Time‐dependent density functional theory study on direction‐dependent electron and hole transfer processes in molecular systems

We report on real‐time time‐dependent density functional theory calculations on direction‐dependent electron and hole transfer processes in molecular systems. As a model system, we focus on α‐sulfur. It is shown that time scale of the electron transfer process from a negatively charged S₈ molecule to a neighboring neutral monomer is comparable to that of a strong infrared‐active molecular vibrations of the dimer with one negatively charged monomer. This results in a strong coupling between the electrons and the nuclei motion which eventually leads to S₈ ring opening before the electron transfer process is completed. The open‐ring structure is found to be stable. The similar infrared‐active peak in the case of hole transfer, however, is shown to be very weak and hence no significant scattering by the nuclei is possible. The presented approach to study the charge transfer processes in sulfur has direct applications in the increasingly growing research field of charge transport in molecular systems. © 2017 Wiley Periodicals, Inc.     

Time‐dependent local‐density approximation in real time: Application to conjugated molecules

The time‐dependent local‐density approximation (TDLDA) is applied to the optical response of conjugated carbon molecules in the energy range of 0–30 eV, with calculations given for carbon chains, polyenes, retinal, benzene, and C₆₀. The major feature of the spectra, the collective π–π* transition, is seen at energies ranging from below 2 to 7 eV and is reproduced by the theory to a few tenths of an electron volt with a good account of systematic trends. However, there is some indication that TDLDA predicts too much fragmentation of the strength function in large molecules. Transition strengths are reproduced with a typical accuracy of 20%. The theory also predicts a broad absorption peak in the range of 15–25 eV, and this feature agrees with experiment in the one case where quantitative data is available (benzene). ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 55–66, 1999     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.     

Charge transfer excitations in TDDFT: A ghost‐hunter index

This work presents a new index, M _AC, enabling the on‐the‐fly detection of ghost charge transfer (CT) states, a major problem in time‐dependent density‐functional theory calculations. This computationally inexpensive index, derived as a modification of the Mulliken estimation of transition energy for CT excitations, relies on two basic ingredients: an effective CT distance, computed using our density‐based index (D _CT), and an orbital weighted estimation of the Ionization Potential and Electron Affinity. Some model systems, representative of both intermolecular and intramolecular CT excitations, were chosen as test cases. The robustness of our approach was verified by analyzing the behavior of functionals belonging to different classes (GGA, global hybrids and range separated hybrids). The results obtained show that ghost states are correctly spotted, also in the delicate case of intramolecular excitations displaying substantial donor‐bridge‐acceptor delocalization, in a regime for which the standard Mulliken formulation attends its limits. © 2017 Wiley Periodicals, Inc.     

Semiconductor nanocrystals possessing broadly size‐ and facet‐dependent optical properties

Cu₂O cubes, octahedra, and rhombic dodecahedra have been shown to exhibit continuous light absorption and emission band shifts with increasing particle sizes from 10 nm to sub‐microcrystals. They also possess clear facet‐dependent optical properties. Ag₃PO₄, Ag₂O, SrTiO₃, and CeO₂ crystals show similar optical size and facet effects. Thus, spectral shifts over a broad size range far beyond the quantum‐size regime should be generally observable in many semiconductor materials. Facet‐dependent optical properties of a semiconductor can be understood to arise from the presence of an ultrathin surface layer with subtle bond and orbital level variations for different crystal faces. Although these optical features seem unexpected, they should be the general behaviors of semiconductor crystals. As more examples of these optical effects are available, we will find that these intrinsic properties of semiconductors have been ignored in the past. Furthermore, if valence and conduction band positions are broadly tunable by particle size, the knowledge should have tremendous impacts on the applications of semiconductors, where band energies are important to efficient interfacial charge transfer.     

