Radicals in aqueous solution: assessment of density-corrected SCAN functional

We study self-interaction effects in solvated and strongly-correlated cationic molecular clusters, with a focus on the solvated hydroxyl radical. To address the self-interaction issue, we apply the DC-r2SCAN method, with the auxiliary density matrix approach. Validating our method through simulations of bulk liquid water, we demonstrate that DC-r2SCAN maintains the structural accuracy of r2SCAN while effectively addressing spin density localization issues. Extending our analysis to solvated cationic molecular clusters, we find that the hemibonded motif in the [CH3S∴CH3SH]+ cluster is disrupted in the DC-r2SCAN simulation, in contrast to r2SCAN that preserves the (three-electron-two-center)-bonded motif. Similarly, for the [SH∴SH2]+ cluster, r2SCAN restores the hemibonded motif through spin leakage, while DC-r2SCAN predicts a weaker hemibond formation influenced by solvent-solute interactions. Our findings demonstrate the potential of DC-r2SCAN combined with the auxiliary density matrix method to improve electronic structure calculations, providing insights into the properties of solvated cationic molecular clusters. This work contributes to the advancement of self-interaction corrected electronic structure theory and offers a computational framework for modeling condensed phase systems with intricate correlation effects.

Infrared Spectroscopy of (Benzene-H2S-Xn)+, X = H2O (n = 1 and 2) and CH3OH (n = 1), Radical Cation Clusters: Microsolvation Effects on the S-π Hemibond

An unconventional covalent bond in which three electrons are shared by two centers is called hemibond. Hemibond formation frequently competes with proton transfer (or ionic hydrogen bond formation), but there have been a few experimental reports on such competition. In the present study, we focus on the (benzene-H₂S)⁺ radical cation cluster, which is a model system of the S-π hemibond. The stability of the S-π hemibond to the microsolvation by water and methanol is explored with infrared spectroscopy of (benzene-H₂S-X_n)⁺, X = H₂O (n = 1 and 2) and CH₃OH (n = 1), clusters. We also perform energy-optimization and vibrational simulations of (benzene-H₂S-X_n)⁺. By comparison among the observed and simulated spectra, we determine the intermolecular binding motifs in (benzene-H₂S-X_n)⁺. While the S-π hemibonded isomer is exclusively populated in (benzene-H₂S-H₂O)⁺, both the hemibonded and proton-transferred isomers coexist in [benzene-H₂S-(H₂O)₂]⁺ and (benzene-H₂S-CH₃OH)⁺. Breaking of the S-π hemibond by the microsolvation is observed, and its solvent and cluster size dependence is interpreted by the proton affinity and the coordination property of the solvent moiety.

Spectroscopic evidence of S∴N and S∴O hemibonds in heterodimer cations

Computational and condensed phase experimental evidence for the existence of S∴N and S∴O hemibonded structures has been reported previously, but no gas phase experimental evidence has been reported. To experimentally explore the existence of the S∴N and S∴O hemibonds in the gas phase, we recorded the infrared photodissociation action spectra of four cationic clusters: [CH₃SH-NH₃]⁺, [CH₃SCH₃-NH₃]⁺, [CH₃SCH₃-H₂O]⁺, and [CH₃OCH₃-H₂O]⁺. Combined with the calculation results, it is found that the S∴N hemibonded structure is competitive with the S⋯HN H-bonded structure, though only the latter structure is actually observed in [CH₃SH-NH₃]⁺. The spectral and theoretical results show that hemibonds can form between the second- (oxygen or nitrogen) and the third-period elements (sulfur) in the heterodimer clusters of [CH₃SCH₃-NH₃]⁺ and [CH₃SCH₃-H₂O]⁺. However, the S∴N and S∴O hemibonded structures are found competitive with the C⋯HN and CH⋯O H-bonded structures, respectively, and both the structures coexist. On the other hand, the O∴O hemibonded structure is much less stable than other hydrogen bonded (H-bonded) structures in [CH₃OCH₃-H₂O]⁺, and it shows no clear contribution to the observed spectrum. This study provides direct spectroscopic evidence for the existence of S∴N and S∴O hemibonds in the gas phase and their competition with the H-bonds, which may be also fundamentally important in biological processes.

Hidden Hemibonding in the Aqueous Hydroxyl Radical

The existence of a two-center, three-electron hemibond in the first solvation shell of ^•OH(aq) has long been a matter of debate. The hemibond manifests in ab initio molecular dynamics simulations as a small-r feature in the oxygen radial distribution function (RDF) for H₂O···^•OH, but that feature disappears when semilocal density functionals are replaced with hybrids, suggesting a self-interaction artifact. Using periodic simulations at the PBE0+D3 level, we demonstrate that the hemibond is actually still present (as evidenced by delocalization of the spin density) but is obscured by the hydrogen-bonded feature in the RDF due to a slight elongation of the hemibond. Computed electronic spectra for ^•OH(aq) are in excellent agreement with experiment and confirm that hemibond-like configurations play an outsized role in the spectroscopy due to an intense charge-transfer transition that is strongly attenuated in hydrogen-bonded configurations. Apparently, 25% exact exchange (as in PBE0) is insufficient to eliminate delocalization of unpaired spins.

