Analysis of exponent values in Gaussian‐type functions for development of protonic and deuteronic basis functions

We analyzed the exponent (α) values in Gaussian‐type functions (GTF) for protons and deuterons in BH₃, CH₄, NH₃, H₂O, HF, and their deuterated molecules for the development of nuclear basis functions, which are used for molecular orbital (MO) calculations that directly include nuclear quantum effects. The optimized α (α_opt) value in the single s‐type ([1s]) GTF for protons is changed due to the difference in flexibility of the electronic basis sets. The difference between the energy obtained by using the α_opt value for each molecule and that obtained by using the average α (α_ave) value for these exponents with the 6‐31G(d,p) electronic basis function is only 2 × 10^?5 a.u. The α_ave values of protonic and deuteronic [1s] GTFs by the present calculation are 24.1825 and 35.6214, respectively. We found that the α_ave values enable the evaluation of the total energy and the geometrical changes in hydrogen bonding, such as O…H? O, O…H? N, and O…H? C, while the α_opt value became small by forming a hydrogen bond. The result using only the [1s] GTF for the protonic and deuteronic basis functions is sufficient to explain the differences of energy and geometry induced by the H/D isotope effect, although the total energy of ～5 × 10^?4 a.u. was improved by using the s‐, p‐, and d‐type ([1s1p1d]) GTFs for protons and deuterons. We clearly demonstrate that the protonic and deuteronic basis functions based on the α_ave value enable us to apply the method to other sample molecules (glycine, malonaldehyde, and formic acid dimer). The protonic and deuteronic basis functions we developed treat the quantum effects of protons and deuterons effectively and extend the application range of the MO calculation to include nuclear quantum effects. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

H/D isotope effect on charge‐inverted hydrogen‐bonded systems: Systematic classification of three different types in H3XH…YH3 (X = C,Si, or Ge,and Y = B,Al, or Ga) with multicomponent calculation

Three different H/D isotope effect in nine H₃XH(D)^…YH₃ (X = C, Si, or Ge, and Y = B, Al, or Ga) hydrogen‐bonded (HB) systems are classified using MP2 level of multicomponent molecular orbital method, which can take account of the nuclear quantum nature of proton and deuteron. First, in the case of H₃CH(D)^…YH₃ (Y = B, Al, or Ge) HB systems, the deuterium (D) substitution induces the usual H/D geometrical isotope effect such as the contraction of covalent R(C? H(D)) bonds and the elongation of intermolecular R(H(D)^…Y) and R(C^…Y) distances. Second, in the case of H₃XH(D)^…YH₃ (X = Si or Ge, and Y = Al or Ge) HB systems, where H atom is negatively charged called as charge‐inverted hydrogen‐bonded (CIHB) systems, the D substitution leads to the contraction of intermolecular R(H(D)^…Y) and R(X^…Y) distances. Finally, in the case of H₃XH(D)^…BH₃ (X = Si or Ge) HB systems, these intermolecular R(H(D)^…Y) and R(X^…Y) distances also contract with the D substitution, in which the origin of the contraction is not the same as that in CIHB systems. The H/D isotope effect on interaction energies and spatial distribution of nuclear wavefunctions are also analyzed. © 2015 Wiley Periodicals, Inc.     

An MP2 study on pre-reactive complexes (CH_2)_2O … XY (X,Y = H,F,Cl,Br,I)

The structures, energies, atomic chaiges and IR spectra of complexes (CH2)2O…XY (X, Y = H, F, Cl, Br, and I) have been examined by means of ab initio molecular orbital theory at the second-order level of Moller-Plesset perturbation correction. It is found that the hydrogen bond O…H-X is non-linear. The attraction between X and the H atoms in oxirane ring causes O…H-X bond bending. The hydrogen bond slighdy weakens the bond strength of C-O, and leads the bending and stretching mode of IR to shift to the red. The calculation results show that there is no evidence of a significant extent of proton transfer to give (CH2)2OH …X- in the isolated complexes.     

