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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Photophysical Properties and Electronic Structure of Zinc(II) Porphyrins Bearing 0–4 meso -Phenyl Substituents: Zinc Porphine to Zinc Tetraphenylporphyrin (ZnTPP)

Six zinc(II) porphyrins bearing 0–4 meso-phenyl substituents have been examined spectroscopically and theoretically. Comparisons with previously examined free base analogues afford a deep understanding of the electronic and photophysical effects of systematic addition of phenyl groups in porphyrins containing a central zinc(II) ion versus two hydrogen atoms. Trends in the wavelengths and relative intensities of the absorption bands are generally consistent with predictions from time-dependent density functional theory calculations and simulations from Gouterman’s four-orbital model. These trends derive from a preferential effect of the meso-phenyl groups to raise the energy of the highest occupied molecular orbital. The calculations reveal additional insights, such as a progressive increase in oscillator strength in the violet-red (B-Q) absorption manifold with increasing number of phenyls. Progressive addition of 0–4 phenyl substituents to the zinc porphyrins in O 2 -free toluene engenders a reduction in the measured lifetime of the lowest singlet excited state (2.5–2.1 ns), an increase in the S 1 → S o fluorescence yield (0.022–0.030), a decrease in the yield of S 1 → T 1 intersystem crossing (0.93–0.88), and an increase in the yield of S 1 → S o internal conversion (0.048–0.090). The derived rate constants for S 1 decay reveal significant differences in the photophysical properties of the zinc chelates versus free base forms. Here, the unexpected finding of a larger rate constant for internal conversion for zinc chelates versus free bases is particularly exemplary. Collectively, the findings afford fundamental insights into the photophysical properties and electronic structure of meso-phenylporphyrins, which are widely used as benchmarks for tetrapyrrole-based architectures in solar energy and life sciences research.

14 SOLAR ENERGY↗
DOE OSTI2026

Covalency of M–N Bonds in Isomorphous Lanthanide and Actinide 5-(2-Pyridyl)-1H-tetrazolate Complexes

Experimental and computational analyses of [M(pdtz) 3 (H 2 O) 3 ]·3.5H 2 O (M 3+ = Pu 3+ −Cm 3+ , La 3+ −Nd 3+ , and Sm 3+ −Ho 3+ , pdtz− = 5-(2-pyridyl)-1H-tetrazolate) were conducted to understand potential differences in bonding between lanthanide and actinide complexes with a N-donor ligand. Structural analyses show that the An−N bond distances in the Pu 3+ , Am 3+ , and Cm 3+ complexes are within error of one another. Whereas in the lanthanide series, there is a nearly linear decrease in the Ln−N bond lengths from La 3+ to Ho 3+ (excluding Pm 3+ ). The An−N bond lengths are ∼0.015 Å shorter than their similarly-sized lanthanide analogs, in agreement with computational results that suggest greater covalent character in these bonds versus those with lanthanides. QTAIM analysis indicates that the An−N orbital mixing remains essentially unchanged from Pu 3+ to Cm 3+ , consistent with the nearly identical An−N bond lengths. However, upon deconvolution of the NLMOs into orbital compositions, the metal orbital contributions to An−N bonding decreases slightly overall wherein the 6d involvement remains constant, 7s involvement slightly increases, and 5f participation decreases. The molecular orbital energy diagram indicates that energy degeneracy between the 5f metal and 2p ligand orbitals increases from Pu 3+ to Cm 3+ and counteracts the contraction of the 5f orbtials. Together with prior reports of decreasing energy degeneracy between 5f and 3p orbitals from Np 3+ to Cf 3+ , these observations provide guidance on understanding how chemical bonding evolves in the actinide series.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Terpolymer Donor with Inside Alkyl Substituents on Thiophene π ‐Bridges toward Thiazolothiazole A 2 ‐Unit Enables 18.21% Efficiency of Polymer Solar Cells

