[Paper Review] Extending numerical simulations in SIMPSON: Electron paramagnetic resonance, dynamic nuclear polarisation, propagator splitting, pulse transients, and quadrupolar cross terms

David L. Goodwin, José P. Carvalho+5 more|arXiv (Cornell University)|Feb 17, 2026

Advanced NMR Techniques and Applications0 citations

TL;DR

This paper introduces a C++ reimplementation of SIMPSON (v6.0) with new features for simulating EPR, pulsed DNP, propagator splitting, pulse transients, and higher-order quadrupolar cross terms, plus improved visualization and workflow integration.

ABSTRACT

Aimed at the simulation, design, and interpretation of advanced pulse experiments crossing the boundaries between nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), including the rapidly emerging, hybrid discipline of pulsed dynamic nuclear polarisation (DNP), we present a host of novel features in the widely used SIMPSON software package addressing these aspects. Along with this come new features for advanced pulse sequence evaluation in terms of propagator splitting, high-order spin operator cross terms, and pulse phase transients. These fundamental new tools are introduced in a C++-based next generation of the SIMPSON software, which improves calculations speed in some aspects, is better prepared for further developments, and facilitates easier community contributions to the open-source software package.

Motivation & Objective

• Extend SIMPSON to simulate electron spin dynamics and hybrid EPR/NMR experiments including DNP.
• Improve computational efficiency through propagator splitting and modern C++ architecture.
• Provide advanced features for pulse sequence evaluation, optimal control, and higher-order quadrupolar terms.
• Enhance usability and community contributions via open-source development and modern tooling.

Proposed method

• Develop a C++ based next generation of SIMPSON with object oriented design to accelerate calculations.
• Introduce electron spin interactions formalism compatible with EPR and DNP calculations using irreducible tensor operators and Wigner transforms.
• Add new syntax and commands for electron spin channels, g-tensors, hyperfine couplings, dipole interactions, and exchange terms to support EPR/DNP simulations.
• Implement propagator splitting to speed up time evolution in density matrix calculations.
• Provide pulse transient handling, shaped rotor modulations, and RF field distribution through rfmap and related commands.
• Integrate SIMPSON with visualization and workflow tools such as SimPlot, easy nmr, and SimView for data analysis and teaching.

Figure 1: Examples of visualisation of and data integration with simpson simulations. (A) The e asy nmr workflow with three different simpson simulations. The left frame shows the three simulation objects, each forwarding data to a plotting object. The right frame shows the content of each object, h

Experimental results

Research questions

• RQ1 How can SIMPSON be extended to accurately simulate electron spin dynamics alongside nuclear spins in EPR and pulsed DNP experiments?
• RQ2 What computational strategies, such as propagator splitting, can reduce the overhead of density-matrix evolution in large spin systems?
• RQ3 How can pulse shaping, transients, and RF field inhomogeneities be modeled within SIMPSON to improve realism of simulations?
• RQ4 What new syntax and data structures are required to support electron spins, hyperfine and dipolar interactions, and quadrupolar cross terms in simulations?
• RQ5 How can the enhanced SIMPSON interface and tooling improve usability and community contribution to open-source magnetic resonance simulations?

Key findings

• A substantial enhancement of SIMPSON to include electron spins and DNP capable simulations alongside NMR calculations.
• Propagation splitting significantly improves efficiency for time-propagation and optimal control tasks in larger spin ensembles.
• New electron spin interaction formalisms and associated syntax allow defining g-tensors, hyperfine, dipolar, and exchange interactions in a consistent framework.
• Pulse shaping with rotor modulations and rfmap support enables modeling of spatial RF inhomogeneity and MAS-induced temporal modulations.
• The updated SIMPSON architecture promotes easier community contributions and interoperability with visualization tools such as SimPlot, SimView, and eAsyNMR.

Figure 2: (A) Pulse sequence diagrams for 2-pulse and 3-pulse eseem experiments. (B) Simulated echo intensity, $\langle\hat{\mathrm{S}}_{x}\rangle$ ), as a function of the delay time $\tau$ for 2-pulse eseem for a single orientation of an electron-proton two-spin system with ideal pulses (using puls