Equilibrium Structure Research Articles

No Unique Scaling Law for Igneous Dikes

AbstractIn linear elastic fracture mechanics (LEFM), veins, dikes, and sills grow in length when the stress intensity factor at the tip reaches a critical value: the host rock fracture toughness . This criterion is applied broadly in LEFM models for crack growth and it is often assumed that the pressure inside the crack is uniform. When applied to intrusion length versus thickness scaling, a significant issue arises in that derived , which is about 100–1,000 times that of measured values for rocks at upper crustal depths. The same scaling relationships applied to comparatively short mineral vein data gives , approaching the expected range. Here we propose that intrusions preserve non‐equilibrated pressures as cracks controlled by kinetics, and therefore cannot be treated in continuum with fracture‐controlled constant pressure (equilibrium) structures such as veins, or many types of scaled analogue model. Early stages of dike growth (inflation) give rise to increasing length and thickness, but magma pressure gradients within intrusions may serve to drive late‐stage lengthening at the expense of maximum thickness (relaxation). For cracks in 2D, we find that intrusion scaling in non‐equilibrium growth is controlled by the magma injection rate and initial dike scaling, effective (2D) host rock modulus, magma viscosity and cooling rate, which are different for all individual intrusions and sets of intrusions. A solidified intrusion can therefore achieve its final dimensions via many routes, with relaxation acting as a potentially significant factor, hence there is no unique scaling law for dike intrusions.

Evidence of anharmonicity in the vibrational spectrum of protonated ethylene

The vibrational spectrum of protonated ethylene, H+(C2H4), in the 2000 to 3500 cm−1 region is re-investigated. The spectrum is obtained by predissociation of the H+(C2H4)Ar2 complex following vibrational excitation, which leads to elimination of an argon atom. The equilibrium structure of this cation has the excess proton in a bridged position, where it undergoes large amplitude motions in the CH+C plane. These large amplitude vibrational motions result in features in the spectrum that cannot be assigned to Δv=1 transitions predicted by harmonic treatments. The origins of the anharmonicities that lead to these higher order transitions are explored. Based on vibrational perturbation theory and reduced dimensional calculations, transitions to states with two quanta in the HCH bending vibrations and the state with one quantum of excitation in the two vibrations of the bridging proton in the CH+C plane are found to carry significant intensity in this region of the spectrum.

Macromolecular complex viscosity from space-filling equilibrium structure

Macromolecular theory for the rheology of polymer liquids usually proceeds from a scale much larger than chemical bonding. For instance, a bead in a general rigid bead-rod theory can represent a length of the polymer. This is why we sculpt the shape of the macromolecule with a rigid bead-rod model. From the macromolecular hydrodynamics that follow, we then discover that the rheology of polymeric liquids depends on the macromolecular moments of inertia. In this paper, we use this discovery to arrive at a way of proceeding directly from the chemical bonding diagram to dimensionless complex viscosity curves. From the equilibrium conformation of the macromolecule, its atomic masses and positions, we first arrive at the macromolecular principal moments of inertia. From these, we then get the shapes of the complex viscosity curves from first principles thusly. We call this the macromolecular moment method. The zero-shear viscosity and relaxation time must still be fit to measurement. Using space-filling equilibrium structures, we explore the roles of (i) end group type, (ii) degree of polymerization, and (iii) pendant group type. We compare our results with complex viscosity measurements of molten atactic polystyrene.

Precise equilibrium structures of 1H- and 2H-1,2,3-triazoles (C2H3N3) by millimeter-wave spectroscopy.

The 1H- and 2H-1,2,3-triazoles are isomeric five-membered ring, aromatic heterocycles that may undergo chemical equilibration by virtue of intramolecular hydrogen migration (tautomerization). Using millimeter-wave spectroscopy in the 130-375GHz frequency range, we measured the spectroscopic constants for thirteen 1H-1,2,3-triazole and sixteen 2H-1,2,3-triazole isotopologues. Herein, we provide highly accurate and highly precise semi-experimental equilibrium (re SE) structures for the two tautomers based on the spectroscopic constants of each set of isotopologues, together with vibration-rotation interaction and electron-mass distribution corrections calculated using coupled-cluster singles, doubles, and perturbative triples calculations [CCSD(T)/cc-pCVTZ]. The resultant structures are compared with a "best theoretical estimate" (BTE), which has recently been shown to be in exceptional agreement with the semi-experimental equilibrium structures of other aromatic molecules. Bond distances of the 1H tautomer are determined to <0.0008 Å and bond angles to <0.2°. For the 2H tautomer, bond angles are also determined to <0.2°, but bond distances are less precise (2σ ≤ 0.0015). Agreement between BTE and re SE values is discussed.

