SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Following the definition of diversity in the literature[149], for each task, we calculate diversity of the proposed molecules using the following equation:
$$
\text {D i v e r s i t y} = 1 - \frac {2}{n (n - 1)} \sum_ {X, Y} \operatorname {s i m} (X, Y) \tag {1}
$$
The expression  $\mathrm{sim}(X,Y)$  computes the pairwise molecular similarity for all  $n$  structures calculated as the Tanimoto distance of the Morgan fingerprints, which were obtained with a radius of size 3 and a 2048 bit size [150]. The individual results for the diversity evaluations of all the benchmark tasks are provided in Tables S6-S9. Overall, we observe mostly relatively small differences in the diversity of the proposed molecules between the different models, except for the chemical reaction substrate design benchmarks. We hypothesize that the strict structural requirement of the corresponding tasks are responsible for this observation as only molecules with the correct reactive core structure are subjected to the property simulation workflow. Additionally, we observe that all generative models except for SMILES-LSTM-HC show consistently a relatively high diversity across all four groups of benchmarks. The molecules proposed by SMILES-LSTM-HC for the organic photovoltaics and for the chemical reaction substrate benchmarks have quite a low diversity compared to the other generative models. Nevertheless, these results suggest that the diversity metric can be insightful in cases of especially low values, but otherwise does not allow to distinguish between the performance of the generative models in a reliable way.
Table S6: Diversity results for the organic photovoltaics benchmarks. Models are trained on a subset of the Harvard Clean Energy Project Database. Results are provided as mean and standard deviation of the best target objective values that are obtained in five independent runs in the form mean  $\pm$  standard deviation. Metrics:  $PCE_{PCBM}$ : PCBM power conversion efficiency;  $PCE_{PCDTBT}$ : PCDTBT power conversion efficiency; SAscore: synthetic accessibility score.
\( {PC}{E}_{PCBM} - {SA}\mathrm{{score}} \)	\( {PC}{E}_{PCDTBT} - {SA}\mathrm{{score}} \)
SMILES-VAE	\( {72.4} \pm {2.6}\% \)	\( {81.6} \pm {3.0}\% \)
SELFIES-VAE	\( {91.1} \pm {0.3}\% \)	\( {91.6} \pm {0.3}\% \)
MoFLOW	\( {88.9} \pm {3.2}\% \)	\( {88.0} \pm {2.2}\% \)
SMILES-LSTM-HC	\( {33.6} \pm {7.2}\% \)	\( {25.8} \pm {13.5}\% \)
SELFIES-LSTM-HC	\( {90.6} \pm {0.6}\% \)	\( {90.5} \pm {1.6}\% \)
REINVENT	\( {88.4} \pm {0.1}\% \)	\( {88.3} \pm {0.1}\% \)
GB-GA	\( {86.2} \pm {0.4}\% \)	\( {89.2} \pm {0.3}\% \)
JANUS	\( {88.2} \pm {0.6}\% \)	\( {88.9} \pm {0.2}\% \)
Table S7: Diversity results for the organic emitters design benchmark objectives. Models are trained on a subset of the GDB-13 dataset. Results are provided as mean and standard deviation of the best objective values from five independent runs in the form mean  $\pm$  standard deviation. Metrics:  $\Delta E(S_1 - T_1)$ : singlet-triplet gap;  $f_{12}$ :  $S_1$  and  $S_0$  transition oscillator strength;  $\Delta E(S_0 - S_1)$ :  $S_0$  and  $S_1$  vertical excitation energy.
ΔE(S1-T1)	f12	+ f12 - ΔE(S1·T1)	- ΔE(S0·S1) - 3.2; eV
SMILES-VAE	90.1 ± 1.1%	78.5 ± 2.7%	80.4 ± 5.3%
SELFIES-VAE	93.0 ± 0.2%	89.5 ± 0.6%	92.1 ± 0.6%
MoFlow	92.2 ± 1.4%	89.1 ± 0.2%	90.3 ± 0.6%
SMILES-LSTM-HC	89.90 ± 0.01%	89.91 ± 0.01%	89.91 ± 0.01%
SELFIES-LSTM-HC	89.91 ± 0.01%	89.91 ± 0.01%	89.91 ± 0.01%
REINVENT	90.8 ± 0.2%	90.8 ± 0.1%	90.9 ± 0.1%
GB-GA	92.0 ± 0.2%	91.1 ± 0.6%	92.1 ± 0.4%
JANUS	91.7 ± 0.1%	92.6 ± 0.1%	92.3 ± 0.2%
Table S8: Diversity metrics for protein-ligand design benchmarks, based on models trained on a subset of the DTP Open Compound Collection. Metrics show mean and standard deviation of optimal target objective values over five independent runs (mean  $\pm$  standard deviation). Benchmark metrics:  $\Delta E_{X}$  denotes docking score for protein target  $X$ .
