A Density Functional Theory for Studying Ionization Processes in Water Clusters

Delocalization error poisons the density-functional many-body expansion

The many-body expansion is a fragment-based approach to large-scale quantum chemistry that partitions a single monolithic calculation into manageable subsystems. This technique is increasingly being used as a basis for fitting classical force fields to electronic structure data, especially for water and aqueous ions, and for machine learning. Here, we show that the many-body expansion based on semilocal density functional theory affords wild oscillations and runaway error accumulation for ion-water interactions, typified by F-(H2O) N with N ≳ 15. We attribute these oscillations to self-interaction error in the density-functional approximation. The effect is minor or negligible in small water clusters, explaining why it has not been noticed previously, but grows to catastrophic proportion in clusters that are only moderately larger. This behavior can be counteracted with hybrid functionals but only if the fraction of exact exchange is ≳50%, whereas modern meta-generalized gradient approximations including ωB97X-V, SCAN, and SCAN0 are insufficient to eliminate divergent behavior. Other mitigation strategies including counterpoise correction, density correction (i.e., exchange-correlation functionals evaluated atop Hartree-Fock densities), and dielectric continuum boundary conditions do little to curtail the problematic oscillations. In contrast, energy-based screening to cull unimportant subsystems can successfully forestall divergent behavior. These results suggest that extreme caution is warranted when the many-body expansion is combined with density functional theory.

A theoretical study of the photochemistry of 1,3-cyclopentadiene and its cyano derivatives bound to a water dimer: Assessing reactivity of ionized clusters and possible photoproducts

We theoretically investigate the photoionization scenarios of molecular complexes involving cyclopentadiene and cyanocyclopentadiene bound to water dimers. Using electronic structure calculations within density-functional theory (DFT) and time dependent DFT (TD-DFT), we explore the potential photochemical pathways following ionization, and determine the charge transfer excitations related to the possible subsequent reactions. Our findings suggest that the investigated photochemical pathways of the hydrated complexes take place in two well-defined ultraviolet regions: (i) 8.2-9.5 eV for the cyclic compounds and (ii) 11.2-11.4 eV for the bound water dimer. We quantify how H-bonding effects can influence the photoionization channels. Before forming possible photoproducts, we also examine the regiospecificity of OH addition to 1,3-cyclopentadiene and its cyano derivatives We analyze our results in light of photoionization studies of jet-cooled molecular complexes and possible implications in astrochemical environments.

Detection and Correction of Delocalization Errors for Electron and Hole Polarons Using Density-Corrected DFT

Modeling polaron defects is an important aspect of computational materials science, but the description of unpaired spins in density functional theory (DFT) often suffers from delocalization error. To diagnose and correct the overdelocalization of spin defects, we report an implementation of density-corrected (DC-)DFT and its analytic energy gradient. In DC-DFT, an exchange-correlation functional is evaluated using a Hartree-Fock density, thus incorporating electron correlation while avoiding self-interaction error. Results for an electron polaron in models of titania and a hole polaron in Al-doped silica demonstrate that geometry optimization with semilocal functionals drives significant structural distortion, including the elongation of several bonds, such that subsequent single-point calculations with hybrid functionals fail to afford a localized defect even in cases where geometry optimization with the hybrid functional does localize the polaron. This has significant implications for traditional workflows in computational materials science, where semilocal functionals are often used for structure relaxation. DC-DFT calculations provide a mechanism to detect situations where delocalization error is likely to affect the results.