Infrared Spectroscopy and Anharmonic Vibrational Analysis of (H2O-Krn)+ (n = 1-3): Hemibond Formation of the Water Radical Cation

The hemibond is a nonclassical covalent bond formed between a radical (cation) and a closed shell molecule. The hemibond formation ability of water has attracted great interest, concerning its role in ionization of water. While many computational studies on the water hemibond have been performed, clear experimental evidence has been hardly reported because the hydrogen bond formation overwhelms the hemibond formation. In the present study, infrared photodissociation spectroscopy is applied to (H₂O-Kr_n)⁺ (n = 1-3) radical cation clusters. The observed spectra of (H₂O-Kr_n)⁺ are well reproduced by the anharmonic vibrational simulations based on the hemibonded isomer structures. The firm evidence of the hemibond formation ability of water is revealed.

The mobility and solvation structure of a hydroxyl radical in a water nanodroplet: a Born-Oppenheimer molecular dynamics study

Hydroxyl radicals (OH*) play a crucial role in atmospheric chemistry and biological processes. In this study, Born-Oppenheimer molecular dynamics simulations are performed under ambient conditions for a hydroxyl radical in a water nanodroplet containing 191 water molecules. Density functional theory calculations are performed at the BLYP-D3 level with some test calculations at the B3LYP-D3 level. In two 150 ps trajectories, either with OH* initially located in the interior region or at the surface of the water nanodroplet, the OH* radical ends up in the subsurface layer of the nanodroplet, which is different from the "surface preference" predicted from previous empirical force field simulations. The solvation structure of OH* contains fluctuating hydrogen bonds, as well as a two-center three-electron hemibond in some cases. The mobility of OH* is enhanced by hydrogen transfer, which has a free energy barrier of ∼4.6 kcal mol-1. The results presented in this study deepen our understanding of the structure and dynamics of OH* in aqueous solutions, especially around the air-water interface.

Structure, stability, infrared spectra, and bonding of OHm(H2O)7 (m = 0, ±1) clusters: ab initio study combining the particle swarm optimization algorithm

The various structural candidates of anionic, neutral, and cationic water clusters OHm(H2O)7 (m = 0, ±1) have been globally predicted by combining the particle swarm optimization method and quantum chemical calculations. Geometry optimization and vibrational analysis for the optimal structures were performed with the MP2/aug-cc-pVDZ method, and the energy profile was further refined at the CCSD(T)/CBS level. Special attention was paid to the relationships between configurations and energies, particularly the first solvation shell coordination number of OH- and OH. For OH-(H2O)7, OH(H2O)7, and OH+(H2O)7 clusters, the most stable species at room temperature are predicted to be the tetra-solvated multi-ring structure A6, the tri-solvated hemibond cage structure N1, and the single five-membered ring structure C2, respectively. The temperature effects on the stability of these three systems were also explored via Gibbs free energies. Furthermore, for the OH-(H2O)7 clusters, the assignments of vibrational transitions in the OH stretching region are in good agreement with the studies of small hydroxide ion-water clusters, and the IR spectra of two isomers (tetra-solvated multi-ring A6 and penta-solvated cage A3) may match future experimental observation well. By topological analysis and reduced density gradient analysis, the structural characteristics and bonding strengths of the studied clusters were investigated. This work indicates the excellent performance of the PSO search algorithm and CALYPSO on water clusters, and may further provide extensive insights into the chemical behavior such as the transport mechanism of OH- ions and OH radicals in the aqueous phase.

Effects of solvent molecules on hemi-bonded (CH3SH)2+: infrared absorption of [(CH3SH)2-X]+ with X = H2O, (CH3)2CO, or NH3 and (CH3SH)n+ (n = 3-6)

