Fundamental Vibrational Frequencies Research Articles

Free flexural vibrations of standard wide-flange H-beams with consideration of the shear effect

The subject of the paper is a simply supported standard wide-flange H-beam. Cross sections of this beam is analytically described as a three-layer structure. The shear effect in its succesive layers is taking into account with consideration of the classical shear stress formula called Zhuravsky shear stress. Based on Hamilton’s principle, two differential equations of motion are obtained. These equations are analytically solved and the fundamental natural frequency of flexural vibration for this beam is derived. Examplary calculations are carried out for selected five I-beams.

Vibration behavior prediction of submerged nanobeams with axially traveling supports: numerical, analytical, and machine learning approaches

This work surveyed the vibration behavior and stability analysis of an underwater moving flexible nanosize beam, implementing numerical and analytical methods as well as tree-based machine learning (ML) algorithms. Dynamic modeling is performed based on the nonlocal stress-strain gradient theory (NSSGT), incorporating variable environmental conditions, surface energy, and rotational inertia effects. The natural frequencies and instability threshold are computed numerically. The exact closed-form mathematical expression for the critical towing velocity of the nanosize beam is determined analytically. Also, decision tree regression and least-squares boosting tree (LSBT) regression algorithms are exploited to predict stability boundaries and the fundamental vibration frequency, and their efficiency is surveyed accordingly. Comparative studies and parametric investigations are conducted. The impressions of geometry, added mass coefficient, scale ratio parameter, surface layer characteristics, fluid mass ratio, humidity, temperature rise, and external magnetic field intensity on the nanosystem dynamics are examined and illuminated. It is detected that the results of the analytical method and ML-based approaches are consistent with those reported by the numerical technique and literature. The results asserted that the proposed ML algorithms have acceptable performance and excellent effectiveness in computational time and cost. It is comprehended that the dynamic features of submerged traveling nanobeams drastically depend on the rotational inertia effects and thickness-dependent scale effects. The stability of the immersed movable nanoscale beams is perceived to improve by increasing the scale ratio parameter and the added mass coefficient. From the perspective of the optimal design of engineering instrumentation tools, the outcomes of the current article can be applied as an inclusive benchmark.

Approximate closed-form solutions for free vibration of circular arches with discrete lateral braces

Discrete lateral braces are commonly employed to enhance the out-of-plane stability of arches. However, these braces generate coupling effects among vibration modes, which significantly impact the vibration characteristics of the arches. This paper presents an analytical solution for the free vibration analysis of two-hinged arches with equally-spaced lateral translational and/or rotational braces. A simplified method of evaluating the fundamental frequency for the out-of-plane vibration of arches with equally-spaced lateral braces is introduced. The method relies on the conventional approach of representing arch braces through elastic springs, but here the out-of-plane deflection of the braced arch is constructed by adding related coupled sinusoidal functions to that of the unbraced arch, satisfying both the boundary and kinematic conditions. Subsequently, the fundamental frequency and threshold bracing stiffness or stiffness requirement are derived using the Rayleigh–Ritz method. Finite element analysis (FEA) is applied to investigate the flexural-torsional vibration mode and fundamental frequency of arches with discrete braces, and the results from FEA closely match the theoretical predictions. The effects of number of lateral translational and/or rotational brace, out-of-plane slenderness, included angle, bracing stiffness and bracing position on the fundamental frequency are comprehensively analyzed. It is found that when the fundamental frequency of the braced arch increases due to changes in bracing stiffness, the mode shape displays more intricate behavior, rather than following a straightforward low-to-high mode growth pattern. Furthermore, it is observed that in some cases, the addition of rotational bracing stiffness can markedly enhance the maximum fundamental frequency of the arch with both translational and rotational braces.

Performance of EOM-CCSD(T)(a)*-Based Quartic Force Fields in Computing Fundamental, Anharmonic Vibrational Frequencies of Molecular Electronically Excited States with Application to the Ã1A″ State of :CCH2 (Vinylidene).

