Calculation of electron detachment energies for water cluster anions: an appraisal of electronic structure methods, with application to (H2O)20- AND (H2O)24-

We present benchmark calculations of vertical electron detachment energies (VDEs) for various conformers of (H2O)n-, using both wave function and density functional methods, in sequences of increasingly diffuse Gaussian basis sets. For small clusters (n < or = 6), a systematic examination of VDE convergence reveals that it is possible to converge this quantity to within approximately 0.01 eV of the complete-basis limit, using a highly diffuse but otherwise economical Pople-style basis set of double-zeta quality, with 28 atom-centered basis functions per water molecule. Floating-center basis functions can be useful but are not required to obtain accurate VDEs. Second-order M?ller-Plesset perturbation (MP2) theory suffices to obtain VDEs that are within 0.05 eV of the results from both experiment and coupled-cluster theory, and which always err toward underbinding the extra electron. In contrast to these consistent predictions, VDEs calculated using density functional theory (DFT) vary widely, according to the fraction of Hartree-Fock exchange in a given functional. Common functionals such as BLYP and B3LYP overestimate the VDE by 0.2-0.5 eV, whereas a variant of Becke's "half and half" functional is much closer to coupled-cluster predictions. Exploratory calculations for (H2O)20- and (H2O)24- cast considerable doubt on earlier calculations that were used to assign the photoelectron spectra of these species to particular cluster isomers.     

Photoinduced electron transfer and solvation in iodide-doped acetonitrile clusters

We have used ultrafast time-resolved photoelectron imaging to measure charge transfer dynamics in iodide-doped acetonitrile clusters I(-)(CH(3)CN)(n) with n = 5-10. Strong modulations of vertical detachment energies were observed following charge transfer from the halide, allowing interpretation of the ongoing dynamics. We observe a sharp drop in the vertical detachment energy (VDE) within 300-400 fs, followed by a biexponential increase that is complete by approximately 10 ps. Comparison to theory suggests that the iodide is internally solvated and that photodetachment results in formation of a diffuse electron cloud in a confined cavity. We interpret the initial drop in VDE as a combination of expansion of the cavity and localization of the excess electron on one or two solvent molecules. The subsequent increase in VDE is attributed to a combination of the I atom leaving the cavity and rearrangement of the acetonitrile molecules to solvate the electron. The n = 5-8 clusters then show a drop in VDE of around 50 meV on a much longer time scale. The long-time VDEs are consistent with those of (CH(3)CN)(n)(-) clusters with internally solvated electrons. Although the excited-state created by the pump pulse decays by emission of a slow electron, no such decay is seen by 200 ps.     

BX4- and AlX4- superhalogen anions (X = F, Cl, Br): an ab initio study

The vertical electron detachment energies (VDEs) of 30 MX 4 (-) (M = B, Al; X = F, Cl, Br) anions were calculated at the OVGF level with the 6-311+G(3df) basis sets. The largest vertical electron binding energy was found for the AlF 4 (-) system (9.789 eV). The strong VDE dependence on the symmetry of the species, ligand type, ligand-central atom distance, and bonding/nonbonding/antibonding character of the highest occupied molecular orbital was observed and discussed.     

Conformationally averaged vertical detachment energy of finite size NO3(-)·nH2O clusters: a route connecting few to many

We report conformationally averaged VDEs (VDE(w)(n)) for different sizes of NO(3)(-)·nH(2)O clusters calculated by using uncorrelated HF, correlated hybrid density functional (B3LYP, BHHLYP) and correlated ab intio (MP2 and CCSD(T)) theory. It is observed that the VDE(w)(n) at the B3LYP/6-311++G(d,p), B3LYP/Aug-cc-Pvtz and CCSD(T)/6-311++G(d,p) levels is very close to the experimentally measured VDE. It is shown that the use of calculated results of the conformationally averaged VDE for small-sized solvated negatively-charged clusters and a microscopic theory-based general expression for the same provides a route to obtain the VDE for a wide range of cluster sizes, including bulk.     

