Equilibrium Structure Research Articles

Equilibrium Values for the Si-H Bond Length and Equilibrium Structures of Silyl Iodide and Halosilylenes.

The equilibrium structures of silyl iodide, SiH3I, and silylene halides, SiHX (X = F, Cl, Br, I), were determined by using the mixed regression method, where approximate values of the rotational constants are supplemented by the structural parameters of a different origin. For this goal, it is shown that the r(Si-H) bond length can be determined by using the isolated SiH stretching frequency and that an accurate estimation of the bond angles is obtained by an MP2 calculation with a basis set of triple zeta quality. To check the accuracy of the experimental structures, they were also optimized by means of all electron CCSD(T) calculations using basis sets of quadruple zeta quality.

Radial Oscillations of Strange Quark Stars Admixed with Dark Matter

We investigate the equilibrium structure and radial oscillations of strange quark stars admixed with fermionic dark matter. For strange quark matter, we employ a stiff equation of state from a color-superconductivity improved bag model. For dark matter, we adopt the cold free Fermi gas model. We rederive and numerically solve the radial oscillation equations of two-fluid stars based on general relativity, in which the dark matter and strange quark matter couple through gravity and oscillate with the same frequency. Our results show that the stellar maximum mass and radius are reduced by inclusion of dark matter. As to the fundamental mode of the radial oscillations, the frequency f0 is also reduced comparing to pure strange stars, and f02 reaches the zero point at the maximum stellar mass with dM/dϵq,c=0. Therefore, the stability criteria f02>0 and dM/dϵq,c>0 are consistent in our dark matter-mixed strange quark stars with a fixed fraction of dark matter. We also find a discontinuity of f0 as functions of the stellar mass, in contrast to the continuous function in pure strange stars. And it is also accompanied with discontinuity of the oscillation amplitudes as well as a discontinuous in-phase-to-out-phase transition between oscillations of dark matter and strange quark matter.

Tracing Prebiotic Molecules: Rotational Spectroscopy of Deuterated Glycolaldehyde and (Z)-1,2-Ethenediol.

Glycolaldehyde, an important prebiotic molecule, along with its monodeuterated species and its higher energy tautomer, (Z)-1,2-ethenediol, has been detected in the interstellar medium. Although the elemental D/H ratio in the universe is only ∼1.6 × 10-5, the deuterium relative abundance in interstellar molecules might be by far larger than this. As such, it provides a remarkable and almost unique diagnostic tool. In particular, it might help elucidate the reaction mechanisms that lead to the formation of the so-called complex organic molecules. It is therefore crucial to extend the census of the interstellar deuterated molecules. To this aim, in this work, we present for the first time a spectroscopic investigation of the rotational spectra of the CHDOD-CHO bideuterated variant of glycolaldehyde and of mono- and bideuterated species of (Z)-1,2-ethenediol (CHOD═CHOD, CHOD═CHOH, and CHOH═CHOD rotamers). For each species, more than a hundred transitions have been assigned. Their analysis led to the accurate determination of all rotational constants as well as quartic and sextic centrifugal distortion terms, thus providing spectroscopic line catalogs suitable for supporting astronomical searches. In addition, the rotational constants of the bideuterated glycolaldehyde isotopologue studied in this work allowed us to improve the semiexperimental equilibrium structure determination for this molecule.

Some Reflections on Two Significant Contributions of Ron Jones: Specificity of Factors and Non-traded Goods

This article pays tribute to Professor Ronald W. Jones by reflecting upon how two significant, yet simple and elegant, analytical structures developed by him have been used by researchers to address a wide set of issues relevant for developed and developing countries alike and hold the potential to analyse some unexplored issues of relevance in the future. One is the specific-factor model, and the other is the composite-traded and non-traded model that came out of his Frank Graham Lecture in 1976. These two important competitive general equilibrium structures provide significant and relevant departures from the Ricardian and Heckscher–Ohlin–Samuelson models, highlighting the role of both factor scarcity and local demand. JEL Codes: F11, F13, F21

