The interaction of metastable helium atoms with alkaline earth atoms: He*(23 S,21 S)+Mg,Ca, Sr and Ba

We have carried out experimental and theoretical studies of Penning ionization processes occurring in thermal energy collisions of state-selected metastable He*(2³ S) and He*(2¹ S) atoms with ground state alkaline earth atoms X(X=Mg, Ca, Sr, Ba). Penning ionization electron energy spectra for these eight systems, measured with a crossed-beam set-up perpendicular to the collision velocity at energy resolutions 40–70 meV, are reported; relative populations of the different ionic X ⁺ (ml) states are presented and well depths D*_e for the He*+X entrance channel potentials with uncertainties around 25 meV are derived from the electron spectra as follows: He*(2³ S)+Mg/Ca/Sr/Ba: 130/250/240/260 meV; He*(2¹ S) +Mg/Ca/Sr/Ba: 300/570/550/670 meV. The spectra show substantial differences for the three ionic states X ⁺(² S), X ⁺(² P) and X ⁺(² D) and reveal that transitions to a repulsive potential — attributed to He+X ⁺(² P)² Σ formation — are mainly involved for the X ⁺(² P) channel. Ab initio calculations of potential curves, autoionization widths, electron energy spectra and ionization cross sections are reported for the systems He*(2³ S)+Ca and He*(2¹ S)+Ca. The respective well depths D _e ^* are calculated to be 243(15) meV and 544(15) meV; the ionization cross sections at the experimental mean energy of 72 meV amount to 101 Ų and 201 Ų, respectively. Very good overall agreement with the experimental electron spectra is observed.     

Ab initio study of small He cluster ions He n + ,n=2, 3, 4, 5, and low-lying Rydberg states of He4

SCF and CEPA calculations are applied to study the structure of small He cluster ions, He _n ⁺ ,n=2, 3, 4, 5 and some low-lying Rydberg states of He₄. The effect of electron correlation upon the equilibrium structures and binding energies is discussed. He ₃ ⁺ has a linear symmetric equilibrium geometry with a bond length of 2.35a ₀ and a binding energyD _e =0.165 eV with respect to He ₂ ⁺ +He (experimentally:D ₀=0.17 eV which corresponds toD _e ≈0.20 eV). He ₄ ⁺ is a very floppy molecular ion with several energetically very similar geometrical configurations. Our CEPA calculations yield a T-shaped form with a He ₃ ⁺ centre (R _e = 2.35a ₀) and one inductively bound He atom (4.39a ₀ from the central He atom of He ₃ ⁺ ) as equilibrium structure. Its binding energy with respect to He ₃ ⁺ +He is 0.031 eV. A linear symmetric configuration consisting of a He ₂ ⁺ centre with a bond length of 2.10a ₀ and two inductively bound He atoms (4.20a ₀ from the centre of He ₂ ⁺ ) is only 0.02–0.03 eV higher in energy. We expect that in larger He cluster ions structures with He ₂ ⁺ and He ₃ ⁺ centres andn?2 orn?3 inductively bound He atoms have nearly the same energies. In He₄ a low-lying metastable Rydberg state (³ Π symmetry for linear He ₄ ^* ,³ B ₁ for the T-shaped form) exists which is slightly stronger bound with respect to He ₃ ^* +He than the corresponding ion.     

Detailed electron spectrometric study of the ionization of H2 by He* (21 S, 23 S)

The energy spectra of electrons released in thermal energy (≈ 50 meV) ionizing collisions of He*(2¹ S, 2³ S) with H₂ have been measured with high resolution and low background. Based on a detailed data analysis, we report accurate H ₂ ⁺ (v′) vibrational populationsP(v′) for both He*(2¹ S)+H₂(v′=0–10) and He*(2³ S)+H₂(v′=0–15) and the spectral shapeS(ε) for the individual vibrational peaks. The vibrational populationsP(v′) are quite similar to the Franck-Condon factorsf _v ′0 for unperturbed H₂(v″=0)→H ₂ ⁺ (v′) transitions, but, more in detail, the ratiosP(v′)/f _v ′0 show a characteristically differentv′-dependence for He*(2³ S), He*(2¹ S), and HeI_α(58.4 nm) ionization. The vibrational level separations in the He*(2¹ S, 2³ S)+H₂ spectra agree with those in the HeI photoelectron spectrum to within 1–2 meV. The spectral shapesS(ε) are characteristically different for He*(2¹ S)+H₂ and He*(2³ S)+H₂, reflecting the respective differences in the entrance channel potentials, as determined previously in ab initio calculations and from scattering experiments.     

