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Quantum-Electrodynamical Time-Dependent Density Functional Theory. I. A Gaussian Atomic Basis Implementation

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TLDR
In this paper, the authors proposed an implementation that uses dimensionless amplitudes for describing the photonic contributions to quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) electron-photon eigenstates.
Abstract
Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and coworkers, we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron-photon eigenstates. The leads to a symmetric QED-TDDFT coupling matrix, which is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating wave approximation, and the Tamm-Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energy and composition of polaritons associated with lower-energy electronic states.

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Understanding polaritonic chemistry from ab initio quantum electrodynamics

TL;DR: In this paper , the theoretical foundations and first principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a specific focus on polaritonic chemistry, are presented.
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Enhanced Diastereocontrol via Strong Light-Matter Interactions in an Optical Cavity.

TL;DR: In this article , a cavity quantum electrodynamics (QED) generalization of time-dependent density functional theory was developed and demonstrated computationally that strong light-matter coupling can alter the de of the chiral group-directed photoisomerization of BINOL.
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Semiclassical Real-Time Nuclear-Electronic Orbital Dynamics for Molecular Polaritons: Unified Theory of Electronic and Vibrational Strong Couplings.

TL;DR: In this article , a semiclassical approach is developed for describing molecular polaritons by self-consistently propagating the real-time dynamics of classical cavity modes and a quantum molecular subsystem described by the nuclear-electronic orbital (NEO) method, where electrons and specified nuclei are treated quantum mechanically on the same level.
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Real-space, real-time approach to quantum-electrodynamical time-dependent density functional theory.

TL;DR: In this article , the quantum-electrodynamical time-dependent density functional theory equations are solved by time propagating the wave function on a tensor product of a Fock-space and real-space grid.

Reduced-density-matrix-based ab initio cavity quantum electrodynamics

TL;DR: In this article , a reduced-density-matrix (RDM)-based approach to ab initio cavity quantum electrodynamics is developed, where the expectation value of the Pauli-Fierz Hamiltonian is expressed in terms of one-and two-body electronic and photonic RDMs, and the elements of these RDMs are optimized directly in polynomial time by semidefinite programming techniques, without knowledge of the full wave function.
References
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Journal ArticleDOI

Generalized Gradient Approximation Made Simple

TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.
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Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density

TL;DR: Numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, show that density-functional formulas for the correlation energy and correlation potential give correlation energies within a few percent.
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Density-functional exchange-energy approximation with correct asymptotic behavior.

TL;DR: This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
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A New Mixing of Hartree-Fock and Local Density-Functional Theories

TL;DR: In this article, a new coupling of Hartree-Fock theory with local density functional theory was proposed to improve the predictive power of the Hartree−Fock model for molecular bonding, and the results of tests on atomization energies, ionization potentials, and proton affinities were reported.
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Toward reliable density functional methods without adjustable parameters: The PBE0 model

TL;DR: In this paper, an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so-called PBE generalized gradient functional with a predefined amount of exact exchange is presented.
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