A Full-Dimensional ab initio Intermolecular Potential Energy Surface and Dipole Moment Surfaces for H2O-Ar

Background: The H2O–Ar system has attracted significant interest in recent years because it is an important model to study inelastic scattering between atoms and triatomic molecules. A high-accuracy intermolecular potential energy surface (IPES) is the foundation for theoretical study on molecular collision dynamics for H2O–Ar. In addition, dipole moment surfaces (DMSs) are one of the prerequisites for spectral simulation. Objective: This study aimed to obtain a full-dimensional intermolecular potential energy surface and dipole moment surfaces for the van der Waals complex H2O–Ar. Methods: In this study, ab initio energy points were computed at the frozen-core (FC) explicitly correlated coupled-cluster [FC-CCSD(T)-F12a] level, with the augmented correlation-consistent polarized valence quadruple-zeta basis set plus bond functions. The permutation invariant polynomial neural network (PIP-NN) approach is adopted to fit the IPES, while the DMSs are constructed at the MP2/AVTZ level and fitted by the NN approach. Results: With a root-mean-square-error (RMSE) of 0.284 cm-1, the IPES can accurately describe the motion of the H2O–Ar complex between R = 4 and 20 a0 in the energy range up to 10000 cm-1. The fitting errors of all the data points are 6.192 and 6.509 mDebye for the X and Z components, respectively. The global minimum of -140.633 cm-1 has the plane geometry, while the dipole moment of H2O–Ar is 1.853 Debye at the equilibrium structure. Conclusion: In summary, we report a full-dimensional intermolecular potential energy surface for H2O–Ar. The IPES precisely reproduces CCSD(T)-F12a electronic energies with a large basis set. The corresponding dipole moment surfaces have also been reported. In comparison with previous work, the employment of the high-level ab initio method will make our IPES more reliable. Several typical 2D contour plots of the IPES and DMSs are also shown. The argon atom has a weak effect on the dipole moment of the H2O–Ar complex. The FORTRAN codes to generate 6D potentials and dipole moments reported here are available on request from the authors.

Can two competing on-demand service platforms be profitable?

Can two competing on-demand service platforms be profitable in equilibrium? This question is well-studied for firms competing purely on price in a single-sided market, but it is not well-understood for competing service platforms that use price to influence passenger demand and wage to influence driver participation in a “two-sided” market. To fill this research gap, we analyze the equilibrium structure of different variants of a 2-stage non-cooperative game in which both platforms use lower prices and waiting time to compete for more customers and higher wages and utilization to entice more providers to participate.To explicate our analysis and isolate the effect of each element, we first examine a parsimonious and stylized model that is based on the case when both firms operate under seven operational assumptions: (1) Non-exclusive providers; (2) Non-exclusive customers; (3) Pure pricing strategies; (4) Constant pricing; (5) Homogeneous services; (6) Homogeneous providers; and (7) Homogeneous customers. We find that only one platform can sustain in a payoff dominant stable equilibrium. Then we examine whether this “winner-take-all” equilibrium would persist when those operational environmental assumptions are relaxed separately. Our analysis reveals that the “winner-take-all” phenomenon continues to persist under promotional pricing strategies, service differentiation, and heterogeneous service providers. Interestingly, we find both platforms can sustain profitably when each platform engages providers (or customers) exclusively, when platforms adopt time-based pricing strategies, or when customers are heterogeneous. Our results offer insights into different operating environments under which both platforms can both sustain profitably in equilibrium.

