Focal Point Analysis Research Articles

Convergent abinitio analysis of the multi-channel HOBr + H reaction.

High-level potential energy surfaces for three reactions of hypobromous acid with atomic hydrogen were computed at the CCSDTQ/CBS//CCSDT(Q)/complete basis set level of theory. Focal point analysis was utilized to extrapolate energies and gradients for energetics and optimizations, respectively. The H attack at Br and subsequent Br-O cleavage were found to proceed barrierlessly. The slightly submerged transition state lies -0.2kcal mol-1 lower in energy than the reactants and produces OH and HBr. The two other studied reaction paths are the radical substitution to produce H2O and Br with a 4.0kcal mol-1 barrier and the abstraction at hydrogen to produce BrO and H2 with an 11.2kcal mol-1 barrier. The final product energies lie -37.2, -67.9, and -7.3kcal mol-1 lower in energy than reactants, HOBr + H, for the sets of products OH + HBr, H2O + Br, and H2 + BrO, respectively. Additive corrections computed for the final energetics, particularly the zero-point vibrational energies and spin-orbit corrections, significantly impacted the final stationary point energies, with corrections up to 6.2kcal mol-1.

Interfacial blending in co-axially electrospun polymer core-shell fibers and their interaction with cells via focal adhesion point analysis

Electrospun polymer scaffolds have gained prominence in biomedical applications, including tissue engineering, drug delivery, and wound dressings, due to their customizable properties. As the interplay between cells and materials assumes fundamental significance in biomaterials research, understanding the relationship between fiber properties and cell behaviour is imperative. Nevertheless, altering fiber properties introduces complexity by intertwining mechanical and surface chemistry effects, challenging the differentiation of their individual impacts on cell behaviour. Core-shell fibers present an appealing solution, enabling the control of mechanical properties of scaffolds, flexibility in material and drug selection, efficient encapsulation, strong protection of bioactive drugs against harsh environments, and controlled, prolonged drug release. This study addresses a key challenge in core-shell fiber design related to the blending effect between core and shell polymers. Two types of fibers, PMMA and core-shell PC-PMMA, were electrospun, and thorough analyses confirmed the desired core-shell structure in PC-PMMA fibers. Surface chemistry analysis revealed PC diffusion to the PMMA shell of the core-shell fiber during electrospinning, subsequently prompting an investigation of the fiber’s surface potential. Conducting cellular studies on osteoblasts by super-resolution confocal microscopy provided insights into the direct influence of interfacial polymer blending and, consequently, altered fiber surface and mechanical properties on cell focal adhesion points, bridging the gap between material attributes and cell responses in core-shell fibers.

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.

Fulminic acid: a quasibent spectacle.

Fulminic acid (HCNO) played a critical role in the early development of organic chemistry, and chemists have sought to discern the structure and characteristics of this molecule and its isomers for over 200 years. The mercurial nature of the extremely flat H-C-N bending potential of fulminic acid, with a nearly vanishing harmonic vibrational frequency at linearity, remains enigmatic and refractory to electronic structure theory, as dramatic variation with both orbital basis set and electron correlation method is witnessed. To solve this problem using rigorous electronic wavefunction methods, we have employed focal point analyses (FPA) to ascertain the ab initio limit of optimized linear and bent geometries, corresponding vibrational frequencies, and the HCN + O(3P) → HCNO reaction energy. Electron correlation treatments as extensive as CCSDT(Q), CCSDTQ(P), and even CCSDTQP(H) were employed, and complete basis set (CBS) extrapolations were performed using the cc-pCVXZ (X = 4-6) basis sets. Core electron correlation, scalar relativistic effects (MVD1), and diagonal Born-Oppenheimer corrections (DBOC) were all included and found to contribute significantly in determining whether vibrationless HCNO is linear or bent. At the all-electron (AE) CCSD(T)/CBS level, HCNO is a linear molecule with ω5(H-C-N bend) = 120 cm-1. However, composite AE-CCSDT(Q)/CBS computations give an imaginary frequency (51i cm-1) at the linear optimized geometry, leading to an equilibrium structure with an H-C-N angle of 173.9°. Finally, at the AE-CCSDTQ(P)/CBS level, HCNO is once again linear with ω5 = 45 cm-1, and inclusion of both MVD1 and DBOC effects yields ω5 = 32 cm-1. A host of other topics has also been investigated for fulminic acid, including the dependence of re and ωi predictions on a variety of CBS extrapolation formulas, the question of multireference character, the N-O bond energy and enthalpy of formation, and issues that give rise to the quasibent appellation.

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 + .

