Source-linked AI summary
Resolving transition metal chemical space: feature selection for machine learning and structure-property relationships
Jon Paul Janet, Heather J. Kulik
TL;DR
Transition-metal ML requires representations that remain accurate with costly calculations and small training sets. The paper develops revised autocorrelation functions and systematic feature selection for organic and inorganic properties, achieving about 1 kcal/mol spin-splitting MUEs with compact subsets and transferable performance across bond-length and redox tasks.
Problem
Model selection and transferable feature-set identification are essential for ML screening, particularly for modest-sized data sets where descriptor quality is critical.
Method
The paper introduces adaptable-resolution heuristic topological descriptors and systematically compares feature-selection methods for electronic and geometric property prediction.
Results
1.00 kcal/mol spin-splitting MUE was achieved with RAC-155, while selected subsets also produced strong bond-length and redox-potential performance.
Takeaways & Limitations
Feature-selection results distinguish local electronic descriptors as important for spin splitting and broader distal effects as relevant to other inorganic properties.
Takeaways & Limitations
Optimal feature sets still differ by model pairing, and the redox data set remains small and should be enlarged in future work.
Abstract
from arXiv · showhide
Machine learning (ML) of quantum mechanical properties shows promise for accelerating chemical discovery. For transition metal chemistry where accurate calculations are computationally costly and available training data sets are small, the molecular representation becomes a critical ingredient in ML model predictive accuracy. We introduce a series of revised autocorrelation functions (RACs) that encode relationships between the heuristic atomic properties (e.g., size, connectivity, and electronegativity) on a molecular graph. We alter the starting point, scope, and nature of the quantities evaluated in standard ACs to make these RACs amenable to inorganic chemistry. On an organic molecule set, we first demonstrate superior standard AC performance to other presently-available topological descriptors for ML model training, with mean unsigned errors (MUEs) for atomization energies on set-aside test molecules as low as 6 kcal/mol. For inorganic chemistry, our RACs yield 1 kcal/mol ML MUEs on set-aside test molecules in spin-state splitting in comparison to 15-20x higher errors from feature sets that encode whole-molecule structural information. Systematic feature selection methods including univariate filtering, recursive feature elimination, and direct optimization (e.g., random forest and LASSO) are compared. Random-forest- or LASSO-selected subsets 4-5x smaller than RAC-155 produce sub- to 1-kcal/mol spin-splitting MUEs, with good transferability to metal-ligand bond length prediction (0.004-5 Å MUE) and redox potential on a smaller data set (0.2-0.3 eV MUE). Evaluation of feature selection results across property sets reveals the relative importance of local, electronic descriptors (e.g., electronegativity, atomic number) in spin-splitting and distal, steric effects in redox potential and bond lengths.
1. Introduction
The paper addresses the difficulty of building transferable, efficient ML representations for inorganic chemistry, where computational costs are high and transition-metal properties depend strongly on local ligand environments. It introduces adaptable heuristic topological descriptors and feature-selection tools for predicting electronic and geometric properties.
- Motivation: Model selection and transferable feature-set identification are essential challenges for ML models intended to augment or replace first-principles screening.Descriptor sets are especially critical for modest-sized data sets and should be cheap, low-dimensional, and preserve target similarity.
- Motivation: Descriptors effective for organic molecules have proven unsuitable for inorganic materials and molecules because transition-metal properties depend strongly on direct ligand atom identity and bonding environment.Spin-state- and coordination-environment-dependent bonding produces a higher-dimensional space requiring sophisticated descriptors.
- Prior work: 3 kcal/mol spin-splitting RMSE and 0.02-0.03 Å metal-ligand bond-length errors were previously obtained with heuristic, topological-only near-sighted descriptors.These descriptors required no precise three-dimensional information and outperformed established whole-complex organic chemistry descriptors.
- Contribution: The work introduces systematic heuristic topological descriptors with adjustable locality, applies them to organic and inorganic test sets, and uses rigorous feature selection to identify optimal feature compositions.The target properties include spin-state splitting, redox potential, and bond length.
- Contribution: The descriptors require no structural information, enabling rapid ML prediction before prior structural calculation and supporting bond-length prediction and structure generation.The paper frames these capabilities as relevant to candidate-material evaluation, potential-energy-surface fitting, and discovery applications.
2. Approach to Feature Construction and Selection
The approach constructs autocorrelation descriptors from molecular connectivity and heuristic atomic properties, then compares descriptor scope, depth, and feature-selection strategies for organic and inorganic prediction tasks. Revised ACs are designed to capture chemically relevant local-to-global relationships without requiring Cartesian or internal coordinates.
- Autocorrelation Functions as Descriptors: Autocorrelation functions encode relationships between atomic properties on a molecular graph, using connectivity rather than Cartesian or internal coordinates.ACs are compact and system-size invariant, unlike several commonly used structural descriptors.
- Autocorrelation Functions as Descriptors: The five heuristic atomic properties include nuclear charge, electronegativity, topology, identity, and covalent atomic radius.Covalent radius contributes spatial information through trends distinct from nuclear charge and electronegativity.
- Depth Selection: 18 kcal/mol MUE at zero depth decreased to 8.8 kcal/mol at maximum three-depth ACs, while six-depth ACs increased test error slightly to 9.2 kcal/mol.The three-depth set contains 20 dimensions, corresponding to four length scales across five properties.
- Descriptor Comparison: At 16,000 training molecules, 3d-AC test-set MUEs were 68% lower than CM-ES and 43% lower than 2B, but 12NP3B4B performed better by 74% or 4.5 kcal/mol.The advantage of 12NP3B4B was attributed to its encoded bond-distance information, whereas 3d-AC is connectivity-only.
