Programme

• Claudine Katan and Jacky Even: Insight into some open questions for 3D/2D/0D halide perovskites
• Mohit Chaudary: Optical Properties of Noble-Metal Clusters using the DFT+U Method
• Tanguy Ferré: IR and Raman spectroscopy in group-III monochalcogenides: from monolayer to bulk
• Tomasz Gryber: Fatigue Mechanism of Reversible Photocyclisation in Diarylethenes
• Muhammed Gunes: Charge density as a functional of the potential: Connector Theory approach
• Francesco Sottile: Resonant Inelastic X-ray Scattering

In realistic (DFT+DMFT) calculations of correlated materials, the matrix of the partially-screened electron-electron Coulomb interaction is usually approximated in spherical symmetry and parameterized by Slater integrals (or, equivalently, Racah parameters). Few works have considered the real point-group symmetry of the Coulomb matrix. We suggest parameterizing the Coulomb matrix by its eigenvalues on the irreducible representations of the point group: this respects the point-group symmetry of the system and, compared to other approaches, is completely basis-independent. The permutation symmetry of the 1-electron states in the Coulomb matrix is also taken into account in the two cases of real and complex wavefunctions, to further reduce the number of independent parameters. Finally we apply this method to 3d-transition-metal monoxides.

In this talk, I will present joint work on the mathematical aspects ([4,5]) of Density Matrix Embedding Theory (DMET) ([1,2,3]), an embedding theory designed with the reduced density matrix (1-RDM). After specifying a precise mathematical framework, we prove in [6] that the 1-RDM of the ground state is a fixed point when interactions are neglected. We then prove the existence and analyticity of a fixed point of this algorithm in the weak interaction limit, and study the convergence of the DMET iterative scheme. Finally, we expose numerical simulations in agreement with our results.

[1] G. Knizia and G. Chan, Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory, PRL 109, 18 (2012)
[2] G. Knizia and G. Chan,Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory,J. Chem. Theory Comput. 9, 3, (2013)
[3] S. Wouters, C. Jiménez-Hoyos, Q. Sun, G. Chan A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry, J. Chem. Theory Comput. 12, 6 (2016)
[4] X. Wu, M. Lindsey, T. Zhou, Y. Tong and L. Lin, Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting, Phys. Rev. B 102, 085123, (2020)
[5] F. Faulstich, R. Kim, Z. Cui, Z. Wen, G. Chan and L. Lin, Pure State v-Representability of Density Matrix Embedding Theory, J. Chem. Theory Comput. , 18, 2, (2022)
[6] É. Cancès, F. Faulstich, A. Kirsch, E. Letournel, A. Levitt, Some mathematical insights on DMET, to be published (2023)

The GW-Bethe-Salpeter Equation (BSE) approach is a promising method for the calculation of optical excitations in complex systems. In this contribution, I will present a cubic scaling implementation of the starting-point independent and accurate1 quasiparticle self-consistent GW (qsGW)2-BSE approach in a spinor (two-component orbital) basis.3 This implementation allows us to calculate spin-orbit effects on optical excitations which is of high importance for the description of various processes like intersystem crossing or transition metal L-edge X-ray absorption spectroscopy. I will describe the main steps of the algorithm which includes i) quadratic scaling algorithms for the independent particle polarizability within the random phase approximation and the GW self-energy4-6 ii) full use of Kramers symmetry to reduce the prefactor of the two-component calculations significantly and iii) a low-order scaling algorithm to calculate the matrix elements of the BSE Hamiltonian.7 I will present benchmark results for small molecules and show some preliminary applications to third generation emitters for OLED.

