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A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules. [ABSTRACT FROM AUTHOR]

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. Applications for molecules in cavities show the accuracy of the approach. Examples include the coupling strength and light frequency dependence of the energies, wave functions, optical absorption spectra, and Rabi splitting magnitudes in cavities, as well as a description of high harmonic generation in cavities. [ABSTRACT FROM AUTHOR]

Deformed explicitly correlated Gaussian (DECG) basis functions are introduced, and their matrix elements are calculated. All matrix elements can be calculated analytically in a closed form, except the Coulomb one, which has to be approximated by a Gaussian expansion. The DECG basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole self-interaction term in the Pauli–Fierz Hamiltonian. Examples are presented showing the accuracy and necessity of deformed Gaussian basis functions to accurately solve light–matter coupled systems in cavity QED. [ABSTRACT FROM AUTHOR]

A dual time propagation approach is introduced to describe electron scattering and ionization. The space is divided into two regions, a central region with a full time-dependent Hamiltonian and an outer region where the kinetic operator and the laser field dominate. The two regions are connected by a source term. Time-dependent density functional theory calculations of wave packet scattering on molecules and photoelectron spectrum due to circularly polarized laser are presented to illustrate the efficiency and applicability of the approach. [ABSTRACT FROM AUTHOR]

Erratum: "Real-space, real-time approach to quantum-electrodynamical time-dependent density functional theory" [J. Chem. Phys. In Eq. (2.22), a term, HT ht , is missing. [Extracted from the article]