---
title: ML-PES (CASPT2/aug-cc-pVTZ) for H₂COO Dynamics
url: https://www.emergentmind.com/topics/machine-learned-potential-energy-surface-caspt2-aug-cc-pvtz
type: topic
---

# ML-PES (CASPT2/aug-cc-pVTZ) for H₂COO Dynamics

A machine learned potential energy surface (ML-PES) trained to CASPT2/aug-cc-pVTZ reference data represents a high-fidelity, global multidimensional fit of electronic energies and forces using neural network (NN) architectures, with all training and validation conducted against “gold standard” multireference quantum chemistry. In the context of the H₂COO (Criegee intermediate) reaction system, this permits quantitative probing of all relevant reaction channels, branching ratios, and nonstatistical fate under atmospheric conditions using molecular dynamics (MD) simulations on a computationally tractable, subchemical-accuracy surface [2507.18964, 2402.10047, 2601.11936]. 

## 1. Quantum Chemical Reference: CASPT2/aug-cc-pVTZ

The reference electronic structure data underlying these ML-PESs are computed using complete active space second-order perturbation theory (CASPT2) in conjunction with the augmented correlation-consistent triple-zeta basis set (aug-cc-pVTZ) as implemented in MOLPRO, with a CASSCF(12,11) active space. This protocol captures strong nondynamical correlation and provides robust energetics across minima, transition states (TS), and dissociation channels [2507.18964, 2601.11936]. All stationary points, reaction paths, and asymptotic product energies—covering >150 kcal/mol—are computed at this level, which avoids both single-reference bias and significant basis set incompleteness.

## 2. Data Generation and Coverage

ML-PES construction begins from large-scale sampling of relevant molecular configurations. For H₂COO, the dataset has evolved as follows:

- Initial points: 5 162 geometries covering the parent–cyclic intermediate (cyc-H₂CO₂) region, harvested via adaptive sampling and normal-mode displacements [2507.18964].
- Extended sampling: MD at the semiempirical GFN2-xTB level (via ASE), systematic perturbations along IRCs, and active learning to target product and TS regions, adding ~9 200 points, with coverage up to ≈280 kcal/mol above the reactant [2507.18964].
- Final reference set: After outlier rejection ($|E_\mathrm{PES} - E_\mathrm{ref}| > 10$ kcal/mol), 13 877 geometries for PES2025 [2507.18964], expanded by an additional 1 053 product-region points in subsequent work to reach a total of 14 930 distinct CASPT2/aug-cc-pVTZ structures [2601.11936].
- Data splits: 80% training, 10% validation, 10% test (≈12 000/1 500/1 500 for the largest set) [2601.11936].

This dataset spans all accessible minima, TSs, intermediate structures, and dissociation limits across all known decomposition channels, ensuring full-dimensional global coverage [2601.11936].

## 3. Machine Learning Architecture: PhysNet Representation

PhysNet, a continuous-filter convolutional neural network (NN), forms the basis of all recent CASPT2/aug-cc-pVTZ H₂COO ML-PES implementations. The model utilizes only interatomic distances as input, expanded into Gaussian radial-basis descriptors:
$$
g_k(r_{ij}) = \exp[-(r_{ij} - \mu_k)^2/\sigma^2],
$$
with centers $\mu_k$ spaced every 0.1 Å and width $\sigma=0.5$ Å [2402.10047]. Atom-centered learnable embeddings are updated through 3–5 message-passing blocks, yielding atomic energies $E_i$ and additive molecular total energy [2507.18964, 2402.10047, 2601.11936]. Locality is enforced via distance cutoffs (5–10 Å), and permutational invariance is achieved by design. Forces and, in some variants, partial charges and dipoles, are obtained via analytic differentiation.

## 4. Model Training, Validation, and Metrics

Training involves minimization of a composite loss function including energy, force, and (optionally) charge and dipole errors, with application-specific weighting:
$$
L = w_E |E - E^\mathrm{ref}| + \frac{w_F}{3N} \sum_{i,\alpha} |-\frac{\partial E}{\partial r_{i,\alpha}} - F_{i,\alpha}^\mathrm{ref}| + w_Q |\sum_i q_i - Q^\mathrm{ref}| + \frac{w_p}{3}\sum_\alpha |\sum_i q_i r_{i,\alpha} - p_\alpha^\mathrm{ref}| + L_\text{nh}
$$
[2507.18964]. Optimization typically uses Adam or AMSGrad, with early stopping on plateaus in validation RMSE and regularization via non-harmonic terms but no explicit L₂ penalty [2507.18964, 2402.10047].

