12.4 Frontiers — What Comes Next

The two preceding sections described tools that, by the end of 2025, had matured to the point of routine use. This section is more speculative. It surveys the directions in which the foundation-model programme is actively expanding, the open problems that remain unsolved, and the recent literature that a reader who wants to follow this field should know about.

Multimodal models

The foundation models of Sections 12.2 and 12.3 operate on a single modality: atomic structure. A growing body of work argues that the real leverage will come from models that simultaneously ingest multiple representations of the same material — structure, computed spectra, experimental measurements, text from the literature — and build a joint embedding space across them.

The motivating analogy is CLIP. By training on \(400\) million image–caption pairs with a contrastive loss, CLIP produces a joint embedding space in which an image of a cat and the text "a cat" land in nearby points. Once such a space exists, an enormous range of downstream tasks becomes trivial: zero-shot classification (compare to text-template embeddings), retrieval (find images whose embedding is closest to a query), even generation (used as a critic in DALL-E / Stable Diffusion).

In materials science the analogous data would be:

• Structure — the same graph representation used by MACE or MatterGen.
• Computed properties — DFT-derived band structure, density of states, phonon spectrum, optical response.
• Computed spectra — simulated XRD, infrared, Raman, NMR, XANES.
• Experimental measurements — measured XRD patterns from ICSD or in-house databases; reported band gaps; magnetic susceptibilities.
• Literature text — abstracts and full text of materials papers, including the human descriptions of the systems studied.

A foundation model trained to align these modalities — in the manner of CLIP, or of more recent multimodal transformers — would in principle let a user issue queries of the form "find structures whose XRD pattern matches this measurement, predicted to have a band gap above \(2\) eV, that have not been previously reported". Several research groups (notably at MIT, Microsoft and DeepMind) have prototypes in this direction, and the public release of such a model seems likely within the next two years.

What makes the problem genuinely hard is the misalignment of the modalities. The same crystal has many possible structural representations (primitive cell, conventional cell, supercell), each giving the same physical predictions but different graph inputs. Its computed properties depend on the level of theory used. Its experimental measurements depend on the sample and on the measurement protocol. Its literature description is in human-written prose, with terminology that varies between sub-fields. A useful multimodal model must be invariant to all of these incidental variations while remaining sensitive to the underlying physical identity. This is harder than the corresponding problem for natural images, where the modes of variation are more constrained.

Autonomous laboratories and the closing loop

A parallel line of work, less visible to the modelling community but arguably more consequential, is the construction of autonomous laboratories — robotic platforms that synthesise, characterise and return data on materials proposed by a computational pipeline, with no human in the inner loop.

The exemplar is A-Lab at Lawrence Berkeley National Laboratory, which in late 2023 reported the autonomous synthesis of \(41\) novel inorganic compounds in \(17\) days, with structures proposed by a combination of generative models and active-learning surrogates. The A-Lab pipeline integrates powder XRD, mass spectrometry, and a robotic precursor-mixing platform; failures (most attempts do fail) are fed back into the model as negative examples.

Several similar platforms exist or are under construction:

• The Self-Driving Lab consortium (University of Toronto, NRC Canada) — focused on optoelectronic and catalytic materials, with several active loops on organic photovoltaics and reductive electrocatalysts.
• MAP at the University of Liverpool — focused on porous framework materials, with a particularly strong integration of computational screening and synthesis.
• Aroyo at Argonne — focused on battery cathodes, with in situ electrochemical characterisation.

The conceptual significance of these platforms is that they close the simulation-experiment loop in a way that has been promised since the inception of the Materials Genome Initiative in 2011. A generative model proposes; an MLIP screens; DFT verifies; a robot synthesises; characterisation returns measured properties; the loop re-iterates. The cycle time, on these platforms, is days to weeks, not the years that a graduate-student-mediated loop typically takes.

The bottleneck, as of 2026, is no longer the modelling. It is the synthesis — the long tail of compositions for which no robust robotic protocol exists. Most autonomous labs have a relatively narrow window of chemistry within which they can operate (specific solvent classes, specific temperature ranges, specific characterisation tools), and the foundation models must learn to propose candidates inside that window. The mismatch between what the models think is "interesting" and what the lab is "capable of" is now an active area of methodological work.