Adsorption of Pesticides, Antibiotics and Microcystin-LR by Graphene and Hexagonal Boron Nitride Nano-Systems: A Semiempirical PM7 and Theoretical HSAB Study

In recent years, graphene (CC) and hexagonal boron nitride (h-BN) have been widely used in water purification and environmental remediation because of their unique physical and chemical properties. Therefore, based on the reaction enthalpy, equilibrium structure, atomic charge, molecular, orbital and electronic spectrum provided by a semiempirical PM7 method, the adsorption of pesticides, antibiotics and microcystin-LR on graphene and hexagonal boron nitride (h-BN) nano-systems was examined. For the adsorption of diazinon, parathion, oxacillin and ciprofloxacin, the results show that as the bond length decreases and the atomic partial charge increases, the adsorption energy increases. The removal efficiency for antibiotics is higher than that for pesticides. Regarding the co-adsorption of pesticides/antibiotics and microcystin-LR on nano-systems, hydrogen bonds play a crucial role in stabilizing the whole structure. In addition, the non-covalent interaction (NCI) diagrams show the adsorption strength of the nano-systems to the pesticides/antibiotics. The energy gap and HSAB global descriptors are calculated based on the energy values of HOMO and LUMO. It is proved that the graphene nano-system has excellent electron-accepting ability, and suitable sensor materials can be designed.

Impacts of zonal winds on planetary oscillations and Saturn ring seismology

ABSTRACT The excitation of density and bending waves in Saturn’s C ring by planetary oscillation modes presents a unique opportunity to learn about gas giant interiors and rotation. However, theoretical complications related to Saturn’s rapid and differential rotation pose a barrier to the full utilization of ring wave detections. We calculate oscillation modes using a complete, non-perturbative treatment of differential rotation modelled after Saturn’s zonal winds in self-consistently computed, polytropic equilibria. We find that previous, approximate treatments of the effects of differential rotation in Saturn overestimate shifts in the frequencies of fundamental modes (f modes) thought to be responsible for the majority of the waves detected in the C ring, due to an omitted modification of the equilibrium shape and structure of the planet by differential rotation. The bias introduced by these frequency overestimates is small, but significant relative to the uncertainties afforded by Cassini data. We additionally consider the non-perturbative effects of Saturn-like differential rotation on the rotational mixing of f modes and internal gravity modes (g modes), which is relevant to detections of multiple density waves with very closely split pattern speeds. We find that higher-order rotational effects can produce orders-of-magnitude enhancements in the surface gravitational perturbations of g modes dominated by large spherical harmonic degrees ℓ, regardless of frequency separation from the sectoral f mode. Despite this enhancement, we find that the observed fine splitting of density waves is unlikely to involve g modes dominated by ℓ ≳ 10. This restriction may aid in the inference of possible internal structures for Saturn.

High-resolution CH stretch spectroscopy of jet-cooled cyclopentyl radical: First insights into equilibrium structure, out-of-plane puckering, and IVR dynamics.

First, high-resolution sub-Doppler infrared spectroscopic results for cyclopentyl radical (C5H9) are reported on the α-CH stretch fundamental with suppression of spectral congestion achieved by adiabatic cooling to Trot ≈ 19(4) K in a slit jet expansion. Surprisingly, cyclopentyl radical exhibits a rotationally assignable infrared spectrum, despite 3N - 6 = 36 vibrational modes and an upper vibrational state density (ρ ≈ 40-90 #/cm-1) in the critical regime (ρ ≈ 100 #/cm-1) necessary for onset of intramolecular vibrational relaxation (IVR) dynamics. Such high-resolution data for cyclopentyl radical permit detailed fits to a rigid-rotor asymmetric top Hamiltonian, initial structural information for ground and vibrationally excited states, and opportunities for detailed comparison with theoretical predictions. Specifically, high level ab initio calculations at the coupled-cluster singles, doubles, and perturbative triples (CCSD(T))/ANO0, 1 level are used to calculate an out-of-plane bending potential, which reveals a C2 symmetry double minimum 1D energy surface over a C2v transition state. The inversion barrier [Vbarrier ≈ 3.7(1) kcal/mol] is much larger than the effective moment of inertia for out-of-plane bending, resulting in localization of the cyclopentyl wavefunction near its C2 symmetry equilibrium geometry and tunneling splittings for the ground state too small (<1MHz) to be resolved under sub-Doppler slit jet conditions. The persistence of fully resolved high-resolution infrared spectroscopy for such large cyclic polyatomic radicals at high vibrational state densities suggests a "deceleration" of IVR for a cycloalkane ring topology, much as low frequency torsion/methyl rotation degrees of freedom have demonstrated a corresponding "acceleration" of IVR processes in linear hydrocarbons.

