Theoretical Calculation of Boron Isotopic Separation Factors in Ion

Article pubs.acs.org/jced

Theoretical Calculation of Boron Isotopic Separation Factors in Ion-Exchange Chromatography Fan Zhou, Jingshuang Zhang, Peng Bai, and Xianghai Guo* Department of Pharmaceutical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300350, China Key Laboratory of Systems Bioengineering (Ministry of Education), Tianjin University, Tianjin, 300072, China ABSTRACT: N-Methylglucamine-modified polystyrene (NMG = N-methylglucamine) is a boron-specific resin widely used to remove boron from water by ion-exchange chromatography, which is reported to have the highest separation factor of boron isotopes (10B and 11B) up to date. In this paper, we calculated its boron isotopic separation factor (S) by quantum chemistry. Boric acid in the mobile phase is expected to interact with the functional group of the resin to form a monochelate complex. The polymer chain of the resin is proved to have little influence on S. HF/6-31G level of theory well meets the expectation of current calculations, while the higher level theories (B3LYP, M06-2X, and MP2) lead to larger errors. The inclusion of thermal scaling factors and explicit solvent molecules bring negligible improvement to S. The change of S with different pH values was obtained as well. Finally, S of various functional groups of chelating resins were calculated, among which phenols and carboxylic acids are found to have a distinctly larger S than alcohols.

1. INTRODUCTION There are two boron isotopes, 10B and 11B, existing in nature. 10 B is widely used in nuclear and medical industry for its large cross-section (3837 barns) to absorb thermal neutrons. Meanwhile, the abundance of 10B is required to be more than 85%, which in natural distribution is merely 19.8%.1−6 Many efforts have been done to enrich 10B from nature.7,8 Ion-exchange chromatography is one of the most promising methods, which is efficient, safe, and energy-saving.9−14 As is known, 10B prefers to stay in the resin phase with a tetrahedral geometry [B(OH)4−], while 11B would concentrate in the solution phase with a trigonal structure [B(OH)3].15 In this way, the two boron isotopes will separate from each other through the ion exchange process between the mobile phase (boric acid solution) and stationary phase (solid resin):5,16 10

parts, macroporous polystyrene matrix and functional group. The functional groups are usually polyols, among which N-methylglucamine (NMG) is most studied. It has five hydroxyls and a tertiary amine end that can provide more complexation sites and form a stable complex with boron. Amberlite IRA-743 is an example of a widespread resin with NMG as functional group. Boron, in the form of borate ion, is supposed to esterificate with the polyol parts of the functional group to form a tetrahedron (C):17

And the boron-isotope exchange reaction R1 turns out to be

B(OH)3 (aq) + 11B(OH)4 − = 11B(OH)3 (aq) + 10B(OH)4 −

(R1)

In 1997, Oi et al. calculated the boron-isotope separation factor of Amberlite IRA-743 resin to be 1.022 at 298.15 K by the equation of Kakihana and Kanzaki.17 In 2000, Sonoda et al. measured the separation factor of N-methyl-D-glucamine type resin (MGR) to be 1.027 when pH values of the boric acid solution were less than 7.15 Moreover, molecular orbital calculations have been performed to obtain separation factors between B(OH)3 and B(OH)4−, BF3 and BF3·C6H5OCH3.16,19−21

where the molecules with overbars exist in the resin phase and those without overbars are in the solution phase. Here, the boron isotopic separation factor, S, is defined as S = [10B/11B]resin/[10B/11B]solution.17 It is mainly related to the interaction between boric acid and resin, which highlights the importance of resin in this method. A large separation factor can shorten the length of column and make a great contribution to the industrialization of chromatography. Chelating resin has recently drawn much attention for its relative larger S than the strongly and weakly basic ion-exchange resins.15,17,18 Moreover, its easy regeneration operation makes it possible to be applied in industry. Chelating resin consists of two © XXXX American Chemical Society