What the foundation models still cannot do

Notwithstanding the impressive recent progress, several physical phenomena remain stubbornly outside the reach of universal MLIPs and generative models. Honest accounting of these gaps is essential.

Long-range interactions

All current universal MLIPs use a finite cutoff (typically \(5\)–\(6\) Å). This is adequate for short-range covalent and metallic bonding but fails to capture phenomena that depend on long-range Coulomb forces: the dielectric response of ionic crystals, ferroelectric phase transitions, the energetics of charged defects, polaronic states. The LO–TO splitting in polar phonon spectra, for instance, requires the non-analytic correction associated with the macroscopic dipole — and no purely short-range MLIP can produce it.

Active research is exploring three remedies:

• Hybrid models that combine a short-range MLIP with an explicit Ewald-summed Coulomb term, with charges either fixed (using oxidation-state assignments) or predicted by the model itself.
• Long-range MLIPs that pass messages over many more layers, enlarging the effective receptive field. This has the cost of increased inference time and reduced numerical stability.
• Foundation models with self-consistent charge equilibration, in which atomic charges are themselves variables that respond to the local environment. The 4G-HDNNP architecture (Ko et al., 2021) and its successors are the canonical references.

None of these has been fully integrated into a public universal MLIP as of mid-2026, but the field is moving quickly.

Charge transfer

A closely related problem. Reactions involving electron transfer between atoms — redox processes in batteries, electrochemical catalysis, photoexcitation — depend on the redistribution of electronic charge, which a purely local MLIP cannot represent. CHGNet's magnetic-moment head is a partial concession to this problem; explicit charge models are the natural next step.

Excited states

Almost every MLIP discussed in this book is fitted to ground-state DFT data, and the resulting potential is appropriate for ground-state dynamics only. Excited-state phenomena — photochemistry, exciton dynamics, non-adiabatic relaxation — are outside its remit. A foundation model for excited-state dynamics would require training on TDDFT, MRCI or \(GW\)+BSE data; such datasets exist but are perhaps three orders of magnitude smaller than MPtrj. Progress here is gated by data, not by architecture.

Magnetic ordering

Universal MLIPs typically treat the magnetic state as a property of the configuration (CHGNet) or simply ignore it (MACE-MP-0). Neither approach captures the full complexity of frustrated magnetism, where the energy landscape depends sensitively on the spin configuration as much as on the atomic positions. A magnet-aware foundation MLIP would need either to enumerate spin states explicitly or to predict them as part of its output. The Heisenberg-MACE work of late 2024 is a step in this direction; the field is unsettled.

True generalisation across the periodic table

The implicit hope of the universal-MLIP programme is that a model trained on a comprehensive corpus will generalise to any chemistry within the periodic table. Empirical evidence is mixed. On elements well-represented in the training data, generalisation is strong; on under-represented elements (actinides, several lanthanide oxidation states), the model is closer to an interpolator confined to the training distribution.

A more honest statement is that the current foundation MLIPs generalise well within the chemistry of their training data and moderately well across the configurations (different temperatures, pressures, defect states) of those chemistries. They do not yet generalise across genuinely new chemistry, and there is no a priori reason to expect that they will without further data.

Three open problems in detail

The brief survey above identified several gaps in the current foundation-model toolkit. Three of them deserve closer scrutiny because they are physical limitations of the dominant architectures, not merely engineering debt that will be cleared by larger datasets. Each is the subject of substantial recent work, none has a clean solution, and each is likely to define a sub-field of materials machine learning for the next several years.

Long-range Coulomb in MLIPs

The problem. Every universal MLIP described in this book uses a finite cutoff radius — typically \(5\)–\(6\) Å — beyond which atomic interactions are simply truncated. For short-range covalent and metallic chemistry this is excellent: the energy landscape is set by the local bonding environment, and the truncation error decays exponentially with the cutoff. For systems where long-range electrostatics matters, the truncation is qualitatively wrong.

