Geometrical Relaxation Research Articles

Mesh Simplification for Unfolding*

AbstractWe present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing for map distortions or multiple patches. Instead, we propose a geometric relaxation of the problem: We modify the input shape until it admits an overlap‐free unfolding. We achieve this by locally displacing vertices and collapsing edges, guided by the unfolding process. We validate our algorithm quantitatively and qualitatively on a large dataset of complex shapes and show its proficiency by fabricating real shapes from paper.

Scalable crystal structure relaxation using an iteration-free deep generative model with uncertainty quantification

In computational molecular and materials science, determining equilibrium structures is the crucial first step for accurate subsequent property calculations. However, the recent discovery of millions of new crystals and super large twisted structures has challenged traditional computational methods, both ab initio and machine-learning-based, due to their computationally intensive iterative processes. To address these scalability issues, here we introduce DeepRelax, a deep generative model capable of performing geometric crystal structure relaxation rapidly and without iterations. DeepRelax learns the equilibrium structural distribution, enabling it to predict relaxed structures directly from their unrelaxed ones. The ability to perform structural relaxation at the millisecond level per structure, combined with the scalability of parallel processing, makes DeepRelax particularly useful for large-scale virtual screening. We demonstrate DeepRelax’s reliability and robustness by applying it to five diverse databases, including oxides, Materials Project, two-dimensional materials, van der Waals crystals, and crystals with point defects. DeepRelax consistently shows high accuracy and efficiency, validated by density functional theory calculations. Finally, we enhance its trustworthiness by integrating uncertainty quantification. This work significantly accelerates computational workflows, offering a robust and trustworthy machine-learning method for material discovery and advancing the application of AI for science.

Do Molecular Geometries Change Under Vibrational Strong Coupling?

As pioneering experiments have shown, strong coupling between molecular vibrations and light modes in an optical cavity can significantly alter molecular properties and even affect chemical reactivity. However, the current theoretical description is limited and far from complete. To explore the origin of this exciting observation, we investigate how the molecular structure changes under strong light-matter coupling using an ab initio method based on the cavity Born-Oppenheimer Hartree-Fock ansatz. By optimizing H2O and H2O2 resonantly coupled to cavity modes, we study the importance of reorientation and geometric relaxation. In addition, we show that the inclusion of one or two cavity modes can change the observed results. On the basis of our findings, we derive a simple concept to estimate the effect of the cavity interaction on the molecular geometry using the molecular polarizability and the dipole moments.

Coherent coupling of localized surface plasmons and surface plasmons in borophene-based metamaterial

The strong coherent coupling in different electromagnetic modes can control the light-matter interaction more conveniently. Here, we theoretically researched the hybridization between the borophene surface plasmon (BSP) mode and the borophene localized surface plasmon (BLSP) mode in borophene grating structure. This coupling effect leads to the emergence of multiple hybrid modes. The absorption spectra of the system are investigated through finite difference time domain (FDTD) simulation and coupled oscillator model (COM). Results show that the coherent coupling of BSP and BLSP can be achieved by adjusting the carrier density of the borophene gratings. A Rabi splitting effect with frequency of 21.6 THz can be observed. Furthermore, we investigated the effects of geometric structural parameters, incident angle, and relaxation time on the correlated coupling spectra. Our work may deepen the understanding of light–matter interactions and provide a reference for borophene-based active photonic devices in the near-infrared region.

A Thorough Examination of the Variables Affecting the Quantum Efficiency of Radiative Decay of Trichlorotriphenylmethyl Radicals.

Fluorescence quantum efficiency is determined by the competition between radiation and nonradiation processes of the excited states. Understanding the factors affecting the radiation and nonradiative decay rates is of great significance for the design of luminescent materials. The excitation state deactivation mechanisms of singlet and triplet states have been extensively studied, providing a comprehensive understanding of the processes involved in the relaxation of these states. However, research on free radical systems involving doublet states is relatively scarce. Therefore, in this study, radiation and nonradiative decay rates and the mechanism of a series of trichlorotriphenylmethyl-based radicals were investigated theoretically. The results indicate that the relative rotations of electron donor and acceptor, as well as the internal rotations of trichlorotriphenylmethyl moiety, play important roles in energy dissipation through nonradiative channels. The effect of a solid-state environment on the radiation and nonradiative decay rates of radicals was investigated using a combination of quantum mechanics and molecular mechanics methods. The results indicate that the solid-state environment restricts the expansion of the conjugated system in the excited state of radicals, leading to a slight decrease in radiative decay rate. In addition, the solid-state environment reduces the reorganization energy and also affects the adiabatic excitation energy of radicals. The reduction in reorganization energy results in a decrease in nonradiative rate, while the opposite effect is observed for adiabatic excitation energy. The nonradiative rate of radicals in a solid-state environment is thus inflected by a combination of molecular geometric structure relaxation and ground-excited state energy gap.

