Calculations Of Optical Spectra Research Articles

FOS: A fully integrated open-source program for Fast Optical Spectrum calculations of nanoparticle media

FOS, which means light in Greek, is an open-source program for Fast Optical Spectrum calculations of nanoparticle media. This program takes the material properties and a description of the system as input, and outputs the spectral response including the reflectance, absorptance, and transmittance. Previous open-source codes often include only one portion of what is needed to calculate the spectral response of a nanoparticulate medium, such as Mie theory or a Monte Carlo method. FOS is designed to provide a convenient fully integrated format to remove the barrier as well as providing a significantly accelerated implementation with compiled Python code, parallel processing, and pre-trained machine learning predictions. This program can accelerate optimization and high throughput design of optical properties of nanoparticle or nanocomposite media, such as radiative cooling paint and solar heating liquids, allowing for the discovery of new materials and designs. FOS also enables convenient modeling of lunar dust coatings, combustion particulates, and many other particulate systems. In this paper we discuss the methodology used in FOS, features of the program, and provide four case studies. Program SummaryProgram Title: FOS: Fast Optical Spectrum calculations of nanoparticle mediaCPC Library link to program files: https://doi.org/10.17632/mk3xhprm6j.1Developer's repository link:https://github.com/FastOpticalSpectrum/FOSLicensing provisions: GNU General Public License version 3Programming language: Python 3.10Nature of problem: Calculation of scattering and absorption properties, and the spectral response of nanoparticle media.Solution method: Calculation of scattering and absorption properties is done through Mie theory or can be pre-calculated by the user. Calculation of the spectral response is done through either Monte Carlo simulations or a Machine Learning method.Additional comments including restrictions and unusual features: The executable program is built for Windows computers. The Python code can be used for other operating systems such as Mac, Linux, or Unix.

A DFT study of structural, electronic, mechanical, optical, and hydrogen storage properties of quaternary hydride phase Li4BN3H10

In this paper, we investigated the structural, electronic, mechanical and optical properties of Li4BN3H10 using the ultra-soft pseudopotential method which is based on the density functional theory (DFT) with CASTEP code. The optimized lattice parameters of Li4BN3H10 correlate well with the theoretical calculations and experimental measurements that are currently available. Using elastic constants, the material's stability was verified. Based on the elastic constants, we discovered several mechanical features of the material. Between 0 and 20 eV, optical spectra calculations are made, taking into account the real and imaginary parts of the dielectric function ε(ω), reflectivity R(ω), index of refraction n(ω), coefficients of extinction k(ω) and absorption α(ω). The dielectric function is wide close to the middle ultraviolet (4.13–6.20 eV). The extinction coefficient of the Li4BN3H10 has the ability to worn for implements like Bragg's reflectors, optical and optoelectronic equipments. The optical parameters of Li4BN3H10 disclose that our working constructions have an elevated dielectric constant, with a greatest absorption in the visible range holding out over 1.49 × 105 cm−1 Li4BN3H10 is deemed to be an appropriate material for optoelectronic applications based on calculated optical results. The gravimetric hydrogen storage capacities of Li4BN3H10 compound is 11.06 wt %. These promising capacities exceed the 6.5 wt % target set by the US Department of Energy for 2025.

First principle studies on structural, elastic, electronic, optical, and thermoelectric properties of new perovskite TlTaO3: For renewable energy applications.

The structural, optoelectronics, and transport properties of TlTaO3 compounds were determined utilizing the full potential augmented plane wave approach using first-principle method. We have considered the generalized gradient approximation for structural optimization and modified Becke-Johnson for electronic properties. The electronic properties reveal that the studied TlTaO3 possesses direct bandgap of magnitude 1.52 eV. Between 0 and 12 eV, optical spectra calculations are made, taking into account the real and imaginary parts of the dielectric function, refractive index, and loss function. The transport properties are estimated considering Boltzmann transport theory. The Seebeck coefficient, electrical conductivity, thermal conductivity, and power factor are all assessed using the Boltzmann transport theory. The optimized thermoelectric response of the examined TlTaO3 is produced by the improved carrier mobility, which also improves the thermoelectric efficiency of the TlTaO3. The obtained results will act as a theoretical road map for upcoming experimental and commercial TlTaO3 applications.

