Unveiling the quantum secrets of triel metal triangles: a tale of stability, aromaticity, and relativistic effects

Low lying electronic states of Al3-, Ga3-, In3-, and Tl3- have been characterized using high level multiconfigurational quasi degenerate perturbation theory on the multiconfigurational self-consistent field. Among these species, the singlet states emerge as the predominant energy minima, displaying remarkable stability. However, within the Tl3- series, our investigation leads to the identification of the high-spin , as the most stable spin state, a result corroborated by previous experimental detection via photoelectron spectroscopy. Similarly, we have also identified the singlet state of In3- as the signal detected previously experimentally. By applying Mandado's rules and an array of aromaticity indicators, it is conclusively demonstrated that both the singlet and quintet states exhibit multiple-fold aromaticity, while the triplets exhibit conflicting aromaticity. Furthermore, this investigation highlights the significant impact of relativistic effects, as they enhance the stability of the state relative to its singlet counterpart. These findings shed new light on the electronic structures and properties of these ions, offering valuable insights into their chemical behavior and potential applications.

Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

Understanding Aromaticity in [5]Helicene-Bridged Cyclophanes: A Comprehensive Study

This study explores the aromaticity of doubly [5]helicene-bridged (1,4)cyclophane and triply [5]helicene-bridged (1,3,5)cyclophane via calculations of the magnetic response and of electronic aromaticity indices. The primary objective is to assess the π-electron delocalization to determine whether they sustain global ring currents associated with π aromaticity. The molecules show local ring currents in the presence of an external magnetic field. The ring currents flow diatropically in the stacked six-membered rings and in the helicene arms. However, these π currents are not interconnected due to the discontinuity of the π delocalization at the C-C single bonds connecting the central six-membered rings to the helicene arms. Electronic indices suggest that the helicene-arm systems have significantly smaller electron delocalization than benzene. The reduction in the delocalization does not compromise their ability to exhibit ring currents in the presence of an external magnetic field. The analysis provides further evidence that the magnetic criteria yield a different degree of aromaticity for the helicene arms than obtained in the calculation of the electronic aromaticity indices. However, both approaches confirm that the studied molecules are not globally aromatic.

All-Purpose Measure of Electron Correlation for Multireference Diagnostics

We present an analytical relationship between two natural orbital occupancy-based indices, I N D ¯ and INDmax, and two established electron correlation metrics: the leading term of a configuration interaction expansion, c0, and the D2 diagnostic. Numerical validation revealed that I N D ¯ and INDmax can effectively substitute for c0 and D2, respectively. These indices offer three distinct advantages: (i) they are universally applicable across all electronic structure methods, (ii) their interpretation is more intuitive, and (iii) they can be readily incorporated into the development of hybrid electronic structure methods. Additionally, we draw a distinction between correlation measures and correlation diagnostics, establishing MP2 and CCSD numerical thresholds for INDmax, which are to be used as a multireference diagnostic. Our findings further demonstrate that establishing thresholds for other electronic structure methods can be easily accomplished using small data sets.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

Electric-field induced second harmonic generation responses of push-pull polyenic dyes: experimental and theoretical characterizations

The second-order nonlinear optical properties of four series of amphiphilic cationic chromophores involving different push-pull extremities and increasingly large polyenic bridges have been investigated both experimentally, by means of electric field induced second harmonic (EFISH) generation, and theoretically, using a computational approach combining classical molecular dynamics (MD) and quantum chemical (QM) calculations. This theoretical methodology allows to describe the effects of structural fluctuations on the EFISH properties of the complexes formed by the dye and its iodine counterion, and provides a rationale to EFISH measurements. The good agreement between experimental and theoretical results proves that this MD + QM scheme constitutes a useful tool for a rational, computer-aided, design of SHG dyes.

Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.