On the unusual stability of valence anions of thymine based on very rare tautomers: A computational study

We characterized anionic states of thymine using various electronic structure methods, with the most accurate results obtained at the CCSD(T)/aug-cc-pVDZ level of theory followed by extrapolations to complete basis set limits. We found that the most stable anion in the gas phase is related to an imino-oxo tautomer, in which the N1H proton is transferred to the C5 atom. This valence anion, aT(c5)(nl), is characterized by an electron vertical detachment energy (VDE) of 1251 meV and it is adiabatically stable with respect to the canonical neutral nT(can) by 2.4 kcal/mol. It is also more stable than the dipole-bound (aT(dbs)(can)), and valence anion aT(val)(can) of the canonical tautomer. The VDE values for aT(dbs)(can)and T(val)(can) are 55 and 457 meV, respectively. Another, anionic, low-lying imino-oxo tautomer with a VDE of 2458 meV has a proton transferred from N3H to C5 aT(c5)(n3). It is less stable than aT(val)(can) by 3.3 kcal/mol. The mechanism of formation of anionic tautomers with the carbons C5 or C6 protonated may involve intermolecular proton transfer or dissociative electron attachment to the canonical neutral tautomer followed by a barrier-free attachment of a hydrogen atom to C5. The six-member ring structure of the anionic tautomers with carbon atoms protonated is unstable upon an excess electron detachment. Within the PCM hydration model, the low-lying valence anions become adiabatically bound with respect to the canonical neutral; becomes the most stable, being followed by aT(c5)(nl), aT(c5)(n3), aT(can), and aT(c5)(nl).     

Accuracy and limitations of second-order many-body perturbation theory for predicting vertical detachment energies of solvated-electron clusters

Vertical electron detachment energies (VDEs) are calculated for a variety of (H(2)O)(n)(-) and (HF)(n)(-) isomers, using different electronic structure methodologies but focusing in particular on a comparison between second-order M?ller-Plesset perturbation theory (MP2) and coupled-cluster theory with noniterative triples, CCSD(T). For the surface-bound electrons that characterize small (H(2)O)(n)(-) clusters (n< or = 7), the correlation energy associated with the unpaired electron grows linearly as a function of the VDE but is unrelated to the number of monomers, n. In every example considered here, including strongly-bound "cavity" isomers of (H(2)O)(24)(-), the correlation energy associated with the unpaired electron is significantly smaller than that associated with typical valence electrons. As a result, the error in the MP2 detachment energy, as a fraction of the CCSD(T) value, approaches a limit of about -7% for (H(2)O)(n)(-) clusters with VDEs larger than about 0.4 eV. CCSD(T) detachment energies are bounded from below by MP2 values and from above by VDEs calculated using second-order many-body perturbation theory with molecular orbitals obtained from density functional theory. For a variety of both strongly- and weakly-bound isomers of (H(2)O)(20)(-) and (H(2)O)(24)(-), including both surface states and cavity states, these bounds afford typical error bars of +/-0.1 eV. We have found only one case where the Hartree-Fock and density functional orbitals differ qualitatively; in this case the aforementioned bounds lie 0.4 eV apart, and second-order perturbation theory may not be reliable.     

Photoelectron spectrum of valence anions of uracil and first-principles calculations of excess electron binding energies

The photoelectron spectrum (PES) of the uracil anion is reported and discussed from the perspective of quantum chemical calculations of the vertical detachment energies (VDEs) of the anions of various tautomers of uracil. The PES peak maximum is found at an electron binding energy of 2.4 eV, and the width of the main feature suggests that the parent anions are in a valence rather than a dipole-bound state. The canonical tautomer as well as four tautomers that result from proton transfer from an NH group to a C atom were investigated computationally. At the Hartree-Fock and second-order Moller-Plesset perturbation theory levels, the adiabatic electron affinity (AEA) and the VDE have been converged to the limit of a complete basis set to within +/-1 meV. Post-MP2 electron-correlation effects have been determined at the coupled-cluster level of theory including single, double, and noniterative triple excitations. The quantum chemical calculations suggest that the most stable valence anion of uracil is the anion of a tautomer that results from a proton transfer from N1H to C5. It is characterized by an AEA of 135 meV and a VDE of 1.38 eV. The peak maximum is as much as 1 eV larger, however, and the photoelectron intensity is only very weak at 1.38 eV. The PES does not lend support either to the valence anion of the canonical tautomer, which is the second most stable anion, and whose VDE is computed at about 0.60 eV. Agreement between the peak maximum and the computed VDE is only found for the third most stable tautomer, which shows an AEA of approximately -0.1 eV and a VDE of 2.58 eV. This tautomer results from a proton transfer from N3H to C5. The results illustrate that the characteristics of biomolecular anions are highly dependent on their tautomeric form. If indeed the third most stable anion is observed in the experiment, then it remains an open question why and how this species is formed under the given conditions.     

