2.1. Datasets

Molecules reported as SMMs comprise numerous chemical species like phthalocyanine complexes, metallocenes and polyoxometalate complexes (Duan et al., 2022). Salen-type metal complexes were selected as the focus of this study. Salen-type ligands can be effortlessly synthesized from aldehydes and amines to form complexes with various 3d and 4f metals. Several SMM structures have been reported, including mononuclear, binuclear and 3d–4f multinuclear complexes (Liu et al., 2015). From these varied structures, it is expected that structures specific to SMMs can be identified.

The dataset was created using approximately 800 papers from 2011–2021 that were found using the keywords `salen + SMM' using Google Scholar. Data on the crystal structures and whether they exhibited SMM behaviour were collected from these studies, and a dataset was created. Non-SMM molecules were defined as those that did not exhibit magnetic relaxation behaviour according to AC magnetic susceptibility measurements. Tunnelling effects are suppressed under an appropriate DC magnetic field, increasing the likelihood of SMM behaviour. If the measurement results exist under both zero and DC magnetic fields, priority is given to the results under the zero magnetic field.

CIF files were obtained from the CSD (Groom et al., 2016). The crystal structures were verified using the Mercury crystal drawing software (Macrae et al., 2020). The molecular structures were then converted to molecular structure files (XYZ files) by excluding non-pertinent molecules such as crystal water and were utilized as coordinate data. The explanatory variables were the molecular structures retrieved from the crystal structures, while the objective variable was the SMM behaviour.

2.2. Input representation

The input representations of the molecular structures typically include molecular descriptors, graphs and SMILES (Elton et al., 2019). This study utilized 3D images (voxels) as input representations to represent the metal complexes. Although their memory-intensive requirements compared with other input representations, voxel usage is expected to retain the 3D information of the molecules. Their use has been demonstrated for compounds of different sizes and structures, including organic molecules, inorganic solids and proteins (Ryan et al., 2018; Amidi et al., 2018; Kuzminykh et al., 2018; Li et al., 2021; Park & Seok, 2022). These results represent the structural features of metal complexes with different central metals and structures.

The dimensions of the voxels were set to 64 × 64 × 64, with the element type represented by the assigned colour (RGB value) for each element. One side of the voxel was established at 12 Å to preserve the molecular structure. 3D molecular images were created by placing spherical voxels at 3D atomic coordinates obtained from the XYZ file, and 3D molecular images were created (Fig. 1). A balance between voxel resolution and computational resources must be achieved, and an appropriate voxel size must be determined via trial-and-error experimentation.

Figure 1 Voxel diagram of the metal complex. Create a 64 × 64 × 64 × 3 array and specify the colour of each element [R, G, B] for the voxels within a radius r centred on the atom position. [0,0,0] is specified for empty space. In addition, the size of the sphere was changed for each element in proportion to the ionic radius. It is an intuitive and highly versatile descriptor, requiring no special pre-processing.

2.3. Model architecture

A 3D convolutional neural network (3D-CNN) was used as the deep-learning model to create a binary classification model that predicts whether a molecule is an SMM based on its molecular structure (Fig. 2); this multilayer neural network consists of convolutional layers and fully connected layers. The input image is output as a scalar value between 0 and 1 by the last fully connected layer after the 3D convolutional layer extracts the 3D image features (Jogin et al., 2018). In this study, SMMs were set to 0 and non-SMMs to 1; however, which was 0 did not affect the results. ResNet with residue connections (He et al., 2019) was selected as the network structure owing to its impressive image classification accuracy. ResNet can effectively construct deep CNN models with many layers through residual connections between the convolutional layers. The model comprises multiple Res-blocks connected via the GAP layer to fully connected layers. The Res-blocks employ the activation function pre-positioning type, with the ReLU layer positioned before the confluence. Furthermore, a bottleneck-type structure was adopted for these blocks to reduce computational demands. Batch normalization (Bjorck et al., 2018) and a 20% dropout (Gal & Ghahramani, 2015) were used to prevent overlearning. The ReLU function (Agarap, 2019) was used as the activation function, and the sigmoid function (Cybenko, 1989) was used as the final layer.

Figure 2 Conceptual diagram of SMM prediction. The CIF file was edited using crystal drawing software such as Mercury. Crystal water contained in the crystal was removed, and the structure of only the target complex molecule was converted into an XYZ file. The XYZ file is converted into voxels, and 3D-CNN predicts whether it is SMM or non-SMM.