Received: September 13, 2016 Accepted: December 5, 2016

A

DOI: 10.1021/acs.jced.6b00802 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Specifications of the Four AIR−Boric Acid Interaction Compounds compd

chemical formula

C1

C7H17NO7

C2

C7H13NO5

C3

C16H28NO7

C4

C16H24NO5

systematic name 4-((1R,2R)-1,2-dihydroxy-3-(methylamino)propyl)2,2-dihydroxy-5-(hydroxymethyl)-1,3,2dioxaborolan-2-uide (3R,5S)-5-hydroxy-3-((methylamino)methyl)2,8,9,10-tetraoxa-1-boratricyclo[4.2.1.11,4]decan1-uide 4-((1R,2R)-3-((4-ethylbenzyl) (methyl)ammonio)1,2-dihydroxypropyl)-2,2-dihydroxy-5(hydroxymethyl)-1,3,2-dioxaborolan-2-uide (3R,5S)-3-(((4-ethylbenzyl) (methyl)ammonio) methyl)-5-hydroxy-2,8,9,10-tetraoxa-1boratricyclo[4.2.1.11,4]decan-1-uide

Scheme 1. Thermochemical Cycle between R3 and R4

Figure 1. Structures of AIR-boric acid interaction models. C1: monochelate structure with only functional group of Amberlite IRA743 involved. C2: tetradentate structure with only functional group of Amberlite IRA-743 involved. C3: monochelate structure with one repeat unit of Amberlite IRA-743 involved. C4: tetradentate structure with one repeat unit of Amberlite IRA-743 involved.

AIR-boric acid interaction models, C1 to C4, and the superscript “*” and “θ” stand for the standard states of solution and gas, respectively. According to the SMD implicit solvation model,23−25 the solvation free energies between the two boron isotopes are the same, that is,

Despite all of the progress made in this regard, quantum chemistry calculation of separation factors of chelating resins has been lacking. Hence, in this manuscript, we first found out the right AIR-boric acid interaction model (Figure 1), which represented the product of the complexation reaction between boric acid and Amberlite IRA-743 (AIR). Then, it was used to perform a large amount of quantum chemistry calculations (Table 5) to find out the method and basis set whose result was in good agreement with the reported value. Meanwhile, the effects of scaling factor and solvent were studied. At last, the chosen method was used to obtain the S of AIR at different pH and S of various functional groups. The results are of big significance for later design and synthesis of chelating resins having large 10B/11B separation factors. There are two viewpoints in literature concerning the interaction of boric acid with Amberlite IRA-743. One is that the borate ion would esterificate with the two cis hydroxyls of NMG group to form a monochelate complex while another opinion supports the formation of a 1:1 tetradentate complex.17,18,22 In order to have further insight into this question, we performed a theoretical research based on the four AIR−boric acid interaction models in Table 1 and Figure 1.

ΔGS*[11B(OH)3 ] = ΔGS*[10 B(OH)3 ]

(2)

ΔGS*[C(10 B)] + ΔGS*[C(11B)]

(3)

So eq 1 can be simplified to θ * (R3) = ΔGgas ΔGaq (R4)

(4)

So in this work, the implicit solvation model is not included. The Gaussian0926 package was used to perform the Hartree− Fock (HF) self-consistent field,27,28 the density functional theory using the exchange-correlation functional (B3LYP29,30 and M06-2X31), and the second-order Møller−Plesset perturbation (MP2)32 methods. The basis sets studied included split valence basis sets (3-21G and 6-31G), polarized basis sets [6-31G(d) and 6-31G(d,p)], and basis sets with diffuse functions [6-31+G, 6-31+G(d), and 6-31+G(d,p)].33 The frequency calculation would help us get Gibbs free energies of the reactants and products in R4. The structures used were optimized first at the same level of theory. Then the equilibrium constant of the reversible reaction R4, the value of which were equivalent with the separation factor, can be calculated by eqs 5 to 7:34

2. COMPUTATIONAL METHODS Noting that the boron-isotope exchange reaction takes place in aqueous solution, the reaction free energy of R3 can be determined using the free energy cycle shown in Scheme 1, according to

θ ΔGgas (R4)/Hartree = G[11B(OH)3 ]/Hartree + G[C(10 B)]

/Hartree − G[10B(OH)3 ]/Hartree − G[C(11B)]/Hartree (5)

θ * (R3) = ΔGgas ΔGaq (R4) + ΔGS*[11B(OH)3 ]

θ 2625.5ΔGgas (R4)/Hartree

+ ΔGS*[C(10 B)] − ΔGS*[10 B(OH)3 ] − ΔGS*[C(11B)]

= −(R /8.314 × 10−3 kJ·mol−1· K−1)(T /K) ln K θ

(1)

where ΔGθgas(R4) is the free energy of R4 in which all reactants and products are in their gas phase, ΔGS* is the aqueous solvation free energy of a given molecule, C represents the four

S = Kθ

(6) (7)

