Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Theoretical study on electronic and spin structures of [Fe2S2](2+,+) cluster: reference interaction site model self-consistent field (RISM-SCF) and multireference second-order Møller-Plesset perturbation theory (MRMP) approach

Electronic structures of [Fe(2)S(2)(SCH(3))(4)](2-,3-) in DMSO solution are calculated using reference interaction site model complete active space self-consistent field (RISM-CASSCF)/multireference second-order M?ller-Plesset perturbation theory (MRMP) method. For the reduced state, we obtain both the low-spin Fe(3+)Fe(2+) localized and high-spin Fe(2.5+)Fe(2.5+) delocalized forms, which are very close in energy. The spin interaction constants obtained from the energies of states with various spin multiplicities are in good agreement with the available experimental estimates both for the oxidized and for the reduced states. The dynamic electron correlation effect is found to be important in estimating the spin interaction between the Fe ions. The redox potentials are calculated to be 2.87 and 2.78 eV for the localized and delocalized reduced states, respectively, which are close to the experimental values. We devise a simple model for calculating the free energy curves of the reduction process based on the RISM-SCF theory. The activation barrier height is calculated to be 7.4 kcal/mol at the equilibrium geometry of oxidized state, indicating that the reduction reaction will occur efficiently in DMSO solvent. The effect of solvent fluctuation on the free energy profiles is discussed on the basis of the present calculations.     

Ab initio molecular dynamics simulation of the aqueous Ru2+/Ru3+ redox reaction: the Marcus perspective

A well-behaved (low spin) transition metal aqua ion, Ru(aq)(2+), is used as a model system in an ab initio molecular dynamics study of a redox half reaction to which the Marcus theory of electron transfer is assumed to apply. Using constraint methods, we show that aqueous Ru(2+) can be reversibly transformed to Ru(3+) under the control of the classical solvent electrostatic potential as order parameter. The mean force is found to vary linearly with the order parameter in accordance with the Marcus theory. As can be expected for a half reaction, the slope in the oxidized and reduced states are asymmetric differing by approximately a factor of two. As a further test, we verify that the corresponding quadratic potential of mean force is in excellent agreement with the free energy profile obtained from the Gaussian distribution of potential fluctuations sampled from free (unconstrained) runs of the reduced and oxidized system. Similar to experimental electrochemical methods, our simulation scheme enables us to manipulate the effective thermodynamic driving force and align the free energy minima of product and reactant state. The activation energy and reaction entropy computed under these conditions are discussed and analyzed from the Marcus perspective.     

Electronic structure and solvation of copper and silver ions: a theoretical picture of a model aqueous redox reaction

Electronic states and solvation of Cu and Ag aqua ions are investigated by comparing the Cu(2+) + e(-)--> Cu(+) and Ag(2+) + e(-)--> Ag(+) redox reactions using density functional-based computational methods. The coordination number of aqueous Cu(2+) is found to fluctuate between 5 and 6 and reduces to 2 for Cu(+), which forms a tightly bound linear dihydrate. Reduction of Ag(2+) changes the coordination number from 5 to 4. The energetics of the oxidation reactions is analyzed by comparing vertical ionization potentials, relaxation energies, and vertical electron affinities. The model is validated by a computation of the free energy of the full redox reaction Ag(2+) + Cu(+) --> Ag(+) + Cu(2+). Investigation of the one-electron states shows that the redox active frontier orbitals are confined to the energy gap between occupied and empty states of the pure solvent and localized on the metal ion hydration complex. The effect of solvent fluctuations on the electronic states is highlighted in a computation of the UV absorption spectrum of Cu(+) and Ag(+).     

Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach

Electron transfer (ET) reactions are one of the most important processes in chemistry and biology. Because of the quantum nature of the processes and the complicated roles of the solvent, theoretical study of ET processes is challenging. To simulate ET processes at the electronic level, we have developed an efficient density functional theory (DFT) quantum mechanical (QM)/molecular mechanical (MM) approach that uses the fractional number of electrons as the order parameter to calculate the redox free energy of ET reactions in solution. We applied this method to study the ET reactions of the aqueous metal complexes Fe(H(2)O)(6)(2+/3+) and Ru(H(2)O)(6)(2+/3+). The calculated oxidation potentials, 5.82 eV for Fe(II/III) and 5.14 eV for Ru(II/III), agree well with the experimental data, 5.50 and 4.96 eV, for iron and ruthenium, respectively. Furthermore, we have constructed the diabatic free energy surfaces from histogram analysis based on the molecular dynamics trajectories. The resulting reorganization energy and the diabatic activation energy also show good agreement with experimental data. Our calculations show that using the fractional number of electrons (FNE) as the order parameter in the thermodynamic integration process leads to efficient sampling and validate the ab initio QM/MM approach in the calculation of redox free energies.     

Structural,spectroscopic, and redox consequences of a central ligand in the FeMoco of nitrogenase: a density functional theoretical study

Broken symmetry density functional and electrostatics calculations have been used to shed light on which of three proposed atoms, C, N, or O, is most likely to be present in the center of the FeMoco, the active site of nitrogenase. At the Mo(4+)4Fe(2+)3Fe(3+) oxidation level, a central N(3-) anion results in (1) calculated Fe-N bond distances that are in very good agreement with the recent high-resolution X-ray data of Einsle et al.; (2) a calculated redox potential of 0.19 eV versus the standard hydrogen electrode (SHE) for FeMoco(oxidized) + e(-) --> FeMoco(resting), in good agreement with the measured value of -0.042 V in Azotobacter vinelandii; and (3) average M?ssbauer isomer shift values (IS(av) = 0.48 mm s(-1)) compatible with experiment (IS(av) = 0.40 mm s(-1)). At the more reduced Mo(4+)6Fe(2+)1Fe(3+) level, the calculated geometry around a central N(3-) anion still correlates well with the X-ray data, but the average M?ssbauer isomer shift value (IS(av) = 0.54 mm s(-1)) and the redox potential of -2.21 eV show a much poorer agreement with experiment. These calculated structural, spectroscopic, and redox data indicate the most likely iron oxidation state for the resting FeMoco of nitrogenase to be 4Fe(2+)3Fe(3+). At this favored oxidation state, oxygen or carbon coordination leads to (1) Fe-O distances in poor agreement and Fe-C distances in good agreement with experiment and (2) calculated redox potentials of +0.97 eV for O(2-) and -1.31 eV for C(4-). The calculated structural parameters and/or redox data suggest either O(2-) or C(4-) is unlikely as a central anion.     

Gas-phase oxidation of Cm+ and Cm2+ --thermodynamics of neutral and ionized CmO

Fourier transform ion cyclotron resonance mass spectrometry was employed to study the products and kinetics of gas-phase reactions of Cm (+) and Cm (2+); parallel studies were carried out with La (+/2+), Gd (+/2+) and Lu (+/2+). Reactions with oxygen-donor molecules provided estimates for the bond dissociation energies, D[M (+)-O] (M = Cm, Gd, Lu). The first ionization energy, IE[CmO], was obtained from the reactivity of CmO (+) with dienes, and the second ionization energies, IE[MO (+)] (M = Cm, La, Gd, Lu), from the rates of electron-transfer reactions from neutrals to the MO (2+) ions. The following thermodynamic quantities for curium oxide molecules were obtained: IE[CmO] = 6.4 +/- 0.2 eV; IE[CmO (+)] = 15.8 +/- 0.4 eV; D[Cm-O] = 710 +/- 45 kJ mol (-1); D[Cm (+)-O] = 670 +/- 40 kJ mol (-1); and D[Cm (2+)-O] = 342 +/- 55 kJ mol (-1). Estimates for the M (2+)-O bond energies for M = Cm, La, Gd, and Lu are all intermediate between D[N 2-O] and D[OC-O] - that is, 167 kJ mol (-1) < D[M (2+)-O] < 532 kJ mol (-1) - such that the four MO (2+) ions fulfill the thermodynamic requirement for catalytic oxygen-atom transport from N2O to CO. It was demonstrated that the kinetics are also favorable and that the CmO (2+), LaO (2+), GdO (2+), and LuO (2+) dipositive ions each catalyze the gas-phase oxidation of CO to CO2 by N2O. The CmO 2 (+) ion appeared during the reaction of Cm (+) with O 2 when the intermediate, CmO (+), was not collisionally cooled - although its formation is kinetically and/or thermodynamically unfavorable, CmO 2 (+) is a stable species.     