- Descriptor Comparison: 3d-AC achieved a test MUE only 2% higher than 12NP3B4B at 1,000 training points and 19% higher at 16,000 points for dipole-moment prediction.Learning rates were comparable among 3d-AC, 2B, and 12NP3B4B, while CM-ES had a slightly steeper rate despite poorer performance.
- Descriptor Scope: ACs are promising size-invariant, connectivity-only descriptors, but their transferability from organic to inorganic complexes remains limited without inorganic adaptations.The paper therefore evaluates revised descriptors and feature selection on inorganic properties.
- Revised Autocorrelation Functions: Revised ACs modify the starting point, scope, and evaluated quantities to support inorganic chemistry, including metal-centered and ligand-centered restricted scopes.Ligand-centered ACs are averaged over coordinating atoms and ligands so differing denticities receive equal treatment.
3. Computational Details
The study constructs transition-metal datasets and computes spin-state, bond-length, ionization, and redox properties using DFT-based workflows.
- 3a. Organization of data sets: Feature selection and model training target adiabatic spin-state splitting and minimum metal–ligand bond lengths, while redox calculations address M(II/III) potentials.The modeled metals include Cr, Mn, Fe, Co, and Ni oxidation-state combinations.
- 3a. Organization of data sets: 1345 complexes comprise the spin-state splitting dataset, covering homoleptic and heteroleptic structures with variable ligand field strength, connecting atoms, and denticity.The dataset uses up to one unique axial and equatorial ligand type and evaluates multiple spin-state-related properties.
- 3a. Organization of data sets: 226 structures comprise the redox dataset, including 41 previously studied complexes and 185 newly generated structures.New structures combine Cr, Mn, Fe, and Co with five neutral monodentate ligands and up to two axial ligand types.
- 3a. Organization of data sets: Redox potentials are computed from adiabatic ionization energies with solvent, vibrational enthalpy, and zero-point energy corrections at 300 K.The workflow uses a thermodynamic cycle and aqueous solvation free energies.
- 3b. First-principles Simulation Methodology: DFT calculations primarily use B3LYP with 20% Hartree–Fock exchange, LANL2DZ effective core potentials, and 6-31G* basis functions.The computational setup includes geometry optimization, unrestricted spin treatment, and convergence controls.
- 3b. First-principles Simulation Methodology: Aqueous environments are modeled with COSMO implicit solvation using ε=78.39, while vibrational entropy and zero-point corrections come from numerical Hessians.The solvent cavity uses scaled van der Waals radii, including a specified iron radius.
4. Results and Discussion
RAC-155 and selected subsets improve prediction of spin splitting and transfer effectively to bond lengths and redox potentials. Results also show that descriptor locality and electronic content matter differently across properties.
- 1.00 kcal/mol MUE is achieved for spin-splitting prediction with RAC-155, substantially outperforming Coulomb-matrix descriptors.
- LASSO-28 removes over 80% of RAC-155 features while retaining comparable spin-splitting performance and achieving the best overall sub-kcal/mol MUE.Its PCA representation also shows weaker size dependence and closer placement of related complexes.
- RAC-12 uses 12 descriptors and remains accurate, with test RMSE and MUE only 1.1 and 0.9 kcal/mol above the 13-times-larger RAC-155 set.Seven RAC-12 descriptors are proximal and five incorporate electronegativity or electronegativity differences.
- Feature selection favors proximal descriptors, but second-shell, distal, and global descriptors remain important for high spin-splitting accuracy.LASSO-28 contains 10 difference-type RACs and only five whole-ligand or whole-complex descriptors.
- Bond-length prediction yields approximately 0.014 Å RMSE and 0.005 Å MUE for most subsets, while PROX-23 produces 2–3-times larger errors.The results indicate that middle and distal features are important for geometric prediction.
5. Conclusions
The paper introduces revised autocorrelation descriptors for machine learning of inorganic quantum-mechanical properties and demonstrates their transferability from organic to inorganic chemistry. Feature selection produces smaller, property-dependent descriptor sets while preserving accurate predictions and revealing locality patterns in transition-metal structure–property relationships.
- Descriptor design: RACs revise autocorrelation descriptors by changing their starting points, molecular scope, and atomic-property quantities for inorganic chemistry.The descriptors extend prior ACs to encode modified atomic-property relationships with an equivalent locality bias.
- Organic chemistry: Organic-molecule tests showed superior standard AC performance for atomization energies using only topological information, especially with distances truncated at three bonds.The reported result is described as the best yet performance for this setting.
- Inorganic prediction: 1 kcal/mol test-set MUE was obtained for the full RAC-155 set in inorganic spin-splitting prediction, versus 15-20x larger errors from whole-molecule structural descriptors.This confirms transferability of RACs from organic to inorganic chemistry with KRR models.
- Feature selection: LASSO and random-forest selection yielded smaller subsets, including LASSO-28 and randF-41, with improved or comparable sub- to 1-kcal/mol spin-splitting test MUEs.A common 12-variable descriptor set produced a 1.9 kcal/mol spin-splitting test MUE, half the error of MCDL-25.
- Feature selection: The selected descriptors transferred to bond-length and redox-potential prediction, reaching 0.005 Å and 0.23 eV test MUEs, respectively.Random forest and the spin-splitting-selected randF-26 showed the best combined transferability.
- Locality and limitations: Redox-selected features indicated that redox potential is more non-local and topological than spin-splitting or bond lengths, but invariant KRR data clustering limited further gains.No improvement was observed for redox-selected redox-potential features, and bond-length-selected features gave only modest improvement for bond lengths.