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AIMNet2-NSE

Overview

AIMNet2-NSE (Neutral Spin Equilibrated) is the model for open-shell molecular systems. It extends the AIMNet2 architecture with spin-multiplicity awareness, using num_charge_channels=2 to handle both charge and spin state information. This allows it to describe radicals, triplet states, and other systems with unpaired electrons that closed-shell models cannot treat correctly.

Supported elements: H, B, C, N, O, F, Si, P, S, Cl, As, Se, Br, I (14 elements)

Registry alias: aimnet2-nse (loads ensemble member aimnet2-nse_0)

Ensemble members: aimnet2-nse_0 through aimnet2-nse_3 (4 models)

Legacy names

The previously published aimnet2nse alias and aimnet2nse_0 … aimnet2nse_3 member keys still resolve and remain supported.

DFT reference: wB97M-D3/def2-TZVPP (same functional as the default AIMNet2)

Strengths and Limitations

Strengths

  • Handles open-shell systems with proper spin-state dependence
  • Uses the mult parameter to specify spin multiplicity (2S+1)
  • High-quality wB97M-D3 reference data including open-shell species
  • Can describe bond dissociation curves where standard models fail
  • Essential for radical stability comparisons and spin-state energetics

Limitations

Single-determinant DFT reference

AIMNet2-NSE is trained on unrestricted Kohn-Sham DFT data, which uses a single Slater determinant. It is not reliable for systems with genuine multi-reference character, including:

  • Biradicals with significant open-shell singlet character
  • Near-degenerate spin states in transition-metal-free systems
  • Strongly stretched bonds in singlet states (e.g., homolytic dissociation on a singlet surface)

If you suspect multi-reference character, validate against CASSCF or MRCI calculations.

Spin contamination

The underlying DFT reference data may contain spin contamination from unrestricted KS calculations. The model learns from this data as-is, so predictions for heavily spin-contaminated states should be treated with caution.

Same element and system scope

No transition metals, molecular (gas-phase) training data only. For Pd-containing open-shell systems, neither this model nor AIMNet2-Pd is currently suitable -- use DFT directly.

How Spin Multiplicity Works

AIMNet2-NSE accepts a mult parameter specifying the spin multiplicity (2S+1) of the system:

Multiplicity (mult) Unpaired electrons Example systems
1 (singlet) 0 Closed-shell molecules, singlet carbenes
2 (doublet) 1 Organic radicals, radical anions/cations
3 (triplet) 2 Triplet oxygen, triplet carbenes, diradicals

The multiplicity is passed as a floating-point tensor alongside the molecular charge:

result = calc({
    "coord": coords,
    "numbers": numbers,
    "charge": torch.tensor(0.0),
    "mult": torch.tensor(2.0),   # Doublet radical
}, forces=True)

For closed-shell calculations with AIMNet2-NSE, set mult=1.0. This allows direct comparison of open-shell and closed-shell energies on the same potential energy surface.

Typical Use Cases

  • Radical stability -- compare bond dissociation energies across different C-H, N-H, or O-H bonds
  • Spin-state energetics -- singlet-triplet gaps for carbenes, nitrenes, and other reactive intermediates
  • Bond dissociation -- homolytic bond cleavage where the products are radicals
  • Radical reaction paths -- hydrogen atom transfer, radical addition, beta-scission

Quick Example

Computing the C-H bond dissociation energy of methane:

import torch
from aimnet.calculators import AIMNet2Calculator

calc = AIMNet2Calculator("aimnet2nse", compile_model=True)

# Methane (CH4) - singlet, closed shell
ch4_coords = torch.tensor([
    [ 0.0000,  0.0000,  0.0000],  # C
    [ 0.6276,  0.6276,  0.6276],  # H
    [-0.6276, -0.6276,  0.6276],  # H
    [-0.6276,  0.6276, -0.6276],  # H
    [ 0.6276, -0.6276, -0.6276],  # H
])
ch4_numbers = torch.tensor([6, 1, 1, 1, 1])

e_ch4 = calc({
    "coord": ch4_coords,
    "numbers": ch4_numbers,
    "charge": torch.tensor(0.0),
    "mult": torch.tensor(1.0),  # Singlet
})["energy"].item()