All of the calculations were performed at 298.15 K and 0.1 MPa. B



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Table 2. Calculated Adsorption Energies, ΔE, of the Four AIR−Boric Acid Interaction Models (C1−C4) at Temperature T = 298.15 K and Pressure p = 0.1 MPaa

3. RESULTS AND DISCUSSION 3.1. Adsorption Energies of the Four AIR−Boric Acid Interaction Models. Optimized structures of C1−C4, which were obtained by HF/6-31G level of theory, are displayed in Figure 2. In the structure of C1 and C3, boric acid connects

ΔE (kJ/mol)

a

method

C1

C2

C3

C4

HF/6-31G B3LYP/6-31G MP2/6-31G

−39.2 −40.7 −61.6

340.7 314.1 274.0

−1343.7 −1376.1 −1416.3

−962.9 −990.5 −1030.6

The standard uncertainty is u(ΔE) = 0.1 kJ/mol.

On the other side, errors of R4 (C1) and R4 (C3) are discovered to be obviously less than those of R4 (C2) and R4 (C4) within every theoretical method. An increasing trend of S as well as their error can be found when the theory becomes more and more accurate in every column. For the smallest HF/3-21G, separation factors of R4 (C2) and R4 (C4) are overestimated to be more than 1.03, showing that models of C2 and C4 are inappropriate to reflect the 10B/11B separating situation of AIR. This adds confidence to the conclusion that it is more likely to form the monochelate compound between boric acid and Amberlite IRA-743 than the relatively unstable tetradentate complex. A few water molecules were added into B(OH)3 and the four models’ systems to simulate the solution environment, whose optimized structures are shown in Figure 3. In the figure, hydrogen bonds are found between water molecules and the solutes. The isotope-exchange reaction changes into 10

B(OH)3 (H 2O)3 + C(11B)(H 2O)6 ⇌ 11B(OH)3 (H 2O)3 + C(10 B)(H 2O)6

(R5)

The separation factors in this case are calculated and tabulated in Table 4. Similarly, the S of R5 (C1) and R5 (C3) are closer to 1.022 than R5 (C2) and R5 (C4). The results are found to have small differences (0.004 on average) from those of R4 (C1−C4). This phenomenon agrees with the conclusion from the implicit solvation model made in the second part of this paper. So we can say that solvent has little influence on the results and it is reasonable to use R4 to do the following research. In fact, the calculation becomes very demanding after the addition of water molecules. Furthermore, thermal (ZPE, H, S) scaling factors reported by Radom et al.35,36 were used to calculate S, results of which are listed in the parentheses in Table 3. The same trend is found among them, and the discrepancy between the scaled and unscaled results is also 0.004 on average. Another small difference (about 0.002) can be found between the S of R4 (C1) and R4 (C3) in Table 3, which implies the little impact of polymer chain on S. Considering the calculation cost and time, we chose C1 as the follow-up calculation model. 3.3. Choice of Functional and Basis Sets for Further Calculations. Besides those in Table 3, separation factors of R4 (C1) obtained by other methods and basis sets are presented in Table 5:

Figure 2. Optimized structures of C1−C4 from HF/6-31G.

with the resin by two oxygen atoms and several hydroxyl groups remain free. While in C2 and C4, four hydroxyls are used to esterify with B(OH)4− to form a tetradentate structure. Structures in this figure agree well with those reported by Yoshimura et al.22 In addition, the adsorption energies (ΔE) of C1, C2, C3, and C4 were calculated by HF/6-31G, B3LYP/6-31G, and MP2/6-31G theories. ΔE is defined by ΔE = E(C) + nE(H 2O) − E(AIR) − E(B(OH)4 − )

C = C1−C4, n = 2 (for C1 and C3) or 4 (for C2 and C4), where E is the sum of the corresponding molecule’s electronic and zeropoint energies; n is the number of water molecules. Results are summarized in Table 2, from which we can see some differences between results of the three theories. But the trend that ΔE of C1 (and C3) is less than C2 (and C4) can be discovered for all of them, which implies that the structures of C1 and C3 are more stable. 3.2. Choice of AIR−Boric Acid Interaction Model for Further Calculation. Table 3 shows the calculated separation factors of R4 (C1), R4 (C2), R4 (C3), and R4 (C4) as well as their errors to the only experimental value of 1.022. The values without parentheses were all calculated by molecules’ harmonic frequencies. All S-values in this table fall in the range between 1.015 and 1.060, and their errors are between −31.8% and 172.7%.

