{"title":"SQQ: Python Joint Toolkit for Water-Shell Topology Analysis","authors":"Jiangtao Pang, Quan Sun","doi":"10.1021/acs.jpca.6c05769","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c05769","url":null,"abstract":"<p>Order parameters are essential for molecular dynamicsstructuresof crystalline water, as they provide quantitative measures of phasechange. Yet conventional descriptors cannot directly resolve water-ringconnectivity, face adjacency, or cage closure. Here, we develop theGraph-guided Ring Overlap Workflow (GROW) algorithm and its open-sourceimplementation, Shell Quant Qualifier (SQQ), to connect molecularcoordinates with cage and phase topology. SQQ constructs hydrogen-bondor oxygen–oxygen water graphs, identifies chordless rings asfaces, and reconstructs cages by expanding connected face sets alongexposed edges. Since GROW tests branches without predefining the finalface arrangement, it can distinguish standard cages, uncommon cagecompositions, and isomers that share the same face counts. SQQ mapscage occupancy, face-sharing clusters, hydrate domains, and phaseboundaries while preserving the molecular identities behind each result.Tests on standard, perturbed, and periodically translated sI, sII,and sH crystals recover the expected network edges, cage types, andcage–water assignments. Comparisons on a hydrate-growth trajectoryshow close population agreement with GRADE and TRACE when graph definitionsand ring ranges are aligned, while examples explain differences causedby recognition rules. In the benchmark, SQQ completed the system containingmore than one million waters within 3 min. Through its Python andC++ engine, SQQ provides an end-to-end workflow for multiframe cagedetection, phase analysis, visualization, and traceable structuralreporting.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 41","pages":"8187–8199"},"PeriodicalIF":3.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149173728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Full-Dimensional Quantum Dynamics of the H + CH2D2 → H2 + CHD2 Reaction: Mode-Specific Chemistry in an Asymmetric Methane Isotopologue","authors":"Zhaojun Zhang, Dong H. Zhang","doi":"10.1021/acs.jpca.6c05608","DOIUrl":"10.1021/acs.jpca.6c05608","url":null,"abstract":"<p>Thehydrogen abstraction reaction H + CH<sub>2</sub>D<sub>2</sub> →H<sub>2</sub> + CHD<sub>2</sub> serves as an essentialbenchmark for polyatomic reaction dynamics, yet its lack of <em>C</em><sub>3<em>v</em></sub> symmetry has precluded full-dimensionalquantum mechanical treatments. Here, we report the first full-dimensional(12D) time-dependent wave packet study of this reaction on an accuratepotential energy surface. Our calculations reveal a striking hierarchyof mode-specific efficacy: excitation of the reacting CH<sub>2</sub> stretching modes enhances reactivity by factors of 8.7 and 7.6,while vibrational energy deposited into the spectator CD<sub>2</sub> modes proves less effective than translational energy. The torsionaland rocking motions exhibit moderate promotional effects. At combustion-relevanttemperatures, CH<sub>2</sub> stretching excitations collectively contributeover 53% of the thermal rate constant at 2000 K. This work establishesthe first rigorous quantum mechanical baseline for mode-selectivechemistry in an asymmetric methane isotopologue and provides a powerfulframework for elucidating bond-specific dynamics in complex polyatomicsystems.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 41","pages":"8120–8127"},"PeriodicalIF":3.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149101111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nathan Taton, William B. Stoll, Kaleb Mallon, Luke Kwan, Ljupcho Pejov, Michael T. Ruggiero, Tomče Runčevski
