QMeCha: quantum Monte Carlo package for fermions in embedding environments

We present the first open access version of the QMeCha (Quantum MeCha) code, a quantum Monte Carlo (QMC) package developed to study many-body interactions between different types of quantum particles, with a modular and easy-to-expand structure. The present code has been built to solve the Hamiltonian of a system that can include nuclei and fermions of different mass and charge, e.g. electrons and positrons, embedded in an environment of classical charges and quantum Drude oscillators. To approximate the ground state of this many-particle operator, the code features different wavefunctions. For the fermionic particles, beyond the traditional Slater determinant, QMeCha also includes Geminal functions such as the Pfaffian, and presents different types of explicit correlation terms in the Jastrow factors. The classical point charges and quantum Drude oscillators, described through different variational ansätze, are used to model a molecular environment capable of explicitly describing dispersion, polarization, and electrostatic effects experienced by the nuclear and fermionic subsystem. To integrate these wavefunctions, efficient variational Monte Carlo and diffusion Monte Carlo protocols have been developed, together with a robust wavefunction optimization procedure that features correlated sampling.

💡 Research Summary

The paper introduces QMeCha (Quantum MeCha), a new open‑access quantum Monte Carlo (QMC) software package designed to treat many‑body systems that combine fermionic particles (electrons, positrons, nuclei) with classical point charges and quantum Drude oscillators (QDOs). The code is released under a CC BY‑NC‑ND license on GitHub (github.com/QMeCha) and aims to provide a modular, extensible framework for embedding quantum subsystems in realistic environments.

The physical model implemented in QMeCha consists of three coupled Hamiltonian components. The fermionic part describes N_f particles of unit mass and charge ±1 within the Born‑Oppenheimer approximation, including kinetic energy and full Coulomb interactions with each other and with fixed nuclei. The QDO part treats each oscillator as a pair of a positively charged center and a negatively charged “drudon” particle bound by a harmonic spring; the drudons have kinetic energy, the harmonic potential, and Coulomb interactions with all other drudons and QDO centers. The embedding part adds Coulomb couplings between fermions, QDOs, and optional classical point charges that can represent polar groups or fragments of a larger molecular environment. Short‑range divergences are handled by a screened Coulomb kernel based on the error‑function damping, with species‑dependent cutoff parameters.

QMeCha supports a rich set of trial wave‑functions. In addition to the conventional Slater determinant, it implements Pfaffian and antisymmetrized geminal power (AGP) forms, which allow explicit pairing correlations and are particularly advantageous for electron‑positron systems. Jastrow correlation factors are provided with generic cusp‑condition terms and a dynamical component that can depend explicitly on electron‑positron distances, thereby capturing short‑range correlation beyond the determinant. Separate correlation functions for fermion‑QDO and drudon‑fermion pairs are also available, enabling a fully correlated description of the embedded system at the wave‑function level.

The computational engine includes both variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). VMC uses Metropolis sampling and a correlated‑sampling based optimization scheme that combines linear method updates with stochastic reconfiguration (SR) to efficiently minimize the energy and variance. DMC employs a size‑consistent algorithm that reduces finite‑time‑step errors when computing energy differences, while preserving the nodal surface defined by the trial wave‑function. The code architecture is modular: new wave‑functions, pseudopotentials, or embedding models can be added as plug‑ins without modifying the core. Pseudopotentials are supported in the standard semi‑local form, allowing the replacement of core electrons to reduce computational cost.

Three application domains are showcased. First, van‑der‑Waals interactions in large biomolecules are investigated; DMC results are benchmarked against LNO‑CCSD(T) calculations, demonstrating that QMeCha can provide reference‑quality interaction energies for protein‑ligand complexes. Second, the package is applied to positronic chemistry, where electron‑positron bound states are modeled with Pfaffian + Jastrow wave‑functions. The results show improved binding energies and wave‑function quality compared with conventional Hartree‑Fock‑based approaches, highlighting the importance of explicit electron‑positron pairing. Third, the El‑QDO embedding scheme is employed to study solvation effects in water clusters. By combining QDOs with classical point charges, QMeCha accurately reproduces solvation energies, excitation energies, and bond‑energy variations of dimers embedded in aqueous environments, illustrating the efficiency of the QDO model for long‑range dispersion and polarization.

Overall, QMeCha delivers a comprehensive, scalable QMC platform for quantum‑classical hybrid systems, with open‑source availability encouraging community contributions and future extensions such as molecular dynamics coupling, GPU acceleration, and multi‑spin extensions. The authors discuss ongoing challenges, including more sophisticated screening functions, better treatment of nuclear quantum effects, and integration with existing electronic‑structure packages, outlining a clear roadmap for the evolution of the code.