Source-linked AI summary
Combining SchNet and SHARC: The SchNarc machine learning approach for excited-state dynamics
Julia Westermayr, Michael Gastegger, Philipp Marquetand
TL;DR
Photodynamics simulations require multiple learned electronic properties, while Hessian and reference computations can be costly. SchNarc extends SchNet for these properties and couples it with SHARC; its models reach chemical accuracy in tested cases, while phase-free coupling training and ML can reduce computational demands.
Problem
Hessian computation can remain the time-limiting step in quantum-dynamics simulations, motivating efficient machine-learning approaches for multiple electronic states.
Method
SchNarc extends SchNet with separate prediction blocks for energies, spin-orbit couplings, and nonadiabatic couplings, using phase-free training and energy derivatives for forces.
Results
The models reach chemical accuracy, with some errors below 0.043 eV (1 kcal/mol), while phase-free coupling training gives comparably accurate results.
Takeaways & Limitations
Machine-learned properties can substantially decrease expensive molecular-dynamics simulation times and support efficient Hessian computations for treated electronic states.
Takeaways & Limitations
The phase-free coupling approach neglects Berry-phase effects, an assumption that may not hold in quantum-dynamics simulations.
Abstract
from arXiv · showhide
In recent years, deep learning has become a part of our everyday life and is revolutionizing quantum chemistry as well. In this work, we show how deep learning can be used to advance the research field of photochemistry by learning all important properties for photodynamics simulations. The properties are multiple energies, forces, nonadiabatic couplings and spin-orbit couplings. The nonadiabatic couplings are learned in a phase-free manner as derivatives of a virtually constructed property by the deep learning model, which guarantees rotational covariance. Additionally, an approximation for nonadiabatic couplings is introduced, based on the potentials, their gradients and Hessians. As deep-learning method, we employ SchNet extended for multiple electronic states. In combination with the molecular dynamics program SHARC, our approach termed SchNarc is tested on a model system and two realistic polyatomic molecules and paves the way towards efficient photodynamics simulations of complex systems.
Data availability
The datasets and molecular properties are stored in an Atomic Simulation Environment database format, with some datasets publicly available and others planned for GitHub release.
- Some datasets are already available, while others are planned for release on github.com/schnarc.
- Molecular geometries and their corresponding properties are stored in the Atomic Simulation Environment database format.
1 SchNet for excited states
SchNet is adapted to predict excited-state energies, forces, SOCs, and NACs using shared molecular representations and property-specific outputs. A phase-less loss handles arbitrary coupling signs, while the models achieve chemical accuracy for the reported molecular systems.
- SchNet for excited states: SchNet is adapted to train excited-state energies, forces, spin-orbit couplings, and nonadiabatic couplings.
- SchNet for excited states: The shared SchNet descriptor represents atoms within a defined chemical and structural environment and feeds separate prediction blocks for energies, SOCs, and NACs.Forces are derived from energy outputs with respect to atomic coordinates.
- Standard loss function, L2: The standard L2 loss combines energy, force, SOC, and NAC errors using trade-off factors that account for their different magnitudes.The QC and ML indices denote reference values and SchNet predictions, respectively.
- Phase-less loss function, Lph: The phase-less loss evaluates coupling errors across possible state-phase assignments and selects the minimum error for training on sign-inconsistent SOCs and NACs.State phases are represented by vectors whose entries are +1 or -1, and coupled properties are adjusted by products of state phases.
- Phase-less loss function, Lph: The combined phase-less loss removes arbitrary-phase influence during learning and reduces the computational costs of training-set generation.
- Machine learning models: The CH2NH+ and CSH2 models reach chemical accuracy, with some errors below 0.043 eV (1 kcal/mol).The reported test errors are mean absolute values over all states.
2 Training sets and reference computations
Training sets are constructed for SO2, CH2NH+, and CSH2 using reference dynamics, adaptive sampling, scans, and recomputed quantum-chemistry data. The resulting datasets support SchNarc tests against reference dynamics while retaining molecule-specific restrictions and costs.
- Training systems: SchNet excited-state models are trained for SO2, CH2NH+, and CSH2.
- Training set generation: CH2NH+ training data include 4,000 phase-corrected points and 3,998 converged recomputed points without phase correction.The recomputed data use MR-CISD(6,4)/aug-cc-pVDZ with COLUMBUS.
- Training set generation: CSH2 uses reaction-coordinate scans and adaptive excited-state sampling, producing a 4,703-point training set after filtering small triplet–triplet gaps.Dynamics up to 3 ps can be reproduced at 4,855 apparently converged data points.
- Training set generation: SO2 training sets use a one-shot LVC model, Wigner-sampled initial conditions, and reference SHARC trajectories propagated with NAC vectors.Separate singlet-only and singlet-plus-triplet datasets contain 280,200 data points each.
- Training set generation: The remaining SO2 trajectories are reserved for comparison with SchNarc dynamics, with symmetry restricting modeled NACs to S1–S2 and T1–T3 pairs.
- Training set generation: SO2 requires more data because its training points come directly from fast LVC dynamics rather than adaptive sampling, which would be more costly and time-intensive.The SO2 system is intended as an easy-to-use but challenging validation test rather than a minimum-size training set.
3 Nonadiabatic couplings
The section presents two strategies for obtaining nonadiabatic couplings: a phase-free virtual-property approach and a Hessian-based approximation. The approximation is useful near conical intersections but has threshold, symmetry, and computational-scaling constraints.
- NAC construction: SchNarc constructs a virtual property from the electronic Hamiltonian derivative and obtains nonadiabatic couplings from its multidimensional anti-derivative.The approach is motivated by expressing coupling terms through derivatives of the electronic Hamiltonian and energy gaps.
- NAC construction: The virtual-property approach omits Berry-phase effects because the nonadiabatic-coupling vector field is not conservative and line integrals remain path dependent.The authors assume mixed ML-classical dynamics are mostly unaffected, while noting this may not hold for quantum dynamics simulations.
- NAC approximation: The NAC approximation uses energy-potential Hessians and is especially relevant when quantum-chemistry implementations lack direct NAC vectors.The approximation is described as particularly useful for linear-response methods, especially ADC(2) between the ground and first excited states.
- NAC approximation: The approximation is applied only near conical intersections, using default energy-gap thresholds of 0.5 eV for singlet-singlet and 1.0 eV for triplet-triplet states.SchNarc computes Hessians only when a relevant gap falls within the threshold; otherwise, NAC vectors are set to zero.
- NAC approximation: The approximation is limited to same-symmetry electronic states, and the energy-gap thresholds may require case-specific adjustment.For CH2NH+, the threshold is increased by 30% because the potential-energy-surface gaps are overestimated.
- Timing: For a 24-atom molecule, evaluating one Hessian took around 45 seconds on a CPU and 14 seconds on a GPU, while larger systems or more states increase cost.The reported timings motivate computing only Hessians for states close to the active state during dynamics.