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At least 289 records · Page 16

Ultrafast Symmetry Control in Photoexcited Quantum Dots

Symmetry control is essential for realizing unconventional properties, such as ferroelectricity, nonlinear optical responses, and complex topological order, thus it holds promise for the design of emerging quantum and photonic systems. Nevertheless, fast and reversible control of symmetry in materials remains a challenge, especially for nanoscale systems. Here, reversible symmetry changes are unveiled in colloidal lead chalcogenide quantum dots on picosecond timescales. Using a combination of ultrafast electron diffraction and total X-ray scattering, in conjunction with atomic-scale structural modeling and first-principles calculations, it is revealed that symmetry-broken lead sulfide quantum dots restore to a centrosymmetric phase upon photoexcitation. The symmetry restoration is driven by photoexcited electronic carriers, which suppress lead off-centering for about 100 ps. Furthermore, the change in symmetry is closely correlated with the electronic properties, and the bandgap transiently red-shifts in the symmetry-restored quantum dots. Overall, this study elucidates reversible symmetry changes in colloidal quantum dots, and more broadly defines a new methodology to optically control symmetry in nanoscale systems on ultrafast timescales.

36 MATERIALS SCIENCE↗

Broadband Ultrafast Dynamics of Refractory Metals: TiN and ZrN

Transition metal nitrides have recently gained attention in the fields of plasmonics, plasmon-enhanced photocatalysis, photothermal applications, and nonlinear optics because of their suitable optical properties, refractory nature, and large laser damage thresholds. Here we report comparative studies of the transient response of films of titanium nitride (TiN), zirconium nitride (ZrN), and gold (Au) under femtosecond excitation. Broadband transient optical characterization helps to adjudicate earlier, somewhat inconsistent reports regarding hot electron lifetimes based upon single wavelength measurements. These pump–probe experiments show sub-picosecond transient dynamics only within the epsilon-near-zero window of the refractory metals. The dynamics are dominated by photoinduced interband transitions resulting from ultrafast electron energy redistribution. The enhanced reflection modulation in the epsilon-near-zero window makes it possible to observe the ultrafast optical response of these films at low pump fluences. These results indicate that electron–phonon coupling in TiN and ZrN is 25–100 times greater than in Au. Strong electron–phonon coupling drives the sub-picosecond optical response and facilitates greater lattice heating compared to Au, making TiN and ZrN promising for photothermal applications. The spectral response and dynamics of TiN and ZrN are only weakly sensitive to pump fluence and pump excitation energy. However, the magnitude of the response is much greater at higher pump photon energies and higher fluences, reaching peak observed values of 15% in TiN and 50% in ZrN in the epsilon-near-zero window.

36 MATERIALS SCIENCE↗

Resonance Effect in Brunel Harmonic Generation in Thin Film Organic Semiconductors

Abstract Nonlinear optical properties of organic semiconductors (OSCs) have been extensively investigated in the perturbative regime, while strong light induced high‐order processes in solid‐state OSCs are less studied. Here, below‐threshold harmonic generation is examined, both experimentally and theoretically, in two solid‐state thin film OSCs, that is, tetraphenylporphyrin and zinc tetraphenylporphyrin. Results show that the π–π* excitations of the porphyrin ring system generate the harmonic emission. The contribution of the Brunel harmonic to the 5th harmonic emission is uncovered, where the resonant 5‐photon transition ( S 0 → S 2 transition) is found to lead to an early onset of non‐perturbative behavior. A similar resonance effect is expected in Brunel harmonic generation in other organic materials.

