Isotopic Reduced Partition Function Ratios Research Articles

Nitrogen Isotopic Reduced Partition Function Ratios of Glycine and Serine in Water.

The nitrogen isotopic reduced partition function ratio (RPFR) of glycine (Gly) and serine (Ser) in water has been evaluated by a couple of methods. The experimental fact that those amino acids are present in the zwitterionic form in water has been best reproduced when trihydrated Gly and Ser molecules were treated by the discrete microsolvation method coupled with the self-consistent reaction field (SCRF) approach. The RPFR values of Gly and Ser in water at 25 °C are evaluated as 1.11152 and 1.11070, respectively, and the equilibrium constant of the nitrogen isotope exchange reaction between the two amino acids is calculated as 1.0007 ± 0.0008 at 25 °C. Equivalent results may be obtained by the SCRF method for non- and monohydrated molecules in the zwitterionic form.

Oxygen and Hydrogen Isotopic Preference in Hydration Spheres of Magnesium and Calcium Ions

Molecular orbital calculations were performed to estimate the 18O/16O and D/H isotopic reduced partition function ratios (rpfrs) of water molecules around magnesium and calcium ions. As model for water molecules in the ith hydration sphere of the cation in aqueous solutions containing that cation, we considered water molecules in the ith hydration sphere that were surrounded by water molecules in the (i+1)th hydration sphere in clusters, M2+(H2O)n (M = Mg or Ca; n up to 100). The calculations indicated that the decreasing order of the 18O preference over 16O in the primary hydration sphere is Mg2+ > Ca2+ > bulk water. That is, water molecules in the primary hydration spheres of the Mg2+ and Ca2+ ions are expected to be enriched in the heavier isotope of oxygen relative to water molecules in bulk, and the degree of the enrichment is larger for the Mg2+ ion than for the Ca2+ ion. No such preference was observed for hydrogen isotopes in any hydration sphere or for oxygen isotopes in the secondary and outer hydration spheres.

Oxygen and Hydrogen Isotopic Preference in Hydration Spheres of Chloride and Sulfate Ions

Abstract Molecular orbital calculations were performed to estimate the 18O/16O and D/H isotopic reduced partition function ratios (RPFRs) of water molecules around chloride and sulfate ions. Cl-(H2O) n and SO4 2-(H2O) n clusters with n up to 120 were considered as models of aqueous solution containing those anions. The calculations indicated that the decreasing order of the 18O preference over 16O in the primary hydration sphere is: (bulk water) > SO4 2- > Cl-. That is, water molecules in the primary hydration spheres of those anions are expected to be depleted in the heavier isotope of oxygen relative to water molecules in bulk, and the degree of the depletion is larger for the chloride ion than for the sulfate ion. Similar tendency was also observed for the isotope preference of hydrogen. No such isotopic preference was observed either for oxygen or for hydrogen in the secondary and outer hydration spheres.

18O/16O and D/H Isotopic Preference in Hydration Spheres of Alkali Metal Ions

Abstract With the final goal set at theoretical elucidation of experimentally observed isotope salt effects, molecular orbital calculations were performed to estimate the 18O/16O and D/H isotopic reduced partition function ratios (RPFRs) of water molecules around lithium, sodium, and potassium ions. As model water molecules in the ith hydration sphere of the cation in aqueous solutions containing that cation, we considered water molecules in the ith hydration sphere that were surrounded by water molecules in the (i+1)th hydration sphere in clusters, M+(H2O)n (M = Li, Na or K; n up to 100). The calculations indicated that the decreasing order of the 18 O preference over 16 O in the primary hydration sphere is: Li+ > (bulk water) ≥ Na+ > K+. That is, water molecules in the primary hydration spheres of the Li+, Na+, and K+ ions are, respectively, enriched, slightly depleted, and depleted in the heavier isotope of oxygen relative to water molecules in bulk. No such preference was observed for hydrogen isotopes in any hydration sphere or for oxygen isotopes in the secondary and outer hydration spheres.

D/H and 18O/16O Isotopic Reduced Partition Function Ratios ofWater Molecules around a Sodium Ion

With the final goal set at theoretical elucidation of experimentally observed isotope salt effects, molecular orbital calculations were performed to estimate the D/H and 18O/16O isotopic reduced partition function ratios (RPFRs) of water molecules around a sodium ion. As model water molecules in the ith hydration sphere of the sodium ion in sodium ion-bearing aqueous solution, we considered water molecules in the ith hydration sphere that were surrounded by water molecules in the (i+1)th hydration sphere in clusters, Na+(H2O)n (n up to 100). The calculations indicated that the 18O/16O RPFR in the primary hydration sphere is slightly smaller than that of bulk water while the D/H RPFR is practically the same as that of bulk water, and that the influence of the existence of the sodium ion is limited to the primary hydration sphere.