2.4. Model training

As the dataset used in this study was unbalanced data with SMM:non-SMM of 2:1, undersampling (Mohammed et al., 2020) was used to reduce the SMM data to eliminate data unbalances. The dataset was split 6:2:2 into training, validation and test data. The CNN was trained with the Adam optimiser using AMSGrad (Reddi et al., 2019) with hyperparameters ɛ = 1 × 10⁻⁷, β₁ = 0.9 and β₂ = 0.999. The learning rate was reduced from an initial value of 1 × 10⁻² to 1 × 10⁻⁵ using the cosine reduction rate (Loshchilov & Hutter, 2016). The batch size was set to eight to account for GPU memory. The loss function used was the cross-entropy error (Bishop, 1995), which was trained to minimize. The correct response rate and AUC were used as model evaluation indices. Data augmentation (Shorten & Khoshgoftaar, 2019) was performed during training to reduce over-learning. As the molecular structure was obtained in atomic coordinates, voxels were generated after rotation, scaling and translation to 3D coordinates. By performing data augmentation, the model is expected to prevent overlearning and acquire rotational and translational invariance. The CNN was trained for 1000 epochs. These hyperparameters were derived by trial and error.

2.5. Software and libraries

All the programs were implemented using Python 3. TensorFlow 2.0 (Abadi et al., 2016) was used as the machine learning library. The NumPy (Harris et al., 2020) and SciPy (Virtanen et al., 2020) libraries were used for coordinate transformation and voxel generation. Open Babel (O'Boyle et al., 2011) was used to transform the molecular structure files, and CSD Python API (Moghadam et al., 2020) was used to obtain and manipulate the crystal structures. The model training was performed on a Windows 10 OS workstation with an Intel Xeon E5-2620 v3 (12 cores, 24 threads) CPU, 128 GB RAM and a GPU (NVIDIA Tesla K40, 12GB).

3.1. Dataset overview

A histogram of the metal complexes is presented in Fig. 3 to determine the composition of the molecules included in the dataset. This classification is based on seven categories: (i) complexes consisting of a single lanthanide ion, (ii) homonuclear lanthanide ion binuclear complexes, (iii) homonuclear transition metal binuclear complexes, (iv) 3d–4f complexes, (v) 4d–4f or 5d–4f complexes, (vi) complexes consisting of a single transition metal, and (vii) actinide ions (uranium). Histograms illustrating the number of atoms and nuclei in the SMMs and non-SMMs are provided in the supporting information (Figs. S1 and S2).

Figure 3 Histogram of SMM and non-SMM molecules included in the dataset. Blue indicates SMM molecules, and orange indicates non-SMM molecules. (1) Complexes consisting of a single lanthanoid ion. (2) Homonuclear lanthanide ion dinuclear complexes. (3) Homonuclear transition metal dinuclear complexes. (4) 3d–4f complexes. (5) 4d–4f complexes or 5d–4f complexes. (6) Complexes consisting of a single transition metal. (7) Complexes containing actinide ions (uranium).

Figs. 3, S1 and 2 indicate that the differences were not pronounced depending on the number of atoms or nuclei. Histograms depicting complexes containing lanthanide ions show that those containing Dy ions display a significant proportion of SMM properties (Fig. S2a), consistent with several previous results (Zhang et al., 2013; Dey et al., 2018). Complexes containing Dy, Gd and Tb ions constituted a significant proportion of the data. However, for the other lanthanide ions, the quantity of data was minimal, and no distinctions in the SMM properties due to elemental variations were discernible. For the 3d–4f complexes, Dy–Zn complexes are the most prevalent molecules with SMM properties, and Dy–Cu, Dy–Ni and Tb–Zn complexes are also included. Alternatively, Dy–d complexes are still prevalent in molecules lacking SMM properties. However, note that Tb–Cu complexes were the most common (Figs. S3 and S4). It is challenging to use traditional machine learning to forecast SMM properties because of the difficulty in identifying differences by element or number of nuclei and the presence of Dy complexes that do not exhibit SMM properties.