Dynamics of electron solvation in I(-)(CH3OH)n clusters (4 ≤ n ≤ 11)

The dynamics of electron solvation following excitation of the charge-transfer-to-solvent precursor state in iodide-doped methanol clusters, I(-)(CH(3)OH)(n = 4-11), are studied with time-resolved photoelectron imaging. This excitation produces a I···(CH(3)OH)(n)(-) cluster that is unstable with respect to electron autodetachment and whose autodetachment lifetime increases monotonically from ~800 fs to 85 ps as n increases from 4 to 11. The vertical detachment energy (VDE) and width of the excited state feature in the photoelectron spectrum show complex time dependence during the lifetime of this state. The VDE decreases over the first 100-400 fs, then rises exponentially to a maximum with a ~1 ps time constant, and finally decreases by as much as 180 meV with timescales of 3-20 ps. The early dynamics are associated with electron transfer from the iodide to the methanol cluster, while the longer-time changes in VDE are attributed to solvent reordering, possibly in conjunction with ejection of neutral iodine from the cluster. Changes in the observed width of the spectrum largely follow those of the VDEs; the dynamics of both are attributed to the major rearrangement of the solvent cluster during relaxation. The relaxation dynamics are interpreted as a reorientation of at least one methanol molecule and the disruption and formation of the solvent network in order to accommodate the excess charge.     

Theoretical studies on photoelectron and IR spectral properties of Br2.-(H2O)n clusters

We report vertical detachment energy (VDE) and IR spectra of Br2.-.(H2O)n clusters (n=1-8) based on first principles electronic structure calculations. Cluster structures and IR spectra are calculated at Becke's half-and-half hybrid exchange-correlation functional (BHHLYP) with a triple split valence basis function, 6-311++G(d,p). VDE for the hydrated clusters is calculated based on second order Moller-Plesset perturbation (MP2) theory with the same set of basis function. On full geometry optimization, it is observed that conformers having interwater hydrogen bonding among solvent water molecules are more stable than the structures having double or single hydrogen bonded structures between the anionic solute, Br2.-, and solvent water molecules. Moreover, a conformer having cyclic interwater hydrogen bonded network is predicted to be more stable for each size hydrated cluster. It is also noticed that up to four solvent H2O units can reside around the solute in a cyclic interwater hydrogen bonded network. The excess electron in these hydrated clusters is localized over the solute atoms. Weighted average VDE is calculated for each size (n) cluster based on statistical population of the conformers at 150 K. A linear relationship is obtained for VDE versus (n+3)(-1/3) and bulk VDE of Br2.- aqueous solution is calculated as 10.01 eV at MP2 level of theory. BHHLYP density functional is seen to make a systematic overestimation in VDE values by approximately 0.5 eV compared to MP2 data in all the hydrated clusters. It is observed that hydration increases VDE of bromine dimer anion system by approximately 6.4 eV. Calculated IR spectra show that the formation of Br2.--water clusters induces large shifts from the normal O-H stretching bands of isolated water keeping bending modes rather insensitive. Hydrated clusters, Br2.-.(H2O)n, show characteristic sharp features of O-H stretching bands of water in the small size clusters.     