Quest for the Most Aromatic Pathway in Charged Expanded Porphyrins

Despite the central role of aromaticity in the chemistry of expanded porphyrins, the evaluation of aromaticity remains difficult for these extended macrocycles. The presence of multiple conjugation pathways and different planar and nonplanar π-conjugation topologies makes the quantification of global and local aromaticity even more challenging. In neutral expanded porphyrins, the predominance of the aromatic conjugation pathway passing through the imine-type nitrogens and circumventing the amino NH groups is established. However, for charged macrocycles, the question about the main conjugation circuit remains open. Accordingly, different conjugation pathways in a set of neutral, anionic, and cationic expanded porphyrins were investigated by means of several aromaticity indices rooted in the structural, magnetic, and electronic criteria. Overall, our results reveal the predominance of the conjugation pathway that passes through all nitrogen atoms to describe the aromaticity of deprotonated expanded porphyrins, while the outer pathway through the perimeter carbon atoms becomes the most aromatic in protonated macrocycles. In nonplanar and charged macrocycles, a discrepancy between electronic and magnetic descriptors is observed. Nevertheless, our work demonstrates AV_min remains the best tool to determine the main conjugation pathway of expanded porphyrins.

Three-centre electron sharing indices (3c-ESIs) as a tool to differentiate among (an)agostic interactions and hydrogen bonds in transition metal complexes

The agostic bond plays an important role in chemistry, not only in transition metal chemistry but also in main group chemistry. In some complexes with M⋯H-X (X = C, N) interactions, differentiation among agostic, anagostic, and hydrogen bonds is challenging. Here we propose the use of three-centre electron sharing indices to classify M⋯H-X (X = C, N) interactions.

How Reliable Are Modern Density Functional Approximations to Simulate Vibrational Spectroscopies?

We show that properties of molecules with low-frequency modes calculated with density functional approximations (DFAs) suffer from spurious oscillations along the nuclear displacement coordinate due to numerical integration errors. Occasionally, the problem can be alleviated using extensive integration grids that compromise the favorable cost-accuracy ratio of DFAs. Since spurious oscillations are difficult to predict or identify, DFAs are exposed to severe performance errors in IR and Raman intensities and frequencies or vibrational contributions to any molecular property. Using Fourier spectral analysis and digital signal processing techniques, we identify and quantify the error due to these oscillations for 45 widely used DFAs. LC-BLYP and BH&H are revealed as the only functionals showing robustness against the spurious oscillations of various energy, dipole moment, and polarizability derivatives with respect to a nuclear displacement coordinate. Given the ubiquitous nature of molecules with low-frequency modes, we warrant caution in using modern DFAs to simulate vibrational spectroscopies.

Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths Based on Popular Density Functional Approximations

We present a benchmark study of density functional approximation (DFA) performances in predicting the two-photon-absorption strengths in π-conjugated molecules containing electron-donating/-accepting moieties. A set of 48 organic molecules is chosen for this purpose, for which the two-photon-absorption (2PA) parameters are evaluated using different DFAs, including BLYP, PBE, B3LYP, PBE0, CAM-B3LYP, LC-BLYP, and optimally tuned LC-BLYP. Minnesota functionals and ωB97X-D are also used, applying the two-state approximation, for a subset of molecules. The efficient resolution-of-identity implementation of the coupled-cluster CC2 model (RI-CC2) is used as a reference for the assessment of the DFAs. Two-state models within the framework of both DFAs and RI-CC2 are used to gain a deeper insight into the performance of different DFAs. Our results give a clear picture of the performance of the density functionals in describing the two-photon activity in dipolar π-conjugated systems. The results show that global hybrids are best suited to reproduce the absolute values of 2PA strengths of donor–acceptor molecules. The range-separated functionals CAM-B3LYP and optimally tuned LC-BLYP, however, show the highest linear correlations with the reference RI-CC2 results. Hence, we recommend the latter DFAs for structure–property studies across large series of dipolar compounds.

Excited State Dynamics and Conjugation Effects of the Photoisomerization Reactions of Dihydroazulene

Herein, we present an investigation of the excited state dynamics of the Dihydroazulene photoswitch and its photoinduced reaction to Vinylheptafulvene. The focus is on how the introduction of a benzannulated...

