Neutral excitation density-functional theory: an efficient and variational first-principles method for simulating neutral excitations in molecules

Finite confinement potentials, core and shell size effects on excitonic and electron-atom properties in cylindrical core/shell/shell quantum dots

The effects of confinement potentials of the first and second materials, core size and first shell thickness on the confinement of electron, electron-donor atom, and exciton in cylindrical core/shell/shell quantum dot (CSSQD) are studied taking into account the finite confinement potential model. The confinement of charge carriers in CSSQD with two finite confinement potentials models of the barrier materials are studied. Within the effective mass and parabolic band approximation, the 3D time-independent Schrödinger equation has been resolved. To obtain the ground state quasiparticles energies, we have used the variational technique. Our results show that the donor atom and exciton binding energy, as well as the electron energy, strongly depend on the core radius, first shell thickness, confinement potentials of the barrier materials, and their structures (A and B). Moreover, the confinement potential effect of the first material on the energies is more pronounced when their thickness is large and the core radius is small. So, the external potential effect is more significant when the first shell thickness and potential are small. Also, The binding energy of an on-center (off-center) donor atom is greater (weaker) than that of the exciton, whatever the structure of the confinement potential. In addition, the transition from a type-A to a type-B confinement system has been observed. The findings might be used to modify the electronic and excitonic properties in nanomaterials science.

Transition-Based Constrained DFT for the Robust and Reliable Treatment of Excitations in Supramolecular Systems

Despite the variety of available computational approaches, state-of-the-art methods for calculating excitation energies, such as time-dependent density functional theory (TDDFT), are computationally demanding and thus limited to moderate system sizes. Here, we introduce a new variation of constrained DFT (CDFT), wherein the constraint corresponds to a particular transition (T), or a combination of transitions, between occupied and virtual orbitals, rather than a region of the simulation space as in traditional CDFT. We compare T-CDFT with TDDFT and ΔSCF results for the low-lying excited states (S1 and T1) of a set of gas-phase acene molecules and OLED emitters and with reference results from the literature. At the PBE level of theory, T-CDFT outperforms ΔSCF for both classes of molecules, while also proving to be more robust. For the local excitations seen in the acenes, T-CDFT and TDDFT perform equally well. For the charge transfer (CT)-like excitations seen in the OLED molecules, T-CDFT also performs well, in contrast to the severe energy underestimation seen with TDDFT. In other words, T-CDFT is equally applicable to both local excitations and CT states, providing more reliable excitation energies at a much lower computational cost than TDDFT cost. T-CDFT is designed for large systems and has been implemented in the linear-scaling BigDFT code. It is therefore ideally suited for exploring the effects of explicit environments on excitation energies, paving the way for future simulations of excited states in complex realistic morphologies, such as those which occur in OLED materials.

Ensemble Density Functional Theory of Neutral and Charged Excitations : Exact Formulations, Standard Approximations, and Open Questions

Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and N-centered ensemble formalisms, which are mathematically very similar and allow for an in-principle-exact description of neutral and charged electronic excitations, respectively, are discussed. Key exact results, for example, the equivalence between the infamous derivative discontinuity problem and the description of weight dependencies in the ensemble exchange-correlation density functional, are highlighted. The variational evaluation of orbital-dependent ensemble Hartree-exchange (Hx) energies is discussed in detail. We show in passing that state-averaging individual exact Hx energies can lead to severe (although solvable) v-representability issues. Finally, we explore the possibility of using the concept of density-driven correlation, which has been introduced recently and does not exist in regular ground-state DFT, for improving state-of-the-art correlation density-functional approximations for ensembles. The present review reflects the efforts of a growing community to turn ensemble DFT into a rigorous and reliable low-cost computational method for excited states. We hope that, in the near future, this contribution will stimulate new formal and practical developments in the field.

Spinning Molecules, Spinning Spins: Modulation of an Electron Spin Exchange Interaction in a Highly Anisotropic Hyperfine Field

An investigation of spin and conformational dynamics in a series of symmetric Cu-Cu porphyrin dimer solutions is presented using electron paramagnetic resonance (EPR) spectroscopy. Previous spectral simulations focused on the isotropic exchange interaction (J avg) between the Cu centers. In this work, an additional line broadening parameter (J mod) is explored in detail via variable temperature X-band EPR in liquid solution for several different structures. The J mod phenomenon is due to fluctuations in the spin exchange interaction caused by conformational motion of the porphyrin planes. The J mod parameter scales with the inverse of the rotational barriers that determine the Boltzmann-weighted torsional angle distribution between neighboring porphyrin planes. Arrhenius plots allow for extraction of the activation energies for rotation, which are 5.77, 2.84, and 5.31 kJ/mol for ethyne-bridged (porphinato)copper(II)-(porphinato)copper(II), butadiyne-bridged (porphinato)copper(II)-(porphinato)copper(II), and ethyne-bridged (porphinato)copper(II)-(porphinato)zinc(II)-(porphinato)copper(II) complexes, respectively. DFT calculations of these torsional barriers match well with the experimental results. This is the first report of a J mod analysis within a highly anisotropic hyperfine field and demonstrates the utility of the theory for extraction of dynamic information.

Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane-Wave Basis Set

A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane-wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density-dependent (ODD) functionals including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate π* orbitals where the importance of complex orbitals is illustrated. The application of this method to several metal-to-ligand charge-transfer and metal-centered excited states of an Fe^II photosensitizer complex is described, and the results are compared to reported experimental estimates. This method is also used to study the effect of the Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.

Systematic improvement of molecular excited state calculations by inclusion of nuclear quantum motion: A mode-resolved picture and the effect of molecular size

The energies of molecular excited states arise as solutions to the electronic Schrödinger equation and are often compared to experiment. At the same time, nuclear quantum motion is known to be important and to induce a redshift of excited state energies. However, it is thus far unclear whether incorporating nuclear quantum motion in molecular excited state calculations leads to a systematic improvement of their predictive accuracy, making further investigation necessary. Here, we present such an investigation by employing two first-principles methods for capturing the effect of quantum fluctuations on excited state energies, which we apply to the Thiel set of organic molecules. We show that accounting for zero-point motion leads to much improved agreement with experiment, compared to "static" calculations that only account for electronic effects, and the magnitude of the redshift can become as large as 1.36 eV. Moreover, we show that the effect of nuclear quantum motion on excited state energies largely depends on the molecular size, with smaller molecules exhibiting larger redshifts. Our methodology also makes it possible to analyze the contribution of individual vibrational normal modes to the redshift of excited state energies, and in several molecules, we identify a limited number of modes dominating this effect. Overall, our study provides a foundation for systematically quantifying the shift of excited state energies due to nuclear quantum motion and for understanding this effect at a microscopic level.

Orbital Optimized Density Functional Theory for Electronic Excited States

Density functional theory (DFT) based modeling of electronic excited states is of importance for investigation of the photophysical/photochemical properties and spectroscopic characterization of large systems. The widely used linear response time-dependent DFT (TDDFT) approach is, however, not effective at modeling many types of excited states, including (but not limited to) charge-transfer states, doubly excited states, and core-level excitations. In this perspective, we discuss state-specific orbital optimized (OO) DFT approaches as an alterative to TDDFT for electronic excited states. We motivate the use of OO-DFT methods and discuss reasons behind their relatively restricted historical usage (vs TDDFT). We subsequently highlight modern developments that address these factors and allow efficient and reliable OO-DFT computations. Several successful applications of OO-DFT for challenging electronic excitations are also presented, indicating their practical efficacy. OO-DFT approaches are thus increasingly becoming a useful route for computing excited states of large chemical systems. We conclude by discussing the limitations and challenges still facing OO-DFT methods, as well as some potential avenues for addressing them.

Study of interaction of metal ions with methylthymol blue by chemometrics and quantum chemical calculations

In this study, we determine the acidity constants of methylthymol blue (MTB) and association constants of its complexes with the ZnII, CuII, and FeII metal ions (MIs), through theoretical and experimental means. The complexes were characterized using UV-Visible absorption spectroscopy combined with soft/hard chemometrics methods and quantum chemical calculations. Quantum chemical calculations revealed that electronic transitions in the UV-Visible spectra of MTB have mixed n → π* and π → π* characters. The results of molar ratio and multivariate curve resolution alternating least squares (MCR-ALS) revealed the formation of successive 1:2 and 1:1 complexes (MI:MTB) for the ZnII and CuII systems. However, the formation of successive 1:1 and 2:1 complexes are suggested for FeII by the molar ratio and MCR-ALS. The majority of transitions observed in the UV-Visible spectra of the Zn(MTB) and Cu(MTB) complexes have ligand-to-ligand charge transfer (LLCT) characters. However, the transitions in the UV-Visible spectrum of the Fe(MTB) complex have LLCT and metal-to-ligand charge transfer (MLCT) characters. For the Fe2(MTB) complex, the lowest energy transition of has an LLCT character. However, its higher energy transitions are a mixture of LLCT, MLCT, and metal-to-metal charge transfer (MMCT) characters. The correlation between experimental and computed wavelengths revealed that the 1:1 complexes of ZnII and CuII prefer square pyramidal geometries. However, the FeII complexes always show octahedral geometry.