3.2. Learning results

The learning curve is illustrated in Fig. S5, indicating positive progress as the loss decreases with learning. The similarity between the training and generalization errors suggests that the deep-learning model is robust to unknown data. The final accuracy and AUC were approximately 70% (Table 1). The confusion matrix illustrated in Fig. 4 exhibits substantial values for the diagonal components. Distinguishing SMMs from molecular structures alone is challenging, even for the human eye. Notably, the deep-learning model demonstrated 70% accuracy, and the prediction in this study was based solely on voxel information generated from the type of element and its positional relationship.

Figure 4 Confusion matrix in test data.

It is expected that enhancing the descriptors and refining the learning model will result in improved accuracy. In particular, utilizing spin and orbital angular momentum is crucial in magnetism. Previous studies have employed charge distributions and spin densities to obtain voxel information (Kuzminykh et al., 2018; Ghosh et al., 2019; Casey et al., 2020). Quantum chemical calculations can determine these values. However, such calculations require significant computational time and resources when dealing with chemical species containing transition and lanthanide metals. These calculations are unfeasible for studies involving hundreds or tens of thousands of molecules, like in this study. In addition, it would be desirable to compare the performance with the results obtained using graphs, molecular descriptors and voxels. However, numerous methods are inadequate for molecules containing metal ions, necessitating the renovation of programs. Unfortunately, this action was not performed in the current investigation because of time restrictions. Further studies are required to address this issue.

3.3. Visualization of learning results

Grad-CAM (Selvaraju et al., 2017) was used to visualize the area of focus of the model for the inputs. The Grad-CAM diagram indicates that the model is concentrated near the central metal (Fig. 5). Notably, the model recognizes that the central metal initiates magnetism in metal complexes. Fig. S6 demonstrates the successful and unsuccessful predictions, and the model does not focus on significantly misguided areas, even in failed predictions. Furthermore, this model is not expected to focus on particular ligands or functional groups to perform optimally in unfamiliar molecular structures.

Figure 5 Visualization of CNN prediction results using Grad-CAM. The red blocks in the image are the parts that make a significant contribution when CNN makes predictions. It is obtained as voxels 64 × 64 × 64 in size, but was divided into 64 2D images of 64 × 64 for plotting.

In contrast, we expected to discover new structural features that would go beyond the thinking of chemists; however, for this study, we could only obtain the same insights. The opaque nature of deep-learning predictions impedes thorough analysis, leading to tentative conclusions. However, commonly employed chemoinformatics techniques [graph-neural networks (GNNs) and recurrent neural networks (RNNs)] frequently lack visualization methods compared with CNNs. This attribute of CNNs is advantageous for property prediction, rendering it a potent technique in fields lacking a comprehensive understanding of the reaction mechanism, for example in protein–ligand docking and catalysis studies.

3.4. Proof of SMM search with the CSD

Magnetic measurements were conducted in the solid state; therefore, the SMM molecular design must account for the molecular structure within the crystal structure. Predicting the crystal structure of the metal complexes is necessary to design SMM molecules from scratch. However, a method to achieve this goal is yet to be established. Fortunately, the CSD contains one million crystal structures, of which only a small proportion have undergone AC susceptibility measurements. Predicting the SMM behaviour of the crystal structures registered in the CSD was validated as a model case for designing SMM molecules using deep learning.

Approximately 20 000 crystal structures of metal complexes containing Schiff bases were obtained using the program ConQuest. Using the CSD Python API, the molecular structures of the metal complexes were extracted from the crystal structures by removing crystalline water and other components. The SMM behaviours of the molecular structures predicted by the learned model are shown in Fig. 6. The focus was on the top 10 molecules predicted to be the most SMM-like and the bottom 10 predicted to be the least SMM-like. The original publications were searched using CCDC numbers, and the pivotal metal and magnetic measurements are summarized in Tables 2 and 3. Numerous molecules predicted to be SMMs were confirmed to exhibit SMM behaviour. Conversely, many molecules predicted to be non-SMMs have not been measured for AC susceptibility.