Ab initio adiabatic and quasidiabatic potential energy surfaces of lowest four electronic states of the H+ + O2 system

Ab initio global adiabatic and quasidiabatic potential energy surfaces of lowest four electronic (1-4 (3)A(")) states of the H(+)+O(2) system have been computed in the Jacobi coordinates (R,r,γ) using Dunning's cc-pVTZ basis set at the internally contracted multireference (single and double) configuration interaction level of accuracy, which are relevant to the dynamics studies of inelastic vibrational and charge transfer processes observed in the scattering experiments. The computed equilibrium geometry parameters of the bound [HO(2)](+) ion in the ground electronic state and other parameters for the transition state for the isomerization process, HOO(+)?OOH(+) are in good quantitative agreement with those available from the high level ab initio calculations, thus lending credence to the accuracy of the potential energy surfaces. The nonadiabatic couplings between the electronic states have been analyzed in both the adiabatic and quasidiabatic frameworks by computing the nonadiabatic coupling matrix elements and the coupling potentials, respectively. It is inferred that the dynamics of energy transfer processes in the scattering experiments carried out in the range of 9.5-23 eV would involve all the four electronic states.     

Ultrafast nuclear dynamics induced by photodetachment of Ag2- and Ag2O2-: oxygen desorption from a molecular silver surface

Femtosecond nuclear dynamics of mass-selected neutral Ag2 and Ag2O2 clusters are investigated with the 'negative ion-to neutral-to positive ion'(NeNePo) technique. For the bare silver dimer, wave packet dynamics occurring in the neutral electronic ground state and in the first excited triplet state are observed after photodetachment from the anion with 3.05 eV photon energy. While the dynamics in the ground state lead to an oscillatory structure in the NeNePo-pump-probe spectra with a vibrational constant of 185 cm-1, the dynamics in the triplet state are assigned to a bound-free transition leading to dissociation. Photodetachment from the Ag2O2- complex results in the desorption of O2. The experimental data clearly show the influence of the desorbing oxygen ligand on the nuclear dynamics of the silver dimer inducing a red shift in the vibrational frequency and an intensity enhancement of the oscillatory signal.     

The anomalous shape of the cross section for the formation of SF3+ fragment ions produced by electron impact on SF6 revisited

The partial ionization cross section for the formation of SF(3) (+) fragment ions following electron impact on SF(6) is known to have a pronounced structure in the cross section curve slightly above 40 eV. We used the mass-analyzed ion kinetic energy (MIKE) scan technique to demonstrate the presence of a channel contributing to the SF(3) (+) partial ionization cross section that we attribute to the Coulomb explosion of doubly charged metastable SF(4) (2+) ions into two singly charged ions SF(3) (+) and F(+), with a threshold energy of about 45.5 eV. Thus the observed unusual shape of the SF(3) (+) partial ionization cross section is the result of two contributions, (i) the direct formation of SF(3) (+) fragment ions via dissociative ionization of SF(6) with a threshold energy of 22 eV and (ii) the Coulomb explosion of metastable SF(4) (2+) ions with a threshold energy of about 45.5 eV. A detailed analysis of the MIKE spectrum reveals an average kinetic energy release of about 5 eV in the Coulomb explosion of the SF(4) (2+) ions with evidence of a second channel corresponding to an average kinetic energy release of about 1.1 eV.     

