arXiv subjects

Abdallah Ammar

Publications and source records attributed to Abdallah Ammar.

17 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↗

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↗

arXiv2024

On the use of complex GTOs for the evaluation of radial integrals involving oscillating functions

We study two classes of radial integrals involving a product of bound and continuum one-electron states. Using a representation of the continuum part with an expansion on complex Gaussian Type Orbitals, such integrals can be performed analytically. We investigate the reliability of this scheme for low-energy physical parameters. This study serves as a premise in view of potential applications in molecular scattering processes.

physics.chem-ph↗

arXiv2024

Calculation of electron-impact and photo-ionization cross sections of methane using analytical Gaussian integrals

The ionization by photon or electron impact of the inner (2a1) and outer (1t2) valence orbitals of the CH4 molecule is investigated theoretically. In spite of a number of approximations, including a monocentric approach and a rather simple distorting molecular potential, the calculated cross sections are overall similar to those of other theoretical methods, and in reasonable agreement with experimental data. The originality of the present approach stands in the way we evaluate the transition matrix elements. The key ingredient of the calculation scheme is that the continuum radial wave function of the ejected electron is represented by a finite sum of complex Gaussian type orbitals. This numerically expensive optimization task is then largely compensated by rather simple and rapid analytical calculations of the necessary integrals, and thus all ionization observables, including cross section angular distributions. The proposed and implemented Gaussian approach is proved to be numerically very reliable in all considered kinematical situations with ejected electrons up to 2.7 a.u.. The analytical formulation of the scheme is provided here for bound molecular states described by monocentric Slater type orbitals; however, Gaussian type orbitals may be equally be employed. In combination with complex Gaussian functions for the continuum states, an all Gaussian approach with multicentric bound states can be envisaged.

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

Go Green: Selected Configuration Interaction as a More Sustainable Alternative for High Accuracy

Recently, a new distributed implementation of the full configuration interaction (FCI) method has been reported [Gao et al. J. Chem Theory Comput. 2024, 20, 1185]. Thanks to a hybrid parallelization scheme, the authors were able to compute the exact energy of propane (\ce{C3H8}) in the minimal basis STO-3G. This formidable task involves handling an active space of 26 electrons in 23 orbitals or a Hilbert space of \SI{1.3d12} determinants. This is, by far, the largest FCI calculation reported to date. Here, we illustrate how, from a general point of view, selected configuration interaction (SCI) can achieve microhartree accuracy at a fraction of the computational and memory cost, via a sparse exploration of the FCI space. The present SCI calculations are performed with the \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) algorithm, as implemented in a determinant-driven way in the \textsc{quantum package} software. The present study reinforces the common wisdom that among the exponentially large number of determinants in the FCI space, only a tiny fraction of them significantly contribute to the energy. More importantly, it demonstrates the feasibility of achieving comparable accuracy using more reasonable and sustainable computational resources, hence reducing the ever-growing carbon footprint of computational chemistry.

physics.chem-ph↗

arXiv2024

The $GW$ Approximation: A Quantum Chemistry Perspective

We provide an in-depth examination of the $GW$ approximation of Green's function many-body perturbation theory by detailing both its theoretical and practical aspects in the realm of quantum chemistry. First, the quasiparticle context is introduced before delving into the derivation of Hedin's equations. From these, we explain how to derive the well-known $GW$ approximation of the self-energy. In a second time, we meticulously explain each step involved in a $GW$ calculation and what type of physical quantities can be computed. To illustrate its versatility, we consider two contrasting systems: the water molecule, a weakly correlated system, and the carbon dimer, a strongly correlated system. Each stage of the process is thoroughly detailed and explained alongside numerical results and illustrative plots. We hope that the contribution will facilitate the dissemination and democratization of Green's function-based formalisms within the computational and theoretical quantum chemistry community.

physics.chem-ph↗

arXiv2024

Cumulant Green's function methods for molecules

The cumulant expansion of the Green's function is a computationally efficient beyond-$GW$ approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous $GW$ approximation of many-body perturbation theory, \textit{ab initio} cumulant expansions performed on top of $GW$ ($GW$+C) have demonstrated the capability to handle multi-particle processes by incorporating higher-order correlation effects or vertex corrections, yielding better agreements between experiment and theory for satellite structures. While widely employed in condensed matter physics, very few applications of $GW$+C have been published on molecular systems. Here, we assess the performance of this scheme on a series of 10-electron molecular systems (\ce{Ne}, \ce{HF}, \ce{H2O}, \ce{NH3}, and \ce{CH4}) where full configuration interaction estimates of the outer-valence quasiparticle and satellite energies are available.

physics.chem-ph↗

arXiv2024

Can $GW$ Handle Multireference Systems?

