The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the alpha and beta electrons to achieve the two-electron excited states of minimal basis H(2) and HeH(+) [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H(2), HeH(+), lithium hydride, ethylene, and butadiene.

Intense laser field dissociations of the acetylene dication C(2)H(2)(2+) are studied by an ab initio Ehrenfest dynamics method with time-dependent density functional theory. Various field frequencies (9.5 to approximately 13.6 eV) and field directions are applied to a Boltzmann ensemble of C(2)H(2)(2+) molecules. With the laser field perpendicular to the molecular axis, four fragmentation channels are observed at high frequency with no dominant pathway. With the field parallel to the molecular axis, fragmentations occur at all frequencies and the amount of C-H bond breakage increases with laser frequency. Selective dissociation patterns are observed with low-frequency fields parallel to the molecular axis. A systematic analysis of excited-state potential energy surfaces is used to rationalize the simulation results.

We demonstrate using symmetry adapted cluster theory with configuration$\backslash$ninteraction \(SAC-CI)\ that charging of small \PbSe\ nanocrystals$\backslash$n\(NCs)ġreatly modifies their electronic states and optical excitations.$\backslash$nConduction and valence band transitions that are not available in$\backslash$nneutral \NCs\ dominate low energy electronic excitations and show$\backslash$nweak optical activity. At higher energies these transitions mix with$\backslash$nboth single excitons \(SEs)\ and multiple excitons \(MEs)\ associated$\backslash$nwith transitions across the band-gap. As a result, both \SEs\ and$\backslash$n\MEs\ are significantly blue-shifted, and \MEġeneration is drastically$\backslash$nhampered. The overall contribution of \MEs\ to the electronic excitations$\backslash$nof the charged \NCs\ is small even at very high energies. The calculations$\backslash$nsupport the recent view that the observed strong dependence of the$\backslash$n\ME\ yields on the experimental conditions is likely due to the effects$\backslash$nof \NC\ charging.

Linear response time-dependent hybrid density functional theory has been applied for the first time to describe optical transitions characteristic of Co2+- and Mn2+-doped ZnO quantum dots (QDs) with sizes up to 300 atoms (\~1.8 nm diam) and to investigate QD size effects on the absorption spectra. Particular attention is given to charge-transfer (CT or “photoionization”) excited states. For both dopants, CT transitions are calculated to appear at sub-band-gap energies and extend into the ZnO excitonic region. CT transitions involving excitation of dopant d electrons to the ZnO conduction band occur lowest in energy, and additional CT transitions corresponding to promotion of ZnO valence band electrons to the dopant d orbitals are found at higher energies, consistent with experimental results. The CT energies are found to depend on the QD diameter. Analysis of excited-state electron and hole density distributions shows that, for both CT types, the electron and hole are localized to some extent around the impurity ion, which results in “heavier” photogenerated carriers than predicted from simple effective mass considerations. In addition to CT transitions, the Co2+-doped ZnO QDs also exhibit characteristic d-d excitations whose experimental energies are reproduced well and do not depend on the size of the QD.

Real-time time-dependent Hartree-Fock (TDHF)/density functional theory (TDDFT) has been gaining in popularity because of its ability to treat phenomena beyond the linear response and because it has the potential to be more computationally powerful than frequency domain TDHF/TDDFT. Within real-time TDHF/TDDFT, we present a method that gives the excited state triplet energies starting from a singlet ground state. Using a spin-dependent field, we break the spin-symmetry of the R and ? density matrices, which incorporates a triplet contribution into the superposition state. The R electron density follows the applied field, and the ? electron density responds to the perturbation from the changing R electron density. We examine the individual R/? responses during the electron density propagation. Singlet-triplet transitions appear as ‘dark’ states: they are present in the R/? responses but are absent from the total electron density response