The multichannel i-propyl + O2 reaction system: A model of secondary alkyl radical oxidation.

The i-propyl + O2 reaction mechanism has been investigated by definitive quantum chemical methods to establish this system as a benchmark for the combustion of secondary alkyl radicals. Focal point analyses extrapolating to the abinitio limit were performed based on explicit computations with electron correlation treatments through coupled cluster single, double, triple, and quadruple excitations and basis sets up to cc-pV5Z. The rigorous coupled cluster single, double, and triple excitations/cc-pVTZ level of theory was used to fully optimize all reaction species and transition states, thus, removing some substantial flaws in reference geometries existing in the literature. The vital i-propylperoxy radical (MIN1) and its concerted elimination transition state (TS1) were found 34.8 and 4.4kcal mol-1 below the reactants, respectively. Two β-hydrogen transfer transition states (TS2, TS2') lie above the reactants by (1.4, 2.5) kcal mol-1 and display large Born-Oppenheimer diagonal corrections indicative of nearby surface crossings. An α-hydrogen transfer transition state (TS5) is discovered 5.7kcal mol-1 above the reactants that bifurcates into equivalent α-peroxy radical hanging wells (MIN3) prior to a highly exothermic dissociation into acetone + OH. The reverse TS5 → MIN1 intrinsic reaction path also displays fascinating features, including another bifurcation and a conical intersection of potential energy surfaces. An exhaustive conformational search of two hydroperoxypropyl (QOOH) intermediates (MIN2 and MIN3) of the i-propyl + O2 system located nine rotamers within 0.9kcal mol-1 of the corresponding lowest-energy minima.

Focal-Point Analysis to Achieve Accurate CCSD(T) Data Set References for Static Polarizabilities.

Static polarizability is an important ingredient for describing optical phenomena, intermolecular interactions, etc. It also offers a way to gauge the accuracy of the electronic structure methods. However, polarizability data sets that include a large variety of species with high-quality reference data are still lacking. In this work, we calibrate the reference data of two existing data sets, HR46 (Hickey and Rowley J. Phys. Chem. A 2014, 118, 3678-3687.) and T145 (Thakkar et al. Chem. Phys. Lett. 2015, 635, 257-261.), consisting of molecules with sizes up to 15 atoms. We apply the focal-point analysis (FPA) to the isotropic and anisotropic polarizability calculations, achieving the MP2 correlation contribution by the complete basis set (CBS) extrapolation of aug-cc-pCV[Q5]Z, augmented by the CCSD(T) correlation contribution from the CBS extrapolation of aug-cc-pV[XY]Z with [XY] = [Q5], [TQ], and [DT], respectively, to accommodate the computation to the system size. We conclude that our reference data are close to the CCSD(T)/aug-cc-pCV[Q5]Z quality, which are beneficial to the future assessment and benchmark studies of other electronic structure methods, in particular, density functional approximations.

Benchmark computational investigations for the basic model of the salt-water complex: NaCl(H2O) and its anion NaCl(H2O).

The microsolvation of salts in water is a fundamental physicochemical process. In this work, the aqueous salt complex NaCl(H2O) and its anion NaCl(H2O)- were investigated using comprehensive calculations, including the costly and accurate CCSD(T)-F12a and focal point analysis (FPA) methods. For the neutral NaCl(H2O), three isomers exist, two of which are mirror-symmetric with almost identical structures and their corresponding anions are also mirror-symmetric. For the NaCl(H2O)- anion, there are four isomers. Several transition states are found for the first time. The structural rearrangements of neutral NaCl(H2O) and NaCl(H2O)- anions are mainly caused by breaking and forming of the hydrogen bonds and the enhancement and weakening of interactions between Na and O atoms. The distributions of the anion complexes from 15-300 K are computed and compared to recent experimental results. The analysis of the intermolecular weak interactions shows the weak van der Waals interactions between Na and O atoms, as well as hydrogen bonding between H and Cl. Moreover, the theoretically predicted anion photoelectron spectra are assigned and analyzed in detail, and they agree with experimental spectra satisfactorily. The Na-Cl stretching vibrational mode dominates the vibrational structure in both anion spectra with some minor contributions from the intermolecular motions between H2O and NaCl.

