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Here, the molecular electronic wave functions are expressed in quasi-atomic form. The corresponding global energy expression exhibits the unified resolution of the various modes of chemical bonding in terms of physical interactions. The bonding patterns in several molecules is elucidated.
Infrared (IR) spectroscopy using ultracold helium nanodroplet matrices has proven to be a powerful method to interrogate encapsulated ions, molecules, and clusters. Due to the helium droplets’ high ionization potential, optical transparency, and ability to pick up dopant molecules, the droplets offer a unique modality to probe transient chemical species produced via photo- or electron impact ionization. Here, in this work, helium droplets were doped with acetylene molecules and ionized via electron impact. Ion-molecule reactions within the droplet volume yield larger carbo-cations that were studied via IR laser spectroscopy. This work is focused on cations containing four carbon atoms. The spectra of C 4 H 2 + , C 4 H 3 + , and C 4 H 5 + are dominated by diacetylene, vinylacetylene, and methylcyclopropene cations, respectively, which are the lowest energy isomers. On the other hand, the spectrum of C 4 H 4 + ions hints at the presence of several co-existing isomers, the identity of which remains to be elucidated.
We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ΔE estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree–Fock included (0%–54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ΔE is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn–Sham orbitals gives results within 4–11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ~5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.
For this work, we rely on a total of 23 (cluster size, 8 structural, and 14 connectivity) descriptors to investigate structural patterns and connectivity motifs associated with water cluster aggregation. In addition to the cluster size n (number of molecules), the 8 structural descriptors can be further categorized into (i) one-body (intramolecular): covalent OH bond length (r OH ) and HOH bond angle (θ HOH ), (ii) two-body: OO distance (r OO ), OHO angle (θ OHO ), and HOOX dihedral angle ($\phi$ HOOX ), where X lies on the bisector of the HOH angle, (iii) three-body: OOO angle (θ OOO ), and (iv) many-body: modified tetrahedral order parameter (q) to account for two-, three-, four-, five-coordinated molecules (q m , m = 2, 3, 4, 5) and radius of gyration (R g ). The 14 connectivity descriptors are all many-body in nature and consist of the AD, AAD, ADD, AADD, AAAD, AAADD adjacencies [number of hydrogen bonds accepted (A) and donated (D) by each water molecule], Wiener index, Average Shortest Path Length, hydrogen bond saturation (% HB), and number of non-short-circuited three-membered cycles, four-membered cycles, five-membered cycles, six-membered cycles, and seven-membered cycles. We mined a previously reported database of 4 948 959 water cluster minima for (H 2 O) n , n = 3–25 to analyze the evolution and correlation of these descriptors for the clusters within 5 kcal/mol of the putative minima. It was found that r OH and % HB correlated strongly with cluster size n, which was identified as the strongest predictor of energetic stability. Marked changes in the adjacencies and cycle count were observed, lending insight into changes in the hydrogen bond network upon aggregation. A Principal Component Analysis (PCA) was employed to identify descriptor dependencies and group clusters into specific structural patterns across different cluster sizes. The results of this study inform our understanding of how water clusters evolve in size and what appropriate descriptors of their structural and connectivity patterns are with respect to system size, stability, and similarity. The approach described in this study is general and can be easily extended to other hydrogen-bonded systems.
