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Emmanuel Giner

Publications and source records attributed to Emmanuel Giner.

At least 19 recordsLinked to original sources
arXiv2026

Transcorrelated Random-Phase Approximation

We extend the random-phase approximation (RPA) to the non-Hermitian transcorrelated (TC) Hamiltonian, which explicitly includes three-body interactions generated by a Jastrow correlation factor. We consider both the direct RPA (dRPA) and RPA with exchange (RPAx). We apply the resulting TC-dRPA and TC-RPAx methods to calculate ground-state correlation energies and vertical excitation energies for atoms (\ce{He} and \ce{Ne}) and small molecules (\ce{H2O}, \ce{NH3}, \ce{CH4}, and \ce{H2CO}). For ground-state correlation energies, the TC treatment substantially improves accuracy and accelerates basis set convergence, reducing errors by nearly an order of magnitude relative to conventional RPA calculations. By contrast, it yields only marginal improvements in vertical excitation energies. We attribute this limited effect to the ground-state optimization of the Jastrow factor, which does not adequately capture the distinct electronic character of excited states. These results establish TC-RPA as an accurate and computationally efficient approach to ground-state energetics, while highlighting the need for state-specific Jastrow optimization to achieve reliable descriptions of excited states.

physics.chem-ph↗
arXiv2026

Algebra of quantum mechanics via classical phonons. I: The Schrodinger equation as the Newtonian equation of motion and quantum observables as classical averages

The Schrodinger equation for a single spinless particle is formally obtained via a classical phonon model, namely the Frenkel-Kontorova model. Starting from a one-dimensional lattice of coupled harmonic oscillators, we show that the continuous limit of the corresponding Newtonian equation of motion yields the Klein-Gordon equation for a real-valued field. By introducing a complex-valued change of variables mixing the real-valued displacement and velocity fields, and by separating fast and slow time scales, the Klein-Gordon equation is written as the Schrodinger equation within the non-relativistic limit. This complex change of variable also allows to rewrite classical global observables of the phonon field, such as the total energy or momentum, as the corresponding quantum observables. Additionally, we show that when a friction force is incorporated into the classical model, the corresponding Klein-Gordon equation can be rewritten as a Schrodinger equation with a non-Hermitian Hamiltonian. While the global approach is limited here to the non-relativistic regime and does not address the measurement problem, quantization or relativistic effects, it nonetheless illustrates how quantum algebra and complex-valued wave functions can be exactly reproduced using classical dynamics. The relativistic regime for a spinless particle and the link between commutators and Poisson brackets is addressed in the second part of this series.

quant-ph↗
arXiv2026

Algebra of quantum mechanics via classical phonons. II: Klein-Gordon dynamics, the Heisenberg formalism, the Dirac canonical commutation rule and the Poincare algebra through the continuous Poisson bracket formalism

In the first part of this series we have shown how the Schrodinger equation for a single particle and the corresponding non relativistic quantum observables can be obtained from a purely classical phonon model through the Newtonian equations of motion. In this work we focus instead on how the classical Hamiltonian formalism applied to the same phonon system allows to recover the feature of relativistic quantum mechanics for a single spinless particle. Using the classical nature of the phonon model, we naturally define continuous Poisson brackets between classical observables, which allows to recover the dynamics of such observables, i.e. the Ehrenfest relations associated to real-valued Klein-Gordon fields. The Poisson brackets also permits to obtain the generic form of constants of motions, thus generalizing the concept of inner products and momentum on Klein-Gordon fields. We then connect the formalism of real-valued classical functionals with that of hermitian operators and complex-valued wave functions. This is done through the introduction of a non-local complex-valued change of variables which allows to rewrite the real-valued Klein-Gordon equation in a form akin to the Schrodinger equation, and the classical observables as quantum expectation values. Then, we show how this change of variables allows to rewrite the classical Poisson brackets as commutators of hermitian operators. This points out the strict equivalence between the Heisenberg formalism and the formalism of classical Poisson bracket. Eventually, we illustrate how the Poisson brackets allows to recover the transformations of Poincare group in 1+1 dimension together with its algebra. The latter makes the link between the Lorentz invariant inner product of Mostafazadeh and the Casimir invariant associated to the mass of particle.

