Protonation Equilibria and Stepwise Hydrolysis Behavior of a Series of

ARTICLE pubs.acs.org/JPCB

Protonation Equilibria and Stepwise Hydrolysis Behavior of a Series of Thiomonophosphate Anions Hideshi Maki,* Yoshiki Ueda, and Hiroyuki Nariai Department of Chemical Science and Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, Hyougo 657-8501, Japan ABSTRACT: The stepwise protonation constants of a series of thiomonophosphate anions, i.e., monothiomonophosphate, dithiomonophosphate, trithiomonophosphate, and tetrathiomonophosphate anions, were determined by 31P NMR chemical shift measurements in aqueous solution. Despite the remarkably fast hydrolysis rates of these anions, the protonation processes of all thiomonophosphate anions may be evaluated accurately without any previous purification, because the NMR signals corresponding to thiomonophosphate anions and hydrolyzed residues are well resolved. The stepwise protonation constants decrease with an increase in the number of sulfur atoms bound to the central phosphorus atom. It was revealed that the logarithms of the stabilities of the proton complexes of the series of thiomonophosphate anions decrease “linearly” with an increase in the number of sulfur atoms in the anions. The intrinsic 31 P NMR chemical shifts due to orthophosphate and tetrathiomonophosphate anions show upfield shifts upon successive protonations of the anions, whereas the shifts of mono-, di-, and trithiomonophosphate anions move downfield relative to the anions upon protonation. Furthermore, more asymmetric molecular structures experience greater changes in their X
P
Y bond angles upon protonation or complex formation, leading to drastic changes in the nuclear screening. The symmetry of the molecular structure is related to the direction of the 31P NMR chemical shift change upon successive protonation of thiomonophosphate anions.

1. INTRODUCTION The thiomonophosphate anions, i.e., dithiomonophosphate anion, PO2S23-, trithiomonophosphate anion, POS33-, and tetrathiomonophosphate anion, PS43-, are very unstable in water. As previously described, the rate of the substitution of water oxygen for sulfur in these thiomonophosphate anions is remarkably fast,1 and so it is hard to measure the protonation constants of these anions using thermodynamic methods, such as potentiometric titration. Accordingly, in contrast to the well-known protonation behavior of polyphosphate anions, little work has been carried out on the protonation equilibria of the series of thiophosphate ligands.2
4 In recent years some studies have been made on monothiomonophosphate derivatives.5
11 The fundamental kinetics of the hydrolytic behavior of monothiophosphate analogues are very useful for biochemical applications such as nucleic acid metabolism and enzyme reactions.12
17 The Brønsted plot for the nonenzymatic hydroxide catalyzed hydrolysis of a diethyl thiophosphate substrate showed a linear dependence between the pseudo-first-order rate constant and the pKa of the substrate,8 and the hydrolytic dethiophosphorylation and desulfurization of 20 -, 30 -, and 50 -phosphoromonothioates have been investigated from the pH-Rate profiles of the hydrolytic reactions and the acid
base properties of these anions.9 Song et al., have studied in detail the protonation properties of adenosine 50 -O-thiomonophosphate in aqueous solution.10 Sigel et al. have not only r 2011 American Chemical Society

determined the 1:1 complex formation constants of 50 -O-thiomonophosphate but also used linear free energy relationships to nczyk et al. consider the structures of the complexes.11 Salamo
have accomplished the divergent syntheses of new dendritic polythionophosphates by simple one-pot phosphitylation of monothiophosphate derivatives.18,19 However, so far studies of the other, i.e., di-, tri-, and tetrathiomonophosphate derivatives have been scarce. Since these thiomonophosphates hydrolyze readily in aqueous solution, the acid
base properties and the complex formation behavior are difficult to observe. This work is intended as an investigation of the protonation behaviors of not only the monothiophosphate anion but the di-, tri-, and tetrathiomonophosphates that are diverse analogues of several thiophosphate derivatives. It is expected that this information will be useful for the interpretation of the protonation and complex formation behavior of the derivatives. However, it is difficult to investigate the protonation behavior of the thiomonophosphate anions by a general thermodynamic technique such as potentiometric titration because of the hydrolyses of the anions; hence, to overcome this problem, 31P NMR spectroscopy was employed in this work. NMR is used extensively to monitor chemical changes Received: December 14, 2010 Revised: February 28, 2011 Published: March 14, 2011 3571

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happening during chemical equilibria and is particularly useful because the signal from starting materials, intermediate and side products may be resolved, allowing the progress of a reaction to be productively examined without previous purification. In the present study, the stepwise protonation constants along with the intrinsic 31P NMR chemical shifts of the phosphorus nuclei belonging to the series of thiomonophosphate anions have been evaluated using pH titration profiles of the appropriate 31P NMR chemical shifts. The directions and the magnitudes of these phosphorus shift changes are compared.