Three-electron two-center (3e-2c) hemi-bonds play important roles in the oxidation and electron transport of proteins and are implicated to be involved in some neurodegenerative diseases. Our previous investigations on infrared (IR) spectra of (CH3SH)2+ using vacuum-ultraviolet photoionization, infrared dissociation, and time-of-flight detection have shown that (CH3SH)2+ is (3e-2c)-bonded. To investigate the influence of the solvent molecules on the (3e-2c)-bonded (CH3SH)2+ in a supersonic jet, we added H2O or (CH3)2CO or NH3 or (CH3SH)n (n = 1-4) to (CH3SH)2+ and investigated their IR action spectra. The (3e-2c)-bonded (CH3SH)2+ ion core was maintained when a molecule of H2O or (CH3)2CO or CH3SH binds, indicating that the ion core is more stable than the hydrogen bond, whereas the (3e-2c)-bond became broken by a NH3 molecule because the proton transfer led to a more stable hydrogen-bonded structure. The spectral features of the SH-stretching modes of (CH3SH)n+ (n = 3-6) indicate that the (3e-2c)-bonded (CH3SH)2+ ion core is maintained and the first two additional CH3SH are H-bonded to the free SH groups of the ion core. For larger clusters with n = 5 and 6, the additional solvent molecules likely bind to the first solvation shell. These results show also that the (3e-2c)-bonded S∴S structure is more stable than the S∴O and S∴N structures in [(CH3SH)2-X]+ with X = H2O or (CH3)2CO or CH3SH or NH3.

Influence of the microsolvation on hemibonded and protonated hydrogen sulfide: infrared spectroscopy of [(H2S)n(X)1]+ and H+(H2S)n(X)1 (n = 1 and 2, X = water, methanol, and ethanol)

Changes of the excess charge accommodation motif in hemibonded and protonated hydrogen sulfide by microsolvation are studied by infrared spectroscopy of [(H2S)n(X)1]+ and H+(H2S)n(X)1 (n = 1 and 2, X = water, methanol, and ethanol) clusters. While the hemibond in the (H2S)2+ ion core is stable to the microhydration by a single water molecule, the hemibond is broken by the proton transfer with the microsolvation by a single methanol or ethanol molecule. Hetero hemibond formation between hydrogen sulfide and these solvent molecules is not observed. On the other hand, the excess proton in H+(H2S)n can be easily transferred to the solvent molecule, even though the proton affinity of the solvent molecule is lower than that of hydrogen sulfide. Implications of these results to the charge accommodation by sulfur under the biological conditions are discussed.

Spectral Characterization of Three-Electron Two-Center (3e-2c) Bonds of Gaseous CH3S∴S(H)CH3 and (CH3SH)2+ and Enhancement of the 3e-2c Bond upon Protonation

The three-electron two-center (3e-2c) bond plays an important role in structures and electron communication in biological systems involving cationic sulfur compounds. Although the nature of 3e-2c bonds and their theoretical formalism have attracted great interest, direct spectral identifications of 3e-2c-bound molecules are scarce. We observed the infrared spectra of the weakly 3e-2c-bound CH₃S∴S(H)CH₃ and the strongly 3e-2c-bound (CH₃SH)₂⁺ in a supersonic jet using infrared (IR) dissociation with vacuum-ultraviolet photoionization and time-of-flight detection. Protonation of CH₃S∴S(H)CH₃ to form [CH₃(H)S∴S(H)CH₃]⁺ significantly enhances the 3e-2c bond, characterized by a large red shift of the SH-stretching band with enhanced IR intensity, shortening of the calculated S-S distance from 3.00 to 2.86 Å, and a dissociation energy increased from ∼23 to 162 kJ mol^-1.

Quantum chemical study of the structure, spectroscopy and reactivity of NO+.(H2O) n=1-5 clusters

Quantum chemical methods including Møller-Plesset perturbation (MP2) theory and density functional theory (DFT) have been used to study the structure, spectroscopy and reactivity of NO⁺(H₂O) _n=1-5 clusters. MP2/6-311++G** calculations are shown to describe the structure and spectroscopy of the clusters well. DFT calculations with exchange-correlation functionals with a low fraction of Hartree-Fock exchange give a binding energy of NO⁺(H₂O) that is too high and incorrectly predict the lowest energy structure of NO⁺(H₂O)₂, and this error may be associated with a delocalization of charge onto the water molecule directly binding to NO⁺ Ab initio molecular dynamics (AIMD) simulations were performed to study the NO⁺(H₂O)₅ [Formula: see text] H⁺(H₂O)₄ + HONO reaction to investigate the formation of HONO from NO⁺(H₂O)₅ Whether an intracluster reaction to form HONO is observed depends on the level of electronic structure theory used. Of note is that methods that accurately describe the relative energies of the product and reactant clusters did not show reactions on the timescales studied. This suggests that in the upper atmosphere the reaction may occur owing to the energy present in the NO⁺(H₂O)₅ complex following its formation.This article is part of the theme issue 'Modern theoretical chemistry'.

Reactivity of the O2+·(H2O)n and NO+·(H2O)n cluster ions in the D-region of the ionosphere

Ab initio molecular dynamics simulations reveal different reactivities of NO⁺·(H₂O)_n and O₂⁺·(H₂O)_n cluster ions in the D-region of the ionosphere.

