Vibration intervals for tritiated H+3 and D+3

Ab initio calculated values of fundamental vibrational frequencies and zero-point energies are presented for HTD⁺, D₂T⁺, T₂D⁺, H₂T⁺, T₂H⁺ and T⁺₃.     

An ab initio calculation of symmetric bending and stretching vibrational states of the H3O+ and D3O+ ions

Calculations are reported for the symmetric bending and stretching vibrational states of H₃O⁺ and D₃O⁺ including coupling between these two modes. The calculations were carried out by using a potential surface calculated by the SCF CI method and expressed in terms of symmetric internal coordinates. The transition energy of the ν₂ (1^? ← 0⁺) inversion mode is found to be 985 cm^?1, which is comparable to the experimental value of 954.417 cm^?1 observed by Haese and Oka. The calculated inversion doubling of the lowest state is 51 cm^?1.     

On the Search for H5O2+centered Water Clusters in the Gas Phase

In searching for H₅O₂⁺-centered water clusters, we employed vibrational predissociation spectroscopy and ab initio calculations. Structures of the clusters were characterized by the free- and hydrogen-bonded-OH stretches of ion cores and solvent molecules. Systematic examination of H⁺(H₂O)_5–7 in a supersonic expansion reveals the presence of both cyclic and noncyclic forms of H₅O₂⁺-centered water clusters. The proton transfer intermediate H₅O₂⁺(H₂O)₄ was identified, for the first time, by its characteristic hydrogen-bonded-OH stretches of the ion core at 3178 cm^?1. Also discovered at n = 7 is the H₅O₂⁺-containing five-membered ring isomer, whose existence is evidenced by the observation of a bonded-OH stretching doublet at 3544 and 3555 cm^?1 of the solvent molecules. The observations are in accord with ab initio calculations which forecast that H₅O₂⁺(H₂O)₄ and H₅O₂⁺(H₂O)₅ are, respectively, the lowest-energy isomers of protonated water hexamers and heptamers.     

Algorithm for variational calculations of molecular symmetry in solving anharmonic vibrational problems

A universal program for variational calculations of molecular symmetry in solving anharmonic vibrational problems, realized by the author, is described. The program uses the group-theoretical method. Symmetrized basis wave functions are constructed with the aid of the generalized KJebsch-Gordan series suggested by the author. The method of constructing symmetrized basis wave functions and the program for adequate calculations of molecular symmetry were verified for many molecules of different symmetry groups: O_h, O, T_d, T_h, T, D_∞h, C_t8v, D_nd, D_nh, D_n, C_nv, C_nh, S_2n, C_n, C_i, C_s, and C₁ where 2 ≤n ≤6. It was confirmed that the program provides correct results and high-speed operation. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1146–1153, November–December, 1997.     

Molecular orbital studies on small molecules using H2+-type elliptical basis orbitals. Application to H2+, H2, He2++ and H3+

H₂⁺-type elliptical orbitals are defined in Section 1. These orbitals, which in elliptical coordinates involve a factor (1 + ξ)^σ, are employed in variational calculations on the ground states of H₂⁺ and H₂ (Sections 2 and 3). Various choices of σ are explored for H₂⁺, while two choices are used for H₂ : the “boundary condition” (Equation 6) and the “cusp condition” (Equation 9) values. Variational energies are calculated and compared to the results of similar calculations. Section 3 concludes by employing the H₂⁺-type orbitals in LCETO-MO-SCF calculations on the ground states of H₂ and He₂⁺⁺. For both molecules a four-function basis set with two (nonlinear) variational parameters yields more than 99% of the Hartree-Fock limit. Section 4 deals with LCETO-MO-SCF calculations on triangular H₃⁺. Three four-function basis sets are used, and the best energy is -1.2306 a.u., which is in reasonable agreement with the Hartree-Fock limit, -1.2999 a.u. Our best basis set is a four-term two-center expansion of the wave function with only one nonlinear variational parameter. Section 5 concludes the paper with a summary of the methods used to evaluate the integrals which arise in SCF calculations in the H₂⁺-type elliptical orbital basis.     