Jet formation model from accretion disks of electron-ion-photon gas

The problem of Astrophysical Jet formation from relativistic accretion disks through the establishment of relativistic disk-powerful jet equilibrium structure is studied applying the Beltrami-Bernoulli equilibrium approach of Shatashvili and Yoshida 2011; Arshilava et al. 2019. Accretion disk is weakly magnetized consisting of fully ionized relativistic electron-ion plasma and photon gas strongly coupled to electrons due to Thompson Scattering. Analysis is based on the generalized Shakura-Sunyaev α-turbulent dissipation model for local viscosity (being the main source of accretion), in which the contributions from both the photon and ion gases are taken into account. Ignoring the self-gravitation in the disk we constructed the analytical self-similar solutions for the equilibrium relativistic disk-jet structure characteristic parameters in the field of gravitating central compact object for the force-free condition. It is shown, that the magnetic field energy in the Jet is several orders greater compared to that of accretion disk, while jet-outflow is locally Super-Alfvénic with local Plasma-beta <1 near the jet-axis. The derived solutions can be used to analyze the astrophysical jets observed in binary systems during the star formation process linking the jet properties with the parameters of relativistic accretion disks of electron-ion-photon gas.

Millimeter-wave and high-resolution infrared spectroscopy of the low-lying vibrational states of pyridazine isotopologues.

The gas-phase rotational spectrum from 8 to 750GHz and the high-resolution infrared (IR) spectrum of pyridazine (o-C4H4N2) have been analyzed for the ground and four lowest-energy vibrationally excited states. A combined global fit of the rotational and IR data has been obtained using a sextic, centrifugally distorted-rotor Hamiltonian with Coriolis coupling between appropriate states. Coriolis coupling has been addressed in the two lowest-energy coupled dyads (ν16, ν13 and ν24, ν9). Utilizing the Coriolis coupling between the vibrational states of each dyad and the analysis of the IR spectrum for ν16 and ν9, we have determined precise band origins for each of these fundamental states: ν16 (B1) = 361.213 292 7 (17) cm-1, ν13 (A2) = 361.284 082 4 (17) cm-1, ν24 (B2) = 618.969 096 (26) cm-1, and ν9 (A1) = 664.723 378 4 (27) cm-1. Notably, the energy separation in the ν16-ν13 Coriolis-coupled dyad is one of the smallest spectroscopically measured energy separations between vibrational states: 2122.222 (72) MHz or 0.070 789 7 (24) cm-1. Despite ν13 being IR inactive and ν24 having an impractically low-intensity IR intensity, the band origins of all four vibrational states were measured, showcasing the power of combining the data provided by millimeter-wave and high-resolution IR spectra. Additionally, the spectra of pyridazine-dx isotopologues generated for a previous semi-experimental equilibrium structure (reSE) determination allowed us to analyze the two lowest-energy vibrational states of pyridazine for all nine pyridazine-dx isotopologues. Coriolis-coupling terms have been measured for analogous vibrational states across seven isotopologues, both enabling their comparison and providing a new benchmark for computational chemistry.

Elucidating the structural and conformational preferences of bioactive chromone and its monohydrate through advanced rotational spectroscopy.

Chromones are a class of naturally occurring compounds, renowned for their diverse biological activities with significant relevance in medicine and biochemistry. This study marks the first analysis of rotational spectra of both the chromone monomer and its monohydrate through Fourier transform microwave spectroscopy. The observation of nine mono-substituted 13C isotopologues facilitated a semi-experimental determination of the equilibrium structure of the chromone monomer. In the case of chromone monohydrate, two distinct isomers were identified, each characterized by a combination of O-H⋯O and C-H⋯O hydrogen bonds involving the chromone's carbonyl group. This study further delved into intermolecular non-covalent interactions, employing different theoretical approaches. The relative population ratio of the two identified isomers was estimated to be about 2:1 within the supersonic jet.

Equilibrium structure and shape of Ag and Pt nanoparticles grown on silica surfaces: From experimental investigations to the determination of a metal-silica potential.