Size Isn't Everything: Geometric Tuning in Polycyclic Aromatic Hydrocarbons and Its Implications for Carbon Nanodots.

Recent developments in light-emitting carbon nanodots and molecular organic semiconductors have seen renewed interest in the properties of polycyclic aromatic hydrocarbons (PAHs) as a family. The networks of delocalized π electrons in sp2-hybridized carbon grant PAHs light-emissive properties right across the visible spectrum. However, the mechanistic understanding of their emission energy has been limited due to the ground state-focused methods of determination. This computational chemistry work, therefore, seeks to validate existing rules and elucidate new features and characteristics of PAHs that influence their emissions. Predictions based on (time-dependent) density functional theory account for the full 3-dimensional electronic structure of ground and excited states and reveal that twisting and near-degeneracies strongly influence emission spectra and may therefore be used to tune the color of PAHs and, hence, carbon nanodots. We particularly note that the influence of twisting goes beyond torsional destabilization of the ground-state and geometric relaxation of the excited state, with a third contribution associated with the electric transition dipole. Symmetries and peri-condensation may also have an effect, but this could not be statistically confirmed. In pursuing this goal, we demonstrate that with minimal changes to molecular size, the entire visible spectrum may be spanned by geometric modification alone; we have also provided a first estimate of emission energy for 35 molecules currently lacking published emission spectra as well as clear guidelines for when more sophisticated computational techniques are required to predict the properties of PAHs accurately.

Central Ring Puckering Enhances the Stokes Shift of Xanthene Dyes.

Small-molecule dyes are generally designed based on well-understood electronic effects. However, steric hindrance can promote excited-state geometric relaxation, increasing the difference between the positions of absorption and emission bands (the Stokes shift). Accordingly, we hypothesized that sterically induced central ring puckering in xanthene dyes could be used to systematically increase their Stokes shift. Through a combined experimental/quantum-chemical approach, we screened a group of (9-acylimino)-pyronin dyes with a perturbed central ring geometry. Our results showed that an atom with sp3 hybridization in position 10 of (9-acylimino)-pyronins induces central ring puckering and facilitates excited-state geometric relaxation, thereby markedly enhancing their Stokes shifts (by up to ~2000 cm-1). Thus, we prepared fluorescent (9-acylimino)-pyronin pH sensors, which showed a Stokes shift disparity between acid and base forms of up to ~8700 cm-1. Moreover, the concept of ring puckering-enhanced Stokes shift can be applied to a wide range of xanthene analogues found in the literature. Therefore, central ring puckering may be reliably used as a strategy for enhancing Stokes shifts in the rational design of dyes.

Electron superhalogens as positronium superhalogens.

Positronium (Ps) exhibits the ability to form energetically stable complexes with atoms and molecules before annihilation occurs. In particular, F, a halogen, shows the highest reported positronium binding energy (2.95 eV) in the periodic table. Superhalogens are defined as molecules with electron affinities exceeding that of Cl (3.61 eV), the atom with the highest electron affinity. Building upon the concept of superhalogens, we can define Ps-superhalogens as molecules with Ps binding energies surpassing that of F. This study explores structural and energetic aspects of positronium and positron binding to neutral and anionic superhalogen molecules of the MXk+1 family (M = Li, Na, Be, Mg, B, Al, Si, P; X = F, Cl, Br), respectively and where k represents the highest formal valence of M. We perform multicomponent MP2 calculations for positron systems, which reveal how positron affinities vary with the type and number of halogen atoms present. The analysis of the results emphasizes the predominant role of electrostatic interactions in determining the positron affinity, with negligible effects of electronic and geometric relaxation upon positron attachment. We predict the energetic stability of 22 of the 24 PsMXk+1 complexes with respect to the chemically relevant dissociation channels: e+ emission, Ps emission and M-X bond breaking. Our findings reveal six MFk+1 systems that qualify as Ps-superhalogens, showing a positronium binding energy exceeding 2.95 eV. Of these, AlF4 stands out by setting a new record for the highest positronium binding energy among neutral molecules, reaching 4.36 eV.