The lifetime of the (μHe) 2S + metastable state in helium gas

The ion-clustering mechanism of the quenching of the metastable 2S-state of the muonic helium ion (μHe) _2S ⁺ in gaseous helium is studied on the basis of quantum-chemical calculations of clusters He _n (μHe)⁺. It is shown that the quenching rates do not depend on the cluster ordern atn ≥ 2. In the helium gas at the pressure 0.1 ?p(atm) ? 10 the quenching of (μHe) _2S ⁺ proceeds, mainly, at the vibrationally excited levels of He(μHe) _2S ⁺ cluster, while atp ? 10 atm, at the ground vibrational state of the cluster He₂(μHe) _2S ⁺ . Atp ≥0.1 atm the calculated quenching rates agree with the recent experimental data.     

Spectroscopic properties of the Ar 2 * (5p) excimer states

The transitions between Ar ₂ ^* (5p) and Ar ₂ ^* (4sΣ _u) have been investigated by absorption spectrometry. The fine structure of the Ar ₂ ^* (5p ³ Π _g) was attributed to a predominantly Hund’s case a coupling. A spin orbit coupling constant of A = (9.8±0.3) cm^-1 results. Absorption by the singlet system allows one to determine the triplet/singlet splitting between the Ar ₂ ^* (4s Σ _u) states to be (540 ± 100) cm^-1. The transition probabilities of the Ar ₂ ^* (5p) and Ar ₂ ^* (6p) levels were determined by saturation spectrometry yielding values between (0.2–2.5) · 10⁶ s^-1.     

Photofragment spectroscopy of N 2 + in the near UV

Photofragment spectroscopy of N ₂ ⁺ has been studied in the wavelength range 343–404 nm using an excimer-pumped dye laser with a spectral resolution of 0.2 cm^?1. The observed bands are assigned to transitions from thev″=23?26 levels of theX ²Σ _g ⁺ state to highlying rovibrational levels (v′≈46–48) of theB ²Σ _u ⁺ state, forming quasibound (predissociating) states above the dissociation limit N⁺(³ P)+N(⁴ S ⁰). Measurement of the photofragment kinetic energies allows to establish an absolute energy scale for the transitions with respect to the dissociation limit. Molecular constants for the lower and upper states of the observed transitions are determined. The measurements allow the first direct determination of the N ₂ ⁺ dissociation energyD ₀ ⁰ (N ₂ ⁺ ). Some high-resolution (0.04 cm^?1) measurements show the fine-structure splitting and lifetime broadening of the excitation lines.     

Pressure and isotope effects on the proton jump of the hydroxide ion at 25°C

The limiting molar conductances Λ⁰ of potassium deuteroxide KOD in D₂O and potassium hydroxide KOH in H₂O were determined at 25°C as a function of pressure to disclose the difference in the proton-jump mechanism between an OH^? (OD^?) and a H₃O⁺ (D₃O⁺) ion. The excess conductance of the OD^? ion in D₂O λ _E ^O (OD ^-), as estimated by the equation $$\lambda _E^O (OD^ - ) = \Lambda ^O (KOD/D_2 O) - \Lambda ^O (KCl/D_2 O)$$ increases a little with pressure as well as the excess conductance of the OH^? ion in H₂O $$\lambda _E^O (OH^ - ) = \Lambda ^O (KOH/H_2 O) - \Lambda ^O (KCl/H_2 O)$$ However, their rates of increase with pressure are much smaller than those of the excess deuteron and proton conductances, λ _E ^O (D ⁺) and λ _E ^O (H ⁺). With respect to the isotope effect on the excess conductance, λ _E ^O (OH ^-)/λ _E ^O (D ⁺) decreases with presure as in the case of λ _E ^O (H ⁺)/λ _E ^O (D ⁺), but the value of λ _E ^O (OH ^-)/λ _E ^O (OD ^-) itself is much larger than that of λ _E ^O (H ⁺)/λ _E ^O (D ⁺) at each pressure. These results are ascribed to the difference in the pre-rotation of water molecules, which is brought about by the difference in the intial orientation of the rotating water molecule adjacent to the OH^? (OD^?) or the H₃O⁺ (D₃O⁺) ion.     