AB initio calculations of the stability of the OH+4 and FH+3 ions

Some geometric configurations of the OH⁺₄ and FH⁺₃ ions have been calculated by the SCF MO LCAO method using linear combinations of gaussian lobe functions. The total electronic energies of the systems under study are lower than the sum of the energies for H₂O and H⁺₂ or OH⁺₃ and H, and HF and H⁺₂ or FH⁺₂ and H, respectively.     

Ionic Fragmentation Mechanisms of 2,2,2‐Trifluoroethanol Following Excitation with Synchrotron Radiation

Gaseous 2,2,2‐trifluoroethanol (TFE) is excited with synchrotron radiation between 10 and 1000 eV and the ejected electrons and positive ions are detected in coincidence. In the valence‐electron energy region, the most abundant species is CH₂OH⁺. Other fragments, including ions produced by atomic rearrangements, are also detected; the most abundant are COH⁺, CFH₂⁺ and CF₂H₂⁺. The energies of electronic transitions from C 1 s, O 1 s and F 1 s orbitals to vacant molecular orbitals are determined. A site‐specific C 1 s excitation is observed. The photofragmentation mechanisms after the excitation of core‐shell electrons are inferred from analysis of the shape and slope of the coincidence between two charged fragments in the bi‐dimensional coincidence spectra. The spectra are dominated by islands that correspond to the coincidence of H⁺ with several charged fragments. One of the most important channels leads to the formation of CH₂OH⁺ and CF₃⁺ in a concerted mechanism.     

Parallel ab initio and molecular mechanics investigation of polycoordinated Zn(II) complexes with model hard and soft ligands: Variations of binding energy and of its components with number and charges of ligands

In this study we compare the binding energies of polycoordinated complexes of Zn²⁺ within cavities composed of model “hard” (H₂O, OH⁻) or “soft” (CH₃SH, CH₃S⁻) ligands. Ab initio supermolecule computations are performed at the HF and MP2 levels using extended basis sets to determine the binding energies and their components as a function of: the number of ligands, ranging from three to six; the net charge of the cavity; and the “hard” versus “soft” character of the ligands. These ab initio computations are used to test the reliability of the SIBFA molecular mechanics procedure, originally formulated and calibrated on the basis of ab initio computations, for such charged systems. The SIBFA intermolecular interaction energies match the corresponding ab initio values using a coreless effective potential split‐valence basis set with a relative error of ≤3%. Extensions to binuclear Zn²⁺ complexes, such as those that occur in the Zn‐binding sites of Gal4 and β‐lactamase proteins, are performed to test the applicability of the methodology for such systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1011–1039, 2000     

A density functional theory study of the Cu+·(CO)n (n = 1–3) complexes

Density functional theory calculations, with an effective core potential for the copper ion, and large polarized basis set functions have been used to construct the potential energy surface of the Cu⁺·(CO)_n (n = 1–3) complexes. A linear configuration is obtained for the global minimum of the Cu⁺·CO and Cu⁺·(CO)₂ complexes with a bond dissociation energy (BDE) of 35.9 and 40.0 kcal mol^-1, respectively. For the Cu⁺·(CO)₃ complex, a trigonal planar geometry is obtained for the global minimum with a BDE of 16.5 kcal mol^?1. C-coordinated copper ion complexes exhibit stronger binding energy than O-coordinated complexes as a result of C_lp → 4s σ-donation. The computed sequential BDEs of Cu⁺·(CO)_n (n = 1–4) complexes agree well with experimental findings, in which the electrostatic energy and σ-donation play an important role in the observed trend.     

Experimentally determined and calculated values of the energies required to form doubly charged ions of the bromomethanes CH3Br,CH2Br2 and CHBr3

Two experimental techniques were used to determine the double ionization energies of CH₃Br, CH₂Br₂ and CHBr₃. In one, these energies were measured directly by double-charge-transfer spectroscopy. In the other, charge stripping of [CH₃Br]⁺, [CH₂Br₂]⁺ and [CHBr₃]⁺ ions was investigated and the ionization energies of the singly charged ions were measured. The double ionization energies of the molecules obtained by adding known single ionization energies of the molecules to the single ionization energies of the ions were in good agreement with those determined by double-charge-transfer spectroscopy. The relevant mean values from the two techniques were 28.9 ± 0.5, 27.5 ± 0.5 and 29.1 ± 0.5 eV for the double ionization energy of CH₃Br, CH₂Br₂ and CHBr₃, respectively. The results of ab initio calculations using second-order Møller-Plesset perturbation theory were in good agreement with the observed double ionization energies; they were consistently slightly lower than the experimental values.     