Spectroscopy and metastability of CO2 2+ molecular ions

The spectroscopy and metastability of the carbon dioxide doubly charged ion, the CO(2) (2+) dication, have been studied with photoionization experiments: time-of-flight photoelectron photoelectron coincidence (TOF-PEPECO), threshold photoelectrons coincidence (TPEsCO), and threshold photoelectrons and ion coincidence (TPEsCO ion coincidence) spectroscopies. Vibrational structure is observed in TOF-PEPECO and TPEsCO spectra of the ground and first two excited states. The vibrational structure is dominated by the symmetric stretch except in the TPEsCO spectrum of the ground state where an antisymmetric stretch progression is observed. All three vibrational frequencies are deduced for the ground state and symmetric stretch and bending frequencies are deduced for the first two excited states. Some vibrational structure of higher electronic states is also observed. The threshold for double ionization of carbon dioxide is reported as 37.340+/-0.010 eV. The fragmentation of energy selected CO(2) (2+) ions has been investigated with TPEsCO ion coincidence spectroscopy. A band of metastable states from approximately 38.7 to approximately 41 eV above the ground state of neutral CO(2) has been observed in the experimental time window of approximately 0.1-2.3 mus with a tendency towards shorter lifetimes at higher energies. It is proposed that the metastability is due to slow spin forbidden conversion from bound excited singlet states to unbound continuum states of the triplet ground state. Another result of this investigation is the observation of CO(+)+O(+) formation in indirect dissociative double photoionization below the threshold for formation of CO(2) (2+). The threshold for CO(+)+O(+) formation is found to be 35.56+/-0.10 eV or lower, which is more than 2 eV lower than previous measurements.     

Inner-valence states of N2+ and the dissociation dynamics studied by threshold photoelectron spectroscopy and configuration interaction calculation

The N2(+) states lying in the ionization region of 26-45 eV and the dissociation dynamics are investigated by high-resolution threshold photoelectron spectroscopy and threshold photoelectron-photoion coincidence spectroscopy. The threshold photoelectron spectrum exhibits several broad bands as well as sharp peaks. The band features are assigned to the N2(+) states associated with the removal of an inner-valence electron, by a comparison with a configuration interaction calculation. In contrast, most of the sharp peaks on the threshold photoelectron spectrum are allocated to ionic Rydberg states converging to N2(2+). Dissociation products formed from the inner-valence N2(+) states are determined by threshold photoelectron-photoion coincidence spectroscopy. The dissociation dynamics of the inner-valence ionic states is discussed with reference to the potential energy curves calculated.     

Total reorganization energy and its components in processes of one-electron oxidation of phosphorus compounds in acetonitrile

The ionization processes of phosphorus(III) and (IV) compounds oxidized in the potential range of 1.8–4.0 Vvs. Ag/0.01M AgNO₃ in MeCN were studied by chronovoltammetry on a Pt ultramicroelectrode in acetonitrile and by photoelectron spectroscopy in the gas phase. A relationship between the half-wave potential (E _1/2) and vertical ionization potential (IP _v)E _1/2=0.89IP _v–6.27 is fulfilled in a wide potential range from−0.37 to 3.98 V. The total reorganization energy of the system (1.45–2.50 V) and the energy of reorganization of the solvate shell (0.9–1.9 eV) were estimated. Translated fromIzvestiya Akademii Nauk. seriya Khimicheskaya, No. 4, pp. 682–689, April, 1999.     