{"title":"Raman Spectroscopic Characterization of the Benzene:Acetonitrile (3:1) Cocrystal Relevant to Titan, Saturn’s Moon","authors":"Nathan Taton, William B. Stoll, Kaleb Mallon, Luke Kwan, Ljupcho Pejov, Michael T. Ruggiero, Tomče Runčevski","doi":"10.1021/acs.jpca.6c04868","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c04868","url":null,"abstract":"<p>Titan, Saturn’s largest moon, hosts active organicchemistryand surface environments where small molecules are expected to crystallizeas molecular minerals. Benzene and acetonitrile, both predicted tobe present on Titan, were shown to form a thermodynamically stablebenzene:acetonitrile (3:1) cocrystal that may occur as an evaporitephase along the margins of Titan’s hydrocarbon lakes. Here,we report a detailed morphological and Raman spectroscopic study ofthis cocrystal, supported by periodic density functional theory (DFT)calculations. Optical microscopy reveals that the cocrystal exhibitsa distinct sheaf-like spherulitic microstructure, unlike the equiaxedgrains of solid benzene and the dendritic growth of solid acetonitrile.The distinct crystal habit results from the crystal structure of thecocrystal and the peritectic mode of crystal growth. Raman spectrashow characteristic frequency shifts relative to the pure components,together with additional bands arising from the reduced symmetry ofthe cocrystal lattice. The calculations reproduce the observed vibrationalfeatures and support their assignment, showing that, compared to thepure components, the benzene vibrational features are relatively weaklyperturbed, whereas acetonitrile is more strongly influenced by thepolar channel environment and linear ordering within the structureof the cocrystal. These results establish a robust spectroscopic fingerprintfor the cocrystal and provide new constraints on the solid-state chemistryand possible evaporite mineralogy of Titan. Such laboratory characterizationsare timely in light of the recently concluded Cassini–Huygensmission, as well as the forthcoming Dragonfly mission to Titan.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 41","pages":"8138–8145"},"PeriodicalIF":3.0,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anoop Ajaya Kumar Nair, Julian Bessner, Timo Jacob, Elvar Ö Jónsson
{"title":"C-Pol: Point-Charge Perturbation Scheme for Mapping Tensor Moment Surfaces.","authors":"Anoop Ajaya Kumar Nair, Julian Bessner, Timo Jacob, Elvar Ö Jónsson","doi":"10.1021/acs.jpca.6c04295","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c04295","url":null,"abstract":"<p><p>Molecular polarizability tensors beyond the dipole-dipole level are key inputs to polarizable force fields, polarizable embedding, and machine-learned response models, yet routines to compute them exist in few quantum chemistry codes and are largely confined to atom-centered Gaussian basis sets. We present a general, backend-agnostic implementation of moment-based point-charge perturbation that removes this restriction. The molecular charge density is perturbed by external point charges available in any QM/MM-capable code, whether real-space-grid, plane-wave, or atom-centered, and the dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole tensors are recovered from finite differences of the perturbed multipole moments extrapolated to the zero-perturbation limit. The accuracy and generality of the method are established through three independent implementations spanning complementary numerical representations: GPAW (real-space grids), NWChem, and PySCF (atom-centered basis sets). Energy-based reference values (Gaussian 16) for all 19 commonly occurring point groups are reproduced within 3%. Furthermore, the finite-difference values agree with analytic coupled-perturbed Hartree-Fock results to within 4%, at comparable cost for medium-sized systems and more favorable scaling for larger ones. Relative to conventional energy-based schemes that require basis set extrapolation, the method reduces the number of SCF evaluations by a factor of 27. It is distributed as the open-source package C-Pol.