Due to the infinite summation of bubble diagrams, the $GW$ approximation of Green's function perturbation theory has proven particularly effective in the weak correlation regime, where this family of Feynman diagrams is important. However, the performance of $GW$ in multireference molecular systems, characterized by strong electron correlation, remains relatively unexplored. In the present study, we investigate the ability of $GW$ to handle closed-shell multireference systems in their singlet ground state by examining four paradigmatic scenarios. Firstly, we analyze a prototypical example of a chemical reaction involving strong correlation: the potential energy curve of \ce{BeH2} during the insertion of a beryllium atom into a hydrogen molecule. Secondly, we compute the electron detachment and attachment energies of a set of molecules that exhibit a variable degree of multireference character at their respective equilibrium geometries: \ce{LiF}, \ce{BeO}, \ce{BN}, \ce{C2}, \ce{B2}, and \ce{O3}. Thirdly, we consider a \ce{H6} cluster with a triangular arrangement, which features a notable degree of spin frustration. Finally, the dissociation curve of the \ce{HF} molecule is studied as an example of single bond breaking. These investigations highlight a nuanced perspective on the performance of $GW$ for strong correlation, depending on the level of self-consistency, the choice of initial guess, and the presence of spin-symmetry breaking at the Hartree-Fock level.

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

TREXIO: A File Format and Library for Quantum Chemistry

TREXIO is an open-source file format and library developed for the storage and manipulation of data produced by quantum chemistry calculations. It is designed with the goal of providing a reliable and efficient method of storing and exchanging wave function parameters and matrix elements, making it an important tool for researchers in the field of quantum chemistry. In this work, we present an overview of the TREXIO file format and library. The library consists of a front-end implemented in the C programming language and two different back-ends: a text back-end and a binary back-end utilizing the HDF5 library which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for the Fortran, Python, and OCaml programming languages. In addition, a suite of tools has been developed to facilitate the use of the TREXIO format and library, including converters for popular quantum chemistry codes and utilities for validating and manipulating data stored in TREXIO files. The simplicity, versatility, and ease of use of TREXIO make it a valuable resource for researchers working with quantum chemistry data.

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↗

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↗

arXiv2022

Optimization of large determinant expansions in quantum Monte Carlo

We present a new method for the optimization of large configuration interaction (CI) expansions in the quantum Monte Carlo (QMC) framework. The central idea here is to replace the non-orthogonal variational optimization of CI coefficients performed in usual QMC calculations by an orthogonal non-Hermitian optimization thanks to the so-called transcorrelated (TC) framework, the two methods yielding the same results in the limit of a complete basis set. By rewriting the TC equations as an effective self-consistent Hermitian problem, our approach requires the sampling of a single quantity per Slater determinant, leading to minimal memory requirements in the QMC code. Using analytical quantities obtained from both the TC framework and the usual CI-type calculations, we also propose improved estimators which reduce the statistical fluctuations of the sampled quantities by more than an order of magnitude. We demonstrate the efficiency of this method on wave functions containing $10^5-10^6$ Slater determinants, using effective core potentials or all-electron calculations. In all the cases, a sub-milliHartree convergence is reached within only two or three iterations of optimization.

physics.chem-ph↗

arXiv2021

A complex Gaussian approach to molecular photoionization

We develop and implement a Gaussian approach to calculate partial cross-sections and asymmetry parameters for molecular photoionization. Optimal sets of complex Gaussian-type orbitals (cGTOs) are first obtained by non-linear optimization, to best fit sets of Coulomb or distorted continuum wave functions for relevant orbital quantum numbers. This allows us to represent the radial wavefunction for the outgoing electron with accurate cGTO expansions. Within a time-independent partial wave approach, we show that all the necessary transition integrals become analytical, in both length and velocity gauges, thus facilitating the numerical evaluation of photoionization observables. Illustrative results, presented for NH3 and H2O within a one-active-electron monocentric model, validate numerically the proposed strategy based on a complex Gaussian representation of continuum states.

physics.chem-ph↗

arXiv2021

Multicenter integrals involving complex Gaussian type functions

Multicentric integrals that involve a continuum state cannot be evaluated with the usual quantum chemistry tools and require a special treatment. We consider an initial molecular bound state described by multicenter spherical or cartesian Gaussian functions. An electron ejected through an ionization process will be described by an oscillating continuum wavefunction that enters the matrix element necessary for cross section calculations. Within a monocentric approach, we have recently shown how such integrals can be evaluated analytically by using a representation of the continuum state by a set of complex Gaussian functions. In this work we tackle the multicentric situation. The method, developed in either spherical or cartesian coordinates, and validated by numerical tests, makes use of existing mathematical tools extended to the complex plane.

quant-ph↗

arXiv2020

Fitting continuum wavefunctions with complex Gaussians: Computation of ionization cross sections

We implement a full nonlinear optimization method to fit continuum states with complex Gaussians. The application to a set of regular scattering Coulomb functions allows us to validate the numerical feasibility, to explore the range of convergence of the approach, and to demonstrate the relative superiority of complex over real Gaussian expansions. We then consider the photoionization of atomic hydrogen, and ionization by electron impact in the first Born approximation, for which the closed form cross sections serve as a solid benchmark. Using the proposed complex Gaussian representation of the continuum combined with a real Gaussian expansion for the initial bound state, all necessary matrix elements within a partial wave approach become analytical. The successful numerical comparison illustrates that the proposed all-Gaussian approach works efficiently for ionization processes of one-center targets.

physics.comp-ph↗