All separation factors in this table are larger than 1, which implies that 10B is preferentially fractionated into the resin phase. C



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Table 3. Calculated Separation Factors of R4 with Different AIR−Boric Acid Interaction Models (C1−C4) at Temperature T = 298.15 K and Pressure p = 0.1 MPaa separation factors (S)b c

method

R4 (C1)

error (%)

R4 (C2)

errorc (%)

R4 (C3)

errorc (%)

R4 (C4)

errorc (%)

HF/3-21G HF/6-31G HF/6-31G(d)d HF/6-31G(d,p) B3LYP/6-31G(d)d B3LYP/6-31+G(d,p) MP2/6-31G(d)d

1.017 1.023 1.030 (1.028) 1.032 1.033 (1.027) 1.048 1.031 (1.028)

−22.7 4.5 36.4 (27.3) 45.5 50.0 (22.7) 118.2 40.9 (27.3)

1.033 1.041 1.041 (1.038) 1.043 1.048 (1.041) 1.060 1.044 (1.042)

50 86.4 86.4 (72.7) 95.5 118.2 (86.4) 172.7 100.0 (90.9)

1.015 1.021 1.029 (1.027) 1.030 1.032 (1.028) 1.047 1.030

−31.8 −4.5 31.8 (22.7) 36.4 45.5 (27.3) 113.6 36.4

1.031 1.039 1.039 (1.037) 1.041 1.046 (1.040) 1.057 1.043

40.9 77.3 77.3 (68.2) 86.4 109.1 (81.8) 159.1 95.5

a Standard uncertainty is u(S) = 0.001. bThe experimental value is 1.022 reported in ref 17. c100[(S − 1) − (1.022 − 1)]/(1.022 − 1). dNumbers in parentheses are S calculated with scaling factors.

with its harmonic frequencies calculated from HF/6-31G in Table 6. Besides AIR, the same comparison occurs to 10B(OH)3 and 11B(OH)3. Certain differences are found between calculated and experimental frequencies for all of these three species, but the trend is well-predicted. The correlation coefficients squared (R2) between experimental and theoretical frequencies of 10 B(OH)3, 11B(OH)3, and AIR are 0.970, 0.966, and 0.985, respectively. Moreover, the isotopic shifts between 10B(OH)3 and 11B(OH)3 are listed in the five, six, and seven columns, from which we can see that the errors between experimental and theoretical shifts are relatively small (−25 cm−1 to 23 cm−1); i.e., harmonic frequencies from HF/6-31G can well reflect the difference between the two boron isotopes. This may be the reason for an accurate separation factor. As Liu et al. said, the isotopic effect on frequencies are usually in mid-IR range, so that higher theoretical levels which can often produce better lowfrequency positions are simply unnecessary here.37 The use of HF and small basis set for isotopic calculations were also supported by Oi and Schauble.16,38 Another explanation for the present conclusion is that the approach we used (static electronic structure calculations for small clusters) does not capture the large configurational space characteristic of the polymer resin and there may exist canceling effect of the errors. So further research is needed on this issue. Accordingly, taking into consideration the accuracy and cost, we choose the HF/6-31G method for the following calculations about different pH and different functional groups, and the scaling factors are not considered any more. 3.4. Separation Factors of R4 (C1) at Different pH Values. As reported by Kakihana et al.,5 the main species formed in aqueous solution of boric acid were B(OH)3, B3O3(OH)4− (1,3,5,2λ4,4,6-trioxatriborinane-2,2,4,6-tetraol), B3O3(OH)52− (1,3,5,2λ4,4λ4,6-trioxatriborinane-2,2,4,4,6-pentaol), and B(OH)4−. Figure 4 depicts their optimized structures from HF/6-31G. Boron and oxygen atoms have a trigonal and planar structure in B(OH)3 and a tetrahedral structure in B(OH)4−, while in B3O3(OH)4− and B3O3(OH)52−, they have both trigonal and tetrahedral structures.

Figure 3. Optimum structures of B(OH)3(H2O)3, C1(H2O)6, C2(H2O)6, C3(H2O)6, and C4(H2O)6 from HF/6-31G.