Abstract PM6 is a widely used D–A copolymer donor in the polymer solar cells (PSCs). Incorporating second electron‐withdrawing (A 2 ) units into PM6 backbone by ternary D–A 1 –D–A 2 random copolymerization strategy is an effective approach to further improve its photovoltaic performance. Here, the authors synthesize the PM6‐based terpolymers by introducing thiazolothiazole as the A 2 units connecting with thiophene π‐bridges attaching alkyl substituent towards the A 2 unit (PMT‐CT) or towards D‐unit (PMT‐FT), and study the effect of the alkyl substituent position on the photovoltaic performance of them. Two terpolymers PMT‐FT‐10 and PMT‐CT‐10 are obtained by incorporating 10% A 2 units in the terpolymers. The film of PMT‐CT‐10 shows slightly up‐shifted highest occupied molecular orbital (HOMO) energy levels while better co‐planar structure than that of PMT‐FT‐10. Meanwhile, the PMT‐CT‐10:Y6 blend film exhibits better molecular packing properties, more proper phase separation and more balanced hole and electron mobilities, which are beneficial to more efficient exciton dissociation, efficient charge transport and weaker bimolecular recombination. Consequently, the PMT‐CT‐10 based PSCs obtain the highest power conversion efficiency of 18.21%. The results indicate that side chain position on the thiophene π‐bridges influence the device performance of the terpolymer donors, and PMT‐CT‐10 is a high efficiency polymer donor for the PSCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Improving Excited-State Potential Energy Surfaces via Optimal Orbital Shapes

In this work, we demonstrate that, rather than resorting to high-cost dynamic correlation methods, qualitative failures in excited-state potential energy surface predictions can often be remedied at no additional cost by ensuring that optimal molecular orbitals are used for each individual excited state. This approach also avoids the weighting choices required by state-averaging and dynamic weighting and obviates their need for expensive wave function response calculations when relaxing excited-state geometries. Although multistate approaches are of course preferred near conical intersections, other features of excited-state potential energy surfaces can benefit significantly from our single-state approach. In three different systems, including a double bond dissociation, a biologically relevant amino hydrogen dissociation, and an amino-to-ring intramolecular charge transfer, we show that state-specific orbitals offer qualitative improvements over the state-averaged status quo.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Inverse Trans Influence and Uranium-Arene σ-Bonding Drive Molecular Geometry: Ligand Modification from Hard to Soft Flips the Oxide from Axial to Equatorial

A rare example of an equatorially bound terminal uranium(V) oxo complex in a chelating sulfur-based ligand environment, namely [(mes( Me,Ad ArS) 3 )U V (O eq )(THF)] (2), is presented. Octahedrally coordinated 2 is obtained by reaction of the mesitylene-anchored tris-thiophenolate-coordinated uranium(III) complex [U III ((SAr Ad,Me ) 3 mes)] (1) with the oxygen-atom transfer reagent N 2 O. The observed, equatorially bound oxo ligand in 2 is in stark contrast to its known tris-aryloxide analog, [(mes( Me,Ad ArO) 3 )U V (O ax )(THF)] (A), where the oxo ligand occupies the typically observed axial coordination site. Complexes 1 and 2 are characterized by single-crystal X-ray diffraction analyses and spectroscopic and magnetochemical methods, including 1 H NMR, UV/vis/NIR electronic absorption, as well as EPR spectroscopy and SQUID magnetometry, thus confirming the C S symmetry and the pentavalent oxidation state of 2. Encompassing quantum chemical calculations (DFT and CASPT2) on 2 and its tris-phenolate analog A, support and rationalize the structural and electronic differences. The molecular orbital pictures show that a stabilizing σ-bonding interaction arising from the U–O eq inverse trans influence (ITI) is present in 2 but missing in A. In 2, the sulfur 3p orbitals are closer in energy to the uranium 5f manifold than the arene π-system, leading to an ITI, while U–arene σ- or δ-bonding is not observed. Although the arene orbitals remain separated from the uranium 5f orbitals in A, the absence of an ITI allows the arene a 2u orbital to engage in a σ-type interaction with the metal. Thus, incorporating a tris-thiophenolate to an arene anchor introduces a new design concept in molecular f-element chemistry. This approach stabilizes an equatorially bound U(V) oxo center, contrasting with its tris-phenolate counterpart, where oxo coordination is axial. The observed geometric divergence, driven by competing ITI and U–arene interactions, not only tunes electronic structure but also leads to differentiated reactivity: only the phenolate analogs activate H 2 O, while the thiolates do not.

