Periodic Reporting for period 1 - SCOML (Machine learning methods for excited-state dynamics simulations in light-induced spin-crossover complexes)
Période du rapport: 2023-10-01 au 2025-09-30
Spin-crossover complexes are transition-metal coordination compounds characterized by their ability to switch magnetic properties in response to external stimuli such as light, temperature, magnetic fields, or pressure. In Fe(II)-based spin-crossover compounds, the transition occurs between the low-spin singlet state and the high-spin quintet state
Within the SCOML project, we aim to investigate light-induced processes in which the system is initially prepared in its low-spin state and then excited to high-energy singlet states. Following excitation, the system undergoes a relaxation pathway involving ultrafast, radiationless (vibronically driven) transitions that ultimately populate the high-spin state. At sufficiently low temperatures, the system can become trapped in this metastable high-spin state, leading to a measurable change in total magnetization. This phenomenon is known as Light-Induced Excited Spin-State Trapping (LIESST).
Such complexes hold great promise as molecular switches in emerging spintronics and photonics technologies. Despite significant experimental advances in characterizing these materials, computational approaches still face major challenges in providing a quantitative description of the light-induced spin-crossover mechanism. The main difficulty lies in the high computational cost of accurately simulating excited-state dynamics in medium-sized transition-metal complexes. This is due to the breakdown of the Born–Oppenheimer approximation in ultrafast radiationless processes, combined with the need to explicitly account for vibronic coupling between electronic potential energy surfaces. These requirements ultimately translate into an extremely large number of ab initio electronic structure single-point calculations.
As a result, this class of systems remains largely unexplored from a computational perspective, leaving experimental efforts without robust quantitative tools to rationalize the observed relaxation pathways. This lack of synergy hampers the systematic improvement of material performance. The central objective of the SCOML project is therefore to establish a proof of concept for a novel machine-learning-based strategy designed to enable the systematic exploration of spin-crossover materials and the identification of new compounds with improved properties.
Within the SCOML project, we aim to investigate light-induced processes in which the system is initially prepared in its low-spin state and then excited to high-energy singlet states. Following excitation, the system undergoes a relaxation pathway involving ultrafast, radiationless (vibronically driven) transitions that ultimately populate the high-spin state. At sufficiently low temperatures, the system can become trapped in this metastable high-spin state, leading to a measurable change in total magnetization. This phenomenon is known as Light-Induced Excited Spin-State Trapping (LIESST).
Such complexes hold great promise as molecular switches in emerging spintronics and photonics technologies. Despite significant experimental advances in characterizing these materials, computational approaches still face major challenges in providing a quantitative description of the light-induced spin-crossover mechanism. The main difficulty lies in the high computational cost of accurately simulating excited-state dynamics in medium-sized transition-metal complexes. This is due to the breakdown of the Born–Oppenheimer approximation in ultrafast radiationless processes, combined with the need to explicitly account for vibronic coupling between electronic potential energy surfaces. These requirements ultimately translate into an extremely large number of ab initio electronic structure single-point calculations.
As a result, this class of systems remains largely unexplored from a computational perspective, leaving experimental efforts without robust quantitative tools to rationalize the observed relaxation pathways. This lack of synergy hampers the systematic improvement of material performance. The central objective of the SCOML project is therefore to establish a proof of concept for a novel machine-learning-based strategy designed to enable the systematic exploration of spin-crossover materials and the identification of new compounds with improved properties.
The main goal of the SCOML project is to develop a robust computational framework capable of performing excited-state dynamics in transition-metal compounds using the Tully Surface Hopping (TSH) technique. Since a fully ab initio treatment of this problem is computationally unfeasible, we developed a machine-learning-based approach.
Two systems have been investigated. The first is a toy model consisting of an octahedrally coordinated Fe(II)(CO)6 complex. This molecule, with its relatively small number of atoms, was chosen to build and test the computational workflow. The second system is the experimentally characterized Fe(II)(ptz)6 compound, for which experimental measurements are available, allowing direct comparison with theory.
