Ab Initio Calculation of the Ultraviolet–Visible (UV-vis) Absorption Spectrum, Electron-Loss Function, and Reflectivity of Solids

Theoretical study of short-range exchange interaction based on semiconductor dielectric function model toward time-dependent dielectric density functional theory

This study explores various models of semiconductor dielectric functions, with a specific emphasis on the large wavenumber spectrum and the derivation of the screened exchange interaction. Particularly, we discuss the short-range effect of the screened exchange potential. Our investigation reveals that the short-range effect originating from the high wavenumber spectrum is contingent upon the dielectric constant of the targeted system. To incorporate dielectric-dependent behaviors concerning the short-range aspect into the dielectric density functional theory (DFT) framework, we utilize the local Slater term and the Yukawa-type term, adjusting the ratio between these terms based on the dielectric constant. Additionally, we demonstrate the efficacy of the time-dependent dielectric DFT method in accurately characterizing the electronic structure of excited states in dyes and functional molecules. Several theoretical approaches have incorporated parameters dependent on the system to elucidate short-range exchange interactions. Our theoretical analysis and discussions will be useful for those studies.

A Perspective on the Simulation of Electronic Circular Dichroism and Circularly Polarized Luminescence Spectra in Chiral Solid Materials

Chiral materials have shown tremendous potential for many technological applications, such as optoelectronics, sensing, magnetism, information technology, and imaging. Characterization of these materials is mostly based on chiroptical spectroscopies, such as electronic circular dichroism (ECD) and circularly polarized luminescence (CPL). These experimental measurements would greatly benefit from theoretical simulations for interpretation of the spectra as well as predictions on new materials. While ECD and CPL simulations are well established for molecular systems, they are not for materials. In this Perspective, we describe the theoretical quantities necessary to simulate ECD and CPL spectra in oriented systems. Then, we discuss the approximate strategies currently used to perform these calculations, what computational machinery is already available to develop more general approaches, and some of the open challenges for the simulation of ECD and CPL spectra in solid materials. When methods that are as reliable and computationally efficient as those for molecules are developed, these simulations will provide invaluable insight and guidance for the rational design of optically active materials.

Structural, electronic, optical and thermodynamic properties of AlAuO2 and AlAu094Fe006O2 compounds scrutinized by density functional theory (DFT)

In this study, density functional theory (DFT) simulations have been used to study the structural, electrical and optical properties of AlAuO2 and AlAu094Fe006O2. Initially, the estimated bandgap of AlAuO2 0.45, 0.486, 0.419 and 2.49 eV in Perdew-Burke-Ernzerhof (PBE), Revised Perdew-Burke-Ernzerhof (RPBE), PBE for solids (PBE sol) and Becke three-parameter Lee-Yang-Parr (B3LYP) method respectively while AlAu094Fe006O2 has a zero-band gap after 6 % Fe doping. Then, density of state (DOS) and partial density of state (PDOS) were studied to determine the characteristics of the various orbitals of AlAuO2. The bonding characteristics and thermal stability of this crystal are determined by the Mulliken population charge and thermos physical parameters. Band edge of AlAuO2 was calculated which revealed that the AlAuO2 has suitable oxidation and reduction potential to degrade the contamination. A remarkable absorption has recorded for both AlAuO2 and AlAu094Fe006O2 in visible and ultraviolet region and capability to utilize photocatalytic dye degradation and hydrogen production through water splitting.

Decomposition analysis on the excitation behaviors of thiazolothiazole (TTz)-based dyes via the time-dependent dielectric density functional theory approach

Thiazolothiazole (TTz)-based materials have been attracting much attention because of their widespread applications. In this paper, we discuss the excited electronic behaviors of asymmetric TTz dyes in solvents based on the time-dependent dielectric density functional theory method. Based on dipole moment and charge distribution (population) analyses, we discuss large intramolecular electron transfers, which are triggered by photon excitations, toward the acceptor part of dyes. In addition, we explore the contributions of geometrical changes and solvent reorientations (reorganizations) to the solvatofluorochromic phenomena based on a decomposition technique. The decomposition analysis shows that the solvent reorientation effect mainly contributes to changes in the fluorescent spectra in response to solvents.

