In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.

The electronic structure of several many-electron atoms, confined within a penetrable spherical box, was studied using the Hartree-Fock (HF) method, coupling the Roothaan's approach with a new basis set to solve the corresponding one-electron equations. The resulting HF wave-function was employed to evaluate the Shannon entropy, S q , in configuration space. Confinements imposed by impenetrable walls induce decrements on S q when the confinement radius, R c , is reduced and the electron-density is localized. For confinements commanded by penetrable walls, S q exhibits an entirely different behavior, because when an atom starts to be confined, S q delivers values less than those observed for the free system, in the same way that the results presented by impenetrable walls. However, from a confinement radius, S q shows increments, and precisely in these regions, the spatial restrictions spread to the electron density. Thus, from results presented in this work, the Shannon entropy can be used as a tool to measure the electron density delocalization for many-electron atoms, as the hydrogen atom confined in similar conditions.confined atoms, correct asymptotic behavior, Hartree-Fock, Shannon entropy, wave-function 1 | I N TR ODU C TI ON The confined atoms model is an important topic in physics and chemistry since atoms under spatial restrictions exhibit unusual characteristics, which differ to those on the same systems without such constraints. For example, effects over atoms confined by the fullerene have been analyzed using a model with a radial potential similar to a shell with width and size fitted to reproduce experimental information. [1][2][3] The simulation of the hydrogen atom submitted to high external pressures is another example of confined atoms. [4][5][6][7][8][9] In this case, the hydrogen atom was clamped at the center of one sphere, of radius R c , with impenetrable walls and consequently, wave-function or electron-density satisfy Dirichlet's boundary conditions. On this line, walls with infinite potential have been applied to study many-electron atoms, using wave-function techniques [10][11][12][13][14][15][16] or the density functional theory, [17,18] and some of these results have been contrasted with experimental values to predict sd electronic transitions observed when some metals are submitted to high pressures. [19,20] In early stages of the quantum mechanics, Sommerfeld proposed that positive eigenvalues found under this model indicate an electron delocalization. [5,21] Naturally, it is not easy to probe such a delocalization in systems where spatial restrictions trap electrons instead of the nuclear attraction. [22][23][24][25][26][27][28] The confinement by impenetrable boxes overestimates the response of physical observables, and, therefore, penetrable walls are more convenient to contrast the corresponding results with an experimental counterpart. [29][30][31][32][33] Such a model was proposed by Gorecki and Byers-Brown to reproduce the behavior of the helium atom submitted to high pressur...

No abstract

The potential energy surface of [Cu(HO)] clusters with n = 12, 16, and 18 was explored by using a modified version of the simulated annealing method. Such exploration was carried out by using the PM7 semiempirical method to obtain around 100,000 isomers, which provide candidates to be optimized with PBE0-D3, M06-2X, and BHLYP exchange-correlation functionals coupled with the 6-311++G** basis set. These methods based on the Kohn-Sham approach delivered isomers with coordination numbers of 4, 5, and 6. The analysis used to obtain coordination numbers was based on geometrical parameters and the quantum theory of atoms in molecules (QTAIM) approach. Our methodology found only one isomer with fourfold coordination and its probabilities to appear in these clusters are quite small for high temperatures. The procedure used in this article predicts important populations of fivefold and sixfold coordination clusters, in fact, the fivefold coordination dominates for PBE0-D3 and BHLYP methods, although the sixfold coordination starts to be important when the number of water molecules is increased. The nature of axial and equatorial contacts is discussed in the context of the QTAIM and the noncovalent interaction index (NCI), which gives a clear classification of such orientations. Also, these methods suggest a partial covalent interaction between the Cu and water molecules in both positions; equatorial and axial.

Confinement and pressure have profound effects on the electronic structure of atoms and molecules. In this work, we study the effects of a harmonic confinement on the electronic structure of the lithium dimer. To do this, we use quantum chemistry methods that include much of the electronic correlation (Coupled Cluster and CASSCF). The confinement induces a change, with respect to the free molecule, in the electronic configuration of Li2. There is a critical confinement value for which the ground state stops being the singlet 1∑g+ and becomes the triplet 3∑g−. We also study changes in the bonding pattern. Li2 conserves the bonding pattern of the free molecule independently of the strength of confinement, as it is revealed by the electron localization function.