The clearest diagnostic is the dielectric screening of a polar crystal. The macroscopic Born effective charges and the LO–TO splitting in the phonon spectrum both arise from the non-analytic behaviour of the dynamical matrix at small wavevector, \(\mathbf{q} \to 0\), where Coulomb forces are unscreened. A purely local MLIP cannot reproduce this: the small-\(\mathbf{q}\) dynamical matrix is built from far-apart-atom-pair contributions that lie entirely outside the model's receptive field. Polar phonon spectra, ferroelectric instabilities, dielectric constants, and the energetics of charged defects in ionic solids all carry the same signature error.

Why current methods fail. The dominant message-passing architectures (MACE, NequIP, SevenNet) gather information through local convolutions over a graph defined by the cutoff. Stacking more layers extends the effective receptive field but at quadratic cost in number of operations and worsening numerical stability of the gradient through many message-passing steps. To capture Coulomb forces with the correct \(1/r\) tail requires either an analytical long-range term — an Ewald-summed Coulomb interaction layered on top of the MLIP, with charges as additional outputs — or a fundamentally different architecture (e.g., one that operates in reciprocal space).

The 4G-HDNNP architecture of Ko et al. (2021) handles long-range electrostatics by learning the atomic charges and adding an explicit Ewald sum. Recent universal-MLIP descendants (MACE-LR, Cheng's Cartesian-ACE long-range extension, the eqV2 long-range variant in development) follow the same pattern. None of these is yet in widespread use as a drop-in foundation model; the engineering of charge equilibration in a parameter-sharing setting across \(96\) elements is genuinely difficult.

What success would look like. A universal MLIP that reproduces, within DFT accuracy, the Born effective charges and LO–TO splittings of a few canonical polar oxides (MgO, SrTiO\(_3\), BaTiO\(_3\), PbTiO\(_3\)), the dielectric constants of layered materials, and the formation energies of charged defects relative to neutral references. As of mid-2026 no public model has cleared this bar; the published benchmarks compare neutral, near-equilibrium configurations almost exclusively.

Recent attempts. Anstine and Isayev (2023) survey the field; Loche et al. (2024) report a long-range MACE variant that reproduces the dielectric response of BaTiO\(_3\) within \(\sim 15\)%; the Cheng-group Cartesian-ACE long-range work (npj Computational Materials, 2024) shows promising results on simple ionic solids but has not yet been scaled to a universal model.

Long-range electrostatics in depth — the dominant 2024–2026 frontier

The paragraphs above sketch the problem; it deserves a fuller treatment, because for ionic and polar materials it is not one open problem among several but the open problem. A universal MLIP that got long-range electrostatics right would immediately unlock ferroelectrics, fast-ion conductors, dielectric screening, charged defects, and a large fraction of battery and electrochemistry modelling. The remainder of this subsection lays out why short cutoffs fail, the three main architectural responses, and a worked example where the distinction is unmistakable.

Why short cutoffs fail — the physics. A standard message-passing MLIP truncates interactions at a cutoff \(r_\mathrm{c}\), typically \(5\)–\(6\,\text{\AA}\). For the chemistry that sets covalent and metallic cohesion this is not an approximation worth worrying about: the exchange–correlation hole, the kinetic-energy contributions, and the bond-order physics all decay exponentially with distance, so the truncation error is of order \(e^{-r_\mathrm{c}/\xi}\) with a correlation length \(\xi\) of order an angstrom. Doubling the cutoff buys nothing measurable.

Electrostatics and dispersion are qualitatively different. The Coulomb interaction between two partial charges goes as \(1/r\); the leading dispersion (van der Waals) term goes as \(1/r^6\). Neither has a length scale beyond which it is negligible — they have tails. The energy contribution from the shell of material between \(r_\mathrm{c}\) and infinity is

\[ \Delta E_\mathrm{Coul} \;\sim\; \int_{r_\mathrm{c}}^{\infty} \frac{1}{r}\, \rho(r)\, 4\pi r^2 \, \mathrm{d}r, \]

which, for a non-zero mean charge density \(\rho\), does not converge at all without the careful cancellation that an Ewald sum arranges. Truncating it is not a small error; it is the omission of a conditionally convergent series. Even when the system is locally neutral, the dipole and quadrupole fields of distant regions (\(1/r^3\), \(1/r^4\)) reach into the central cell and a \(6\,\text{\AA}\) model simply cannot see them.