quant-ph↗
arXiv2025

QMCkl: A Kernel Library for Quantum Monte Carlo Applications

Quantum Monte Carlo (QMC) methods deliver highly accurate electronic structure calculations but are computationally intensive. The quantum Monte Carlo kernel library (QMCkl) provides a modular, portable collection of high-performance kernels implementing the core building blocks of QMC calculations. It offers a C-compatible API, supports the TREXIO standard for input, and covers essential QMC kernels including atomic and molecular orbitals, cusp corrections, Jastrow factor, and the necessary derivatives also to perform variational and structural optimization. QMCkl separates algorithmic development from hardware-specific tuning by combining human-readable reference implementations with performance-optimized kernels that produce identical numerical results. The library enables consistent, efficient, and reproducible simulations across different QMC codes and architectures, and achieves substantial speedups in the evaluation of the energy and its derivatives. Beyond QMC, QMCkl can accelerate deterministic quantum chemistry workflows and visualization tools, promoting cross-code interoperability and simplifying high-performance scientific software development.

physics.chem-ph↗
arXiv2025

Real-Space Chemistry on Quantum Computers: A Fault-Tolerant Algorithm with Adaptive Grids and Transcorrelated Extension

First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and Coulomb operators achieve quadratic instead of quartic computational scaling of two-electron interactions. However, existing schemes employ uniform discretizations, so the resolution required to capture electron-nuclear cusps in high-density regions oversamples low-density regions, wasting computational resources. We address this by deploying non-uniform, molecule-adaptive grids that concentrate points where electronic density is high. Using Voronoi partitions of these grids, the molecular Hamiltonian is expressed in a Hermitian form and in a transcorrelated, isospectral form that eliminates Coulomb singularities and yields cusp-free eigenfunctions. Both formulations slot naturally into quantum eigenvalue solvers: Hermitian Quantum Phase Estimation (QPE) and the recent generalised Quantum Eigenvalue Estimation (QEVE) protocol for its non-Hermitian, transcorrelated counterpart. Numerical validation on benchmark systems confirms that this non-heuristic ab initio framework offers a promising path for accurate ground-state chemistry on quantum hardware.

quant-ph↗
arXiv2025

Prediction of the aqueous redox properties of functionalized quinones using a new QM/MM variational formulation

We recently proposed a method coupling quantum mechanics (QM) methods and molecular density functional theory (MDFT) to describe mixed quantum-classical systems [J. Chem. Phys. 161, 014113 (2024)]. This approach is particularly appropriate to account for solvent effect into QM calculations. We introduce a new variational formulation for the grand potential of a mixed quantum-classical system. Within the Born-Oppenheimer approximation and neglecting electronic entropy, the quantum solute is described by a product of electronic and nuclear density matrices, both depending parametrically on coordinates of the classical solvent. It can then be shown that a functional of the total density matrix satisfies a variational principle for the grand potential. Using a mean-field approximation, we express the grand potential of the mixed quantum-classical system as a variational problem which depends only on the nuclear density matrix, which experiences an external field generated by the electronic and classical one-particle densities. In practice, the grand potential is computed by a series of coupled classical and quantum DFT calculations, together with geometry optimization.

physics.chem-ph↗
arXiv2024

A variational formulation of the free energy of mixed quantum-classical systems: coupling classical and electronic density functional theories