A combination of experimental and numerical investigations on metallic silver and platinum nanoparticles deposited on silica substrates is presented, with a focus on metal-substrate interactions. Experimentally, the nanoparticles, obtained by ultra-high vacuum atom deposition, are characterized by grazing-incidence small-angle x-ray scattering and high resolution transmission electronic microscopy to determine their structure and morphology and, in particular, their aspect ratio (height/diameter), which quantifies the metal-substrate interaction, from the as-grown to equilibrium state. Numerically, the interactions between the metal and the silica species are modeled with the Lennard-Jones (12, 6) potential, with two parameters for each metal and silica species. The geometric parameters were found in the literature, while the energetic parameters were determined from our experimental measurements of the aspect ratio. The parameters are as follows: σAg-O = 0.278nm, σAg-Si = 0.329nm, ɛAg-O = 75meV, and ɛAg-Si = 13meV for Ag-silica and σPt-O = 0.273nm, σPt-Si = 0.324nm, ɛPt-O = 110meV, and ɛPt-Si = 18 meV for Pt-silica. The proposed Ag-silica potential reproduces quantitatively the unexpected experimental observation of the variation of the aspect ratio for Ag nanoparticles larger than 5nm, which has been interpreted as a consequence of the silica roughness. The nanoparticle orientation, structure, and disorder are also considered. This metal-silica potential for Ag and Pt should be helpful for further studies on pure metals as well as their alloys.

Rotational spectrum, structure, and quadrupole coupling of cyclopropylchloromethyldifluorosilane.

Cyclopropylchloromethyldifluorosilane, c-C3H5SiF2CH2Cl, has been synthesized, and its rotational spectrum has been recorded by chirped-pulse Fourier transform microwave spectroscopy. The spectral analysis of several isotopologues indicates the presence of two distinct conformations in the free-jet expansion, which are interconvertible through a rotation of the chloromethyl group. A partial substitution structure is presented for the lower energy conformation and is compared to the equilibrium structure obtained from quantum chemical calculations. Additionally, the presence of the chlorine nucleus leads to the rotational transitions splitting into multiple hyperfine components and χaa, a measure of the electric field gradient along the a axis, is unusually small at merely +0.1393(73) MHz. Various common abinitio and density functional theory methods fail to predict good quadrupole coupling constants (in the principal axis system) that adequately reproduce the observed hyperfine splitting, although diagonalizing the quadrupole coupling tensor from the principal axis system into a nucleus-centered axis system reveals that, overall, these methods calculate reasonably the electric field gradient about the chlorine nucleus. Finally, a total of nine electric dipole forbidden, quadrupole allowed transitions are observed in the rotational spectra of the parent species of the higher energy conformation and the 37Cl isotopologue of the lower energy conformation. These include those of x-type (no change in parity of Ka or Kc), which, to our knowledge, is the first time such transitions have been observed in a chlorine-containing molecule.

Electric field-induced clustering in nanocomposite films of highly polarizable inclusions

A nanocomposite film containing highly polarizable inclusions in a fluid background is explored when an external electric field is applied perpendicular to the planar film. For small electric fields, the induced dipole moments of the inclusions are all polarized in field direction, resulting in a mutual repulsion between the inclusions. Here we show that this becomes qualitatively different for high fields: the total system self-organizes into a state which contains both polarizations, parallel and antiparallel to the external field such that a fraction of the inclusions is counter-polarized to the electric field direction. We attribute this unexpected counter-polarization to the presence of neighboring dipoles which are highly polarized and locally revert the direction of the total electric field. Since dipoles with opposite moments are attractive, the system shows a wealth of novel equilibrium structures for varied inclusion density and electric field strength. These include fluids and solids with homogeneous polarizations as well as equilibrium clusters and demixed states with two different polarization signatures. Based on computer simulations of an linearized polarization model, our results can guide the control of nanocomposites for various applications, including sensing external fields, directing light within plasmonic materials, and controlling the functionality of biological membranes.

Frustrated metastable-to-equilibrium grain boundary structural transition in NbMoTaW due to segregation and chemical complexity

Grain boundary structural transitions can lead to significant changes in the properties and performance of materials. In multi-principal element alloys, understanding these transitions becomes complex due to phenomena such as local chemical ordering and multi-component segregation. Using atomistic simulations, we explore a metastable-to-equilibrium grain boundary structural transition in NbMoTaW. The transition, characterized by structural disordering and reduced free volume, shows high sensitivity to its local chemical environment. Most notably, the transition temperature range of the alloy is more than twice that of a pure metal. Differences in composition between coexisting metastable and equilibrium structures highlight the change in local site availability due to structural relaxation. Further examination of grain boundaries with fixed chemical states at varying temperatures reveals that the amount of segregation significantly influences the onset temperature yet has minimal effect on the transition width. These insights underscore the profound effect of chemical complexity and ordering on grain boundary transitions in complex concentrated alloys, marking a meaningful advancement in our understanding of grain boundary behavior at the atomic level.