2. EXPERIMENTAL METHODS 2.1. Chemicals. All chemicals used in this work were of analytical grade. The sodium salt of monothiomonophosphate dodecahydrate, Na3PO3S 3 12H2O, was synthesized via hydrolysis of P2S5.20,21 A 20 g sample of P2S5 was added gradually to 100 mL of 5 mol L
1 NaOH aqueous solution and reacted for 10 min below 50 °C with stirring. The precipitate was removed by suction filtration; 40 mL of ethanol was then added to the filtrate, and this mixture was placed on ice. The reaction product was collected by suction filtration, washed with acetone, and dried in air. About 40 g of the product was dissolved in 140 mL of water, heated to 70 °C, and cooled immediately to 60 °C. Then 40 mL of ethanol was added, and the mixture was cooled on ice and then filtered by suction. About 10 g of the precipitate was dissolved in 70 mL of water below 50 °C and filtered by suction. The filtrate was then cooled gradually on ice and 7.8 g of pure Na3PO3S 3 12H2O was prepared. The total yield was 11%. The successful synthesis of Na3PO3S 3 12H2O without hydrolysis was confirmed, since an aqueous solution of the salt produced only a singlet resonance in the 31P NMR spectrum. Anal. Calcd: Na, 17.41; P, 7.82; S, 8.09; H2O, 54.57. Found: Na, 17.82; P, 7.98; S, 7.70; H2O, 52.98. The sodium salt of tetrathiomonophosphate octahydrate, Na3PS4 3 8H2O, was synthesized via addition of P2S5 to Na2S 3 9 H2O as previously reported.20 Then 80 g of Na2S 3 9H2O and 8 g of P2S5 were mixed in a porcelain dish, the mixture was melted at 1000 °C and reacted for 15 min. Next, 80 mL of boiling water was added to the melt, and filtered immediately. After leaving for 1 day, the precipitate was collected by suction filtration, and 20 g of the reaction product was dissolved in 100 mL of 0.025 mol L
1 Na2S þ 0.1 mol L
1 NaOH aqueous solution. The solution was cooled on ice and 120 mL of ethanol was added; 6.5 g of pure Na3PS4 3 8H2O was prepared. The total yield was 24%. Anal. Calcd: Na, 18.52; P, 8.32; S, 34.45; H2O, 38.71. Found: Na, 18.90; P, 8.39; S, 33.88; H2O, 39.61. 2.2. 31P NMR Measurements. All NMR spectra were recorded on a Bruker DPX-250 (5.87T) superconducting Fouriertransform pulse NMR spectrometer with a 10 mm tunable broadband probe was used at 101.258 MHz at 25.0 ( 1.0 °C. An acquisition time was 1.0 s, and the FID were collected in 50000 data points, and was used a sweep width of 25 kHz, that is, the digital resolution in the frequency dimension was 1.0 Hz (0.0099 ppm). In order to avoid saturation of the resonances, the intervals between each FID scan were 5.0 s or over.22 The NMR chemical shifts were recorded against an external standard of 85% H3PO4 in 10% D2O. Since it was not added D2O to all sample solutions in order to retain the solvent purity, the spectrometer were not field-frequency locked during the measurement of all sample solutions. All spectra were recorded in the absence of 1H decoupling. A 3 mL quantity of ca. 0.01 mol L
1 Na3PO3S or

Figure 1. Representative 31P NMR spectra of a ca. 0.01 mol L
1 Na3PO3S aqueous solution at 101.258 MHz in the absence of 1H decoupling. All resonances are singlets. Experimental details are given in the text.