Separation of the vibrational,rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates

A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H₂O, H₂S, NO₂, SO₂, and ClO₂ molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 239–254, March–April, 1995. Translated by I. Izvekova     

The Formation of OH*(<Superscript>2</Superscript>Σ<Superscript>+</Superscript>) Radical in the Reaction of Hydrogen with Oxygen behind a Shock Wave in Nonequilibrium Conditions

The mechanism of formation of the electronically excited radical OH*(A²Σ⁺) has been studied by analyzing calculations quantitatively describing the results of shock wave experiments carried out in order to determine the moment of maximum OH* radiation at temperatures T < 1500 K and pressures P ≤ 2 atm in the H₂ + O₂ mixtures diluted by argon when the vibrational nonequilibrium is a factor determining the mechanism and rate of the overall process. In kinetic calculations, the vibrational nonequilibrium of the initial H₂ and O₂ components, the HO₂, OH(X²Π), O₂*(¹Δ) intermediates, and the reaction product H₂O were taken into account. The analysis showed that under these conditions the main contribution to the overall process of OH* formation is caused by the reactions OH + Ar → OH* + Ar, H₂ + HO₂ → OH* + H₂O, H₂ + O*(¹D) → OH* + H, HO² + O → OH* + O² and H + H²O → OH* + H², which occur in the vibrational nonequilibrium mode (their activation barrier is overcome due to the vibrational excitation of reactants), and by H + O₃ → OH* + O₂ and H + H₂O₂ → OH* + H₂O, which are reverse to the reactions of chemical quenching.     

Neutron diffraction study on protonated and hydrated layered perovskite

A layered perovskite compound with Na⁺, D₃O⁺ ions (H₃O⁺) and D₂O molecules (H₂O) in the interlayer, D_xNa_1−xLaTiO₄·yD₂O, has been prepared by an ion-exchange/intercalation reaction with dilute DCl solution, using an n=1 Ruddlesden-Popper phase, NaLaTiO₄. Its structure has been analyzed in order to clarify the interlayer structure by Rietveld method, using powder neutron diffraction data. The structure analysis revealed that the layered structure changed from the space group P4/nmm-I4/mmm after the ion-exchange/intercalation reaction, and it induced the transformation of perovskite layers from staggered to an eclipsed configuration. The D₂O molecules and D₃O⁺ ions loaded in the interlayer statistically occupied the sites around a body center position of rectangular space surrounded by eight apical O atoms of TiO₆ octahedra in upper and lower layers.     

Equilibrium structure and vibrational frequencies of the O4 molecule

SCF closed shell calculations were performed to determine the equilibrium structure and vibrational frequencies of the O₄ molecule by means of Payne's method and with the help of the molecule's symmetry coordinates. The equilibrium geometry corresponds to symmetry group D_2d with R = 1.505 Å and h = 0.094 Å. The vibrational frequencies are: ν₅(E) = 885.5 cm^?1, ν₃(B₁) = 1051.9 cm^?1, ν₁(A₁) = 1018.3 cm^?1, ν₄(B₂) = 880.3 cm^?1. The second vibrational coordinate (A₁) corresponds to a double-well potential. The first vibrational levels were calculated by a variational method.     

Modeling Chemical Composition for an Atmospheric Pressure DC Discharge in Air with Water Cathode by 0-D model

This paper reports the results of the chemical composition modeling for an atmospheric pressure DC air discharge with water cathode. The modeling was based on the combined solution of Boltzmann equation for electrons, equations of vibrational kinetics for ground states of N₂, O₂, H₂O and NO molecules, equations of chemical kinetics and plasma conductivity equation. Calculations were carried out using experimental values of E/N and gas temperatures for the discharge currents range of 20–50 mA. The effect of H₂O concentration on the plasma composition was studied. The main particles of plasma were shown to be O₂(a¹Δ, b¹Σ), O(³P), NO, NO₂, HNO₃, H₂O₂ and OH. Effective vibrational temperatures of molecules were higher than gas temperature and they did not depend on the discharge current. Distribution functions on vibrational levels for N₂, O₂, H₂O and NO ground states were non-equilibrium ones.     

