Density Functional Theory for Electronic Excited States

Abstract

This chapter provides a basic introduction to excited-state extensions of density functional theory (DFT), including time-dependent (TD-)DFT in both its linear-response and its explicitly time-dependent formulations. As applied to the Kohn-Sham DFT ground state, linear-response theory affords an eigenvalue-type problem for the excitation energies in a basis of singly-excited Slater determinants, and is widely known simply as "TDDFT" despite its frequency-domain formulation. This form of TDDFT is the mostly widely-used quantum-chemical method for excited states, due to a favorable combination of low cost and reasonable accuracy. The chapter surveys the accuracy of linear-response TDDFT, which is generally more sensitive to the details of the exchange-correlation functional as compared to ground-state DFT, and also describes some known systemic problems exhibited by this approach. Some of those problems can be corrected on a case-by-case basis using orbital-optimized, excited-state self-consistent field (SCF) calculations, in what is known as excited-state Kohn-Sham theory or a "Delta-SCF" procedure, a class of methods that includes restricted open-shell Kohn-Sham theory. Recent successes of these approaches are highlighted, including double excitations and core-level excitations. Finally, explicitly time-dependent (or "real-time") TDDFT involves propagation of the molecular orbitals in time following an external perturbation, according to the Kohn-Sham analogue of the time-dependent Schroedinger equation. The time-dependent approach has been used to model strong-field electron dynamics, and in the weak-field limit it provides a route to broadband spectra based on the time evolution of the dipole moment function. This is useful for describing high-energy excitations (as in x-ray spectroscopy) and in systems where the density of states is high, as demonstrated by a few examples.

References in corpus (50)

• Development of Novel Density Functionals for Thermochemical Kinetics
• The Magnus expansion and some of its applications
• Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections
• Progress in Time-Dependent Density-Functional Theory
• Time-dependent density functional theory: Past, present, and future
• Random-phase approximation and its applications in computational chemistry and materials science
• A density functional theory with correct long-range asymptotic behavior
• The Ground State Correlation Energy of the Random Phase Approximation from a Ring Coupled Cluster Doubles Approach
• Quasiparticle spectra from a non-empirical optimally-tuned range-separated hybrid density functional
• Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction
• Time-dependent density functional theory for strong electromagnetic fields in crystalline solids
• Saddles in the energy landscape probed by supercooled liquids
• Perspectives on double-excitations in TDDFT
• Orbital Optimized Density Functional Theory for Electronic Excited States
• Dielectric continuum methods for quantum chemistry
• Excited state orbital optimization via minimizing the square of the gradient: General approach and application to singly and doubly excited states via density functional theory
• Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
• Reference Energies for Double Excitations
• Kohn-Sham decomposition in real-time time-dependent density-functional theory: An efficient tool for analyzing plasmonic excitations
• Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy
• Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining sub eV Error from a Restricted Open-Shell Kohn-Sham Approach
• Troubleshooting Time-Dependent Density-Functional Theory for Photochemical Applications: Oxirane
• Charge-Transfer in Time-Dependent Density Functional Theory
• Application of time-dependent density functional theory to optical activity
• Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory
• Long-range corrected hybrid meta-generalized-gradient approximations with dispersion corrections
• Half or full core-hole in density functional theory X-ray absorption spectrum calculations of water?
• Accurate X-Ray Absorption Predictions for Transition Metal Oxides: An Advanced Self-Consistent-Field Approach Inspired by Many-Body Perturbation Theory
• Tuning Range-Separated Density Functional Theory for Photocatalytic Water Splitting Systems
• $\sigma$-SCF: A Direct Energy-targeting Method To Mean-field Excited States
• Evaluating 0-0 Energies with Theoretical Tools: a Short Review
• Quasi-saddles as relevant points of the potential energy surface in the dynamics of supercooled liquids
• Existence, Uniqueness, and Construction of the Density-Potential Mapping in Time-Dependent Density-Functional Theory
• Relativistic Orbital Optimized Density Functional Theory for Accurate Core-Level Spectroscopy
• Gaussian continuum basis functions for calculating high-harmonic generation spectra
• Efficient Simulation of Near-Edge X-ray Absorption Fine Structure (NEXAFS) in Density-Functional Theory: Comparison of Core-Level Constraining Approaches
• Calculation of photoelectron spectra within the time-dependent configuration interaction singles scheme
• On the optimal basis set for electron dynamics in strong laser fields: The case of molecular ion H${}_2^{+}$
• Density-Dependent Onset of the Long-Range Exchange: A Key to Donor-Acceptor Properties
• Quantifying the error of the core-valence separation approximation
• Beyond the Coulson-Fischer point: Characterizing single excitation CI and TDDFT for excited states in single bond dissociations
• Random-phase approximation excitation energies from approximate equation-of-motion ring coupled-cluster doubles
• Comment on ``Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids'' [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]
• Studies of Spuriously Shifting Resonances in Time-dependent Density Functional Theory
• Dynamical Kernels for Optical Excitations
• Importance of local exact exchange potential in hybrid functionals for accurate excited states
• Self-Adaptive Real-Time Time-Dependent Density Functional Theory for X-ray Absorptions
• Taming Convergence in the Determinant Approach for X-Ray Excitation Spectra
• Predicting Core Electron Binding Energies in Elements of the First Transition Series Using the $\Delta$-Self-Consistent-Field Method
• Revisiting the performance of time-dependent density functional theory for electronic excitations: Assessment of 43 popular and recently developed functionals from rungs one to four

Cited by in corpus (2)

• On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)
• Controlling $⟨{\hat{S}}^2⟩$ in Broken-symmetry Density Functional Theory Calculations via Constrained Optimization