In terms of ab initio electronic structure methods, different possibilities were explored to balance accuracy with computational efficiency. After careful testing, we opted to construct our database using N-Electron Valence State Perturbation Theory (NEVPT2) on top of a Complete Active Space Self-Consistent Field (CASSCF) wavefunction. For the toy system, we employed an active space of six d-electrons in five orbitals (6e,5o). For Fe(II)(ptz)6, we included two additional σ-bonding doubly occupied orbitals, giving a total active space of ten electrons in seven orbitals (10e,7o). In the calculations, we considered four singlet states, six triplet states, and three to five quintet states.
The computational tool we developed automatically links three main components:
(i) ORCA for the ab initio calculations,
(ii) a PyTorch wrapper for training a neural-network model of the electronic properties (modified SPaiNN), and
(iii) SHARC to perform TSH simulations using machine-learning predictions.
This entire workflow is managed by a Python code we developed, named pyVC, which is freely available on GitHub.
Particular attention was devoted to the training of Spin–Orbit Coupling (SOC) elements, which are essential for describing the spin-crossover transition. Because a large number of states are coupled by SOC in each calculation, obtaining accurate training is challenging. To address this, we developed a strategy to train Spin–Orbit Coupling Reduced Matrix Elements (RMEs) instead. RMEs are directly related to SOC elements and can be recovered from them using the Wigner–Eckart theorem. The advantages of this approach are twofold:
1) RMEs are defined at the spin-free level of the wavefunction, so the number of independent elements is significantly smaller than for the SOC matrix itself.
2)SOC elements are complex numbers, and learning their relative phases between real and imaginary parts is non-trivial. In contrast, RMEs are purely imaginary, which reduces the learning problem to a single component.
Another source of inaccuracy arises from the possible swapping of electronic roots between database entries, which complicates the training of coupling elements. To mitigate this issue, we tested a strategy based on molecular orbital rotations and alignment of CI vectors, ensuring consistent wavefunction character across geometries.
Beyond SOCs, pyVC can also train on energies, forces, and non-adiabatic coupling (NAC) vectors. In this project, however, we bypassed NAC training entirely and instead employed a curvature-based approximation to estimate NACs at intersystem crossing points.
Finally, the full code was applied to the Fe(II)(ptz)6 complex. Our preliminary results demonstrate the capability of the approach to simulate spin-crossover transitions, with good qualitative agreement with experimental data.
The newly developed code pyVC is flexible and not restricted to transition-metal-based systems. It has the potential to assist the study of excited-state dynamics whenever multi-reference methods are required to capture strong electronic correlation. The results of this project pave the way for systematic computational studies of light-induced spin transitions, helping to close the gap between experimental observations and theoretical modeling.
Throughout the process of testing and developing the code, a large number of calculations were performed. The resulting databases, containing all the data, are openly accessible for reuse.
Two systems have been investigated. The first is a toy model consisting of an octahedrally coordinated Fe(II)(CO)6 complex. This molecule, with its relatively small number of atoms, was chosen to build and test the computational workflow. The second system is the experimentally characterized Fe(II)(ptz)6 compound, for which experimental measurements are available, allowing direct comparison with theory.
In terms of ab initio electronic structure methods, different possibilities were explored to balance accuracy with computational efficiency. After careful testing, we opted to construct our database using N-Electron Valence State Perturbation Theory (NEVPT2) on top of a Complete Active Space Self-Consistent Field (CASSCF) wavefunction. For the toy system, we employed an active space of six d-electrons in five orbitals (6e,5o). For Fe(II)(ptz)6, we included two additional σ-bonding doubly occupied orbitals, giving a total active space of ten electrons in seven orbitals (10e,7o). In the calculations, we considered four singlet states, six triplet states, and three to five quintet states.