Dynamics of the D+ + H2 and H+ + D2 reactions: a detailed comparison between theory and experiment

An extensive set of experimental measurements on the dynamics of the H(+) + D(2) and D(+) + H(2) ion-molecule reactions is compared with the results of quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical quasiclassical trajectory (SQCT) calculations. The dynamical observables considered include specific rate coefficients as a function of the translational energy, E(T), thermal rate coefficients in the 100-500 K temperature range. In addition, kinetic energy spectra (KES) of the D(+) ions reactively scattered in H(+) + D(2) collisions are also presented for translational energies between 0.4 eV and 2.0 eV. For the two reactions, the best global agreement between experiment and theory over the whole energy range corresponds to the QCT calculations using a gaussian binning (GB) procedure, which gives more weight to trajectories whose product vibrational action is closer to the actual integer QM values. The QM calculations also perform well, although somewhat worse over the more limited range of translational energies where they are available (E(T) < 0.6 eV and E(T) < 0.2 eV for the H(+) + D(2) and D(+) + H(2) reactions, respectively). The worst agreement is obtained with the SQCT method, which is only adequate for low translational energies. The comparison between theory and experiment also suggests that the most reliable rate coefficient measurements are those obtained with the merged beams technique. It is worth noting that none of the theoretical approaches can account satisfactorily for the experimental specific rate coefficients of H(+) + D(2) for E(T)≤ 0.2 eV although there is a considerable scatter in the existing measurements. On the whole, the best agreement with the experimental laboratory KES is obtained with the simulations carried out using the state resolved differential cross sections (DCSs) calculated with the QCT-GB method, which seems to account for most of the observed features. In contrast, the simulations with the SQCT data predict kinetic energy spectra (KES) considerably cooler than those experimentally determined.     

pH manipulation: a facile method for lowering oxidation state and keeping good yield of poly(m-phenylenediamine) and its powerful Ag+ adsorption ability

A method of pH manipulation has been used to improve chemically oxidative polymerization of m-phenylenediamine (mPD) through concurrent addition of NaOH when adding oxidant (NH(4))(2)S(2)O(8). pH detection and open-circuit potential technique were adopted to monitor the polymerization process of mPD and to explain the oxidation state-pH and yield-pH relationships. Results from Fourier transformed infrared (FTIR) and X-ray photoelectron (XPS) spectroscopies indicate that a low oxidation state is under control by regulating NaOH concentration. At 2.5 M NaOH, the oxidation state of poly(m-phenylenediamine) (PmPD) is 64.7 mol % (measured by molar content of quinoid imine from XPS), while the yield is 84%. The synthesized PmPD possesses better Ag(+) adsorption performance when lowering its oxidation state. Moreover, the Ag(+) adsorbance of PmPD can reach 1693 mg g(-1). Meanwhile, Ag(+) adsorption mechanism was studied by pH tracking, X-ray diffraction (XRD) patterns, and X-ray photoelectron spectroscopy. The adsorption process includes redox reaction, chelation, and physical adsorption.     

Application of mean-field and surface-hopping approaches for interrogation of the Xe3+ molecular ion photoexcitation dynamics

The dissociation dynamics of the excited Xe(3) (+) molecular ion through the Pi(12)(u) and Pi(12)(g) conical intersection was interrogated by computational simulation in which no adjustable parameters were used. The electronic ground and excited state potential energy surfaces were generated by the diatomics-in-molecules method, and the Ehrenfest mean-field and Tully surface-hopping approaches treated the nonadiabatic interactions. Reproduction of the experimental spectrum of the symmetric photofragmentation as a function of excitation energy was obtained within the region of interest (2.5-3.75 eV), with the exception of a 0.25 eV width on the red side of the spectral apex. Good agreement was obtained with the experimental dissociated photofragment kinetic energy spectra. It was determined that the greatest contribution to the nonadiabatic coupling between the two states originated from the bending vibrational mode of the molecule in the Sigma(12)(u), ground electronic state before excitation.     