Photofragmentation of 2‐Deoxy‐D‐Ribose Molecules in the Gas Phase

We have measured the synchrotron‐induced photofragmentation of isolated 2‐deoxy‐D ‐ribose molecules (C₅H₁₀O₄) at four photon energies, namely, 23.0, 15.7, 14.6, and 13.8 eV. At all photon energies above the molecule′s ionization threshold we observe the formation of a large variety of molecular cation fragments, including CH₃⁺, OH⁺, H₃O⁺, C₂H₃⁺, C₂H₄⁺, CH_xO⁺ (x=1,2,3), C₂H_xO⁺ (x=1–5), C₃H_xO⁺ (x=3–5), C₂H₄O₂⁺, C₃H_xO₂⁺ (x=1,2,4–6), C₄H₅O₂⁺, C₄H_xO₃⁺ (x=6,7), C₅H₇O₃⁺, and C₅H₈O₃⁺. The formation of these fragments shows a strong propensity of the DNA sugar to dissociate upon absorption of vacuum ultraviolet photons. The yields of particular fragments at various excitation photon energies in the range between 10 and 28 eV are also measured and their appearance thresholds determined. At all photon energies, the most intense relative yield is recorded for the m/q=57 fragment (C₃H₅O⁺), whereas a general intensity decrease is observed for all other fragments— relative to the m/q=57 fragment—with decreasing excitation energy. Thus, bond cleavage depends on the photon energy deposited in the molecule. All fragments up to m/q=75 are observed at all photon energies above their respective threshold values. Most notably, several fragmentation products, for example, CH₃⁺, H₃O⁺, C₂H₄⁺, CH₃O⁺, and C₂H₅O⁺, involve significant bond rearrangements and nuclear motion during the dissociation time. Multibond fragmentation of the sugar moiety in the sugar–phosphate backbone of DNA results in complex strand lesions and, most likely, in subsequent reactions of the neutral or charged fragments with the surrounding DNA molecules.     

Basis set and correlation effects on computed positive ion hydrogen bond energies of the complexes AHn · AHn + 1+1: AHn = NH3, OH2, and FH

Basis set expansion and correlation effects on computed hydrogen bond energies of the positive ion complexes AH_n · AH_{n + 1}⁺¹, for AH_n = NH₃, OH₂ and FH, have been evaluated. The addition of diffuse functions on nonhydrogen atoms is the single most important enhancement of split-valence plus polarization basis sets for computing hydrogen bond energies. Basis set enhancement effects appear to be additive in these systems. The correlation energy contribution to the stabilization energies of these complexes is significant, with the second order term being the largest term and having a stabilizing effect. The third order term is smaller and of opposite sign, while the fourth order term is smaller yet and stabilizing. As a result, computed MP4 stabilization energies are bracketed by the MP2 and MP3 energies. The overall effect of basis set enhancement is to decrease hydrogen bond energies, whereas the addition of electron correlation increases stabilization energies.     

Bond energies (Pt-NH<Subscript>3</Subscript>, Pt-Cl) and proton affinity of cisplatin: A density functional theory approach

The energies of the Pt-NH₃ and Pt-Cl bonds of cisplatin are calculated by means of a density functional theory method with the B3LYP functional and various basis sets. The calculated bond energies of 37.38 kcal·mol⁻¹ and 64.35 kcal·mol⁻¹ for Pt-NH₃ and Pt-Cl, respectively, agree well with the experimental values (37.28 kcal·mol⁻¹ and 69.31 kcal·mol⁻¹ respectively) derived from enthalpy changes. The proton and lithium ion affinities of cisplatin are also obtained with the B3LYP functional. Structural characterizations for the protonated and lithiated cisplatin complexes are given. Protonation and lithiation alter the geometric parameters, and the gas-phase proton affinity (198.71 kcal·mol⁻¹) is much higher than the lithium ion affinity (70.32 kcal·mol⁻¹).     