BiFeO₃ is a technologically relevant multiferroic perovskite. While a vast literature exists on its electronic, optical, and multiferroic properties, some of its optically active electronic excitations remain to be understood or have been interpreted in ambiguous ways. This applies in particular to features below the absorption onset that feature prominently in resonant Raman scattering [1]. Here we present a detailed study of the electronic structure and resonant Raman spectrum of BiFeO₃ from first principles. Using many-body perturbation theory (MBPT) on top of density functional theory (DFT), we first analyze and characterize its optical absorption spectrum in terms of excitons and atomic orbitals, focusing in particular on spin-flip excitations that are strongly localized. We then use the state-of-the-art method for the ab initio calculation of resonant Raman intensities [2,3] to analyze the resonant coupling of these finite-spin excitations with phonons. Our results show that these only optically weak excitations couple strongly with phonons and leave a clear imprint on the resonant Raman spectrum, making the latter an even more powerful tool to probe "darker" electronic excitations. Furthermore, we explain the Raman resonances in BiFeO₃ by analysing the involved excitons and phonons in the atomic orbital and real-space picture.

[1] M. C. Weber, et al. Phys. Rev. B, 93, 125204 (2016).
[2] S. Reichardt and L. Wirtz, Phys. Rev. B, 99, 174312 (2019).
[3] S. Reichardt and L. Wirtz, Sci. Adv., 6, eabb5915 (2020)

Excitons - bound electron-hole pairs - feature very prominently in the optical spectra of two-dimensional (2D) materials and heterostructures and play a key role in any opto-electronic application. They also can strongly couple to lattice degrees of freedom, as evidenced by their imprint on resonant Raman scattering intensities [1,2]. In 2D heterostructures, this sort of strong coupling and its signature in observables such as Raman intensities offers an ideal setting to learn about electron- and exciton-phonon coupling both within and across material layers. Here we focus on the example of a van der Waals heterostructure of monolayer tungsten diselenide (WSe2) and hexagonal boron nitride (hBN). Its Raman spectrum features the normally silent out-of-plane optical phonon mode of hBN that becomes active due to symmetry breaking and - most curiously - very strongly enhanced due to resonant exciton-phonon scattering [1]. While the resonant scattering pathways have been identified as involving excitons in WSe2 that couple to the phonons in hBN [1], a microscopic understanding of this interlayer exciton-phonon coupling is still missing. We provide such understanding using the state-of-the-art method for the computation for resonant Raman scattering intensities [2,3], which allows a detailed atomistic and quantum mechanical dissection of the Raman scattering process. Supplemented by a classical picture, our work sheds light on the microscopic mechanism behind exciton-phonon coupling in 2D heterostructures.

[1] C. Jin, et al. Nat. Phys., 13, 127-131, (2017).
[2] S. Reichardt and L. Wirtz. Sci. Adv. 6, eabb5915, (2020).
[3] S. Reichardt and L. Wirtz. Phys. Rev. B 99, 174312, (2019).

The search for good approximations to the electron self-energy is still of high interest. The standard and most widely used approximation is Hedin’s GW expression, which has become the state-of-the-art for the band structure calculations of solids. However, the validity of the GW approximation is limited to a range of materials where correlations are weak to moderate, and to describe more correlated materials remains a challenge. Going beyond GW is not straightforward, and there is no unique and well-established method. Moreover, even once an expression has been chosen, there are many possible choices of ingredients that make the situation ambiguous. For instance, if one stays at the GW level or if one adds second order diagrams in terms of the screened Coulomb interaction W to go beyond GW, it still remains to be defined which W is to be used. This question is still waiting for an answer, and there is no consensus in the Many-Body Perturbation Theory (MBPT) community. Recently, the combination of Time Dependent Density Functional Theory (TDDFT) and MBPT has become a popular way to add approximate vertex corrections beyond GW, using the exchange-correlation kernel (fxc) from TDDFT. My talk will address some of the open questions, and in particular, those linked to the use of fxc. I will discuss both the use of exact TDDFT ingredients and of approximations to them. Our goal is to improve total energy calculations for a large range of materials using the one-body Green's function. For illustrations, we use the symmetric Hubbard dimer model at half-filling (two-electrons).

