Solvating machine-learning interatomic potentials for solution-phase chemistry

Anton Z. Ni; Joonho Lee

physics.chem-phOct 12, 2026

Solvating machine-learning interatomic potentials for solution-phase chemistry

Authors: Anton Z. Ni, Joonho Lee

Organizations: Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA

Abstract

Most machine-learning interatomic potentials (MLIPs) are trained on gas-phase data, which limits their use for chemistry in solution. Here, we introduce AnySolv, a transferable implicit solvation potential that provides solvent-dependent energy and force corrections to existing gas-phase potentials without retraining them. It is trained on 1.4 million solvation energies and forces computed with density functional theory (DFT) and SMD in 36 solvents, spanning charged, open-shell, and transition-state structures. Because solvents are represented by continuous physical descriptors, AnySolv supports 179 solvents, including those absent from training. On external benchmarks, AnySolv reproduces DFT-SMD solvation energies to 2-4 meV mean absolute error at more than three orders of magnitude lower cost, and it matches the accuracy of DFT-SMD against experimental solvation free energies. This enables screening of the mechanisms of 120 nucleophilic aromatic substitution reactions in six phases as well as molecular dynamics simulations that reproduce the experimentally observed solvent-dependent conformational preferences of alanine dipeptide. By providing transferable solvation corrections to existing MLIPs, AnySolv enables scalable simulations of solvent-dependent chemical reactivity and molecular dynamics.

Figures & tables

Figure 1: Overview of AnySolv. AnySolv predicts the solvation energy $\Delta E$ and forces $\Delta\mathbf{F}$ of a solute with coordinates $\mathbf{R}$ , charge $q$ , and spin multiplicity $M$ in a continuum solvent described by the descriptor vector $\mathbf{s}$ , and adding them to any gas-phase MLIP gives the energy and forces in solution. From there, we can obtain solvent-dependent potential energy surfaces. This enables us to efficiently probe reaction mechanisms and perform molecular dynamics with implicit solvent.

Descriptor	Definition	$T_{k}$	$\sigma_{k}$
$n$	index of refraction (293 K)	$n-1$	0.0684
$\alpha$	Abraham H-bond acidity, $\Sigma\alpha_{2}^{H}$	–	0.182
$\beta$	Abraham H-bond basicity, $\Sigma\beta_{2}^{H}$	–	0.235
$\gamma$	surface tension (cal mol -1 Å -2 )	–	11.69
$\varepsilon$	dielectric constant (298 K)	$1-1/\varepsilon$	0.165
$\phi$	aromaticity	–	0.322

Table 1: Details of solvent descriptors. We list the solvent descriptors, the transformation

T_{k}

applied to each ( Eq. 4 ; “–” denotes the identity), and the population standard deviation

\sigma_{k}

of the transformed values over the 179 solvents of the Minnesota Solvent Descriptor Database. Aromaticity is the fraction of non-hydrogen atoms that are aromatic carbon; electronegative halogenicity is the fraction of non-hydrogen atoms that are F, Cl, or Br.

Figure 2: Solvent embedding in AnySolv. Teal blocks are introduced in this work; gray blocks are unchanged from UMA-S-1.2. A similar grafting can be applied to other graph neural network architectures.

		MoE			compact
Solutes	$n$	$\Delta E$	$\|\Delta\mathbf{F}\|$	$\cos$	$\Delta E$	$\|\Delta\mathbf{F}\|$	$\cos$
all	36,847	0.016	0.026	0.970	0.020	0.030	0.963
neutral	27,523	0.012	0.021	0.974	0.014	0.024	0.970
cations	4,894	0.024	0.038	0.948	0.034	0.046	0.932
anions	4,430	0.028	0.038	0.971	0.042	0.052	0.953

Table 2: Errors in solvation energy on the held-out test set. We provide the solvation-energy MAE

\Delta E

in eV, the force-magnitude MAE

|\Delta\mathbf{F}|

in eV/Å, and the mean cosine similarity between predicted and reference solvation forces.