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":" ","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149163437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Full-Dimensional Reactive Potential Energy Surfaces of OCS+ for S+ Dissociation: Ground and Excited States","authors":"Cangtao Yin, Stefan Willitsch, Markus Meuwly","doi":"10.1021/acs.jpca.6c03146","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c03146","url":null,"abstract":"<p>Full-dimensional reactive potential energy surfaces (PESs)forthe OCS<sup>+</sup> cation are constructed to describe S<sup>+</sup> loss in the electronic ground state and seven low-lying electronicallyexcited states. High-level <em>ab initio</em> reference energieswere computed at the MRCI+Q/aug-cc-pVTZ level and were used to generatePESs employing reproducing kernel Hilbert space representations (RKHS).The PESs accurately reproduce the measured dissociation limits toCO(X<sup>1</sup>Σ<sup>+</sup>) + S<sup>+</sup> in differentelectronic states. The topology of the PESs reveals multiple linearand T-shaped minima, pronounced angular anisotropy, and state-crossingmanifolds. Exploratory quasi-classical trajectory simulations on allPESs confirm numerical stability and energy conservation, illustratingthe suitability of the surfaces for dynamical applications. The presentwork represents the most comprehensive characterization to date ofthe lowest PESs of OCS<sup>+</sup> and provides a reliable foundationfor future studies of the photodissociation of OCS<sup>+</sup> andthe chemi-ionization dynamics of OCS.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 40","pages":"7887–7895"},"PeriodicalIF":3.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149124921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. Giri, S. Rana, U. Lourderaj, N. Sathyamurthy, E. Yurtsever, K. Dulitz, F. A. Gianturco
{"title":"Testing a Potential Averaging for Quantum Inelastic Dynamics","authors":"K. Giri, S. Rana, U. Lourderaj, N. Sathyamurthy, E. Yurtsever, K. Dulitz, F. A. Gianturco","doi":"10.1021/acs.jpca.6c03968","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c03968","url":null,"abstract":"<p>To obtain the inelastic cross sections for rotation state-changingprocesses, two crucial ingredients are required: the intermolecularforces from <em>ab initio</em> quantum chemical methods andthe full coupled channels (CC) treatment of the quantum scattering.The present work supports earlier work that there is a possible pathwhich reduces the computational demands by simplifying the multidimensionalpotential energy surface while using the exact CC quantum dynamicsto extract scattering attributes. This is applied successfully tothe case of <sup>11</sup>BN<sup>–</sup>(<em>X</em><sup>2</sup>Σ<sup>+</sup>, <em>j</em><sub>1</sub>) in collisionwith H<sub>2</sub>(<em>X</em><sup>1</sup>Σ<span><span><sup>+</sup><sub><em>g</em></sub></span></span>, <em>j</em><sub>2</sub> = 0), the former being an anionof interest in laser cooling at cryogenic temperatures. The exactCC calculations of the quantum dynamics, using either the full four-dimensional(4D) potential energy surface (PES) or its two-dimensional (2D) averaging(discussed in the main text), show that quantum attributes from thetwo procedures turn out to be essentially the same. These findingsindicate that the computational savings attained by reducing the dimensionsof the PES while keeping the quantum dynamics exact are a realisticoption for the case of the hydrogen molecule in its rovibrationalground state as a partner in low-temperature collision processes withmolecular ionic species.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 40","pages":"8036–8043"},"PeriodicalIF":3.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149124875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thomas Bierkandt, Patrick Hemberger, Nina Gaiser, Patrick Oßwald, Markus Köhler, Nils Hansen
{"title":"Resolving C6H6 Isomers from the Propargyl Self-Reaction at Combustion-Relevant Temperatures by PEPICO Spectroscopy","authors":"Thomas Bierkandt, Patrick Hemberger, Nina Gaiser, Patrick Oßwald, Markus Köhler, Nils Hansen","doi":"10.1021/acs.jpca.6c03346","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c03346","url":null,"abstract":"<p>The recombination of the resonance-stabilized propargyl(C<sub>3</sub>H<sub>3</sub>) radical is a key step in the formationof thefirst aromatic ring in combustion environments. In addition to benzene,several other C<sub>6</sub>H<sub>6</sub> isomers can also form, asMiller and Klippenstein [<em>J. Phys. Chem. A</em> <strong>2003</strong>, <em>107</em> (39), 7783–7799] theoretically demonstratedby mapping the complex potential energy surface of the C<sub>3</sub>H<sub>3</sub> + C<sub>3</sub>H<sub>3</sub> system. In