ΔE1SYH	ΔE6Y2F	ΔE4LDE
SMILES-VAE	80.2 ± 0.2%	91.0 ± 1.0%	89.9 ± 1.4%
SELFIES-VAE	92.8 ± 0.4%	91.9 ± 0.7%	90.6 ± 0.8%
MoFLOW	92.5 ± 1.6%	92.5 ± 1.5%	92.6 ± 1.6%
SMILES-LSTM-HC	91.19 ± 0.01%	91.14 ± 0.04%	91.15 ± 0.02%
SELFIES-LSTM-HC	91.223 ± 0.001%	91.11 ± 0.01%	91.11 ± 0.01%
REINVENT	92.4 ± 0.2%	92.4 ± 0.3%	92.4 ± 0.1%
GB-GA	92.1 ± 0.3%	92.2 ± 0.2%	92.2 ± 0.1%
JANUS	91.5 ± 0.3%	91.6 ± 0.7%	90.9 ± 1.0%
Table S9: Diversity results for chemical reaction substrate design benchmarks. Models, trained on a benchmark dataset generated with STONED-SELFIES cycles, yield mean and standard deviation of optimal objective values over five runs (mean ± standard deviation). Benchmark metrics:  $\Delta E^{\ddagger}$ : Activation energy of the reaction;  $\Delta E_r$ : Reaction energy.
ΔE‡	ΔER	ΔE‡ + ΔER	-ΔE‡ + ΔER
SMILES-VAE	70.4 ± 10.0%	81.7 ± 1.6%	66.5 ± 7.3%	64.1 ± 5.1%
SELFIES-VAE	69.2 ± 4.4%	66.9 ± 5.9%	64.3 ± 4.3%	68.4 ± 12.6%
MoFLOW	90.6 ± 1.9%	87.1 ± 3.2%	84.9 ± 4.4%	85.7 ± 3.7%
SMILES-LSTM-HC	34.2 ± 13.2%	37.6 ± 11.2%	3.8 ± 1.5%	18.4 ± 15.4%
SELFIES-LSTM-HC	59.3 ± 11.3%	75.6 ± 5.4%	55.6 ± 19.8%	72.5 ± 5.8%
REINVENT	88.0 ± 0.4%	88.3 ± 0.3%	83.2 ± 0.8%	83.2 ± 0.8%
GB-GA	81.6 ± 1.1%	83.3 ± 2.2%	76.3 ± 1.6%	80.8 ± 0.6%
JANUS	77.3 ± 2.6%	81.2 ± 1.4%	68.9 ± 4.0%	71.4 ± 2.0%
S4 Additional Discussion
In this section, we will put our findings into perspective and compare them to the pre-existing knowledge in the field. Specifically, we will address two major talking points. First, we will compare the molecular design benchmarks developed as part of TARTARUS to existing benchmarks that are currently being used. Second, we will investigate the results obtained in the various molecular design objectives in detail and discuss their potential implications for the current status of artificial molecular design and future directions for the field.
S4.1 Benchmarking with TARTARUS
First, we would like to emphasize that the benchmark results provided as part of this work largely serve as a demonstration of how the objectives can be used to compare the performance of different algorithmic approaches. They should not be viewed as final performance judgement for any of the methods used as model hyperparameters were not optimized comprehensively. Additionally, changing the constraints with respect to computer time and property evaluations will likely lead to different results calling for further efforts towards better benchmark standardization and the introduction of various benchmark scenarios. We believe that explicitly considering the number of evaluations and computation times are still important to make the use of molecular design algorithms more accessible and relevant to the scientific community as long run times are detrimental to widespread application. Nevertheless, we think that useful insights are still to be garnered from our preliminary benchmark results. When looking at all the outcomes combined, one curious observation is that, unlike many previous benchmarking efforts, we do not find one algorithm to perform the best, or at least close to the best, across all the tasks considered. This suggests that the newly introduced design objectives differ significantly in their structure requirements and algorithmic demands. Thus, we believe that different domains of chemistry and material sciences have different structure and design requirements that could potentially motivate the development of algorithms tailored to specific problem domains. At the very least, it suggests that significant further developments are necessary in the field in order to create a true champion algorithm for the design tasks considered.