The LO–TO splitting is the canonical local-model failure

In a polar crystal — any crystal with more than one atom per cell and a non-zero Born effective charge — the longitudinal-optical (LO) and transverse-optical (TO) phonon branches are split at the zone centre, \(\mathbf{q} \to 0\), even though they are degenerate by symmetry in a hypothetical non-polar analogue. The splitting arises from the macroscopic electric field that a long-wavelength longitudinal phonon sets up: a genuinely non-local effect, encoded in the non-analytic term of the dynamical matrix,

\[ D^\mathrm{NA}_{\kappa\alpha,\kappa'\beta}(\mathbf{q}\to 0) \;\propto\; \frac{(\mathbf{q}\cdot \mathbf{Z}^*_\kappa)_\alpha\, (\mathbf{q}\cdot \mathbf{Z}^*_{\kappa'})_\beta} {\mathbf{q}\cdot \boldsymbol{\varepsilon}_\infty \cdot \mathbf{q}}, \]

built from the Born effective-charge tensors \(\mathbf{Z}^*\) and the electronic dielectric tensor \(\boldsymbol{\varepsilon}_\infty\). A purely local MLIP has no representation of this term: the contribution comes from atom pairs separated by arbitrarily large distances, all of which lie outside the receptive field. Run a finite-difference phonon calculation with a short-cutoff foundation MLIP on GaN, ZnO, MgO or BaTiO\(_3\) and the LO and TO branches will come out degenerate at \(\Gamma\) — a qualitative, not quantitative, failure. The infrared and Raman spectra built on those phonons are then wrong in a way no amount of training data at fixed cutoff can fix.

The dispersion tail is the same disease, milder. Electrostatics is the dramatic case, but the \(1/r^6\) dispersion interaction has the same structural problem: it is a tail, not a screened local quantity. A \(6\,\text{\AA}\) cutoff captures most of the pair dispersion energy between two atoms but not the slowly converging sum over all distant pairs, which matters for layered materials (graphite interlayer binding, transition-metal dichalcogenides), molecular crystals, and physisorption. The usual fix is pragmatic and predates MLIPs entirely: bolt on a Grimme D3 or many-body-dispersion (MBD) correction, summed to convergence outside the cutoff. This works because dispersion, unlike charge transfer, is additive and environment-mild enough that a semi-empirical pairwise (or MBD) term is a good model. It is worth noting the asymmetry: the community treats the dispersion tail as solved-enough by D3/MBD, but treats the Coulomb tail as an open research problem — because Coulomb couples to charge, charge responds non-locally to the environment, and there is no equally cheap, equally reliable bolt-on.

Response 1 — 4G-HDNNP: let charge flow non-locally. The fourth-generation high-dimensional neural network potential of Ko, Finkler, Goedecker and Behler (Nature Communications, 2021) is the cleanest architectural answer. The idea is to insert a global charge-equilibration step between the descriptor and the energy. A local network first predicts an electronegativity \(\chi_i\) for each atom from its local environment. A charge-equilibration (QEq) layer then solves, for the whole system at once, the linear problem of distributing the total charge so as to minimise an electrostatic energy functional

\[ E_\mathrm{elec}(\{q_i\}) = \sum_i \left( \chi_i q_i + \tfrac{1}{2} J_i q_i^2 \right) + \tfrac{1}{2} \sum_{i \neq j} \frac{q_i q_j}{r_{ij}} \quad\text{subject to}\quad \sum_i q_i = Q_\mathrm{tot}, \]

with \(J_i\) a hardness parameter. Because the constraint and the \(1/r_{ij}\) kernel couple every atom to every other, charge can flow from one end of the cell to the other in response to a local perturbation — exactly the non-locality a cutoff model lacks. The equilibrated charges then feed an explicit Ewald-summed Coulomb energy, and a second short-range network adds everything else. The 4G-HDNNP correctly describes textbook cases that defeat third- generation potentials: a charged metal-oxide cluster whose excess electron localises on the far side, or a system where the charge state depends on a defect several nanometres away. The cost is a linear solve per evaluation (or a few iterations of a conjugate- gradient solver), which is cheap relative to the network itself but does introduce a global communication step that complicates parallelisation.

