Déterminant de Slater | EPFL Graph Search

En mécanique quantique le déterminant de Slater d'ordre N est une expression de la fonction d'onde d'un système de N électrons (ou autres fermions) identiques. Il est exprimé sous la forme d'un déterminant constitué avec les N spinorbitales \phi_{k_i} (\mathbf{\xi}) individuelles des différents fermions. Cette écriture permet à la fonction d'onde du système de satisfaire la condition d'antisymétrie lors de l'échange de deux fermions et en vertu du principe de Pauli. En effet, un déterminant change de signe lors de la permutation de deux indices quelconques de ses colonnes ou lignes. Il est également nul si deux lignes ou colonnes sont identiques, donc physiquement si deux fermions sont dans le même état, conformément au principe de Pauli. Du fait de l'utilisation de fonctions d'onde monofermioniques, un déterminant de Slater ne correspond à la fonction d'onde du système que si les interactions entre fermions peuvent être considérées comme négligeables (modèle à fermi

Fermionic wave functions from neural-network constrained hidden states

Giuseppe Carleo

We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving “hidden” additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint that is optimized, together with the single-particle orbitals, using a neural network parameterization. This construction draws inspiration from the success of hidden-particle representations but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proved to be universal. We apply this construction to the ground-state properties of the Hubbard model on the square lattice, achieving levels of accuracy that are competitive with those of state-of-the-art variational methods.

2022

Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction

Jérôme Florian Gonthier, Ewa Maria Pastorczak, Antonio Prlj

We introduce an intramolecular energy decomposition scheme for analyzing non-covalent interactions within molecules in the spirit of symmetry-adapted perturbation theory (SAPT). The proposed intra-SAPT approach is based upon the Chemical Hamiltonian of Mayer [Int. J. Quantum Chem. 23(2), 341-363 (1983)] and the recently introduced zeroth-order wavefunction [ J. F. Gonthier and C. Corminboeuf, J. Chem. Phys. 140(15), 154107 (2014)]. The scheme decomposes the interaction energy between weakly bound fragments located within the same molecule into physically meaningful components, i.e., electrostatic-exchange, induction, and dispersion. Here, we discuss the key steps of the approach and demonstrate that a single-determinant wavefunction can already deliver a detailed and insightful description of a wide range of intramolecular non-covalent phenomena such as hydrogen bonds, dihydrogen contacts, and pi - pi stacking interactions. Intra-SAPT is also used to shed the light on competing intra-and intermolecular interactions.

American Institute of Physics2015

Quantifying Electronic Phenomena in Organic Chromophores

Antonio Prlj

Challenging ground and excited state problems in the chemistry of common organic chromophores are investigated with state-of-the-art quantum chemical methods. We present a comprehensive excited state molecular dynamics analysis of (a) fundamental building blocks in organic electronics (thiophene and its derivatives), (b) aggregation-induced emission systems (tetraphenylethylene), and (c) organic fluorophores used for imaging and sensing applications (BODIPY and its derivatives). We identify the efficient excited state deactivation pathways which are essential to understanding the photochemical stability and emissive properties of these compounds. The internal conversion mechanisms of theoretically challenging thiophene and bithiophene molecules are investigated with a trajectory surface hopping approach utilizing reliable electronic structure methods. We gain new insights into the photochemistry and photophysics of these systems, including a new mechanism in thiophene excited state decay and the increased photostability of bithiophene, thereby complementing earlier theoretical and experimental literature. The origin of the non-emissive behavior of tetraphenylethylene in the gas phase is explained by identifying energetically accessible conical intersections which promote radiationless decay. It is implied that restricted access to the conical intersection induces strong emission upon aggregation - a phenomenon that attracted significant research attention recently. Finally, the concept of conical intersection accessibility is utilized to explain the fluorescence quenching in certain meso-substituted BODIPY derivatives. We deliver a full mechanistic picture of the nonradiative decay of these molecules, invoking the role of excited state charge transfer and weak intramolecular interactions. Understanding the failures of quantum chemical electronic structure methods is crucial for subsequent improvements of commonly applied theoretical approximations. To elucidate the origins behind the unbalanced description of the low-lying pipi* excited states of heteroaromatic molecules (including thiophene and its derivatives, or in general fused heteroaromatics), we employ a range of quantum chemical approaches, from more approximate time-dependent density functional theory (TDDFT) to highly accurate wavefunction-based methods. The drawbacks of standard TDDFT were ascribed to the ubiquitous adiabatic approximation, rather than different functional approximations. On the other hand, the performance of wavefunction-based methods is found to be largely dependent on the treatment of electron correlation, which is key for a balanced description of excited states with disparate electronic character. Non-covalent molecular interactions are at the origin of many chemical and physical phenomena. While quantifying intermolecular interactions has become a routine task, intramolecular interactions are still considered particularly difficult to treat by theoretical methods. Here, we develop an original wavefuction-based method for quantifying intermolecular and intramolecular interactions on equal footing. The method, intra-SAPT, makes use of a single Slater determinant wavefunction, subject to perturbational corrections. The scheme decomposes interaction energies into physically meaningful components: electrostatics-exchange, induction and dispersion.

EPFL2017

Quantifying Electronic Phenomena in Organic Chromophores

Antonio Prlj

EPFL2017