Characterization of solvated electrons in hydrogen cyanide clusters: (HCN)n- (n=3, 4)

Theoretical studies of the solvated electrons (HCN)n- (n=3, 4) reveal a variety of electron trapping possibilities in the (HCN)n (n=3, 4) clusters. Two isomers for (HCN)3- and four isomers for (HCN)4- are obtained at the MP2aug-cc-pVDZ+dBF (diffusive bond functions) level of theory. In view of vertical electron detachment energies (VDEs) at the CCSD(T) level, the excess electron always "prefers" locating in the center of the system, i.e., the isomer with higher coordination number shows larger VDE value. However, the most stable isomers of the solvated electron state (HCN)3- and (HCN)4- are found to be the linear Cinfinitynu and Dinfinityh structures, respectively, but not the fullyl symmetric structures which have the largest VDE values.     

Extra electron in (H2O)24- cluster isomers: a theoretical study

The isomers of (H(2)O)(24) (-) tetrakaidecahedral cluster are studied by applying the Becke-3-parameter density functional theory and Lee-Yang-Parr correlation functional (B3LYP) and 6-311++G** basis set. Three isomers are selected on the basis of stabilization energy values. The vertical electron dissociation energies (VDE) of these isomers are 1.353, 0.404, and 0.258 eV, respectively. The experimental VDE value of 1.31 eV [J. Chem. Phys. 92, 3980 (1990)] for this cluster size is in excellent agreement with that calculated for isomer 1, suggesting the dominance of this isomer in the experiment. Four water molecules in this isomer share most of the -1 charge. These four water molecules have non-H-bonding H (NHB H) atoms turned toward the cavity, and the inward turned H atoms exhibit a significant lowering of O-H stretch frequency compared to that of a monomer. Isomers 2 and 3 have all 12 NHB H atoms projected outward and have the -1 charge distributed among 7-8 water molecules on the cluster surface.     

Benchmark calculations on the electron detachment energies of MO3* and M2O6* (M = Cr, Mo, W)

Neutral and anionic molecules of the monomers and dimers of the group VIB transition metal oxides (MO3 and M2O6) were studied with density functional theory (DFT) and coupled cluster CCSD(T) theory. Franck-Condon simulations of the photoelectron spectra were carried out for the transition from the ground state of the anion to that of the neutral molecule. Molecular structures from the DFT and CCSD(T) methods are compared. Electron detachment energies reported in the literature were evaluated. The calculated adiabatic and vertical electron detachment energies (ADEs and VDEs) were compared with the experimental results. CCSD(T) gives results within 0.12 eV for the ADEs. CCSD(T) predicts VDEs that are in error by as much as 0.3 eV for M = Cr. DFT hybrid functionals were found to give poor results for the ADEs and VDEs for M = Cr due to the substantial amount of multireference character in the wavefunction, whereas the pure DFT functionals give superior results. For M = Mo and W, excellent agreement was found for both CCSD(T) and many DFT fucntionals. The BP86 functional yields the best overall results for the VDEs of all the metal oxide clusters considered. Heats of formation calculated at the CCSD(T) level extrapolated to the complete basis set limit are also in good agreement with available experimental data.     

Anion of the formic acid dimer as a model for intermolecular proton transfer induced by a pi* excess electron

The neutral and anionic formic acid dimers have been studied at the second-order Moller-Plesset and coupled-cluster level of theory with single, double, and perturbative triple excitations with augmented, correlation-consistent basis sets of double- and triple-zeta quality. Scans of the potential-energy surface for the anion were performed at the density-functional level of theory with a hybrid B3LYP functional and a high-quality basis set. Our main finding is that the formic acid dimer is susceptible to intermolecular proton transfer upon an excess electron attachment. The unpaired electron occupies a pi(*) orbital, the molecular moiety that accommodates an excess electron "buckles," and a proton is transferred to the unit where the excess electron is localized. As a consequence of these geometrical transformations, the electron vertical detachment energy becomes substantial, 2.35 eV. The anion is barely adiabatically unstable with respect to the neutral at 0 K. However, at standard conditions and in terms of Gibbs free energy, the anion is more stable than the neutral by +37 meV. The neutral and anionic dimers display different IR characteristics. In summary, the formic acid dimer can exist in two quasidegenerate states (neutral and anionic), which can be viewed as "zero" and "one" in the binary system. These two states are switchable and distinguishable.     