Linear scaling approach for optical excitations using maximally localized Wannier functions

We present a theoretical method for calculating optical absorption spectra based on maximally localized Wannier functions, which is suitable for large periodic systems. For this purpose, we calculate the exciton Hamiltonian, which determines the Bethe–Salpeter equation for the macroscopic polarization function and optical absorption characteristics. The Wannier functions are specific to each material and provide a minimal and therefore computationally convenient basis. Furthermore, their strong localization greatly improves the computational performance in two ways: first, the resulting Hamiltonian becomes very sparse and, second, the electron–hole interaction terms can be evaluated efficiently in real space, where large electron–hole distances are handled by a multipole expansion. For the calculation of optical spectra we employ the sparse exciton Hamiltonian in a time-domain approach, which scales linearly with system size. We demonstrate the method for bulk silicon—one of the most frequently studied benchmark systems—and envision calculating optical properties of systems with much larger and more complex unit cells, which are presently computationally prohibitive.

Resonant mode coupling approximation for calculation of optical spectra of stacked photonic crystal slabs. Part II

We propose the further development of the resonant mode coupling approximation for the calculation of optical spectra of stacked periodic nanostructures in terms of the scattering matrix. We previously showed that given the resonant input and output vectors as well as background scattering matrices of two subsystems, one can easily calculate those for the combined system comprising two subsystems. It allows us to write a resonant approximation for the combined system and speed up the calculation significantly for typical wave scattering problems. This approach is best suitable for isolated resonances when the approximation of a constant background scattering matrix is reasonable. In this article, we aim at expanding the applicability of the resonant mode coupling approximation by utilizing more complicated approximations for the background matrices. In particular, we show that consideration of energy-dependent correction terms for the background matrices remarkably reduces the calculation error of the resonant parameters. Here we first consider a linear approximation of the background scattering matrices which is subsequently used as a base for a piecewise-linear approximation. We show that the latter allows one to keep the approximation error negligibly small with only a few sample points and to apply the resonant mode coupling approximation within almost arbitrary large energy ranges. Finally, we consider the approximation of background matrices by arbitrary matrix functions and propose a technique to derive resonant poles in this case. The methods described here could be considered an alternative approach for calculating the optical spectra of stacked systems.

Resonant mode coupling approximation for calculation of optical spectra of stacked photonic crystal slabs. Part I

We develop the resonant mode coupling approximation to calculate the optical spectra of a stack of two photonic crystal slabs in terms of the scattering matrix. The method is based on the derivation of input and output resonant vectors in each slab in terms of the Fourier modal method in the scattering matrix form. We show that using the resonant mode coupling approximation of the scattering matrices of the upper and lower slabs, one can construct the total scattering matrix of the stack. The formation of the resonant output and input vectors of the stacked system is rigorously derived by means of an effective Hamiltonian. We demonstrate that the proposed procedure dramatically decreases the computation time without sufficient loss of accuracy. We believe that the proposed technique can be a powerful tool for fast-solving inverse scattering problems using stochastic optimization methods such as genetic algorithms or machine learning.

Double k-Grid Method for Solving the Bethe-Salpeter Equation via Lanczos Approaches.

Convergence with respect to the size of the k-points sampling grid of the Brillouin zone is the main bottleneck in the calculation of optical spectra of periodic crystals via the Bethe-Salpeter equation (BSE). We tackle this challenge by proposing a double grid approach to k-sampling compatible with the effective Lanczos-based Haydock iterative solution. Our method relies on a coarse k-grid that drives the computational cost, while a dense k-grid is responsible for capturing excitonic effects, albeit in an approximated way. Importantly, the fine k-grid requires minimal extra computation due to the simplicity of our approach, which also makes the latter straightforward to implement. We performed tests on bulk Si, bulk GaAs and monolayer MoS2, all of which produced spectra in good agreement with data reported elsewhere. This framework has the potential of enabling the calculation of optical spectra in semiconducting systems where the efficiency of the Haydock scheme alone is not enough to achieve a computationally tractable solution of the BSE, e.g., large-scale systems with very stringent k-sampling requirements for achieving convergence.