Electron-induced fragmentation of water droplets: Simulation study

The transport of free electrons in a water environment is still poorly understood. We show that additional insight can be brought about by investigating fragmentation patterns of finite-size particles upon electron impact ionization. We have developed a composite protocol aiming to simulate fragmentation of water clusters by electrons with kinetic energies in the range of up to 100 eV. The ionization events for atomistically described molecular clusters are identified by a kinetic Monte Carlo procedure. We subsequently model the fragmentation with classical molecular dynamics simulations, calibrated by non-adiabatic quantum mechanics/molecular mechanics simulations of the ionization process. We consider one-electron ionizations, energy transfer via electronic excitation events, elastic scattering, and also the autoionization events through intermolecular Coulombic decay. The simulations reveal that larger water clusters are often ionized repeatedly, which is the cause of substantial fragmentation. After losing most of its energy, low-energy electrons further contribute to fragmentation by electronic excitations. The simultaneous measurement of cluster size distribution before and after the ionization represents a sensitive measure of the energy transferred into the system by an incident electron.

Proton Transfer Reaction Rates in Phenol-Ammonia Cluster Cation

Proton transfer (PT) in an interaction system of a hydroxyl-amino group (OH-NH) plays a crucial role in photoinduced DNA and enzyme damage. A phenol-ammonia cluster is a prototype of an OH-NH interaction and is sometimes used as a DNA model. In the present study, the reaction dynamics of phenol-ammonia cluster cations, [PhOH-(NH₃)_n]⁺ (n = 1-5), following ionization of the neutral parent clusters, were investigated using a direct ab initio molecular dynamics (AIMD) method. In all clusters, PTs from PhOH⁺ to (NH₃)_n were found postionization, the reaction of which is expressed as PhOH⁺-(NH₃)_n → PhO-H⁺(NH₃)_n. The time of the PT was calculated as 43 (n = 1), 26 (n = 2), and 13 fs (n = 3-5), suggesting that the rate of PT increases with an increase in n and is saturated at n = 3-5. The difference in the PT rate originates strongly from the proton affinity of the (NH₃)_n cluster. In the case of n = 3-5, a second PT was found, the reaction of which is expressed as PhO-H⁺(NH₃)_n → PhO-NH₃-H⁺(NH₃)_n-1, and a third PT occurred at n = 4 and 5. The time of the PT was calculated as 10-13 (first PT), 80-100 (second PT), and 150-200 fs (third PT) in the case of larger clusters (n = 4 and 5). The reaction mechanism based on the theoretical results is discussed herein.

Role of hemibonding in the structure and ultraviolet spectroscopy of the aqueous hydroxyl radical

The presence of a two-center, three-electron hemibond in the solvation structure of the aqueous hydroxl radical has long been debated, as its appearance can be sensitive to self-interaction error in density functional theory.

Probing solvation and reactivity in ionized polycyclic aromatic hydrocarbon–water clusters with photoionization mass spectrometry and electronic structure calculations

Synchrotron based mass spectrometry coupled with theoretical calculations provides insight into polycyclic aromatic hydrocarbon water interactions.

Dissociative ionization dynamics of dielectric gas C3F7CN

Fluoronitrile C₃F₇CN is a promising candidate for the replacement of SF₆ dielectric gas in high-voltage insulation.

Ionization of Ammonia Nanoices with Adsorbed Methanol Molecules

Large ammonia clusters represent a model system of ices that are omnipresent throughout the space. The interaction of ammonia ices with other hydrogen-boding molecules such as methanol or water and their behavior upon an ionization are thus relevant in the astrochemical context. In this study, ammonia clusters (NH₃) _N with the mean size N̅ ≈ 230 were prepared in molecular beams and passed through a pickup cell in which methanol molecules were adsorbed. At the highest exploited pickup pressures, the average composition of (NH₃) _N(CH₃OH) _M clusters was estimated to be N: M ≈ 210:10. On the other hand, the electron ionization of these clusters yielded about 75% of methanol-containing fragments (NH₃) _n(CH₃OH) _mH⁺ compared to 25% contribution of pure ammonia (NH₃) _nH⁺ ions. On the basis of this substantial disproportion, we propose the following ionization mechanism: The prevailing ammonia is ionized in most cases, resulting in NH₄⁺ core solvated most likely with four ammonia molecules, yielding the well-known "magic number" structure (NH₃)₄NH₄⁺. The methanol molecules exhibit a strong propensity for sticking to the fragment ion. We have also considered mechanisms of intracluster reactions. In most cases, proton transfer between ammonia units take place. The theoretical calculations suggested the proton transfer either from the methyl group or from the hydroxyl group of the ionized methanol molecule to ammonia to be the energetically open channels. However, the experiments with selectively deuterated methanols did not show any evidence for the D⁺ transfer from the CD₃ group. The proton transfer from the hydroxyl group could not be excluded entirely or confirmed unambiguously by the experiment.