In the last decades, 2D materials such as graphene have gained attention for all sort of applications. Among these materials, borophene has gained popularity for applications that go from transparent conductors to superconductivity[1,2]. Given its polymorphism and anisotropy, it constitutes an ideal prototype for the study of 2D materials. It is there- fore interesting to investigate how the atomic structure influences its electronic structure, and how these changes affect the properties of the material: optical absorption, loss func- tion, and charge density evolution with respect to an external perturbation in the linear regime. In this work we have selected a set of borophene polymorphs structurally different to each other and we have compared them in commensurable unit cells . We have found out striking similarities among the structures, but we have also noted how the slight differences change the properties from polymorph to polymorph. Our calculations were performed with Abinit (ground-state), with DP (full polarizability), and with SRden (density evolution) [3-5].

[1] Mannix, A.J., Zhang, Z., Guisinger, N.P. et al. Nature Nanotech 13, 444–450 (2018)
[2] Y. V. Kaneti, D. P. Benu, X. Xu, B. Yuliarto, Y. Yamauchi, and D. Golberg, Chemical Reviews, vol. 122, no. 1, pp. 1000–1051, Jan 2022.
[3] X. Gonze et al. Comput. Phys. Commun. 248, 107042 (2020)
[4] F. Sottile, L. Reining, and V. Olevano. The dp code. [Online].
[5] A. Lorin, Ph.D. dissertation, Instit Polytechnique de Paris, 2020.

High-pressure high-temperature (HPHT) syntheses of β boron and amorphous carbon have produced α boron at some P and T values while the initial aim was to synthesize boron carbide [1, 2]. To understand the role of carbon in the formation of α boron, we have computed the free energy of unit cells of α boron with carbon impurities within the density functional theory (DFT) [2]. The formation energy suggests that some icosahedra of α boron could accommodate some impurities without drastic changes in properties such as lattice parameters and band gap. Meanwhile, the formation energy of defects that have two or more carbon atoms turned out to vary by the distance between carbon atom(s) [3], some of them decreasing drastically when charged [4].
Acknowledgments
DFT calculations have been performed using the Quantum ESPRESSO software [5]. We acknowledge access to high performance computing (HPC) resources provided by the Partnership for Advanced Computing in Europe (PRACE Project No. 2019204962), by the French HPC centers of TGCC, CINES, and IDRIS (GENCI Project 2210) as well as to the 3L-hpc local computer cluster partly supported by the DIM SIRTEQ (région Île de France) and École Polytechnique. Financial supports from DGA is also acknowledged.

[1] A. Chakraborti, N. Guignot, N. Vast, Y. Le Godec, J. Phys. Chem. Solids. 159, 110253 (2021).
[2] A. Chakraborti, Y. Cho, J. Sjakste, B. Baptiste, L. Henry, N. Guignot, Y. Le Godec, N. Vast, Acta Mater. 249, 118820 (2023).
[3] Y. Cho, J. Sjakste, N. Vast, in preparation (2023).
[4] Y. Cho, J. Sjakste, N. Vast, in preparation (2023).
[5] P. Giannozzi et al., J. Phys. : Condens. Matter 29, 465901 (2017).

Quantum computers have shown promises to solve problems that are currently intractable on classical computers, and quantum chemistry has been identified as one of the killer applications of quantum computers in the near term [1]. The talk will be divided in three parts: (i) a general introduction to quantum computing and how to encode the electronic structure problem on quantum computers, (ii) a description of the two main algorithms used to infer ground and excited states, namely the quantum phase estimation (QPE) [2] and the variational quantum eigensolver (VQE) [3], and (iii) an overview of the developments achieved in our group together with our collaborators [4-8]. I will describe how information beyond the ground-state energy can be extracted, such as molecular properties [4] and excited-state energies, using for instance an extension of VQE called ensemble VQE [5,6]. Finally, I will briefly mention how a counter-intuitive mapping can pave the way toward the implementation of density functional theory on quantum computers, for which no quantum advantage had been envisioned so far [7].