How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring*

Large conjugated rings with persistent currents are novel promising structures in molecular-scale electronics. A six-porphyrin nanoring structure that allegedly sustained an aromatic ring current involving 78π electrons was recently synthesized. We provide here compelling evidence that this molecule is not aromatic, contrary to what was inferred from the analysis of 1 H-NMR data and computational calculations that suffer from large delocalization errors. The main reason behind the absence of an aromatic ring current in these nanorings is the low delocalization in the transition from the porphyrins to the bridging butadiyne linkers, which disrupts the overall conjugated circuit. These results highlight the importance of choosing a suitable computational method to study large conjugated molecules and the appropriate aromaticity descriptors to identify the part of the molecule responsible for the loss of aromaticity.

Impact of van der Waals interactions on the structural and nonlinear optical properties of azobenzene switches

The geometrical structures, relative Z-E energies, and second-order nonlinear responses of a collection of azobenzene molecules symmetrically substituted in the meta-position with functional groups of different bulkiness are investigated using various ab initio and density functional approximations. We show that RI-MP2 and RI-CC2 approximations provide very similar geometries and relative energies and evidence that London dispersion interactions existing between bulky meta-substituents stabilize the Z conformer. The ωB97X-D exchange-correlation functional provides an accurate description of these effects and gives a good account of the nonlinear optical response of the molecules. We show that density functional approximations should include no less than 50% of Hartree-Fock exchange to provide accurate hyperpolarizabilities. A property-structure analysis of the azobenzene derivatives reveals that the main contribution to the first hyperpolarizability comes from the azo bond, but phenyl meso-substituents can enhance it.

How Many Electrons Does a Molecular Electride Hold?

Electrides are very peculiar ionic compounds where electrons occupy the anionic positions. In a crystal lattice, these isolated electrons often form channels or surfaces, furnishing electrides with many traits with promising technological applications. Despite their huge potential, thus far, only a few stable electrides have been produced because of the intricate synthesis they entail. Due to the difficulty in assessing the presence of isolated electrons, the characterization of electrides also poses some serious challenges. In fact, their properties are expected to depend on the arrangement of these electrons in the molecule. Among the criteria that we can use to characterize electrides, the presence of a non-nuclear attractor (NNA) of the electron density is both the rarest and the most salient feature. Therefore, a correct description of the NNA is crucial to determine the properties of electrides. In this paper, we analyze the NNA and the surrounding region of nine molecular electrides to determine the number of isolated electrons held in the electride. We have seen that the correct description of a molecular electride hinges on the electronic structure method employed for the analyses. In particular, one should employ a basis set with sufficient flexibility to describe the region close to the NNA and a density functional approximation that does not suffer from large delocalization errors. Finally, we have classified these nine molecular electrides according to the most likely number of electrons that we can find in the NNA. We believe this classification highlights the strength of the electride character and will prove useful in designing new electrides.

Performance of DFT functionals for calculating the second-order nonlinear optical properties of dipolar merocyanines

Evolution of the static HRS hyperpolarizability of a tricyanopropylidene-based merocyanine dye with the length of the polyenic bridge, as calculated using various ab initio and DFT approximations.

All-metal σ-antiaromaticity in dimeric cluster anion {[CuGe9Mes]2}4

In this work, we report a dimeric cluster anion, {[CuGe9Mes]2}4-, which was isolated as the [K(2,2,2-crypt)]+ salt and characterized by using single-crystal X-ray diffraction and ESI mass spectroscopy. The title cluster represents the first locally σ-antiaromatic compound in the solid state, as well as the first heteroatomic antiaromatic compound.

A new tuned range-separated density functional for the accurate calculation of second hyperpolarizabilities

Among the nine functionals benchmarked, the most accurate γ are obtained by Tα-LC-BLYP, reducing about half the errors of LC-BLYP.

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.

Nine questions on energy decomposition analysis

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.