Electronic Excitations in Crystalline Solids through the Maximum Overlap Method

The maximum overlap method (MOM) has emerged from molecular quantum chemistry as a convenient practical procedure for studying excited states. Unlike the Aufbau principle, during self-consistent field (SCF) iterations, the MOM forces orbital occupation to be maximally similar to that of a reference state. Although still within a single-particle framework, this approach allows for the evaluation of excitation energies (Δ-SCF) and geometry optimization of electronic configurations other than the ground state. In this work, we present an extension of the MOM to periodic crystalline solids, within the framework of an atom-centered Gaussian basis set. In order to obtain a realistic concentration of excited electrons, we allow excitation in only one—or a few—points of the Brillouin zone, leading to a fractional occupation of crystalline Kohn–Sham states. Since periodic SCF solution techniques involve an iteration between direct and reciprocal spaces, only totally symmetric excitations are allowed in our treatment, in order to preserve the translational symmetry: vertical Γ-point excitations or collective excitations in a sphere around Γ. Other types of excitations are accessible through folding of the Brillouin zone subsequent to the creation of a supercell. The features and performance of the method are presented through its application to prototypical solids such as bulk silicon, diamond, and lithium fluoride and comparing the results with the available experimental data. The demonstrative application to nickel oxide and solid CuI(piperazine)—a luminescent copper halide compound—highlights the promising potential of the MOM in solid-state quantum chemistry.

A theoretical study on solvatofluorochromic asymmetric thiazolothiazole (TTz) dyes using dielectric-dependent density functional theory

In this work, the excitation energies of asymmetric thiazolothizaole (TTz) dye molecules have been theoretically studied using dielectric-dependent density functional theory (DFT). In the dielectric-dependent DFT approach, the ratio (fraction) of the nonlocal Hartree exchange term incorporated into the DFT exchange-correlation functional is a system-dependent parameter, which is inversely proportional to the dielectric constant of the target material. The dielectric-dependent DFT method is closely related to the Coulomb hole and screened exchange (COHSEX) approximation in the GW method and therefore has been applied to crystalline systems with periodic boundary conditions, such as semiconductors and inorganic materials. By focusing on the solvatofluorochromic phenomena of asymmetric TTz dyes, we show that excitation energy calculations obtained from the dielectric-dependent DFT method can reproduce the corresponding experimental UV-vis absorption and emission spectra of dyes in solvents.

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Application on α-Quartz, Tartaric Acid Crystal, and Chiral (n,m)-Carbon Nanotubes

The self-consistent coupled-perturbed (SC-CP) method in the CRYSTAL program has been adapted to obtain electromagnetic optical rotation properties of chiral periodic systems based on the calculation of the magnetic moment induced by the electric field. Toward that end, an expression for the magnetic transition moment is developed, which involves an appropriate electronic angular momentum operator. This operator is forced to be hermitian so that the chiroptical properties are real. In our formulation, the trace of the optical rotatory power matrix is gauge-origin-invariant as long as the electric dipole transition matrix elements are obtained using the velocity (rather than position) operator. On the other hand, the component along the optic axis is invariant in general for uniaxial and biaxial crystals. Under the same conditions, these properties also do not depend on the so-called missing integers that occur in the treatment of the electric dipole moment of quasi-one-dimensional periodic systems or the analogue of missing integers for the case of higher dimensionality. Tests on a model H₂O₂ polymer confirm the formalism and, as desired, show that the calculated properties are independent of the size and definition of the unit cell. In addition, an empirical relation to a finite oligomer gauge-including atomic orbital (GIAO) calculation is found. Applications, with comparison to experiment, are carried for α-quartz, tartaric acid crystal, and carbon nanotubes. Future developments of this initial approach to chiroptical properties in the solid state are noted.

Modeling UV-Vis spectra of low dimensional materials using electrostatic embedding: The case of CdSe

We present a generalization of a self-consistent electrostatic embedding approach (SC-Ewald) devised to investigate the photophysical properties of 3D periodic materials, to systems in one- or two-dimensional (2D) reduced periodicity. In this approach, calculations are carried out on a small finite molecular cluster extracted from a periodic model, while the crystalline environment is accounted for by an array of point charges which are fitted to reproduce the exact electrostatic potential (at ground or the excited state) of the infinite periodic system. Periodic density functional theory (DFT) calculations are combined with time dependent DFT calculations to simulate absorption and emission properties of the extended system under investigation. We apply this method to compute the UV-Vis. spectra of bulk and quantum-confined 0D quantum dots and 2D extended nanoplatelets of CdSe, due to their relevance as sensitizers in solar cells technologies. The influence of the size and shape of the finite cluster model chosen in the excited state calculations was also investigated and revealed that, although the long-range electrostatics of the environment are important for the calculation of the UV-Vis, a subtle balance between short- and long-range effects exists. These encouraging results demonstrate that this self-consistent electrostatic embedding approach, when applied in different dimensions, can successfully model the photophysical properties of diverse material classes, making it an attractive low-cost alternative to far more computationally demanding electronic structure methods for excited state calculations.

