Théorie de l'orbitale moléculaire

La théorie de l'orbitale moléculaire (TOM) est un des socles de la chimie théorique du . Jusqu'alors les chimistes théoriciens étaient prisonniers des succès du modèle de la liaison covalente de Lewis. Les méthodes spectroscopiques du montrent les limites de l'idée de liaisons localisées en résolvant des structures chimiques jusque-là inédites. Par exemple la mésomérie ou résonance était vue, à tort, comme le passage rapide d'une conformation à une autre (résonance de Kekulé), ce qui n'était pas vérifié ni dans le spectre infrarouge ni dans la réactivité de molécules comme le benzène. De plus, le paramagnétisme de certaines molécules et complexes, notamment le dioxygène est inexplicable sans l'idée d'orbitales moléculaires. Cette théorie réconcilie surtout la mécanique quantique et les autres branches de la chimie, en plus de permettre le développement de la chimie numérique. Dans cette théorie, les orbitales atomiques se combinent linéairement pour former un ensemble d'orbitales li

Helical versus linear Jahn-Teller distortions in allene and spiropentadiene radical cations

Marc Hamilton Folkmann Garner, Rubén Laplaza Solanas

The allene radical cation can be stabilized both by Jahn-Teller distortion of the bond lengths and by torsion of the end-groups. However, only the latter happens and the allene radical cation relaxes into a twisted D-2 symmetry structure with equal double-bond lengths. Here we revisit the Jahn-Teller distortion of allene and spiropentadiene by assessing the possible implications of their helical pi-systems in the radical cations. We describe a general relation between the structure and the number of pi-electrons in spiroconjugated and linearly conjugated systems. Through constrained optimizations we compare the stabilization achieved by bond-length alternation and axial torsion in the radical cations, which we explain with a simple frontier molecular orbital (MO) picture. While structurally different, allene and spiropentadiene have similar helical frontier MOs. Both cations relax through torsion because the stabilization of their helical frontier MOs is bigger than that which can be achieved by linear pi-conjugation. Electrohelicity thus manifests in molecular systems with partial occupation as a helical pi-conjugation effect, which evidently provides more stabilization than its linear counterpart in terms of the Jahn-Teller distortion. This mechanism may be a driving factor for the relaxation in a range of spiroconjugated and linearly conjugated cationic systems.

ROYAL SOC CHEMISTRY2022

Spectral properties of extended systems from Koopmans-compliant functionals

Riccardo De Gennaro

Electronic-structure simulations have been impacting the study of materials properties thanks to the simplicity of density-functional theory, a method that gives access to the ground state of the system. Although very important, ground-state properties represent just part of the information, and often technological applications rely more on excited-state properties. In the context of density-functional theory, the latter are difficult to extract and one usually has to resort to more sophisticated approaches. In the last years, Koopmans spectral functionals have emerged as an effective method which combines the feasibility of density-functional theory with the accuracy of more complex methods, such as many-body perturbation theory. While retaining its simplicity, Koopmans functionals extend the domain of density-functional theory providing direct access to charged excitations, and ultimately to the photoemission spectra of materials. This approach has been extensively employed in finite systems, displaying an accuracy which is comparable to that of state-of-the-art many-body perturbation theory methods. In extended systems, calculations were bound to the supercell (Gamma-only) method, preventing the access to the full band structure of the system. In this work we overcome this limitation, proving that a band structure description of the energy spectrum is possible, and providing a scheme to carry out calculations in crystalline materials. The first result of this work consists in proving the compliance of Koopmans functionals with the translation symmetry of the system. The validity of Bloch's theorem, thus the possibility of describing the spectrum via a band structure picture, depends on this condition. Because of the orbital-density-dependent nature of the functional, the invariance of the total energy with respect to unitary transformations of the one-electron orbitals is broken. The energy is then minimized by a particular set of orbitals, called ``variational'', which are strongly localized in space. In extended periodic systems, the localized, thus non-periodic, character of the variational orbitals is inherited by the effective orbital-density-dependent Hamiltonians, which apparently break the translation symmetry of the system. Here we show that, by requiring the variational orbitals to be Wannier functions, the translation symmetry is preserved and Bloch's theorem holds. In the second part, we devise a scheme to unfold the band structure from supercell (Gamma-only) calculations, and reconstruct the k-dependence of the quasiparticle energies. This method is then used to compute the band structures of a set of benchmark semiconductors and insulators. Finally, we describe a novel formulation of Koopmans functionals for extended periodic systems, which exploits from the beginning the translation properties of Wannier functions to realize a primitive cell-based implementation of Koopmans functionals. Results obtained from this second approach are also discussed. In the last part, we present the preliminary study of impurity states arising in crystalline materials in the presence of point defects.

EPFL2022

Spectral properties of extended systems from Koopmans-compliant functionals

Riccardo De Gennaro

EPFL2022