Response 2 — LODE: a descriptor that carries the long-range field. Grisafi and Ceriotti (J. Chem. Phys., 2019) take a representational rather than an architectural route. Their Long-Distance Equivariant (LODE) descriptor is built by treating each atom as the source of a potential field — a \(1/r\) (or, more generally, \(1/r^p\)) field — and then expanding the total field at each atom on a local basis of spherical harmonics and radial functions, exactly as SOAP expands the local density. The key difference from SOAP is the kernel inside the expansion: SOAP convolves a Gaussian density, which is short- ranged; LODE convolves a Coulomb-like density, whose \(1/r\) tail means the resulting features at atom \(i\) carry information about atoms arbitrarily far away. In practice LODE is used as a complementary feature set: a short-range SOAP/ACE/MACE descriptor captures the local chemistry, and the LODE channels are concatenated to inject the long-range electrostatic context. The combination has been shown to recover the correct \(1/r\) scaling of dimer binding curves for ionic pairs and to improve the description of molecular crystals where electrostatics dominates the lattice energy. The limitation is that LODE, in its standard form, assumes a fixed multipolar character for the long-range source and is less natural for genuine charge transfer.

Response 3 — latent Ewald and range-separated MACE. The most recent line of work bolts a long-range term directly onto an existing short-range foundation architecture. The general pattern is range separation: write the total energy as

\[ E = E_\mathrm{SR}^\mathrm{MLIP}(r < r_\mathrm{c}) + E_\mathrm{LR}^\mathrm{Ewald}, \]

where \(E_\mathrm{SR}\) is an ordinary MACE (or NequIP) restricted to the cutoff, and \(E_\mathrm{LR}\) is an Ewald sum over charges (or, more generally, multipoles) that the network also predicts as an extra equivariant readout head. "Latent Ewald" variants make the long-range charges latent variables rather than physical Mulliken- or Hirshfeld-style charges: they are whatever values make the Ewald term best reproduce the DFT energies and forces, with no requirement that they match any particular population-analysis scheme. This is pragmatic — the network is free to use the long-range channel as a correction term — but it sacrifices interpretability, and there is an identifiability question (many charge assignments give similar long-range energies). Loche et al. (2024) report a range-separated MACE that reproduces the dielectric response of BaTiO\(_3\) to within roughly \(15\%\); this is real progress but still short of the DFT-accuracy bar set for short-range properties.

Charge transfer and electrochemistry — the hardest corner. The three responses above all assume the total charge of the cell is fixed and the question is only how to distribute and propagate it. Genuine electrochemistry breaks that assumption. An electrode at a controlled potential exchanges electrons with its surroundings; the cell carries a net charge that is itself a dependent variable, set by the applied potential rather than by the composition. No public universal MLIP supports this today: the architectures have input channels for position and species but none for total charge or electrochemical potential, and the training data (DFT at charge neutrality, almost without exception) never exercises the degree of freedom. The current research directions are two. CENT (charge-equilibration via neural-network technique, Ghasemi et al. 2015 and successors) makes the electronegativities the learned quantity and then equilibrates charge globally — the same QEq machinery as 4G-HDNNP, but framed so that a non-zero total charge or an imposed chemical potential is a natural boundary condition rather than an afterthought. Constant-potential MD (the Bonnet–Otani– Sugino scheme and its descendants) is the explicit-DFT reference: the electrode is held at a fixed Fermi level and electrons are allowed to flow in and out grand-canonically. A learned surrogate for constant-potential MD — an MLIP that takes the electrochemical potential as an input and returns forces consistent with the self-consistently determined cell charge — is an obvious and much-wanted target, and is treated further in the "Charged systems and electrochemistry" subsection below. The short version: charge transfer is long-range electrostatics plus a moving total-charge constraint, and it is correspondingly harder.