D/H and18o/16O Isotopic Reduced Partition Function Ratios of Water Molecules around a Sodium Ion

D/H and¹⁸o/¹⁶O Isotopic Reduced Partition Function Ratios of Water Molecules around a Sodium Ion

Calculation of equilibrium stable isotope partition function ratios for aqueous zinc complexes and metallic zinc

The goal of this study is to determine reduced partition function ratios for a variety of species of zinc, both as a metal and in aqueous solutions in order to calculate equilibrium stable isotope partitioning. We present calculations of the magnitude of Zn stable-isotope fractionation ( 66,67,68Zn/ 64Zn) between aqueous species and metallic zinc using measured vibrational spectra (fit from neutron scattering studies of metallic zinc) and a variety of electronic structure models. The results show that the reduced metal, Zn(0), will be light in equilibrium with oxidized Zn(II) aqueous species, with the best estimates for the Zn(II)–Zn(0) fractionation between hexaquo species and metallic zinc being Δ 66/64Zn aq-metal ∼ 1.6‰ at 25 °C, and Δ 66/64Zn aq-metal ∼ 0.8‰ between the tetrachloro zinc complex and metallic zinc at 25 °C using B3LYP/aug-cc-pVDZ level of theory and basis set. To examine the behavior of zinc in various aqueous solution chemistries, models for Zn(II) complex speciation were used to determine which species are thermodynamically favorable and abundant under a variety of different conditions relevant to natural waters, experimental and industrial solutions. The optimal molecular geometries for [Zn(H 2O) 6] 2+, [Zn(H 2O) 6]·SO 4, [ZnCl 4] 2− and [Zn(H 2O) 3(C 3H 5O(COO) 3)] − complexes in various states of solvation, protonation and coordination were calculated at various levels of electronic structure theory and basis set size. Isotopic reduced partition function ratios were calculated from frequency analyses of these optimized structures. Increasing the basis set size typically led to a decrease in the calculated reduced partition function ratios of ∼0.5‰ with values approaching a plateau using the aug-cc-pVDZ basis set or larger. The widest range of species were studied at the B3LYP/LAN2DZ/6-31G ∗ level of theory and basis-set size for comparison. Aqueous zinc complexes where oxygen is bound to the metal center tended to have the largest reduced partition function ratios, with estimated fractionations ranging from 2.2 to 2.9‰ ( 66Zn/ 64Zn) at 25 °C relative to metallic zinc. The tetrahedrally coordinated tetrachloro zinc complex, where zinc is bound exclusively to chloride, had the lowest reduced partition function ratio for a Zn(II) species (Δ 66/64Zn aq-metal ∼ 1–1.3‰ at 25 °C). Increasing the number of waters in the second shell of solvation of the above complexes led to variable results, most commonly leading to a decrease of ∼0.2 to 0.3‰ in calculated Δ 66/64Zn aq-metal at 25 °C. These estimates are useful in the interpretation of observed fractionations during the electrochemical deposition of zinc, where aqueous-metal fractionations of up to 5.5‰ are observed. The models show these are not caused by an equilibrium fractionation process. These results suggest that the redox cycle of zinc during industrial processing may be responsible for isotopically distinct reservoirs of zinc observed in polluted environments. The leaching of metallic zinc or zinc tailings from industrial sites could lead to the observed heavy signature in river systems, the magnitude of which will be reliant on the source material and the aqueous species that form.

Boron isotope fractionation accompanying formation of potassium, sodium and lithium borates from boron-bearing solutions