Here we present a joint experimental and computational study on the geometric and electronic structures of deprotonated sulfamic acid (SA) clusters [(SA) n –H] – (n = 1, 2) employing negative ion photoelectron spectroscopy and high-level ab initio calculations. The photoelectron spectra provide the vertical/adiabatic detachment energy (VDE/ADE) of the sulfamate anion (SM – ) H 2 N•SO 3 – at 4.85 ± 0.05 and 4.58 ± 0.08 eV, respectively, and the VDE and ADE of the SM – •SA dimer at 6.41 ± 0.05 and 5.87 ± 0.08 eV, respectively. The significantly increased electron binding energies of the dimer confirm the enhanced electronic stability upon the addition of one SA molecule. The CCSD(T)-predicted VDEs/ADEs agree excellently with the experimental data, confirming the identified structures as the most stable ones. Two types of dimer isomers possessing different hydrogen bonding (HB) motifs are identified, corresponding to SM – binding to a zwitterionic SA (SM – •SA z ) and a canonical SA (SM – •SA c ), respectively. Two N–H$\cdots$O HBs and one superior O–H$\cdots$O HB are formed in the lowest-lying SM – •SA c , while SM – •SA z has three moderate N–H$\cdots$O HBs, with the former being 4.71 kcal/mol more stable. Further theoretical analyses reveal that the binding strength advantage of SM – •SA c over SM – •SA z arises from its significant contributions of orbital interactions between fragments, illustrating that sulfamate strongly interacts with its parent SA acid and preferably chooses the canonical SA in the subsequent cluster formations. Given the prominent presence of SA, this study provides the first evidence that the canonical dimer model of sulfamic acid should exist as a superior configuration during cluster growth.
Infrared (IR) action spectroscopy is utilized to characterize carbon-centered hydroperoxy-cyclohexyl radicals (·QOOH) transiently formed in cyclohexane oxidation. The oxidation pathway leads to three nearly degenerate ·QOOH isomers, β-, γ-, and δ-QOOH, which are generated in the laboratory by H-atom abstraction from the corresponding ring sites of the cyclohexyl hydroperoxide (CHHP) precursor. The IR spectral features of jet-cooled and stabilized ·QOOH radicals are observed from 3590 to 7010 cm −1 (∼10–20 kcal mol −1 ) at energies in the vicinity of the transition state (TS) barrier leading to OH radicals that are detected by ultraviolet laser-induced fluorescence. The experimental approach affords selective detection of β-QOOH, arising from its significantly lower TS barrier to OH products compared to γ and δ isomers, which results in rapid unimolecular decay and near unity branching to OH products. The observed IR spectrum of β-QOOH includes fundamental and overtone OH stretch transitions, overtone CH stretch transitions, and combination bands involving OH or CH stretch with lower frequency modes. The assignment of β-QOOH spectral features is guided by anharmonic frequencies and intensities computed using second-order vibrational perturbation theory. The overtone OH stretch (2ν OH ) of β-QOOH is shifted only a few wavenumbers from that observed for the CHHP precursor, yet they are readily distinguished by their prompt vs slow dissociation rates to OH products.
Protonated formic acid (PFA) is purported to be the active species in the catalytic activation of condensation reactions at the acidic interface of microdroplets. Here, we investigate the fundamental interaction between PFA and water with cryogenic ion vibrational spectroscopy of the binary PFA–H 2 O complexes generated via electrospray ionization followed by buffer gas cooling to about 20 K. The patterns displayed by the isomer-specific IR spectra of D 2 -tagged PFA–H 2 O indicate that two distinct, non-interconverting rotamers are present at low temperatures based on the cis and trans structures of the HCO 2 $H$$^{+}_{2}$ core ion. Both of these occur with the water molecule attached to the OH that is in a cis-configuration relative to the CH group (denoted E), but differ in the E vs Z (cis vs trans relative to the CH group) orientation of the spectator OH. This assignment scheme corrects a previous theoretical analysis that invoked a scenario in which structures with E- and Z-bound water molecules interconvert at low (20 K) temperatures. Isomer-specific bands arising from the OH stretches and water bending modes are deconvoluted using isotopomer-specific spectroscopy of the complexes with partial H/D exchange. The dependence of the nominal shared proton OH stretch frequency on the deuteration of the tethered water confirms strong coupling between this mode and the water bending fundamental.
Femtosecond structural dynamics of diiodomethane (CH 2 I 2 ) triggered by ultraviolet (UV) photoabsorption at 290 and 330 nm are studied using time-resolved coincident Coulomb explosion imaging driven by a near-infrared probe pulse. Here, we map the dominant single-photon process, the cleavage of the carbon–iodine bond producing rotationally excited CH 2 I radical, identify the contributions of the three-body (CH 2 + I + I) dissociation and molecular iodine formation channels, which are primarily driven by the absorption of more than one UV photon, and demonstrate the existence of a weak reaction pathway involving the formation of short-lived transient species resembling iso-CH 2 I 2 -like geometries with a slightly shorter I–I separation compared to the ground-state CH 2 I 2 . These transient molecular configurations, which can be separated from the other channels by applying a set of conditions on the correlated momenta of three ionic fragments, are formed within ∼100 fs after the initial photoexcitation and decay within the next 100 fs.
