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.

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 assesed 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.

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the “natural selection” process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross‐validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the “standard model” of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

We introduce a simple and general scheme to derive from wavefuntion analysis the most appropriate atomic/fragment electron configurations in a molecular system, from which oxidation states can be inferred. The method can be applied for any level of theory for which the first-order density matrix is available, and unlike others, it is not restricted to transition metal complexes. The method relies on the so-called spin-resolved effective atomic orbitals which for the present purpose is extended here to deal with molecular fragments/ligands. We describe in detail the most important points of the new scheme, in particular the hierarchical fragment approach devised for practical applications. A number of transition metal complexes with different formal oxidation states and spin states and a set of organic and inorganic compounds are provided as illustrative examples of the new scheme. Challenging systems such as transition state structures are also tackled on equal footing.

Two of the most popular rules to characterize the aromaticity of molecules are those due to Hückel and Baird, which govern the aromaticity of singlet and triplet states. In this work, we study how these rules fade away as the ring structure increases and an optimal overlap between p orbitals is no longer possible due to geometrical restrictions. To this end, we study the lowest-lying singlet and triplet states of neutral annulenes with an even number of carbon atoms between four and eighteen. First of all, we analyze these rules from the Hückel molecular orbital method and, afterwards, we perform a geometry optimization of the annulenes with several density functional approximations in order to analyze the effect that the distortions from planarity produce on the aromaticity of annulenes. Finally, we analyze the performance of three density functional approximations that employ different percentages of Hartree-Fock exchange (B3LYP, CAM-B3LYP and M06-2X) and Hartree-Fock. Our results reveal that functionals with a low percentage of Hartree-Fock exchange at long ranges suffer from severe delocalization errors that result in wrong geometrical structures and the overestimation of the aromatic character of annulenes.

In this work, we demonstrate that there is a continuum of different formulations for the decomposition of ⟨Ŝ(2)⟩ that fulfills all physical requirements imposed to date. We introduce a new criterion based upon the behavior of single-electron systems to fix the value of the parameter defining that continuum, and thus we put forward a new general formula applicable for both single-determinant and correlated wave functions. The numerical implementation has been carried out in the three-dimensional physical space for several atomic definitions. A series of representative closed-shell and open-shell systems have been used to illustrate the performance of this new decomposition scheme against other existing approaches. Unlike other decompositions of ⟨Ŝ(2)⟩, the new scheme provides very small local-spin values for genuine diamagnetic molecules treated with correlated wave functions, in conformity with the physical expectations.

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen

The absolutely localized molecular orbital (ALMO) model is a fully variational approach which permits polarization of molecules interacting in a cluster while prohibiting charge-transfer (or dative interactions) between individual molecules. The ALMO model can be applied within any density functional theory calculation--the B3LYP functional is employed in this work. ALMO DFT calculations of observables such as optimized geometry, vibrational frequencies and their intensities, and vertical detachment energies are performed for the water dimer, the chloride-water complex and the cyanide-water complex. The vibrational spectra are obtained both within the harmonic approximation and by quasiclassical trajectory simulations. By comparing these ALMO DFT calculations with full DFT calculations using precisely the same functional and basis, the role of charge-transfer on observables in these model hydrogen bonding systems can be assessed. The results can be further interpreted using ALMO-based energy decomposition analysis, which help to reveal the origin of sensitivity or insensitivity of observables to dative interactions. Analysis of the results also suggests that the B3LYP functional, while qualitatively adequate, appears to somewhat overestimate charge-transfer effects.