Hydrocarbons↗
DOE OSTI2022

Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations

The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree–Fock virtual orbitals by natural orbitals (NOs). Here, in this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller–Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties—electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F–Ts), and parity-violating energy differences for H 2 Z 2 (Z = O–Se)—we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Trapping Ca + inside a molecular cavity: computational study of the potential energy surfaces for Ca + -[ n ]cycloparaphenylene, n = 5–12

Ion trap quantum computing utilizes electronic states of atomic ions such as Ca + to encode information on to a qubit. To explore the fundamental properties of Ca + inside molecular cavities, we describe here a computational study of Ca + bound inside neutral [n]-cycloparaphenylenes (n = 5–12), often referred to as “nanohoops”. This ab initio study characterizes optimized structures, harmonic vibrational frequencies, potential energy surfaces, and ion molecular orbital distortion as functions of increasing nanohoop size. Here the results of this work provide a first step in guiding experimental studies of the spectroscopy of these ion-molecular cavity complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Charge Transport Characteristics of Molecular Electronic Junctions Studied by Transition Voltage Spectroscopy

The field of molecular electronics is prompted by tremendous opportunities for using a single-molecule and molecular monolayers as active components in integrated circuits. Until now, a wide range of molecular devices exhibiting characteristic functions, such as diodes, transistors, switches, and memory, have been demonstrated. However, a full understanding of the crucial factors that affect charge transport through molecular electronic junctions should yet be accomplished. Remarkably, recent advances in transition voltage spectroscopy (TVS) elucidate that it can provide key quantities for probing the transport characteristics of the junctions, including, for example, the position of the frontier molecular orbital energy relative to the electrode Fermi level and the strength of the molecule–electrode interactions. These parameters are known to be highly associated with charge transport behaviors in molecular systems and can then be used in the design of molecule-based devices with rationally tuned electronic properties. This article highlights the fundamental principle of TVS and then demonstrates its major applications to study the charge transport properties of molecular electronic junctions.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Clar’s Goblet on Graphene: Field-Modulated Charge Transfer in a Hydrocarbon Heterostructure

In certain configurations, the aromatic properties of benzene ring structured molecules allow for unpaired, reactive valence electrons (known as radicals). Clar’s goblets are such molecules. With an even number of unpaired radicals, these nanographenes are topologically frustrated hydrocarbons in which π-bonding network and topology of edges give rise to the magnetism. Clar’s goblets are therefore valued as prospective qubits provided they can be modulated between magnetic states. Here, using first-principles DFT, we demonstrate the effects of adsorption on both molecule and substrate in a graphene–Clar’s goblet heterostructure. We look at the energy difference bewteen FM and AFM states of the system and discuss underlying physical and chemical mechanisms in reference to the highest occupied molecular orbital (HOMO) and second HOMO (HOMO–1). We find that the HOMO of the molecule in the FM state is right at the Fermi surface, which leads to the hybridization between molecular state and the graphene state near the Dirac point. Furthermore, we investigate qualitative changes in charge realignment and magnetic state under a variable electric field. Transitions from FM to AFM and back to FM states are observed.