36 MATERIALS SCIENCE↗

Electrochemical Control of the Ultrafast Lattice Response of a Layered Semimetal

The unique layer-stacking in two-dimensional (2D) van der Waals materials facilitates the formation of nearly degenerate phases of matter and opens novel routes for the design of low-power, reconfigurable functional materials. Electrochemical ion intercalation between stacked layers offers a promising approach to stabilize bulk metastable phases and to explore the effects of extreme carrier doping and strain. However, in situ characterization methods to study the structural evolution and dynamical functional properties of these intercalated materials remains limited. Here a novel experimental platform is presented capable of simultaneously performing electrochemical lithium-ion intercalation and multimodal ultrafast characterization of the lattice using both electron diffraction and nonlinear optical techniques. Using the layered semimetal WTe 2 as a model system, the interlayer shear phonon mode that modulates stacking between 2Dlayers is probed, showing that small amounts of lithiation enhance the amplitude and lifetime of the phonon, contrary to expectations. This results from the dynamically fluctuating and anharmonic structure between nearly degenerate phases at room temperature, which can be stabilized by electronic carriers accompanying the inserted lithium ions. At high lithiation, the T d ’ structure emerges and quenches the phonon response. This work defines new approaches for using electrochemistry to engineer the dynamic structure of 2D materials.

36 MATERIALS SCIENCE↗

Growth of Large‐Sized 2D Ultrathin SnSe Crystals with In‐Plane Ferroelectricity

Abstract Tin (II) selenide (SnSe) is an emerging 2D material with many intriguing properties, such as record‐high thermoelectric figure of merit (ZT), purely in‐plane ferroelectricity, and excellent nonlinear optical properties. To explore these functional properties and related applications, a crucial step is to develop controllable routes to synthesize large‐area, ultrathin, and high‐quality SnSe crystals. Physical vapor deposition (PVD) constitutes a reliable method to synthesize 2D SnSe, however, effects of various growth parameters have not yet been systematically investigated, and current PVD‐synthesized flakes are often thick (>10 nm) with small lateral sizes (<10 µm). In this work, high‐quality 2D SnSe crystals are synthesized via low‐pressure PVD, which display in‐plane ferroelectric domains observed by piezoresponse force microscopy and polarization‐dependent reflection spectroscopy. Detailed studies regarding the roles of various parameters are further carried out, including substrate pre‐annealing, growth duration, temperature, and pressure, which enable to rationally optimize the growth and obtain 2D SnSe crystals with lateral sizes up to ≈23.0 µm and thicknesses down to ≈2.0 nm (3–4 layers). This work paves the way for the controlled growth of large‐area 2D SnSe, facilitating the future exploration of many interesting multiferroic properties and applications with atomic thickness.

2D materials↗

Technical Routes to Achieve High Circular Polarized Luminescence in Chiral Perovskites: A Mini‐Review

Chiral hybrid organic-inorganic perovskites (HOIPs) have emerged as promising materials for optoelectronic and spintronic applications, leveraging unique properties such as circularly polarized luminescence (CPL), circularly polarized nonlinear optical (NLO) emission, and chiral-induced spin selectivity (CISS). However, challenges remain in stabilizing these materials under environmental stresses and precisely controlling chirality for scalable use. This review summarizes five main strategies to induce chirality in HOIPs, i.e., direct incorporation of chiral cations, surface modification with chiral ligands, ion doping, template-induced chirality, and chiral metasurfaces. Each approach offers distinct advantages for optimizing CPL efficiency and device stability, paving the way for next-generation applications in CPL detectors, information encryption, spintronic devices, etc.

14 SOLAR ENERGY↗

Lattice dynamics and thermoelectric properties of diamondoid materials

Abstract The diamondoid compounds are a large family of important semiconductors, which possess various unique transport properties and had been widely investigated in the fields of photoelectricity and nonlinear optics. For a significantly long period of time, diamondoid materials were not given much attention in the field of thermoelectricity. However, this changed when a series of diamondoid compounds showed a thermoelectric figure of merit ( ZT ) greater than 1.0. This discovery sparked considerable interest in further exploring the thermoelectric properties of diamondoid materials. This review aims to provide a comprehensive view of our current understanding of thermal and electronic transport in diamondoid materials and stimulate their development in thermoelectric applications. We present a collection of recent discoveries concerning the lattice dynamics and electronic structure of diamondoid materials. We review the underlying physics responsible for their unique electrical and phonon transport behaviors. Moreover, we provide insights into the advancements made in the field of thermoelectricity for diamondoid materials and the corresponding strategies employed to optimize their performance. Lastly, we emphasize the challenges that lie ahead and outline potential avenues for future research in the domain of diamondoid thermoelectric materials.