Highly accurate anharmonic vibrational frequencies of electronically excited states are not as easily computed as their ground electronic state counterparts, but recently developed approximate triple excited state methods may be changing that. One emerging excited state method is equation of motion coupled cluster theory at the singles and doubles level with perturbative triples computed via the (a)* formalism, EOMEE-CCSD(T)(a)*. One of the most employed means for the ready computation of vibrational anharmonic frequencies for ground electronic states is second-order vibrational perturbation theory (VPT2), a theory based on quartic force fields (QFFs),fourth-order Taylor series expansions of the potential portion of the internuclear Watson Hamiltonian. The combination of these two is herein benchmarked for its performance for use as a means of computing rovibrational spectra of electronically excited states. Specifically, the EOMEE-CCSD(T)(a)* approach employing a complete basis set extrapolation along with core electron inclusion and relativity (the so-called "CcCR" approach) defining the QFF produces anharmonic fundamental vibrational frequencies within 2.83%, on the average, of reported gas-phase experimentally assigned values for the test set including the states of HCF, HCCl, HSiF, HNO, and HPO. However, some states have exceptional accuracy in the fundamentals, most notably for ν2 of HCCl in which the CcCR QFF value is within 1.8 cm-1 at 927.9 cm-1 (or 0.2%) of the experiment. Additionally, this approach produces rotational constants to, on the absolute average, within 0.41% of available experimental data, showcasing notable accuracy in the computation of rovibronic spectral data. Furthermore, utilizing a hybrid approach composed of harmonic CcCR force constants along with a set of simple EOMEE-CCSD(T)(a)*/aug-cc-pVQZ QFF cubic and quartic force constants is faster than using pure CcCR and better represents those modes that suffer from numerical instability in the anharmonic portion of the QFF, implying that this so-called "CcCR + QZ" QFF approach may be the best for future applications. Finally, complete, rovibrational spectral data are provided for :CCH2, a molecule of potential astrochemical interest, in order to aid in its potential future experimental rovibronic characterization.

Accurate ab initio spectroscopic studies of promising interstellar ethanolamine iminic precursors

Context. The detection of NH2CH2CH2OH (ethanolamine) in molecular cloud G+0.693-0.027 adds an additional player to the pre-biotic molecules discovered so far in the interstellar medium (ISM). As this molecule might be formed through condensed-phase hydrogenation steps, detecting one or more of the molecules involved might help to elucidate the chemical pathway leading to its production. Aims. The chemical path involves the formation of four chemical species. In this work, we study the energies of the isomers involved, indicate the best candidates for detection purposes, and provide the distortion constants of the most energetically favoured isomers undetected so far. Methods. We used highly accurate CCSD(T)-F12/cc-pCVTZ-F12 computations to predict the lowest energy isomers as well as their spectroscopic constants, taking corrections for core electron correlation and scalar relativity into account. Results. We studied 14 isomers. We find that the lowest energy isomer proposed in previous studies is not the actual minimum. We provide a set of rotational and distortion constants of the two new most stable isomers together with their fundamental vibrational frequencies in order to guide the search for these important astrochemical precursors of prebiotic molecules in the ISM.

COMPLEXES OF WATER-SOLUBLE LOCAL PLANT POLYPHENOL DERIVATIVES AND THEIR BIOLOGICAL ACTIVITY

The article is devoted to obtaining water-soluble complexes of iminoazo derivatives of gossypol, studying their physicochemical properties and biological activity. Aromatic, heterocyclic amines and sulfanilamide preparations were used as amine components in obtaining iminoazo derivatives of gossypol and their water-soluble complexes. The maximum values of wavelengths and the corresponding optical densities were determined in the UV spectra of compounds in acetone solvent. In order to determine the structure of the compounds, the infrared spectrum was taken and analyzed: the shift of the fundamental vibrational frequencies up to 31 cm-1 showed that the water-poly-N-vinylpyrrolidone in the compound is connected to a lesser extent as a result of hydrogen bonding. Obtaining complexes of azoderivatives of gossypol imines with poly-N-vinylpyrrolidone is related to the multi-functionality of the reactive groups of the ligand compound; formed hydrogen bonds due to the oxygen of the cycloamide group. For the first time, six new water-soluble complexes iminoazo derivatives of gossypol with poly-N-vinylpyrrolidone were obtained. The results of determination of interferon-inducing activity of compounds were analyzed. The activity was compared with the effectiveness of azo-, iminoazo derivatives of gossypol. According to the obtained results, it was shown that the effectiveness of water-soluble complexes iminoazo derivatives of gossypol.