[1] Cao, Y. et al. (2019). Quantum chemistry in the age of quantum computing. Chemical reviews, 119(19), 10856-10915.
[2] Kitaev, A. Y. (1995). Quantum measurements and the Abelian stabilizer problem. arXiv preprint quant-ph/9511026.
[3] Peruzzo, A. et al. (2014). A variational eigenvalue solver on a photonic quantum processor. Nature communications, 5(1), 4213.
[4] O’Brien et al. (2019). Calculating energy derivatives for quantum chemistry on a quantum computer. npjQI, 5(1), 113.
[5] Yalouz, S. et al. (2021). A state-averaged orbital-optimized hybrid quantum–classical algorithm for a democratic description of ground and excited states. QST, 6(2), 024004.
[6] Yalouz, S. et al. (2022). Analytical nonadiabatic couplings and gradients within the state- averaged orbital-optimized variational quantum eigensolver. JCTC, 18(2), 776-794.
[7] Senjean, B. et al. (2023). Toward density functional theory on quantum computers?. SciPost Physics, 14(3), 055.
[8] Marécat, Q. et al. (2023). Recursive relations and quantum eigensolver algorithms within modified Schrieffer-Wolff transformations for the Hubbard dimer. PRB, 107(15), 155110.

In realistic (DFT+DMFT) calculations of correlated materials, the matrix of the partially-screened electron-electron Coulomb interaction is usually approximated in spherical symmetry and parameterized by Slater integrals (or, equivalently, Racah parameters). Few works have considered the real point-group symmetry of the Coulomb matrix. We suggest parameterizing the Coulomb matrix by its eigenvalues on the irreducible representations of the point group: this respects the point-group symmetry of the system and, compared to other approaches, is completely basis-independent. The permutation symmetry of the 1-electron states in the Coulomb matrix is also taken into account in the two cases of real and complex wavefunctions, to further reduce the number of independent parameters. Finally we apply this method to 3d-transition-metal monoxides.

Recently, metal-organic frameworks (MOFs) have attracted much attention as functional materials due to their extraordinary tunability in terms of physico-chemical properties. In this talk, I will show our recent efforts to engineer two different families of stimuli-responsive MOFs for applications in gas capture and release, i.e. photoresponsive and spin crossover MOFs. The methodological aspects and implementations will be discussed extensively. The optical properties of photoresponsive MOFs are studied using the Bethe-Salpeter formalism, where periodic calculations of the whole crystal will be compared with molecular calculations performed by employing an embedding scheme to account for environmental effects both at the ground state and at the BSE/GW level. Spin crossover molecules and MOFs are studied by adopting several computational schemes developed in our group, from a Hubbard U-density corrected scheme to an artificial neural network-machine-learned functional, specifically designed to accurately predict spin splitting energies. For both families of MOFs, challenges and opportunities in their development will be discussed offering insights for future advancements in the field.

In this talk I will present a general approach to study periodic Coulomb systems. The main idea is to isolate a supercell from the periodic structure and modify its topology to that of a Clifford Torus. While an ordinary torus is curved, a Clifford torus is flat. Therefore a supercell can be represented on it without deformation. Like an ordinary torus, a Clifford torus has no boundaries which makes the extrapolation of results to the thermodynamic limit smooth. I will show how we have successfully applied our strategy to the calculation of Madelung constants and Wigner crystals. [1,2,3] If time permits, I will also discuss some recent work in which we introduce a multi-channel Dyson equation. This equation couples different many-body Green’s functions. I will focus on the multi-channel Dyson equation that couples the one-body Green’s function to the three-body Green’s function. I will show how this equation can be used to model photoemission spectral functions. [4]

[1] N. Tavernier, G. L. Bendazzoli, V. Brumas, S. Evangelisti, and J. A. Berger, J. Phys. Chem. Lett. 11, 7090 (2020)
[2] E. Alves, G. L. Bendazzoli, S. Evangelisti, and J. A. Berger, Phys. Rev. B 103, 245125 (2021)
[3] M. Escobar Azor, E. Alves, S. Evangelisti, and J. A. Berger, J. Chem. Phys. 155, 124114 (2021)
[4] G. Riva, T. Audinet, M. Vladaj, P. Romaniello and J.A. Berger, SciPost Phys. 12, 093 (2022)