this work,we investigated the propargyl self-reaction experimentally by flashpyrolysis in a resistively heated silicon carbide microreactor atcombustion-relevant temperatures of 1000 and 1190 K and at pressuresnear 10–20 mbar. Using photoion mass-selected threshold photoelectronspectra (ms-TPES) obtained with photoelectron photoion coincidence(PEPICO) techniques, we identified six C<sub>6</sub>H<sub>6</sub> species:2-ethynyl-1,3-butadiene, benzene, fulvene, <em>cis</em>- and <em>trans</em>-1,3-hexadien-5-yne, and 3,4-dimethylenecyclobutene.We further determined their branching ratios by least-squares fittinga linear combination of individual reference spectra to the experimentalmass-selected photoelectron spectrum of <em>m/z</em> 78. Inagreement with theoretical predictions, we found 2-ethynyl-1,3-butadieneto be the most abundant C<sub>6</sub>H<sub>6</sub> isomer, followedby benzene and fulvene.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 40","pages":"7996–8010"},"PeriodicalIF":3.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149124817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Brian J. Esselman, Michael J. Carrillo, Madeleine G. Atwood, Nitai P. Sahoo, Zoe K. Deems, Michael J. Tubergen, Maria A. Zdanovskaia, R. Claude Woods, Robert J. McMahon
{"title":"Rotational Spectroscopy and Partial Semi-Experimental Equilibrium (reSE) and Substitution (rsSE) Structures of Cyclobutenone (c-C4H4O)","authors":"Brian J. Esselman, Michael J. Carrillo, Madeleine G. Atwood, Nitai P. Sahoo, Zoe K. Deems, Michael J. Tubergen, Maria A. Zdanovskaia, R. Claude Woods, Robert J. McMahon","doi":"10.1021/acs.jpca.6c04937","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c04937","url":null,"abstract":"<p>Partial semi-experimentalequilibrium (<em>r</em><sub><em>e</em></sub><sup>SE</sup>) and substitution (<em>r</em><sub><em>s</em></sub><sup>SE</sup>) structuresof cyclobutenone(<em>c</em>-C<sub>4</sub>H<sub>4</sub>O, <em>C</em><sub><em>s</em></sub>, <em>μ</em><sub><em>a</em></sub> = 3.4 D) have been determined for the first timevia rotational spectroscopy. The rotational spectrum of this reactivespecies, which contains a highly strained four-membered ring, hasbeen measured from 9 to 735 GHz. Over 3800 transitions for the groundvibrational state of the normal isotopologue of cyclobutenone weremeasured, assigned, and least-squares fit to sextic distorted-rotorA- and S-reduced Hamiltonians in the I<sup><em>r</em></sup> representation, providing a complete set of quartic and sextic centrifugaldistortion parameters. Rotational transitions for each of the singlysubstituted heavy-atom isotopologues were measured at natural abundance.Rotational constants (<em>B</em><sub>0</sub>) for the sixisotopologues were converted to equilibrium values (<em>B</em><sub><em>e</em></sub>) using CCSD(T)/cc-pCVTZ vibration-rotationinteraction and electron-mass corrections, enabling the determinationof partial <em>r</em><sub><em>e</em></sub><sup>SE</sup> and <em>r</em><sub><em>s</em></sub><sup>SE</sup> structures that define all of the heavy-atom parameters of cyclobutenone.The two different sets of semi-experimental structural parameters(<em>r</em><sub><em>e</em></sub><sup>SE</sup> and <em>r</em><sub><em>s</em></sub><sup>SE</sup>) are comparedto the “best theoretical estimate” (BTE <em>r</em><sub><em>e</em></sub>) values, which are derived from theCCSD(T)/cc-pCV5Z <em>r</em><sub><em>e</em></sub> structurewith additional corrections addressing finite basis set, higher-levelelectron correlation, and relativistic effects, as well as incorporatingthe diagonal Born–Oppenheimer correction. Additionally, transitionsof the four lowest-energy vibrationally excited states have been assigned,measured, and least-squares fit to A-reduced, sextic centrifugallydistorted-rotor Hamiltonians in the I<sup><em>r</em></sup> representation. While ν<sub>21</sub> was well-modeled usinga single-state Hamiltonian, 2ν<sub>21</sub>, ν<sub>14</sub>, and ν<sub>20</sub> form an anharmonic- and Coriolis-coupledtriad and were treated by a three-state Hamiltonian model.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 40","pages":"7953–7965"},"PeriodicalIF":3.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149124910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Zagorec-Marks, G. S. Kocheril, H. J. Lewandowski