Four different numerical algorithms suitable for a linear scaling implementation of time-dependent Hartree-Fock and Kohn-Sham self-consistent field theories are examined. We compare the performance of modified Lanczos, Arooldi, Davidson, and Rayleigh quotient iterative procedures to solve the random-phase approximation (RPA) (non-Hermitian) and Tamm-Dancoff approximation (TDA) (Hermitian) eigenvalue equations in the molecular orbital-free framework. Semiempirical Hamiltonian models are used to numerically benchmark algorithms for the computation of excited states of realistic molecular systems (conjugated polymers and carbon nanotubes). Convergence behavior and stability are tested with respect to a numerical noise imposed to simulate linear scaling conditions. The results single out the most suitable procedures for linear scaling large-scale time-dependent perturbation theory calculations of electronic excitations.

We demonstrate using symmetry adapted cluster theory with configuration$\backslash$ninteraction \(SAC-CI)\ that charging of small \PbSe\ nanocrystals$\backslash$n\(NCs)greatly modifies their electronic states and optical excitations.$\backslash$nConduction and valence band transitions that are not available in$\backslash$nneutral \NCs\ dominate low energy electronic excitations and show$\backslash$nweak optical activity. At higher energies these transitions mix with$\backslash$nboth single excitons \(SEs)\ and multiple excitons \(MEs)\ associated$\backslash$nwith transitions across the band-gap. As a result, both \SEs\ and$\backslash$n\MEs\ are significantly blue-shifted, and \MEgeneration is drastically$\backslash$nhampered. The overall contribution of \MEs\ to the electronic excitations$\backslash$nof the charged \NCs\ is small even at very high energies. The calculations$\backslash$nsupport the recent view that the observed strong dependence of the$\backslash$n\ME\ yields on the experimental conditions is likely due to the effects$\backslash$nof \NC\ charging.

Real-time, time-dependent density functional theory (RT-TDDFT) is used for the evaluation of the frequency dependence of the polarizability and hyperpolarizability of molecules intended for application in electro-optic devices. These first-principles computational methods are powerful but costly. Significantly easier calculations based on a simplified version of second-order time-dependent perturbation theory, the ‘‘two-state model’’ (TSM), are here used to provide another estimate of the frequency dependence. Furthermore, the TSM calculations can be done in the presence of a dielectric reaction field (the polarizable continuum model method) to provide estimates of the solvent dependent properties in addition to the frequency-dependent properties. Here we use RT-TDDFT to assess the accuracy of the frequency dependence of the TS, and a ground-state finite field calculation to assess the effect of additional states on the static hyperpolarizability. Both frequency and dielectric responses are important for evaluation of the suitability of molecules in nonlinear optical applications.

Multielectron excited states have become a hot topic in many cutting-edge research fields, such as the photophysics of polyenes and in the possibility of multiexciton generation in quantum dots for the purpose of increasing solar cell efficiency. However, obtaining multielectron excited states has been a major obstacle as it is often done with multiconfigurational methods, which involve formidable computational cost for large systems. Although they are computationally much cheaper than multiconfigurational wave function based methods, linear response adiabatic time-dependent Hartree-Fock (TDHF) and density functional theory (TDDFT) are generally considered incapable of obtaining multielectron excited states. We have developed a real-time TDHF and adiabatic TDDFT approach that is beyond the perturbative regime. We show that TDHF/TDDFT is able to simultaneously excite two electrons from the ground state to the doubly excited state and that the real-time TDHF/TDDFT implicitly includes double excitation within a superposition state. We also present a multireference linear response theory to show that the real-time electron density response corresponds to a superposition of perturbative linear responses of the S(0) and S(2) states. As a result, the energy of the two-electron doubly excited state can be obtained with several different approaches. This is done within the adiabatic approximation of TDDFT, a realm in which the doubly excited state has been deemed missing. We report results on simple two-electron systems, including the energies and dipole moments for the two-electron excited states of H(2) and HeH(+). These results are compared to those obtained with the full configuration interaction method.