A theoretical study of the adiabatic and vertical ionization potentials of water

Theoretical predictions of the three lowest adiabatic and vertical ionization potentials of water were obtained from the Feller-Peterson-Dixon approach. This approach combines multiple levels of coupled cluster theory with basis sets as large as aug-cc-pV8Z in some cases and various corrections up to and including full configuration interaction theory. While agreement with experiment for the adiabatic ionization potential of the lowest energy ²B₁ state was excellent, differences for other states were much larger, sometimes exceeding 10 kcal/mol (0.43 eV). Errors of this magnitude are inconsistent with previous benchmark work on 52 adiabatic ionization potentials, where a root mean square of 0.20 kcal/mol (0.009 eV) was found. Difficulties in direct comparisons between theory and experiment for vertical ionization potentials are discussed. With regard to the differences found for the ²A₁/²Π_u and ²B₂ adiabatic ionization potentials, a reinterpretation of the experimental spectrum appears justified.

Assessment of Real-Time Time-Dependent Density Functional Theory (RT-TDDFT) in Radiation Chemistry: Ionized Water Dimer

Ionization in the condensed phase and molecular clusters leads to a complicated chain of processes with coupled electron-nuclear dynamics. It is difficult to describe such dynamics with conventional nonadiabatic molecular dynamics schemes since the number of states swiftly increases as the molecular system grows. It is therefore attractive to use a direct electron and nuclear propagation such as the real-time time-dependent density functional theory (RT-TDDFT). Here we report a RT-TDDFT benchmark study on simulations of singly and doubly ionized states of a water monomer and dimer as a prototype for more complex processes in a condensed phase. We employed the RT-TDDFT based Ehrenfest molecular dynamics with a generalized gradient approximate (GGA) functional and compared it with wave-function-based surface hopping (SH) simulations. We found that the initial dynamics of a singly HOMO ionized water dimer is similar for both the RT-TDDFT/GGA and the SH simulations but leads to completely different reaction channels on a longer time scale. This failure is attributed to the self-interaction error in the GGA functionals and it can be avoided by using hybrid functionals with large fraction of exact exchange (represented here by the BHandHLYP functional). The simulations of doubly ionized states are reasonably described already at the GGA level. This suggests that the RT-TDDFT/GGA method could describe processes following the autoionization processes such as Auger emission, while its applicability to more complex processes such as intermolecular Coulombic decay remains limited.

Reactivity and energy level of a localized hole in liquid water

Reaction and redox level of hole capture in liquid water from first principles.

Ab initio dynamics and photoionization mass spectrometry reveal ion-molecule pathways from ionized acetylene clusters to benzene cation