Excited states of gaseous ions. V. The predissociation of the h2o+ ion

The B?² state of H₂O⁺ is predissociated twice. First, by the ã⁴B₁ state, giving OH⁺ + H fragments via spinorbit coupling interaction. Secondly, by a²A state, giving H ⁺ OH fragments via spin-orbit coupling and Coriolis interactions. A vibrational analysis of the photoelectron band of the B? state of H₂O⁺ and D₂O⁺ is carried out. This provides the vibrational frequencies of the H₂O⁺, D₂O⁺ and HDO⁺ ions, as well as a vibrational assignment of the peaks. The H₂O⁺ ion in its B?²B₂ state is found to have a OH bond length of 1.12 A and a valence angie of 78°.In order to describe the unimolecular fragmentation process, a distinction is introduced between the totally symmetric, optically active vibrational modes, and the antisymmetric ones which are coupled to the continuum. The former are supplied with photon or electron impact energy, but only the latter are chemically efficient. The dynamics of the dissociation process depends therefore on the couplings among normal modes. This is studied in the framework of two models. In Model 1, it is assumed that, as a result of the anharmonicity of the potential energy surface, only even overtones of the antisymmetric vibration are excited by Fermi resonance. In Model II, excitation of the odd overtones is provided by vibronic coupling. Model II is in better agreement with experiment than Model I. Calculated and experimental results have been compared on the following points: isotopic shift on the appearance potential of OH⁺ and OD⁺ ions, shapes of the photoionization curves, fragmentation pattern with 21 eV photons, presence of a unimolecular metastable transition, production of O⁺ ions. All the vibrational levels situated above the dissociation asymptote are totally predissociated. Autoionization is shown in this case to contribute only to the formation of molecular H₂O⁺ ions, and not to that of the OH⁺ fragments. For 21 eV electrons, the contribution due to direct ionization is calculated to represent about 25% of the total cross section, the rest being due to autoionization.     

Thermal-energy charge transfer of Ar+ with H2O: Internal and kinetic energy of the product H2O+

The reaction of Ar⁺ with H₂O has been investigated at near-thermal energy. The product ions H₂O⁺ and ArH⁺ account for 90 and 10% of the total reaction rate, respectively. Kinetic energy measurements and emission spectroscopy of the H₂O⁺ product ions are reported. It is concluded that at least 60% of H₂O⁺ ions are in the X? state with ≈2.4 eV vibrational energy while up to 40% are in the à state with a mean vibrational energy of 1.4 eV; the à state vibrational distribution has been determined. It is shown that both H₂O⁺ states are populated via an energetically “non-resonant” charge transfer process.     

Diaquahydrogenium hexachloroantimonate (V). Observed and calculated infrared spectra

The diaquahydrogenium hexachloroantimonates(V) H₅O₂⁺SbCl₆^-(I) and D₅O₂⁺SbCl₆^-(II) were prepared by the reaction of SbCl₅ · 2H₂O and SbCl₅ · 2D₂O with HCl or DCl respectively. The infrared spectra were assigned. In addition ab initio calculations were performed on the system H₅O₂⁺, for which frequencies and IR absorbances of three mutually perpendicular modes of the H-bonded proton and D-bonded deuteron were calculated.     

Mode Selective Stereomutation and Parity Violation in Disulfane Isotopomers H2S2, D2S2, T2S2

We report quantitative calculations of stereomutation tunneling in the disulfane isotopomers H₂S₂, D₂S₂, and T₂S₂, which are chiral in their equilibrium geometry. The quasi‐adiabatic channel, quasi‐harmonic reaction path Hamiltonian approach used here treats stereomutation including all internal degrees of freedom. The torsional motion is handled as an anharmonic reaction coordinate in detail, whereas all the remaining degrees of freedom are taken into account approximately. We predict how stereomutation is catalyzed or inhibited by excitation of the various vibrational modes. The agreement of our theoretical results with spectroscopic data from the literature on H₂S₂ and D₂S₂ is excellent. We furthermore predict the influence of parity violation on stereomutation as characterized approximately by the ratio (ΔE_pv/ΔE_±) of the (local or vibrationally averaged) parity violating potential ΔE_pv and the tunneling splittings ΔE_± in the symmetrical case. This ratio is exceedingly small for the reference molecules H₂O₂ and D₂O₂, and still very small (2⋅10⁻⁶ cm⁻¹) for H₂S₂, which, thus, all exhibit essentially parity conservation in the dynamics. However, for D₂S₂ it is ca. 0.002, and for T₂S₂ it is ca. 1, which seems to be the first case where such intermediate mixing through parity violation is quantitatively predicted for spectroscopically accessible molecules. The consequences for the spectroscopic detection of molecular parity violation are discussed briefly also in relation to other molecules.     