Configuration of a gravel-rubber geotechnical seismic isolation system from laboratory and field tests

We present the outcomes derived from controlled laboratory experiments on utilizing gravel rubber mixtures (GRM) as a geotechnical seismic isolation (GSI) stratum beneath the foundational structure of the EuroProteas prototype. The study encompassed three distinct GRM compositions characterized by varying rubber proportions relative to the total mixture weight (0%, 10%, and 30%) employed as the foundation soil. These GSI-structure systems were subjected to external harmonic forces applied atop the structure of EuroProteas across a broad spectrum of frequencies and force magnitudes. Preceding the commencement of field experiments, resonant column and cyclic triaxial compression assessments were conducted on specimens featuring identical rubber fractions and mean grain size ratios. Our laboratory tests revealed that an increase in rubber content resulted in a reduction of the shear modulus (Go) and an augmentation of the damping ratio (Do) while concurrently inducing a more linear character in the G/Go-logγ-D profiles. The findings derived from the laboratory examinations align closely with those ascertained from field investigations. Expressly, it was confirmed that a GSI layer with a thickness of 0.50 meters, composed of a GRM incorporating 30% rubber content, exhibited a discernible reduction in the overall stiffness of the GSI-structure system, accompanied by a corresponding alteration in its fundamental vibrational frequency. The enhanced damping within the system manifested through observable reductions in acceleration recordings and diminished strain development at the base of the GRM layer with 30% rubber content, encompassing a wide range of frequencies.

A wealth of structures for the Ge2H2+ radical cation: comparison of theory and experiment.

Five structures of Ge2H2 and Ge2H2+ are investigated in this study. Optimized geometries at the CCSD(T)/cc-pwCVQZ-PP level of theory were obtained. Focal point analyses were performed on these optimized geometries to determine relative energies using the CCSD(T) method with polarized basis sets up to quintuple-zeta. Energy corrections include full T and pertubative (Q) coupled-cluster effects plus anharmonic corrections to the zero-point vibrational energy. Relative ordering in energy from lowest to highest of the five Ge2H2+ structures is butterfly, germylidene, monobridged, trans, then linear. In neutral Ge2H2, the monobridged structure lies lower in energy than the germylidene structure. Fundamental vibrational frequencies and IR intensities were computed for the minima at the CCSD(T)/cc-pwCVTZ-PP level of theory to compare with experimental research. Partial atomic charges and natural bonding orbital analyses indicated that the positive charge of Ge2H2+ is contained in the region of the Ge-Ge bond.

Research on vibration stability of a mirror bender system for synchrotron radiation.

This paper accurately predicts and quantifies the vibration response characteristics of a mirror bender system with the finite element simulation and experiment. The results show that the fundamental frequency of the roll angle vibration is 24.66Hz, and the fundamental frequency of the pitch angle vibrationis 116.21Hz. The overall error is within 11.15% in comparision with the first six natural frequencies obtained from experiments and simulations. The vertical support rod, being one of the weakest links in the overall structural stiffness, is a crucial factor limiting the increase in the natural frequency of the mirror system. Before and after the injection of cooling water, the pitch angle vibration was 123.63 and 199.04 nrad, respectively. An increase in the cooling water flow rate from 1 to 1.5 l/min has almost no effect on pitch angle vibrations. This study provides references and guidance for improving the stability of the mirror system.

Damage inference and residual capacity assessment for an E-Defense 2018 ten-story RC test structure

This paper presents an enhanced vision-based, post-earthquake performance assessment framework for RC building structures. This framework incorporates a damage inference method that can estimate the stiffness and strength reduction factors of components in stories without damage inspection based on the inter-story drift. The framework was validated by the application to the full-scale shaking table test of an E-Defense 2018 ten-story RC structure. The vision-based damage detection method effectively detected multicategory seismic damage on the component surfaces, and the damage states estimated by the vision-based method were consistent with the results estimated by the measured plastic hinge rotation. The proposed inter-story drift-based damage inference method reasonably estimated the reduction factors of components in the stories without damage photos. The numerical model updated by the reduction factors of damaged components provided accurate estimates of the fundamental vibrational frequencies after different levels of seismic shaking, and the drift-based inference method significantly improved the results compared with the trivial linear interpolation method. The residual capacity curves provided by pushover analysis of the updated model using the reduction factors as per FEMA 306 & Chiu et al. reasonably captured the hysteretic responses of the structure.