Electron ionization of methane: the dissociation of the methane monocation and dication

Time-of-flight mass spectrometry and two-dimensional coincidence techniques have been used to determine, for the first time, the relative precursor-specific partial ionization cross sections following electron-methane collisions. Precursor-specific partial ionization cross sections quantify the contribution of single, double, and higher levels of ionization to the partial ionization cross section for forming a specific ion (e.g. CH(+)) following electron ionization of methane. Cross sections are presented for the formation of H(+), H(2)(+), C(+), CH(+), CH(2)(+), and CH(3)(+), relative to CH(4)(+), at ionizing electron energies from 30 to 200 eV. We can also reduce our dataset to derive the relative partial ionization cross sections for the electron ionization of methane, for comparison with earlier measurements. These relative partial ionization cross sections are in good agreement with recent determinations. However, we find that there is significant disagreement between our partial ionization cross sections and those derived from earlier studies. Inspection of the values of our precursor-specific partial ionization cross sections shows that this disagreement is due to the inefficient collection of energetic fragment ions in the earlier work. Our coincidence experiments also show that the lower energy electronic states of CH(4)(2+) populated by electron double ionization of CH(4) at 55 eV are the same (ground (3)T(1), first excited (1)E(1)) as those populated by 40.8 eV photoionization. The (3)T(1) state dissociating to form CH(3)(+) + H(+) and CH(2)(+) + H(2)(+) and the (1)E(1) to form CH(2)(+) + H(+) and CH(+) + H(+). At this electron energy, we also observe population of the first excited triplet state of CH(4)(2+) ((3)T(2)) which dissociates to both CH(2)(+) + H(+) + H and CH(+) + H(+) + H(2).     

Oxidation of gas-phase protactinium ions, Pa+ and Pa2+: formation and properties of PaO2(2+)(g), protactinyl

Oxidation reactions of bare and ligated, monopositive, and dipositive Pa ions in the gas phase were studied by Fourier transform ion cyclotron resonance mass spectrometry. Seven oxidants were employed, ranging from the thermodynamically robust N(2)O to the relatively weak CH(2)O-all oxidized Pa(+) to PaO(+) and PaO(+) to PaO(2)(+). On the basis of experimental observations, it was established that D[Pa(+)-O] and D[OPa(+)-O] > or = 751 kJ mol(-1). Estimates for D[Pa(+)-O], D[OPa(+)-O], IE[PaO], and IE[PaO(2)] were also obtained. The seven oxidants reacted with Pa(2+) to produce PaO(2+), indicating that D[Pa(2+)-O] > or = 751 kJ mol(-1). A particularly notable finding was the oxidation of PaO(2+) by N(2)O to PaO(2)(2+), a species, which formally comprises Pa(VI). Collision-induced dissociation of PaO(2)(2+) suggested the protactinyl connectivity, {O-Pa-O}(2+). The experimentally determined IE[PaO(2)(+)] approximately 16.6 eV is in agreement with self-consistent-field and configuration interaction calculations for PaO(2)(+) and PaO(2)(2+). These calculations provide insights into the electronic structures of these ions and indicate the participation of 5f orbitals in bonding and a partial "6p hole" in the case of protactinyl. It was found that PaO(2)(2+) catalyzes the oxidation of CO by N(2)O-such O atom transport via a dipositive metal oxide ion is distinctive. It was also observed that PaO(2)(2+) is capable of activating H(2) to form the stable PaO(2)H(2+) ion.     

Threshold photoelectron spectroscopy on inner-valence ionic states of NO

The NO(+) states lying in the ionization region of 20-40 eV have been investigated by high-resolution threshold photoelectron spectroscopy and a configuration interaction calculation. Substantial agreement between the structures on the present experimental and theoretical spectra in the 21-27 eV range enables us to assign the relevant inner-valence ionic states unambiguously. The dissociation products from the ion states are measured with threshold photoelectron-photoion coincidence spectroscopy, and the dissociation processes are discussed with reference to the potential energy curves calculated. Sharp peaks are observed in the ionization region of 27.5-35 eV, which are allocated to ionic Rydberg states converging to NO(2+).