The effect of basis set superposition error on the convergence of interaction energies

 For the intermolecular interaction energies of ion-water clusters [OH⁻(H₂O) _n (n=1,2), F⁻(H₂O), Cl⁻(H₂O), H₃O⁺(H₂O) _n (n=1,2), and NH₄ ⁺(H₂O) _n (n=1,2)] calculated with correlation-consistent basis sets at MP2, MP4, QCISD(T), and CCSD(T) levels, the basis set superposition error is nearly zero in the complete basis set (CBS) limit. That is, the counterpoise-uncorrected intermolecular interaction energies are nearly equal to the counterpoise-corrected intermolecular interaction energies in the CBS limit. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are more reliable than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies evaluated using the MP2/aug-cc-pVDZ level is reliable. Received: 14 March 2001 / Accepted: 25 April 2001 / Published online: 9 August 2001     

Coordination Chemistry of Gold Catalysts in Solution: A Detailed NMR Study

Coordination chemistry of gold catalysts bearing eight different ligands [L=PPh₃, JohnPhos (L2), Xphos (L3), DTBP, IMes, IPr, dppf, S‐tolBINAP (L8)] has been studied by NMR spectroscopy in solution at room temperature. Cationic or neutral mononuclear complexes LAuX (L=L2, L3, IMes, IPr; X=charged or neutral ligand) underwent simple ligand exchange without giving any higher coordinate complexes. For L2AuX the following ligand strength series was determined: MeOH?hex‐3‐yne <MeCN≈OTf^??Me₂S<2,6‐lutidine<4‐picoline<CF₃CO₂^?≈DMAP<TMTU<PPh₃<OH^?≈Cl^?. Some heteroligand complexes DTBPAuX exist in solution in equilibrium with the corresponding symmetrical species. Binuclear complexes dppf(AuOTf)₂ and S‐tolBINAP(AuOTf)₂ showed different behavior in exchange reactions with ligands depending on the ligand strength. Thus, PPh₃ causes abstraction of one gold atom to give mononuclear complexes LLAuPPh₃⁺ and (Ph₃P)_nAu⁺, but other N and S ligands give ordinary dicationic species LL(AuNu)₂²⁺. In reactions with different bases, LAu⁺ provided new oxonium ions whose chemistry was also studied: (DTBPAu)₃O⁺, (L2Au)₂OH⁺, (L2Au)₃O⁺, (L3Au)₂OH⁺, and (IMesAu)₂OH⁺. Ultimately, formation of gold hydroxide LAuOH (L=L2, L3, IMes) was studied. Ligand‐ or base‐assisted interconversions between (L2Au)₂OH⁺, (L2Au)₃O⁺, and L2AuOH are described. Reactions of dppf(AuOTf)₂ and S‐tolBINAP(AuOTf)₂ with bases provided more interesting oxonium ions, whose molecular composition was found to be [dppf(Au)₂]₃O₂²⁺, L8(Au)₂OH⁺, and [L8(Au)₂]₃O₂²⁺, but their exact structure was not established. Several reactions between different oxonium species were conducted to observe mixed heteroligand oxonium species. Reaction of L2AuNCMe⁺ with S^2? was studied; several new complexes with sulfide are described. For many reversible reactions the corresponding equilibrium constants were determined.     

Reactions of the dications C7H6, C7H7, and C7H8 with methane: Predominance of doubly charged intermediates

The reactions of methane with the dications C₇H₆²⁺, C₇H₇²⁺, and C₇H₈²⁺ generated by electron ionization of toluene are studied using mass-spectrometry tools. It is shown that the reactivity is dominated by the formation of doubly charged intermediates, which can either eliminate molecular hydrogen to yield doubly charged products or undergo charge-separation reactions leading to the formation of a methyl cation and the corresponding C₇H_n+1⁺ monocation. Typical processes observed for dications, like electron transfer or proton transfer, are largely suppressed. The theoretically derived mechanism of the reaction between C₇H₆²⁺ and CH₄ indicates that the formation of the doubly charged intermediate is kinetically preferred at low internal energies of the reactants. In agreement, the experimental results show a pronounced hydrogen scrambling and dominant formation of the doubly charged products at low collision energies, whereas direct hydride transfer prevails at larger collision energies.     