Probing the Properties of Polynuclear Superhalogens without Halogen Ligand via ab Initio Calculations: A Case Study on Double‐Bridged [Mg2(CN)5]−1 Anions

An ab initio study of the superhalogen properties of eighteen binuclear double‐bridged [Mg₂(CN)₅]^?1 clusters is reported herein by using various theoretical methods. High‐level CCSD(T) results indicate that all the clusters possess strong superhalogen properties owing to their high vertical electron detachment energies (VDEs), which exceed 6.8 eV (highest: 8.15 eV). The outer valence Green's function method provides inaccurate relative VDE values; hence, this method is not suitable for this kind of polynuclear superhalogens. Both the HF and MP2 results are generally consistent with the CCSD(T) level regarding the relative VDE values and—especially interesting—the average values of the HF and MP2 VDEs are extremely close to the CCSD(T) results. The distributions of the extra electrons of the anions are mainly aggregated into the terminal CN units. These distributions are apparently different from those of previously reported triple‐bridged isomers and may be the reason for the decreased VDE values of the clusters. In addition, comparisons of the VDEs of binuclear and mononuclear superhalogens as well as studies of the thermodynamic stabilities with respect to the detachment of various CN^?1 ligands are also performed. These results confirm that polynuclear structures with pseudohalogen ligands can be considered as probable new superhalogens with enhanced properties.     

Hydrated electron: Nonempirical cluster approach

Interface water anions composed of several chainlike or cyclic fragments were simulated with a 6‐31++G** basis set at the unrestricted Hartree–Fock level with the second‐order Moeller–Plesset perturbation theory corrections taken into account. The estimated vertical electron detachment energies (VDEs) of (H₂O) anions were approximated by a VDE‐n^?1/3 dependence close to the experimental one. A hypothesis about the predominant formation of interface structures under conditions of molecular flows is put forward. The atomic population analysis, character of the highest occupied molecular orbital, and changes in the geometry of interface anions with an increase in their molecular size reveal the compact localization of the excess electron density in water clusters and allow evaluating the effective excess‐electron radius of condensed water as 2.5 Å, in good agreement with a similar empirical estimate. The scope of the data obtained shows the relatively low probability of the formation of octahedral hydration shells compared to the tetrahedral coordination of solvating water molecules. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Can a dipole-bound electron form a pseudo-atom? An atoms-in-molecules study of the hydrated electron

Non-nuclear local maxima, or attractors, of electron density are a rare but very interesting feature of the electron density distribution in molecules and solids. Recently, non-nuclear attractors (NNAs) and the corresponding pseudoatoms of electron density have been identified with the quantum theory of atoms in molecules for some anionic clusters formed by several polar solvent molecules and an excess electron bound in either a solvated-electron or dipole-bound fashion. This contribution reports a detailed study of the topology of the electron density for a series of dipole-bound water cluster anions, as calculated with Hartree-Fock, M?ller-Plesset perturbation theory, and coupled-cluster methods together with basis sets augmented with extra diffuse basis functions to accommodate the excess electron. For dipole-bound clusters, electron densities obtained with insufficient inclusion of electron correlation effects and tight basis sets feature a well-pronounced pseudoatom due to the excess electron, which ultimately disappears when a higher level of electronic structure theory and a more diffuse basis set are used. On the other hand, for solvated-electron clusters, where the excess electron is surrounded by solvent molecules, the existence of NNAs does not seem to be an artifact of the method employed, but rather a genuine feature of the electron density distribution. Pseudoatoms of electron density thus appear to be an exclusive feature of confined environments and are unlikely to be found on the tip of a cluster dipole or on solid surfaces.     