Noether invariance theory for the equilibrium force structure of soft matter

We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether theorem for invariant variations. We consider the consequences of the shifting that emerge at second order in the displacement field that parameterizes the transformation. In a natural way the standard two-body density distribution is generated. Its second spatial derivative is thereby balanced by two further and different two-body correlation functions, which respectively introduce thermally averaged force correlations and force gradients in a systematic and microscopically sharp way into the framework. Separate exact self and distinct sum rules express this balance. We exemplify the validity of the theory on the basis of computer simulations for the Lennard–Jones gas, liquid, and crystal, the Weeks–Chandler–Andersen fluid, monatomic Molinero–Moore water at ambient conditions, a three-body-interacting colloidal gel former, the Yukawa and soft-sphere dipolar fluids, and for isotropic and nematic phases of Gay–Berne particles. We describe explicitly the derivation of the sum rules based on Noether’s theorem and also give more elementary proofs based on partial phase space integration following Yvon’s theorem.

Unlocking a new hydrogen-bonding marker: C-O bond shortening in vicinal diols revealed by rotational spectroscopy.

The conformational space of cis-1,2-cyclohexanediol, a model molecule for cyclic vicinal diols, was investigated using rotational spectroscopy and density functional theory calculations. Four low energy conformers within an energy window of 5 kJ mol-1 were identified computationally. A rotational spectrum of jet-cooled cis-1,2-cyclohexanediol was recorded with a chirped pulse Fourier transform microwave spectrometer. Two sets of rotational transitions were observed and could be assigned to conformers of cis-1,2-cyclohexanediol. The non-observation of other low energy conformers was explained by conformational conversion barrier height calculations and results from experimental spectra recorded with different carrier gases. Eight isotopologues, including those with 13C and 18O, of the lowest energy conformer were observed, allowing the determination of the semi-experimental equilibrium structure, reSE. Interestingly, the structural analysis revealed that the C-O bond length of the intramolecular hydrogen-bond donor is shorter than that of the acceptor. This appears to be a general characteristic of vicinal diols and can be used as a novel hydrogen-bond marker in such compounds.

Logic-Informed Graph Neural Networks for Structural Form-Finding

Computational form-finding methods hold great potential concerning resource-efficient structural design. The Combinatorial Equilibrium Modeling (CEM), an equilibrium-based form-finding method based on graphic statics and graph theory, allows the design of cross-typological tension–compression structures starting from an input topology diagram in the form of a graph. This paper presents a novel Logic-Informed Graph Neural Network (LIGNN) that integrates the validity conditions of CEM topology diagrams into the learning process through semantic loss terms. A Primary-LIGNN (P-LIGNN) and a Modification-LIGNN (M-LIGNN) are introduced and incorporated together with the CEM into a general form-finding-based computational structural design workflow that transforms input topologies into parametric models of equilibrium structures. An implementation of this computational design workflow for the conceptual design of pedestrian bridge structures is made, and presented through a case study, for which a synthetic training dataset of topology diagrams for the LIGNNs has been developed.

Argon Nanocluster Filled Between Twisted Bilayer Graphene: Molecular Dynamics Simulation

In 2004, graphene was discovered by Novoselov and Geim. With the development of technology，twisted bilayer graphene (tBLG) has become a hot research topic. On the basis of predecessors, we further study the confined spaces between twisted bilayer graphene. The interlayer spacing between them is expected to modify properties of atoms and molecules confined at the atomic interfaces. The effects of twist angle, interlayer spacing of the tBLG and temperature (20 K–70 K) on the equilibrium structure of argon cluster are systematically studied by means of molecular dynamics simulation with the tBLG being considered to be fixed. As the interlayer spacings of tBLGs with different twist angles increase at a fixed temperature 20 K, the equilibrium structures of the argon cluster transform from a monoatomic layer to multilayer structure. For different twist angles at the fixed interlayer spacing, the structures of the argon cluster gradually form periodic pattern (similar to moiré pattern). The effects of temperature and non-equiliblium suddenly heating process on the structures of argon clusters between tBLGs are also studied by molecular dynamics simulation. Our results may provide a theoretical support for the preparation of new carbon-based intercalated composites and the application of graphene.