Two-level iterative solver for linear response time-dependent density functional theory with plane wave basis set

We present a two-level iterative solver for linear response time-dependent density functional theory by combining two forms of the Casida equation in the Kohn-Sham orbital representation and in Hutter's formulation. This two-level iterative solver has been implemented with the plane wave pseudopotential method for excited-state simulations of molecular and low-dimensional solid materials. Numerical studies with the Davidson algorithm demonstrate that this two-level iterative solver yields excited-state properties for molecules (benzene C₆H₆ and fullerene C₆₀) and low-dimensional semiconductors [two-dimensional molybdenum disulfide MoS₂ monolayer and rutile titanium dioxide TiO₂(110) surface] with significantly reduced computational cost and storage requirement compared with standard iterative algorithms. We apply our approach to investigate the photoinduced charge separation of methanol molecules adsorption on the rutile TiO₂(110) surface from the exciton perspective and validate that the photogenerated hole can be captured by methanol molecules.

Relationships between Orbital Energies, Optical and Fundamental Gaps, and Exciton Shifts in Approximate Density Functional Theory and Quasiparticle Theory

The relationships between Kohn-Sham (KS) and generalized KS (GKS) density functional orbital energies and fundamental gaps or optical gaps raise many interesting questions including the physical meanings of KS and GKS orbital energies when computed with currently available approximate density functionals (ADFs). In this work, by examining three diverse databases with various ADFs, we examine such relations from the point of view of the exciton shift of quasiparticle theory. We start by calculating a large number of excitation energies by time-dependent density functional theory (TDDFT) with a large number of ADFs. To relate the exciton shift implicit in TDDFT to the exciton shift that is explicit in Green's function theory, we define the exciton shift in TDDFT as the difference of the response shift and the quasiparticle shift. We found a strong correlation between the response shift and the amount of Hartree-Fock exchange included in the density functional, with the response shift varying between -1 and 5 eV. This range is an order of magnitude larger than the mean errors of the TDDFT excitation energies. This result suggests that, with currently available functionals, the KS or GKS orbital energies should be treated as intermediate mathematical variables in the calculation of excitation energies rather than as the energies of independent-particle reference states for quasiparticle theory.

The CRYSTAL code, 1976-2020 and beyond, a long story

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree-Fock (HF). The cost for HF or hybrids is only about 3-5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores.

An all-electron study of the low-lying excited states and optical constants of Al2O3 in the range 5-80 eV

This paper reports calculated energies and electronic structures of O(2p), O(2s) and Al(2p) excited states in bulk [Formula: see text]-Al₂O₃, at the [Formula: see text] and [Formula: see text] surfaces and in the presence of O vacancy defects, obtained from all-electron HF, B3LYP, GGA and LDA calculations based on a recently described direct [Formula: see text]-SCF approach (Mackrodt et al 2018 J. Phys.: Condens. Matter 30 495901). The closely related frequency-dependent optical constants derived from B3LYP calculations within the CPHF/DF framework are also reported, where both sets of results are shown to compare favourably with the experimental spectra. The differences between the directly calculated excited state energies, which in [Formula: see text]-Al₂O₃ are equal to the leading excitation edges, based on the four functionals, are substantially less than the differences between the corresponding (ground state) band gaps, as reported previously for AFII NiO (Mackrodt et al 2018 J. Phys.: Condens. Matter 30 495901). For the B3LYP functional, these energies are 8.7 eV, 12.5 eV and 73.7 eV for the O(2p), O(2s) and Al(2p) excitations respectively. The O(2p) edge is predicted to be degenerate, with distinct excitations from O(2p) states that are parallel to and perpendicular to the c-axis, in agreement with the reported spectra (Tomiki et al 1993 J. Phys. Soc. Japan 62 573). Detailed analyses of the charge and spin distributions in the four bulk excited states indicate that these are essentially charge-transfer excitonic, with acceptor sites at the nearest neighbour positions. Despite the close proximity of the O([Formula: see text]) and O(2p[Formula: see text]) excited state energies, the charge and spin distributions are predicted to be quite different.