Influence of high-energy local orbitals and electron-phonon interactions on the band gaps and optical absorption spectra of hexagonal boron nitride

We report ab initio band diagram and optical absorption spectra of hexagonal boron nitride ($h$-BN), focusing on unravelling how the completeness of the basis set for $GW$ calculations and electron-phonon interactions (EPIs) impact on them. The completeness of the basis set, an issue which was seldom discussed in previous optical spectra calculations of $h$-BN, is found crucial in providing converged quasiparticle band gaps. In the comparison among three different codes, we demonstrate that by including high-energy local orbitals in the all-electron linearized augmented plane waves based $GW$ calculations, the quasiparticle direct and fundamental indirect band gaps are widened by $\ensuremath{\sim}0.2$ eV, giving values of 6.81 eV and 6.25 eV, respectively at the $G{W}_{0}$ level. EPIs, on the other hand, reduce them to 6.62 eV and 6.03 eV respectively at 0 K, and 6.60 eV and 5.98 eV respectively at 300 K. With clamped crystal structure, the first peak of the absorption spectrum is at 6.07 eV, originating from the direct exciton contributed by electron transitions around $K$ in the Brillouin zone. After including the EPIs-renormalized quasiparticles in the Bethe-Salpeter equation, the exciton-phonon coupling shifts the first peak to 5.83 eV at 300 K, lower than the experimental value of $\ensuremath{\sim}6.00$ eV. This accuracy is acceptable to an ab initio description of excited states with no fitting parameter.

First-principles study on the structural, electronic, elastic and thermal properties of P42/mnm-BSi

Using first-principles density functional theory, a tetragonal silicon–boron binary structure with space group P42/mnm is predicted in present work. This structure is confirmed to be dynamically and mechanically stable below 19.3 GPa, and possesses lower energy than other candidates. Based on the plane wave pseudopotential method, the electronic structure, elastic constant, bulk modulus, shear modulus, Young’s modulus, lattice thermal conductivity and phonon lifetime of P42/mnm-BSi are systematically studied. Interestingly, a four-center and six-electron delocalized π bond is found in P42/mnm-BSi, which is the most important factor for its structural stability. The optical spectra calculations reveal that P42/mnm-BSi is a wide band-gap semiconductor with an indirect band-gap of 2.5 eV and has a promising application in the photoelectric devices. The calculated lattice thermal conductivity along the [001] crystal direction is 145 Wm−1 K−1 that is about three times higher than that along both the [100] and [010] directions, which is originated from the different group velocity along the crystal axis. Moreover, the acoustic–optical coupling has some positive influences on lattice thermal conductivity. This study gives a fundamental understanding of the structural, electronic, elastic and heat transport properties in P42/mnm-BSi.

Optical spectra of 2D monolayers from time-dependent density functional theory.

The optical spectra of two-dimensional (2D) periodic systems provide a challenge for time-dependent density-functional theory (TDDFT) because of the large excitonic effects in these materials. In this work we explore how accurately these spectra can be described within a pure Kohn-Sham time-dependent density-functional framework, i.e., a framework in which no theory beyond Kohn-Sham density-functional theory, such as GW, is required to correct the Kohn-Sham gap. To achieve this goal we adapted a recent approach we developed for the optical spectra of 3D systems [S. Cavo, J. A. Berger and P. Romaniello, Phys. Rev. B, 2020, 101, 115109] to those of 2D systems. Our approach relies on the link between the exchange-correlation kernel of TDDFT and the derivative discontinuity of ground-state density-functional theory, which guarantees a correct quasi-particle gap, and on a generalization of the polarization functional [J. A. Berger, Phys. Rev. Lett., 2015, 115, 137402], which describes the excitonic effects. We applied our approach to two prototypical 2D monolayers, h-BN and MoS2. We find that our protocol gives a qualitatively good description of the optical spectrum of h-BN, whereas improvements are needed for MoS2 to describe the intensity of the excitonic peaks.