Xie, Hongyao↗

Combining Chemistry, Material Science, Inspiration from nature, and Serendipity to Develop Stimuli-responsive Polymeric Materials

Neither of us can remember people talking about stimuli-responsive polymers when we were students. Even though this was still in the last century, it was almost 70 years after Staudinger's seminal paper "uber Polymerisation"![1] By the time we entered graduate school in the early 1990 s, the first papers on polymer light emitting diodes appeared, while research on electrically conducting, nonlinear optical, and other "functional" polymers was already in full swing. Looking back, there were some stimuli-responsive materials that were around at the time, but it took the better part of the last 30 years until the field had developed into what we think is one of the most vibrant areas of polymer science. Before the potential usefulness of this class of materials was recognized, researchers were focused on developing polymeric materials that would not respond to external influences, and in fact maintain (in particular) their mechanical properties in a wide range of environments. This has led to the development of many environmentally robust polymers, which have come to impact basically every aspect of our daily life. Ironically, this long-sought stability now comes back to haunt us in the form of plastic pollution, but this is another story. The concept of materials that adapt their properties in response to changing environmental conditions might appear like a complete reversal with respect to the original goals of creating stable materials. However, eventually a) it was recognized that materials that respond to a specific stimulus in a predictable and useful manner would significantly broaden the potential usefulness of polymers, and b) the field of polymer science had developed to the point where the rational design, preparation, and characterization of such materials became possible. The expression 'stimuli-responsive polymer' had been first used in the 1980's, however its use really only gained popularity a few decades later. In the early days, terms such as environmentally-sensitive or environmentally-responsive polymers, stimuli-reversible or stimuli-sensitive polymers, or polymers with phase transitions have also been used.

Rowan, Stuart J.↗

An Exact Expression for Multidimensional Spectroscopy of a Spin‐Boson Hamiltonian

Multidimensional coherent spectroscopy is a powerful tool to characterize nonlinear optical response functions. Typically, multidimensional spectra are interpreted via a perturbative framework that straightforwardly provides intuition into the density matrix dynamics that give rise to specific spectral features. When the goal is to characterize system coupling to a thermal bath however, the perturbative formalism becomes unwieldy and yields less intuition. Here, an approach developed by Vagov et al. is extended to provide an exact expression for multidimensional spectra of a spin-boson Hamiltonian up to arbitrary order of electric field interaction. Furthermore, the utility of this expression is demonstrated by modeling polaron formation and coherent exciton-phonon coupling in quantum dots, which strongly agree with experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multi-Functional Applications of H-Glass Embedded with Stable Plasmonic Gold Nanoislands

Metal nanoparticles (MNPs) are synthesized using various techniques on diverse substrates that significantly impact their properties. However, among the substrate materials investigated, the major challenge is the stability of MNPs due to their poor adhesion to the substrate. Herein, it is demonstrated how a newly developed H-glass can concurrently stabilize plasmonic gold nanoislands (GNIs) and offer multifunctional applications. The GNIs on the H-glass are synthesized using a simple yet, robust thermal dewetting process. The H-glass embedded with GNIs demonstrates versatility in its applications, such as i) acting as a room temperature chemiresistive gas sensor (70% response for NO 2 gas); ii) serving as substrates for surface-enhanced Raman spectroscopy for the identifications of Nile blue (dye) and picric acid (explosive) analytes down to nanomolar concentrations with enhancement factors of 4.8 × 10 6 and 6.1 × 10 5 , respectively; and iii) functioning as a nonlinear optical saturable absorber with a saturation intensity of 18.36 × 10 15 W m -2 at 600 nm, and the performance characteristics are on par with those of materials reported in the existing literature. In conclusion, this work establishes a facile strategy to develop advanced materials by depositing metal nanoislands on glass for various functional applications.