Na3PS4 added to the 10 mmφ NMR tube. Small aliquots of HNO3 or NaOH aqueous solution was added by a micro syringe in order to define the pH of the solutions, and the pH meter readings were recorded just before the 31P NMR measurements. The pH meter readings were carried out with an Orion 250A pH meter. In the case of Na3PO3S aqueous solution, which hydrolyzes not so rapidly, HNO3 or NaOH aqueous solution was added stepwise, in the case of Na3PS4 aqueous solution, which hydrolyze very rapidly, the sample solutions were prepared newly every 31P NMR measurements. All 31P NMR measurements were carefully carried out at an ionic strength of 0.10 by NaNO3. 2.3. Potentiometric Titrations. Stepwise protonation constants of a monothiomonophosphate anion were also determined by potentiometric titrations in a thermostatting titration cell at 25.0 ( 0.5 °C. A potentiometer (an Orion 720A Ionalyzer) equipped with a glass electrode (an Orion 91
01) and a single junction reference electrode (an Orion 90
01) was used for a potentiometric titration. Before and after the titrations of the sample solutions, the glass electrode was calibrated as a hydrogen concentration probe by titrating known amounts of HNO3 with CO2-free NaOH solutions and determining the equivalence point by Gran’s method23 that determines the standard potential, E0, and the liquid junction potential, j. Titrant solutions containing a 0.01 mol L
1 Na3PO3S were titrated with a standard HNO3 solution. All the titration procedures were carried out under N2 atmosphere in 0.10 mol L
1 NaNO3 as a supporting electrolyte.

3. RESULTS AND DISCUSSION Representative 31P NMR spectra of Na3PO3S and Na3PS4 aqueous solutions are shown in Figures 1 and 2, respectively; monothiomonophosphate anions in Na3PO3S aqueous solution produced only a singlet resonance at all pH values as shown in Figure 1, whereas Na3PS4 aqueous solution produced three singlet resonances at all pH values as shown in Figure 2. This 3572

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Figure 2. Representative 31P NMR spectra of a ca. 0.01 mol L
1 Na3PS4 aqueous solution at 101.258 MHz in the absence of 1H decoupling. All resonances are singlets. Experimental details are given in the text. The three resonances arise from (a) tetrathiomonophosphate anions, (b) trithiomonophosphate anions, and (c) dithiomonophosphate anions. The details for each resonance assignment are given in the text.

suggests that Na3PS4 aqueous solution contains at least three magnetically inequivalent phosphorus nuclei. Maier and Van Wazer have reported that P
S linkages appear to be cleaved very quickly and that the sulfur atoms are rapidly substituted by oxygen atoms from the water.1 Klement suggests that tetrathiomonophosphate anions hydrolyze stepwise to trithiomonophosphate (POS33-), dithiomonophosphate (PO2S23-), and monothiomonophosphate (PO3S3-) anions in water. A previous qualitative investigation of the hydrolysis of the tetrathiomonophosphate anion (PS43-) indicates a half-life for this species of ca. 20 min in water at 25 °C.20 The hydrolysis rate of PO2S23- is relatively slow under the experimental conditions used in this work, so the resonance due to HnPO3S(3
n)
(n = 0
3) has not been detected on the spectra of Na3PS4 aqueous solutions shown in Figure 2. It follows from what has been discussed that the protonation equilibrium for HnPO3S(3
n)
(n = 0
3) may exist in Na3PO3S aqueous solution as follows: PO3 S3
þ 3Hþ h HPO3 S2
þ 2Hþ h H2 PO3 S
þ Hþ h H3 PO3 S0

ð1Þ

(3
n)


(3
n)


(n = 0
3), HnPOS3 and the equilibria for HnPO2S2 (n = 0
3), and HnPS4(3
n)
(n = 0
3) coexist in Na3PS4 aqueous solution as follows: PO4
m Sm 3
þ 3Hþ h HPO4
m Sm 2
þ 2Hþ h H2 PO4
m Sm
þ Hþ h H3 PO4
m Sm 0

ðm ¼ 2
4Þ ð2Þ

In general, the 31P NMR chemical shift changes with the variation in the electronegativity difference between the central

Figure 3. 31P NMR chemical shifts of various thiomonophosphate anions as a function of pH at 25.0 ( 1.0 °C and I = 0.10 (NaNO3). Solid lines refer to the calculated curves by the use of the pertinent parameters of Tables 1 and 2, see eq1. Key: (a) HnPO3S(3
n)
(n = 0
3); (b) HnPO2S2(3
n)
(n = 0
2); (c) HnPOS3(3
n)
(n = 0
2); (d) HnPS4(3
n)
(n = 0
2).