Can Density Functional Theory Be Trusted for High-Order Electric Properties? The Case of Hydrogen-Bonded Complexes

This work reports on an extensive assessment of the performance of a wide palette of density functional approximations in predicting the (high-order) electric properties of hydrogen-bonded complexes. To this end, we compute the electronic and vibrational contributions to the electric polarizability and the first and second hyperpolarizabilities, using the CCSD(T)/aug-cc-pVTZ level of theory as reference. For all the studied properties, the average absolute errors below 20% can only be obtained using the CAM-B3LYP functional, while LC-BLYP and MN15 are shown to be only slightly less accurate (average absolute errors not exceeding 30%). Among Minnesota density functionals, i.e., M06, M06-2X, and MN15, we only recommend the latter one, which quite accurately predicts the electronic and vibrational (hyper)polarizabilities. We also analyze the optimal tuning of the range-separation parameter μ for the LC-BLYP functional, finding that this approach does not bring any systematic improvement in the predictions of electronic and vibrational (hyper)polarizabilities and the accuracy of computed properties is largely system-dependent. Finally, we report huge errors in predicting the vibrational second hyperpolarizability by ωB97X, M06, and M06-2X functionals. Based on the explicit evaluation of anharmonic terms contributing to the second hyperpolarizability, this failure is traced down to a poor determination of third- and fourth-order energy derivatives with respect to normal modes. These results reveal serious flaws of some density functional approximations and suggest caution in selecting the appropriate functional to calculate not only electronic and vibrational (hyper)polarizabilities but also other molecular properties that contain vibrational anharmonic contributions.

Cover Feature: The Coulomb Hole of the Ne Atom (ChemistryOpen 4/2019)

The Cover Feature displays the profile of the Coulomb hole of Ne surrounded by a cloud of neon atoms. Our quantum chemical calculations show that correlation of the core electrons manifests itself as a shoulder in the profile of the Coulomb hole at short interelectronic distances. This feature is very sensitive to the quality of the basis set in the core region. For the rest of second‐row atoms, except Li, a shoulder or a maximum is also obtained at short electron‐electron distances, which is also due to the correlation of the electrons in the K shell. More information can be found in the Full Paper by M. Rodríguez‐Mayorga et al. on page 411 in Issue 4, 2019 (DOI: 10.1002/open.201800235).

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.

Partition of optical properties into orbital contributions

A new tool to analyze the response property through the partition of nonlinear optical properties in terms of orbital contributions (PNOC), valuable in the assessment of the electronic structure methods in the NLOPs computations, is presented.

Overcoming the Failure of Correlation for Out-of-Plane Motions in a Simple Aromatic: Rovibrational Quantum Chemical Analysis of c-C3H2

Truncated, correlated, wave function methods either produce imaginary frequencies (in the extreme case) or nonphysically low frequencies in out-of-plane motions for carbon and adjacent atoms when the carbon atoms engage in π bonding. Cyclopropenylidene is viewed as the simplest aromatic hydrocarbon, and the present as well as previous theoretical studies have shown that this simple molecule exhibits this behavior in the two out-of-plane bends (OPBs). This nonphysical behavior has been treated by removing nearly linear dependent basis functions according to eigenvalues of the overlap matrix, by employing basis sets where the spd space saturatation is balanced with higher angular momentum functions, by including basis set superposition/incompleteness error (BSSE/BSIE) corrections, or by combining standard correlation methods with explicitly correlated methods to produce hybrid potential surfaces. However, this work supports the recently described hypothesis that the OPB problem is both a method and a basis set effect. The correlated wave function's largest higher-order substitution term comes from a π → π* excitation where constructive interference of both orbitals artificially stabilizes the OPB. By employing schema to overcome this issue, the symmetric OPB ν₉ is the predicted to be the second-brightest transition, and it will be observed very close to 775 cm^-1. However, more work from the community is required to formulate better how carbon atoms interact with their adjacent atoms in π-bonded systems. Such bonds are ubiquitous in all of chemistry and beyond.

