In recent years, the development and application of real-time time-dependent density functional theory (RT-TDDFT) has gained momentum as a computationally efficient method for modeling electron dynamics and properties that require going beyond a linear response of the electron density. However, the RT-TDDFT method within the adiabatic approximation can unphysically shift absorption peaks throughout the electron dynamics. Here, we investigate the origin of these time-dependent resonances observed in RT-TDDFT spectra. Using both exact exchange and hybrid exchange-correlation approximate functionals, adiabatic RT-TDDFT gives time-dependent absorption spectra in which the peaks shift in energy as populations of the excited states fluctuate, while exact wave function methods yield peaks that are constant in energy but vary in intensity. The magnitude of the RT-TDDFT peak shift depends on the frequency and intensity of the applied field, in line with previous studies, but it oscillates as a function of time-dependent molecular orbital populations, consistent with a time-dependent superposition electron density. For the first time, we provide a rationale for the direction and magnitude of the time-dependent peak shifts based on the molecular electronic structure. For three small molecules, H2, HeH+, and LiH, we give contrasting examples of peak-shifting to both higher and lower energies. The shifting is explained as coupled one-electron transitions to a higher and a lower lying state. Whether the peak shifts to higher or lower energies depends on the relative energetics of these one-electron transitions.

Organic electro-optic (OEO) materials integrated into silicon–organic hybrid devices afford significant improvements in size, weight, power, and bandwidth performance of integrated electronic/photonic systems critical for current and next generation telecommunication, computer, sensor, transportation, and defense technologies. Improvement in molecular first hyperpolarizability (β), and in turn electro-optic activity, is crucial to optimizing device performance. Common hybrid density functional theory (DFT) methods, while attractive due to their computational scaling, often perform poorly for optical properties in systems with substantial intramolecular charge-transfer character, such as OEO chromophores. This study evaluates the utility of the long-range corrected (LC) DFT methods for computation of the molecular second-order nonlinear optical response. We compare calculated results for a 14-molecule benchmark set of OEO chromophores with the corresponding experimentally measured β and one-photon absorption energy, λmax. We analyze the distance dependence of the fraction of exact exchange in LC-DFT methods for accurately computing these properties for OEO chromophores. We also examine systematic tuning of the range-separation parameter to enforce Koopmans’/ionization potential theorem. This tuning method improves prediction of excitation energies but is not reliable for predicting the hyperpolarizabilities of larger chromophores since the tuning parameter value can be too small, leading to instabilities in the computation of βHRS. Additionally, we find that the size dependence of the optimal tuning parameter for the ionization potential has the opposite size dependence of optimal tuning parameter for best agreement with the experimental λmax, suggesting the tuning for the ionization potential is unreliable for extended conjugated systems.

Recent advances in algorithms and computational hardware have enabled the calculation of excited states with time-dependent density functional theory (TDDFT) for large systems of O(1000) atoms. Unfortunately, the aqueous charge transfer problem in TDDFT (whereby many spuriously low-lying charge transfer excited states are predicted) seems to become more severe as the system size is increased. In this work, we concentrate on the common case where a chromophore is embedded in aqueous solvent. We examine the role of exchange-correlation functionals, basis set effects, ground state geometries, and the treatment of the external environment in order to assess the root cause of this problem. We conclude that the problem rests largely on water molecules at the boundary of a finite cluster model, i.e., "edge waters." We also demonstrate how the TDDFT problem can be related directly to ground state problems. These findings demand caution in the commonly employed strategy that rests on "snapshot" cutout geometries taken from ground state dynamics with molecular mechanics. We also find that the problem is largely ameliorated when the range-separated hybrid functional LC-$ømega$PBEh is used.

Nanocarbon-based photovoltaics offer a promising new architecture for the next generation of solar cells. We demonstrate that a key factor determining the efficiency of single-walled carbon nanotube (SWCNT)/fullerene devices is the chirality of the SWCNT. This is shown via current density vs voltage measurements of nanocarbon devices prepared with (9,7), (7,6) and (6,5) SWCNTs, as well as density-functional theory (DFT) density of states calculations of C60 adsorbed onto the corresponding SWCNTs. The trends in efficiency are rationalized in terms of the relative energies of the fullerene and SWCNT conduction band energy levels.

We describe a new interface of the GPU parallelized TeraChem electronic structure package and the Amber molecular dynamics package for quantum mechanical (QM) and mixed QM and molecular mechanical (MM) molecular dynamics simulations. This QM/MM interface is used for computation of the absorption spectra of the photoactive yellow protein (PYP) chromophore in vacuum, aqueous solution, and protein environments. The computed excitation energies of PYP require a very large QM region (hundreds of atoms) covalently bonded to the chromophore in order to achieve agreement with calculations that treat the entire protein quantum mechanically. We also show that 40 or more surrounding water molecules must be included in the QM region in order to obtain converged excitation energies of the solvated PYP chromophore. These results indicate that large QM regions (with hundreds of atoms) are a necessity in QM/MM calculations.

Nonperturbative electronic dynamics using the time-dependent Hartree-Fock (TDHF) and time-dependent Kohn-Sham (TDKS) theories with the adiabatic approximation is a powerful tool in obtaining insights into the interaction between a many-electron system and an external electromagnetic field. In practical applications of TDHF/TDKS using a truncated basis set, the electronic dynamics and molecular properties become gauge-dependent. Numerical simulations are carried out in the length gauge and velocity gauge to verify the extent of gauge-dependence using incomplete basis sets. Electronic dynamics of two many-electron systems, a helium atom and a carbon monoxide molecule in high-intensity linearly polarized radiation fields are performed using the TDHF and TDKS with two selected adiabatic exchange-correlation (xc) functionals. The time evolution of the expectation values of the dipole moment and harmonic spectra are calculated in the two gauges, and the basis set dependence on the gauge-invariance of these properties is investigated.

Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response Tamm–Dancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results).