phosphorus atom and its adjacent substituents, and a decrease in the electronegativity of the adjacent substituents will cause a downfield shift of the 31P NMR resonance of the central phosphorus atom.24 Hence the three resonances can be seen in Figure 2, where the lowest field resonances (a) were assigned to HnPS4(3
n)
(n = 0
3), the highest field resonances (c) to HnPO2S2(3
n)
(n = 0
3) and the intermediate field resonances (b) to HnPOS3(3
n)
(n = 0
3). As can be seen in Figures 1 and 2, the pH dependence of the chemical shifts of the series of thiomonophosphate anions can be interpreted in terms of the protonation of these thiomonophosphate anions. The pH titration profiles of the 31P NMR chemical shifts of the phosphorus atoms belonging to the anions are shown in Figure 3. In spite of the presence of many kinds of protonated species, only sharp singlet resonances are observed in the 31P NMR spectra over the entire pH range. This indicates that the proton exchanges of these thiomonophosphate anions are much faster than the NMR time scale.25 Therefore, the NMR chemical shifts of the phosphorus nuclei belonging to the anions, HnL(3-n)(n = 0
3, L = PO3S, PO2S2, POS3, PS4), are averaged by fast exchange over all species that are present in the equilibria 1 and 2, and can be written as26 δP ¼

δL3
½L3
 þ δHL2
½HL2
 þ δH2 L
½H2 L
 þ δH3 L ½H3 L CL ðL ¼ PO3 S, PO2 S2 , POS3 , PS4 Þ

ð3Þ

where CL is the total concentration of the ligand in solution, δP is the observed 31P NMR chemical shift, and δL3-, δHL2-, δH2L
, and δH3L refer to the intrinsic chemical shifts of the phosphorus nuclei belonging to each species. In addition, the stepwise 3573

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protonation constants of the thiomonophosphate anions, Kn (n = 1
3), are defined as follows: Kn ¼

½Hn Lð3
nÞ
 ðn ¼ 1
3Þ ½Hþ ½Hn
1 Lð4
nÞ


ð4Þ

Using the mass action law for this system of equilibria, the observed chemical shift can be expressed as:

HnPO3S(3
n)
(n = 0
2), n, can be calculated by dividing the concentrations of bound Hþ ions, [Hþ]b, by the total concentration of ligand ions, CL. Because [Hþ]b is given as the difference of the total concentration of Hþ ions, CH, and the free Hþ ion concentration of the equilibrium solution, [Hþ], n can be determined as follows: n¼

3

δP ¼

ðδL3
þ

∑ K1 :::Ki ½Hþ i δH L

ð3
iÞ


i

i¼1

Þ

3

ð1 þ

∑ K1:::Ki ½Hþ i Þ

ð5Þ

ð6Þ

Using eq 4, n can also be expressed as follows: n¼

i¼1

The values of the stepwise protonation constants and intrinsic chemical shifts that minimize the error-square sum of chemical shifts, Σ(δP,obs
δP,calc)2, were calculated using a nonlinear least-squares curve-fitting method. The logarithmic stepwise protonation constant, log Kn, and the intrinsic chemical shift of each species thus obtained from plots of δP versus pH (Figure 3) are listed in Tables 1 and 2, respectively. The log K3 and δP values of H3PO2S20, H3POS30, and H3PS40 could not be computed, because these triprotonated species were barely formed at any pH in this work. The solid lines in Figure 3 are calculated curves obtained by using the pertinent values from Tables 1 and 2 and show good agreement with the experimental results. Moedritzer et al. have measured the 31P NMR chemical shifts of free PO3S3-, PO2S23-, and POS33- ligands in aqueous solutions containing 3% Na2S as: δPO3S3
= 33.8 ppm, δPO2S23
= 61.9 ppm and δPOS33
= 86.5 ppm.29 The above values are in good agreement with the parameters in Tables 1 and 2, supporting the 31P NMR peak assignment and data treatment of our work. On the other hand, another interesting feature can be seen in Figure 1. The line width of the singlet peak at pH 7.47 is noticeably broader than the other peaks. The comparatively low frequency radiation used for NMR spectroscopy and the small natural linewidths obtained, means that many time-dependent chemical processes affect the NMR spectra profoundly. The time-dependent process in the singlet peak at pH 7.47 is the exchange rate of the protonation equilibria between the oxygen atom and the sulfur atom in a HnPO3S(3
n)
(n = 0
2) anion indeed. The exchange rate in acidic and alkaline conditions is much faster than 31P NMR time scale. In a neutral pH region, however, since the exchange rate slows down remarkably, the proton exchange perturbs the 31P NMR relaxation due to a HnPO3S(3
n)
(n = 0
2) anion, as a consequence the line width of the NMR resonance increases. The hydrolysis rate of PO3S3- is slower than those of PO2S23
, POS33
, and PS43
, so the log Kn (n = 1
3) values of HnPO3 S(3
n)
(n = 0
2) can be determined by a potentiometric titration method. The average number of bound Hþ ions per