Singlet and triplet excited states of a series of BODIPY dyes as calculated by TDDFT and DLPNO-STEOM-CCSD methods.

The singlet and triplet excited states of three iodine substituted BODIPY dyes differing by their substituents (-phenyl, -phenylOH and -phenylNO2) at the meso position of the BODIPY core (BOD) are investigated using (TDA)-TDDFT and DLPNO-STEOM-CCSD calculations. An assessment of hybrid (B3LYP and MN15) and double hybrid (SOS-PBE-QIDH and SOS-ωPBEPP86) exchange-correlation functionals is performed with respect to the DLPNO-STEOM-CCSD method for four types of transitions, namely , , and . It is found that MN15 and SOS-PBE-QIDH provide a balanced description of the excited state energies when compared to the DLPNO-STEOM-CCSD results. An investigation of the effects of the solvent (dichloromethane), of the substituent and of geometrical relaxation in the excited states is then performed. In particular, the study discusses the possibility of populating charge transfer states ( and ) following photoexcitation in the first and second absorption bands in these systems.

A Novel Method to Predict the Permeability of Heterogeneous Sandstones Using Multiple Echo Spacing NMR Measurements

Abstract We propose a novel method for estimating the permeability of heterogeneous sandstones based on the nuclear magnetic resonance (NMR) data with multiple echo spacings. The decaying curves and their corresponding spectra are obtained for different echo spacings to investigate the relaxation property, the diffusion term, and the signal loss contributed by higher echo spacing. Moreover, an empirical model is developed to correlate permeability with the differential decay rate. The result shows that the geometric transversal relaxation time is positively related to echo spacing, which disobeys the traditional cognition. Moreover, the absolute value of the differential decay rate is positively correlated with the echo spacing and exhibits a power law behavior. More interestingly, it is observed that the permeability diminishes in a power law behavior with respect to fitting parameters. This marks the first attempt to establish a relationship between the permeability and NMR data with different echo spacings, which is hopeful to be extended to other complex reservoirs with the availability of multiple echo spacing data.

Deep contrastive learning of molecular conformation for efficient property prediction.

Data-driven deep learning algorithms provide accurate prediction of high-level quantum-chemical molecular properties. However, their inputs must be constrained to the same quantum-chemical level of geometric relaxation as the training dataset, limiting their flexibility. Adopting alternative cost-effective conformation generative methods introduces domain-shift problems, deteriorating prediction accuracy. Here we propose a deep contrastive learning-based domain-adaptation method called Local Atomic environment Contrastive Learning (LACL). LACL learns to alleviate the disparities in distribution between the two geometric conformations by comparing different conformation-generation methods. We found that LACL forms a domain-agnostic latent space that encapsulates the semantics of an atom's local atomic environment. LACL achieves quantum-chemical accuracy while circumventing the geometric relaxation bottleneck and could enable future application scenarios such as inverse molecular engineering and large-scale screening. Our approach is also generalizable from small organic molecules to long chains of biological and pharmacological molecules.

Target-learning the Latent Space of a Variational Autoencoder model for the Inverse Design of Stable Perovskites

At the forefront of discoverable materials are perovskites that stand out as some of the most chemically diverse and multifunctional energy materials. Theoretically, the estimated number of ternary perovskites exceeds a hundred thousand distinct compounds, notwithstanding that only a small fraction of this estimate has been reported in existing crystal databases. Therefore, the study takes advantage of the reliable, inexpensive and rapid opportunity offered by deep generative modeling for accelerating the search for unknown perovskites. In the process of making such findings, an inverse design-modeling scheme is resolved, which aims at assimilating deterministic target properties with their corresponding perovskite structure. The inverse design pipeline is architectured by combining a generative Variational AutoEncoder (VAE) model with Target-Learning (TL) feed-forward neural networks to form the TL-VAE perovskite generator, thereby making the complete modeling process semi-supervisory. The TL feed-forward neural network model serves the purpose of organizing the non-linear latent space of the VAE model and further assists in isolating deterministic target properties that are of interest to the core objective of the study. The property to be target-learned in the latent space is the formation energy, which is a crucial indicator for calibrating perovskite stability. The results report the discovery of promising new perovskite candidates, which are unique and polymorphic material variants. Upon conducting Density Functional Theory (DFT) validation on the newly identified perovskites, candidates that undergo full geometrical relaxation are recommended for further investigation and/or synthesization. In conclusion, the study demonstrates the efficacy of the inverse design TL-VAE model for the generation of stable ternary perovskites.