On the detectability of interstellar diaminomethane ((NH2)2CH2)

ABSTRACT The recent synthesis of diaminomethane ((NH2)2CH2) under simulated interstellar conditions implies that this molecule is likely present in the interstellar medium (ISM), and this work provides the highly accurate quantum chemically computed rotational constants and IR frequencies for comparison to experiment that may aid in its potential future detection. This simplest geminal diamine of prebiotic note has a transition for its ν18 fundamental frequency at 702.5 cm−1 (14.23 μm) with an intensity on level with that of the antisymmetric stretch in carbon dioxide. Additionally, its 1.72 D dipole moment for the most stable C2v conformer should make it detectable with radiotelescopes as well. The C2 conformer may also be detectable in similar regions where the C2v form is present, but only warmer or higher-energy regions will allow for possible observation of the C1 conformer. In any case, rotational constants for these other two conformers are also provided in addition to the full set of fundamental vibrational frequencies for the C2v conformer. These data will assist with further laboratory classification and possible interstellar detection of this prebiotic molecule.

Isomerism of : Accurate structural, energetic, and spectroscopic characterization.

A recent work [Ye et al. Mon. Not. R. Astron. Soc. 2023, 525, 1158] on the gas-phase formation of t-HC(O)SH, already detected in the interstellar medium, pointed out that the trans form of HC(S)OH is a potential candidate for astronomical observations. Prompted by these results, the family of isomers has been investigated from an energetic point of view using a double-hybrid density functional in combination with a partially augmented triple-zeta basis set. This preliminary study showed that the most stable species of the family are the cis and trans forms of HC(O)SH and HC(S)OH. For their structural and spectroscopic characterization, a composite scheme based on coupled cluster (CC) calculations that incorporates up to the quadruple excitations and accounts for the extrapolation to the complete basis set limit and core correlation effects has been employed. This approach opens to the prediction of rotational constants with an accuracy of 0.1%. A hybrid scheme, based on harmonic frequencies computed using the CC singles, doubles and a perturbative treatment of triples method (CCSD(T)) in conjunction with a quadruple-zeta basis set, allowed us to obtain fundamental vibrational frequencies with a mean absolute error of about 1%.

Mechanical response of tensegrity-origami solar modules

This work studies the mechanics of novel origami solar modules with tensegrity architecture for integration in the dynamic solar façades of energy-efficient buildings. The analyzed modules are deployed by adjusting the rest lengths of cables attached to given nodes, so as to form a tensegrity origami. Their stiffness is tuned by adjusting the pretension of the actuation cables, when the deployment motion is locked. The insertion of solar thermal or photovoltaic panels into the rigid elements of the module makes it possible to form positive-energy solar systems. The work studies the kinematics and the mechanics of the investigated structures through analytic and numerical methods. Two folding motions are examined: to open and close the modules and to track sun rays. The rapid prototyping of a physical mock-up permits an experimental validation of the force–displacement response in a given configuration of the sun-tracking motion. A procedure for the computation of the fundamental vibration modes and vibration frequencies of a quadrangular solar module is also given, and the expected response of the system under wind loading is outlined.

Structural, spectroscopic and second harmonic generation evaluation of 1,2,4-triazolinium tartrate - tartaric acid as a promising nonlinear optical material

Crystallization of 1,2,4-triazole with (2R,3R)-(+)-tartaric acid (l (+)-tartaric acid) in a 1:2 ratio yields the ionic co-crystals of 1,2,4-triazolium tartrate – tartaric acid (1:1), (C2H4N3) (C4H5O6)‧C4H6O6 – (abbreviated as TATT). TATT crystallizes in the tetragonal system with a non-centrosymmetric P41212 space group of eight molecules per unit cell. Apart from ionic interaction by the building ions and N–H‧‧‧O, the 1,2,4-triazolinium cation and the tartrate anion interact through hydrogen bonds and O–H‧‧‧O with tartaric acid to form a supramolecular complex (C2H4N3) (C4H5O6)‧C4H6O6 (TATT). Hydrogen bonds further organise these supramolecular complexes into a three-dimensional network. The interactions between the building blocks of the co-crystal were analyzed using Hirshfeld surface and 2D fingerprint plots. Normal coordinate force field calculations based on density functional theory (DFT) and structure optimizations were utilized to interpret the molecular structure and fundamental vibrational frequencies. The wave numbers' complete vibrational assignments were determined through potential energy distribution (PED). The HOMO and LUMO energy gap calculations explained the charge transfer interactions within the supramolecular unit. For the TATT co-crystal, the efficiency of the second harmonic generation (SHG) process was investigated under 800 nm irradiation using the Kurtz–Perry powder technique. The ionic co-crystal demonstrated a low SHG efficiency on the order of 10−1 compared to that of KDP.