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures.

In this work, three versions of self-consistent field/Kohn-Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small- to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

On the performance of composite schemes in determining equilibrium molecular structures.

Determination of equilibrium molecular structures is an essential ingredient in predicting spectroscopic parameters that help in identifying molecular carriers of microwave transitions. Here, the performance of two different ab initio composite approaches for obtaining equilibrium structures, "energy scheme" and "geometry scheme," is explored and compared to semi-experimental equilibrium structures. This study is performed for a set of 11 molecules which includes diatomics, linear triatomics, and a few non-linear molecules. The ab initio calculations were performed using three tiers of composite chemical recipes. The current results show that as the overall rigor of calculation is increased, the semi-experimental and the ab initio numbers agree to within 0.0003 Å for all molecules in the test set. The composite approach based on correcting the potential energy surface (energy scheme) and the one based on correcting the geometry directly (geometry scheme) show excellent agreement with each other. This work represents a step toward development of efficient and highly accurate procedures for computing ab initio equilibrium structures.

Studying the adsorption of emerging organic contaminants in zeolites with dispersion-corrected density functional theory calculations: From numbers to recommendations.

Adsorption energies obtained from dispersion-corrected density functional theory (DFT) calculations show a considerable dependence on the choice of exchange-correlation functional and dispersion correction. A number of investigations have employed different approaches to compute adsorption energies of small molecules in zeolites, using reference values from high-level calculations and/or experiments. Such comparative studies are lacking for larger functional organic molecules such as pharmaceuticals or personal care products, despite their potential relevance for applications, e. g., in contaminant removal or drug delivery. The present study aims to fill this gap by comparing adsorption energies and, for selected cases, equilibrium structures of emerging organic contaminants adsorbed in MOR- and FAU-type all-silica zeolites. A total of 13 dispersion-corrected DFT approaches are compared, including methods using a pairwise dispersion correction as well as non-local van der Waals density functionals. While absolute values of adsorption energies vary widely, qualitative trends across the set of zeolite-guest combinations are not strongly dependent on the choice of functional. For selected cluster models, DFT adsorption energies are compared to reference values from coupled cluster (DLPNO-CCSD(T)) calculations. Although all DFT approaches deliver systematically more negative adsorption energies than the coupled cluster reference, this tendency is least pronounced for the rev-vdW-DF2 functional.

A computational implementation of Vector-based 3D Graphic Statics (VGS) for interactive and real-time structural design

This article presents a computational implementation for the Vector-based Graphic Statics (VGS) framework making it an effective CAD tool for the design of spatial structures in static equilibrium (VGS-tool). The paper introduces several key features that convert a purely theoretical graph and geometry based framework into a fully automated computational procedure, including the following new contributions: a general algorithm for constructing 3-dimensional interdependent force and force diagrams; the implementation of a procedure that allows the interdependent transformation of both diagrams; an approach to apply specific constraints to the computationally generated diagrams; the integration of the algorithms as a plug-in for a CAD environment (Grasshopper3D of Rhino3D). The main features of the proposed framework are highlighted with a design case study developed using the newly introduced CAD plug-in (namely the VGS-tool). This plugin uses synthetic-oriented and intuitive graphical representation to allow the user to design spatial structures in equilibrium as three-dimensional trusses. The goal is to facilitate collaboration between structural engineers and architects during the conceptual phase of the design process.

Equilibrium structure of nitrogen dioxide revisited

The equilibrium structure of nitrogen dioxide was determined using different methods: experimental, semiexperimental, mass-dependent, using an empirical correction to the effective (r 0) structure, and ab initio optimizations. For this goal, recently determined rotational constants of vibrationally excited states have been used. The coupled cluster method, CCSD(T), fails to give an accurate structure. However, an accurate structure can be obtained by taking into account a small correction calculated at the CCSDTQ level of theory. Furthermore, the multireference configuration interaction method, MRCI + Q, gives a satisfactory result which can still be improved by interpolation. The semiexperimental and mass-dependent methods, as well as the corrected r 0 structure give accurate results and are furthermore much easier to use than the experimental method. It has to be noted that the different methods give compatible results. The mean of the results gives the following equilibrium structure: r(NO) = 1.1944(6) Å and ∠(ONO) = 133.89(11)°.