H4: 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 H4 molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurgence 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 H4 D(4h)/D(2h) potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D(2h)-D(4h) transition of H4 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 interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H4 PES. By introducing interpair nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to the equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.

An electronic aromaticity index for large rings

We introduce a new electronic aromaticity index, AV1245, consisting of an average of the 4-center indices along the ring that keep a positional relationship of 1, 2, 4, 5.

New Approximation to the Third-Order Density. Application to the Calculation of Correlated Multicenter Indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation.

Scalar and Spin-Orbit Relativistic Corrections to the NICS and the Induced Magnetic Field: The case of the E12(2-) Spherenes (E = Ge, Sn, Pb)

Can relativistic effects modify the NICS and the B(ind) values? In this manuscript we evaluate the relativistic corrections incorporated via the zeroth-order regular approximation to the calculations of nucleus-independent chemical shifts and the induced magnetic field (B(ind)) in the E12(2-) spherenes (E = Ge, Sn, Pb). We found that both electron delocalization descriptors are strongly affected by the relativistic corrections. For instance, for plumbaspherene, the difference in values from the nonrelativistic to the relativity-included calculation is almost 40 ppm! Our results show that the changes observed in the NICS and B(ind) values in the title cages are a consequence of the treatment of the relativistic effects. If these effects are included as scalar or spin-orbit calculations, then we can establish the next trend: Ge12(2-) is a nonaromatic species, Sn12(2-) is a low aromatic species, and Pb12(2-) is strongly aromatic, according to calculated NICS and B(ind) values. Thus, any prediction of electron delocalization in molecules containing heavy elements without considering an adequate treatment for relativistic effects may lead to an erroneous chemical interpretation.

The Electronic Structure of the Al3(-) Anion: Is it Aromatic?

Multiconfigurational high-level electronic structure calculations show that the Al3(-) ring-like cluster anion has three close low-lying electronic states of different spin, all of them having strong multiconfigurational character. The aromaticity of the cluster has, therefore, been studied by means of total electron delocalization and normalized multicenter electron delocalization indices evaluated from the multiconfigurational wave functions of each state. The lowest-lying singlet and triplet states are found to be highly aromatic, whereas the next lowest-lying state, the quintet state, has much less, though non-negligible, aromatic character.

Quantifying aromaticity with electron delocalisation measures

Aromaticity cannot be measured directly by any physical or chemical experiment because it is not a well-defined magnitude. Its quantification is done indirectly from the measure of different properties that are usually found in aromatic compounds such as bond length equalisation, energetic stabilisation, and particular magnetic behaviour associated with induced ring currents. These properties have been used to set up the myriad of structural-, energetic-, and magnetic-based indices of aromaticity known to date. The cyclic delocalisation of mobile electrons in two or three dimensions is probably one of the key aspects that characterise aromatic compounds. However, it has not been until the last decade that electron delocalisation measures have been widely employed to quantify aromaticity. Some of these new indicators of aromaticity such as the PDI, FLU, ING, and INB were defined in our group. In this paper, we review the different existing descriptors of aromaticity that are based on electron delocalisation properties, we compare their performance with indices based on other properties, and we summarise a number of applications of electronic-based indices for the analysis of aromaticity in interesting chemical problems.

On the existence and characterization of molecular electrides

Molecular electrides exist and can be designed using some guidelines and a set of computational criteria.

A theoretical study of the aromaticity in neutral and anionic borole compounds

A theoretical assessment of the degree of (anti)aromaticity in various borole compounds reveals distinct substituent effects.

Benchmark calculations of metal carbonyl cations: relativistic vs. electron correlation effects

In this paper we present benchmark results for isoelectronic metal carbonyl complexes of the groups 11 and 12 of the periodic table. The focus is on the geometry, vibrational frequencies, bond dissociation energy and chemical bonding. The description of these complexes requires a good balance between electron correlation and relativistic effects. Our results demonstrate that the combination of the effective core potential and the MP2 method gives quantitative results for the first- and the second-row transition metal complexes and only qualitative agreement for the third-row complexes. In order to obtain quantitative results for the whole series the use of four-component or X2C methods is mandatory. The fourth-row transition metal carbonyl complexes from groups 11 and 12 have been studied for the first time. The metal-carbon bond strength pattern along the group is shown to be highly dependent on the correct description of the relativistic effects. Finally, the relativistic effects on the bonding are studied by means of electron density difference maps, the analysis of the bond critical points of the electron density and the mechanism for σ-donation and π-backdonation. Our analysis indicates that the fourth-row complexes exhibit a strong covalent character induced by relativistic effects.