Transition-metal mediated heteroatom removal by reactions of FeL+ [L=O,C4H6, c-C5H6, c-C5H5, C6H6, C5H4(=CH2)] with furan,thiophene, and pyrrole in the gas phase

Reactions of Fe⁺ and FeL⁺ [L=O, C₄H₆, c-C₅H₆, C₅H₅, C₆H₆, C₅H₄(=CH₂)] with thiophene, furan, and pyrrole in the gas phase by using Fourier transform mass spectrometry are described. Fe⁺, Fe(C₅H₅)⁺, and FeC₆H ₆ ⁺ yield exclusive rapid adduct formation with thiophene, furan, and pyrrole. In addition, the iron-diene complexes [FeC₄H ₆ ⁺ and Fe(c-C₅H₆)⁺], as well as FeC₅H₄(=CH₂)⁺ and FeO⁺, are quite reactive. The most intriguing reaction is the predominant direct extrusion of CO from furan by FeC₄H₆ ⁺, Fe(c-C₅H₆)⁺, and FeC₅H₄(=CH₂)⁺. In addition, FeC₄H ₆ ⁺ and Fe(c-C₅H₆)⁺ cause minor amounts of HCN extrusion from pyrrole. Mechanisms are presented for these CO and HCN extrusion reactions. The absence of CS elimination from thiophene may be due to the higher energy requirements than those for CO extrusion from furan or HCN extrusion from pyrrole. The dominant reaction channel for reaction of Fe(c-C₅H₆)⁺ with pyrrole and thiophene is hydrogen-atom displacement, which implies D^O(Fa(N₅H₅)⁺-C₄H₄X)>D^O(Fe(C₅H₅)⁺-H)=46±5 kcal mol^?1. D^O(Fe⁺-C₄H₄S) and D^O(Fe⁺-C₄H₅N)=D^O(Fe⁺-C₄H₆)=48±5 kcal mol^?1. Finally, 55±5 kcal mol^?1=D^O(Fe⁺-C₆H₆)>D^O(Fe⁺-C₄H₄O)>D^O(Fe⁺-C₂H₄)=39.9±1.4 kcal mol^?1. FeO⁺ reacts rapidly with thiophene, furan, and pyrrole to yield initial loss of CO followed by additional neutral losses. D^O(Fe⁺-CS)>D^O(Fe⁺-C₄H₄S)≈48±5 kcal mol^?1 and D^O(Fe⁺-C₄H₅N)≈48±5 kcal mol^?1>D^O(Fe⁺-HCN)>D^O(Fe⁺-C₂H₄)=39.9±1.4 kcal mil^?1.     

Deuterium exchange in the systems of H2O+/H2O and H3O+/H2O

The reactions of H₂O⁺, H₃O⁺, D₂O⁺, and D₃O⁺ with neutral H₂O and D₂O were studied by tandem mass spectrometry. The H₂O⁺ and D₂O⁺ ion reactions exhibited multiple channels, including charge transfer, proton transfer (or hydrogen atom abstraction), and isotopic exchange. The H₃O⁺ and D₃O⁺ ion reactions exhibited only isotope exchange. The variation in the abundances of all ions involved in the reactions was measured over a neutral pressure range from 0 to 2 × 10⁻⁵ Torr. A reaction scheme was chosen, which consisted of a sequence of charge transfer, proton transfer, and isotopic exchange reactions. Exact solutions to two groups of simultaneous differential equations were determined; one group started with the reaction of ionized water, and the other group started with the reactions of protonated water. A nonlinear least-squares regression technique was used to determine the rate coefficients of the individual reactions in the schemes from the ion abundance data. Branching ratios and relative rate coefficients were also determined in this manner.A delta chi-squared analysis of the results of the model fitted to the experimental data indicated that the kinetic information about the primary isotopic exchange processes is statistically the most significant. The errors in the derived values of the kinetic information of subsequent channels increased rapidly. Data from previously published selected ion flow tube (SIFT) study were analyzed in the same manner. Rigorous statistical analysis showed that the statistical isotope scrambling model was unable to explain either the SIFT or the tandem mass spectrometry data. This study shows that statistical analysis can be utilized to assess the validity of possible models in explaining experimentally observed kinetic behaviors.     