		MoE			compact			DFT-SMD
Solutes	$n$	$\Delta E_{\mathrm{sp}}$	$\Delta E_{\mathrm{opt}}$	$\Delta G_{\mathrm{solv}}$	$\Delta E_{\mathrm{sp}}$	$\Delta E_{\mathrm{opt}}$	$\Delta G_{\mathrm{solv}}$	$\Delta E_{\mathrm{sp}}$
Solv@TUM neutral	4,510	0.92 ( $-$ 0.27)	0.89 ( $-$ 0.24)	0.99 ( $-$ 0.48)	0.92 ( $-$ 0.26)	0.89 ( $-$ 0.22)	0.98 ( $-$ 0.45)	0.93 ( $-$ 0.24)
FlexiSol neutral	529	2.48 ( $+$ 1.29)	2.46 ( $+$ 1.03)	2.47 ( $+$ 0.52)	2.48 ( $+$ 1.29)	2.45 ( $+$ 1.03)	2.45 ( $+$ 0.57)	2.51 ( $+$ 1.34)
MNSol neutral	2,530	0.83 ( $-$ 0.24)	0.84 ( $-$ 0.35)	0.95 ( $-$ 0.52)	0.82 ( $-$ 0.22)	0.83 ( $-$ 0.33)	0.93 ( $-$ 0.50)	0.83 ( $-$ 0.22)
MNSol cations	132	4.77 ( $+$ 3.92)	4.60 ( $+$ 3.64)	4.56 ( $+$ 3.64)	4.78 ( $+$ 3.92)	4.60 ( $+$ 3.64)	4.60 ( $+$ 3.69)	4.79 ( $+$ 3.94)
MNSol anions	222	5.59 ( $+$ 3.25)	5.08 ( $+$ 2.40)	5.17 ( $+$ 2.60)	5.73 ( $+$ 3.57)	5.19 ( $+$ 2.70)	5.29 ( $+$ 2.92)	5.49 ( $+$ 3.13)

Table 3: Solvation free energies against experiment. We provide the MAE and, in parentheses, the mean signed error (model minus experiment), both in kcal/mol, for the three protocols and both models, with our DFT-SMD single points at the level of theory of the training labels in the last column. The datasets are those of Section III.1 .

Figure 3: Solvation energy errors for zwitterions. Errors are shown for extended

\mathrm{H_{3}N^{+}}

–

(\mathrm{CH_{2}})_{n}

–

\mathrm{COO^{-}}

zwitterions as a function of charge separation in six solvents, for the MoE model (solid) and a model trained without the charge-separation augmentation (dashed); the vertical line marks the 24 Å effective cutoff. Inset: the MoE model errors on an expanded scale.

	$\Delta G^{\ddagger}$ (kcal/mol)			$\Delta G_{\mathrm{rxn}}$ (kcal/mol)			$r^{\ddagger}_{\mathrm{C-Cl}}$ (Å)			$r^{\mathrm{pdt}}_{\mathrm{C-Cl}}$ (Å)
Phase	DFT-SMD	MoE	compact	DFT-SMD	MoE	compact	DFT-SMD	MoE	compact	DFT-SMD	MoE	compact
gas phase	43.1	43.0	43.0	41.2	41.4	41.4	2.45	2.46	2.46	2.77	2.77	2.77
$n$ -hexane	32.8	32.7	33.5	18.9	18.8	18.9	2.33	2.32	2.32	3.00	3.06	3.04
chloroform	27.0	26.8	28.2	1.1	$-$ 0.3	$-$ 5.5	2.27	2.26	2.24	3.25	3.43	4.60
methanol	23.8	23.5	25.0	$-$ 10.9	$-$ 11.4	$-$ 19.6	2.23	2.22	2.22	3.62	3.51	4.49
acetonitrile	23.4	23.7	25.1	$-$ 11.3	$-$ 12.0	$-$ 21.1	2.23	2.23	2.23	3.61	3.49	4.50