Progress in the fabrication and characterisation low dimensional materials brings new perspectives in condensed matter physics and vast technological opportunities. It also raises new questions on the effects of dimensionality. Our understanding of materials properties relies on the intrinsic quasiparticles of a periodic structure: electrons and phonons. The electron-phonon interaction is thus a fundamental component of condensed matter, and it plays a key role in spectroscopy, electron and heat transport, as well as superconductivity. It is discussed from a modelling and simulation perspective, with a focus on the consequences of reduced dimensions.  Mostly 2D and 1D systems are considered, such that the crystal retains some degree of periodicity. Various effects are discussed, from the modification of the joint density of states to more fundamental changes in the nature and behaviour of the electron-phonon interaction itself. Phonons with atomic displacements in the non-periodic direction are obviously specific to low dimensional systems. Because they involve long-range Coulomb interactions, polar phonons are also strongly modified, both in their dispersion (LO-TO splitting) and their coupling to electrons (Fröhlich interaction). A powerful feature of low-dimensional materials is the ability to use the available space in the non-periodic direction to place other materials of device components that will tune the electron-phonon properties of the system. For example, as routinely done in experiments, a gate can be placed around 2D materials to induce large variations in the carrier density. It is then essential to understand the consequences of this electrostatic doping on the electron-phonon interaction. Finally, the emergence remote interactions between electrons and phonons in different components of van der Waals heterostructures will be discussed.

For 3D crystals, the longitudinal formalism of time-dependent density functional theory can be used to calculate the absorption spectrum, which is the response to a transverse field. It relies on (i) the Erhenreich result that the transverse-transverse contraction of the macroscopic dielectric tensor is equal to the longitudinal-longitudinal one in the optical limit [1], and (ii) the so-called Adler and Wiser formula [2] that relates the longitudinal-longitudinal contraction of the macroscopic dielectric tensor to the macroscopic average of the inverse dielectric function $\varepsilon^{-1}_{00}(\mathbf{q},\omega)= 1 + \frac{4\pi}{|\mathbf{q}|^2} \chi_{00} (\mathbf{q},\omega)$ in the optical limit, where $\chi$ is the polarizability. Powerful reciprocal space codes have been developed within this framework. For isolated nano-objects, this periodic formalism has been first used within a supercell approach to isolate the object from its replicas. Beyond the increase of the size of calculation, it has been shown that the macroscopic average leads to the effective medium theory with vacuum [3]. Cutoff potentials [4] have been proposed to solve the problem of the increasing size of the matrices. They still present a vacuum dependence and prevent to access to the perturbation parallel to the cutoff direction. Finally, a scheme called Selected-G and the slab potential overcome these drawbacks for 2D objects [5]. It is equivalent to a mixed space approach, where the in-plane directions are described in reciprocal space and the out-of-plane one in real space. In this talk, at the light of the classical electromagnetism like the Lorentz oscillators model and the Airy formula for the reflectance and the transmittance of an electromagnetic field, the relationship between the anisotropic response function, and quantities like the ratio between the total and external potentials and the optical response will be examined. In particular, we will show that the Adler and Wiser formula cannot apply anymore for a 2D object. For the in-plane component, it is a consequence of the reduced screening and we provide a new expression to calculate the macroscopic dielectric function. For the out-of plane, it comes from the difficulty to define the thickness of the object [6,7]. Calculting the response function to the total macroscopic potential, we show that to properly account for the properties of a 2D object, the interfaces must be included in the thickness, and that the response function behaves like a linear combination of the absorption and the plasmon spectra, exhibiting the same features as the reflectance or the transmittance of an electromagnetic field impiging an ultra thin layer [6,8].

