Matej Ditte

We present the first open access version of the QMeCha (Quantum MeCha /’mεkə/) code, a quantum Monte Carlo package developed to study many-body interactions between different types of quantum particles, with a modular and easy-to-expand structure. QMeCha is now available under a CC BY-NC-ND license through the repository github.com/QMeCha. The present code has been developed 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 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 subsystems. 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.

The reaction of tris[3,5-bis(trifluoromethyl)phenyl]telluronium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (BArF^-) salt with phosphine oxides OPR₃ in 1,2-dichloroethane is exothermic and leads to the population of the three Te σ-holes. Quite unprecedented, careful adjustment of the stoichiometry of reagents allowed the selective crystallization of the Lewis adducts containing one, two, or three Te-bonded OPR₃, according to X-ray diffraction. ¹H and ¹⁹F Diffusion-ordered NMR spectroscopy-monitored titrations of the telluronium salt by OPPh₃ reveal the growth of the hydrodynamic volume of the various cationic adducts, alongside a unique behavior of the BArF^- counterion that suggests its aggregation at high cationic molecular sizes. Isotherm titration calorimetry experiments show that the association equilibrium constants of OPR₃ binding to Te σ-holes follow the order K_a1 > K_a2 > K_a3, with respective values decreasing by 1 up to 2 orders of magnitude as the σ-holes are populated. Analysis of Te-O bonding by DFT methods confirms their dominant Coulombic character. The minor covalent character is nonetheless required to ensure telluronium-ligand cohesion. DFT calculations of the association thermochemistry raise the tangible contribution of ion "pairs" to the association enthalpy as a major issue for modeling: the allegedly "non-coordinating" BArF^- taking part in elusive multipolar ion-pairs is far from being an irrelevant thermochemical contributor.

We present a comprehensive investigation of the El-QDO embedding method [Phys. Rev. Lett. 131, 228001 (2023)], where molecular systems described through the electronic Hamiltonian are immersed in a bath of charged quantum harmonic oscillators, i.e., quantum Drude oscillators (QDOs). In the El-QDO model, the entire system of electrons and drudons─the quantum particles in the QDOs─is modeled through a single Hamiltonian which is solved through quantum Monte Carlo (QMC) methods. We first describe the details of the El-QDO Hamiltonian, of the proposed El-QDO ansatz, and of the QMC algorithms implemented to integrate both electronic and drudonic degrees of freedom. Then we analyze short-range regularization functions for the interacting potential between electrons and QDOs in order to accurately treat equilibrium and repulsive regions, resolving the overpolarization error that occurs between the electronic system and the environment. After benchmarking various regularization (damping) functions on the cases of argon and water dimers, the El-QDO method is applied to study the solvation energies of the benzene and water dimers, verifying the accuracy of the El-QDO approach compared to accurate fully electronic ab initio calculations. Furthermore, through the comparison of the El-QDO interaction energies with the components of Symmetry-Adapted Perturbation Theory calculations, we illustrate the El-QDO's explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the electronic subsystem and the environment.

The quantum Drude oscillator (QDO) model has been widely used as an efficient surrogate to describe the electric response properties of matter as well as long-range interactions in molecules and materials. Most commonly, QDOs are coupled within the dipole approximation so that the Hamiltonian can be exactly diagonalized, which forms the basis for the many-body dispersion method [Phys. Rev. Lett. 108, 236402 (2012)]. The dipole coupling is efficient and allows us to study non-covalent many-body effects in systems with thousands of atoms. However, there are two limitations: (i) the need to regularize the interaction at short distances with empirical damping functions and (ii) the lack of multipolar effects in the coupling potential. In this work, we convincingly address both limitations of the dipole-coupled QDO model by presenting a numerically exact solution of the Coulomb-coupled QDO model by means of quantum Monte Carlo methods. We calculate the potential-energy surfaces of homogeneous QDO dimers, analyzing their properties as a function of the three tunable parameters: frequency, reduced mass, and charge. We study the coupled-QDO model behavior at short distances and show how to parameterize this model to enable an effective description of chemical bonds, such as the covalent bond in the H2 molecule.

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.