A dual-level state-specific time-dependent density-functional theory

A highly efficient new algorithm for time-dependent density-functional theory (TDDFT) calculations is presented. In this algorithm, a dual-level approach to speed up DFT calculations (Nakajima and Hirao, J Chem Phys 2006, 124, 184108) is combined with a state-specific (SS) algorithm for TDDFT (Chiba et al., Chem Phys Lett 2006, 420, 391). The dual-level SS-TDDFT algorithm was applied to excitation energy calculations of typical small molecules, the Q bands of the chlorophyll A molecule, the charge-transfer energy of the zincbacteriochlorin-bacteriochlorin model system, and the lowest-lying excitation of the circumcoronene molecule. As a result, it was found that the dual-level SS-TDDFT gave correct excitation energies with errors of 0.2-0.3 eV from the standard TDDFT approach, with much lower CPU times for various types of excitation energies of large-scale molecules.     

Application of the dressed time-dependent density functional theory for the excited states of linear polyenes

Dressed Time-Dependent Density Functional Theory (Maitra et al., J Chem Phys 2004, 120, 5932) is applied to selected linear polyenes. Limits of validity of the approximation are briefly discussed. The implementation strategy is described. Results for the 2(1)B(u) and 2(1)A(g) states of selected linear polyenes are presented and compared with accessible experimental and theoretical results.     

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.     

Exploring odd-even effects of simple oligomer-like DRCNnT series: a study based on density functional theory/time-dependent density functional theory calculations

Odd-even effects of short-circuit current density and power conversion efficiency (PCE) are an interesting phenomenon in some organic solar cells. Although some explanations have been given, why they behave in such a way is still an open question. In the present work, we investigate a set of acceptor-donor-acceptor simple oligomer-like small molecules, named the DRCNnT (n = 5-9) series, to give an insight into this phenomenon because the solar cells based on them have high PCE (up to 10.08%) and show strong odd-even effects in experiments. By modeling the DRCNnT series and using density functional theory, we have studied the ground-state electronic structures of the DRCNnT (n = 5-9) series in condensed phase. The calculated results reproduce the experimental trends well. Furthermore, we find that the exciton-binding energies of the DRCNnT series may be one of the key parameters to explain this phenomenon because they also show odd-even effects. In addition, by studying the effects of alkyl branch and terminal group on odd-even effects of dipole moment, we find that eliminating one or two alkyl branches does not break the odd-even effects of dipole moments, but eliminating one or two terminal groups does. Finally, we conclude that removing one alkyl branch close to the terminal group of DRCN5T can decrease highest occupied molecular orbital (HOMO) energy (thus increasing open circuit voltage) and increase dipole moment (thus enhancing charge separation and short-circuit current). This could be a new and simple method to increase the PCE of DRCN5T-based solar cells.     

Description of core excitations by time-dependent density functional theory with local density approximation, generalized gradient approximation, meta-generalized gradient approximation, and hybrid functionals

Time-dependent density functional theory (TDDFT) is employed to investigate exchange-correlation-functional dependence of the vertical core-excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, the calculated X1s-->pi* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time-dependent Hartree-Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke-Half-and-Half-Lee-Yang-Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta-GGA functionals show a strong atom-dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom-dependent.     

Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method

An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor–corrector time integration schemes. The Coulomb contribution to the Kohn–Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.     

Density functional calculations on triply excited states of lithium isoelectronic sequence

Triply excited states of many-electron atomic systems are characterized by the presence of strong electron correlation, closeness to more than one threshold, and degeneracy with many continua; therefore, they offer unusual challenges to theoretical methodologies. In the present article, we computed with reasonable accuracy all the n=2 intrashell triply excited states (2s²2p ²P; 2s2p^{2 2}D, ⁴P, ²P, ²S; and 2p^{3 2}D, ²P, ⁴S) of three-electron atomic systems (Z=2, 3, 4, 6, 8, 10) by using a density functional formalism developed recently in our laboratory, based on the nonvariational Harbola–Sahni exchange potential in conjunction with a parametrized local Wigner and Lee–Yang–Parr correlation potentials. Nonrelativistic energies and densities are obtained by solving a Kohn–Sham-type differential equation. The calculated results are compared with available experimental and other theoretical data. The 2p³(⁴S)→1s2p²(⁴P) transition wavelength for the isoelectronic series is also computed. The overall good agreement of our results with the literature data indicates the reliability of the present density functional methodology for excited states of many-electron systems. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 317–332, 1997     