½Hþ b ðCH
½Hþ Þ ¼ CL CL

K1 ½Hþ  þ 2K1 K2 ½Hþ 2 þ 3K1 K2 K3 ½Hþ 3 1 þ K1 ½Hþ  þ K1 K2 ½Hþ 2 þ K1 K2 K3 ½Hþ 3

ð7Þ

The n versus log [Hþ] plots obtained for HnPO3S(3
n)
(n = 0
2) are shown in Figure 4. The log Kn (n = 1
3) values at 25.0 ( 0.5 °C and I = 0.10 (NaNO3) have been obtained from the nonlinear least-squares curve-fitting as log K1 = 9.83 ( 0.02, log K2 = 5.22 ( 0.05, and log K3 = 0.97 ( 0.02. The solid line in Figure 4 is calculated from the appropriate log Kn (n = 1
3) values, and shows good agreement with the experimental results. It should be noted that the log Kn (n = 2
3) values determined by the 31P NMR and potentiometric titration methods were almost within experimental error of one another, despite the difference in principles of the two methods. This indicates the validity of the stepwise protonation constants as well as the intrinsic shift values evaluated by the present study. On the other hand, there is also a difference between the log K1 values determined from both methods, i.e., 9.83 (potentiometric titration) and 10.12 (31P NMR). This inconsistency has not been observed for any other condensed polyphosphates or imidopolyphosphates. This implies that that cationic Naþ counterions form a 1:1 complex with the thiomonophosphate anion. This complex formation reduces the partial negative charge of the central phosphorus atom, facilitating the nucleophilic attack on the central phosphorus atom from bulk water molecules, and accelerating the hydrolysis rates of thiomonophosphate anions, as shown in Scheme 1. This acceleration is remarkable in case of PO2S23
, POS33
, and PS43
, and the protonation constants of these anions cannot be determined by potentiometric titration. Because a potentiometric titration requires many hours, these anions hydrolyze to PO3S3- anion during the titration. Kura have reported that the ion-pair formation between phosphorus groups and Naþ ions in aqueous solution of inorganic cyclic polyphosphates renders the phosphorus atom more positive by reducing the electron density around the phosphorus atom and more susceptible to the nucleophilic attack by OH
anion from the water.30,31 His work adequately supports our discussion about the accelerating the hydrolysis rates of thiomonophosphate anions.

Table 1. Logarithmic Stepwise Protonation Constants of Various Thiomonophosphate Anionsa Determined by the pH Profiles of 31 P NMR Chemical Shifts of the Anions in Aqueous Solutions,b T = 25.0 ( 1.0 °C, I = 0.10 (NaNO3) HnPO4(3
n)


HnPO3S(3
n)


HnPO2S2(3
n)


log K1

12.33c,d

10.12 ( 0.02 (9.83 ( 0.02)e

log K2

c,d

7.20

5.25 ( 0.01 (5.22 ( 0.05)e

log K3

2.15c,d

0.99 ( 0.01 (0.97 ( 0.02)e

HnPOS3(3
n)


HnPS4(3
n)


8.37 ( 0.03

7.55 ( 0.05

6.19 ( 0.04

3.90 ( 0.01

3.35 ( 0.03

2.82 ( 0.03

f

f

f

The errors given are equimultiple the standard deviation resulting from the nonlinear least-squares calculations. b In the absence of D2O for fieldfrequency locking. c From ref 27. d At 25 °C, and no supporting electrolyte was added. e These constants determined by potentiometric titrations at 25.0 ( 0.5 °C and I = 0.10 (NaNO3) in this work. f Corresponding species were scarcely formed. a