Comment on “Is Leasing Greener Than Selling?” and Remark on the Focal Point Analysis in Durable Goods Models

The focal point analysis is a viable approach to analyze models of finitely durable goods in infinite time horizon. Agrawal, Ferguson, Toktay, and Thomas [Agrawal VV, Ferguson M, Toktay LB, Thomas VM (2012) Is leasing greener than selling? Management Sci. 58(3):523–533.] study the focal point of steady-state firm–consumer games for leasing and selling models. We note that the optimal solution for their selling model does not reflect self-replicated leases mirroring the lease offered by the firm and show that the solution is indeed erroneous as it violates the constraint on consumer-type cutoffs. Although this does not affect the structure of their propositions, that is, outlining thresholds for more profitability and greenness of selling compared with leasing, it renders the thresholds incorrect. We first uncover and fix the root cause of the error. We then distinguish the focal point analysis from the rental price approach and note a few remarks for future durable goods models. This paper was accepted by Jayashankar Swaminathan, operations management. Supplemental Material: Data are available at https://doi.org/10.1287/mnsc.2022.4637 .

A quantum-chemical perspective on the laser-induced alignment and orientation dynamics of the CH3 X (X = F, Cl, Br, I) molecules.

Motivated by recent experiments, the laser‐induced alignment‐and‐orientation (A&O) dynamics of the prolate symmetric top CH3X (X = F, Cl, Br, I) molecules is investigated, with particular emphasis on the effect of halogen substitution on the rotational constants, dipole moments, and polarizabilities of these species, as these quantities determine the A&O dynamics. Insight into possible control schemes for preferred A&O dynamics of halogenated molecules and best practices for A&O simulations are provided, as well. It is shown that for accurate A&O ‐dynamics simulations it is necessary to employ large basis sets and high levels of electron correlation when computing the rotational constants, dipole moments, and polarizabilities. The benchmark‐quality values of these molecular parameters, corresponding to the equilibrium, as well as the vibrationally averaged structures are obtained with the help of the focal‐point analysis (FPA) technique and explicit electronic‐structure computations utilizing the gold‐standard CCSD(T) approach, basis sets up to quintuple‐zeta quality, core‐correlation contributions and, in particular, relativistic effects for CH3Br and CH3I. It is shown that the different A&O behavior of the CH3X molecules in the optical regime is mostly caused by the differences in their polarizability anisotropy, in other terms, the size of the halogen atom. In contrast, the A&O dynamics of the CH3X series induced by an intense few‐cycle THz pulse is mostly governed by changes in the rotational constants, due to the similar dipole moments of the CH3X molecules. The A&O dynamics is most sensitive to the B rotational constant: even the difference between its equilibrium and vibrationally‐averaged values results in noticeably different A&O dynamics. The contribution of rotational states having different symmetry, weighted by nuclear‐spin statistics, to the A&O dynamics is also studied.

Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance.

Hierarchical, convergent ab initio benchmark computations were performed followed by a systematic analysis of DFT performance for five pericyclic reactions comprising Diels-Alder, 1,3-dipolar cycloaddition, electrocyclic rearrangement, sigmatropic rearrangement, and double group transfer prototypes. Focal point analyses (FPA) extrapolating to the ab initio limit were executed via explicit quantum chemical computations with electron correlation treatments through CCSDT(Q) and correlation-consistent Gaussian basis sets up to aug′-cc-pV5Z. Optimized geometric structures and vibrational frequencies of all stationary points were obtained at the CCSD(T)/cc-pVTZ level of theory. The FPA reaction barriers and energies exhibit convergence to within a few tenths of a kcal mol−1. The FPA benchmarks were used to evaluate the performance of 60 density functionals (eight dispersion-corrected), covering the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. The meta-hybrid M06-2X functional provided the best overall performance [mean absolute error (MAE) of 1.1 kcal mol−1] followed closely by the double-hybrids B2K-PLYP, mPW2K-PLYP, and revDSD-PBEP86 [MAE of 1.4–1.5 kcal mol−1]. The regularly used GGA functional BP86 gave a higher MAE of 5.8 kcal mol−1, but it qualitatively described the trends in reaction barriers and energies. Importantly, we established that accurate yet efficient meta-hybrid or double-hybrid DFT potential energy surfaces can be acquired based on geometries from the computationally efficient and robust BP86/DZP level.

Comment on 'Is Leasing Greener than Selling?' and Remark on the Focal Point Analysis in Durable Goods Models

Comment on 'Is Leasing Greener than Selling?' and Remark on the Focal Point Analysis in Durable Goods Models

Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics.

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg [J. Chem. Phys. 107, 432 (1997)]. This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H2O)6]2+ and [Fe(NH3)6]2+ molecules. A focal pointanalysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple-ζ basis set predicts the spin splittings of [Fe(H2O)6]2+ and [Fe(NH3)6]2+ to be -35.7 and -17.1 kcal mol-1, respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.

