Performance of DFT Methods in the Calculation of Optical Spectra of TCF-Chromophores

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Electron Donor and Acceptor Influence on the Nonlinear Optical Response of Diacetylene-Functionalized Organic Materials (DFOMs): Density Functional Theory Calculations

Herein, we report the quantum chemical results based on density functional theory for the polarizability (α) and first hyperpolarizability (β) values of diacetylene-functionalized organic molecules (DFOM) containing an electron acceptor (A) unit in the form of nitro group and electron donor (D) unit in the form of amino group. Six DFOM 1–6 have been designed by structural tailoring of the synthesized chromophore 4,4′-(buta-1,3-diyne-1,4-diyl) dianiline (R) and the influence of the D and A moieties on α and β was explored. Ground state geometries, HOMO-LUMO energies, and natural bond orbital (NBO) analysis of all DFOM (R and 1–6) were explored through B3LYP level of DFT and 6-31G(d,p) basis set. The polarizability (α), first hyperpolarizability (β) values were computed using B3LYP (gas phase), CAM-B3LYP (gas phase), CAM-B3LYP (solvent DMSO) methods and 6-31G(d,p) basis set combination. UV-Visible analysis was performed at CAM-B3LYP/6-31G(d,p) level of theory. Results illustrated that much reduced energy gap in the range of 2.212–2.809 eV was observed in designed DFOM 1–6 as compared to parent molecule R (4.405 eV). Designed DFOM (except for 2 and 4) were found red shifted compared to parent molecule R. An absorption at longer wavelength was observed for 6 with 371.46 nm. NBO analysis confirmed the involvement of extended conjugation and as well as charge transfer character towards the promising NLO response and red shift of molecules under study. Overall, compound 6 displayed large <α> and β_tot, computed to be 333.40 (a.u.) (B3LYP gas), 302.38 (a.u.) (CAM-B3LYP gas), 380.46 (a.u.) (CAM-B3LYP solvent) and 24708.79 (a.u.), 11841.93 (a.u.), 25053.32 (a.u.) measured from B3LYP (gas), CAM-B3LYP (gas) and CAM-B3LYP (DMSO) methods respectively. This investigation provides a theoretical framework for conversion of centrosymmetric molecules into non-centrosymmetric architectures to discover NLO candidates for modern hi-tech applications.

Investigation of NLO Properties of Fluorescent BORICO Dyes: a Comprehensive Experimental and Theoretical Approach

BORICO dyes with N, N-diethyl as a strong donor and BF₂ complexed iminocoumarin six member core as strong acceptor are investigated as an efficient non linear optical chromophores. Extended π-conjugation over iminocoumarin moiety is useful to make ICT character of BORICO dyes more significant and is established on the scale of Generalised Mulliken Hush analysis scale. Bond length alternation and bond order alternation values for three BORICO chromophores estimates the cyanine like framework for optimal non linear optical response. The frontier molecular orbital diagrams obtained from density functional theory calculations shows that there is charge transfer from donor to accepter as well as effective overlap between them making the basis for optimal NLO response of BORICO chromophores. The theoretical values of linear and non linear optical responses for three BORICO NLOphores obtained by using three different functionals B3LYP, CAMB3LYP and BHandHLYP with 6-311+g(d,p) basis set are quite consistent for the values of static dipole moment (μ), linear polarizability (α) and first hyperpolarizability (β). However in case of the γ values calculation, compare to the similar values obtained by CAMB3LYP and BHandHLYP functionals, B3LYP overestimates the same. The vibrational motions play decisive role in the overall non linear optical properties of BORICO chromophores.

Design of novel tetra-hetero[8]circulenes: a theoretical study of electronic structure and charge transport characteristics

Tetra-hetero[8]circulenes were theoretically designed and emerged as good candidates for ambipolar organic semiconductors.

Nonlinear optical chromophores based on Dewar's rules: enhancement of electro-optic activity by introducing heteroatoms into the donor or bridge

In this work, we investigated the enhancement of the electro-optic response by introducing electron-rich heteroatoms as additional donors to the donor or bridge of a conventional second-order nonlinear optical chromophore.

Smooth heuristic optimization on a complex chemical subspace

In the present work, several heuristic reordering algorithms for deterministic optimization on a combinatorial chemical compound space are evaluated for performance and efficiency.