# Methyl radical (CH3) - doublet
ch3_coords = torch.tensor([
    [ 0.0000,  0.0000,  0.0000],  # C
    [ 1.0770,  0.0000,  0.0000],  # H
    [-0.5385,  0.9326,  0.0000],  # H
    [-0.5385, -0.9326,  0.0000],  # H
])
ch3_numbers = torch.tensor([6, 1, 1, 1])

e_ch3 = calc({
    "coord": ch3_coords,
    "numbers": ch3_numbers,
    "charge": torch.tensor(0.0),
    "mult": torch.tensor(2.0),  # Doublet radical
})["energy"].item()

# Hydrogen atom - doublet
h_coords = torch.tensor([[0.0, 0.0, 0.0]])
h_numbers = torch.tensor([1])

e_h = calc({
    "coord": h_coords,
    "numbers": h_numbers,
    "charge": torch.tensor(0.0),
    "mult": torch.tensor(2.0),  # Doublet
})["energy"].item()

bde = e_ch3 + e_h - e_ch4
print(f"C-H BDE (methane): {bde:.4f} eV")
print(f"C-H BDE (methane): {bde * 23.0609:.1f} kcal/mol")

ASE Integration

When using AIMNet2-NSE through the ASE interface, set the spin multiplicity via the mult parameter:

from ase.io import read
from ase.optimize import BFGS
from aimnet.calculators import AIMNet2ASE, AIMNet2Calculator

base_calc = AIMNet2Calculator("aimnet2nse", compile_model=True)

# Doublet radical
atoms = read("radical.xyz")
atoms.calc = AIMNet2ASE(base_calc, charge=0, mult=2)

opt = BFGS(atoms)
opt.run(fmax=0.01)

print(f"Optimized energy: {atoms.get_potential_energy():.6f} eV")

To change the spin state during a calculation:

atoms.calc.set_mult(3)  # Switch to triplet
e_triplet = atoms.get_potential_energy()

atoms.calc.set_mult(1)  # Switch to singlet
e_singlet = atoms.get_potential_energy()

gap = e_triplet - e_singlet
print(f"Singlet-triplet gap: {gap:.4f} eV ({gap * 23.0609:.1f} kcal/mol)")

Computational Details

Training Data

AIMNet2-NSE is trained on unrestricted wB97M-D3/def2-TZVPP calculations spanning singlet, doublet, and triplet states. The training set includes closed-shell molecules, organic radicals, and excited-state-like geometries to provide broad coverage of open-shell chemistry.

Architecture Difference

The key architectural difference from the standard AIMNet2 model is num_charge_channels=2. The first channel handles molecular charge (as in all AIMNet2 models), and the second channel encodes spin multiplicity. This allows the model to learn spin-dependent energy contributions without separate models for each spin state.

Long-Range Corrections

External DFT-D3 and long-range Coulomb modules are included, configured identically to the default AIMNet2 model.

Ensemble Averaging

models = [AIMNet2Calculator(f"aimnet2nse_{i}") for i in range(4)]
data = {
    "coord": coords,
    "numbers": numbers,
    "charge": torch.tensor(0.0),
    "mult": torch.tensor(2.0),
}
results = [m(data, forces=True) for m in models]

energies = torch.stack([r["energy"] for r in results])
print(f"Energy: {energies.mean().item():.6f} +/- {energies.std().item():.6f} eV")

References

Anstine, D. M.; Zubatyuk, R.; Isayev, O. AIMNet2: A Neural Network Potential to Meet your Neutral, Charged, Organic, and Elemental-Organic Needs. Chemical Science 2025, 16, 10228--10244. DOI: 10.1039/D4SC08572H

Anstine, D. M.; Zubatyuk, R.; Isayev, O. AIMNet2-NSE: A Neural Network Potential for Organic Radical Chemistry. Angew. Chem. Int. Ed. 2025. DOI: 10.1002/anie.202516763