Analytical photoion spectroscopy applied to dissociative single and double photoionization of diatomic molecules (H2, N2, O2, CO,and NO)

This work reports the principle, advantage, and limitations of analytical photoion spectroscopy which has been applied to dissociative photoionization processes for diatomic molecules such as H₂, N₂, CO, and NO. Characteristic features observed in the differential photoion spectra are summarized with a focus on (pre)dissociation of(i) multielectron excitation states commonly observed in the inner valence regions,(ii) shape resonances, and(iii) doubly charged parent ions. Possible origins for negative peaks in the differential spectra are discussed. This spectroscopy is applied to the reported photoion branching ratios for D₂ (and H₂ at high energies). The main findings are as follows: (1) The direct dissociation of theX ²Σ _g ⁺ (1sσ _g ) state of D ₂ ⁺ , the two-electron excited state¹Σ _u ⁺ (2pσ _u 2sσ _g ) of D₂, and the²Σ _u ⁺ (2pσ _u ) state of D ₂ ⁺ appear clearly in the differential spectrum, as previously observed for H₂. (2) Decay of H ₂ ⁺ (D ₂ ⁺ ) to H⁺ (D⁺) above 38 eV is due to the direct dissociation of highly excited states of H ₂ ⁺ (D ₂ ⁺ ) such as the²Σ _g ⁺ (2sσ _g ) and high-lying Rydberg states converging on H ₂ ²⁺ (D ₂ ²⁺ ). (3) In the ionization continuum of H ₂ ²⁺ (D ₂ ²⁺ ) peculiar dissociation pathways are observed. The differential photoion spectra for O₂ derived from the reported photoion branching ratios are also presented. The (pre)dissociation of theb ⁴Σ _g ^? ,B ²Σ _g ^? , III²Π _u ,²Σ _u ^? , and^2,4Σ _g ^? states of O ₂ ⁺ appears as the corresponding positive values in the spectra in accord with previous observations. Some other dissociation pathways possibly contributing to the spectra are discussed including dissociative double ionization.     

Energy and polarization dependence of chemi-ionization processes inK(42 P 3/2)−K(42 P 3/2) collisions

Using crossed molecular beams we have investigated ionizing collisions between potassium atoms in their 4² P _3/2-states, leading to the exit channelsK ₂ ⁺ +e ^?,K ⁺+K ^?, andK(4² S _1/2)+K ⁺+e ^?, respectively. Measurements of the total ionization cross section as well as of the cross sections for the individual channels are reported as a function of both the relative collision energy (0.2 to 2.4 eV) and the angle between the electric field vector of the exciting laser light and the relative velocity vector. The results are interpreted in terms of the molecular states of theK ₂ ^* quasi molecule which are involved in the ionization process.     

Quantum chemical DFT calculations of the local structure of the hydrated electron and dielectron

The adiabatic bound state of an excess electron is calculated for a water cluster (H₂O) ₈ ^? in the gas phase using the DFT-B3LYP method with the extended 6-311++G(3df,3pd) basis set. For the liquid phase the calculation is performed in the polarizable continuum model (PCM) with regard to the solvent effect (water, ? = 78.38) in the supermolecule-continuum approximation. The value calculated by DFT-B3LYP for the vertical binding energy (VBE) of an excess electron in the anionic cluster (VBE(H₂O) ₈ ^? = 0.59 eV) agrees well with the experimental value of 0.44 eV obtained from photoelectron spectra in the gas phase. The VBE value of the excess electron calculated by PCM-B3LYP for the (H₂O) ₈ ^? cluster in the liquid phase (VBE = 1.70 eV) corresponds well to the absorption band maximum λ_max = 715 nm (VBE = 1.73 eV) in the optical spectrum of the hydrated electron hydr e _hydr ^? . Estimating the adiabatic binding energy (ABE)e _hydr ^t- in the (H₂O) ₈ ^? cluster (ABE = 1.63 eV), we obtain good agreement with the experimental free energy of electron hydration ΔG ₂₉₈ ⁰ (e _hydr ^? ) = 1.61 eV. The local model (H₂O) ₈ ^2? of the hydrated dielectron is considered in the supermolecule-continuum approximation. It is shown that the hydrated electron and dielectron have the same characteristic local structure: -O-H{↑}H-O- and -O-H{↑↓}H-O-respectively.     

