arXiv subjects

Mario Piris

Publications and source records attributed to Mario Piris.

At least 19 recordsLinked to original sources

arXiv2025

5- and 6-membered rings: A natural orbital functional study

The Global Natural Orbital Functional (GNOF) provides a straightforward approach to capture most electron correlation effects without needing perturbative corrections or limited active spaces selection. In this work, we evaluate both the original GNOF and its modified variant GNOFm on a set of twelve 5- and 6-membered molecular rings, systems characterized primarily by dynamic correlation. This reference set is vital as it comprises essential substructures of more complex molecules. We report complete-basis-set limit correlation energies for GNOF, GNOFm, and the benchmark CCSD(T) method. Across the Dunning basis sets, both functionals deliver a balanced and accurate description of the molecular set, with GNOFm showing small but systematic improvements while preserving the overall robustness of the original formulation. These results confirm the reliability of the GNOF family and its ability to capture dynamic correlation effects.

physics.chem-ph↗

arXiv2025

Metal-Insulator Transition described by Natural Orbital Functional Theory

The metal-insulator transition (MIT) is a fundamental phenomenon in condensed matter physics and a hallmark of strong electronic correlations. Hydrogen-based systems offer a simple yet powerful model for investigating the MIT, as their insulating behavior arises purely from electron-electron interactions. In this work, we study finite hydrogen clusters with cubic geometries using Natural Orbital Functional Theory (NOFT), a method capable of accurately describing correlated systems beyond mean-field approaches. We focus on two key signatures of the MIT: the fundamental energy gap and the harmonic average of the atomic one-particle reduced density matrix. Our results show that NOFT captures the transition from insulating to metallic behavior as the interatomic distance decreases. By extrapolating the energy gap to the thermodynamic limit, we estimate a critical distance rc ~ 1.2 Ang, in excellent agreement with quantum Monte Carlo benchmarks. These findings demonstrate the reliability of NOFT for describing strong correlation effects in large-scale models.

cond-mat.str-el↗

arXiv2025

Enhancing the Computational Efficiency of the DoNOF Program through a New Orbital Sorting Scheme

This work presents a novel approach to distribute orbitals into subspaces within electron-pairing-based natural orbital functionals (NOFs). This approach modifies the coupling between weakly and strongly occupied orbitals by applying an alternating orbital sorting strategy. In contrast to the previous orbital sorting that enforced electron pairing within subspaces of contiguous orbitals, the new approach provides greater flexibility, enabling a calculation scheme where the size of the subspaces can be gradually expanded. As a consequence, one can start using subspaces of only one weakly occupied orbital (perfect pairing) and progressively enlarge their size by incorporating more weakly occupied orbitals (extended pairing) up to the maximum size allowed by the basis set. In this way, the alternate orbital sorting allows solving first a simpler problem with small subspaces and leverage its orbital solution for the more intensive problem with larger subspaces, thereby reducing the overall computational cost and improving convergence, as we observed in the DoNOF program. The efficiency provided by the new sorting approach has been validated through benchmark calculations in H2O, H2O2, and NH3. In particular, we compared three strategies: i) solving directly the calculation with the largest subspaces (one-shot strategy), as was usually done before this work, ii) starting with perfect pairing and stepwise increasing the number of orbitals in the subspaces one by one until reaching the maximum size (incremental strategy), and iii) starting with perfect pairing and transitioning directly to the maximum subspace size (two-step strategy). Our results show that the two-step approach emerges as the most effective strategy, achieving the lowest computational cost while maintaining high accuracy.

physics.chem-ph↗

arXiv2024

Advancing Natural Orbital Functional Calculations Through Deep Learning-Inspired Techniques for Large-Scale Strongly Correlated Electron Systems