Group 15 and 16 Nitrene‐Like Pnictinidenes

Pnictinidenes are an increasingly relevant species in main group chemistry and generally exhibit proclivity for the triplet electronic ground state. However, the elusive singlet electronic states are often desired for chemical applications. We predict the singlet-triplet energy differences (ΔEST =ESinglet -ETriplet ) of simple group 15 and 16 substituted pnictinidenes (Pn-R; Pn=P, As, Sb, or Bi) with highly reliable focal-point analyses targeting the CCSDTQ/CBS level of theory. The only cases we predict to have favorable singlet states are P-PH2 (-3.2 kcal mol-1 ) and P-NH2 (-0.2 kcal mol-1 ). ΔEST trends are discussed in light of the geometric predictions as well as qualitative natural bond order analysis to elucidate some of the important electronic structure features. Our work provides a rigorous benchmark for the ΔEST of fundamental Pn-R moieties and provides a firm foundation for the continued study of heavier pnictinidenes.

Optimal fusion of multi-focus image: Integrating WNMF and focal point analysis

Image fusion can be used to improve the image utilization, spatial resolution and spectral resolution, which has been widely applied on medicine, remote sensing, computer vision, weather forecast and military target recognition. The goal of image fusion is to reduce the uncertainty and redundancy of the output and increase the reliability of the image on the basis of the maximum combination of relevant information. In this paper, a multi-focus image fusion algorithm based on WNMF and Focal point position analysis is proposed to improve the image fusion method based on nonnegative matrix factorization. In the imaging process, the Gaussian function is used to approximate the point spread function in the optical system. Then calculate the difference between the original image and the approximate point spread function and get the weighted matrix [Formula: see text]. Finally, we apply the weighted nonnegative matrix algorithm to image fusion, and the new fusion image with clear parts is obtained. Experimental results show that the multi-focus image fusion algorithm based on WNMF and Focal point position analysis (MFWF) is better.

Identification and Reactivity of s-cis,s-cis-Dihydroxycarbene, a New [CH2O2] Intermediate.

We report the first preparation of the s-cis,s-cis conformer of dihydroxycarbene (1cc) by means of pyrolysis of oxalic acid, isolation of the lower-energy s-trans,s-trans (1tt) and s-cis,s-trans (1ct) product conformers at cryogenic temperatures in a N2 matrix, and subsequent narrow-band near-infrared (NIR) laser excitation to give 1cc. Carbene 1cc converts quickly to 1ct via quantum-mechanical tunneling with an effective half-life of 22 min at 3 K. The potential energy surface features around 1 were pinpointed by convergent focal point analysis targeting the AE-CCSDT(Q)/CBS level of electronic structure theory. Computations of the tunneling kinetics confirm the time scale of the 1cc → 1ct rotamerization and suggest that direct 1cc → H2 + CO2 decomposition may also be a minor pathway. The intriguing latter possibility cannot be confirmed spectroscopically, but hints of it may be present in the measured kinetic profiles.

Characterization of the 2-methylvinoxy radical + O2 reaction: A focal point analysis and composite multireference study

Vinoxy radicals are involved in numerous atmospheric and combustion mechanisms. High-level theoretical methods have recently shed new light on the reaction of the unsubstituted vinoxy radical with O2. The reactions of 1-methylvinoxy radical and 2-methylvinoxy radical with molecular oxygen have experimental high pressure limiting rate constants, k∞, 5-7 times higher than that of the vinoxy plus O2 reaction. In this work, high-level ab initio quantum chemical computations are applied to the 2-methylvinoxy radical plus O2 system, namely, the formation and isomerization of the 1-oxo-2-propylperoxy radical, the immediate product of O2 addition to the 2-methylvinoxy radical. Multireference methods were applied to the entrance channel. No barrier to O2 addition could be located, and more sophisticated treatment of dynamic electron correlation shows that the principal difference between O2 addition to the vinoxy and 2-methylvinoxy radicals is a larger steric factor for 2-methylvinoxy + O2. This is attributed to the favorable interaction between the incoming O2 molecule and the methyl group of the 2-methylvinoxy radical. Via the focal point approach, energetics for this reaction were determined, in most cases, to chemical accuracy. The coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] correlation energy and Hartree-Fock energies were independently extrapolated to the complete basis set limit. A correction for the effect of higher excitations was computed at the CCSDT(Q)/6-31G level. Corrections for the frozen-core approximation, the Born-Oppenheimer approximation, the nonrelativistic approximation, and the zero-point vibrational energy were included. From the 1-oxo-2-propylperoxy radical, dissociation to reactants is competitive with the lowest energy isomerization pathway. The lowest energy isomerization pathway ultimately forms acetaldehyde, CO, and ·OH as the final products.