Ab Initio Investigation of Intramolecular Charge Transfer States in DMABN by Calculation of Excited State X-ray Absorption Spectra

Dual fluorescence in 4-(dimethylamino)benzonitrile (DMABN) and its derivatives in polar solvents has been studied extensively for the past several decades. An intramolecular charge transfer (ICT) minimum on the excited state potential energy surface, in addition to the localized low-energy (LE) minimum, has been proposed as a mechanism for this dual fluorescence, with large geometric relaxation and molecular orbital reorganization a key feature of the ICT pathway. Herein, we have used both equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) and time-dependent density functional (TDDFT) methods to investigate the landscape of excited state potential energy surfaces across a number of geometric conformations proposed as ICT structures. In order to correlate these geometries and valence excited states in terms of potential experimental observables, we have calculated the nitrogen K-edge ground and excited state absorption spectra for each of the predicted "signpost" structures and identified several key spectral features that could be used to interpret a future time-resolved X-ray absorption experiment.

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy

Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic-level insight into photochemistry. We performed a time-resolved study of ultrafast molecular symmetry breaking through geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft x-rays at the carbon K-edge revealed that the distortion occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the symmetry-broken cation, which were detected in the x-ray signal. These oscillations were damped within 58 ± 13 femtoseconds because vibrational coherence was lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens avenues for exploring complex systems.

Quantum mechanics/fluctuating charge calculations for absorption spectra of aqueous green fluorescent protein chromophore

AbstractWe applied the quantum mechanics/fluctuating charges (QM/FQ) method to simulate the absorption spectra of three protonated forms of p‐hydroxybenzylidene imidazolone (p‐HBDI) in water. Configurations of solute‐solvent were generated from molecular dynamics (MD) simulation within the context of a hybrid scheme in which solute and solvents were treated at QM and molecular mechanics, respectively. Nonperiodic spherical boundary condition was used. To examine the influence on simulated spectra coming from the geometrical relaxation of solute, the MD simulations were carried out for two cases: frozen and flexible molecular geometry of solute. As a result of our calculations, the simulations using the flexible solute's structure delivered vertical excitation energies closer to experimental data than those of a frozen solute, especially for the neutral case. For spectral broadening, changing from fixed geometry of solute to a flexible one led to a significant increase for both neutral and anionic forms of p‐HBDI, but no effect happened for the cationic one.

Theoretical Studies and Design Strategies of Highly Efficient Two-Photon Excited Fluorescent Probes for Hydrogen Sulfide Detection through Simulation of Excited-State Dynamics.

Hydrogen sulfide (H2S) plays a critical role in numerous physiological and pathological processes, but an abnormal level of H2S in living systems can cause various diseases. To detect the level of endogenous H2S in a complicated biological system, the luminous mechanism of "turn-on" probe for H2S monitoring has been deeply explored through the simulation of excited-state dynamic processes, and the effect of different geometric modifications on optical properties has been minutely investigated based on molecular modeling. TD-DFT calculations demonstrate that line-type π-expanding in the molecular skeleton is beneficial for improving two-photon absorption (TPA) ability, but it can give rise to extremely large geometric relaxation, going against fluorescence emission. It is an effective way to suppress molecular skeleton scissoring vibration by introducing strong electron-withdrawing substituent groups (F, Cl, Br, CN) in benzopyran, and these compounds also have superior TPA properties in NIR. One of the potential materials in the application of biological imaging and H2S detection has been obtained, which simultaneously possesses easily distinguished spectra (with a Stokes shift as large as 77 nm), high luminous efficiency (with a quantum yield up to 20.07%), and large TPA cross section (952 GM at 950 nm).

Radical Pairing Interactions and Donor-Acceptor Interactions in Cyclobis(paraquat-p-phenylene) Inclusion Complexes.