M06-SX screened-exchange density functional for chemistry and solid-state physics

Screened-exchange hybrid density functionals are especially recommended for solid-state systems because they combine the advantages of hybrid functionals with the correct physics and lower computational cost associated with the attenuation of Hartree-Fock exchange at long range. We present a screened-exchange hybrid functional, M06-SX, that combines the functional form of the local revM06-L functional with a percentage of short-range nonlocal Hartree-Fock exchange. The M06-SX functional gives good results not only for a large set of training data but also for several databases quite different from the training data. The mean unsigned error (MUE) of the M06-SX functional is 2.85 kcal/mol for 418 atomic and molecular energies (AME418) in Minnesota Database 2019, which is better than all five other screened-exchange hybrid functionals tested in this work. The M06-SX functional also gives especially good results for semiconductor band gaps, molecular dissociation energies, noncovalent interactions, barrier heights, and electronic excitation energies excluding long-range charge transfer excitations. For the LC18 lattice constants database, the M06-SX functional gives an MUE of only 0.034 Å. Therefore, the M06-SX functional is well suited for studying molecular chemistry as well as solid-state physics.

Tellurium Doping and the Structural, Electronic, and Optical Properties of NaYS2(1-x)Te2x Alloys

New ternary and quaternary NaYS_2(1-x)Te_2x alloys (with x = 0, 0.33, 0.67, and 1) are proposed as promising candidates for photon energy conversion in photovoltaic applications. The effects of Te doping on crystal, spectral, and optical properties are studied within the framework of periodic density functional theory. Increasing Te content decreases the band gap (E _g) considerably (from 3.96 (x = 0) to 1.62 eV (x = 0.67)) and fits a quadratic model (E _g(x) = 3.96-6.78x + 4.70x ², (r ² = 0.96, n = 4)). The band gap of 1.62 eV makes the NaYS_0.67Te_1.33 alloy ideal for photovoltaic applications for their ability to absorb in the visible segment of the sunlight spectrum. The calculated exciton binding energies are 9.78 meV for NaYS_1.33Te_0.67 and 6.06 meV for NaYS_0.67Te_1.33. These values of the order of the thermal energy at room temperature suggest an easily dissociable hole-electron pair. The family of NaYS_2(1-x)Te_2x alloys are, therefore, promising candidates for visible photocatalytic devices and worthy of further experimental and theoretical investigations.

Critical Role of the Exchange Interaction for the Electronic Structure and Charge-Density-Wave Formation in TiSe_{2}

We show that the inclusion of screened exchange via hybrid functionals provides a unified description of the electronic and vibrational properties of TiSe_{2}. In contrast to local approximations in density functional theory, the explicit inclusion of exact, nonlocal exchange captures the effects of the electron-electron interaction needed to both separate the Ti-d states from the Se-p states and stabilize the charge-density-wave (CDW) (or low-T) phase through the formation of a p-d hybridized state. We further show that this leads to an enhanced electron-phonon coupling that can drive the transition even if a small gap opens in the high-T phase. Finally, we demonstrate that the hybrid functionals can generate a CDW phase where the electronic bands, the geometry, and the phonon frequencies are in agreement with experiments.

Quantum-Assisted Metrology of Neutral Vitamins in the Gas Phase

It has recently been shown that matter-wave interferometry can be used to imprint a periodic nanostructure onto a molecular beam, which provides a highly sensitive tool for beam displacement measurements. Herein, we used this feature to measure electronic properties of provitamin A, vitamin E, and vitamin K1 in the gas phase for the first time. The shift of the matter-wave fringes in a static electric field encodes the molecular susceptibility and the time-averaged dynamic electric dipole moment. The dependence of the fringe pattern on the intensity of the central light-wave diffraction grating was used to determine the molecular optical polarizability. Comparison of our experimental findings with molecular dynamics simulations and density functional theory provides a rich picture of the electronic structures and dynamics of these biomolecules in the gas phase with β-carotene as a particularly interesting example.

Self-consistent hybrid functionals for solids: a fully-automated implementation

A fully-automated algorithm for the determination of the system-specific optimal fraction of exact exchange in self-consistent hybrid functionals of the density-functional-theory is illustrated, as implemented into the public Crystal program. The exchange fraction of this new class of functionals is self-consistently updated proportionally to the inverse of the dielectric response of the system within an iterative procedure (Skone et al 2014 Phys. Rev. B 89, 195112). Each iteration of the present scheme, in turn, implies convergence of a self-consistent-field (SCF) and a coupled-perturbed-Hartree-Fock/Kohn-Sham (CPHF/KS) procedure. The present implementation, beside improving the user-friendliness of self-consistent hybrids, exploits the unperturbed and electric-field perturbed density matrices from previous iterations as guesses for subsequent SCF and CPHF/KS iterations, which is documented to reduce the overall computational cost of the whole process by a factor of 2.

Application of the dielectric-dependent screened exchange potential approach to organic photocell materials

This paper discusses the fundamental features of the dielectric-dependent screened exchange potential approach for organic molecules and photocell materials.