Natural orbital functional (NOF) theory offers a promising approach for studying strongly correlated systems at an affordable computational cost, with an accuracy comparable to highly demanding wavefunction-based methods. However, its widespread adoption in cases involving a large number of correlated electrons has been limited by the extensive iterations required for convergence. In this work, we present a disruptive approach that embeds the techniques used for optimization in deep learning within the NOF calculation, constituting a substantial advance in the scale of accessible systems. The revamped procedure is based on the adaptive momentum technique for orbital optimization, alternated with the optimization of the occupation numbers, significantly improving the computational feasibility of challenging calculations. This work represents a complete change in the size scale of the systems that can be reached using NOF theory. We demonstrate this with three examples that involve a large number of electrons: (i) the symmetric dissociation of a large hydrogen cluster, (ii) an analysis of occupancies distribution in fullerenes, and (iii) a study of the singlet-triplet energy gap in linear acenes. Notably, the hydrogen cluster calculation, featuring 1000 electrons, represents the largest NOF calculation performed to date and one of the largest strongly correlated electron calculations ever reported. This system, which serves as an ideal model for a strongly correlated Mott insulator, illustrates a metal-to-insulator transition where all electrons participate in the correlation phenomenon, offering insight in a unique challenge. We anticipate that this work will enable the practical application of NOFs to increasingly complex and intriguing systems, leveraging the method's inherent scalability and accuracy.

cond-mat.str-el↗

arXiv2024

Assessing the Global Natural Orbital Functional Approximation on Model Systems with Strong Correlation

In the past decade, natural orbital functional (NOF) approximations have emerged as prominent tools for characterizing electron correlation. Despite their effectiveness, these approaches, which rely on natural orbitals and their associated occupation numbers, often require hybridization with other methods to fully account for all correlation effects. Recently, a global NOF (GNOF) has been proposed [Phys. Rev. Lett. 127, 233001 (2021)] to comprehensively address both dynamic and static correlations. This study evaluates the performance of GNOF on strongly correlated model systems, including comparisons with highly accurate Full Configuration Interaction (FCI) calculations for hydrogen atom clusters in one, two, and three dimensions. Additionally, the investigation extends to a BeH2 reaction, involving the insertion of a beryllium atom into a hydrogen molecule along a C2v pathway. According to the results obtained using GNOF, consistent behavior is observed across various correlation regions, encompassing a range of occupation and orbital schemes. Furthermore, distinctive features are identified when varying the dimensionality of the system.

physics.chem-ph↗

arXiv2023

Advances in Approximate Natural Orbital Functionals: From Historical Perspectives to Contemporary Developments

This chapter provides a comprehensive review of fundamental concepts related to approximate natural orbital functionals (NOFs), emphasizing their significance in quantum chemistry and physics. Focusing on fermions, the discussion excludes considerations of finite temperature and systems with a variable number of particles. The theoretical foundation for approximate NOFs is laid out, with a particular emphasis on functional N-representability. Various two-index reconstructions for the two-particle reduced density matrix (2RDM) are introduced, accompanied by discussions on challenges. The analysis delves deeply into NOFs grounded in electron pairing, specifically focusing on PNOF5, PNOF7, and the Global NOF, a more versatile approach addressing both static and dynamic electron correlation components. The extension of NOFs to multiplets while conserving total spin is presented, and the availability of open-source implementations like DoNOF (http://github.com/DoNOF) and its associated programs is highlighted. A detailed overview of optimization procedures for single-point calculations is provided. Sections on geometry optimization and ab initio molecular dynamics, closely connected to the availability of analytical gradients in NOF theory, are presented. The chapter concludes with the extension of NOFs to both charged and excited states.

physics.chem-ph↗

arXiv2023

Excited states by coupling Piris natural orbital functionals with extended random phase approximation

In this work, we extend the Piris natural orbital functionals (PNOFs) to excited states by coupling their reconstructed second-order reduced density matrices with the extended random-phase approximation (ERPA). We have named the general implementation as PNOF-ERPA, and we refer to specific cases as PNOF-ERPA0, PNOF-ERPA1 and PNOF-ERPA2, according to how the excitation operator is built. The approaches have been tested in the first excited states of H2, HeH+, LiH and Li2, showing good results compared with the full configuration interaction (FCI) method. As expected, an increase in accuracy is observed when going from ERPA0 to ERPA1 and ERPA2. We have also studied the effect of electron correlation included by PNOF5, PNOF7 and the recently proposed global NOF (GNOF) on the predicted excited states. PNOF5 appears to be good and may even provide better results in very small systems, but including more electron correlation becomes important as the system size increases, where PNOF7 and GNOF provide better results. This effect can already be seen in the excitation energies of the neon atom, where GNOF provides more accurate values than PNOF5 and PNOF7. Overall, the extension of PNOF to excited states has been successful, making the PNOF-ERPA method promising for further applications.