{"title":"Bottom-Up Formation of Aromatic Molecules via Sequential Ion–Molecule Reactions Starting at C3H5+","authors":"C. Zagorec-Marks, G. S. Kocheril, H. J. Lewandowski","doi":"10.1021/acs.jpca.6c05332","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c05332","url":null,"abstract":"<p>Aromaticmolecules are important in many fields of chemistry dueto their chemical stability and structural rigidity. Recently, multiplepolycyclic aromatic hydrocarbon (PAH) species have been observed inthe interstellar medium (ISM). While it is well known that PAHs arepresent in the ISM, how these molecules are formed in these environmentsis not fully understood. In order to better understand interstellarPAH formation, two classes of mechanisms have been considered, top-downand bottom-up. Top-down mechanisms explore PAH formation through fragmentationprocesses, and bottom-up mechanisms explore PAH formation throughsmall-molecule aggregation. In bottom-up formation mechanisms, ithas long been theorized that the formation of the first aromatic ringvia ion–molecule reactions is the rate-limiting step. In thisstudy, we experimentally demonstrate the bottom-up formation of atleast three aromatic ions through sequential ion–molecule reactionsunder interstellar conditions. The assignment of the structures ofthese molecules is supported through a combination of experimentalchemical reactivity studies and quantum chemical calculations. Theseresults reveal that aromatic rings can form with high efficiency inthe gas-phase through barrierless reactions and introduce a new potentialformation pathway for polycyclic aromatic hydrocarbons throughoutthe ISM.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 40","pages":"7988–7995"},"PeriodicalIF":3.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149124917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ring Currents in Open-Shell Condensed Benzenoid Homologues of Some Extended Clar’s Goblets","authors":"Timothy K. Dickens, Roger B. Mallion","doi":"10.1021/acs.jpca.6c04818","DOIUrl":"https://doi.org/10.1021/acs.jpca.6c04818","url":null,"abstract":"<p>Mishra et al. have recently synthesized a “π-extendedClar’s goblet”. This is a “concealed”non-Kekuléan condensed benzenoid hydrocarbon formed by (a)adding to Clar’s goblet some extra layers of benzenoid ringsand (b) simultaneously changing the size of the moiety at the centerof the structure from one hexagon to two hexagons─thereby changingthat moiety from “benzenoid” to “naphthalenic”.This idea is generalized and the “topological” ring-currentsin Clar’s goblet, and several of its homologues and oxidationstates, are compared with those arising from these new structures.Quantitative calculations of topological ring-currents in these open-shellsystems necessarily incorporate the technique of “ConfigurationalState Averaging”. Their predictions are compared with thosefrom pictorial current maps generated by more sophisticated <em>ab initio</em> and pseudo-π calculations. It is found that(a) adding or removing electrons from frontier nonbonding orbitalshells makes no difference to the ring current; (b) the number ofunpaired electrons in a given goblet depends on the number of layersin it, but not on its girth; (c) as the goblet becomes “fatter”,the current within the central moiety increases and the central ringsbecome “less empty”; there is, therefore, a greatermixing of current between the upper and lower triangles within eachgoblet as their girths become larger; and (d) the Hückel–London“topological” calculations predict that the directionof the current around the periphery of any goblet will be counterclockwise(diamagnetic)─a conclusion that is invariably confirmed bycalculations at the <em>ipso</em>-centric pseudo-π level.</p>","PeriodicalId":59,"journal":{"name":"The Journal of Physical Chemistry A","volume":"130 40","pages":"8065–8071"},"PeriodicalIF":3.0,"publicationDate":"2026-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149130625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}