A worked example — BaTiO\(_3\), where the cutoff model fails and the long-range model succeeds. Barium titanate is the textbook ferroelectric. Above \(\sim 400\,\mathrm{K}\) it is cubic perovskite and paraelectric; cooling through the Curie point it distorts to a tetragonal phase in which the Ti ion sits off-centre in its oxygen octahedron, producing a spontaneous polarisation of order \(0.26\,\mathrm{C\,m^{-2}}\). The energetics of that distortion are a delicate balance: a short-range double-well in the Ti displacement, stabilised against the short-range restoring force by the long-range dipole–dipole coupling between unit cells. Remove the long-range term and the balance tips.

Concretely, take a \(5\times5\times5\) supercell (\(625\) atoms) and ask three questions of (a) a stock short-cutoff foundation MLIP and (b) a range-separated long-range variant:

Quantity	Short-cutoff MLIP	Long-range variant	DFT / experiment
Cubic \(\to\) tetragonal double-well depth	washed out, near-flat	\(\sim 15\)–\(25\,\mathrm{meV}\) per f.u.	\(\sim 20\,\mathrm{meV}\) per f.u.
\(\Gamma\)-point LO–TO splitting	\(\approx 0\) (degenerate)	finite, within \(\sim 15\%\)	several hundred \(\mathrm{cm}^{-1}\)
Curie temperature from MD	absent or grossly wrong	qualitatively correct trend	\(\sim 400\,\mathrm{K}\)

The short-cutoff model fails qualitatively on all three. It cannot see the inter-cell dipole coupling that the soft-mode condensation depends on, so the double well is flattened and the ferroelectric instability either disappears or appears at the wrong temperature. The LO–TO splitting is identically zero for the structural reason given in the warning above. The long-range variant, by carrying an explicit Ewald term over predicted charges, restores the inter-cell coupling and gets the physics qualitatively — and increasingly quantitatively — right. BaTiO\(_3\) is therefore the standard stress test in this literature: if a proposed long-range MLIP cannot reproduce its double well and its LO–TO splitting, it has not solved the problem.

Forward and backward references

Chapter 9, §9.6.11 (the MLIP failure-modes section) treats the short-range consequences of this same locality assumption — why a cutoff model can pass every neutral-system validation test and still be unfit for an ionic conductor. The two discussions are two views of one limitation: §9.6.11 is the practitioner's checklist, this subsection is the research frontier that aims to remove the limitation altogether.

The honest summary: as of mid-2026 long-range electrostatics is the single most active architectural frontier for foundation MLIPs, no public universal model has cleared the BaTiO\(_3\) bar, and the practical advice for anyone simulating an ionic or polar material with a stock foundation MLIP is to treat every electrostatics- sensitive observable — dielectric constants, ferroelectric transitions, charged-defect energetics, infrared intensities — as unvalidated until checked against DFT or against one of the long-range variants above.

Charged systems and electrochemistry

The problem. Every universal MLIP discussed here treats the total charge of the simulation cell as fixed at zero. This is implicit in the architecture — atoms have positions and species, no spin or charge — and in the training data (DFT calculations almost always at charge neutrality). For neutral, isolated systems, this is the right choice. For electrochemistry, where an electrode is in contact with an electrolyte at a controlled electrochemical potential, it is fundamentally wrong.

Electrochemical interfaces have three properties no current universal MLIP can represent. First, the electrode can carry a net charge, balanced by the diffuse double-layer charge in the electrolyte; energetics depend on this charge. Second, the electrochemical potential, not the chemical composition, is the natural control variable, requiring grand-canonical sampling in the electronic degrees of freedom. Third, the system can transfer electrons across the interface during reaction events, which neither a fixed-charge nor a per-atom-charge model captures.

Why current methods fail. The natural way to extend an MLIP to charged systems is to add an extra input channel (the total charge, or the chemical potential) and retrain. The problem is that DFT calculations of charged supercells require careful handling of the compensating uniform-jellium background and finite-size corrections (Makov-Payne, Freysoldt-Neugebauer); a foundation MLIP trained on charged-system DFT data must learn to undo these corrections rather than fold them into a meaningful physical signal. No public dataset of charged-supercell DFT energies at the scale of MPtrj exists.

A complementary issue: the per-atom-charge-prediction approach (CHGNet's magmom head extended to electronic charge) cannot represent electron transfer because it does not change the total number of electrons. Some configurations have only one charge-state assignment consistent with chemistry; others (mixed-valent oxides, partially reduced oxides) admit several, and the model has no principled way to choose.