Low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W)

Multiple low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W) arise from the occupation of the near-degenerate low-lying virtual orbitals in the neutral clusters. We used density functional theory (DFT) and coupled cluster theory (CCSD(T)) with correlation consistent basis sets to study the structures and energetics of the electronic states of these anions. The adiabatic and vertical electron detachment energies (ADEs and VDEs) of the anionic clusters were calculated with 27 exchange-correlation functionals including one local spin density approximation functional, 13 generalized gradient approximation (GGA) functionals, and 13 hybrid GGA functionals, as well as the CCSD(T) method. For M(3)O(9)(-), CCSD(T) and nearly all of the DFT exchange-correlation functionals studied predict the (2)A(1) state arising from the Jahn-Teller distortion due to singly occupying the degenerate e' orbital to be lower in energy than the (2)A(1)' state arising from singly occupying the nondegenerate a(1)' orbital. For W(3)O(9)(-), the (2)A(1) state was predicted to have essentially the same energy as the (2)A(1)' state at the CCSD(T) level with core-valence correlation corrections included and to be higher in energy or essentially isoenergetic with most DFT methods. The calculated VDEs from the CCSD(T) method are in reasonable agreement with the experimental values for both electronic states if estimates for the corrections due to basis set incompleteness are included. For M(3)O(9)(2-), the singlet state arising from doubly occupying the nondegenerate a(1)' orbital was predicted to be the most stable state for both M = Mo and W. However, whereas M(3)O(9)(2-) was predicted to be less stable than M(3)O(9)(-), W(3)O(9)(2-) was predicted to be more stable than W(3)O(9)(-).     

Electron affinities of small uracil-water complexes: a comparison of benchmark CCSD(T) calculations with DFT

We present benchmark CCSD(T) calculations of the adiabatic electron affinities (AEA) and the vertical detachment energies (VDE) of the uracil molecule interacting with one to three water molecules. Calculations with rather large aug-cc-pVTZ basis set were only tractable when the space of virtual orbitals was reduced to about 60% of the full space employing the OVOS (Optimized Virtual Orbital Space) technique. Because of the microhydration, the valence-bound uracil anion is stabilized leading to gradually more positive values of both AEA and VDE with increasing number of participating water molecules. This agrees with experimental findings. Upon hydration by three water molecules, the electron affinity of uracil increased in comparison with AEA of the isolated molecule by about 250 up to 570 meV, depending on the geometry of the complex. CCSD(T) results confirm trends determined by DFT calculations of the microhydrated uracil and its anion, even if electron affinities of the free and hydrated uracil molecule are overestimated by DFT by up to 300 meV.     

Consistent theoretical description of 1,3-dipolar cycloaddition reactions

The cycloaddition reactions of 18 1,3-dipolar molecules to ethylene and acetylene have been reinvestigated by quantum chemical methods that are based on a second-order perturbation treatment of electron correlation. It is found that SCS-MP2 and the new perturbative B2-PLYP density functional provide accurate reaction barriers and outperform MP2 as well as standard density functionals such as B3-LYP. The new second-order based methods have the additional advantage that they perform better with increasing quality of the one-particle space, as is desired for a good quantum chemical method. The errors for the reaction enthalpies are in general larger than for the barriers when compared to CBS-QB3 literature values, which is related to strong changes in the electronic structures, but the deviations are again smaller than with MP2 or B3-LYP and are also more systematic. The results of a detailed basis set study suggest that properly polarized triple-zeta AO basis sets represent a good compromise between accuracy and computational speed. The combination of very inaccurate density functionals with small (double-zeta) basis sets, which yields good results for the initial part of the reactions due to error compensation, is not recommended.     

Basis set dependence of coupled cluster optical rotation computations

Specific rotations for five notoriously difficult molecules, (S)-methyloxirane, (S)-methythiirane, (S)-2-chloropropionitrile, (1S,4S)-norbornenone, and (1R,5R)-β-pinene, have been computed using coupled cluster (CC) and density functional theory (DFT). The performance of the recently developed LPol basis sets compared to the correlation-consistent sets of Dunning and co-workers has been examined at four wavelengths: 355, 436, 589, and 633 nm. We find that the LPol basis sets are an efficient choice, often outperforming the more commonly used correlation-consistent basis sets of comparable size. The smallest of the four, LPol-ds, performs nearly as well as the rest of the series and often yields results closer to the basis set limit than appreciably larger basis sets. While the performance of the LPol bases is admirable, they still do not alleviate the need for high levels of electron correlation, vibrational corrections, and the inclusion of solvent effects to accurately reproduce experimental rotations. In particular in the case of β-pinene we find that they do not produce agreement between DFT and experiment as was previously suggested.