Spectroscopic observation of two-center three-electron bonded (hemi-bonded) structures of (H2S) n+ clusters in the gas phase

A two-center three-electron 2c-3e bond (hemi-bond) is a non-classical chemical bond, and its existence has been supposed in radical cation clusters with lone pairs. Though the nature of the hemi-bond and its role in the reactivity of radical cations have attracted great interest, spectroscopic observations of hemi-bonded structures have been very scarce. In the present study, the presence of a stable hemi-bonded core (H2S∴SH2)+ in (H2S) n+ (n = 3-6) in the gas phase is demonstrated by infrared spectroscopy combined with quantum chemical calculations. The spectral features of the free SH stretch of the ion core show that the hemi-bond motif of the ion core is maintained up to the completion of the first H-bonded solvation shell. All of the observed spectra are well reproduced by the minimum energy hemi-bonded isomers, and no sign of the proton-transferred ion core type H3S+-SH, which is estimated to have a much higher energy, is found. Spin density calculations show that the excess charge is almost equally delocalized over the two H2S molecules in the cluster for n = 3 to 6. This also indicates the hemi-bond nature of the (H2S∴SH2)+ ion core and the small impact of the formation of a solvation shell on the ion core.

Correcting density-driven errors in projection-based embedding

Projection-based embedding provides a simple and numerically robust framework for multiscale wavefunction-in-density-functional-theory (WF-in-DFT) calculations. The approach works well when the approximate DFT is sufficiently accurate to describe the energetics of the low-level subsystem and the coupling between subsystems. It is also necessary that the low-level DFT produces a qualitatively reasonable description of the total density, and in this work, we study model systems where delocalization error prevents this from being the case. We find substantial errors in embedding calculations on open-shell doublet systems in which self-interaction errors cause spurious delocalization of the singly occupied orbital. We propose a solution to this error by evaluating the DFT energy using a more accurate self-consistent density, such as that of Hartree-Fock (HF) theory. These so-called WF-in-(HF-DFT) calculations show excellent convergence towards full-system wavefunction calculations.

Ab Initio Study of Ionized Water Radical Cation (H2O)8+ in Combination with the Particle Swarm Optimization Method

The structures of cationic water clusters (H₂O)₈⁺ have been globally explored by the particle swarm optimization method in combination with quantum chemical calculations. Geometry optimization and vibrational analysis for the 15 most interesting clusters were computed at the MP2/aug-cc-pVDZ level and infrared spectrum calculation at MPW1K/6-311++G** level. Special attention was paid to the relationships between their configurations and energies. Both MP2 and B3LYP-D3 calculations revealed that the cage-like structure is the most stable, which is different from a five-membered ring lowest energy structure but agrees well with a cage-like structure in the literature. Furthermore, our obtained cage-like structure is more stable by 0.87 and 1.23 kcal/mol than the previously reported structures at MP2 and B3LYP-D3 levels, respectively. Interestingly, on the basis of their relative Gibbs free energies and the temperature dependence of populations, the cage-like structure predominates only at very low temperatures, and the most dominating species transforms into a newfound four-membered ring structure from 100 to 400 K, which can contribute greatly to the experimental infrared spectrum. By topological analysis and reduced density gradient analysis, we also investigated the structural characteristics and bonding strengths of these water cluster radical cations.

Ab initio investigation of structure, stability, thermal behavior, bonding, and infrared spectra of ionized water cluster (H2O)6. J Chem Phys 2016;145:154307. [PMID: 27782468 DOI: 10.1063/1.4964860]

The low-lying isomers of cationic water cluster (H₂O)₆⁺ have been globally explored by using particle swarm optimization algorithm in conjunction with quantum chemical calculations. Compared with previous results, our searching method covers a wide range of structural isomers of (H₂O)₆⁺ and therefore turns out to be more effective. With these local minima, geometry optimization and vibrational analysis are performed for the most interesting clusters at second-order Møller-Plesset (MP2)/aug-cc-pVDZ level, and their energies are further refined at MP2/aug-cc-pVTZ and coupled-cluster theory with single, double, and perturbative triple excitations/aug-cc-pVDZ level. The interaction energies using the complete basis set limits at MP2 level are also reported. The relationships between their structure arrangement and their energies are discussed. Based on the results of thermal simulation, structural change from a four-numbered ring to a tree-like structure occurs at T ≈ 45 K, and the relative population of six lowest-free-energy isomers is found to exceed 4% at some point within the studied temperature range. Studies reveal that, among these six isomers, two new-found isomers constitute 10% of isomer population at 180 K, and the experimental spectra can be better explained with inclusions of the two isomers. The molecular orbitals for six representative cationic water clusters are also studied. Through topological and reduced density gradient analysis, we investigated the structural characteristics and the bonding strengths of these water cluster radical cations.

Structural evolution and solvation of the OH radical in ionized water radical cations (H2O)n+, n = 5–8

Structural evolution of ionized water radical cations (H₂O)_n⁺, n = 5–8, is studied by ab intio methods.