36 MATERIALS SCIENCE↗

BaCu 2 SiS 4 : A New Member of the A II B I 2 M IV Q 4 Chalcogenide Family with a Chiral Crystal Structure

Abstract Noncentrosymmetric ternary and quaternary chalcogenides are studied as promising nonlinear optical (NLO) materials in the mid‐infrared region. Here, we report the synthesis of a new material BaCu 2 SiS 4 in the A II B I 2 M IV Q 4 family ( A =divalent metal; B =monovalent metal; M =tetrel, Q =chalcogen), and discuss its crystal structure, thermal stability, optical behavior, and electronic structure. BaCu 2 SiS 4 crystallizes in the noncentrosymmetric chiral space group P 3 2 21 with lattice parameters a =6.1440(3) Å, c =15.3542(8) Å, V =501.95(6) Å 3 , Z =3. The structure features helical channels formed by corner‐sharing [CuS 4 ] and [SiS 4 ] tetrahedral units. Synthesis was carried out in a molten salt flux, as opposed to a traditional solid‐state route from elements, to minimize the formation of a competing ternary phase, Ba 2 SiS 4 . BaCu 2 SiS 4 is a semiconductor with an experimentally‐determined direct bandgap of ~2.2 eV. The material exhibits second harmonic generation (SHG) activity, confirming the noncentrosymmetric nature of the structure. Analysis of reported A II B I 2 M IV Q 4 crystal structures pointed out a correlation among potential structure types and the radii of the constituent elements. Total energy calculations were carried out to explore the relative stability of several reported crystal structures in this family of compounds.

Sarkar, Arka↗

Vibrational sum frequency generation spectroscopy reveals the inertness of chromium oxide (001) surfaces

Nanoengineered metal oxides such as Cr(III)-oxide (chromia) films have diverse potential applications in corrosion inhibition, remediation, energy generation, catalysis, data storage, and biological and environmental systems. Concerns about material degradation or oxidation to toxic chromate necessitate an understanding of chromia/aqueous interfaces, beginning with their hydroxylation and hydration behavior. Vibrational sum-frequency generation spectroscopy (vSFG) provides specific molecular-level information about water at the oxide/aqueous junction with high surface selectivity. To overcome the strong absorber problem typical of certain metal oxides in the UV–visible range during nonlinear optical studies, we employed molecular beam epitaxy to deposit transparent, epitaxial nanofilms of Cr 2 O 3 with (001) crystalline orientation on sapphire (Al 2 O 3 (001)) substrates, as confirmed by atomic force microscopy and X-ray diffraction. vSFG spectra of the air and water interfaces of the Cr 2 O 3 (001) films reveal hydroxyl features corresponding to both dissociated and molecular water on the surface. In contrast to the dangling hydroxyls found on the bare Al 2 O 3 (001) substrate, the hydroxyl groups on the deposited Cr 2 O 3 (001) nanofilm do not readily undergo isotopic H/D exchange when exposed to varying forms of D 2 O under ambient conditions. When considering the chemistries of the corresponding trivalent cations in aqueous solution, the finding is at variance with their similar acidities and proton exchange dynamics but consistent with markedly slower inner-sphere water ligand exchange of hexaquo Cr 3+ . This finding challenges the idea that proton and water exchange at the water/Cr₂O₃(001) interface are solely correlated, driven by the strength of metal-bridging oxygen bonds and surface hydroxyl distribution, without direct causation.

Boamah-Agyemang, Mavis D. [Pacific Northwest Natio↗

Probing the electrolyte/electrode interface with vibrational sum frequency generation spectroscopy: A review

Over the past decades, Lithium-ion batteries have seen extensive improvements, and as a result are now the primary choice in many applications for their power, energy, and durability. In recent years, battery cost has reduced by orders of magnitude through adoption of new materials and processes. Despite these advances, interfaces in these battery systems are yet to be fully understood. This is seen as a major limitation to further increase cycle life, calendar life, abuse tolerance, and performances. A major obstacle is a lack of comprehensive understanding of the complex dynamic chemical processes occurring at the electrolyte/electrode interface. In this context, vibrational sum frequency generation (vSFG) spectroscopy possesses the unique capability of probing a molecularly thin interfacial layer to obtain molecular-level information through nonlinear optical interaction. Probing the molecular level processes at the interfaces using such a versatile technique would be a game changer in the advancement of current battery research knowledge. This review article summarizes recent vSFG studies on the electrolyte/electrode interface of various electrode materials and nonaqueous electrolytes for LIBs and discusses future research perspectives. Finally, overall, this focused review highlights the advantages and versatility of vSFG that can be used to further advance present-day battery research.