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Table 2. Intrinsic 31P NMR Chemical Shifts of Various Thiomonophosphate Anionsa Determined by the pH Profiles of 31P NMR Chemical Shiftsb of the Anions in Aqueous Solutions,c T = 25.0 ( 1.0 °C, I = 0.10 (NaNO3) HnPO4(3
n)


HnPO3S(3
n)


HnPO2S2(3
n)


HnPOS3(3
n)


HnPS4(3
n)


δL3
/ppm

5.3d,e

30.83 ( 0.03

60.78 ( 0.06

85.25 ( 0.07

109.74 ( 0.02

δHL /ppm δH2L
/ppm

3.1d,e 0.4d,e

35.35 ( 0.03 44.75 ( 0.03

69.36 ( 0.08 89.79 ( 0.11

91.96 ( 0.13 101.77 ( 0.13

106.17 ( 0.05 100.18 ( 0.09

2


δH3L/ppm

0d,e

54.71 ( 0.05

f

f

f

a

The errors given are equimultiple the standard deviation resulting from the nonlinear least-squares calculations. b Referenced to external 85% H3PO4. c In the absence of D2O for field-frequency locking. d From ref 28. e At 27 °C, and a saturated aqueous solution of Na3PO4 was used. f Corresponding species was scarcely formed.

Figure 4. Potentiometric titration curves of the protonation for a monothiomonophosphate anions at 25.0 ( 0.5 °C and I = 0.10 (NaNO3). Solid line refers to the calculated curve by the use of the pertinent parameters of log K1 = 9.83, log K2 = 5.22, and log K3 = 0.83; see eq7.

Scheme 1. Stepwise Nucleophilic Attack to the Central Phosphorus Atom of Sodium Complex of the Series of Thiomonophosphate Anions

As previously studied by Irani et al.32 and by Miyajima et al.,33 the protonation constants of imidopolyphosphate and cycloimidopolyphophate anions increase with an increase in the number of imino groups that constitute the ligand molecules.

Figure 5. Variation of the logarithmic stepwise protonation constants of various thiomonophosphate anions at 25.0 ( 1.0 °C and I = 0.10 (NaNO3) against the number of sulfur atoms attached to the central phosphorus atom of the anions. Key: (b) log K1; (2) log K2; (9) log K3.

Miyajima et al. suggested that the increase in the basicities of the anions can be interpreted in terms of the difference in the electronegativity of the bridging oxygen and nitrogen atoms. On the other hand, the log Kn values of the series of thiomonophosphate anions decrease with an increase in the number of sulfur atoms neighboring the central phosphorus atom, nS, as can be seen in Figure 5, showing that the thiomonophosphoric acids become stronger acids because of the substitution of oxygen with sulfur. Because the difference in the electronegativity of the oxygen and sulfur atoms is larger than that of oxygen and nitrogen atoms, the lower affinity of thiomonophosphate anions for Hþ is not adequately explained by the electronegativity difference. On the hard and soft acids and bases (HSAB) scale, a basic negative donor forms a high stability complex with “hard” cations such as Hþ. Thio groups are not as “hard” on the HSAB scale, so the thiomonophosphate anions form less stable complexes with Hþ. It must be noted that the affinities of thiomonophosphate anions for Hþ are affected cumulatively by the less basic negativity of the anions; hence, the log Kn values decrease linearly with an increase in the number of constituent sulfur atoms within the anions. The correlation of the intrinsic 31P NMR chemical shifts of the series of thiomonophosphate anions and the electric charge on the anions, z, is shown in Figure 6. The successive protonation of the thiomonophosphate anions results in a shift of the 31P NMR resonances of these anions due to the decrease in the electronegativity of the coordinating atoms. Notably, the intrinsic 31P 3575

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Figure 6. Correlation of the intrinsic 31P NMR chemical shifts of various thiomonophosphate anions and electric charge of the anions. Key: (O) orthophosphate anions, HnPO4(3-n)- (n = 0
3), and the other symbols are as in Figure 3.

