angles ◽  
Axial Coordination

<p><a></a>Controlling molecular magnetic anisotropy via structural engineering is delicate and fascinating, especially for single-molecule magnets (SMMs). Herein a family of dysprosium single-ion magnets (SIMs) sitting in pentagonal bipyramid geometry have been synthesized with the variable-size terminal ligands and counter anions, through which the subtle coordination geometry of Dy(III) can be finely tuned based on the size effect. The effective energy barrier (Ueff) successfully increases from 439 K to 632 K and the magnetic hysteresis temperature (under a 200 Oe/s sweep rate) raises from 11 K to 24 K. Based on the crystal-field theory, a semi-quantitative magneto-structural correlation deducing experimentally for the first time is revealed that the Ueff is linearly proportional to the structural-related value S2<sup>0</sup> corresponding to the axial coordination bond lengths and the bond angles. Through the evaluation of the remanent magnetization from hysteresis, quantum tunneling of magnetization (QTM) is found to exhibit negative correlation with the structural-related value S<sub>tun</sub> corresponding to the axial coordination bond angles.<br></p>

Correlating Blocking Temperatures in Single Molecule Magnets with Raman Relaxation

2018 ◽  
Author(s):  
Marcus J. Giansiracusa ◽  
Andreas Kostopoulos ◽  
George F. S. Whitehead ◽  
David Collison ◽  
Floriana Tuna ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Single Molecule ◽  
Energy Barrier ◽  
Thermal Relaxation ◽  
Relaxation Mechanism ◽  
Blocking Temperature ◽  
Single Molecule Magnets ◽  
Single Molecule Magnet ◽  
Key Parameter

We report a six coordinate DyIII single-molecule magnet<br>(SMM) with an energy barrier of 1110 K for thermal relaxation of<br>magnetization. The sample shows no retention of magnetization<br>even at 2 K and this led us to find a good correlation between the<br>blocking temperature and the Raman relaxation regime for SMMs.<br>The key parameter is the relaxation time (𝜏<sub>switch</sub>) at the point where<br>the Raman relaxation mechanism becomes more important than<br>Orbach.

A Combined Spin-Flip and IP/EA Approach for Handling Spin and Spatial Degeneracies: Application to Double Exchange Systems

2018 ◽  
Author(s):  
Shannon Houck ◽  
Nicholas Mayhall
Keyword(s):  
Single Molecule ◽  
Double Exchange ◽  
Computational Effort ◽  
Strongly Correlated ◽  
Single Molecule Magnets ◽  
New Approach ◽  
Spin Flip ◽  
Model Hamiltonian ◽  
Simultaneous Existence ◽  
Exchange Parameters

<div>Many multiconfigurational systems, such as single-molecule magnets, are difficult to study using traditional computational methods due to the simultaneous existence of both spin and spatial degeneracies. In this work, a new approach termed n-spin-flip Ionization Potential/Electron Affinity (<i>n</i>SF-IP or <i>n</i>SF-EA) is introduced which combines the spin-flip method of Anna Krylov with particle-number changing IP/EA methods. We demonstrate the efficacy of the approach by applying it to the strongly-correlated N<sub>2</sub><sup>+</sup> as well as several double exchange systems. We also demonstrate that when these systems are well-described by a double exchange model Hamiltonian, only 1SF-IP/EA is required to extract the double exchange parameters and accurately predict energies for the low-spin states. This significantly reduces the computational effort for studying such systems. The effects of including additional excitations (using a RAS-<i>n</i>SF-IP/EA scheme) are also examined, with particular emphasis on hole and particle excitations.</div>

A Combined Spin-Flip and IP/EA Approach for Handling Spin and Spatial Degeneracies: Application to Double Exchange Systems

2018 ◽  
Author(s):  
Shannon Houck ◽  
Nicholas Mayhall
Keyword(s):  
Single Molecule ◽  
Double Exchange ◽  
Computational Effort ◽  
Strongly Correlated ◽  
Single Molecule Magnets ◽  
New Approach ◽  
Spin Flip ◽  
Model Hamiltonian ◽  
Simultaneous Existence ◽  
Exchange Parameters