Riddles of the structure and vibrational dynamics of HO3 resolved near the ab initio limit.

The hydridotrioxygen (HO3) radical has been investigated in many previous theoretical and experimental studies over several decades, originally because of its possible relevance to the tropospheric HOx cycle but more recently because of its fascinating chemical bonding, geometric structure, and vibrational dynamics. We have executed new, comprehensive research on this vexing molecule via focal point analyses (FPA) to approach the ab initio limit of optimized geometric structures, relative energies, complete quartic force fields, and the entire reaction path for cis-trans isomerization. High-order coupled cluster theory was applied through the CCSDT(Q) and even CCSDTQ(P) levels, and CBS extrapolations were performed using cc-pVXZ (X = 2-6) basis sets. The cis isomer proves to be higher than trans by 0.52 kcal mol-1, but this energetic ordering is achieved only after the CCSDT(Q) milestone is reached; the barrier for cis → trans isomerization is a minute 0.27 kcal mol-1. The FPA central re(O-O) bond length of trans-HO3 is astonishingly long (1.670 Å), consistent with the semiexperimental re distance we extracted from microwave rotational constants of 10 isotopologues using FPA vibration-rotation interaction constants (αi). The D0(HO-O2) dissociation energy converges to a mere 2.80 ± 0.25 kcal mol-1. Contrary to expectation for such a weakly bound system, vibrational perturbation theory performs remarkably well with the FPA anharmonic force fields, even for the torsional fundamental near 130 cm-1. Exact numerical procedures are applied to the potential energy function for the torsional reaction path to obtain energy levels, tunneling rates, and radiative lifetimes. The cis → trans isomerization occurs via tunneling with an inherent half-life of 1.4 × 10-11 s and 8.6 × 10-10 s for HO3 and DO3, respectively, thus resolving the mystery of why the cis species has not been observed in previous experiments executed in dissipative environments that allow collisional cooling of the trans-HO3 product. In contrast, the pure ground eigenstate of the cis species in a vacuum is predicted to have a spontaneous radiative lifetime of about 1 h and 5 days for HO3 and DO3, respectively.

Ring-polymer molecular dynamics studies of thermal rate coefficients for reaction F + H2O → HF + OH

The prototype tetra-atomic reaction F + H2O → HF + OH plays a significant role in both atmospheric and astronomical chemistry. In this work, thermal rate coefficients of this reaction are determined with the ring polymer molecular dynamics (RPMD) method on a full-dimensional potential energy surface (PES). This PES is the most accurate one for the title reaction, as demonstrated by the correct barrier height and reaction energy, compared to the benchmark calculations by the focal point analysis and the high accuracy extrapolated ab initio thermochemistry methods. The RPMD rate coefficients are in excellent agreement with those calculated by the semiclassical transition state theory and a two-dimensional master equation technique, and some experimental measurements. As has been found in many RPMD applications, quantum effects, including tunneling and zero-point energy effects, can be efficiently and effectively captured by the RPMD method. In addition, the convergence of the results with respect to the number of beads is rapid, which is also consistent with previous RPMD applications.

Fingerprints of microscopic superfluidity in HHen+ clusters

ABSTRACTThe structures and the vibrational dynamics of the complexes HHe are investigated experimentally (via mass spectrometry (MS)) and at high levels of electronic-structure theory. The MS measurements reveal interesting trends about the stability of the starting members of the HHe family. The computations establish that the basically linear, strongly bound, symmetric triatomic molecular ion He(H)He, with an equilibrium H–He distance of 0.925 Å and about 2/3 but at least 1/2 of the positive charge on H, is the molecular core of all of the complexes. Definitive quantum-chemical results are obtained for HHe and HHe, including the proton affinity of He (computed to be cm−1 via the focal-point analysis (FPA) scheme), the FPA isomerisation energy between the two linear isomers of HHe ( cm−1), and the dissociation energy of the HHe HHe + He reaction, with an FPA estimate of cm−1. The structural isomers of the He-solvated complexes are discussed up to n=18. A useful notation, [k−l−m]-HHe, is introduced to characterise qualitatively the three possible belts around the He–H–He core in HHe (), where l denotes the number of He atoms in the central belt and denote the number of He atoms in the top and bottom belts. Capping He atoms attached to the belts can be indicated by sub- and superscripts. Several possible indicators of microscopic superfluidity are investigated: He evaporation energies, rotational constants, and vibrational fundamentals.