Semi-experimental equilibrium (re SE) and theoretical structures of hydrazoic acid (HN3).

Hydrazoic acid (HN3) is used as a case study for investigating the accuracy and precision by which a molecular structure-specifically, a semi-experimental equilibrium structure (re SE)-may be determined using current state-of-the-art methodology. The influence of the theoretical corrections for effects of vibration-rotation coupling and electron-mass distribution that are employed in the analysis is explored in detail. The small size of HN3 allowed us to deploy considerable computational resources to probe the basis-set dependence of these corrections using a series of coupled-cluster single, double, perturbative triple [CCSD(T)] calculations with cc-pCVXZ (X = D, T, Q, 5) basis sets. We extrapolated the resulting corrections to the complete basis set (CBS) limit to obtain CCSD(T)/CBS corrections, which were used in a subsequent re SE structure determination. The re SE parameters obtained using the CCSD(T)/cc-pCV5Z corrections are nearly identical to those obtained using the CCSD(T)/CBS corrections, with uncertainties in the bond distances and angles of less than 0.0006 Å and 0.08°, respectively. The previously obtained re SE structure using CCSD(T)/ANO2 agrees with that using CCSD(T)/cc-pCV5Z to within 0.000 08 Å and 0.016° for bond distances and angles, respectively, and with only 25% larger uncertainties, validating the idea that re SE structure determinations can be carried out with significantly smaller basis sets than those needed for similarly accurate, strictly ab initio determinations. Although the purely computational re structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding re SE structural parameters, the discrepancy is rectified by applying corrections to address the theoretical limitations of the CCSD(T)/cc-pCV6Z geometry with respect to basis set, electron correlation, relativity, and the Born-Oppenheimer approximation, thereby supporting the contention that the semi-experimental approach is both an accurate and vastly more efficient method for structure determinations than is brute-force computation.

Ab initio machine learning of phase space averages.

Equilibrium structures determine material properties and biochemical functions. We here propose to machine learn phase space averages, conventionally obtained by ab initio or force-field-based molecular dynamics (MD) or Monte Carlo (MC) simulations. In analogy to ab initio MD, our ab initio machine learning (AIML) model does not require bond topologies and, therefore, enables a general machine learning pathway to obtain ensemble properties throughout the chemical compound space. We demonstrate AIML for predicting Boltzmann averaged structures after training on hundreds of MD trajectories. The AIML output is subsequently used to train machine learning models of free energies of solvation using experimental data and to reach competitive prediction errors (mean absolute error ∼ 0.8 kcal/mol) for out-of-sample molecules-within milliseconds. As such, AIML effectively bypasses the need for MD or MC-based phase space sampling, enabling exploration campaigns of Boltzmann averages throughout the chemical compound space at a much accelerated pace. We contextualize our findings by comparison to state-of-the-art methods resulting in a Pareto plot for the free energy of solvation predictions in terms of accuracy and time.

Reference Energies for Cyclobutadiene: Automerization and Excited States.

Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods. Indeed, due to its high spatial symmetry, especially at the D4h square geometry but also in the D2h rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multiconfigurational characters and single-reference methods, such as standard adiabatic time-dependent density-functional theory (TD-DFT) or standard equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations. In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at D2h and D4h equilibrium structures. In particular, selected configuration interaction (SCI), multireference perturbation theory (CASSCF, CASPT2, and NEVPT2), and coupled-cluster (CCSD, CC3, CCSDT, CC4, and CCSDTQ) calculations are performed. The spin-flip formalism, which is known to provide a qualitatively correct description of these diradical states, is also tested within TD-DFT (combined with numerous exchange-correlation functionals) and the algebraic diagrammatic construction [ADC(2)-s, ADC(2)-x, and ADC(3)]. A theoretical best estimate is defined for the automerization barrier and for each vertical transition energy.