Electron-Pair Distribution in Chemical Bond Formation

The chemical formation process has been studied from relaxation holes, Δh(u), resulting from the difference between the radial intracule density and the nonrelaxed counterpart, which is obtained from atomic radial intracule densities and the pair density constructed from the overlap of the atomic densities. Δh(u) plots show that the internal reorganization of electron pairs prior to bond formation and the covalent bond formation from electrons in separate atoms are completely recognizable processes from the shape of the relaxation hole, Δh(u). The magnitude of Δh(u), the shape of Δh(u) ∀ u < R_eq, and the distance between the minimum and the maximum in Δh(u) provide further information about the nature of the chemical bond formed. A computational affordable approach to calculate the radial intracule density from approximate pair densities has been also suggested, paving the way to study electron-pair distributions in larger systems.

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.

Electron correlation effects in third-order densities

The electronic energy of a system of fermions can be obtained from the second-order reduced density matrix through the contracted Schrödinger equation or its anti-Hermitian counterpart. Both energy expressions depend on the third-order reduced density matrix (3-RDM) which is usually approximated from lower-order densities. The accuracy of these methods depends critically on the set of N-representability conditions enforced in the calculation and the quality of the approximate 3-RDM. There are no benchmark studies including most 3-RDM approximations and, thus far, no assessment of the deterioration of the approximations with correlation effects has been performed. In this paper we introduce a series of tests to assess the performance of 3-RDM approximations in a model system with varying electron correlation effects, the three-electron harmonium atom. The results of this work put forward several limitations of the currently most used 3-RDM approximations for systems with important electron correlation effects.

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.

The electronic structure and stability of germanium tubes Ge30H12 and Ge33H12

To explore the possibility of large cylindrical Ge clusters, we investigated the molecular and electronic structure of the germanium tube Ge₃₀H₁₂, composed of six parallel, planar hexagons using DFT calculations, and Ge₃₃H₁₂ generated from the insertion of Ge atoms at the center of three inner hexagons of Ge₃₀H₁₂.

New electron delocalization tools to describe the aromaticity in porphyrinoids

There are several possible pathways in the macrocycle of large porphyrinoids and, among aromaticity indices, only AV_minis capable of recognizing the most aromatic one.

Tuning the affinity of catechols and salicylic acids towards Al(iii): characterization of Al–chelator interactions

Aluminum is a non-essential element in the human body with unclear harmful effects; therefore, the design and tuning of new and efficient Al(iii) chelating agents is a subject of paramount importance nowadays.

Cycloreversion of the CO2 trimer: a paradigmatic pseudopericyclic [2 + 2 + 2] cycloaddition reaction

Very recently, the CO₂ trimer has been experimentally synthesized, isolated and characterized. This process opens new ways for the withdrawal and storage of this greenhouse gas. The trimer is reported to be stable up to -40 °C, with a lifetime of about 40 min at this temperature. At these or under harsher thermal conditions it reverts to the three monomers. The mechanism of this reaction has been theoretically studied and the electronic character of the associated transition state has been analyzed from a variety of perspectives (energetic, magnetic, electron localization and delocalization functions) which indicate that it has paradigmatic pseudopericyclic character. To allow for a comparative study, the isoelectronic fragmentations of cyclohexane into three units of ethylene and of benzene into three units of acetylene have been included in this work. The study of a similar series of formally forbidden-four-centered [2 + 2] cycloreversions confirmed the pseudopericyclic nature of these reactions when the CO₂ dimer or trimer is involved.

The aromaticity of dicupra[10]annulenes

The aromaticity of dicupra[10]annulenes closely resembles that of naphthalene.

Correction: The aromaticity of dicupra[10]annulenes

Correction for ‘The aromaticity of dicupra[10]annulenes’ by Rafael Grande-Aztatzi et al., Phys. Chem. Chem. Phys., 2017, 19, 9669–9675.

The electron-pair density distribution of the 1,3Πu excited states of H2

The non-monotonic behavior of the electron repulsion energy and the inter-electronic distance, as a function of the internuclear separation, in the 3Πu excited state of the hydrogen molecule has been assessed by explicit calculation and analysis of the electron-pair density distribution functions from high level ab initio full configuration interaction wave functions, for both the 3Πu and the 1Πu states. Additionally, Hund’s rule as applied to these two states has been accounted for in terms of simple electronic shielding effects induced by wave function antisymmetrization.