Time‐dependent density functional theory study of electronic spectrum property for carbazolyl–pyridinyl alternating copolymers

Three A‐B‐type fluorescent copolymers comprised of alternating carbazolyl and pyridinyl units, poly[(2,7‐(N‐(2‐ethylhexyl)carbazolyl)‐alt‐(3,5‐pyridinyl))](PEHCP‐35), poly[(2,7‐(N‐(2‐ethylhexyl)carbazolyl)‐alt‐(2,6‐pyridinyl))] (PEHCP‐26) and poly[(2,7‐(N‐(2‐ethyl‐hexyl)carbazolyl)‐alt‐(2,5‐pyridinyl))] (PEHCP‐25), are studied by means of the density functional theory (DFT/B3LYP/6‐31G). Based on the optimized geometries, the optical properties are calculated by employing time‐dependent density functional theory (TD‐DFT). The bandgaps and optical properties are saturated quickly in PEHCP‐35 and PEHCP‐26. It is known from experiment that PEHCP‐25 is actually an oligomer with a polymerization degree of 4. So the tetramers of PEHCP‐35, PEHCP‐26, and PEHCP‐25 are adopted to study the electronic and optical properties, and the calculated results are in close agreement with experiment. The calculated bandgaps of copolymers obtained from two ways, i.e., HOMO–LUMO gaps and the lowest excitation energies, decrease in the following order PEHCP‐35 > PEHCP‐26 > PEHCP‐25, the same trend as the data obtained from the edge of the electric band but different from the electrochemically obtained data from experiment (PEHCP‐25 > PEHCP‐26 > PEHCP‐35). The outcomes showed that, when excited, a charge transfer from carbazolyl unit to pyridinyl unit occurs, and the lumophor is mainly carbazolyl units. The UV absorption and emission wavelengths both exhibit bathochromic shifts: PEHCP‐35 < PEHCP‐26 < PEHCP‐25. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Sub‐cycle Dynamics of High Harmonic Generation of Ne Atoms Excited by Attosecond Pulses and Driven by Near‐infrared Laser Fields: A Self‐Interaction‐Free TDDFT Approach

In the framework of the self‐interaction‐free time‐dependent density‐functional theory (TDDFT), we have performed three‐dimensional ab initio calculations of Ne atoms in near‐infrared (NIR) laser fields subject to excitation by a single extreme ultraviolet (XUV) attosecond pulse (SAP). The TDDFT equations are solved accurately and efficiently by means of the time‐dependent generalized pseudo spectral (TDGPS) method. We have explored the transient dynamical behavior of the sub‐cycle high harmonic generation (HHG) for transitions from the excited states to the ground state and found oscillation structures with respect to the time delay between the SAP and NIR fields. We investigate the harmonic emission spectrum from singly excited state 2p3s, 2p4s, 2p3d, 2p5s, 2p4d and 2p6s, 2p5d and the virtual states 2p3p‐, 2p4f‐ and 2p4p+ as the function of time delay. We explore the sub‐cycle Stark shift phenomenon in NIR fields and its influence on the photon emission process. Our analysis reveals several novel features of the sub‐cycle transient HHG dynamics and spectra, the quantum interference pattern between different multiphoton excitation pathways, and we identify the mechanisms responsible for the observed peak splitting in the photon emission spectra.     

Probing Rapidly‐Ionizing Super‐Atom Molecular Orbitals in C60: A Computational and Femtosecond Photoelectron Spectroscopy Study

Super‐atom molecular orbitals (SAMOs) are diffuse hydrogen‐like orbitals defined by the shallow potential at the centre of hollow molecules such as fullerenes. The SAMO excited states differ from the Rydberg states by the significant electronic density present inside the carbon cage. We provide a detailed computational study of SAMO and Rydberg states and an experimental characterization of SAMO excited electronic states for gas‐phase C₆₀ molecules by photoelectron spectroscopy. A large band of 500 excited states was computed using time‐dependent density functional theory. We show that due to their diffuse character, the photoionization widths of the SAMO and Rydberg states are orders of magnitude larger than those of the isoenergetic non‐SAMO excited states. Moreover, in the range of kinetic energies experimentally measured, only the SAMO states photoionize significantly on the timescale of the femtosecond laser experiments. Single photon ionization of the SAMO states dominates the photoelectron spectrum for relatively low laser intensities. The computed photoelectron spectra and photoelectron angular distributions are in good agreement with the experimental results.     