Bruce, Adam V.↗
DOE OSTI2026

High-Energy Hybridized States Enable Long-Lived Hot Electrons in Cobaloxime-Silicon Nanocrystal System

Strong electronic coupling is achieved between the molecular catalyst cobaloxime ([Co]) and silicon nanocrystals (Si NCs) bridged by an ethylenepyridine group derived from vinylpyridine (vpy) covalently bound to the Si NC surface (Si-vpy-[Co]). The ethylenepyridine tether in Si-vpy-[Co] is key to dramatic changes to the system’s physical properties which are not observed in the corresponding formylpyridine (fpy) system (Si-fpy-[Co]) consistent with strong electronic coupling previously observed only in dark electrochemical systems. UV−vis absorption spectroscopy reveals new [Co]-centered electronic states in Si-vpy-[Co], and transient absorption spectroscopy finds a strong absorption feature appearing within 250 fs and persisting for at least 5 ns. Astoundingly, spectroelectrochemical measurements reveal that this absorption feature is consistent with both the singly reduced [Co] − and doubly reduced [Co] 2− complexes, leading to the conclusion that these long-lived charges are derived from high-energy “hot” electrons residing in [Co]-centered states. Detailed analysis using cyclic voltammetry, spectroelectrochemistry, electron paramagnetic resonance spectroscopy, and density functional theory (DFT) calculations provides insight into the unique electronic structure created in Si-vpy-[Co]. DFT reveals that the new electronic states arise from hybridization between deep Si NC band states and high-energy molecular orbitals of the ethylenepyridine tether and the [Co] catalyst and are facilitated by σ-bonding character at the ethylenepyridine linkage. This study demonstrates that strong electronic coupling achieved through precise molecular chemistry can change the paradigm of otherwise fixed energy levels in hybrid photoelectrochemical systems for artificial photosynthesis and related applications.

14 SOLAR ENERGY↗
DOE OSTI2021

Resonant Inelastic X-ray Scattering Calculations of Transition Metal Complexes Within a Simplified Time-Dependent Density Functional Theory Framework

We present a time-dependent density functional theory (TDDFT) approach to compute the light-matter couplings between two different manifolds of excited states relative to a common ground state in the context of 4d transition metal systems. These quantities are the necessary ingredients to solve the Kramers-Heisenberg (KH) equation for resonant inelastic X-ray scattering (RIXS) and several other types of two-photon spectroscopies. The procedure is based on the pseudo-wavefunction approach, where the solutions of a TDDFT calculation can be used to construct excited-state wave- functions, and on the restricted energy window approach, where a manifold of excited states can be rigorously defined based on the energies of the occupied molecular orbitals involved in the excitation process. Thus, the present approach bypasses the need to solve the costly TDDFT quadratic-response equations. We illustrate the applicability of the method to 4d transition metal molecular complexes by calculating the 2p4d RIXS maps of three representative ruthenium complexes and comparing them to experimental results. The method can capture all the experimental features in all three complexes to allow the assignment of the experimental peaks, and relative energies correct to within 0.6 eV at the cost of two independent TDDFT calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Ground and excited electronic structures of electride and alkalide units: The cases of Metal-Tren, -Azacryptand, and -TriPip222 complexes

A systematic electronic structure analysis was conducted for M(L) n molecular electrides and their corresponding alkalide units M(L) n @M' (M/M' = Na, K; L = Tren, Azacryptand, TriPip222; n = 1, 2). All complexes belong to the “superalkali” category due to their low ionization potentials. The saturated molecular electrides display M+(L) n - form with a greatly diffuse quasispherical electron cloud. They were identified as “superatoms” considering the contours of populating atomic-type molecular orbitals. The observed superatomic Aufbau order of M(Tren) 2 is 1S, 1P, 1D, 1F, 2S, 2P, and 1G and it is consistent with those of M(Azacryptand) and M(TriPip222) up to the analyzed 1F level. Their excitation energies decrease gradually moving from M(Tren) 2 to M(Azacryptand) and to M(TriPip222). The studied alkalide complexes carry [M(L) n ] + @M' - ionic structure and their dissociation energies vary in the sequence of K(L) n @Na > Na(L) n @Na > K(L) n @K > Na(L) n @K. Similar to molecular electrides, the anions of alkalide units occupy electrons in diffuse Rydberg-like orbitals. In this work, excited states of [M(L) n @M'] 0/+/- and their trends are also analyzed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A perspective on the redox properties of tetrapyrrole macrocycles