Table 4: Performance on the model Menshutkin reaction. Activation free energies

\Delta G^{\ddagger}

and reaction free energies

\Delta G_{\mathrm{rxn}}

\mathrm{NH_{3}}+\mathrm{CH_{3}Cl}\to\mathrm{H_{3}NCH_{3}^{+}}+\mathrm{Cl^{-}}

, and the C–Cl distances at the transition state,

r^{\ddagger}_{\mathrm{C-Cl}}

, and in the product,

r^{\mathrm{pdt}}_{\mathrm{C-Cl}}

, from DFT-SMD and from UMA-S-1.2 with the MoE and compact AnySolv solvation energies.

Trained on OMol25
	Gas phase		Solvated
			$\Delta G^{\ddagger}$		$\Delta G_{\mathrm{rxn}}$
Gas-phase model	$\Delta G^{\ddagger}$	$\Delta G_{\mathrm{rxn}}$	MSE	MAE	MSE	MAE
UMA-S-1.2	0.0	$+$ 0.2	$+$ 0.1	0.3	$-$ 0.7	0.7
MACE-POLAR-1-M	$+$ 0.4	$+$ 0.2	$+$ 0.5	0.5	$-$ 0.4	0.4
OrbMol-v2	$+$ 0.2	$+$ 0.1	$+$ 0.2	0.4	$-$ 0.8	0.8

Table 5: Transferability of AnySolv across different MLIPs. Errors against DFT-SMD (kcal/mol) of the activation free energies

\Delta G^{\ddagger}

and reaction free energies

\Delta G_{\mathrm{rxn}}

\mathrm{NH_{3}}+\mathrm{CH_{3}Cl}\to\mathrm{H_{3}NCH_{3}^{+}}+\mathrm{Cl^{-}}

with the MoE model added to different gas-phase MLIPs. Gas phase: signed error of the gas-phase model alone, without AnySolv. Solvated: mean signed (MSE) and mean absolute (MAE) errors over the six solvents of Table 4 . a Excluding solvents in which the product relaxes to a different ion pair (see text).

Figure 4: S N Ar mechanism screening with UMA-S-1.2 and the MoE model. Each column is one of the 54 reactions that have an intermediate in at least one phase, grouped by substrate, leaving group, and nucleophile, and each cell gives the electronic well depth

D

of its Meisenheimer complex in one phase. The top row gives Kwan et al.’s B3LYP-D3(BJ)/6-31+G*/PCM classification of the same reactions in DMSO. 53 The first color bin,

0<D\leq 0.5

kcal/mol, is the borderline class. The 66 reactions without an intermediate in any phase are not shown.

Figure 5: Free-energy surfaces of alanine dipeptide. We show the free-energy surfaces over the backbone dihedrals

\phi

and

\psi

from well-tempered metadynamics with UMA-S-1.2 and the MoE model at 298.15 K in the gas phase, chloroform, methanol, and water.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

	MoE	compact
initialization	UMA-S-1.2 checkpoint, solvent block grafted	random
parameters, total	291,303,796	6,368,052
expert SO(2) weights	289,406,976	–
router and composition embedding	70,464	–
parameters after merging for one system	6,348,340	6,368,052
experts per SO(2) linear layer	64	1

Appendix

Table A1: Architecture of the two models. Both share the eSEN-based backbone of UMA-S.