physics.chem-ph↗

arXiv2023

Time evolution of natural orbitals in ab initio molecular dynamics

This work combines for the first time ab initio molecular dynamics (AIMD) within the Born-Oppenheimer approximation, with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The most prominent feature of GNOF-AIMD is the ability to display the real-time evolution of natural orbitals, providing detailed information on the time-dependent electronic structure of complex systems and processes, including reactive collisions. The quartet ground-state reaction N($^4$S) + H$_2$($^1\Sigma$) $\rightarrow$ NH($^3\Sigma$) + H($^2$S) is taken as validation test. Collision energy influences on integral cross sections for different initial ro-vibrational states of H$_2$ and rotational-state distributions of NH product are discussed, showing a good agreement with previous high-quality theoretical results.

physics.chem-ph↗

arXiv2022

Electron correlation in the Iron(II) Porphyrin by NOF approximations

The relative stability of the singlet, triplet, and quintet spin states of Iron(II) porphyrin (FeP) represents a challenging problem for electronic structure methods. While it is currently accepted that the ground state is a triplet, multiconfigurational wavefunction-based methods predict a quintet, and density functional approximations vary between triplet and quintet states, leading to a prediction that highly depends on the features of the method employed. The recently proposed Global Natural Orbital Functional (GNOF) aims to provide a balanced treatment between static and dynamic correlation, and together with the previous Piris Natural Orbital Functionals (PNOFs), allowed us to explore the importance of each type of correlation in the stability order of the states of FeP with a method that conserves the spin of the system. It is noteworthy that GNOF correlates all electrons in all available orbitals for a given basis set; in the case of the FeP with a double zeta basis set as used in this work; this means that GNOF can properly correlate 186 electrons in 465 orbitals, significantly increasing the sizes of systems amenable to multiconfigurational treatment. Results show that PNOF5, PNOF7s and PNOF7 predict the quintet to have a lower energy than the triplet state; however, the addition of dynamic correlation via second-order Moller-Plesset corrections (NOF-MP2) turns the triplet state to be lower than the quintet state, a prediction also reproduced by GNOF that incorporates much more dynamic correlation than its predecessors.

physics.chem-ph↗

arXiv2022

Outstanding Improvement in Removing the Delocalization Error by Global Natural Orbital Functional

This work assesses the performance of the recently proposed global natural orbital functional (GNOF) against the charge delocalization error. GNOF provides a good balance between static and dynamic electronic correlation leading to accurate total energies while preserving spin, even for systems with a highly multi-configurational character. Several analyses were applied to the functional, namely i) how the charge is distributed in super-systems of two fragments, ii) the stability of ionization potentials while increasing the system size, and iii) potential energy curves of a neutral and charged diatomic system. GNOF was found to practically eliminate the charge delocalization error in many of the studied systems or greatly improves the results obtained previously with PNOF7.

physics.chem-ph↗

arXiv2022

Benchmarking GNOF against FCI in challenging systems in one, two and three dimensions

This work assess the reliability of the recently proposed [Phys. Rev. Lett. 127, 233001, 2021] global natural orbital functional (GNOF) in the treatment of the strong electron correlation regime. We first use an H10 benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 2D ring, a 2D sheet, and a 3D close-packed pyramid. Second, we study two paradigmatic models for strongly correlated Mott insulators, namely a 1D H50 chain and a 4x4x4 3D H cube. We show that GNOF without hybridization to other electronic structure methods and free of tuned parameters succeeds in treating weak and strong correlation in a more balanced way than the functionals that have preceded it.