A simple approximation for the Pauli potential yielding self‐consistent electron densities exhibiting proper atomic shell structure

A simple approximation for the Pauli potential for the groundstate of atomic systems is given, which in connection with Hohenberg–Kohn variational procedure yields self‐consistent electron densities exhibiting proper atomic shell structure. © 2015 Wiley Periodicals, Inc.     

Efficient blue‐emitting Ir(III) complexes with phenyl‐methyl‐benzimidazolyl and picolinate ligands: A DFT and time‐dependent DFT study

The series of heteroleptic cyclometalated Ir(III) complexes for organic light‐emitting display application have been investigated theoretically to explore their electronic structures and spectroscopic properties. The geometries, electronic structures, and the lowest‐lying singlet absorptions and triplet emissions of Ir‐(pmb)₃ and theoretically designed models Ir‐(Rpmb)₂pic were investigated with density functional theory (DFT)‐based approaches, where pmb = phenyl‐methyl‐benzimidazolyl, pic = picolinate, and R = H/F. Their structures in the ground and excited states have been optimized at the DFT/B3LYP/LANL2DZ and TDDFT/B3LYP/LANL2DZ levels, and the lowest absorptions and emissions were evaluated at B3LYP and M062X level of theory, respectively. The mobility of holes and electrons were studied computationally based on the Marcus theory. Calculations of ionization potentials were used to evaluate the injection abilities of holes into these complexes. The reasons for the higher electroluminescence efficiency and phosphorescence quantum yields in Ir‐(Rpmb)₂pic than in Ir‐(pmb)₃ have been investigated. The designed moleculars are expected to be highly emissive in pure‐blue region. © 2013 Wiley Periodicals, Inc.     

An open‐source framework for analyzing N‐electron dynamics. II. Hybrid density functional theory/configuration interaction methodology

In this contribution, we extend our framework for analyzing and visualizing correlated many‐electron dynamics to non‐variational, highly scalable electronic structure method. Specifically, an explicitly time‐dependent electronic wave packet is written as a linear combination of N‐electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time‐dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open‐source Python program det CI@ORBKIT, which extends the capabilities of our recently published post‐processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom‐centered Gaussian‐type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one‐electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser‐driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher‐level method provided a judicious choice of functional is made. Broadband excitation of a medium‐sized organic chromophore further demonstrates the scalability of the method. In addition, the time‐dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc.     

TD‐DFT benchmarks: A review

Time‐Dependent Density Functional Theory (TD‐DFT) has become the most widely‐used theoretical approach to simulate the optical properties of both organic and inorganic molecules. In this contribution, we review TD‐DFT benchmarks that have been performed during the last decade. The aim is often to pinpoint the most accurate or adequate exchange‐correlation functional(s). We present both the different strategies used to assess the functionals and the main results obtained in terms of accuracy. In particular, we discuss both vertical and adiabatic benchmarks and comparisons with both experimental and theoretical reference transition energies. More specific benchmarks (oscillator strengths, excited‐state geometries, dipole moments, vibronic shapes, etc.) are summarized as well. © 2013 Wiley Periodicals, Inc.     

Ab initio modeling of optical spectra in pH‐sensitive diarylethenes

The photochromic and acidochromic shifts undergone by recently synthesized diarylethene photochromes have been simulated using a Time‐Dependent Density Functional Theory approach relying on a range‐separated functional, namely CAM‐B3LYP. The selected approach is generally accurate for reproducing the variations of the spectral features, though acidochromic shifts are clearly more challenging than their photochromic counterparts. More importantly, an analyzis of the shapes of the relevant molecular orbitals grants insights into the electro‐cyclization of several diarylethenes, therefore partly allowing to understand the presence of experimental deadlocks. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012