Exploring the potential energy surface of E₂P₄ clusters (E=Group 13 element): the quest for inverse carbon-free sandwiches

Inverse carbon-free sandwich structures with formula E2P4 (E=Al, Ga, In, Tl) have been proposed as a promising new target in main-group chemistry. Our computational exploration of their corresponding potential-energy surfaces at the S12h/TZ2P level shows that indeed stable carbon-free inverse-sandwiches can be obtained if one chooses an appropriate Group 13 element for E. The boron analogue B2P4 does not form the D(4h)-symmetric inverse-sandwich structure, but instead prefers a D(2d) structure of two perpendicular BP2 units with the formation of a double B-B bond. For the other elements of Group 13, Al-Tl, the most favorable isomer is the D(4h) inverse-sandwich structure. The preference for the D(2d) isomer for B2P4 and D(4h) for their heavier analogues has been rationalized in terms of an isomerization-energy decomposition analysis, and further corroborated by determination of aromaticity of these species.

Electron delocalization and aromaticity in low-lying excited states of archetypal organic compounds

Aromaticity is a property usually linked to the ground state of stable molecules. Although it is well-known that certain excited states are unquestionably aromatic, the aromaticity of excited states remains rather unexplored. To move one step forward in the comprehension of aromaticity in excited states, in this work we analyze the electron delocalization and aromaticity of a series of low-lying excited states of cyclobutadiene, benzene, and cyclooctatetraene with different multiplicities at the CASSCF level by means of electron delocalization measures. While our results are in agreement with Baird's rule for the aromaticity of the lowest-lying triplet excited state in annulenes having 4nπ-electrons, they do not support Soncini and Fowler's generalization of Baird's rule pointing out that the lowest-lying quintet state of benzene and septet state of cyclooctatetraene are not aromatic.

Ab initio design of chelating ligands relevant to Alzheimer's disease: influence of metalloaromaticity

Evidence supporting the role of metal ions in Alzheimer's disease (AD) has rendered metal ion chelation as a promising therapeutic treatment. The rational design of efficient chelating ligands requires, however, a good knowledge of the electronic and molecular structure of the complexes formed. In the present work, the coordinative properties of a set of chelating ligands toward Cu(II) have been analyzed by means of DFT(B3LYP) calculations. Special attention has been paid to the aromatic behavior of the metalated rings of the complex and its influence on the chelating ability of the ligand. Ligands considered have identical metal binding sites (through N/O coordination) and only differ on the kind and size of the aromatic moieties. Results indicate that there is a good correlation between the stability constants (log β(2)) and the degree of metalloaromaticity determined through the I(NG) and HOMA indices; that is, the higher the metalloaromaticity, the larger the log β(2) value. MOs and aromaticity descriptors confirm that present complexes exhibit Möbius metalloaromaticity. Detailed analysis of the nature of the Cu(II)-ligand bonding, performed through an energy decomposition analysis, indicates that ligands with less aromatic moieties have the negative charge more localized in the metalated ring, thus increasing their σ-donor character and the metalloaromaticity of the complexes they form.

New link between conceptual density functional theory and electron delocalization

In this paper we give a new definition of the softness kernel based on the exchange-correlation density. This new kernel is shown to correspond to the change of electron fluctuation upon external perturbation, thus helping to bridge the gap between conceptual density functional theory and some tools describing electron localization in molecules. With the aid of a few computational calculations on diatomics we illustrate the performance of this new computational tool.

Benchmark Full Configuration Interaction Calculations on the Lowest-Energy (2)P and (4)P States of the Three-Electron Harmonium Atom

Full configuration interaction calculations carried out in conjunction with careful optimization of basis sets and judicious extrapolation schemes for 12 values of the confinement strength ω ranging from 0.1 to 1000.0 provide benchmark energies for the (2)P ground state and the (4)P first excited state of the three-electron harmonium atom, allowing for numerical verification of the recently obtained second-order energy coefficients and confirming the few available results of Monte Carlo studies. The final energy values, obtained by correcting the extrapolated data for residual errors in the low-order energy coefficients, possess accuracy of ca. 20 μHartree for the doublet state and ca. 10 μHartree for the quartet one, making them suitable for calibration and testing of approximate electron correlation methods of quantum chemistry. The energy limits for individual angular momenta ranging from 1 to 4 are also available, facilitating comparisons with results of calculations involving finite basis sets. An example of application involving the BLYP and B3LYP functionals is provided.

Performance of 3D-space-based atoms-in-molecules methods for electronic delocalization aromaticity indices

Several definitions of an atom in a molecule (AIM) in three-dimensional (3D) space, including both fuzzy and disjoint domains, are used to calculate electron sharing indices (ESI) and related electronic aromaticity measures, namely, I(ring) and multicenter indices (MCI), for a wide set of cyclic planar aromatic and nonaromatic molecules of different ring size. The results obtained using the recent iterative Hirshfeld scheme are compared with those derived from the classical Hirshfeld method and from Bader's quantum theory of atoms in molecules. For bonded atoms, all methods yield ESI values in very good agreement, especially for C-C interactions. In the case of nonbonded interactions, there are relevant deviations, particularly between fuzzy and QTAIM schemes. These discrepancies directly translate into significant differences in the values and the trends of the aromaticity indices. In particular, the chemically expected trends are more consistently found when using disjoint domains. Careful examination of the underlying effects reveals the different reasons why the aromaticity indices investigated give the expected results for binary divisions of 3D space.