Spectroscopic and electrochemical properties of mixed-ligand cycloplatinated complexes based on 2-(2-thienyl)pyridine and 2-phenylpyridine with 1,10-phenantroline and its 1,4-diazine derivatives

A comparative study of dipyrido-and dibenzo-substituted 1,4-diazines {dipyrido[f,h]quinoxaline (dpq), dipyrido[a,c]phenazine (dppz), 6,7-dicyanodipyrido[f,h]quinoxaline (dicnq), dibenzo[f,h]quinoxaline, dibenzo[a,c]phenazine, 6,7-dicyanodibenzo[f,h]-quinoxaline}, o-phenantroline (phen), and also of the complexes [Pt(N∧C)(N∧N)]⁺[(N∧C)^? are deproronated forms of 2-phenylpyridine and 2-(2-thienyl)pyridine; (N∧N) is ethylenediamine, phen, dpq, dppz, dicnq] was carried out by the methods of ¹H NMR, electronic absorption, and emission spectroscopy and by cyclic voltammetry. It was found that in frozen solutions of [Pt(N∧C)·(N∧N)]⁺ complexes the photoexcitation energy decay from two lowest in energy electronic excited states has isolated character and is localized on {Pt(N∧C)} and {Pt(N∧N)} metal-complex fragments: (d-π _N∧C ^* ) and (d-π _phen ^* ) [(N∧N) = phen, dpq, dicnq)] or (d-π _N∧C ^* ) and (π-π _diaz ^* ) [(N∧N) = dppz]. Thermal quenching of the luminescence from the (d-π _phen ^* ) and (π-π _diaz ^* ) states gives rise to luminescence of the complexes in liquid solutions at 293 K only from the (d-π _N∧C ^* ) state.     

Population and deactivation of lowest lying barium levels by collisions with He,Ar, Xe and Ba ground state atoms

Excitation transfer between the barium low lying excited states 6s6p ³ P ₁ ⁰ , 6s5d ¹ D ₂ and 6s5d ³ D _J by collisions with He,Ar,Xe and Ba has been investigated. The population densities in all levels involved were probed by absorption or by fluorescence usingcw lasers. The depopulation cross sections of the Ba³ P ₁ ⁰ state by collisions with noble gases were found to be σ_He(³ P ₁ ⁰ )=5.5·10^?16 cm², σ_Ar(³ P ₁ ⁰ )=4.6·10^?16 cm², and σ_Xe(³ P ₁ ⁰ )=1.7·10^?16 cm². For Ar, the collisional depopulation of the³ P ₁ ⁰ level is exclusively due to the transition to the¹ D ₂ state. Under the assumption that the³ D _J metastable states are populated collisionally by¹ D ₂ →³ D _J transfer only, we have deduced the upper limit for the corresponding cross section σ ₁₃ ^Ar =1.5·10^?18 cm². From the Ba¹ D ₂ and Ba³ D _J steady-state diffusion distributions, collisional relaxation rates of the¹ D ₂ and³ D _J levels were evaluated. The collisional relaxation rates by Ar and Ba yielded total cross sections for the depopulation of metastable levels: σ_Ar(¹ D ₂)=1.5·10^?17 cm², σ_Ba(¹ D ₂)?1·10^?13 cm², σ_Ar(³ D _J)=7·10^?21 cm², and σ_Ba(³ D _J)=1·10^?15 cm². Furthermore, it was found that the main contribution of the collisional depopulation of the¹ D ₂ state by Ar is related to back transfer to the³ P _J ⁰ state, whereas the deactivation of the³ D _J metastable state is due to back transfer to the¹ D ₂ state. Taking into account other cross sections reported in literature we can conclude that collisional deactivation of both metastable levels by Ba ground state atoms can be attributed to their mutual collisional mixing.     