25 ENERGY STORAGE↗

Detection of the keto-enol tautomerization in acetaldehyde, acetone, cyclohexanone, and methyl vinyl ketone with a novel VUV light source

The discovery of enols in combustion environments and our atmosphere has garnered increasing attention to the many unanswered questions surrounding enol chemistry. The scarcity of experimental data concerning these enols renders combustion and atmospheric models with a lack of constraining parameters, leading to varying computational predictions. Experimental detection is difficult because mass spectrometry, a powerful tool for probing a wide variety of species, cannot distinguish between enols and their thermodynamically favorable ketone isomers. A solution to this ambiguity is to use tunable vacuum ultraviolet (VUV) light from a synchrotron to identify the presence of the enol by its lower ionization energy compared to the isomer. We present a tabletop-scale VUV light source that implements highly cascaded harmonic generation, a new regime of cascaded nonlinear optics, to provide a set of spectral lines spaced by 1.2 eV. We demonstrate that the variety of photon energies available allows us to detect the keto-enol tautomerization of four aldehydes and ketones. By combining this novel VUV light source with an established microreactor, we first revisit the formation of vinyl alcohol from acetaldehyde and confirm that the observed isomerization is indeed unimolecular. Secondly, we observe the thermal tautomerization of acetone to propen-2-ol for the first time. Finally, we observe the thermal tautomerization of cyclohexanone to 1-cyclohexenol and methyl vinyl ketone to 2-hydroxybutadiene, where the results are in good agreement with those reported at a synchrotron. Furthermore, our measurements can be used to constrain models, inform future experimental studies of enol reactivity, and potentially enhance current understanding of combustion and environmental chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Toggling Stereochemical Activity through Interstitial Positioning of Cations between 2D V 2 O 5 Double Layers

The 5/6s 2 lone-pair electrons of p-block cations in their lower oxidation states are a versatile electronic and geometric structure motif that can underpin lattice anharmonicity and often engender electronic and structural instabilities that underpin the function of active elements in nonlinear optics, thermochromics, thermoelectrics, neuromorphic computing, and photocatalysis. In contrast to periodic solids where lone-pair-bearing cations are part of the structural framework, installing lone-pair-bearing cations in the interstitial sites of intercalation hosts provides a means of a systematically modulating electronic structure through the choice of the group and the period of the inserted cation while preserving the overall framework connectivity. The extent of stereochemical activity and the energy positioning of lone-pair-derived mid-gap states depend on the cation identity, stoichiometry, and strength of anion hybridization. V 2 O 5 polymorphs are versatile insertion hosts that can accommodate a broad range of s-, p-, and d-block cations. However, the insertion of lone-pair-bearing cations remains largely underexplored. In this article, we examine the implications of varying the 6s 2 cations situated in interlayer sites between condensed [V 4 O 10 ] n double layers. Systematic modulations of lattice distortions, electronic structure, and magnetic ordering are observed with increasing strength of stereochemical activity from group 12 to group 14 cations. We compare and contrast p-block-layered M x V 2 O 5 (M = Hg, Tl, and Pb) compounds and map the significance of local off-centering arising from the stereochemical activity of lone-pair cations to the emergence of filled antibonding lone-pair 6s 2 –O 2p-hybridized mid-gap states mediated by second-order Jahn–Teller distortions. Crystallographic studies of cation coordination environments and the resulting modulation of V–V interactions have been used in conjunction with variable-energy hard X-ray photoelectron spectroscopy measurements, first-principles electronic structure calculations, and crystal orbital Hamilton population analyses to decipher the origins of stereochemical activity. Magnetic susceptibility measurements reveal antiferromagnetic signatures for all the three compounds. However, the differences in V–V interactions significantly affect the energy balance of the superexchange interactions, resulting in an ordering temperature of 160 and 260 K for Hg 0.5 V 2 O 5 and δ-Tl 0.5 V 2 O 5 , respectively, as compared to 7 K for δ-Pb 0.5 V 2 O 5 . In δ-Pb 0.5 V 2 O 5 , the strong stereochemical activity of electron lone pairs and the resulting electrostatic repulsions enforce superlattice ordering, which strongly modifies the electronic localization patterns along the [V 4 O 10 ] slabs, resulting in disrupted magnetic ordering and an anomalously low ordering temperature. The results demonstrate a versatile strategy for toggling the stereochemical activity of electron lone pairs to modify the electronic structure near the Fermi level and to mediate superexchange interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Exploration, Prediction, and Experimental Verification of Structure and Optoelectronic Properties in I 2 -Eu-IV-X 4 (I = Li, Cu, Ag; IV = Si, Ge, Sn; X = S, Se) Chalcogenide Semiconductors