Effective model of one-dimensional extended Hubbard systems: Application to linear optical spectrum calculations in large systems based on many-body Wannier functions

We propose an effective model called the "charge model", for the half-filled one-dimensional Hubbard and extended Hubbard models. In this model, spin-charge separation, which has been justified from an infinite on-site repulsion ($U$) in the strict sense, is compatible with charge fluctuations. Our analyses based on the many-body Wannier functions succeeded in determining the optical conductivity spectra in large systems. The obtained spectra reproduce the spectra for the original models well even in the intermediate $U$ region of $U=5-10T$, with $T$ being the nearest-neighbor electron hopping energy. These results indicate that the spin-charge separation works fairly well in this intermediate $U$ region against the usual expectation and that the charge model is an effective model that applies to actual quasi-one-dimensional materials classified as strongly correlated electron systems.

Multiple-peak resonance of optical second harmonic generation arising from band nesting in monolayer transition metal dichalcogenides TX2 on SiO2/Si(001) substrates (T=Mo,W;X=S,Se)

The nonlinear optical response of monolayer transition-metal dichalcogenides $T{X}_{2}\phantom{\rule{0.28em}{0ex}}(T=\mathrm{Mo},\mathrm{W};\phantom{\rule{0.28em}{0ex}}X=\mathrm{S},\phantom{\rule{0.28em}{0ex}}\mathrm{Se})$ on ${\mathrm{SiO}}_{2}/\mathrm{Si}(001)$ substrates was examined using second-harmonic generation (SHG) spectroscopy in combination with differential reflectance (DR) spectroscopy. In the SHG spectroscopy, the second-harmonic intensity corrected by a crystalline quartz reference was obtained for the wavelength of the incident femtosecond laser varied from 750 to 1040 nm. The SHG spectra of all the four ${TX}_{2}$ were dominated by two-photon resonance around the C peaks in the DR spectra that was previously assigned to interband transitions at critical points formed as a result of band nesting. Multiple peaks were observed in each resonance spectrum, which was then decomposed into a few components. The overall feature of the main components---denoted as $\overline{\mathrm{C}1}$ and $\overline{\mathrm{C}2}$---was common among the four ${TX}_{2}$ materials. The optical transitions contributing to these components were concluded to occur at different $k$ points in a ring-shaped area around the \cyrchar\CYRG{} point with the aid of the published results of optical spectrum calculations and the SHG spectrum of bilayer ${\mathrm{MoS}}_{2}$. In addition, one-photon resonance at the $A$ exciton and two-photon resonance at the ${A}^{\ensuremath{'}}$ exciton were observed in ${\mathrm{MoSe}}_{2}$ and ${\mathrm{WSe}}_{2}$, respectively, and their intensities were proven to be significantly lower than those of the resonances around the C peaks.

Variational Quantum Computation of Excited States

The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum computers.

Ab initio analysis of the optical spectra and EPR parameters of Ni2+ ions in CaF2 and CdF2 crystals