physics.chem-ph↗

arXiv2021

Global Natural Orbital Functional: Towards the Complete Description of the Electron Correlation

The current work presents a natural orbital functional (NOF) for electronic systems with any spin value independent of the external potential being considered, that is, a global NOF (GNOF). It is based on a new two-index reconstruction of the two-particle reduced density matrix for spin multiplets. The emergent functional describes the complete intrapair electron correlation, and the correlation between orbitals that make up both the pairs and the individual electrons. The interorbital correlation is composed of static and dynamic terms. The concept of dynamic part of the occupation numbers is introduced. To evaluate the accuracy achieved with GNOF, calculation of a variety of properties is presented. They include the total energies and energy differences between the ground state and the lowest-lying excited state with different spin of atoms from H to Ne, ionization potentials of the first-row transition-metal atoms (Sc-Zn), and the total energies of a selected set of 55 molecular systems in different spin states. GNOF is also applied to the homolytic dissociation of selected diatomic molecules in different spin states and to the rotation barrier of ethylene, both paradigmatic cases of systems with significant multi-configurational character. The values obtained agree with those reported at high level of theory and experimental data.

physics.chem-ph↗

arXiv2020

Resolution of the identity approximation applied to PNOF correlation calculations

In this work, the required algebra to employ the resolution of the identity approximation within Piris Natural Orbital Functional (PNOF) is developed, leading to an implementation named DoNOF-RI. The arithmetic scaling is reduced from fifth-order to fourth-order, and the memory scaling is reduced from fourth-order to third-order, allowing significant computational time savings. After the DoNOF-RI calculation has fully converged, a restart with four-center electron repulsion integrals can be performed to remove the effect of the auxiliary basis set incompleteness, quickly converging to the exact result. The proposed approach has been tested on cycloalkanes and other molecules of general interest to study the numerical results as well as the speed-ups achieved by PNOF7-RI when compared with PNOF7.

physics.chem-ph↗

arXiv2020

Chemical Reactivity Studies by the Natural-Orbital-Functional 2nd-Order-Moller-Plesset (NOF-MP2) method. Water Dehydrogenation by the Scandium Cation

The reliability of the recently proposed natural orbital functional supplemented with second-order M{\o}ller-Plesset calculations, (NOF-MP2), has been assessed for the mechanistic studies of elementary reactions of transition metal compounds by investigating the dehydrogenation of water by the scandium cation. Both high- and low-spin state potential energy surfaces have been searched thoroughly. Special attention has been paid to the assessment of the capability of the NOF-MP2 method to describe the strong, both static and dynamic, electron correlation effects on the reactivity of Sc+(3D,1D) with water. In agreement with experimental observations, our calculations correctly predict that the only exothermic products are the lowest-lying ScO+(1\Sigma) and H2(1\Sigma_g+) species. Nevertheless, an in-depth analysis of the reaction paths leading to several additional products was carried out, including the characterization of various minima and several key transition states. Our results have been compared with the highly accurate multiconfigurational supplemented with quasi degenerate perturbation theory, MCQDPT, wavefunction-type calculations, and with the available experimental data. It is observed that NOF-MP2 is able to give a satisfactorily quantitative agreement, with a performance on par with that of the MCQDPT method.

physics.chem-ph↗

arXiv2020

Analytic gradients for spin multiplets in natural orbital functional theory

Analytic energy gradients with respect to nuclear motion are derived for non-singlet compounds in the natural orbital functional theory. We exploit the formulation for multiplets in order to obtain a simple formula valid for any many-electron system in its ground mixed state with a total spin S and all possible spin projection Sz values. We demonstrate that the analytic gradients can be obtained without resorting to linear response theory or involving iterative procedures. It is required a single evaluation, so integral derivatives can be computed on-the-fly along the calculation and thus improve the effectiveness of screening by the Schwarz inequality. Results for small and medium size molecules with many spin multiplicities are shown. Our results are compared with experimental data and accurate theoretical equilibrium geometries.