With the growing demand for realistic representations of chemical structures and the advent of exascale computing, the intelligent sampling of potential energy surfaces and efficient identification of global minima have become more essential but also more feasible. Building on prior studies demonstrating the efficiency of the Artificial Bee Colony (ABC) swarm intelligence algorithm, we report a hybrid metaheuristic framework that integrates the adaptive exploration capabilities of ABC coupled with the exploitation strengths of genetic algorithms (GA) in a scalable, Python-based implementation. The resulting tool, RANGE (Robust Adaptive Nature-inspired Global Explorer), provides seamless interfaces to multiple potential energy evaluators, either directly or via widely used Python libraries, and is designed for high-performance computing environments. We describe the implementation details of RANGE and evaluate its performance, relative to ABC- or GA-alone based algorithms, on a variety of chemical systems, including molecular clusters and heterogeneous surfaces. In conclusion, our results demonstrate RANGE’s efficiency, robustness, and broad applicability in addressing challenging global optimization problems in computational chemistry and materials science.
Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. In this work, we introduce a hypergraph-based formalism, Blocks & Bonds (B&B), which generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style structural complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the compositional complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based structural complexity and the compositional complexity across all examined systems. Owing to this agreement, the compositional complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol and glucose), DNA-origami lattices, and crystalline assemblies show that B&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter.
We have characterized the excited-state structural dynamics that follow optical excitation of the photoinactive cyanobacteriochrome (CBCR) NpF2164g5 to determine the first events along the photoisomerization reaction coordinate of the phycocyanobilin (PCB) chromophore in red-to-green photoactive CBCRs. Within 25 fs of photoexcitation to the first excited singlet state, S1, a cross peak begins to develop below the diagonal of the broadband two-dimensional electronic spectrum (2DES) owing to the formation of a twisted conformation of the PCB chromophore with an enhanced intramolecular charge-transfer (ICT) character. Excited-state coherent wavepacket motions, including a torsion of the methine bridge between rings C and D and the carbon–hydrogen out-of-plane (HOOP) wagging vibration, are rapidly damped as the cross peak forms. This finding supports an assignment of the torsional and HOOP modes to the reaction coordinate of a coherent nonadiabatic mechanism. The ICT process is accompanied by an ultrafast Stokes shift and rapidly damped oscillations at the torsional mode’s frequency, which are sensed by measurements of the energy gap of the cross peak using its first moment with respect to the detection frequency axis of the 2DES spectrum. Furthermore, these results have the further implication that polar side chains of nearby amino acid residues in the binding site of the PCB chromophore can manipulate the barrier height for photoisomerization in red-to-green photoactive CBCRs and in phytochromes by redistributing the π-electron density along the methine bridge between the C and D rings.
Large and structurally flexible chromophores pose challenges for in silico modeling of photodeactivation due to the many vibrational modes that can funnel the system toward energy degeneracy. In this work, we examine how the multiple degrees of freedom in biliverdin, a prototypical tetrapyrrolic chromophore, cooperate to drive access to the S 1 /S 0 intersection seam in vacuo. We begin by mapping the ground-state potential energy surface to identify representative biliverdin conformers relevant to photoexcitation. We then use a CASSCF-based framework to map the excited-state landscape and characterize the intersection seam, identifying distinct conical-intersection types. Finally, we employ ab initio multiple spawning to resolve the dynamical pathways by which the system accesses these regions. DFT potential-energy and free-energy mappings indicate that, although several conformers are relevant, the “locked-helix” ZsZsZs conformer predominates in the ground state. The intersection seam comprises numerous geometrically distinct regions characterized by varying degrees and combinations of dihedral torsion, pyramidalization, and bond-length alternation. Yet only select regions lie within energetic reach, and moderate barriers separate them from the S 1 minimum. Nonadiabatic dynamics combined with multivariate analyses show that, despite extensive mode coupling during deactivation that guides the system toward multiple regions of the seam, a single dihedral torsion, together with bond-length alternation, predominantly drives energy degeneracy. This work offers new insight into biliverdin’s intrinsic photochemical response and underscores a general feature of flexible chromophores: many modes may participate during photorelaxation, but only a limited subset ultimately dictates seam accessibility.