A series of experiments was conducted in which boron minerals were precipitated by water evaporation from solutions containing boron and potassium, sodium or lithium at 25°C, and boron isotope fractionation accompanying such mineral precipitation was investigated. In the boron-potassium ion system, K2[B4O5(OH)4]·2H2O, santite (K[B5O6(OH)4]·2H2O), KBO2·1.33H2O, KBO2·1.25H2O and sassolite (B(OH)3) were found deposited as boron minerals. Borax (Na2[B4O5(OH)4·8H2O) was found deposited in the boron-sodium ion system, and Li2B2O4·16H2O, Li2B4O7·5H2O, Li2B10O16·10H2O, LiB2O3(OH)·H2O and sassolite in the boron-lithium ion system. The boron isotopic analysis was conducted for santite, K2[B4O5(OH)4]·2H2O, borax and Li2B2O4·16H2O. The separation factor, S, defined as the 11B/10B isotopic ratio of the precipitate divided by that of the solution, ranged from 0.991 to 1.012. Computer simulations for modeling boron mineral formations, in which polyborates were decomposed into three coordinated BO3 unit and four coordinated BO4 unit for the purpose of calculation of their boron isotopic reduced partition function ratios, were attempted to estimate the equilibrium constant, KB, of the boron isotope exchange between the boric acid molecule (B(OH)3) and the monoborate anion (B(OH)4-). As a result, the KB value of 1.015 to 1.029 was obtained. The simulations indicated that the KB value might be dependent on the kind of boron minerals, which qualitatively agreed with molecular orbital calculations independently carried out.

Periodicity in 6Li-to-7Li Isotopic Reduced Partition Function Ratios of Diatomic Lithium Compounds

The UB3LYP/LanL2DZ level calculations were carried out for sixty-seven Li-M diatomic molecules of lithium between LiH and LiBi to explore the periodic properties of their 6Li-to-7Li isotopic reduced partition function ratios (rpfrs) and some other quantities. The Li-M bond distance, the frequency shift upon 7Li/6Li isotope substitution and the rpfr all show plots typical of any chemical and physical property which is a periodic function of the atomic number. The rpfr is strongly correlated with the Li-M bond stretching force constant except for LiH. The present calculations show that the rpfrs of diatomic molecules of group 2, group 12 and group 18 elements are relatively small, which reflects the filled electron shell and subshell characters of those elements. The results of the calculations and the consideration on chemical properties of elements suggest that zinc is a possible substitute for mercury in lithium isotope separation processes utilizing the redox reaction of lithium.

Periodicity in 6Li-to-7Li Isotopic Reduced Partition Function Ratios of Diatomic Lithium Compounds

Periodicity in 6Li-to-7Li Isotopic Reduced Partition Function Ratios of Diatomic Lithium Compounds

Theoretical Estimation of the Solvent Effect of the Lithium Isotopic Reduced Partition Function Ratio

The reduced partition function ratios (RPFRs) of Li + (Solv) n (in which Solv = H 2 O, HAS, and CH 3 OH) clusters with different values were calculated, to investigate the solvent effect of the isotopic effect of the lithium. Structures of three solvated clusters-Li + (H 2 O) n , Li + (H 2 S) n , and Li + (CH 3 OH) n -were optimized by an ab initio molecular orbital method, and their RPFRs were calculated by frequency analysis. The RPFR of the solution was estimated by the extrapolation of the cluster values. The most-stable isomers of all three clusters for n ≥ 4 have four solvent molecules in their first shell. The RPFR is dependent mainly on the number of solvent molecules in the first shell, and the size dependence of the RPFR plateaus at n = 4. The extrapolation of these values can be regarded as the RPFR in the solutions. The RPFRs are ∼1.07 for Li + (H 2 O) n and Li + (CH 3 OH) n and are ∼1.03 for Li + (H 2 S) n . The smaller RPFR of Li + (H 2 S) n is attributed to the smaller binding energy of the Li-S bond, which is weaker than that of the Li-O bond. The present results suggest the possibility of ionophores with S atoms (such as thioether, etc.) for lithium isotopic separation.

Molecular Orbital Estimation of Reduced Partition Function Ratios of Lithium Interacting with Aromatic Hydrocarbons with Condensed Benzene Rings

Molecular orbital calculations at the B3LYP/6-311G(d) level were carried out to elucidate the lithium isotope effects accompanying chemical insertion of lithium from 1-methoxybutane solution containing lithium and naphthalene to graphite. The lithium atom between the graphene layers of graphite was modeled as lithium atoms in 1:1 complexes of lithium and simple aromatic hydrocarbons with condensed benzene rings. The 7Li-to-6Li isotopic reduced partition function ratio (RPFR) was found to be a decreasing function of the number of benzene rings adjacent to the benzene ring above which the lithium atom was located, and was “saturated” at 1.04570 at 25 °C. The most plausible lithium species in the 1-methoxybutane solution was a lithium atom interacting with a naphthalene molecule and solvated by a 1-methoxybutane molecule in the contact ion pair manner. Its RPFR value was 1.07126 at 25 °C. The two RPFR values gave a single-stage separation factor of 1.024 for the lithium isotopes, which agreed well with the experimental value of 1.023.