Phase field modeling of dislocations and obstacles in InSb

We present a phase-field dislocation dynamics (PFDD) model informed by first-principle calculations to elucidate the competitive dislocation nucleation and propagation between the glide and shuffle sets in InSb diamond cubic crystal. The calculations are directly informed with generalized stacking fault energy curves on the (111) slip plane for both the “glide set,” with the smaller interplanar spacing, and the “shuffle set,” with the larger interplanar spacing. The formulation also includes elastic anisotropy and the gradient term associated with the dislocation core. The PFDD calculations show that under no stress the equilibrium structure of screw glide set dislocations dissociates into Shockley partials, while those of the shuffle set dislocations do not dissociate, remaining compact. The calculated dislocation core widths of these InSb dislocations agree well with the measured values for other semiconductor materials, such as Si and GaN. We find that a shuffle set dislocation emits from a dislocation source at an applied stress about three times smaller than that needed to emit leading and trailing partials successively on the glide set plane. Once the partial dislocations in the glide set are emitted, they propagate faster than the shuffle set perfect dislocation at the same stress level.

Anisotropic quark stars in f(R) = R 1+ϵ gravity

Within the metric formalism of f(R) theories of gravity, where R is the Ricci scalar, we study the hydrostatic equilibrium structure of compact stars with the inclusion of anisotropic pressure. In particular, we focus on the f(R) = R 1+ϵ model and we examine small deviations from general relativity for |ϵ| ≪ 1. A suitable definition of mass function is explicitly formulated from the field equations and the value of the Ricci scalar at the center of each star is chosen such that it satisfies the asymptotic flatness requirement. We find that both the mass and the radius of a compact star are larger with respect to the general relativistic counterpart. Furthermore, we remark that the substantial changes due to anisotropy occur mainly in the high-central-density region.

Formula omitted]-type doubling in the rotational spectrum of CH[formula omitted]–He: A group theoretical explanation

In a previous paper, we reported the pure rotational spectrum of the CH3+–He ion observed in a 22-pole ion trap by IR-MW double resonance spectroscopy [Töpfer et al. (2018)]. In that work the K=1 rotational levels in the ground state of the ion were observed to be split, i.e. the K-type doubling was observed. This finding would be consistent with a slightly asymmetric rotor of Cs symmetry, although ab-initio calculations predict that the equilibrium structure of the ion is of C3v symmetry. In the present study we inspect the energy-level correlation-diagram between the semi-rigid symmetric-top (C3v), the free internal-rotor (C3v(M)), and the semi-rigid asymmetric-top models (Cs), by using group theory, especially the correlation and reverse correlation in the symmetry representations. We find that the lowest K=1 rotational levels of the CH3+–He ion can be of A1⊕A2 symmetry rather than of E symmetry, and thus they can be split depending on the nature of the C–He bending vibration.

Formation of structural features of powder materials during cooling after heat treatment

Introduction . Recently, sintered materials and products made of them have been increasingly used in powder metallurgy. In this regard, the issue of obtaining sintered products with high performance properties is acute. To achieve such properties, the materials are subjected to heat treatment. This procedure significantly affects their structure and mechanical properties. In production, sintered materials are most often subjected to subsequent hardening and tempering, as a result of which their equilibrium structure is established, grain growth stops, and strength characteristics improve. The article discusses the problems that arise in the formation of the qualitative structure of dispersed-hardened alloys as a result of their heat treatment. Problem Statement . The objective of this work is to study the phase changes in the process of cooling of powder steels and alloys in order to determine the modes of their heat treatment in order to form optimal conditions for the martensitic transformation of austenite. Theoretical Part . Phase transformations in powder steels occur in the temperature range at which their structures are rearranged, and as a result, the properties of the material change. The main factors affecting the phase transformations are the chemical composition of the alloy, the structure imperfection and the size of the grains. Changes in the structure and properties of alloys are considered in comparison with compact materials. Heat treatment significantly affects the phase and structural characteristics of powder materials, which are related to the mechanical characteristics of the alloys themselves. Conclusions . The conducted studies have shown that with an increase in the heterogeneity of the solid solution of steels, the temperature of the beginning of the martensitic transformation increased. A decrease in the temperature of the martensitic transformation with an increase in the degree of homogeneity of the solid solution occurs due to its enrichment with carbon and other alloying elements (chromium, molybdenum). With an increase in the percentage of carbon, an increase in the porosity of samples, the starting point of martensitic transformation also decreases. The temperature of the beginning of the martensitic transformation is not affected by carbides that are with austenite. These conclusions will help us to evaluate the mechanical properties of materials, as well as to develop recommendations for the practical application of heat treatment in the manufacture of products of complex shape.