An ab initio molecular orbital study of the structures and energies of neutral and charged bimolecular complexes of NH3 with the hydrides AHn (A = N,O, F,P, S,and Cl)

Hartree-Fock 6-31G(d) structures for the neutral, positive ion, and negative ion bimolecular complexes of NH₃ with the first- and second-row hydrides AH_n (AH_n = NH₃, OH₂, FH, PH₃, SH₂, and ClH) have been determined. All of the stable neutral complexes except (NH₃)₂, the positive ion complexes with NH₃ as the proton acceptor, and the negative ion complexes containing first-row anions exhibit conventional hydrogen bonded structures with essentially linear hydrogen bonds and directed lone pairs of electrons. The positive ion complex NH₄⁺ …? OH₂ has the dipole moment vector of H₂O instead of a lone pair directed along the intermolecular line, while the complexes of NH₄⁺ with SH₂, FH, and ClH have structures intermediate between the lone-pair directed and dipole directed forms. The negative ion complexes containing second-row anions have nonlinear hydrogen bonds. The addition of diffuse functions on nonhydrogen atoms to the valence double-split plus polarization 6-31G(d,p) basis set usually decreases the computed stabilization energies of these complexes. Splitting d polarization functions usually destabilizes these complexes, whereas splitting p polarization functions either has no effect or leads to stabilization. The overall effect of augmenting the 6-31G(d,p) basis set with diffuse functions on nonhydrogen atoms and two sets of polarization functions is to lower computed stabilization energies. Electron correlation stabilizes all of these complexes. The second-order Møller–Plesset correlation term is the largest term and always has a stabilizing effect, whereas the third and fourth-order terms are smaller and often of opposite sign. The recommended level of theory for computing the stabilization energies of these complexes is MP2/6-31+G(2d,2p), although MP2/6-31+G(d,p) is appropriate for the negative ion complexes.     

Mass Spectrometric Observation of Doubly Charged Alkaline‐Earth Argon Ions

Doubly charged diatomic ions MAr²⁺ where M=Mg, Ca, Sr or Ba have been observed by mass spectrometry with an inductively coupled plasma ion source. Abundance ratios are quite high, 0.1 % for MgAr²⁺, 0.4 % for CaAr²⁺, 0.2 % for SrAr²⁺ and 0.1 % for BaAr²⁺ relative to the corresponding doubly charged atomic ions M²⁺. It is assumed that these molecular ions are formed through reactions of the doubly charged metal ions with neutral argon atoms within the ion source. Bond dissociation energies (D₀) were calculated and agree well with previously published values. The abundance ratios MAr⁺/M⁺ and MAr²⁺/M²⁺ generally follow the predicted bond dissociation energies with the exception of MgAr²⁺. Mg²⁺ should form the strongest bond with Ar [D₀ (MgAr²⁺)=124 to 130 kJ mol^?1] but its relative abundance is similar to that of the weakest bound BaAr²⁺ (D₀=34 to 42 kJ mol^?1). The relative abundances of the various MAr²⁺ ions are higher than those expected from an argon plasma at T=6000 K, indicating that collisions during ion extraction reduce the abundance of the MAr²⁺ ions relative to the composition in the source. The corresponding singly charged MAr⁺ ions are also observed but occur at about three orders of magnitude lower intensity than MAr²⁺.     

Aromaticity in Group 14 homologues of the cyclopropenylium cation

The nature of the bonding and the aromaticity of the heavy Group 14 homologues of cyclopropenylium cations E₃H₃⁺ and E₂H₂E′H⁺ (E, E′=C–Pb) have been investigated systematically at the BP86/TZ2P DFT level by using several methods. Aromatic stabilization energies (ASE) were evaluated from the values obtained from energy decomposition analysis (EDA) of charged acyclic reference molecules. The EDA‐ASE results compare well with the extra cyclic resonance energy (ECRE) values given by the block localized wavefunction (BLW) method. Although all compounds investigated are Hückel 4n+2 π electron species, their ASEs indicate that the inclusion of Group 14 elements heavier than carbon reduces the aromaticity; the parent C₃H₃⁺ ion and Si₂H₂CH⁺ are the most aromatic, and Pb₃H₃⁺ is the least so. The higher energies for the cyclopropenium analogues reported in 1995 employed an isodesmic scheme, and are reinterpreted by using the BLW method. The decrease in the strength of both the π cyclic conjugation and the aromaticity in the order C?Si>Ge>Sn>Pb agrees reasonably well with the trends given by the refined nucleus‐independent chemical shift NICS(0)_πzz index.     