On the Optimality Conditions in the Weight Minimization Problem for a Shell of Revolution at a Given Vibration Frequency

We consider shallow elastic shells with a given circular boundary and seek an axisymmetric shell shape minimizing the weight at a given fundamental frequency of shell vibrations. Using the resulting formula for the linear part of the increment of the frequency functional, the multiplicity of the minimum natural frequency of vibrations of the shell is estimated. The Fréchet differentiability of the frequency functional is also established, and optimal conditions for minimizing the weight of the shell at a given fundamental vibration frequency are obtained.

Vibration behavior of innovative discretely connected precast concrete sandwich floors

This paper investigates the vertical vibration behavior of an innovative discretely connected precast concrete sandwich floor (DCPCF) in orthogonal slab laying direction (OSLD). An experimental program included the full-scale tests of seven DCPCF specimens and two cast-in-situ floor (CISF) specimens was conducted. In order to evaluate the vertical vibration behavior of the DCPCF, the parameters considered the number of slabs, the number of connectors, the position of slab joints and loading condition were studied according to the vibration mode, fundamental frequency, damping ratio and acceleration response. The test results indicated that the first two vibration modes of DCPCF specimens and CISF specimens were basically the same. The fundamental frequency of the DCPCF was negatively correlated with the number of slab joints and overlying loads, and positively correlated with the number of connectors and the distance of slab joints to the mid-span. The damping ratio of the DCPCF decreased with the decrease of the number of slab joints, the increase of the number of connectors and the distance of slab joints to the mid-span. The vibration response of DCPCF specimens was slightly larger than those of CISF specimens under the same excitation. The peak acceleration increased with the increase of the loading frequency and the number of pedestrians. The closer the loading distribution was to the mid-span, the greater the peak acceleration would be. Based on the vertical vibration theory of elastic thin slab, the calculation methods for predicting the first mode natural frequency and peak acceleration of the DCPCF in OSLD were proposed. The calculated results obtained by the proposed formula showed good agreement with the experiment results.

Exploring the structure–property relationship of ethylenediammonium hydrogen phosphite: Insights from XRD, vibrational, DFT, and biological evaluation

The interaction between the molecules of phosphonic acid (H2P(H)O3) and ethylenediamine (NH2CH2CH2NH2) reacts in an aqueous solution and results in the formation of salt molecules with two NH∙∙∙O hydrogen bonds. The calculated stabilization energy of the 1:1 salt molecule, which represents the strength of the two NH∙∙∙O hydrogen bonds, is 8.063 kcal/mol (33.735 kJ/mol). The title compound crystallizes in the centrosymmetric space group Pbca of the orthorhombic system with eight molecules per unit cell. The three-dimensional supramolecular network is formed by hydrogen bonds between every hydrogen atom in both of the NH3+ groups of the ethylenediammonium cation. Hirshfeld surfaces and two-dimensional fingerprint plots were used to analyze the interactions of ethylenediammonium cations and hydrogen phosphite anions forming a three-dimensional supramolecular structure. Practically, two types of interactions, i.e. NH∙∙∙O and H∙∙∙H, are observed for both building units, ethylenediammonium cation and the hydrogen phosphite anion, which cover 100 % of the HS surface of each unit. Density functional theory (DFT) computations of normal mode force constants and structure optimizations were employed to evaluate the molecular structure, fundamental vibrational frequencies, and vibrational band intensities. The utilization of potential energy distribution (PED) allowed for the determination of comprehensive vibrational assignments for the wave numbers. The interactions involving the charge transfers of the supramolecular unit are explained by the computed HOMO and LUMO energy gap of 5.193 eV. To prove that the EDHP has stabilized, NBO analysis has been done. NBO studies establish that strong intra and intermolecular stabilization exists between the ethylenediammonium cation and the hydrogen phosphite anion. Furthermore, to investigate the synthetic chemical EDHP as a possible drug candidate, molecular docking studies and drug-likeness evaluation have been carried out. The best binding energy of the obtained cluster is −3.85 kcal/mol. The rmsd value is found to be 1.950 (≤2 Å) which is fairly good and confirms the best superimposed docked pose. Thus Molecular docking studies reveal that EDHP molecule has a substantial binding affinity for the SARS-CoV-2 protein and can serve as a promising drug candidate. The bioavailability score of 0.55 from pharmacokinetics study suggests that EDHP may have moderate bioavailability.