Table 2 The top 10 molecules predicted most likely to be SMM `No' if reported not, and `–' if AC susceptibility measurements were not performed.   CCDC Score SMM Metal Reference 1 QURMUN 0.0076 Yes Dy18Zn12 Stavgianoudaki et al. (2016) 2 VUVKEE 0.0189 No† Dy10 Das et al. (2015) 3 REYYEB 0.0228 Yes Dy5Mn4 Alexandropoulos et al. (2013) 4 RECPIB 0.0289 Yes Dy6 Lin et al. (2017) 5 ZEZYIO 0.0327 Yes Dy6 Lin et al. (2012) 6 LOSVOG 0.0331 Yes Dy9 Zou et al. (2015) 7 OPEFOH 0.0441 No Dy6 Schlittenhardt et al. (2021) 8 EZEZUG 0.0453 No† Dy12 Li et al. (2016) 9 YALRAF 0.0472 – UCs Cametti et al. (2005) 10 OPEGAU 0.0475 No Dy6 Schlittenhardt et al. (2021) †Material exhibits magnetic relaxation behaviour under a DC magnetic field.

Table 3 The bottom 10 molecules predicted least likely to be SMM `No' if reported not, and `–' if AC susceptibility measurements were not performed.   CCDC Score SMM Metal Reference 1 PIVGAD 0.9990 – Nd2Cu2 Gheorghe et al. (2007) 2 TOKRAO 0.9990 No Ni15 Muche et al. (2014) 3 VICQUV 0.9991 – Nd2 Zou et al. (2013) 4 VAKLEY 0.9994 – Nd Ling et al. (1989) 5 YUTCAS 0.9994 – Nd2Zn2 Lü et al. (2010) 6 YEBPOL 0.9994 – PrCu2 Gheorghe et al. (2006) 7 XUXNEK 0.9995 – Pr2Cu2 Pointillart et al. (2010) 8 SIGZIU 0.9995 – Nd3Zn6 Song et al. (2018) 9 SIGZEQ 0.9996 – Nd8Zn12 Song et al. (2018) 10 TIYGUF 0.9998 – Nd6Cd18 Yang et al. (2013)

Figure 6 Histogram of predicted SMM properties for approximately 20 000 molecules obtained from the CSD. The closer the frequency is to 0, the more SMM-like it is predicted to be.

Many of the predicted SMM molecules had structures comprising multinuclear Dy complexes. According to equation (1), a larger total number of spins in the complex leads to a more significant value of U_eff. This approach is similar to earlier approaches that enhance the spin multiplicity S using multinuclear complexes of d-metals. Previous studies have shown that symmetry reduction occurs with increased nuclei, and the highest U_eff value was 40 K for ZEZYIO (Lin et al., 2012). This study conducts learning based on the presence or absence of SMM behaviour, with no consideration given to the height of U_eff for simplicity. However, to identify the more promising SMMs, a dataset that considers U_eff should be able to select the best SMMs.

It is important to emphasize that the molecular structure data for the 20 000 molecules used in this study did not include the data used in training. Moreover, while salen-type ligands were prominent in the training phase, a more comprehensive range of ligands (Schiff bases) was included in the 20 000 data points. Thus, the deep-learning model solely predicted unknown molecules without knowing the answers, ultimately selecting the SMM molecules from the CSD. For instance, novel SMM molecules may be uncovered by re-synthesizing molecules that have been predicted to be SMMs but have not been subjected to AC susceptibility and magnetic measurements. The deep-learning-based SMM research model established in this study serves as a practical data-driven chemistry framework.

As referenced in previous research (Sumita et al., 2018, 2022), for AI-assisted molecular design, it is recommended to use data-independent approaches that involve both (1) AI-generated molecular structures and (2) prediction of properties via quantum chemical calculations. AI generates extensive candidate molecules, ranging from tens to hundreds of millions, and property predictions are performed via large-scale supercomputing. The latter is facilitated using supercomputers to predict computational properties. Electronic structure calculations of organic molecules in solution are highly accurate and have successfully controlled UV absorption and created fluorescent molecules (Sumita et al., 2018, 2022). However, solid-state studies on the magnetism of metal complexes encounter two challenges. The first is the obstacle in predicting the crystal structures of metal complexes (Desiraju, 2013; McDonagh et al., 2019). The second is the challenge of simulating magnetism. Novel breakthroughs must be made to resolve these issues. As a compromise, this study designs SMM molecules using molecular structures from a crystal database and data-driven prediction by deep learning. However, the data are limited, and the accuracy of the results depends on the quantity of available data. Moreover, because the results were data-dependent, they were not significantly superior to those obtained by conventional molecular design by conventional chemists. Furthermore, it is not feasible to acquire innovative SMMs solely by predicting molecules with well defined crystal structures. Further research is required in the future.