Crystals with fluorite type structure doped with transition metals (TM) in different oxidation states provide the possibility of investigating optical spectra, magnetic properties and ligand field (LF) parameters of TM in cubic eightfold coordination. If the doped ion in the host crystal matrix has a degenerate ground state then, due to the strong T⊗τ Jahn-Teller (JT) effect, the cubic coordination geometry of the impurity ion will be distorted to octahedral, with the change in its properties. In this paper we present the results of the ab initio investigation of absorption optical spectra, JT stabilization energy in the ground state, spin-Hamiltonian and ligand field parameters of divalent nickel ion doped in cubic CaF2 and CdF2 crystals. The analysis of new cluster [NiF6]4- with trigonal symmetry (D3d) at the Ni2+site was made based on the ab initio multireference methods (MR). All calculations are applied to the [NiF6]4- cluster embedded in an extended point charge field of host matrix ions built according to the Gellé-Lepetit procedure. After density functional theory (DFT) optimization of the doped crystals, the ab initio energy calculation of the electronic states and corresponding wave functions of Ni2+ ions is performed from the complete active space self-consistent field (CASSCF). The improved energy states obtained by using different approaches such as N-electron valence second order perturbation theory (NEVPT2), second order dynamic correlation dressed complete active space (DCD-CAS2), difference dedicate configuration interaction with three degrees of freedom (MRDDCI3) and spectroscopy-oriented configuration interactions (SORCI), were analyzed. In addition, the ab initio ligand field theory (AILFT) procedure allows extracting all LF parameters and spin-orbit coupling constant. The obtained results are discussed and the comparison with the available in the literature corresponding experimental values literature yields a reasonably agreement between theory and experiment, which justifies this new route of investigation.The structural mechanism around Ni2+ center through JT effect, combined with the above mentioned methodology, allows for more consistent and reliable calculations of optical spectra and spin-Hamiltonian parameters of any impurity ions doped in eightfold cubic coordination.

Effect of thermal post-treatment on surface plasmon resonance characteristics of gold nanoparticles formed in glass by UV laser irradiation

Effects of thermal post treatment and of thickness of the initial gold film coated the silicate glass surface, on localized surface plasmon resonance (SPR) of gold nanoparticles formed in glass by UV laser irradiation were studied to develop effective technique for production of gold nanoparticles and their arrays with required and stable characteristics of SPR. Optical spectra of the obtained Au/glass samples showed that SPR of gold nanoparticles formed by irradiation of glasses sputter coated with gold films of thickness 6–10 nm depends of T-treatment, while irradiation of glass coated with gold film ∼70 nm leads to SPR stable of temperature. The origin of such dependences was studied by the structural analysis of gold nanoparticles in Au/glass samples before and after thermal treatment using XRD, EXAFS methods, TEM-EDX images and direct calculations of optical spectra. It was revealed that the changes or stability of SPR parameters under thermal post-treatment of Au/glass samples depend respectively of the presence or absence of tin atoms in the near-surface region (shell) of the gold particles. Thus, if tin atoms are presented in the shell of gold particles (as in “as prepared” Au/glass samples initially coated with gold films of 6–10 nm) then the leave of tin atoms from the particle's volume during the heating leads to partial dissolution of the particles shell and consequently, to decreasing of the particles size, which in turn leads to the observed changes in SPR. The most probable explanation of the presence of tin atoms in the shell of gold particles formed by irradiation of samples initially coated with gold films of thickness 6–10 nm and their absence in the case of sample with film ∼70 nm was proposed, basing on the difference in the effects of the first laser pulse actions on these films on the tin-bath side of the glass samples. The sizes of coherent scattering region in gold nanoparticles before and after thermal treatment of Au/glass samples were determined and the dependence of these sizes upon the thickness of the gold film coating the sample's surface before laser irradiation was revealed.

Optical conductivity calculation of a k.p model semiconductor GaAs incorporating first-order electron-hole vertex correction

The role of excitons in semiconducting materials carries potential applications. Experimental results show that excitonic signals also appear in optical absorption spectra of semiconductor system with narrow gap, such as Gallium Arsenide (GaAs). While on the theoretical side, calculation of optical spectra based purely on Density Functional Theory (DFT) without taking electron-hole (e-h) interactions into account does not lead to the appearance of any excitonic signal. Meanwhile, existing DFT-based algorithms that include a full vertex correction through Bethe-Salpeter equation may reveal an excitonic signal, but the algorithm has not provided a way to analyze the excitonic signal further. Motivated to provide a way to isolate the excitonic effect in the optical response theoretically, we develop a method of calculation for the optical conductivity of a narrow band-gap semiconductor GaAs within the 8-band k.p model that includes electron-hole interactions through first-order electron-hole vertex correction. Our calculation confirms that the first-order e-h vertex correction reveals excitonic signal around 1.5 eV (the band gap edge), consistent with the experimental data.