This phenomenon exactly agrees with what was found by experiment. In addition, we can see a gradually increasing tendency of S and its error from the top to the bottom, which illustrates that high level basis sets are unnecessary for calculations here. In every line, the post-HF and density functional theories do not necessarily yield better S-values than HF. The smallest error comes from HF/ 6-31G in Table 5. Also, scaling factors were used to obtain values in the parentheses, which show a same trend with the unscaled ones. A negligible improvement is discovered after scaling. So it is acceptable to calculate separation factors by harmonic frequencies. Frequencies of Amberlite IRA-743 resin (AIR) were obtained using FT-IR (Thermo NICOLET 6700), which are compared

Table 4. Calculated Separation Factors of R5 with Different AIR−Boric Acid Interaction Models (C1−C4) at Temperature T = 298.15 K and Pressure p = 0.1 MPaa separation factors (S)b

a

method

R5 (C1)

errorc (%)

R5 (C2)

errorc (%)

R5 (C3)

errorc (%)

R5 (C4)

errorc (%)

HF/6-31G B3LYP/6-31G(d)

1.018 1.029

−18.2 31.8

1.038 1.042

72.7 90.9

1.026 1.034

18.2 54.5

1.040 1.043

81.8 95.5

The standard uncertainty is u(S) = 0.001. bThe experimental value is 1.022 reported in ref 17. c100[(S − 1) − (1.022 − 1)]/(1.022 − 1). D



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Table 5. Calculated Separation Factors of R4 (C1) by Different Methods and Basis Sets at Temperature T = 298.15 K and Pressure p = 0.1 MPaa separation factors (S)b c

3-21G 6-31G 6-31+G 6-31G(d) 6-31+G(d) 6-31G(d,p) 6-31+G(d,p)

d

c

HF

error (%)

B3LYP

1.017 (1.015) 1.023 1.029 1.030 (1.028) 1.033 (1.030) 1.032 (1.029) 1.033

−22.7 (−31.8) 4.5 31.8 36.4 (27.3) 50.0 (36.4) 45.5 (31.8) 50.0

1.027 1.032 1.033 (1.027) 1.036 1.035 1.048 (1.036)

errord (%)

M06-2X

errord (%)

MP2c

errord (%)

22.7 45.5 50.0 (22.7) 63.6 59.1 118.2 (63.6)

1.024 1.028 1.027 1.031 1.027 1.031

9.1 27.3 22.7 40.9 22.7 40.9

1.025 1.029 1.031 (1.028)

13.6 31.8 40.9 (27.3)

1.031

40.9

a Standard uncertainty is u(S) = 0.001. bThe experimental value is 1.022 reported in ref 17. cNumbers in parentheses are S calculated with scaling factors. d100[(S − 1) − (1.022 − 1)]/(1.022 − 1).

Table 6. Vibrational Frequencies (cm−1) of Gas-Phase B(OH)3 and Amberlite IRA-743 Resin (AIR) at Temperature T = 298.15 K and Pressure p = 0.1 MPaa 10

11

B(OH)3 d

harmonic

exptl

438 438 537 757 1046 1046 1051 1572 1573 4100 4100 4104

545 545 668 880 1060 1195 1195 1490 1490 3150 3150 3150

isotopic shiftb

B(OH)3 d

harmonic

exptl

436 436 533 734 1045 1045 1051 1519 1520 4100 4100 4104

544 544 639 880 1060 1183 1183 1428 1428 3150 3150 3150

AIRc e

harmonic

exptl

error

2 2 4 23 1 1 0 53 53 0 0 0

1 1 29 0 0 12 12 62 62 0 0 0

1 1 −25 23 1 −11 −12 −9 −9 0 0 0

harmonic

exptl

323 542 673 1132 1168 1324 1399 1432 3129 3940 3992

557 812 853 1038 1080 1459 1510 1659 2921 3400 3746

Harmonic frequencies are all calculated from HF/6-31G. Standard uncertainty of the harmonic frequency is u = 1 cm−1. Expanded uncertainty of the isotopic shift is Uc = 2 cm−1. bThe frequency difference between 10B(OH)3 and 11B(OH)3. cOnly peak frequencies are listed. dThe data are from ref 16. eIsotopic shift (harmoni) − isotopic shift (exptl). a

Figure 4. Optimized structures of B(OH) 3 , B 3 O 3 (OH) 4 − , B3O3(OH)52−, and B(OH)4−.