[1] H. Ehrenreich, The Optical Properties of Solids (Academic, New York, 1965), p. 106.
[2] S. L. Adler, Phys. Rev. 126, 413 (1962) ; N. Wiser, Phys. Rev. 129, 62 (1963).
[3] D. Aspnes, Thin Solid Films 89, 249 (1982).
[4] C. A. Rozzi, D. Varsano, A. Marini, E. K. U. Gross, and A. Rubio, Phys. Rev. B 73, 205119 (2006) ; S. Ismail-Beigi, Phys. Rev. B 73, 233103 (2006).
[5] N. Tancogne-Dejean, Ch. Giorgetti and V. Véniard, Phys. Rev. B 92, 245308 (2015) ; C. Giorgetti, I. Iagupov, and V. Véniard, Phys. Rev. B 101, 035431 (2020).
[6] Stefano Mazzei, Second Harmonic Generation from silicon surfaces functionalized with DNA nucleobases : An ab initio description, Ph.D. thesis, Ecole polytechnique, 2021, https ://etsf.polytechnique.fr/system/files/105736_MAZZEI_2021_archivage-2b_ETSF.pdf.
[7] S. Mazzei and C. Giorgetti Phys. Rev. B 106, 035431 (2022).
[8] S. Mazzei and C. Giorgetti Phys. Rev. B 107, 165412 (2023).

In this talk I will give a general overview on theoretical and numerical approaches to ultrafast processes in molecules aiming to describe photochemical reactions. The focus will be put on the dynamical aspects of the problem, from the quantum to the quantum-classical theories at the basis of the most commonly used algorithms for excited-state molecular dynamics. I will present some applications of the methods from model systems to isolated molecules.

In this talk, I will present an overview of error estimation techniques for the planewave discretization error  in Density Functional Theory (DFT), based on a posteriori error estimation techiques. I will start by comparing different error bounds for linear eigenvalue problems, and then turn to nonlinear eigenvalue problems, such as the ones appearing in DFT. I will also show how errors on quantities of interest such as forces can be efficiently estimated.

In this presentation, we explore the utilization of supercomputers to design new functional materials with a focus on energy applications. The combination of high throughput techniques and rapidly advancing supercomputers enables the automatic screening of vast numbers of hypothetical materials, providing solutions to current technological challenges. Moreover, the integration of machine learning methods with density-functional theory offers a powerful approach to accelerate materials discovery. We summarize our recent efforts in the discovery, characterization, and understanding of inorganic compounds using these innovative approaches, with a specific emphasis on materials for photovoltaics. While characterizing the electronic properties of crystalline bulk materials is crucial, it may not be sufficient when considering electronic devices. Interfaces, such as those found in transistors, light-emitting diodes, and solar cells, play a pivotal role in exploiting quantum processes involving electrons in tailored multilayers. The ability to shape potential gradients at interfaces opens up opportunities for electron manipulation and the development of new functionalities. However, designing interfaces and gaining a deep understanding of their properties present challenges that exceed the current state of the art. We discuss recent advancements in this direction.

X-ray photoelectron spectroscopy (XPS) measures electron removal energies, providing direct access to core and valence electron binding energies, hence probing the electronic structure. In addition, it also provides informations on the chemical composition and type of bonding, which could be inferred from the shift of the binding energy (also known as chemical shift). In this talk we will present a benchmark of ab initio many-body COHSEX and GW approximations, with respect to Hartree-Fock (HF) and density-functional theory (DFT), on the complete electron binding energies of noble gas atoms (He-Rn) which spans 100 keV. We will also present a study of the chemical shift of the carbon 1s electron in a set of molecules, providing insights into the physical origin of the chemical shift. Our results demonstrate that GW achieves an accuracy within 1.2% in XPS binding energies, by systematically restoring the underestimation from density-functional theory (DFT, error of 14%) or the overestimation from Hartree-Fock (HF, error of 4.7%). Such results also imply the correlations of d electrons are very well described by GW.