Combining classical density functional theory (cDFT) with quantum mechanics (QM) methods offers a computationally efficient alternative to traditional QM/molecular mechanics (MM) approaches for modeling mixed quantum-classical systems at finite temperatures. However, both QM/MM and QM/cDFT rely on somewhat ambiguous approximations, the two major ones being: i) the definition of the QM and MM regions as well as the description of their coupling, and ii) the choice of the methods and levels of approximation made to describe each region. This paper addresses the second point and develop an exact theoretical framework that allows us to clarify the approximations involved in the QM/cDFT formulation. We establish a comprehensive density functional theory (DFT) framework for mixed quantum-classical systems within the canonical ensemble. We start by recalling the expression of the adiabatic equilibrium density matrix for a mixed system made of Nqm quantum and Nmm classical particles. Then, we propose a variational formulation of the Helmholtz free energy in terms of the full, non-equilibrium, QM/MM density matrix. Taking advantage of permutational symmetry and thanks to constrained-search methods, we reformulate the computation of the Helmholtz free energy using only the quantum and classical one-body densities.This paper generalizes both cDFT and electronic DFT (eDFT) to QM/MM systems. We then reformulate the functional to make the standard eDFT and cDFT Levy-Lieb functionals explicitly appear, together with a new universal correlation functional for QM/MM systems. A mean-field approximation is finally introduced in the context of solvation problems and we discuss its connection with several existing mixed cDFT-eDFT schemes. An extension to the semi-grand canonical ensemble, where the number of classical particles is allowed to fluctuate, is provided in the supplementary materials.

cond-mat.stat-mech↗
arXiv2024

Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction

Using GPU-accelerated state-vector emulation, we propose to embed a quantum computing ansatz into density-functional theory via density-based basis-set corrections (DBBSC) to obtain quantitative quantum-chemistry results on molecules that would otherwise require brute-force quantum calculations using hundreds of logical qubits. Indeed, accessing a quantitative description of chemical systems while minimizing quantum resources is an essential challenge given the limited qubit capabilities of current quantum processors. We provide a shortcut towards chemically accurate quantum computations by approaching the complete-basis-set limit through coupling the DBBSC approach, applied to any given variational ansatz, to an on-the-fly crafting of basis sets specifically adapted to a given system and user-defined qubit budget. The resulting approach self-consistently accelerates the basis-set convergence, improving electronic densities, ground-state energies, and first-order properties (e.g. dipole moments), but can also serve as a classical, a posteriori, energy correction to quantum hardware calculations with expected applications in drug design and materials science.

physics.chem-ph↗
arXiv2024

Compactification of Determinant Expansions via Transcorrelation

Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects.

physics.chem-ph↗
arXiv2024

Coupling Molecular Density Functional Theory with Converged Selected Configuration Interaction Methods to Study Excited states in Aqueous Solution

This paper presents the first implementation of a coupling between advanced wave function theories and molecular density functional theory (MDFT). This method enables the modeling of solvent effect into quantum mechanical (QM) calculations by incorporating an electrostatic potential generated by solvent charges into the electronic Hamiltonian. Solvent charges are deduced from the spatially and angularly dependent solvent particle density. Such density is obtained through the minimization of the functional associated to the molecular mechanics (MM) Hamiltonian describing the interaction between the fluid particles. The introduced QM/MDFT framework belongs to QM/MM family of methods but its originality lies in the use of MDFT as the MM solver, offering two main advantages. Firstly, its functional formulation makes it competitive with respect to sampling-based molecular mechanics. Secondly, it preserves a molecular-level description lost in macroscopic continuum approaches. Excited states properties of water and formaldehyde molecules solvated into water have been computed at the selected configuration interaction (SCI) level. Excitation energies and dipole moment have been compared with experimental data and previous theoretical work. A key finding is that using the Hartree-Fock method to describe the solute allows for predicting the solvent charge around the ground-state with sufficient precision for the subsequent SCI calculations of excited-states. This significantly reduces the computational cost of the described procedure, paving the way for the study of more complex molecules.

physics.chem-ph↗
arXiv2024

Accelerated basis-set convergence of coupled-cluster excitation energies using the density-based basis-set correction method