Tetrapyrrole macrocycles serve a multitude of roles in biological systems, including oxygen transport by heme and light harvesting and charge separation by chlorophylls and bacteriochlorophylls. Synthetic tetrapyrroles are utilized in diverse applications ranging from solar-energy conversion to photomedicine. Nevertheless, students beginning tetrapyrrole research, as well as established practitioners, are often puzzled when comparing properties of related tetrapyrroles. Questions arise as to why optical spectra of two tetrapyrroles often shift in wavelength/energy in a direction opposite to that predicted by common chemical intuition based on the size of a π-electron system. Gouterman's four-orbital model provides a framework for understanding these optical properties. Similarly, it can be puzzling as to why the oxidation potentials differ significantly when comparing two related tetrapyrroles, yet the reduction potentials change very little or shift in the opposite direction. In order to understand these redox properties, it must be recognized that structural/electronic alterations affect the four frontier molecular orbitals (HOMO, LUMO, HOMO-1 and LUMO+1) unequally and in many cases the LUMO+1, and not the LUMO, may track the HOMO in energy. This perspective presents a fundamental framework concerning tetrapyrrole electronic properties that should provide a foundation for rational molecular design in tetrapyrrole science.

chlorophyll↗
DOE OSTI2023

Photoionization of C 60 at high energies

Calculations of the photoionization cross section of C60 including all valence and core subshells have been carried out for photon energies up to 1 keV using density functional theory (DFT) and time-dependent DFT (TDDFT) within the framework of a fully molecular model. The high-energy valence subshell cross sections behave rather differently than the results from model potentials where the cross section falls far too rapidly with energy. This unphysical behavior of the model calculations is traced to smearing out of the carbon nuclei in the model potentials which makes it difficult for momentum to be conserved at the higher energies. Comparison with 60 times carbon atomic cross section sheds light on similarities and differences. The high energy behavior of individual valence cross sections reflects the amount of C 2s/2p mixing in the molecular orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Anion photoelectron spectroscopy and chemical bonding of ThS 2 – and ThSO –

Anion photoelectron spectra of ThSO – and ThS 2 – were recorded using the third (355 nm) harmonic of an Nd-YAG laser; these provided the measured vertical detachment energies of each anion. The experiments are supported by extensive coupled cluster calculations on ThSO, ThSO – , ThS 2 , and ThS 2 – , as well as the oxygen congeners ThO 2 and ThO 2 – . The ab initio calculations, which included complete basis set extrapolations, spin–orbit effects using four-component coupled cluster, and higher-order correlation contributions through CCSDT(Q), yielded an adiabatic electron affinity for ThO 2 – that was within 0.02 eV of the previously determined experimental value. The singly occupied molecular orbital (SOMO) in all three anions corresponds primarily to the 7s orbital on Th. Successive substitution of S for each O in ThO 2 leads to larger electron affinities and smaller bond angles in the neutral molecules, but larger angles in the anions. As demonstrated by Franck–Condon simulations of the spectra using the CCSD(T) spectroscopic constants, substitution of O by S significantly complicates the resulting detachment spectra due to the lower vibrational frequencies in the sulfur species. Altogether the calculated vertical detachment energies are in very good agreement with the experiment. In addition to the adiabatic electron affinities of each species, atomization energies and heats of formation have also been determined via the FPD approach with expected uncertainties of 1–2 kcal/mol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

NEXAFS spectroscopy of alkylated benzothienobenzothiophene thin films at the carbon and sulfur K-edges