Model performance is quantified as follows:

| Data Split          | MAE (E, kcal/mol) | RMSE (E, kcal/mol) | MAE (F, kcal/mol/Å) | RMSE (F, kcal/mol/Å) | R²             |
|---------------------|-------------------|--------------------|---------------------|----------------------|----------------|
| training (11,100)   |    1.37           |    2.06            |   0.51              |     2.71             | 0.9982         |
| test (1,400–1,500)  |    1.23–1.33      |    2.00–2.14       |   1.01–1.11         |     3.08–3.80        | 0.9983–0.9984  |

No spurious “holes” or unphysical artifacts are detected in the asymptotic regions, as verified by large-scale Diffusion Monte Carlo sampling (2.1×10⁹ geometries) [2507.18964, 2601.11936]. All minimum energy paths (MEPs), IRCs, and stationary points are found to lie within 1–2 kcal/mol of the underlying CASPT2 reference surface [2507.18964, 2601.11936].

## 5. Dynamical Applications: MD and Branching Analysis

The ML-PES enables large-scale direct classical MD, interfaced via CHARMM/pyCHARMM and evaluated on-the-fly with automatic differentiation [2507.18964, 2402.10047]. Simulations employ pure NVE ensembles, 0.1 fs timesteps, and flexible bonds, starting from equilibrated 300 K ensembles or specifically vibrationally-mode-excited initial conditions [2507.18964, 2402.10047].

- Product branching ratios (1 ns, 5 000 runs): CO₂+H₂: 32.3%; H₂O+CO: 19.3%; HCO+OH: 1.6%; unreacted H₂COO: 43.7% [2507.18964].
- Channel-dependent dynamic bifurcation is observed for CO₂+H₂: both “direct” (via OCH₂O) and “indirect” (via formic acid) routes are accessible and quantitatively reproduced by the PES, with energy partitioning and vibrational state populations reflecting pathway distinctness [2507.18964, 2601.11936].
- Lifetimes in highly excited formic acid intermediates exhibit non-RRKM stretched-exponential statistics ($\beta$ = 1.1–1.7), directly attributable to nonstatistical dynamics and confirmed by the robustness of the ML-PES over long trajectory propagation [2601.11936].

Mode-selective excitation along normal coordinates enables controlled access to specific regions of the surface: pure $\nu_{CH}$ excitation drives H-transfer and formic acid formation, while excitation of CH and COO-bend modes accesses dioxirane and subsequent OH-elimination; dynamical outcomes are correctly gated as a function of internal energy and mode composition [2402.10047].

## 6. Assessment of PES Robustness, Limitations, and Transferability

Rigorous validation demonstrates the ML-PES:

- Reproduces CASPT2/aug-cc-pVTZ stationary points, transition-state energies, and dissociation curves along all minimum-energy and multidimensional cuts to within 1–2 kcal/mol [2507.18964, 2601.11936].
- Yields smooth one- and two-dimensional potential slices and no spurious artifacts at large atom separations (up to ≈5 Å), with correct asymptotic approaches to isolated product fragments [2601.11936].
- Supports both near-equilibrium and strongly dissociative dynamics up to ~150 kcal/mol above ground, avoiding extrapolation failures by ensuring adequate high-energy data and targeted product-channel sampling [2601.11936].
- Correctly encodes quantum-chemical symmetry and permutational invariance through architecture and training (e.g., via the PhysNet design and Gaussian distance descriptors) [2402.10047].
- Extrapolation to longer timescales and higher excitation energies is robust within the domain of sampled reference data; however, out-of-domain generalization (e.g., exotic photofragmentation) is not guaranteed without substantial new sampling.

## 7. Significance and Impact in Computational and Atmospheric Chemistry

The CASPT2/aug-cc-pVTZ ML-PES paradigm for species such as H₂COO establishes an accurate, functionally ab initio-quality tool for simulating reaction dynamics and energy partitioning in atmospherically relevant intermediates. Quantitative agreement with both experiment and high-level theory is achieved for branching ratios, barrier heights, and product distributions, allowing the full mechanistic characterization of photoactivated decomposition including nonstatistical effects [2507.18964, 2601.11936]. These PESs enable investigations not accessible by direct quantum chemistry due to system size and trajectory demands and represent a transferable framework for future atmospheric and physical chemistry studies requiring subchemical-accuracy global reactive surfaces.

Source: https://www.emergentmind.com/topics/machine-learned-potential-energy-surface-caspt2-aug-cc-pvtz