Vishikh Athavale

Nonadiabatic molecular dynamics is essential for simulating photoinduced processes, but its application to large molecular systems is often limited by the cost of repeatedly evaluating excited-state energies, forces, and nonadiabatic couplings. Here, we present a GPU-accelerated implementation of trajectory surface hopping within PYSEQM (https://github.com/lanl/PYSEQM/), a PyTorch-based semiempirical quantum chemistry framework. The module combines semiempirical model Hamiltonians with configuration-interaction singles excited states and introduces the nonadiabatic coupling vectors and time-derivative couplings required for surface-hopping dynamics. The implementation further includes treatments of trivial crossings and electronic decoherence, providing a complete framework for propagating coupled electronic and nuclear dynamics. To improve GPU utilization, independent trajectories are propagated concurrently in batches. Benchmark calculations show that this strategy substantially increases aggregate simulation throughput as the batch size is increased for small molecules. We demonstrate the applicability of the method to large molecular systems by simulating the excited-state population dynamics of methyl- and tert-butyl-substituted molecular nanostar dendrimers, which contain dense manifolds of electronically excited states. These calculations show that semiempirical surface-hopping dynamics can be extended to molecular systems that remain challenging for conventional ab initio approaches. In addition, the differentiable PyTorch formulation provides a data-science route for optimizing semiempirical Hamiltonian parameters against reference excited-state properties and, ultimately, dynamical observables. PYSEQM therefore provides a platform for high-throughput nonadiabatic molecular dynamics and for the development of data-driven semiempirical models for photophysics and photochemistry.

Nonadiabatic molecular dynamics is essential for simulating photoinduced processes, but its application to large molecular systems is often limited by the cost of repeatedly evaluating excited-state energies, forces, and nonadiabatic couplings. Here, we present a GPU-accelerated implementation of trajectory surface hopping within PYSEQM (https://github.com/lanl/PYSEQM/), a PyTorch-based semiempirical quantum chemistry framework. The module combines semiempirical model Hamiltonians with configuration-interaction singles excited states and introduces the nonadiabatic coupling vectors and time-derivative couplings required for surface-hopping dynamics. The implementation further includes treatments of trivial crossings and electronic decoherence, providing a complete framework for propagating coupled electronic and nuclear dynamics. To improve GPU utilization, independent trajectories are propagated concurrently in batches. Benchmark calculations show that this strategy substantially increases aggregate simulation throughput as the batch size is increased for small molecules. We demonstrate the applicability of the method to large molecular systems by simulating the excited-state population dynamics of methyl-and tert-butyl substituted molecular nanostar dendrimers, which contain dense manifolds of electronically excited states. These calculations show that semiempirical surface-hopping dynamics can be extended to molecular systems that remain challenging for conventional ab-initio approaches. In addition, the differentiable PyTorch formulation provides a data-science route for optimizing semiempirical Hamiltonian parameters against reference excited-state properties and, ultimately, dynamical observables. PYSEQM therefore provides a platform for high-throughput nonadiabatic molecular dynamics and for the development of data-driven semiempirical models for photophysics and photochemistry.

This Letter introduces excited-state molecular dynamics in PYSEQM, a GPU-accelerated semiempirical quantum chemistry engine implemented in PyTorch. The new module enables Born-Oppenheimer molecular dynamics (BOMD) using configuration-interaction singles and random phase approximation for excited states, allowing long trajectories and large statistical ensembles to be simulated efficiently on a single GPU. We also implement an extended Lagrangian excited-state BOMD (XL-ESMD) scheme that propagates auxiliary electronic variables, enabling relaxed ground and excited-state convergence thresholds without compromising energy conservation. The excited-state BOMD implementation scales smoothly from small chromophores to a nearly 900-atom dendrimer (taking 6.5 s per MD step). PYSEQM also supports batched execution, allowing many geometries or trajectories to be evaluated in a single GPU launch, substantially increasing throughput and making ensemble-based protocols routine. As a demonstration, we compute absorption, emission, and infrared spectra from trajectories propagated on the ground and first excited states. The XL-ESMD scheme yields identical spectra at significantly lower computational cost, establishing the role of extended Lagrangian based dynamics for efficient excited-state BOMD simulations. Beyond raw performance, PYSEQM's PyTorch foundation provides automatic differentiation for forces, efficient GPU batching, and seamless interfacing with machine learning models. These capabilities position PYSEQM as a practical platform for machine learning-augmented excited-state dynamics and lay the foundation for future data-driven nonadiabatic excited-state dynamics modeling of ultrafast spectroscopic probes.