Transient carbon-centered hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation are characterized by infrared (IR) action spectroscopy under jet-cooled conditions with selective detection of hydroxyl (OH) radical products. Two distinct •QOOH isomers with radical sites at a primary carbon of one of the methyl groups (β-Me) or a secondary carbon (β-Et) of the ethyl group are identified by comparison with theoretically calculated IR absorption features for multiple conformers, including C–O, ethyl, and O–O torsions of the two isomers. Here, a master-equation analysis is developed and utilized to explore the conformational cooling process and the resultant conformer population distributions of the two isomers. Most of the IR features observed, including those in the strong fundamental and first overtone OH stretch regions as well as weaker combination bands involving OH stretch with torsion or OOH bend, are in good accord with computed anharmonic frequencies for the most populated conformers of the •QOOH_Et isomer. Relatively weak IR features most evident in the fundamental and first overtone OH stretch regions are ascribed to multiple conformers of the less stable •QOOH_Me isomer, along with a weak feature that is uniquely attributed to a combination band involving asymmetric CH 2 stretch and HCH bend of •QOOH_Me.
151 Eu Mössbauer spectroscopy has been used to investigate the behaviour of EuAl 4 through the four magnetic transitions that occur below 16 K. We find clear evidence for the first transition (T N1 , the onset of order) where an incommensurate modulated magnetic structure appears, and the third (T N3 ) where the modulation disappears at the tetragonal → orthorhombic structural transition. We see no changes at the lowest transition (T N4 ) but find that the modulation amplitude passes through a maximum at T N2 . Data on the isostructural but magnetically simpler EuGa 4 are also presented for comparison.
Novel nanocarbons such as fullerenes, nanotubes, graphene, and nanodiamond reside at the cutting edge of nanoscience and technology. Along with chemical functionalization, geometric constraints (such as extreme curvature in nanotubes or defects within or at the surfaces of diamond nanoparticles) significantly alter the electronic states of the nanocarbon material. Understanding the effects of steric strain on the electronic structure is critical to developing nanoelectronic applications based on these materials. This paper presents a fundamental study of how strain affects the electronic structure in a benchmark series of some fundamental saturated carbon cage compounds. Adamantane, C10H16, the smallest diamondoid and arguably the smallest nanodiamond crystallite, has carbon atoms essentially commensurate with diamond lattice positions and possesses by far the least molecular strain of this series. Twistane also is a C10H16 isomer but the fixed cyclohexane twist conformation of the central ring introduces additional strain into the cage. Octahedrane [(CH)12] and cubane [(CH)8] are considerably more strained, culminating in cubane where carbon–carbon bonds lie either parallel or orthogonal to one another. Using gas-phase near-edge x-ray absorption fine structure spectroscopy to probe the unoccupied electronic states, we observe two major progressions across this series. First, a broad C–C σ* resonance in the absorption splits into two more narrow and intense resonances with increasing strain. Second, the first manifold of states previously associated with tertiary C–H σ* in the diamondoid series appears to broaden and shift to lower energy. This feature is more than twice as intense in cubane than in octahedrane, even though these two molecules have only tertiary carbons, with the chemical formula (CH)x. The spectral differences are entirely due to the shape of the molecules; in particular, in cubane, the features arise from a high degree of p-p interaction between parallel C–C bonds. In contrast to the conventional wisdom that near-edge x-ray absorption is primarily an atomically localized spectroscopy, molecular shape and associated strain lead to the dominant features in spectra acquired from this fundamental series of carbon cage structures.