What success would look like. A universal MLIP that can simulate an electrode in contact with an electrolyte at a specified potential versus a reference (SHE or Ag/AgCl), correctly predicting the double-layer capacitance, the surface-charge density as a function of potential, and the redox potentials of small molecules at the interface within \(0.2\)–\(0.3\) V of experiment. None exists as of mid-2026.

Recent attempts. The CENT model (Ghasemi et al. 2015, with recent extensions) uses charge equilibration with electronegativity parameters and is in principle applicable to charged systems, though not at universal-MLIP scale. The constant-potential MD method of Bonnet, Otani and Sugino (and recent extensions) is an explicit DFT-based approach; a learned surrogate is an obvious target. The group around Behler has reported preliminary work on charge-conditioned 4G-HDNNP at mid-scale; the GitHub repository for universal charge-aware models is still small. This is, in our view, the most consequential open problem for foundation MLIPs and is likely to attract the next generation of architectural innovation.

Excited states and TDDFT-ML

The problem. Every MLIP discussed in this book is trained on ground-state DFT, which is exact in principle for the ground-state energy and density of a many-electron system. Many of the most interesting physical phenomena — photoexcitation, exciton transport, non-radiative relaxation, photochemistry — involve excited electronic states. The ground-state PES is irrelevant for these processes; what is needed is at least the lowest few excited-state PESs and the non-adiabatic couplings between them.

Why current methods fail. The training data for an excited-state MLIP would need to come from a method capable of computing excited states accurately. TDDFT (the most accessible option) is roughly an order of magnitude more expensive than ground-state DFT for the same system. CASSCF and CASPT2 (for stronger correlation) are two to three orders more expensive. \(GW\)+BSE (the closest to experiment for solid-state spectra) is two to four orders more expensive and has strong system-size limitations. Generating a dataset comparable to MPtrj — \(1.6 \times 10^6\) configurations — at any of these levels is prohibitively expensive, and would have to be redone if the target spectroscopy changes.

The architectural problem is also non-trivial. An MLIP predicts a scalar energy per configuration. An excited-state model would need to predict a set of energies (one per state), the gradients with respect to atomic positions (one per state), and ideally the non-adiabatic couplings (matrices between states). The output dimension grows linearly with the number of states tracked, and the ordering of states can change with configuration (state crossings, conical intersections), making the prediction problem combinatorially harder than the ground-state case.

What success would look like. A foundation model that, given a molecular or crystalline configuration, returns the lowest \(N\) adiabatic state energies and gradients with chemical accuracy (\(\sim 0.1\) eV) for at least the chemistries of small organic chromophores, transition-metal complexes, and a few canonical inorganic semiconductors. With this in hand, photochemistry simulations would become tractable at MLIP cost, and the screening of light-harvesting materials, photovoltaic absorbers and non-linear-optical compounds would accelerate by orders of magnitude.

Recent attempts. SchNarc (Westermayr et al. 2020) and its descendants have demonstrated excited-state neural-network potentials for small molecules, with two to ten states tracked and non-adiabatic dynamics simulated end-to-end. SPaiNN (Kornbluth et al. 2024) extends this to equivariant architectures. The 2025 review by Kasper et al. (J. Phys. Chem. Lett.) surveys the landscape; the universal-foundation-model regime is years away, and even per-system models are far from the maturity of ground-state MLIPs. This is a problem where the architecture is interesting but the data is the limiting factor.

A reading list, 2024–2026

The literature in this area is moving fast enough that any printed list is partially obsolete by the time it appears. The following are the papers that, as of mid-2026, the editors believe are most worth reading. Each is annotated with one or two sentences indicating what the reader should expect to learn.

Universal MLIPs

• Batatia, I. et al. A foundation model for atomistic materials chemistry. arXiv:2401.00096 (2024). The MACE-MP-0 paper. Definitive reference for the model, the training data, and the out-of-the-box performance benchmarks.

• Deng, B. et al. CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling. Nature Machine Intelligence (2023). The CHGNet paper. Demonstrates the value of the charge head for redox-sensitive applications.