We present the first application to real molecular systems of the recently proposed linear-response theory for the density-based basis-set correction method [J. Chem. Phys. 158, 234107 (2023)]. We apply this approach to accelerate the basis-set convergence of excitation energies in the equation-of-motion coupled-cluster singles doubles (EOM-CCSD) method. We use an approximate linear-response framework which neglects the second-order derivative of the basis-set correction density functional and consists in simply adding to the usual Hamiltonian the one-electron potential generated by the first-order derivative of the functional. This additional basis-set correction potential is evaluated at the Hartree-Fock density, leading to a very computationally cheap basis-set correction. We tested this approach over a set of about 30 excitation energies computed for five small molecular systems and found that the excitation energies from the ground state to Rydberg states are the main source of basis-set error. These excitation energies systematically increase when the size of the basis set is increased, suggesting a biased description in favour of the excited state. Despite the simplicity of the present approach, the results obtained with the basis-set corrected EOM-CCSD method are encouraging as they yield to a mean absolute deviation of 0.02 eV for the aug-cc-pVTZ basis set, while it is of 0.04 eV using the standard EOM-CCSD method. This might open the path to an alternative to explicitly correlated approaches to accelerate the basis-set convergence of excitation energies.

physics.chem-ph↗
arXiv2023

A density-fitting implementation of the density-based basis-set correction method

This work reports an efficient density-fitting implementation of the density-based basis-set correction (DBBSC) method in the MOLPRO software. This method consists in correcting the energy calculated by a wave-function method with a given basis set by an adapted basis-set correction density functional incorporating the short-range electron correlation effects missing in the basis set, resulting in an accelerated convergence to the complete-basis-set limit. Different basis-set correction density-functional approximations are explored and the complementary-auxiliary-basis-set single-excitation correction is added. The method is tested on a benchmark set of reaction energies at the second-order M{\o}ller-Plesset (MP2) level and a comparison with the explicitly correlated MP2-F12 method is provided. The results show that the DBBSC method greatly accelerates the basis convergence of MP2 reaction energies, without reaching the accuracy of the MP2-F12 method but with a lower computational cost.

physics.chem-ph↗
arXiv2023

Transcorrelated selected configuration interaction in a bi-orthonormal basis and a cheap three-body correlation factor

In this work, we develop a mathematical framework for a Selected Configuration Interaction (SCI) algorithm within a bi-orthogonal basis for transcorrelated (TC) calculations. The bi-orthogonal basis used here serves as the equivalent of the standard Hartree Fock (HF) orbitals. However, within the context of TC, it leads to distinct orbitals for the left and right vectors. Our findings indicate that the use of such a bi-orthogonal basis allows for a proper definition of the frozen core approximation. In contrast, the use of HF orbitals results in bad error cancellations for ionization potentials and atomization energies (AE). Compared to HF orbitals, the optimized bi-orthogonal basis significantly reduces the positive part of the second-order energy (PT2), thereby facilitating the use of standard extrapolation techniques of hermitian SCI. While we did not observe a significant improvement in the convergence of the SCI algorithm, this is largely due to the use in the present work of a simple three-body correlation factor introduced in a recent study. This correlation factor, which depends only on atomic parameters, eliminates the need for re-optimization of the correlation factor for molecular systems, making its use straightforward and user-friendly. Despite the simplicity of this correlation factor, we were able to achieve accurate results on the AE of a series of 14 molecules in a triple-zeta basis. We also successfully broke a double bond until the full dissociation limit while maintaining the size consistency property. This work thus demonstrates the potential of the BiO-TC-SCI approach in handling complex molecular systems.

physics.chem-ph↗
arXiv2023

Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional incorporates the short-range electron correlation effects missing in the basis set. This results in accelerated basis convergences of ground-state energies to the complete-basis-set limit. In this work, we extend the basis-set correction method to a linear-response formalism for calculating excited-state energies. We give the general linear-response equations, as well as the more specific equations for configuration-interaction wave functions. As a proof of concept, we apply this approach to the calculations of excited-state energies in a one-dimensional two-electron model system with harmonic potential and a Dirac-delta electron-electron interaction. The results obtained with full-configuration-interaction wave functions expanded in a basis of Hermite functions and a local-density-approximation basis-set correction functional show that the present approach does not help in accelerating the basis convergence of excitation energies. However, we show that it significantly accelerates basis convergences of excited-state total energies.