physics.chem-ph↗

arXiv2020

DoNOF: an open-source implementation of natural-orbital-functional-based methods for quantum chemistry

The natural orbital functional theory (NOFT) has emerged as an alternative formalism to both density functional (DF) and wavefunction methods. In NOFT, the electronic structure is described in terms of the natural orbitals (NOs) and their occupation numbers (ONs). The approximate NOFs have proven to be more accurate than those of the density for systems with a significant multiconfigurational character, on one side, and scale better with the number of basis functions than correlated wavefunction methods, on the other side. A challenging task in NOFT is to efficiently perform orbital optimization. In this article we present DoNOF, our open source implementation based on diagonalizations that allows to obtain the resulting orbitals automatically orthogonal. The one-particle reduced-density matrix (1RDM) of the ensemble of pure-spin states provides the proper description of spin multiplets. The capabilities of the code are tested on the water molecule, namely, geometry optimization, natural and canonical representations of molecular orbitals, ionization potential, and electric moments. In DoNOF, the electron-pair-based NOFs developed in our group PNOF5, PNOF7 and PNOF7s are implemented. These JKL-only NOFs take into account most non-dynamic effects plus intrapair-dynamic electron correlation, but lack a significant part of interpair-dynamic correlation. Correlation corrections are estimated by the single-reference NOF-MP2 method that simultaneously calculates static and dynamic electron correlations taking as a reference the Slater determinant formed with the NOs of a previous PNOF calculation. The NOF-MP2 method is used to analyze the potential energy surface (PES) and the binding energy for the symmetric dissociation of the water molecule, and compare it with accurate wavefunction-based methods.

physics.comp-ph↗

arXiv2019

An efficient method for strongly correlated electrons in one dimension

The one-particle reduced density matrix functional theory in its natural orbital functional (NOF) version is used to study strongly correlated electrons. We show the ability of the Piris NOF 7 (PNOF7) to describe non-dynamic correlation effects in one-dimensional (1D) systems. An extensive study of 1D systems that includes Hydrogen (H) chains and the 1D Hubbard model with periodic boundary conditions is provided. Different filling situations and large sizes with up to 122 electrons are considered. Compared to quasi-exact results, PNOF7 is accurate in different correlation regimes for the 1D Hubbard model even away from the half-filling, and maintains its accuracy when the system size increases. The symmetric and asymmetric dissociations of the linear H chain composed of 50 atoms are described to remark the importance of long-range interactions in presence of strong correlation effects. Our results compare remarkably well with those obtained at the density-matrix renormalization group level of theory.

cond-mat.str-el↗

arXiv2019

An efficient method for strongly correlated electrons in two-dimensions

This work deals with the problem of strongly correlated electrons in two-dimensions (2D). We give a reduced density matrix (RDM) based tool through which the ground-state energy is given as a functional of the natural orbitals and their occupation numbers. Specifically, the Piris Natural Orbital Functional 7 (PNOF7) is used for studying the 2D Hubbard model and hydrogen square lattices. The singlet ground-state is studied, as well as the doublet mixed quantum state obtained by extracting an electron from the system. Our method satisfies two-index necessary N-representability conditions of the two-particle RDM (2RDM) and guarantees the conservation of the total spin. We show the ability of PNOF7 to describe strong correlation effects in these 2D systems by comparing our results with exact diagonalization, density matrix renormalization group (DMRG), and auxiliary-field quantum Monte Carlo calculations. PNOF7 overcomes variational 2RDM methods with two- and three-index positivity N-representability conditions, reducing computational cost to mean-field scaling. Consistent results are obtained for small and large systems up to 144 electrons, weak and strong correlation regimes, and many filling situations. Unlike other methods, there is no dependence on dimensionality in the results obtained with PNOF7, and no particular difficulties have been observed to converge PNOF7 away from half-filling. Smooth double occupancy of sites is obtained regardless of the filling. Symmetric dissociation of 2D hydrogen lattices shows that long-range nondynamic correlation drammatically affects electron detachment energies. PNOF7 compares well with DMRG along the dissociation curve.

cond-mat.str-el↗