Optimizing calculations of electronic excitations and relative hyperpolarizabilities of electrooptic chromophores

CONSPECTUS: Organic glasses containing chromophores with large first hyperpolarizabilities (β) are promising for compact, high-bandwidth, and energy-efficient electro-optic devices. Systematic optimization of device performance requires development of materials with high acentric order and enhanced hyperpolarizability at operating wavelengths. One essential component of the design process is the accurate calculation of optical transition frequencies and hyperpolarizability. These properties can be computed with a wide range of electronic structure methods implemented within commercial and open-source software packages. A wide variety of methods, especially hybrid density-functional theory (DFT) variants have been used for this purpose. However, in order to provide predictions useful to chromophore designers, a method must be able to consistently predict the relative ordering of standard and novel materials. Moreover, it is important to distinguish between the resonant and nonresonant contribution to the hyperpolarizabiliy and be able to estimate the trade-off between improved β and unwanted absorbance (optical loss) at the target device's operating wavelength. Therefore, we have surveyed a large variety of common methods for computing the properties of modern high-performance chromophores and compared these results with prior experimental hyper-Rayleigh scattering (HRS) and absorbance data. We focused on hybrid DFT methods, supplemented by more computationally intensive Møller-Plesset (MP2) calculations, to determine the relative accuracy of these methods. Our work compares computed hyperpolarizabilities in chloroform relative to standard chromophore EZ-FTC against HRS data versus the same reference. We categorized DFT methods used by the amount of Hartree-Fock (HF) exchange energy incorporated into each functional. Our results suggest that the relationship between percentage of long-range HF exchange and both βHRS and λmax is nearly linear, decreasing as the fraction of long-range HF exchange increases. Mild hybrid DFT methods are satisfactory for prediction of λmax. However, mild hybrid methods provided qualitatively incorrect predictions of the relative hyperpolarizabilities of three high-performance chromophores. DFT methods with approximately 50% HF exchange, and especially the Truhlar M062X functional, provide superior predictions of relative βHRS values but poorer predictions of λmax. The observed trends for these functionals, as well as range-separated hybrids, are similar to MP2, though predicting smaller absolute magnitudes for βHRS. Frequency dependence for βHRS can be calculated using time-dependent DFT and HF methods. However, calculation quality is sensitive not only to a method's ability to predict static hyperpolarizability but also to its prediction of optical resonances. Due to the apparent trade-off in accuracy of prediction of these two properties and the need to use static finite-field methods for MP2 and higher-level hyperpolarizability calculations in most codes, we suggest that composite methods could greatly improve the accuracy of calculations of β and λmax.

Charge transfer excitations in cofacial fullerene-porphyrin complexes

Porphyrin and fullerene donor-acceptor complexes have been extensively studied for their photo-induced charge transfer characteristics. We present the electronic structure of ground states and a few charge transfer excited states of four cofacial porphyrin-fullerene molecular constructs studied using density functional theory at the all-electron level using large polarized basis sets. The donors are base and Zn-tetraphenyl porphyrins and the acceptor molecules are C(60) and C(70). The complexes reported here are non-bonded with a face-to-face distance between the porphyrin and the fullerene of 2.7 to 3.0 Å. The energies of the low lying excited states including charge transfer states calculated using our recent excited state method are in good agreement with available experimental values. We find that replacing C(60) by C(70) in a given dyad may increase the lowest charge transfer excitation energy by about 0.27 eV. Variation of donor in these complexes has marginal effect on the lowest charge transfer excitation energy. The interfacial dipole moments and lowest charge transfer states are studied as a function of face-to-face distance.

Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals

Excitation gaps are of considerable significance in electronic structure theory. Two different gaps are of particular interest. The fundamental gap is defined by charged excitations, as the difference between the first ionization potential and the first electron affinity. The optical gap is defined by a neutral excitation, as the difference between the energies of the lowest dipole-allowed excited state and the ground state. Within many-body perturbation theory, the fundamental gap is the difference between the corresponding lowest quasi-hole and quasi-electron excitation energies, and the optical gap is addressed by including the interaction between a quasi-electron and a quasi-hole. A long-standing challenge has been the attainment of a similar description within density functional theory (DFT), with much debate on whether this is an achievable goal even in principle. Recently, we have constructed and applied a new approach to this problem. Anchored in the rigorous theoretical framework of the generalized Kohn-Sham equation, our method is based on a range-split hybrid functional that uses exact long-range exchange. Its main novel feature is that the range-splitting parameter is not a universal constant but rather is determined from first principles, per system, based on satisfaction of the ionization potential theorem. For finite-sized objects, this DFT approach mimics successfully, to the best of our knowledge for the first time, the quasi-particle picture of many-body theory. Specifically, it allows for the extraction of both the fundamental and the optical gap from one underlying functional, based on the HOMO-LUMO gap of a ground-state DFT calculation and the lowest excitation energy of a linear-response time-dependent DFT calculation, respectively. In particular, it produces the correct optical gap for the difficult case of charge-transfer and charge-transfer-like scenarios, where conventional functionals are known to fail. In this perspective, we overview the formal and practical challenges associated with gap calculations, explain our new approach and how it overcomes previous difficulties, and survey its application to a variety of systems.