Study of structural, electronic, optical and thermal properties of refractory material (CrAlB)

The structural, electronic, optical and thermal properties of ternary transition metal boride (CrAlB) are studied using full potential linearized augmented plane wave method in the framework of the density functional theory. The exchange-correlation potential is solved using the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol-GGA). The structural parameters are optimized to obtain equilibrium lattice constant, bulk modulus and its pressure derivative. The calculated band structure, density of states and electronic charge density show that the material possesses metallic nature and have covalent band character. Optical spectra calculations such as the real and imaginary part of dielectric constant, refractive index, extinction coefficient, reflectivity, absorption coefficient, conductivity, and loss function are performed within the photon energy range of 0–40 eV. In this case the obtained plasma frequency corresponds to 24.12eV. For radiation above this energy the property of CrAlB changes from metallic to dielectric. The calculations of the thermal properties using Gibb's program have been performed in the range 0–5000 K at 0, 20 and 50 GPa of pressure. The studies of optical and thermal properties show that it is an eligible candidate for optoelectronic devices, and the devices working at high temperature. The results for CrAlB are reported for the first time as neither CrAlB has been synthesized nor any theoretical calculation has been performed till so far.

Time-dependent density functional theory calculations for the excitation spectra of III-V ternary alloys

We adopted the time-dependent density functional theory (TDDFT) within the linear augmented Slater-type orbitals (LASTO) basis and the cluster averaging method to compute the {\color{red}excitation} spectra of III-V ternary alloys with arbitrary concentration $x$. The TDDFT was carried out with the use of adiabatic meta-generalized gradient approximation (mGGA), which contains the $1/q^2$ singularity in the dynamical exchange-correlation kernel ($f_{XC,00}(\mathbf{q})$) as $q\rightarrow 0$. We found that by using wave functions obtained in local density approximation (LDA) while using mGGA to compute self-energy correction to the band structures, we can get {\color{red} good overall} agreement between theoretical results and experimental data for the excitation spectra. Thus, our studies provide some insight into the theoretical calculation of optical spectra of semiconductor alloys.

Nonlinear network model analysis of vibrational energy transfer and localisation in the Fenna-Matthews-Olson complex.

Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex of photosynthetic green sulphur bacteria, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level in large protein structures, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the entire trimeric FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes through their influence on pigment properties. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.

Influence of out-of-plane response on optical properties of two-dimensional materials: First principles approach

The ab initio calculation of optical spectra of sheet crystals usually arranges them in a three-dimensional superlattice with a sufficiently large interlayer distance. We show how the resulting frequency-dependent dielectric tensor is related to the anisotropic optical conductivity of an individual sheet or to the dielectric tensor of a corresponding film with thickness $d$. Their out-of-plane component is taken into account, in contrast to usual treatments. We demonstrate that the generalized transfer-matrix method to model the optical properties of a layer system containing a sheet crystal accounts for all tensor components. As long as $d\ensuremath{\ll}\ensuremath{\lambda}$ ($\ensuremath{\lambda}$-wavelength of light) this generalized formulation of the optical properties for anisotropic two-dimensional (2D) systems of arbitrary thickness reproduces the limits found in literature that are based either on electromagnetic boundary conditions for a conducting surface or on an isotropic dielectric tensor. For $s$-polarized light, the results are independent of the sheet description. For oblique incidence of $p$-polarized light, the tensor nature of the optical conductivity (or the dielectric function) of the sheet crystal strongly impacts on reflectance, transmittance, and absorbance due to the out-of-plane optical conductivity. The limit $d\ensuremath{\rightarrow}0$ should be taken in the final expressions. Example spectra are given for the group-IV honeycomb 2D crystals graphene and silicene.