NH4+ Deprotonation at Interfaces Induced Reversible H3O+/NH4+ Co-insertion/Extraction

Ion insertions always involve electrode-electrolyte interface process, desolvation for instance, which determines the electrochemical kinetics. However, it′s still a challenge to achieve fast ion insertion and investigate ion transformation at interface. Herein, the interface deprotonation of NH₄⁺ and the introduced dissociation of H₂O molecules to provide sufficient H₃O⁺ to insert into materials′ structure for fast energy storages are revealed. Lewis acidic ion-NH₄⁺ can, on one hand provide H₃O⁺ itself via deprotonation, and on the other hand hydrolyze with H₂O molecules to produce H₃O⁺. In situ attenuated total reflection-Fourier transform infrared ray method probed the interface accumulation and deprotonation of NH₄⁺, and density functional theory calculations manifested that NH₄⁺ tend to thermodynamically adsorb on the surface of monoclinic VO₂, and deprotonate to provide H₃O⁺. In addition, the inserted NH₄⁺ has a positive effect for stabilizing the VO₂(B) structure. Therefore, high specific capacity (>300 mAh g⁻¹) and fast ionic insertion/extraction (<20 s) can be realized in VO₂(B) anode. This interface derivation proposes a new path for designing proton ion insertion/extraction in mild electrolyte.     

Variational calculations on the vibrational level structure of S0 HDCO

We perform converged high precision variational calculations to determine the frequencies of the vibrational levels in S₀ HDCO, extending up to 5000 cm^?1 of vibrational excitation energy. For these calculations we use our specific vibrational method (recently employed for studies on H₂CO and D₂CO), consisting of a combination of a search/selection algorithm and a Lanczos iteration procedure and based on the Martin, Lee, Taylor potential energy surface for formaldehyde. The calculated level structure is compared to the recently measured frequencies by Ellsworth et al. in order to improve their assignments and further clarify the vibrational mixing pattern and vibrational resonances in HDCO that are very different from the other more symmetric formaldehyde species H₂CO and D₂CO studied recently.     

Single-determinantal open- and closed-shell FSGO calculations for some diatomic molecules

Open-shell single-determinantal calculations are reported here for the molecular species H₂, Li₂⁺, N₂, O₂ (triplet), O₂^2?;, O₂^?, O₂²⁺, O₂⁺, and F₂; corresponding closed-shell calculations are reported for the species H₂, N₂, O₂ (singlet), O₂^2?, O₂²⁺, and F₂. The floating spherical Gaussian orbital (FSGO ) method was employed. The calculated trend in bond lengths of isonucleic diatomic molecules is in agreement with experiment. For heteronucleic diatomic molecules, however, the experimental trend in bond lengths is not obtained; in this connection, the effect of lone pairs on bond length is discussed. The dissociation energies of H₂ and Li₂⁺ are evaluated. The energy gap between the triplet and singlet states of the oxygen molecule is calculated to be 8.96 eV compared to the experimental value of 4.54 eV.     

Vibrational-state-selected ion—molecule reaction cross sections at thermal energies

A method designed to measure relative ion—molecule reaction rates at thermal collision energies for selected reactant ion vibrational states is described. Relative reaction rates are determined for the three endothermic reactions: H₂⁺ (υ)(He,H)HeH⁺, H₂⁺ (υ)(Ne,H)NeH⁺, D₂⁺(υ)(Ne, D)NeD⁺, and for the two exothermic reactions H₂⁺ (υ)(H₂, H)H₃⁺, D₂⁺(υ)(D₂, D)D₃⁺, whereby data are evaluated for υ = 0–8 for H₂⁺ and for υ = 0–12 in the case of D₂⁺. The results are analyzed in terms of a modified statistical model designed for reactions that go through a collision complex. It is found that all data can be satisfactorily described within this model.