The computational tool we developed automatically links three main components:
(i) ORCA for the ab initio calculations,
(ii) a PyTorch wrapper for training a neural-network model of the electronic properties (modified SPaiNN), and
(iii) SHARC to perform TSH simulations using machine-learning predictions.
This entire workflow is managed by a Python code we developed, named pyVC, which is freely available on GitHub.
Particular attention was devoted to the training of Spin–Orbit Coupling (SOC) elements, which are essential for describing the spin-crossover transition. Because a large number of states are coupled by SOC in each calculation, obtaining accurate training is challenging. To address this, we developed a strategy to train Spin–Orbit Coupling Reduced Matrix Elements (RMEs) instead. RMEs are directly related to SOC elements and can be recovered from them using the Wigner–Eckart theorem. The advantages of this approach are twofold:
1) RMEs are defined at the spin-free level of the wavefunction, so the number of independent elements is significantly smaller than for the SOC matrix itself.
2)SOC elements are complex numbers, and learning their relative phases between real and imaginary parts is non-trivial. In contrast, RMEs are purely imaginary, which reduces the learning problem to a single component.
Another source of inaccuracy arises from the possible swapping of electronic roots between database entries, which complicates the training of coupling elements. To mitigate this issue, we tested a strategy based on molecular orbital rotations and alignment of CI vectors, ensuring consistent wavefunction character across geometries.
Beyond SOCs, pyVC can also train on energies, forces, and non-adiabatic coupling (NAC) vectors. In this project, however, we bypassed NAC training entirely and instead employed a curvature-based approximation to estimate NACs at intersystem crossing points.
Finally, the full code was applied to the Fe(II)(ptz)6 complex. Our preliminary results demonstrate the capability of the approach to simulate spin-crossover transitions, with good qualitative agreement with experimental data.
The newly developed code pyVC is flexible and not restricted to transition-metal-based systems. It has the potential to assist the study of excited-state dynamics whenever multi-reference methods are required to capture strong electronic correlation. The results of this project pave the way for systematic computational studies of light-induced spin transitions, helping to close the gap between experimental observations and theoretical modeling.
Throughout the process of testing and developing the code, a large number of calculations were performed. The resulting databases, containing all the data, are openly accessible for reuse.
Within the SCOML project, we carried out the first study of Light-Induced Excited Spin-State Trapping (LIESST) using Tully’s Surface Hopping (TSH) techniques combined with multi-reference ab initio electronic structure methods. This was made possible through the development of a dedicated code that interfaces the quantum chemistry package ORCA with PyTorch for training machine-learning models of various electronic properties.
The resulting software, called pyVC, is also capable of internally interfacing with SHARC to perform TSH simulations powered by machine-learning pre-trained models. A key innovation of our approach is a new strategy for learning Spin–Orbit Coupling (SOC) via Reduced Matrix Elements (RMEs). This enables efficient treatment of open-shell systems, where the number of SOC elements increases rapidly with both spin multiplicity and the number of excited electronic states considered in the simulations.
Preliminary results demonstrate a quantitative description of the spin-crossover phenomenon in good agreement with experimental observations. Furthermore, during the course of this project we performed a large number of ab initio calculations. All of the resulting data have been made freely available, providing a valuable resource for future developments in the computational study of radiationless processes in open-shell systems.
The resulting software, called pyVC, is also capable of internally interfacing with SHARC to perform TSH simulations powered by machine-learning pre-trained models. A key innovation of our approach is a new strategy for learning Spin–Orbit Coupling (SOC) via Reduced Matrix Elements (RMEs). This enables efficient treatment of open-shell systems, where the number of SOC elements increases rapidly with both spin multiplicity and the number of excited electronic states considered in the simulations.
Preliminary results demonstrate a quantitative description of the spin-crossover phenomenon in good agreement with experimental observations. Furthermore, during the course of this project we performed a large number of ab initio calculations. All of the resulting data have been made freely available, providing a valuable resource for future developments in the computational study of radiationless processes in open-shell systems.