Accurate and efficient gradients of molecular energy with respect to nuclear degrees of freedom are essential for geometry optimization and molecular dynamics, including simulations that go beyond the Born–Oppenheimer regime. A common approach involves deriving analytical formulas for new electronic structure methods, which is often conceptually difficult and requires tedious coding. Here, we implement analytical, semi-numerical, and automatic differentiation (AD)-based gradient pathways for semiempirical Hamiltonian models in the PYSEQM software package, leveraging both graphics processing unit (GPU) and central processing unit (CPU) architectures. We further extend these capabilities to excited states calculated using the configuration interaction singles and time-dependent Hartree–Fock ansätze. We benchmark wall time, peak memory usage, and accuracy across three molecular families of varying chemical complexity, including systems of up to a thousand atoms. For ground-state simulations, analytical and AD gradients achieve near-identical GPU runtimes, while semi-numerical gradients are slower on GPU but remain competitive on CPU. For excited states, both analytical and custom AD approaches using implicit differentiation show similar performance and low memory requirements, whereas gradients with full AD are memory-limited. AD gradients match analytical ones in accuracy across all tested systems, aided by a quaternion-based diatomic frame rotation for two-center quantities that ensures smooth energy surfaces. Overall, automatic differentiation emerges as a practical alternative to analytical gradients in semiempirical quantum chemistry, offering high accuracy while allowing seamless integration in AI-driven workflows and popular packages, such as PyTorch and JAX. Our results provide actionable guidance for selecting optimal gradient strategies in large-scale ground- and excited-state molecular dynamics simulations.

We introduce excited-state molecular dynamics (ESMD) in PYSEQM, a GPU-accelerated semiempirical quantum chemistry engine implemented in PyTorch. The new module enables Born-Oppenheimer (single-surface) dynamics using configuration-interaction singles and random phase approximation for excited-states, allowing long trajectories and large statistical ensembles to be simulated efficiently on a single GPU. We also implement an extended-Lagrangian ESMD (XL-ESMD) scheme that propagates auxiliary electronic variables, enabling relaxed ground and excited-state convergence thresholds without compromising energy conservation. The ESMD implementation scales smoothly from small chromophores to a nearly 900-atom dendrimer (taking 6.5 s per ESMD step). PYSEQM also supports batched execution, allowing many geometries or trajectories to be evaluated in a single GPU launch, substantially increasing throughput and making ensemble-based protocols routine. As a demonstration, we compute absorption, emission, and infrared spectra from trajectories propagated on the ground and first excited states, illustrating practical utility of PYSEQM. The XL-ESMD scheme yields identical spectra at significantly lower computational cost, establishing the role of extended Lagrangian based dynamics for efficient ESMD simulations. Beyond raw performance, PYSEQM’s Pytorch foundation provides automatic differentiation for forces, efficient GPU batching, and seamless interfacing with machine learning models. These capabilities position PYSEQM as practical platform for machine learning-augmented excited-state dynamics and lay the foundation for future data-driven nonadiabatic ESMD modeling of ultrafast spectroscopic probes.

Accurate and efficient gradients of molecular energy with respect to nuclear degrees of freedom are essential for geometry optimization and molecular dynamics, including simulations beyond the Born-Oppenheimer regime. A common approach involves deriving analytical formulas for new electronic-structure methods, which is often conceptually difficult and requires tedious coding. Here, we implement analytical, semi- numerical, and automatic differentiation (AD)-based gradient pathways for semiempirical Hamiltonian models in the PYSEQM software package, leveraging both GPU and CPU architectures. We further extend these capabilities to excited states calculated using the Configuration Interaction Singles and Time-Dependent Hartree-Fock ansätze. We benchmark wall time, peak memory usage, and accuracy across three molecular families of varying chemical complexity, including systems of up to a thousand atoms. For ground state simulations, analytical and AD gradients achieve near-identical GPU run times, while semi-numerical is slower on GPU but remains competitive on CPU. For excited states, analytical and a custom AD approach using implicit differentation show similar performance and low memory requirements, whereas gradients with full-AD are memory-limited. Accuracy of AD gradients is excellent across all tested systems aided by a quaternion-based diatomic-frame rotation for two-center quantities that ensures smooth energy surfaces. Overall, automatic differentiation emerges as a practical alter- native for analytic gradients in semiempirical quantum chemistry, offering high accuracy with modest memory overhead. Our results provide actionable guidance for selecting optimal gradient strategies in large-scale ground- and excited-state molecular dynamics simulations.