The growth mechanism of hydrocarbons in ionizing environments, such as the interstellar medium (ISM), and some combustion conditions remains incompletely understood. Ab initio molecular dynamics (AIMD) simulations and molecular beam vacuum-UV (VUV) photoionization mass spectrometry experiments were performed to understand the ion-molecule growth mechanism of small acetylene clusters (up to hexamers). A dramatic dependence of product distribution on the ionization conditions is demonstrated experimentally and understood from simulations. The products change from reactive fragmentation products in a higher temperature, higher density gas regime toward a very cold collision-free cluster regime that is dominated by products whose empirical formula is (C₂H₂) _n⁺, just like ionized acetylene clusters. The fragmentation products result from reactive ion-molecule collisions in a comparatively higher pressure and temperature regime followed by unimolecular decomposition. The isolated ionized clusters display rich dynamics that contain bonded C₄H₄⁺ and C₆H₆⁺ structures solvated with one or more neutral acetylene molecules. Such species contain large amounts (>2 eV) of excess internal energy. The role of the solvent acetylene molecules is to affect the barrier crossing dynamics in the potential energy surface (PES) between (C₂H₂)_n⁺ isomers and provide evaporative cooling to dissipate the excess internal energy and stabilize products including the aromatic ring of the benzene cation. Formation of the benzene cation is demonstrated in AIMD simulations of acetylene clusters with n > 3, as well as other metastable C₆H₆⁺ isomers. These results suggest a path for aromatic ring formation in cold acetylene-rich environments such as parts of the ISM.

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.

Probing Ionic Complexes of Ethylene and Acetylene with Vacuum-Ultraviolet Radiation

Mixed complexes of acetylene-ethylene are studied using vacuum-ultraviolet (VUV) photoionization mass spectrometry and theoretical calculations. These complexes are produced and ionized at different distances from the exit of a continuous nozzle followed by reflectron time-of-flight mass spectrometry detection. Acetylene, with a higher ionization energy (11.4 eV) than ethylene (10.6 eV), allows for tuning the VUV energy and initializing reactions either from a C2H2(+) or a C2H4(+) cation. Pure acetylene and ethylene expansions are separately carried out to compare, contrast, and hence identify products from the mixed expansion: these are C3H3(+) (m/z = 39), C4H5(+) (m/z = 53), and C5H5(+) (m/z = 65). Intensity distributions of C2H2, C2H4, their dimers and reactions products are plotted as a function of ionization distance. These distributions suggest that association mechanisms play a crucial role in product formation closer to the nozzle. Photoionization efficiency (PIE) curves of the mixed complexes demonstrate rising edges closer to both ethylene and acetylene ionization energies. We use density functional theory (ωB97X-V/aug-cc-pVTZ) to study the structures of the neutral and ionized dimers, calculate their adiabatic and vertical ionization energies, as well as the energetics of different isomers on the potential energy surface (PES). Upon ionization, vibrationally excited clusters can use the extra energy to access different isomers on the PES. At farther ionization distances from the nozzle, where the number densities are lower, unimolecular decay is expected to be the dominant mechanism. We discuss the possible decay pathways from the different isomers on the PES and examine the ones that are energetically accessible.

Proton transfer rates in ionized water clusters (H2O)n (n = 2–4)

A proton transfer process is usually dominant in several biological phenomena such as the energy relaxation of photo-excited DNA base pairs and a charge relay process in Ser-His-Glu.

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.

Characterization of a solvent-separated ion-radical pair in cationized water networks: infrared photodissociation and Ar-attachment experiments for water cluster radical cations (H2O)n+(n = 3-8)

We present infrared spectra of nominal water cluster radical cations (H(2)O)(n)(+) (n = 3-8), or to be precise, ion-radical complexes H(+)(H(2)O)(n-1)(OH), with and without an Ar tag. These clusters are closely related to the ionizing radiation-induced processes in water and are a good model to characterize solvation structures of the ion-radical pair. The spectra of Ar-tagged species show narrower bandwidths relative to those of the bare clusters due to the reduced internal energy via an Ar-attachment. The observed spectra are analyzed by comparing with those of the similar system, H(+)(H(2)O)(n), and calculated ones. We find that the observed spectra are attributable to ion-radical-separated motifs in n ≥ 5, as reported in the previous study (Mizuse et al. Chem. Sci.2011, 2, 868-876). Beyond the structural trends found in the previous study, we characterize isomeric structures and determine the number of water molecules between the charged site and the OH radical in each cluster size. In all of the characterized cluster structures (n = 5-8), the most favorable position of OH radical is the next neighbor of the charged site (H(3)O(+) or H(5)O(2)(+)). The positions and cluster structures are governed by the balance among the hydrogen-bonding abilities of the charged site, H(2)O, and OH radical. These findings on the ionized water networks lead to understanding of the detailed processes of ionizing radiation-initiated reactions in liquid water and aqueous solutions.