High-Energy X-ray Diffraction and MD Simulation Study on the Ion-Ion Interactions in 1-Ethyl-3-methylimidazolium Bis(fluorosulfonyl)amide

Ion-ion interactions or liquid structures in low-viscosity ionic liquid, 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)amide, [C₂mIm⁺][FSA^?] were investigated by high-energy X-ray diffraction (HEXRD) experiments and molecular dynamics (MD) simulations. Experimental X-ray structure factor, S ^exp(q) obtained from the HEXRD was successfully deconvoluted into the intra- and the intermolecular components, S _intra ^exp (q) and S _inter ^exp (q), respectively, by taking into account the population of cis and trans conformers of the FSA anion to give the corresponding radial distribution functions, G _intra ^exp (r) and G _inter ^exp (r), respectively. The G _inter ^exp (r) exhibits the peaks at 3.5, 4.6 and 5.4 Å, which is well represented by theoretical radial distribution function, G _inter ^MD (r) obtained from MD simulations. From the space distribution function, SDF calculated by MD simulations, it was found that static structure (distance and orientation) of the nearest neighbor intermolecular interaction between cation and anion in [C₂mIm⁺][FSA^?] is similar to its analogous ionic liquid, [C₂mIm⁺][TFSA^?] where TFSA is bis(trifluoromethanesulfonyl)amide.     

Activation parameters of supercritical and gas-phase β-pinene thermal isomerization

New data on enthalpy and entropy contributions to the energy barrier of β-pinene thermal isomerization were obtained. The rate of β-pinene conversion is higher in supercritical EtOH (P = 120 atm) than in the gas phase (P ≤ 1 atm, without solvent, or for inert carrier gas N₂) at equal temperatures. The highest activation energy E _Σ of total β-pinene conversion is also observed in reactions in the supercritical (sc) condition. Activation parameters ΔH _Σ ^# , ΔS _Σ ^# , and ΔG _Σ ^# depend strongly on the reaction pressure. Thus, at P ≤ 1 atm (gas-phase reaction) the values of ΔS _Σ ^# are negative, while at sc conditions at P = 120 atm is positive. The linear dependences lnk _Σ0 ? E _Σ and ΔS _Σ ^# ? ΔS _Σ ^# indicate an isokinetic relation (IKR) and enthalpy-entropy compensation effect (EEC). The isokinetic temperature was calculated (T _iso = 605.5 ± 22.7 K). It was shown that elevation of temperature reduces the value of ΔG _Σ ^# (T) upon sc thermolysis only, whereas in all gas-phase reactions ΔG _Σ ^# (T) increases. At equal reaction temperatures, the greatest values of K _eq ^# (T) proved to be typical for thermolysis in sc-EtOH. We hypothesize that the rate of total β-pinene conversion increases dramatically due to a considerable shift in equilibrium toward higher concentrations of activated complex y _TS ^# . A detailed analysis of activation parameters shows that the IKR and EEC coincide, evidence of a common mechanism of β-pinene conversion observed under different reaction conditions, including thermolysis in sc-EtOH.     

The Standard Chemical-Thermodynamic Properties of Phosphorus and Some of its Key Compounds and Aqueous Species: An Evaluation of Differences between the Previous Recommendations of NBS/NIST and CODATA

The aqueous chemistry of phosphorus is dominated by P(V), which under typical environmental conditions (and depending on pH and concentration) can be present as the orthophosphate species H₃PO ₄ ⁰ (aq),H₂PO ₄ ^? (aq),HPO ₄ ^2? (aq) or PO ₄ ^3? (aq). Many divalent, trivalent and tetravalent metal ions form sparingly soluble orthophosphate phases that, depending on the solution pH and concentrations of phosphate and metal ions, can be solubility limiting phases. Geochemical and chemical engineering modeling of solubilities and speciation require comprehensive thermodynamic databases that include the standard thermodynamic properties for the aqueous species and solid compounds. The most widely used sources for standard thermodynamic properties are the NBS (now NIST) Tables (from 1982 and earlier, with a 1989 erratum) and the final CODATA evaluation (1989). However, a comparison of the reported enthalpies of formation and Gibbs energies of formation for key phosphate compounds and aqueous species, especially H₂PO ₄ ^? (aq) and HPO ₄ ^2? (aq), shows a systematic and nearly constant difference of 6.3 to 6.9 kJ?mol^?1 per phosphorus atom between these two evaluations. The existing literature contains numerous studies (including major data summaries) that are based on one or the other of these evaluations. In this report we examine and identify the origin of this difference and conclude that the CODATA evaluation is more reliable. Values of the standard entropies of the H₂PO ₄ ^? (aq) and HPO ₄ ^2? (aq) ions at 298.15 K and p?° =1 bar were re-examined in the light of more recent information and data not considered in the CODATA review, and a slightly different value of S _m ^o (H₂PO ₄ ^? , aq, 298.15 K) = (90.6±1.5) J?K^?1?mol^?1 was obtained.     