<div>Many multiconfigurational systems, such as single-molecule magnets, are difficult to study using traditional computational methods due to the simultaneous existence of both spin and spatial degeneracies. In this work, a new approach termed n-spin-flip Ionization Potential/Electron Affinity (<i>n</i>SF-IP or <i>n</i>SF-EA) is introduced which combines the spin-flip method of Anna Krylov with particle-number changing IP/EA methods. We demonstrate the efficacy of the approach by applying it to the strongly-correlated N<sub>2</sub><sup>+</sup> as well as several double exchange systems. We also demonstrate that when these systems are well-described by a double exchange model Hamiltonian, only 1SF-IP/EA is required to extract the double exchange parameters and accurately predict energies for the low-spin states. This significantly reduces the computational effort for studying such systems. The effects of including additional excitations (using a RAS-<i>n</i>SF-IP/EA scheme) are also examined, with particular emphasis on hole and particle excitations.</div>

Hydrazone-based Dysprosium Single Molecule Magnets

2013 ◽  
Vol 3 (2) ◽  
pp. 101-111 ◽  
Author(s):  
Peng Zhang ◽  
Li Zhang ◽  
Jinkui Tang
Keyword(s):  
Single Molecule ◽  
Single Molecule Magnets

The localized electron: magnetic properties

2018 ◽  
Author(s):  
Jean-Pierre Launay ◽  
Michel Verdaguer
Keyword(s):  
Single Molecule ◽  
Model Systems ◽  
Ferromagnetic Coupling ◽  
Single Chain ◽  
Single Molecule Magnets ◽  
Magnetic Systems ◽  
Orbital Interactions ◽  
Prussian Blue Analogues ◽  
Mononuclear Complexes

After preliminaries about electron properties, and definitions in magnetism, one treats the magnetism of mononuclear complexes, in particular spin cross-over, showing the role of cooperativity and the sensitivity to external perturbations. Orbital interactions and exchange interaction are explained in binuclear model systems, using orbital overlap and orthogonality concepts to explain antiferromagnetic or ferromagnetic coupling. The phenomenologically useful Spin Hamiltonian is defined. The concepts are then applied to extended molecular magnetic systems, leading to molecular magnetic materials of various dimensionalities exhibiting bulk ferro- or ferrimagnetism. An illustration is provided by Prussian Blue analogues. Magnetic anisotropy is introduced. It is shown that in some cases, a slow relaxation of magnetization arises and gives rise to appealing single-ion magnets, single-molecule magnets or single-chain magnets, a route to store information at the molecular level.

scholarly journals Tunneling, remanence, and frustration in dysprosium-based endohedral single-molecule magnets

2014 ◽  
Vol 89 (6) ◽  
Author(s):  
Rasmus Westerström ◽  
Jan Dreiser ◽  
Cinthia Piamonteze ◽  
Matthias Muntwiler ◽  
Stephen Weyeneth ◽  
...  
Keyword(s):  
Single Molecule ◽  
Single Molecule Magnets

Regulating the magnetic dynamics of mononuclear β-diketone Dy(iii) single-molecule magnets through the substitution effect on capping N-donor coligands

2021 ◽  
Vol 50 (6) ◽  
pp. 2102-2111
Author(s):  
Jing Xi ◽  
Xiufang Ma ◽  
Peipei Cen ◽  
Yuewei Wu ◽  
Yi-Quan Zhang ◽  
...  
Keyword(s):  
Ab Initio ◽  
Single Molecule ◽  
Substitution Effect ◽  
Single Molecule Magnets ◽  
Magnetic Dynamics ◽  
Magnetic Investigation

Substituent change modulates the coordination symmetries and magnetic dynamics of five mononuclear β-diketonate-Dy(iii) complexes with capping N-donor coligands, which is studied by the combination of magnetic investigation and ab initio calculation.

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