arXiv subjects

Eloy Ramos-Cordoba

Publications and source records attributed to Eloy Ramos-Cordoba.

8 recordsLinked to original sources

arXiv2026

Numerical integration of intracule pair densities with optimized multicenter grids

Intracule pair densities provide insight into electron correlation, but their routine analysis in extended systems is limited by the cost of numerical integration and the restriction of analytical methods to Gaussian basis functions. We present an efficient multicenter integration scheme for intracule densities and their moments. By adapting the topological fuzzy Voronoi cell formalism, we partition intracule space around interatomic displacement vectors, concentrating quadrature points near secondary density maxima that standard single-center grids poorly resolve. Benchmarks on linear alkanes show improved convergence with increasing molecular size, achieving relative errors below 0.02% in electron-electron repulsion energies with fewer quadrature points than single-center methods. The partitioning also enables the decomposition of global two-electron properties into spatial contributions associated with short- and long-range electron-pair separations. Coupling the multicenter grid with kernel density estimation reconstructs smooth radial intracule distributions at large interelectronic distances without the dense angular grids required by conventional surface integration. Validation on the S22 dataset supports the reliability of the method across diverse molecular systems. These developments facilitate intracule analysis in polyatomic systems and the investigation of electron correlation and dispersion interactions.

physics.chem-ph↗

arXiv2022

Range separation of the Coulomb hole

A range-separation of the Coulomb hole into two components, one of them being predominant at long interelectronic separations (hcI ) and the other at short distances (hcII ), is exhaustively analyzed throughout various examples that put forward the most relevant features of this approach and how they can be used to develop efficient ways to capture electron correlation. We show that hcI , which only depends on the first-order reduced density matrix, can be used to identify molecules with a predominant nondynamic correlation regime and differentiate between two types of nondynamic correlation, types A and B. Through the asymptotic properties of the hole components, we explain how hcI can retrieve the long-range part of electron correlation. We perform an exhaustive analysis of the hydrogen molecule in a minimal basis set, dissecting the hole contributions into spin components. We also analyze the simplest molecule presenting a dispersion interaction and how hcII helps identify it. The study of several atoms in different spin states reveals that the Coulomb hole components distinguish correlation regimes that are not apparent from the entire hole. The results of this work hold the promise to aid in developing new electronic structure methods that efficiently capture electron correlation.

physics.chem-ph↗

arXiv2019

The Coulomb Hole of the Ne atom

We analyze the Coulomb hole of Ne from highly-accurate CISD wave functions obtained from optimized even-tempered basis sets. Using a two-fold extrapolation procedure we obtain highly accurate results that recover 97\% of the correlation energy. We confirm the existence of a shoulder in the short-range region of the Coulomb hole of the Ne atom, which is due to an internal reorganization of the $K$-shell caused by electron correlation of the core electrons. The feature is very sensitive to the quality of the basis set in the core region and it is not exclusive to Ne, being also present in most of second-row atoms, thus confirming that it is due to $K$-shell correlation effects.

physics.chem-ph↗

arXiv2019

Singling Out Dynamic and Nondynamic Correlation

The correlation part of the pair density is separated into two components, one of them being predominant at short electronic ranges and the other at long ranges. The analysis of the intracular part of these components permits to classify molecular systems according to the prevailing correlation: dynamic or nondynamic. The study of the long-range asymptotics reveals the key component of the pair density that is responsible for the description of London dispersion forces and a universal decay with the interelectronic distance. The natural range-separation, the identification of the dispersion forces, and the kind of predominant correlation type that arise from this analysis are expected to be important assets in the development of new electronic structure methods in wave function, density, and reduced density-matrix functional theories.

physics.chem-ph↗

arXiv2019

Local descriptors of dynamic and nondynamic correlation

Quantitatively accurate electronic structure calculations rely on the proper description of electron correlation. A judicious choice of the approximate quantum chemistry method depends upon the importance of dynamic and nondynamic correlation, which is usually assessed by scalar measures. Existing measures of electron correlation do not consider separately the regions of the Cartesian space where dynamic or nondynamic correlation are most important. We introduce real-space descriptors of dynamic and nondynamic electron correlation that admit orbital decomposition. Integration of the local descriptors yields global numbers that can be used to quantify dynamic and nondynamic correlation. Illustrative examples over different chemical systems with varying electron correlation regimes are used to demonstrate the capabilities of the local descriptors. Since the expressions only require orbitals and occupation numbers, they can be readily applied in the context of local correlation methods, hybrid methods, density matrix functional theory and fractional-occupancy density functional theory.

physics.chem-ph↗

arXiv2016

Separation of Dynamic and Nondynamic Correlation

The account of electron correlation and its efficient separation into dynamic and nondynamic parts plays a key role in the development of computational methods. In this paper we suggest a physically-sound matrix formulation to split electron correlation into dynamic and nondynamic parts using the two-particle cumulant matrix and a measure of the deviation from idempotency of the first-order density matrix. These matrices are applied to a two-electron model, giving rise to a simplified electron correlation index that ($i$) depends only on natural orbitals and their occupancies, ($ii$) can be straightforwardly decomposed into orbital contributions and ($iii$) splits into dynamic and nondynamic correlation parts that ($iv$) admit a local version. These expressions are shown to account for dynamic and nondynamic correlation in a variety of systems containing different electron correlation regimes, thus providing the first separation of dynamic and nondynamic correlation using solely natural orbital occupancies.

physics.chem-ph↗

arXiv2015

Bonding Description of the Harpoon Mechanism

The lowest-lying states of LiH have been widely used to develop and calibrate many different methods in quantum mechanics. In this paper we show that the electron-transfer processes occurring in these two states are a difficult test for chemical bonding descriptors and can be used to assess new bonding descriptors on its ability to recognize the harpoon mechanism. To this aim, we study the bond formation mechanism in a series of diatomic molecules. In all studied electron-reorganization mechanisms, the maximal electron-transfer variation point along the bond formation path occurs when about half electron has been transferred from one atom to another. If the process takes places through a harpoon mechanism, this point of the reaction path coincides with the avoided crossing. The electron sharing indices and one-dimensional plots of the electron localization function and the Laplacian of the electron density along the molecular axis can be used to monitor the bond formation in diatomics and provide a distinction between the harpoon mechanism and a regular electron-reorganization process.

physics.chem-ph↗

arXiv2015

H$_4$: A Challenging System For Natural Orbital Functional Approximations

The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of $D_{2h}$ to $D_{4h}$ symmetry in H$_4$ molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurge of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H$_4$ $D_{4h}/D_{2h}$ potential energy surface. Thus far, the wrongful behavior of single-reference methods at the $D_{2h}-D_{4h}$ transition of H$_4$ has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually $\textit{interpair}$ nondynamic correlation is the key to a cusp-free qualitatively correct description of H$_4$ PES. By introducing $\textit{interpair}$ nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.

physics.chem-ph↗