Dichlorotriethylphosphine-[N-formyl-N,N′-bis(3,4-dimethoxy)benzyl-trimethylenediamine] platinum(II)

By treatment of 1,3-bis(3,4-dimethoxybenzyl)-3,4,5,6-tetrahydropyrimidinium chloride (1) with KOBu ^t and [PtCl₂(PEt₃)₂]₂ N-coordinated platinum complex (2) is obtained. The Pt atom is coordinated in square planar arrangements by two chloride ions in a trans-configuration, the N-formyl-N,N′-bisaryltrimethylenediamine nitrogen atom, and the phosphine P atom. An extensive three-dimensional network of three C-H…O hydrogen bonds, two C-H…π and one π…π interactions are responsible for the crystal stabilization. Intermolecular hydrogen bonds and C-H…π interactions produce R ₂ ² (6), R ₂ ² (22), R ₂ ² (24), R ₃ ³ (23), R ₄ ⁴ (26), and R ₄ ⁴ (32) rings.     

Fragmentation by electron impact ionization and intracluster reactions of size selected (N2H4) n and (OCS) n clusters

The hydrogen-bonded (N₂H₄) _n clusters and the van der Waals (OCS) _n clusters are size selected in a scattering experiment with a He beam up to the cluster sizen=6. By measuring the angular distributions of the scattered clusters the complete fragmentation pattern of electron impact ionization is obtained. For Hydrazine the two main fragment masses are the protonated species (N₂H₄) _n?1H⁺ and with somewhat weaker intensities also the nominal ion mass (N₂H₄) _n ⁺ . The largest intensity is observed for the monomer ion N₂H ₄ ⁺ to which clusters up ton=5 fragment. For carbonylsulfide, completely different results are obtained. Aside from the fragments of the OCS monomer and the van der Waals cluster fragments (OCS) ₂ ⁺ and (OCS) ₃ ⁺ signals at mass S ₂ ⁺ , S ₃ ⁺ and S₂OCS⁺ are detected. This indicates a fast chemical reaction in the cluster according to: S + OCS → CO + S₂ which occurs for clusters of sizen ≥ 2. Peaks at S ₃ ⁺ and S₂OCS⁺ are seen for the first time forn ≥ 5 according to a further reaction of S₂ in the cluster.     

A theoretical and experimental investigation of the formation of S 2 - from CS2 by electron impact

Theoretical and experimental investigation of the formation of S ₂ ^- from CS₂ by electron impact has been carried out. Molecular orbital calculations show that some of the low lying states of CS ₂ ^- have lower potential energy in the bent geometries suggesting a transformation in the geometric structure of the precursor molecular ion, leading to the formation of S ₂ ^- . In contrast to the formation of S ₂ ^- and S ₂ ^- , the kinetic energy associated with S ₂ ^- is small and disproportionate to the increase in electron energy, indicating the formation of S ₂ ^- in vibrationally excited states due to the mechanism of its formation.     

Velocity cross correlations in binary mixtures of simple fluids

The velocity cross correlation integrals $$D_{{\text{ab}}}^{\text{J}} = (N/3)\mathop \smallint \limits_{\text{o}}^\infty< {\text{v}}_{{\text{1a}}} ({\text{t}}) \cdot {\text{v}}_{{\text{2b}}} (0) > {\text{dt,}} {\text{a}} {\text{ = }} {\text{1,2;}} {\text{b}} {\text{ = }} {\text{1,2}}$$ can be estimated from the intradiffusion coefficients D ₁ ^° and D ₂ ^° at each mole fraction x₁ of component 1 on the basis of the exact relations among the Onsager phenomenological coefficients together with an assumed equation relating the joint diffusion coefficients D _ab ^J . The results from several such equations are compared with experimental data and with similar results derived by Hertz in a different way to represent the behavior of f _ab ≡D _ab ^J x _b in ideal reference systems. In some cases the agreement with experimental data for relatively ideal systems is even better than given by Hertz's results. For greater accuracy in predicting the D _ab ^J from D _a ^dg data one would need a prediction of the limiting value of D _aa ^J at x_a=0 for a=1,2. Presently known theory does not give a basis for estimating this limit reliably.