Dispersion interactions within the Piris natural orbital functional theory: The helium dimer

Exploring the potential of natural orbital functionals

In recent years, Natural Orbital Functional (NOF) theory has gained increasing significance in quantum chemistry, successfully addressing one of the field's most challenging problems: providing an accurate and balanced description of systems with strong electronic correlation. The quest for NOFs that strike the delicate balance between computational tractability and predictive accuracy represents a holy grail for researchers. Today, NOFs provide an alternative formalism to both density functional and wavefunction-based methods, with their appeal rooted in a wonderfully simple conceptual framework. This perspective outlines the basic concepts, strengths and weaknesses, and current status of NOFs, while offering suggestions for their future development.

Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain

The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of the Kohn-Sham scheme and the complexity of the pure N-representability conditions are still impeding its wild utilization. Fortunately, ensemble N-representability conditions derived in the natural orbital basis are known and trivial such that almost every functional of the 1-RDM is actually natural orbital functional, which does not perform well for all the correlation regimes. In this work, we propose a variational minimization scheme in the ensemble N-representable domain that is not restricted to the natural orbital representation of the 1-RDM. We show that splitting the minimization into the diagonal and off-diagonal parts of the 1-RDM can open the way toward the development of functionals of the orbital occupations, which remains a challenge for the generalization of site-occupation functional theory in chemistry. Our approach is tested on the uniform Hubbard model using the Müller and the Töws-Pastor functionals, as well as on the dihydrogen molecule using the Müller functional.

Mechanistic Insights Into the Rhodium-Catalyzed C-H Alkenylation/Directing Group Migration and [3+2] Annulation: A DFT Study

The mechanism of the rhodium-catalyzed C-H alkenylation/directing group migration and [3+2] annulation of N-aminocarbonylindoles with 1,3-diynes has been investigated with DFT calculations. On the basis of mechanistic studies, we mainly focus on the regioselectivity of 1,3-diyne inserting into the Rh-C bond and the N-aminocarbonyl directing group migration involved in the reactions. Our theoretical study uncovers that the directing group migration undergoes a stepwise β-N elimination and isocyanate reinsertion process. As studied in this work, this finding is also applicable to other relevant reactions. Additionally, the role of Na⁺ versus Cs⁺ involved in the [3+2] cyclization reaction is also probed.

del Campo J. Charge delocalization error in Piris Natural Orbital Functionals

Piris Natural Orbital Functionals (PNOF) have been recognized as a low-scaling alternative to study strong correlated systems. In this work, we address the performance of the fifth functional (PNOF5) and the seventh functional (PNOF7) to deal with another common problem, the charge delocalization error. The effects of this problem can be observed in charged systems of repeated well-separated fragments, where the energy should be the sum of the charged and neutral fragments, regardless of how the charge is distributed. In practice, an energetic overstabilization of fractional charged fragments leads to a preference for having the charge delocalized throughout the system. To establish the performance of PNOF functionals regarding charge delocalization error, charged chains of helium atoms and the W4-17-MR set molecules were used as base fragments and their energy, charge distribution and correlation regime were studied. It was found that PNOF5 prefers localized charge distributions, while PNOF7 improves the treatment of interpair static correlation and tends to the correct energetic limit for several cases, although a preference for delocalized charge distributions may arise in highly strong correlation regimes. Overall, it is concluded that PNOF functionals can simultaneously deal with static correlation and charge delocalization errors, resulting in a promising choice to study charge-related problems.

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 the 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.

Comprehensive benchmarking of density matrix functional approximations

The energy usually serves as a yardstick in assessing the performance of approximate methods in computational chemistry. After all, these methods are mostly used for the calculation of the electronic energy of chemical systems. However, computational methods should be also aimed at reproducing other properties, such strategy leading to more robust approximations with a wider range of applicability. In this study, we suggest a battery of ten tests with the aim to analyze density matrix functional approximations (DMFAs), including several properties that the exact functional should satisfy. The tests are performed on a model system with varying electron correlation, carrying a very small computational effort. Our results not only put forward a complete and exhaustive benchmark test for DMFAs, currently lacking, but also reveal serious deficiencies of existing approximations that lead to important clues in the construction of more robust DMFAs.

A natural orbital analysis of the long range behavior of chemical bonding and van der Waals interaction in singlet H2: the issue of zero natural orbital occupation numbers

This paper gives a natural orbital (NO) based analysis of the van der Waals interaction in (singlet) H2 at long distance. The van der Waals interaction, even if not leading to a distinct van der Waals well, affects the shape of the interaction potential in the van der Waals distance range of 5-9 bohrs and can be clearly distinguished from chemical bonding effects. In the NO basis the van der Waals interaction can be quantitatively covered with, apart from the ground state configurations (1σ(g))(2) and (1σ(u))(2), just the 4 configurations (2σ(g))(2) and (2σ(u))(2), and (1π(u))(2) and (1π(g))(2). The physics of the dispersion interaction requires and explains the peculiar relatively large positive CI coefficients of the doubly excited electron configurations (2σ(u))(2) and (1π(g))(2) (the occupancy amplitudes of the 2σ(u) and 1π(gx, y) NOs) in the distance range 5-9 bohrs, which have been observed before by Cioslowski and Pernal [Chem. Phys. Lett. 430, 188 (2006)]. We show that such positive occupancy amplitudes do not necessarily lead to the existence of zero occupation numbers at some H-H distances.

Computational study of Be2 using Piris natural orbital functionals

The third (PNOF3), fourth (PNOF4) and fifth (PNOF5) versions of the Piris natural orbital functional were used to characterize the beryllium dimer. The results obtained were compared to those gained afforded by CASSCF and CASPT2 as well as experimental data. The equilibrium distances (R e), dissociation energies (D e), effective bond orders (EBOs), and rovibrational levels were calculated. PNOF3, PNOF4, and CASPT2 predicted a bonded Be2 molecule, while PNOF5 and CASSCF did not, which demonstrates the importance of the dynamical electron correlation. We observed that PNOF3 yields the most accurate equilibrium distances, while PNOF4 most accurately calculates the rovibrational levels. However, both of these functionals overestimate dissociation energies. Both PNOF3 and PNOF4 predict EBOs that agree with that obtained using CASPT2.