Next, we will investigate the results of each of the molecular design sets in detail. The benchmark tasks inspired by the design of OPVs prove extremely difficult as most models fail to improve upon the reference structures and, if they do, the improvements are very small. This suggests that the provided dataset already contains almost optimal solutions with respect to the fitness functions chosen. Nevertheless, the models should at least be able to reproduce the dataset results. We suspect that these difficulties of some of the models is likely related to uncertainties in the learned structural space [151]. Notably, the property distributions depicted in Figure S8 show that the multiobjective function is mainly dominated by the PCE values. We believe that increasing the relative importance of the SAcore in the objective function could improve this benchmark task even further. Nevertheless, our results suggest that the design of OPVs based on the Scharber model and an explicit account of synthetic accessibility is delicate and proves challenging for many common molecular design algorithms. Based on the judgement of an expert chemist, the best structures proposed by the molecular design algorithms are likely all stable and synthesizable showing the
importance of accounting for that explicitly in molecular design benchmarks. It is interesting to see that the two best structures found in each of the objectives are quite similar which is likely because they do not stray far from the best compounds already contained in the reference dataset. The best structures for the donor design task seem to prefer having a 2,1,3-thiadiazole moiety while the acceptor design task prefers extended annulated  $\pi$ -systems.
Looking at the objectives based on the design of OLEDs, they are all practically relevant as they are directly based on the design of TADF emitters. The molecular design algorithms showing most consistent performance across the three tasks are JANUS and GB-GA. Interestingly, SELFIES-VAE also shows good performance over all three tasks and it outperforms SMILES-VAE very significantly which could suggest difficulties of the SMILES-VAE to learn the underlying property distribution of the training dataset. Notably, none of the molecular design algorithms used outperform the best molecule in the reference data for the oscillator strength benchmark. Additionally, only three of the models, namely SELFIES-VAE, JANUS, and GB-GA, deliver better properties for the combined objective than the reference structures possess. This demonstrates the difficulty of the corresponding benchmark tasks. Looking at the best performing molecules proposed by the models, the best structures are largely stable and synthesizable. However, there are a few features that are not ideal. In particular, the two molecules with the highest oscillator strength have an oxidized benzene ring that is likely reactive. Additionally, the molecule with the highest combined objective is present in its enol tautomer but it is likely that the corresponding ketone is preferred. This suggests that incorporating the SAscore as a constraint helps increase the stability and synthesizability of the generated molecules but also suggests that additional filters are necessary for higher robustness in that regard. Moreover, some structural features required for favorable properties can be derived. In particular, for high oscillator strength values, extended  $\pi$ -systems are beneficial which is well-known in the field of organic electronic materials [152, 153].