An analytic potential energy function for the amide–amide and amide–water intermolecular hydrogen bonds in peptides

An analytic potential energy function is proposed and applied to evaluate the amide–amide and amide–water hydrogen‐bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen‐bonded training dimers. The analytic potential energy function is then employed to calculate the N? H…O?C, C? H…O?C, N? H…OH₂, and C?O…HOH hydrogen‐bonding interaction energies in amide–amide and amide–water dimers containing N‐methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N‐methylformamide, N‐methylpropanamide, N‐ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O…H) and the hydrogen‐bonding energies. The function is also applied to calculate the binding energies in models of β‐sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen‐bonding interaction energies in peptides quickly and accurately. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Mechanistic Origin of Antagonist Effects of Usual Anionic Bases (OH−, CO32−) as Modulated by their Countercations (Na+, Cs+, K+) in Palladium‐Catalyzed Suzuki–Miyaura Reactions

The mechanism of the reaction of trans‐ArPdBrL₂ (Ar=p‐Z‐C₆H₄, Z=CN, H; L=PPh₃) with Ar′B(OH)₂ (Ar′=p‐Z′‐C₆H₄, Z′=H, CN, MeO), which is a key step in the Suzuki–Miyaura process, has been established in N,N‐dimethylformamide (DMF) with two bases, acetate (nBu₄NOAc) or carbonate (Cs₂CO₃) and compared with that of hydroxide (nBu₄NOH), reported in our previous work. As anionic bases are inevitably introduced with a countercation M⁺ (e.g., M⁺OH^?), the role of cations in the transmetalation/reductive elimination has been first investigated. Cations M⁺ (Na⁺, Cs⁺, K⁺) are not innocent since they induce an unexpected decelerating effect in the transmetalation via their complexation to the OH ligand in the reactive ArPd(OH)L₂, partly inhibiting its transmetalation with Ar′B(OH)₂. A decreasing reactivity order is observed when M⁺ is associated with OH^?: nBu₄N⁺> K⁺> Cs⁺> Na⁺. Acetates lead to the formation of trans‐ArPd(OAc)L₂, which does not undergo transmetalation with Ar′B(OH)₂. This explains why acetates are not used as bases in Suzuki–Miyaura reactions that involve Ar′B(OH)₂. Carbonates (Cs₂CO₃) give rise to slower reactions than those performed from nBu₄NOH at the same concentration, even if the reactions are accelerated in the presence of water due to the generation of OH^?. The mechanism of the reaction with carbonates is then similar to that established for nBu₄NOH, involving ArPd(OH)L₂ in the transmetalation with Ar′B(OH)₂. Due to the low concentration of OH^? generated from CO₃^2? in water, both transmetalation and reductive elimination result slower than those performed from nBu₄NOH at equal concentrations as Cs₂CO₃. Therefore, the overall reactivity is finely tuned by the concentration of the common base OH^? and the ratio [OH^?]/[Ar′B(OH)₂]. Hence, the anionic base (pure OH^? or OH^? generated from CO₃^2?) associated with its countercation (Na⁺, Cs⁺, K⁺) plays four antagonist kinetic roles: acceleration of the transmetalation by formation of the reactive ArPd(OH)L₂, acceleration of the reductive elimination, deceleration of the transmetalation by formation of unreactive Ar′B(OH)₃^? and by complexation of ArPd(OH)L₂ by M⁺.     

Photoelectron emission spectroscopy of liquid water

The threshold energy E_t = 10.06 eV (0.002 eV standard deviation) is determined for photoelectron emission by liquid water and is correlated with E_t = 8.45 eV for OH^? (aq). Free energy changes and standard reduction potentials are calculated for both emission processes. Reorganization free energies are correlated to solvation free energies for H₂O⁺(aq) and OH^?(aq).