	ALPB Pretraining	Training with SMD Labels
initialization	MoE: UMA-S-1.2 backbone; compact: random	pretrained weights
labels	GFN2-xTB/ALPB, 21 solvents (5.46 M) + DFT-SMD water (173 k)	DFT-SMD, 36 solvents (1.35 M)
unique training labels	5,633,695	1,355,281
labels sampled per epoch	3,356,976	1,383,400

Appendix

Table A2: Training data and settings of the preliminary GFN2-xTB/ALPB stage and the DFT-SMD stage. Epochs, peak learning rates, steps, and hardware of every run are given in Table A3 ; the loss, optimizer, and schedule are listed in Section II.3 .

stage	model	epochs	peak learning rate	steps	GPUs
ALPB Pretrain	MoE	4	$1.5\times 10^{-4}$	839,244	$4\times$ H200
ALPB Pretrain	compact	8	$4\times 10^{-4}$	1,678,488	$4\times$ H200
DFT-SMD	MoE	4	$5\times 10^{-5}$	345,852	$4\times$ H100
DFT-SMD	compact	4	$5\times 10^{-5}$	345,852	$2\times$ A100

Appendix

Table A3: Final training run of each stage.

Figure A1: Pooled validation loss against optimizer step for the MoE (blue) and compact (orange) models during (a) ALPB pretraining and (b) training with SMD labels.

Figure A2: Composition of the training split. (a) Atoms per molecule for the three DFT-labeled blocks, with the 50-atom cap of the non-water solvents marked by the dotted line; (b) net charge; (c) spin multiplicity; (d) OMol25 subset; (e) solvation energy of the OMol25 labels in each solvent, ordered by the Born factor

1-1/\varepsilon

(in parentheses), with boxes spanning the interquartile range and whiskers the 5th to 95th percentiles.

Solvent	Labels	Solvent	Labels
OMol25 labels
acetone	34,089	1,4-dioxane	34,241
acetonitrile	34,249	ethanol	34,042
aniline	33,804	ethyl acetate	33,784
benzaldehyde	34,289	$n$ -hexadecane	34,303
benzene	34,341	$n$ -hexane	34,317

Appendix

Table A4: Number of training labels per solvent for the OMol25 solute geometries, the AIMNet2 anion geometries, and the charge-separation augmentation (upper to lower blocks), all with DFT-SMD solvation energies and forces, followed by the totals of the four training-set components.

		UMA-S-1.2		MACE-POLAR-1-M
Solutes	$n$	$\Delta E_{\mathrm{opt}}$	$\Delta G_{\mathrm{solv}}$	$\Delta E_{\mathrm{opt}}$	$\Delta G_{\mathrm{solv}}$
Solv@TUM neutral	4,510	0.89 ( $-$ 0.24)	0.99 ( $-$ 0.48)	0.90 ( $-$ 0.24)	1.00 ( $-$ 0.49)
FlexiSol neutral	529	2.46 ( $+$ 1.03)	2.47 ( $+$ 0.52)	2.46 ( $+$ 1.02)	2.48 ( $+$ 0.53)
MNSol neutral	2,530	0.84 ( $-$ 0.35)	0.95 ( $-$ 0.52)	0.84 ( $-$ 0.35)	0.96 ( $-$ 0.52)
MNSol cations	132	4.60 ( $+$ 3.64)	4.56 ( $+$ 3.64)	4.59 ( $+$ 3.64)	4.57 ( $+$ 3.67)
MNSol anions	222	5.08 ( $+$ 2.40)	5.17 ( $+$ 2.60)	5.06 ( $+$ 2.38)	5.22 ( $+$ 2.60)

Appendix

Table A5: MAE and, in parentheses, mean signed error (model minus experiment), both in kcal/mol, of the MoE model with UMA-S-1.2 or MACE-POLAR-1-M as the gas-phase potential.

SAMPL6: RMSE of $\log_{10}P$ against experiment
	MoE	compact
Boltzmann ensemble	0.51	0.51
lowest-free-energy conformer	0.53	0.54
Zwitterions: error against DFT-SMD (kcal/mol)
extended, MAE / max	0.31 / 1.14	0.25 / 1.27
cyclic, MAE / max	0.18 / 1.39	0.21 / 1.54

Appendix

Table A6: Comparison of the MoE and compact models on the charge-separated zwitterions of Section III.4 and the SAMPL6 partition coefficients of Section III.3 .

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