Next, we need to inspect the outcomes of the protein ligand design benchmarks, which also have the lowest number of specific objectives, and is currently the only benchmark set without a multiobjective molecular design task. Most interestingly, while the general setup of all the three objectives is identical, we find the performance of the molecular design algorithms to be varying significantly depending on the specific target. This suggests that designing ligands based on molecular docking for the three proteins chosen differs significantly in terms of structural requirements. Most models succeed at proposing ligands with better docking scores than the best reference compounds for all three target proteins. In terms of the constraints, surprisingly, the VAEs show the poorest performance which hints towards difficulties during training. Otherwise, JANUS also generally shows somewhat lower success rates which is likely caused by its limited features to bias structure generation by reference compounds and its tendency to explore more diverse structural regimes to potentially find new candidate solutions. This is relevant as the success rates are not only measured on the best-performing molecules but over all the structures proposed. In contrast, the LSTM-HC models, REINVENT and GB-GA consistently reach higher success rates demonstrating that they succeed at learning to propose desirable structures based on the reference dataset. Additionally, it likely also implies that exploration far outside of the distribution of the reference dataset is avoided. Thus, overall, REINVENT and GB-GA provide the most promising results in these protein ligand design benchmarks. When looking at the best-performing structures, it is notable that molecules resembling steroids seem to be good binders for at least two of the protein targets selected. Notably, there is one important aspect to be discussed that relates specifically to the dataset of reference compounds and the simulation workflow. While the DTP Open Compound Collection is particularly attractive to be used as training dataset because all these structures have been synthesized and tested experimentally for potential use as drug candidates, it suffers a major drawback in terms of data quality. Unfortunately, the majority of structures lack proper definition of stereochemistry despite often having multiple stereogenic centers. While our computational workflow is deterministic with respect to the particular stereoisomer produced when provided with SMILES without defined stereochemistry, it is still very likely that stereoisomers were produced and simulated that do not correspond to the ones of the actual molecules in the compound collection. Thus, when SMILES without well-defined stereochemistry are submitted to the property prediction workflow, the 3-dimensional structure generated in the process needs to be inspected to derive the stereoisomer computed and guide subsequent experimental validation. For even more realistic drug design benchmarks tasks in the future, a reference dataset of structures that have both been experimentally synthesized before and
When investigating the results of the chemical reaction substrate design benchmark tasks, we find that only the two GAs employed consistently outperform the best reference structures. This is particularly notable as both JANUS and GB-GA achieve large improvements over the best properties in the training set for all but the fourth benchmark objective showing that there is, in principle, significant room for further improvement. Additionally, in many cases, the proposed molecules perform significantly worse than the best-performing reference compounds suggesting that many of the algorithms used seem to have difficulties to learn from the provided dataset. This could potentially point towards peculiarities of the provided training set as it was the only one that was created in a random way from the necessary core structure. It might be too small in size paired with a high diversity of structural moieties making it challenging to extract structure-property relationships. Notably, as expected because it goes against the Bell-Evans-Polanyi principle, the fourth benchmark objective proves to be extremely difficult with the best results providing only comparably small improvements over the reference set. The structures of the best proposed compounds for each of the design objectives provide some preliminary insights into the structural features effecting favorable properties (cf. Figure S4). The sites donating hydrogen atoms seem to prefer being more substituted for both lowering the barriers and lowering the reaction energies. This effect can be understood by a reduction of steric repulsion between these substituents and the bridge substituents when going from tetrahedral to trigonal geometry around the respective carbon atom. Particularly effective for lowering reaction energies seem moieties suitable for conjugation with the newly generated double bond in the product, owing to the stabilizing effect of extended conjugation. To break the correlation between reaction energies and activation energies, the introduction of two mesomerically electron-donating groups appear most suitable, potentially due to the opposing factors of sterics, lowering the reaction energy as outlined above, and electronics. Notably, deciphering substituent effects for these type of dyotropic reactions is known to be difficult [154], and would require more extensive and systematic analysis and corroboration which is outside the scope of this work.
The final benchmark of TARTARUS to be discussed is the model timing comparison. This is important as it can provide information about whether improved optimization performances originate from the utilization of more computational resources and longer training times. It should be noted that the absolute computation times reported are not useful as they strongly depend on the computer hardware available. Hence, we recommend them to be used as a relative rather than an absolute measure. Thus, when new models are being tested for timing, some of the molecular design algorithms provided here as a reference should be run again with the same hardware as internal standards permitting a relative timing comparison to all the other algorithms. Looking at the timing results, apart from the VAEs, we consider training to be still affordable for the deep generative models tested, even without the availability of GPUs. However, without GPUs, training the VAEs is computationally too expensive and is detrimental to its widespread application, and even for the LSTM-HC models it is comparably cumbersome. Additionally, while molecule sampling time, taking roughly on the order of a few minutes in most cases, is generally reasonable, we believe that there is considerable room for further improvement. This is particularly evident from the extremely good timing performance of REINVENT taking less than one minute for that step. Nevertheless, as it is more important to propose several meaningful structures than to generate a large number of structures fast, we believe that the sampling times of the all the algorithms tested are sufficient for practical purposes.