Chasing charge localization and chemical reactivity following photoionization in liquid water

The ultrafast dynamics of the cationic hole formed in bulk liquid water following ionization is investigated by ab initio molecular dynamics simulations and an experimentally accessible signature is suggested that might be tracked by femtosecond pump-probe spectroscopy. This is one of the fastest fundamental processes occurring in radiation-induced chemistry in aqueous systems and biological tissue. However, unlike the excess electron formed in the same process, the nature and time evolution of the cationic hole has been hitherto little studied. Simulations show that an initially partially delocalized cationic hole localizes within ~30 fs after which proton transfer to a neighboring water molecule proceeds practically immediately, leading to the formation of the OH radical and the hydronium cation in a reaction which can be formally written as H(2)O(+) + H(2)O → OH + H(3)O(+). The exact amount of initial spin delocalization is, however, somewhat method dependent, being realistically described by approximate density functional theory methods corrected for the self-interaction error. Localization, and then the evolving separation of spin and charge, changes the electronic structure of the radical center. This is manifested in the spectrum of electronic excitations which is calculated for the ensemble of ab initio molecular dynamics trajectories using a quantum mechanics/molecular mechanics (QM∕MM) formalism applying the equation of motion coupled-clusters method to the radical core. A clear spectroscopic signature is predicted by the theoretical model: as the hole transforms into a hydroxyl radical, a transient electronic absorption in the visible shifts to the blue, growing toward the near ultraviolet. Experimental evidence for this primary radiation-induced process is sought using femtosecond photoionization of liquid water excited with two photons at 11 eV. Transient absorption measurements carried out with ~40 fs time resolution and broadband spectral probing across the near-UV and visible are presented and direct comparisons with the theoretical simulations are made. Within the sensitivity and time resolution of the current measurement, a matching spectral signature is not detected. This result is used to place an upper limit on the absorption strength and/or lifetime of the localized H(2)O(+) ((aq)) species.

Ionization of Water Clusters Mediated by Exciton Energy Transfer from Argon Clusters

The exciton energy deposited in an argon cluster (Arn, ⟨n = 20⟩) using VUV radiation is transferred to softly ionize doped water clusters ((H2O)n, n = 1-9), leading to the formation of nonfragmented clusters. Following the initial excitation, electronic energy is channeled to ionize the doped water cluster while evaporating the Ar shell, allowing identification of fragmented and complete water cluster ions. Examination of the photoionization efficiency curve shows that cluster evaporation from excitons located above 12.6 eV is not enough to cool the energized water cluster ion and leads to their dissociation to (H2O)n-2H(+) (protonated) clusters.

Apparent stoichiometry of water in proton hydration and proton dehydration reactions in CH3CN/H2O solutions

Gradual solvation of protons by water is observed in liquids by mixing strong mineral acids with various amounts of water in acetonitrile solutions, a process which promotes rapid dissociation of the acids in these solutions. The stoichiometry of the reaction XH(+) + n(H(2)O) = X + (H(2)O)(n)H(+) was studied for strong mineral acids (negatively charged X, X = ClO(4)¯, Cl¯, Br¯, I¯, CF(3)SO(3)¯) and for strong cationic acids (uncharged X, X = R*NH(2), H(2)O). We have found by direct quantitative analysis preference of n = 2 over n = 1 for both groups of proton transfer reactions at relatively low water concentrations in acetonitrile. At high water concentrations, we have found that larger water solvates must also be involved in the solvation of the proton while the spectral features already observed for n = 2, H(+)(H(2)O)(2), remain almost unchanged at large n values up to at least 10 M of water.