Understanding molecular interactions in mechanically interlocked molecules (MIMs) is challenging because they can be either donor-acceptor interactions or radical pairing interactions, depending on the charge states and multiplicities in the different components of the MIMs. In this work, for the first time, the interactions between cyclobis(paraquat-p-phenylene) (abbreviated as CBPQTn+ (n = 0-4)) and a series of recognition units (RUs) were investigated using the energy decomposition analysis approach (EDA). These RUs include bipyridinium radical cation (BIPY•+), naphthalene-1,8:4,5-bis(dicarboximide) radical anion (NDI•-), their oxidized states (BIPY2+ and NDI), neutral electron-rich tetrathiafulvalene (TTF) and neutral bis-dithiazolyl radical (BTA•). The results of generalized Kohn-Sham energy decomposition analysis (GKS-EDA) reveal that for the CBPQTn+···RU interactions, correlation/dispersion terms always have large contributions, while electrostatic and desolvation terms are sensitive to the variation in charge states in CBPQTn+ and RU. For all the CBPQTn+···RU interactions, desolvation terms always tend to overcome the repulsive electrostatic interactions between the CBPQT cation and RU cation. Electrostatic interaction is important when RU has the negative charge. Moreover, the different physical origins of donor-acceptor interactions and radical pairing interactions are compared and discussed. Compared to donor-acceptor interactions, in radical pairing interactions, the polarization term is always small, while the correlation/dispersion term is important. With regard to donor-acceptor interactions, in some cases, polarization terms could be quite large due to the electron transfer between the CBPQT ring and RU, which responds to the large geometrical relaxation of the whole systems.

Stress relief heat treatment and mechanical properties of laser powder bed fusion built 21-6-9 stainless steel

In this work, the effectiveness of residual stress relief annealing on a laser powder bed fusion (L-PBF) manufactured austenitic stainless steel, alloy 21-6-9 was investigated. Residual stress levels were gauged using geometrical distortion and relaxation testing results. In the investigated temperature interval (600–850 °C), shape stability was reached after subjecting the as-built material to an annealing temperature of 850 °C for 1 h. Microstructural characterization and tensile testing were also performed for each annealing temperature to evaluate the alloy's thermal stability and the resulting tensile properties. In the as-built state, a yield strength (YS) of 640 MPa, ultimate tensile strength (UTS) of 810 MPa and 4D elongation of 47% were measured. Annealing at 850 °C for 1 h had little measurable effect on ductility (48% 4D elongation) while still having a softening effect (UTS = 775 MPa, YS = 540 MPa). From the microstructural characterization, cell-like features were observed sporadically in the annealed condition and appeared stable up until 800 °C after which gradual dissolution began, with the last remnants disappearing after subjecting the material to 900 °C for 1 h.

Structural, electronic, and optoelectronic properties of XYZ2 (X=Zn,Cd; Y=Si,Sn; Z=pnicogens) Chalcopyrite compounds: First-principles calculations

Structural, optoelectronic and electronic characteristics of the semiconductor chalcopyrite XYZ2 (X=Zn, Cd; Y=Si, Sn; Z=P) are predicted using first-principleS calculations. The (PBE-GGA) is used for the geometrical relaxation whereas the (TB-mBJ) potential is used to determine the ground state properties. The bandgap decreases by substituting Si by Sn in XYP2. The calculated energy bandgap values exhibit good consistency with experimental evidence and prior theoretical findings. The d-states of Zn and Cd contribute greatly to the density of states in XSiP2, Sn-d states are predominant in the XSnP2. Given its great reflectivity in UV region makes XYP2 good candidate for photonic and optoelectronic devices.

Structural, electronic, and optoelectronic properties of XYZ2 (X=Zn,Cd; Y=Si,Sn; Z=pnicogens) Chalcopyrite compounds: First-principles calculations

Structural, optoelectronic and electronic characteristics of the semiconductor chalcopyrite XYZ2 (X=Zn, Cd; Y=Si, Sn; Z=P) are predicted using first-principleS calculations. The (PBE-GGA) is used for the geometrical relaxation whereas the (TB-mBJ) potential is used to determine the ground state properties. The bandgap decreases by substituting Si by Sn in XYP2. The calculated energy bandgap values exhibit good consistency with experimental evidence and prior theoretical findings. The d-states of Zn and Cd contribute greatly to the density of states in XSiP2, Sn-d states are predominant in the XSnP2. Given its great reflectivity in UV region makes XYP2 good candidate for photonic and optoelectronic devices.