Alkylated benzothienobenzothiophenes are an important class of organic semiconductors that exhibit high performance in solution-processed organic field-effect transistors. In this work, we study the near-edge x-ray absorption fine-structure (NEXAFS) spectra of 2,7-didecyl[1]benzothieno[3,2-b][1]benzothiophene (C 10 -BTBT) at both the carbon and sulfur K-edges. Angle-resolved experiments of thin films are performed to characterize the dichroism associated with molecular orientation. First-principles calculations using the density functional theory-based many-body x-ray absorption spectroscopy (MBXAS) method are also performed to correlate the peaks observed and their dichroism with transitions to specific antibonding molecular orbitals. Interestingly, the dichroism of the dominant, lowest energy peak is opposite at the carbon and sulfur K-edges. While the low-energy peak at the carbon K-edge is assigned to carbon 1s → π* transitions with transition dipole moment (TDM) perpendicular to the planar BTBT core, the dominant low energy peak at the sulfur K-edge is assigned to sulfur 1s → σ* transitions with TDM oriented along the long axis of the BTBT core. These differences at the sulfur and carbon K-edges are understood through the MBAXS simulations that find a reordering of the energy of the lowest energy π* and σ* transitions at the sulfur K-edge due to the strong localization of the σ* orbital over the sulfur atom. This work highlights differences in the NEXAFS spectra of organic semiconductors at carbon and sulfur K-edges and provides new insights into peak assignment and x-ray dichroism relevant for studying the molecular orientation of organic semiconductor films.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Secondary electron emission measurements from imidazolium-based ionic liquids

The electron-induced secondary electron emission (SEE) yields of imidazolium-based ionic liquids are presented for primary electron beam energies between 30 and 1000 eV. These results are important for understanding plasma synthesis of nanoparticles in plasma discharges with an ionic liquid electrode. Due to their low vapor pressure and high conductivity, ionic liquids can produce metal nanoparticles in low-pressure plasmas through reduction of dissolved metal salts. In this work, the low vapor pressure of ionic liquids is exploited to directly measure SEE yields by bombarding the liquid with electrons and measuring the resulting currents. The ionic liquids studied are [BMIM][Ac], [EMIM][Ac], and [BMIM][BF 4 ]. The SEE yields vary significantly over the energy range, with maximum yields of around 2 at 200 eV for [BMIM][Ac] and [EMIM][Ac], and 1.8 at 250 eV for [BMIM][BF 4 ]. Molecular orbital calculations indicate that the acetate anion is the likely electron donor for [BMIM][Ac] and [EMIM][Ac], while in [BMIM][BF 4 ], the electrons likely originate from the [BMIM] + cation. The differences in SEE yields are attributed to varying ionization potentials and molecular structures of the ionic liquids. These findings are essential for accurate modeling of plasma discharges and understanding SEE mechanisms in ionic liquids.

ionic liquids↗
DOE OSTI2021

The FMO-DFTB Method

Although the fragment molecular orbital (FMO) method enables electronic structure calculations with near-linear scaling behavior with respect to system size, the computational cost of ab initio methods typically employed in conjunction with FMO is still prohibitive for routine calculations of very large systems or long timescale molecular dynamics simulations. We, therefore, combined the FMO and density-functional tight-binding (DFTB) method, which is one of the emerging semi-empirical quantum chemical methods, and have demonstrated that FMO-DFTB is capable of performing geometry optimizations for systems containing up to one million atoms using limited computational resources. In this chapter, we will review the basics of the DFTB method first before introducing FMO-DFTB, focusing on the relationship with density functional theory and other FMO methodologies. We also demonstrate the latest scalings of FMO-DFTB2 and DFTB3 using three-dimensional water clusters, showing that the most favorable scaling is O(N1.16). Applications of FMO-DFTB to various systems are briefly summarized, and an outlook to future applications is provided.

Nishimoto, Yoshio↗