physics.chem-ph↗
arXiv2023

Bi-orthonormal orbital optimization with a cheap core-electron free three-body correlation factor for Quantum Monte Carlo and Transcorrelation

We introduce a novel three-body correlation factor that is designed to vanish in the core region around each nucleus and approach a universal two-body correlation factor for valence electrons. The Transcorrelated Hamiltonian is used to optimize the orbitals of a single Slater determinant within a biorthonormal framework. The Slater-Jastrow wave function is optimized on a set of atomic and molecular systems containing both second-row elements and $3d$ transition metal elements. The optimization of the correlation factor and the orbitals, along with increasing the basis set, results in a systematic lowering of the Variational Monte Carlo energy for all systems tested. Importantly, the optimal parameters of the correlation factor obtained for atomic systems are transferable to molecules. Additionally, the present correlation factor is computationally efficient, using a mixed analytical-numerical integration scheme that reduces the costly numerical integration from $\mathbb{R}^6$ to $\mathbb{R}^3$.

physics.chem-ph↗
arXiv2023

Overlap-ADAPT-VQE: Practical Quantum Chemistry on Quantum Computers via Overlap-Guided Compact Ans\"atze

ADAPT-VQE is a robust algorithm for hybrid quantum-classical simulations of quantum chemical systems on near-term quantum computers. While its iterative process systematically reaches the ground state energy, ADAPT-VQE is sensitive to local energy minima, leading to over-parameterized ans\"atze. We introduce the Overlap-ADAPT-VQE to grow wave-functions by maximizing their overlap with any intermediate target wave-function that already captures some electronic correlation. By avoiding building the ansatz in the energy landscape strewn with local minima, the Overlap-ADAPT-VQE produces ultra-compact ans\"atze suitable for high-accuracy initializations of a new ADAPT procedure. Spectacular advantages over ADAPT-VQE are observed for strongly correlated systems including massive savings in circuit depth. Since this compression strategy can also be initialized with accurate Selected-Configuration Interaction (SCI) classical target wave-functions, it paves the way for chemically accurate simulations of larger systems, and strengthens the promise of decisively surpassing classical quantum chemistry through the power of quantum computing.

quant-ph↗
arXiv2022

Diffusion Monte Carlo using domains in configuration space

The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60}, 2299 (1999)}], it was shown that the probability for a walker to stay a certain amount of time in the same state obeys a Poisson law and that the on-state dynamics can be integrated out exactly, leading to an effective dynamics connecting only different states. Here, we extend this idea to the general case of a walker trapped within domains of arbitrary shape and size. The equations of the resulting effective stochastic dynamics are derived. The larger the average (trapping) time spent by the walker within the domains, the greater the reduction in statistical fluctuations. A numerical application to the Hubbard model is presented. Although this work presents the method for finite linear spaces, it can be generalized without fundamental difficulties to continuous configuration spaces.

cond-mat.str-el↗
arXiv2022

Extension of selected configuration interaction for transcorrelated methods

In this work we present an extension of the popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework. Although we used in this work the recently introduced one-parameter correlation factor [E. Giner, J. Chem. Phys., 154, 084119 (2021)], the theory presented here is valid for any correlation factor. Thanks to the formalization of the non Hermitian TC eigenvalue problem as a search of stationary points for a specific functional depending both on left-and right-functions, we obtain a general framework allowing different choices for both the selection criterion in SCI and the second order perturbative correction to the energy. After numerical investigations on different second-row atomic and molecular systems in increasingly large basis sets, we found that taking into account the non Hermitian character of the TC Hamiltonian in the selection criterion is mandatory to obtain a fast convergence of the TC energy. Also, selection criteria based on either the first order coefficient or the second order energy lead to significantly different convergence rates, which is typically not the case in the usual Hermitian SCI. Regarding the convergence of the total second order perturbation energy, we find that the quality of the left-function used in the equations strongly affects the quality of the results. Within the near-optimal algorithm proposed here we find that the SCI expansion in the TC framework converges faster than the usual SCI both in terms of basis set and number of Slater determinants.

cond-mat.str-el↗