The formulation of a self-consistent constricted variational density functional theory for the description of excited states

We outline here a self-consistent approach to the calculation of transition energies within density functional theory. The method is based on constricted variational theory (CV-DFT). It constitutes in the first place an improvement over a previous scheme [T. Ziegler, M. Seth, M. Krykunov, J. Autschbach, F. Wang, Chem. Phys. 130 (2009) 154102] in that it includes terms in the variational parameters to any desired order n including n = ∞. For n = 2, CV(n)-DFT is similar to TD-DFT. Adiabatic TD-DFT becomes identical to CV(2)-DFT after the Tamm-Dancoff approximation is applied to both theories. We have termed the new scheme CV(n)-DFT. In the second place, the scheme can be implemented self-consistently, SCF-CV(n)-DFT. The procedure outlined here could also be used to formulate a SCF-CV(n) Hartree-Fock theory. The approach is further kindred to the ΔSCF-DFT procedures predating TD-DFT and we describe how adiabatic TD-DFT and ΔSCF-DFT are related through different approximations to SCF-CV(n)-DFT.     

Efficient pole‐search algorithm for dynamic polarizability: Toward alternative excited‐state calculation for large systems

This study presents an efficient algorithm to search for the poles of dynamic polarizability to obtain excited states of large systems with nonlocal excitation nature. The present algorithm adopts a homogeneous search with a constant frequency interval and a bisection search to achieve high accuracy. Furthermore, the subtraction process of the information about the detected poles from the total dynamic polarizability is used to extract the undetected pole contributions. Numerical assessments confirmed the accuracy and efficiency of the present algorithm in obtaining the excitation energies and oscillator strengths of all dipole‐allowed excited states. A combination of the present pole‐search algorithm and divide‐and‐conquer‐based dynamic polarizability calculations was found to be promising to treat nonlocal excitations of large systems. © 2016 Wiley Periodicals, Inc.     

Understanding the electronic energy transfer pathways in the trimeric and hexameric aggregation state of cyanobacteria phycocyanin within the framework of Förster theory

In the present study, the electronic energy transfer pathways in trimeric and hexameric aggregation state of cyanobacteria C‐phycocyanin (C‐PC) were investigated in term of the Förster theory. The corresponding excited states and transition dipole moments of phycocyanobilins (PCBs) located into C‐PC were examined by model chemistry in gas phase at time‐dependent density functional theory (TDDFT), configuration interaction‐singles (CIS), and Zerner's intermediate neglect of differential overlap (ZINDO) levels, respectively. Then, the long‐range pigment‐protein interactions were approximately taken into account by using polarizable continuum model (PCM) at TDDFT level to estimate the influence of protein environment on the preceding calculated physical quantities. The influence of the short‐range interaction caused by aspartate residue nearby PCBs was examined as well. Only when the protonation of PCBs and its long‐ and short‐range interactions were properly taken into account, the calculated energy transfer rates (1/K) in the framework of Förster model at TDDFT/B3LYP/6‐31+G* level were in good agreement with the experimental results of C‐PC monomer and trimer. Furthermore, the present calculated results suggested that the energy transfer pathway in C‐PC monomer is predominant from β‐155 to β‐84 (1/K = 13.4 ps), however, from α‐84 of one monomer to β‐84 (1/K = 0.3–0.4 ps) in a neighbor monomer in C‐PC trimer. In C‐PC hexamer, an additional energy flow was predicted to be from β‐155 (or α‐84) in top trimer to adjacent β‐155 (or α‐84) (1/K = 0.5–2.7 ps) in bottom trimer. © 2013 Wiley Periodicals, Inc.     