Synthesis, crystal structures, spectroscopy, and quantum chemical studies on the 4-dimethylaminopyridinium-2,4-dinitrophenolate: an organic NLO material for optoelectronics.

In this work, the 4-dimethylaminopyridinium-2,4-dinitrophenolate (4DMAP + 2,4DNP) by slow evaporation solution growth method has been presented. The Fourier transform infrared (FT-IR) (4000-400cm-1) and FT-Raman (4000-50cm-1) spectra were recorded for the grown crystal. The computational calculation has been carried out with density functional theory (DFT) in ground state with Gaussian program package. Optimized geometrical parameters (bond distances, bond angles, and dihedral angles) have been obtained and compared with X-ray crystallography data. The calculated fundamental vibrational frequencies from DFT/B3LYP with 6-311 + + G(d,p) level of theory were scaled so as to agree with the observed results, and the scaling factors were reported. Experimental and computed ultraviolet-visible (UV-Vis) spectra in acetone and methanol solvents were found comparable to each other. Furthermore, the frontier molecular orbitals (FMOs) energies, molecular electrostatic potential (MEP), nonlinear optical (NLO), hirshfeld surface (HS), and global chemical descriptors of the molecule were also calculated. The thermal stability and the melting point of the title compound were analyzed by the thermogravimetric analysis/differential thermal analysis (TGA/DTA) techniques. The mechanical behavior of the organic single crystal was measured by Vickers micro-hardness method. The third-order nonlinear optical properties such as nonlinear refractive index (n2), nonlinear absorption coefficient (β), optical nonlinear susceptibility Reχ(3), and optical nonlinear susceptibility Imχ(3) were calculated by using the open and closed aperture Z-scan technique. The theoretical and experimental NLO values clearly proposed that the nonlinearity of 4DMAP + 2,4DNP molecule could be helped as a potential candidate for optical limiting, frequency doubling, and optical switching applications.

Potential and kinetic interaction of two internal tops in molecules belonging to C2v(M) molecular symmetry group

Fourier analysis of the kinetic and potential interactions of non-coaxial internal tops in the molecules C6H4(OH)2, HO(CH2)OH, HOOOH, HOSOH, HSSSH, and HSOSH was carried out. It was found that for the all six molecules, in which both tops are characterized by a period 2 π, the harmonics with a period of π are dominate, with its contribution to the Fourier representation of potential surfaces increasing in the sequence mentioned above. Contributions of internal tops interactions to the kinetic and potential energies were determined for analyzed molecules. The influence of potential and kinetic interactions of internal tops on 1) the features of tunneling splitting of the ground and excited torsional states of molecules, 2) the landscape of 2D potential energy surfaces, 3) frequencies of fundamental torsional vibrations of hydroxyl and thiol groups, 4) the ratio of trans - and cis - conformer energies is also analyzed.

The heavy Carbene analogues SbH2 + and BiH2 +. Convergent quantum mechanical studies*

In 2021 Olaru, Mebs, and Beckmann reported the synthesis of remarkable cationic carbene analogues P R 2 + and As R 2 + . This work followed the same group's synthesis of Sb R 2 + and Bi R 2 + . To better understand these important systems, Sb H 2 + and Bi H 2 + have been studied with high level ab initio quantum mechanical methods. Geometries were optimised with the CCSDT(Q) method with the cc-pwCVTZ-PP basis set using small core pseudopotentials. Fundamental vibrational frequencies were computed to provide theoretical predictions for future synthetic studies. Relative energies with respect to P n + + H 2 ( Pn = Sb , Bi ) were determined at the CCSDT/CBS level of theory via the Focal Point Analysis method, and anharmonic zero-point vibrational energy and higher order contributions were also computed. For Sb H 2 + , we obtained R = 1.697 Å and θ = 90.8 ∘ with S b + + H 2 → Sb H 2 + reaction enthalpy of ΔH = − 18.71 kcal mol − 1 . For Bi H 2 + , the analogous results were R = 1.774 Å, θ = 89.7 ∘ , and ΔH = − 7.64 kcal mol − 1 for B i + + H 2 → Bi H 2 + .