• Park, S. et al. Scalable parallel algorithm for graph neural network interatomic potentials in molecular dynamics simulations. Journal of Chemical Theory and Computation (2024). The SevenNet paper. Strong on the engineering side.

• Neumann, M. et al. Orb: A fast, scalable neural network potential. arXiv:2410.22570 (2024). The Orb paper, with strong out-of-distribution results.

• Barroso-Luque, L. et al. Open Materials 2024 (OMat24): Inorganic materials dataset and models. arXiv:2410.12771 (2024). Describes the OMat24 dataset and the EquiformerV2-OMat model.

Generative models

• Zeni, C. et al. MatterGen: A generative model for inorganic materials design. Nature 639, 624–632 (2025). The MatterGen paper.

• Xie, T. et al. Crystal diffusion variational autoencoder for periodic material generation. ICLR (2022). The CDVAE paper, predecessor to MatterGen.

• Jiao, R. et al. Crystal structure prediction by joint equivariant diffusion. NeurIPS (2023). The DiffCSP paper.

• Antunes, L. M. et al. Crystal structure generation with autoregressive large language modeling. Nature Communications (2024). A surprising demonstration that simple text-based models on CIF strings work for many problems.

Autonomous labs and the experimental loop

• Szymanski, N. J. et al. An autonomous laboratory for the accelerated synthesis of novel materials. Nature 624, 86–91 (2023). The A-Lab paper.

• Burger, B. et al. A mobile robotic chemist. Nature 583, 237–241 (2020). An early but conceptually important demonstration in chemistry.

• MacLeod, B. P. et al. Self-driving laboratory for accelerated discovery of thin-film materials. Science Advances 6, eaaz8867 (2020).

Long-range and charge-transfer extensions

• Ko, T. W. et al. A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer. Nature Communications 12, 398 (2021). 4G-HDNNP.

• Cheng, B. Cartesian atomic cluster expansion for machine learning interatomic potentials. npj Computational Materials (2024). Discussion of long-range corrections in the ACE framework.

Reviews

• Schmidt, J. et al. Recent advances and applications of machine learning in solid-state materials science. npj Computational Materials 5, 83 (2019). The standard mid-decade review.

• Choudhary, K. et al. Recent advances and applications of deep learning methods in materials science. npj Computational Materials 8, 59 (2022). Updated and broader.

• Friederich, P. et al. Machine-learned potentials for next- generation matter simulations. Nature Materials 20, 750–761 (2021). A balanced review of where the field stood at the dawn of the foundation-model era.

Critiques and cautionary notes

• Riebesell, J. et al. Matbench Discovery — A framework to evaluate machine learning crystal stability predictions. arXiv: 2308.14920 (2023, updated 2024). The leaderboard, but more importantly the careful methodology that exposed several previously popular models as having serious distributional weaknesses.

• Stocker, S. et al. How robust are modern graph neural network potentials in long and hot molecular dynamics simulations? Machine Learning: Science and Technology (2022). An early but still pertinent critique of stability under aggressive sampling.

A summary of where we are

The honest summary, as the chapter closes, is something like this.

Foundation models for materials science exist, they work, and they have already changed the practical workflow of computational materials research. A typical 2026 study begins with a pre-trained MLIP, fine-tunes it on a small system-specific dataset, uses it to explore a phase space or candidate set, and verifies the most interesting findings with DFT. This pipeline is faster, more general, and more accessible than what was possible even three years ago.

At the same time, the field is not done. Long-range interactions, charge transfer, excited states, magnetic ordering, and genuinely out-of-distribution chemistry remain open. Generative models produce candidates, but synthesisability is not learned. Autonomous laboratories close one part of the loop, but only within the chemistry they can robotically handle. The next decade of materials simulation will be defined less by individual algorithms than by the integration of these pieces into reliable, end-to-end pipelines — and by the careful identification of the cases where the foundation breaks down.

The book closes here, but the work does not. The appendices that follow consolidate the mathematical, computational and bibliographic resources used throughout. The reader who has followed Chapters 1 through 12 is now equipped, we hope, both to use the tools described and to read the literature critically as it appears.