Solvation of Lithium Ion in Organic Electrolyte Solutions and Its Isotopie Reduced Partition Function Ratios Studied by ab initio Molecular Orbital Method

To explore local structures around lithium ions and to estimate lithium isotopic reduced partition function ratios (RPFRs) ofsolvated lithium ions in ethylene carbonate (EC), methylethyl carbonate (MEC) and EC/MEC mixed solvent systems, ab initio molecular orbital calculations at the HF/6-31G(d) level of theory were carried out. Both EC and MEC were coordinated to lithium ions using their carboxyl oxygens and the Li-O bond distance increase with increasing solvation number up to 4 in the primary solvation sphere both in EC and MEC systems. Binding energy calculations suggested that EC was preferentially coordinated to the lithium ion in the EC/MEC mixed solvent system. RPFRs of solvated lithium ions were convex functions of the solvation number between 1 and 4 and took the maxima at 3 both in EC and MEC systems. The RPFR value in EC/MEC mixed solvent system was estimated to be 1.07818 at 25°C.

Molecular Orbital Estimation of Reduced Partition Function Ratios of Small Water Clusters

Structures of water clusters, (H2O) n , up to n= 10 were optimized at the HF/6–31G(d) level of theory, and H/D and 16O/18O isotopic reduced partition function ratios (RPFRs) at the optimized structures were calculated. The H/D RPFR values were distinctly different between hydrogen-bonded hydrogen atoms and non-hydrogen-bonded hydrogen atoms, but were nearly independent of the cluster size for n equal to 3 or larger when only the lowest-energy conformers are taken into consideration. The 16O/18O RPFR values were also distinct between hydrogen-bonded oxygen atoms and non-hydrogen-bonded oxygen atoms, but little difference in RPFR value was observed between oxygen atoms with one hydrogen bond and those with two hydrogen bonds. The 16O/18O RPFR values were cluster size independent above n=6. The estimation of RPFRs of liquid water thus seemed possible by considering the lowest energy conformers of small water clusters (n=6–10).

Solvation of Lithium Ion in Organic Electrolyte Solutions and Its Isotopic Reduced Partition Function Ratios Studied by ab initio Molecular Orbital Method.

To explore local structures around lithium ions and to estimate lithium isotopic reduced partition function ratios (RPFRs) ofsolvated lithium ions in ethylene carbonate (EC), methylethyl carbonate (MEC) and EC/MEC mixed solvent systems, ab initio molecular orbital calculations at the HF/6-31G(d) level of theory were carried out. Both EC and MEC were coordinated to lithium ions using their carboxyl oxygens and the Li-O bond distance increase with increasing solvation number up to 4 in the primary solvation sphere both in EC and MEC systems. Binding energy calculations suggested that EC was preferentially coordinated to the lithium ion in the EC/MEC mixed solvent system. RPFRs of solvated lithium ions were convex functions of the solvation number between 1 and 4 and took the maxima at 3 both in EC and MEC systems. The RPFR value in EC/MEC mixed solvent system was estimated to be 1.07818 at 25°C.

QUANTUM-STATISTICAL AND PHENOMENOLOGICAL ANALYSIS OF EQUILIBRIUM ISOTOPE EFFECTS

This article discusses theoretical consequences of quantum-statistical representations of logarithm of isotopic reduced partition function ratio (ln β). Among the effects being under consideration are the localization of equilibrium isotope effect on the molecular structural elements in the vicinity of the site of isotopic substitution, distribution of increments of ln β, relationship between ln β values for the substitution of different atoms, and the influence of anharmonicity. The review also presents the phenomenological analysis of ln β for more than 2000 compounds as well as the classification of equilibrium isotope effects according to the causes of their appearance. Methods for the quantitative statistical estimation of the maximum possible isotope separation factors and criteria for the purposeful search for chemical exchange systems applicable for the practical separation of isotopes are also given.