We report the development and implementation of electronic excited-state capabilities for semiempirical quantum chemical methods at both the Configuration Interaction Singles and Time-Dependent Hartree-Fock levels of theory, integrated within the PYSEQM 2.0 software package (https://github.com/lanl/PYSEQM). PYSEQM is a Python-based package designed for efficient and scalable quantum chemical simulations. Leveraging the PyTorch framework enables PYSEQM to benefit from automatic differentiation and GPU acceleration, leading to substantial performance gains in molecular property evaluations. In particular, our implementation enables efficient calculation of excited-state properties for large molecular systems. Benchmarking on systems with up to a thousand atoms demonstrates that excited-state computations can be completed in under a minute on modern GPUs, making this approach particularly suitable for high-throughput screening, real-time feedback in interactive simulations, and large-scale dynamical studies. Additionally, PYSEQM includes a machine learning interface that supports Hamiltonian parameter reoptimization and neural network training. These capabilities open new avenues for data-driven excited-state dynamics simulations, offering a path toward combining quantum chemical rigor with machine learning efficiency. Overall, this work facilitates access to excited-state quantum chemistry for large systems, while laying the foundation for future hybrid quantum-machine-learning approaches in photochemistry, photophysics, and materials discovery.

We revisit the photodynamics of tetracyanoethylene-hexamethylbenzene (TCNE-HMB), the molecular complex studied by Hochstrasser et al. [J. Chem. Phys. 100, 4797-4810, 1994] that has long challenged the applicability of Marcus's theory of electron transfer for predicting photochemical reactions. Using a novel black-box electronic structure algorithm (time-dependent density functional theory with one double, TDDFT-1D) to efficiently run molecular dynamics that can treat charge recombination, we run ab initio surface hopping molecular dynamics and confirm that, for a polar solvent, charge recombination rates can be incredibly fast (indeed faster than the solvent relaxation time); for nonpolar solvents, the rate is much slower. We demonstrate that, although Marcus theory cannot be directly applied, these nonequilibrium (and sometimes incredibly fast) photoexcited dynamics can be effectively explained within a two-state model without any evidence of a transition through a conical intersection. Most importantly, for this paradigmatic model system, we are able to identify two nuclear coordinates of interest (rather than the single coordinate predicted by Marcus or a full set of internal quantum modes studied by Bixon and Jortner): the solvent relaxation in the first shell (that strongly modulates the energies of the charge transfer state and differentiates time scales for relaxation) and a nuclear displacement in the TCNE-HMB complex arising from a handful of vibrations that induces non-Born-Oppenheimer motion and eventually facilitates an abrupt electronic transition to the ground state. Altogether, these findings suggest a tractable generalization of Marcus theory for future simulations of photochemistry with non-innocent solvent environments in the spirit of a Hamiltonian suggested by Stuchebrukhov (J. Chem. Phys. 107, 3821, 1997).

We calculate the gradients of Boys diabatic state energies and couplings when the electronic vector space is generated by configuration interaction singles. Our approach follows the Lagrangian approach of Paz and Glover (rather than direct differentiation of the adiabatic-to-diabatic approaches that have been published previously). The result is that we achieve a dramatic increase in savings over previous approaches, and the present approach should be immediately useful to scientists focused on electronic relaxation, especially chemists studying electron transfer who wish to go beyond the Condon approximation. A future extension to time-dependent density functional theory in the Tamm–Dancoff approximation is clear.

We report robust initial guesses for the amplitudes and z-vectors in a configuration interaction singles or Tamm–Dancoff approximation calculation that consistently reduce the total number of iterations required for an excited state calculation often by over 50%. The end result of these guesses is that the practicing chemist can expect to generate excited state optimized structures with a total wall time reduced by as much as 30% in the future without any approximations—simply by using information gathered at one geometry and applying it to another geometry.