Recently, there has been extensive research into photovoltaic, thermoelectric, and nonlinear optical applications of chalcogenide semiconductors within the large set of defect-resistant I 2 -II-IV-X4 (I = Li, Cu, Ag; II = Ba, Sr, Eu, Pb; IV = Si, Ge, Sn; X = S, Se) compounds. Five Eu-including compounds have previously been reported within this family, but a comparative study of possible structures and electronic properties of all 18 Eu-based combinations is still absent. Herein, we use hybrid density functional theory to study rare-earth-including I 2 -II-IV-X 4 semiconductors with Eu on the II site, in order to further understand this family and test the geometric tolerance factor approach (reported in our previous work) as a tool for predicting potential stable structures. We investigate how the exchange mixing parameter of the HSE06 density functional, α, affects the energetic positions of electronic levels, especially of the localized f-electron orbitals near the band edges of the extended semiconductor structures, using literature photoemission and band gap data of EuS for comparison. Lowest-energy quaternary structure candidates, energy band structures, and densities of states are computationally predicted for all 18 materials. Based on its predicted photovoltaics-relevant band gap, the previously unknown compound Cu 2 EuSnSe 4 was selected and synthesized. Furthermore, the experimental structure, lattice parameters, and band gap of Cu 2 EuSnSe 4 are consistent with the computational predictions, confirming a 1.55 eV band gap.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Intercalation-Induced Topotactic Phase Transformation of Tungsten Disulfide Crystals

Recent research has demonstrated the potential for topological superconductivity, anisotropic Majorana bound states, optical nonlinearity, and enhanced electrochemical activity for transition metal dichalcogenides (TMDs) with a 2M structure. These unique TMD compounds exhibit metastability and, upon heating, undergo a transition to the thermodynamically stable 2H phase. The 2M phase is commonly made at high temperatures using traditional solid-state methods, and this metastability further complicates the growth of large 2M WS 2 crystals. Herein, a novel synthetic method was developed, focusing on a molten salt reaction to synthesize large 2H crystals and then inducing transformation to the 2M phase through intercalation and thermal treatment. The 2H crystals were intercalated via a room-temperature sodium naphthalenide solution, producing a previously unreported Na-intercalated 2H WS 2 phase. Thermal heating was required to facilitate the phase transition to the intercalated 2M crystal structure. This phase transition was studied by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), selected area electron diffraction (SAED), electron dispersive X-ray spectroscopy (EDS), and Raman spectroscopy, which confirmed the synthesis of the intercalated 2M phase. Upon deintercalation, crystal and powder samples showed superconductivity with a T c of 8.6–8.7 K, similar to previously reported values. The generality of this process was further demonstrated using alkali metal triethyl borohydride to intercalate 2H WS 2 and produced the desired 2M phase. This novel synthetic method has broad implications for discovering metastable phases in other TMD families and layered materials. Furthermore, separation of the intercalation and phase transition also has the potential to allow for large-scale synthesis of this technologically important phase with greater control over each step of the reaction.

36 MATERIALS SCIENCE↗

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets↗