Ab initio Molecular Orbital Calculations of Reduced Partition Function Ratios of Hydrated Lithium Ions in Ion Exchange Systems

Abstract Molecular orbital (MO) calculations at the HF/6-31G(d) level were carried out for the aquolithium ions, Li+(H2O)n (n = 3, 4, 5, 6, 8, 10 and 12) and the aquolithium ions interacting with the methyl sul­fonate ion (MeS-), Li+MeS-(H2O)n (n = 0, 3,4, 5, 6, 7, 8 and 10) which were, respectively, intended to be substitutes for lithium species in the solution and resin phases of ion exchange systems for lithium isotope separation. For each of the species considered, at least one optimized structure with no negative frequency was obtained, and the 7Li-to-6Li isotopic reduced partition function ratio (RPFR) was esti­mated for the optimized structure. The solvation number in the primary solvation sphere was four, both in the solution and resin phases; three waters and MeS" formed the primary solvation sphere in the res­ in phase. Additional water molecules moved off to the secondary solvation sphere. It was found that consideration on the primary solvation sphere alone was insufficient for estimations of reduced parti­tion function ratios of aquolithium ions. Although the agreement between the experimentally obtained lithium isotope fractionation and the calculated results is not satisfactory, it is pointed out that the HF/6-31 G(d) level of the theory is usable for elucidation of lithium isotope effects in aqueous ion exchange systems.

Theoretical Estimation of Lithium Isotopic Reduced Partition Function Ratio for Lithium Ions in Aqueous Solution

The reduced partition function ratio for lithium ions in an aqueous solution is derived from the extrapolation of the values of the reduced partition function ratio ( ) of hydrated lithium ion clusters [Li(H2O)n]+ up to n = 6. In [Li(H2O)n]+ clusters, the values can be calculated from the normal vibration frequencies according to Bigeleisen and Mayer's theory. To obtain the values of , the normal vibration frequency calculations were carried out for optimized structures of [Li(H2O)n]+ (n = 1−6) using the RHF/6-31+G(d), RHF/6-31++G(d,p), RHF/6-311+G(d) and MP2/6-31+G(d) methods by means of the ab initio molecular orbital method. All of those structures having high symmetry were confirmed to have real harmonic frequencies at the RHF/6-31+G(d) and RHF/6-31++G(d,p) levels. For the two RHF methods, the value of increases to about 1.07 with an increase of the hydration number n, and reaches maximum at n = 4. In the most stable isomers of [Li(H2O)n]+ clusters for n = 5 and 6, respectively, the first hydration shell is saturated with the four water molecules, and the size dependence of the values converges for n ≥ 4. The converged value 1.07 can, therefore, be regarded as the reduced partition function ratio for lithium ions in aqueous solution, and gives the upper limit of the isotopic separation factor in an aqueous solution−exchanger system.

Ab initio Molecular Orbital Calculations of Reduced Partition Function Ratios of Polyboric Acids and Polyborate Anions

Abstract Molecular orbital calculations at the HF/6-3 lG(d) level were carried out for polyboric acids and poly-borate anions up to a pentamer to estimate their 11B -to-10B isotopic reduced partition function ratios (RPFRs) and examine the additivity of logarithms of RPFRs. Approximate RPFR-values calculated by the use of the additivity agreed with exact RPFR-values within a margin of 1% error. This error was equivalent to a 5% error on ln(RPFR). The equilibrium constants of mono boron isotope exhange reac-tions between three-coordinate boron and four-coordinate boron ranged from 1.0203 to 1.0360 at 25 °C, indicating the importance of exact evaluation of RPFRs of polymers.

Calculations of Reduced Partition Function Ratios of Monomeric and Dimeric Boric Acids and Borates by the ab initio Molecular Orbital Theory

With the final goal to elucidate boron isotope fractionation observed experimentally, molecular orbital calculations were performed on boric acid and borate monomers and dimers. The geometries of B(OH)3 and B(OH)4 − were first optimized and their vibrational frequencies were calculated at their optimized structures. The estimated 11B-to-10B isotopic reduced partition function ratios (RPFRs) of B(OH)3 and B(OH)4 − and the calculated equilibrium constant of the boron isotope exchange reaction between the two boron species revealed that a more advanced molecular orbital theory with a higher level basis set did not necessarily yield better results. It was concluded that HF/6-31G(d) calculations were most appropriate for the present purpose. The RPFRs of the dimers, H4B2O5, H5B2O6AJA- and H6B2AJA-, estimated from the RPFRs of the monomers by the use of additivity of the logarithm of RPFRs agreed with those calculated using the frequencies of the dimers within a margin of 1%. This error corresponded to the error of 5% on In(RPFR). The equilibrium constant of boron isotope exchange reaction between two boron species among the monomer and dimers at 25°C varied from 1.0207 to 1.0360, indicating the importance of accurate estimation of the RPFRs of polyboric acids and polyborates in real systems.