When there exist B3O3(OH)4−, B3O3(OH)52−, and B(OH)4− in solution, R4 changes into the following three reactions, R6, R7, and R8 (all molecules are gases in our calculations). The exchanged boron atoms in B3O3(OH)4− and B3O3(OH)52− are those who have trigonal structures. Tetrahedral boron atoms are not chosen for that their separation factors are proven to be unity or so (R8). Separation factors of R6, R7, and R8, calculated by HF/6-31G, are shown in Table 7. A decreasing trend can be found from left to right in the table. The contents of the above four species differ with pH values. When the pH is lower than 6, there exists only B(OH)3 in solution, and R4 takes place, the separation factor of which is 1.023 mentioned in Table 3 and Table 5. With the increase of pH, B3O3(OH)4−, B3O3(OH)52−, and B(OH)4− continually arise in solution, and S begins to decline due to the

existence of R6, R7, and R8. At last, when pH is greater than 10, only B(OH)4− and R8 remain which makes S tend to 1 (1.004). This variation trend of S is in keeping with what was reported by Sonoda et al.15 Hence, acidic conditions are more favorable for the separation of boron isotopes and the quantity of B3O3(OH)4−, B3O3(OH)52−, and B(OH)4− in solution should be controlled. E



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two groups are promising in promoting the industrialization of chromatography. So the active development of such resins is strongly needed then.

Table 7. Calculated Separation Factors (S) of Different Boron-Isotope Exchange Reactions at Temperature T = 298.15 K and Pressure p = 0.1 MPaa S a

R6

R7

R8

1.020

1.017

1.004

■

Standard uncertainty is u(S) = 0.001.

*E-mail: [email protected]. Phone: +86-22-27406869. Fax: +86-22-27406869. Address: Tianjin University, No. 135, Yaguan Road, Jinnan District, Tianjin 300350, China.

3.5. Separation Factors of Various Functional Groups in Chelating Resins. Besides NMG, reported functional groups of various chelating resins also include catechol, propanediol, 2,4-dihydroxybenzoic, and so on.39−43 To have a look at their separation performance toward 10B and 11B, we calculated their separation factors under the assumption that they all form monochelate complexes with boron. Table 8 lists the results from

ORCID

Fan Zhou: 0000-0001-8332-5828 Xianghai Guo: 0000-0002-1519-4050 Funding

This research was supported by the National Natural Science Foundation of China (No. 21202116), Independent Innovation Foundation of Tianjin University (No. 2016XZC-0071), and Natural Science Foundation of Tianjin (No. 16JCYBJC20300).

Table 8. Calculated Separation Factors of Various Functional Groups at Temperature T = 298.15 K and Pressure p = 0.1 MPaa functional groups

Notes

separation factors (S)

The authors declare no competing financial interest.

Alcohols glycol propanediol glycerol mannitol sorbitol glucose Phenols catechol 3-nitro catechol 3-methyl catechol Carboxylic Acids salicylic acid 2,4-dihydroxybenzoic phthalic acid a

AUTHOR INFORMATION

Corresponding Author

■

1.021 1.023 1.019 1.023 1.024 1.015

ACKNOWLEDGMENTS We thank Dr. Peng Bai (University of Minnesota) for his suggestions on a draft of this manuscript.

■

REFERENCES

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1.028 1.029 1.028 1.026 1.026 1.023

The standard uncertainty is u(S) = 0.001.

HF/6-31G. A small difference is found between molecules of alcohols, the average of which is 1.021. Phenols and carboxylic acids have separation factors obviously larger than alcohols, the average of which are 1.028 and 1.025, respectively. So these two kinds of functional groups are promising alternatives to NMG, whose larger factors can greatly reduce the equipment investment. But back to where we were, this conclusion needs many more experimental efforts to verify.

4. CONCLUSIONS Theoretically speaking, boric acid is more likely to react with the two cis hydroxyls of NMG to form complexes like C1 and C3, which are more stable than C2 and C4. The calculated results of S from C1 and C3 are closer to the experimental value. Moreover, HF theory with the 6-31G basis set meets our expectations for calculating boron isotopic separation factors of chelating resins. Advanced theories and higher basis sets in this paper will lead to larger errors, which may be caused by static electronic structure calculations for small clusters that does not capture the large configurational space characteristic of the polymeric resin. Thermal scaling factors and the solvent have little effect on the results of S. Furthermore, that S decreases with the increase of pH is successfully validated by calculating S between different borates and C1. Finally, in view of the separation factor, carboxylic acids and phenols are better than alcohols. Chelating resins with the former F



Article

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Theoretical Calculation of Boron Isotopic Separation Factors in Ion

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