Prediction of excited‐state properties of oligoacene crystals using polarizable continuum model‐tuned range‐separated hybrid functional approach

A methodology combining the polarizable continuum model and optimally‐tuned range‐separated (RS) hybrid functional was proposed for the quantitative characterization of the excited‐state properties in oligoacene (from anthracene to hexacene) crystals. We show that it provides lowest vertical singlet and triplet excitation energies, singlet‐triplet gap, and exciton binding energies in very good agreement with the available experimental data. We further find that it significantly outperforms its non‐tuned RS counterpart and the widely used B3LYP functional, and even many‐body perturbation theory within the GW approximation (based on a PBE starting point). Hence, this approach provides an easily applicable and computationally efficient tool to study the excited‐state properties of organic solids of complexity. © 2017 Wiley Periodicals, Inc.     

Role of doping and sheet size in tailoring optoelectronic properties of germanene: A TDDFT study

Germanene is a novel 2D material with promising optoelectronic properties, tuning of which is to be explored. This work demonstrates that doping and increasing the sheet size can alter optical and electronic properties of germanene via perturbation of the band structure. This feature has also been observed in other nanostructures, notably, silicon nanostructures, and may be attributed to quantum confinement effects. Our main findings on H‐terminated germanene are, (i) band gap can be reduced by 30%, (ii) exciton binding energy can be reduced by 60%, and (iii) absorption spectra can be tuned from UV to visible range. We employ time‐dependent density functional theory to investigate the role of dopants, boron (B), phosphorus (P), carbon (C), silicon (Si), and zirconium (Zr). Width of the germanene sheet is varied from 0.78 nm to 2.78 nm. Frequency and energy calculations are carried out to analyze the infrared (IR) and ultra‐violet (UV)‐visible (VIS) spectra.     

Theoretical investigations on the carbazole‐based conjugated polymers containing electron‐donating divinylaryl

The polycarbazoles have been proved to efficiently suppress the keto defect emission. Three carbazole‐based conjugated polymers, poly[9‐methyl‐3‐(4‐vinylstyryl)‐9H‐carbazole] (PBC), poly[9‐methyl‐3‐(2‐(5‐vinylthiophen‐2‐yl)vinyl)‐9H‐carbazole] (PBT) and poly[9‐methyl‐3‐(2‐(5‐vinylfuran‐2‐yl)vinyl)‐9H‐carbazole] (PBF), were investigated by quantum‐chemical techniques, and gain a detailed understanding of the influence of carbazole units and the introduction of electron‐donating on the electronic and optical properties. The electronic properties of the neutral molecules, HOMO‐LUMO gaps (ΔE), in addition to ionization potential (I_p) and electron affinity (E_a), are studied using B3LYP density functional theory. The lowest excitation energies (E_g) and the absorption wavelength are studied using the time dependent density functional theory (TDDFT). The calculated results show that all three series of polymers have good planarity. And the highest‐occupied molecular orbital (HOMO) energies lift about 0.36–0.61 eV and thus the I_P decrease about 0.01–0.19 eV compared to polycarbazole, suggesting the significant improved hole‐accepting and transporting abilities. By introducing the electron‐donating 1,4‐divinylphenylene or 2,5‐divinylthiophene or 2,5‐divinylfuran units in the backbone, and the lowest‐unoccupied molecular orbital (LUMO) energies decrease 0.20–0.39 eV. In addition, PBC, PBT and PBF have longer maximal absorption wavelengths than polycarbazole. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 706–714, 2009     

Is combining meta‐GGA correlation functionals with the OPTX exchange functional useful?

The recent generalized gradient approximation (GGA) density functional OCS1 of Handy and Cohen is implemented in the deMon code and tested on a carefully selected set of problems. OCS1 is found to be accurate for molecular atomization energies, transition metal–ligand bonds, and systems with intramolecular hydrogen bonds. However, OCS1 encounters problems for systems with intermolecular hydrogen bonds. It also tends to elongate bond lengths systematically, and sometimes significantly. The OPTX exchange is combined with three meta‐GGA correlation functionals, Lap3, τ1, and τ2, the latter reported for the first time. The new meta‐GGA scheme OPTX exchange plus τ2 correlation called Oτ2 yields improved molecular geometries, NMR shielding constants, and an improved barrier height for the H+H₂ reaction. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006