Hydrophobic π-π stacking interactions and hydrogen bonds drive self-aggregation of luteolin in water

Luteolin is a flavonoid obtained from different plant species. It is known for its versatile biological activities. However, the beneficial effects of luteolin have been limited to small concentrations as a result of poor water solubility. This study aimed at investigating the hydrophobic interaction and hydration of luteolin towards the improvement of its solubility when used as a drug. We report the aggregation properties of luteolin in water by varying the number of monomers using atomistic molecular dynamics simulation. Results show that the equilibrium structure of luteolin occurs in an aggregated state with different structural arrangements. As the monomers size increase, the antiparallel flipped conformation dominates over T-shaped antiparallel, T-shaped parallel, and antiparallel conformations. The formation of intramolecular hydrogen bonding of 0.19 nm between the keto-enol groups results in hydrophobic characteristics. A larger cluster exhibits slow hydrogen bond dynamics for luteolin-luteolin than luteolin-water interaction. Water structure at large cluster size exhibited slow dynamics and low self-diffusion of luteolin. The existence of hydrophobic π-π and hydrogen bonds between luteolin molecules drives strong self-aggregation resulting in poor water solubility. Breakage of these established interactions would result in increased solubility of luteolin in water.

Development of coarse-grained potential of silica species

ABSTRACT Understanding the molecular transformation of silica aggregates during silica polymerisation is crucial to control the properties of final products such as zeolite, nanoparticles, mesoporous silica and other polymorphs. Nevertheless, molecular events during synthesis are challenging to probe using experimental techniques. Computational tools are beneficial to probe molecular length and time scales; however, the complex systems with significant degrees of freedom require significant computational resources. In this work, we have developed coarse-grained (CG) potentials for silica system wherein every silica tetrahedron (Si(OH)O) having ‘z’ number of bridging oxygen is mapped to a unique CG silica bead (). Different composition of these CG silica beads represent a polymerised silica system with varying degrees of condensation. We performed molecular dynamics (MD) simulations of all-atom silica system to obtain reference radial distribution functions between various silica species (), which was used in Monte Carlo simulations of the CG system to obtain CG potentials. We iteratively refined the CG potentials using iterative Boltzmann inversion and inverse Monte Carlo techniques. We found two attractive minima in the CG potential between arising due to direct and indirect interactions of species representing first and second coordination shells. The strength of CG potential increases for both of minima with increasing number of bridging oxygen in species. We performed MD simulations of CG silica beads using developed CG potentials at two degree of condensations and found equilibrium structure of spherical silica nanoparticle. We found that and species are predominantly located at the centre of nanoparticles, whereas species are present uniformly.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning.

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5+, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5+, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5+ and C2H5+ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5+ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5+.

Accurate Adiabatic and Diabatic Potential Energy Surfaces for the Reaction of He + H2.

The accurate adiabatic and diabatic potential energy surfaces, which are for the two lowest states of He + H2, are presented in this study. The Molpro 2012 software package is used, and the large basis sets (aug-cc-pV5Z) are selected. The high-level MCSCF/MRCI method is employed to calculate the adiabatic potential energy points of the title reaction system. The triatomic reaction system is described by Jacobi coordinates, and the adiabatic potential energy surfaces are fitted accurately using the B-spline method. The equilibrium structures and electronic energies for the H2 are provided, and the corresponding different levels of vibrational energies of the ground state are deduced. To better express the diabatic process of the whole reaction, avoid crossing points being calculated and conical intersection also being optimized. Meanwhile, the diabatic potential energy surfaces of the reaction process are constructed. This study will be helpful for the analysis of histopathology and for the study in biological and medical mechanisms.