S5 Computational Details
S5.1 Molecular Design Algorithms
S5.1.1 VAE
We implemented a variational autoencoder (VAE) architecture from the literature [31]. In particular, the encoder used three 1D convolutional layers with filter sizes of 9, 9, and 10 convolution kernels, followed by one fully connected layer that encodes a latent space of size 292. The decoder fed into three layers of gated recurrent unit (GRU) networks [107] with a hidden dimension of 501 each. Based on the respective training dataset to be used and the encoding used for representing
have well-defined stereochemistry that reflects the experimental samples needs to be used.
the molecules (i.e., SMILES or SELFIES), we modified the alphabet size for converting the list of molecules into one-hot encodings. Additionally, the string length of the largest molecule from the dataset is used to pad sequences to the same length. Based on the dataset, these two parameters lead to minor modifications in the sizes of the first and last layers of the encoder and decoder, respectively. For each dataset, the models are trained using 24 CPUs and a single GPU, with training times ranging between 2 and 10 hours. Generally,  $80\%$  of the reference molecules are used for training, while the remaining ones are used for testing. We manually optimize the learning rate, learning rate decay rate, number of epochs for training, and the batch size based on performance on the test set. After obtaining a fully trained model, we perform structure optimization. The best known molecule for a given task, i.e., the one with the most favorable score, is converted into a one-hot encoding and passed through the encoder to the latent space. Subsequently, Gaussian noise is added to the latent space vector to produce a population of vectors. These vectors are passed through the decoder to produce molecules that are evaluated via the respective objective function. The best molecule resulting from this population is then used to repeat this procedure.
S5.1.2 JANUS
Throughout the benchmarks, we used the default implementation of JANUS (https://github.com/aspuru-guzik-group/JANUS). We used version 1.0.3 of SELFIES, and the default valence constraints implemented in that version of SELFIES were employed. Additionally, no structure filters were employed in the genetic operators. For initiation, the file sample_start_smiles.txt was populated with the 1,000 best molecules from the corresponding benchmark reference dataset. The generation_size parameters and the other parameters that influence the generations are modified based on the respective benchmark task. An artificial neural network (ANN) classifier is used for additional selection pressure for all the tasks (cf. JANUS+C in the original publication [7]).
S5.1.3 GB-GA
We employed of the implementation provided by Jensen [34] in the following repository: https://github.com/jensengroup/GB_GA/. For initiation, the file ZINC_first_1000.smi was populated with the 1,000 best molecules from the corresponding benchmark reference dataset for preconditioning to derive both mutation and crossover probabilities. The file scoring-functions.py was modified each time to incorporate the corresponding fitness functions from different benchmark tasks.
S5.1.4 LSTM-HC
The long short-term memory hill climbing (LSTM-HC) approach uses a pre-trained long short-term memory (LSTM) [105] recurrent neural network (RNN) to generate sequences of molecular strings [33], and can be implemented with either SELFFIES or SMILES. For each molecule, the string representation characters are transformed into one-hot encoded vectors, which are padded up to the length of the longest string in the respective reference dataset for each benchmark task. Similar to how it was implemented in the literature [33], the model consisted of 3 stacked LSTMs, each with 1024 hidden dimensions and a dropout ratio of 0.2, followed by a linear layer that outputs the logits of the next predicted character in the string sequence. That way, the output returns the probability for observing a certain subsequent character, given the preceding characters in the sequence. The model was pre-trained with a batch size of 128, using the ADAM optimizer [155] with a learning rate of 0.001. For optimization in each of the benchmark tasks, the top 2 known molecules with the best fitness values are used to create seeds for the LSTM structure generation. For SMILES, the strings are truncated randomly at  $25\%$  to  $75\%$  of the size of the original sequence. For SELFFIES, the strings are first randomized 5 times using reordered SMILES that represent the same molecule before they are being truncated. Subsequently, the truncated strings are passed into the model and the next characters are generated by sampling from the probability distribution that is generated by the LSTM output. Each iteration, the model generates 500 new molecules for evaluation, and the top 2 molecules are selected for the subsequent iteration. Additionally, the model is retrained after each iteration on the set of new molecules for 10 epochs at a lower learning rate of 0.0001.
S5.1.5 MoFlow