NMR chemical shifts (a) and (e) show upfield shifts upon the successive protonation of HnPO4(3
n)
(n = 0
3) and HnPS4(3
n)
(n = 0
3) respectively, whereas the shifts b, c, and d show downfield shifts compared with those of mono-, di-, and trithiomonophosphate anions, respectively. Approximate quantum chemical calculations34,35 have shown that the change in the chemical shift, Δδ, for the anions may be treated by the following relationship:24,36,37 Δδ ¼ 180Δχ0
147Δnπ
AΔθ

ð8Þ

where Δχ0 is the change in the effective electronegativity of the phosphorus atom, Δnπ is the concomitant change in the phosphorus dπ-orbital occupation due to variation in the π character of the P
X bonds thus induced, Δθ is the change in the bond angle, and A is an arbitrary parameter to accommodate variations between oxoacids. Orthophosphate and tetrathiomonophosphate anions have only one kind of coordinating atom, and all of the P
O or P
S bonds in the anions are equivalent. Therefore, the coordinating atoms that surround the central phosphorus atom in the anions occupy positions at the corners of a regular tetrahedron, with ideal symmetry Td. Hence it is obvious that the O
P
O or S
P
S bond angles of orthophosphate and tetrathiomonophosphate anions, do not change with successive protonation (i.e., Δθ = 0) in 31P NMR time scale, and that the change in electronegativity, Δχ0, which originates from the decrease in negative charge with the protonation, certainly predominates for the upfield shifts observed for the phosphorus nuclei in the HnPO4(3
n)
(n = 0
3) and HnPS4(3
n)
(n = 0
3) series. On the other hand, HnPO3S(3
n)
(n = 0
3), HnPO2S2(3
n)
(n = 0
3), and HnPOS3(3
n)
(n = 0
3) have two kinds of coordinating atoms, and all the bonds between coordinating atoms and the central phosphorus atom in the anions are not equivalent. Therefore, the 31P NMR signal due to the anions show drastic downfield shifts with successive protonation because of the changes in the O
P
O, O
P
S, and S
P
S bond angles, i.e., the contribution of the Δθ term in eq 8. It should be noted that asymmetry of the molecular structure is related to the amount of change in the bond angles with

Figure 7. Correlation of the intrinsic 31P NMR chemical shifts of various thiomonophosphate anions and the number of sulfur atoms attached to the central phosphorus atom. Key: (O) free ligands, PO4-mSm3- (m = 0
4); (4) monoprotonated anions, HPO4-mSm2(m = 0
4); (0) diprotonated anions, H2PO4-mSm
(m = 0
4); (]) triprotonated anions, H3PO4-mSm0 (m = 0, 1).

protonation or complex formation, and makes the nuclear screening drastically change. The relationships between the intrinsic 31P NMR chemical shifts and the number of sulfur atoms in thiomonophosphate anions are shown in Figure 7. It is noteworthy that the changes in the intrinsic 31P NMR chemical shifts induced by successive protonation of the anions increase in the order of PO43- and PS43(less than 10 ppm) < PO3S3- and POS33- (ca. 15 ppm) < PO2S23(ca. 30 ppm). Because the PO2S23- anion contains two oxygen atoms and two sulfur atoms as coordination atoms, the molecular structure of this anion is the most asymmetric, so the changes in the O
P
O, O
P
S, and S
P
S bond angles in the anion with successive protonations are the most remarkable in the series of thiomonophosphate anions, and the nuclear screening of the central phosphorus atom in the anion is drastically changed by the contribution of the Δθ term.

4. CONCLUSIONS The stepwise protonation constants and the intrinsic 31P NMR chemical shifts of each protonated species of a series of thiomonophosphate anions were determined. The acidities of these anions increase linearly with an increase in the number of sulfur atoms in the anions, and this trend is in agreement with the HSAB (hard and soft acids and bases) concept. The direction and the magnitude of the pH variations of the 31P NMR chemical shifts are affected by the asymmetry of the thiomonophosphate molecular structures, because this asymmetry affects the amount of the change in the X
P
Y bond angles induced by the successive protonations. An inconsistency between the log K1 value of PO3S3
anion determined by potentiometry and from the pH profile of the 31P NMR chemical shifts was observed, which suggests sodium complex formation within this series of thiomonophosphate anions. This complex will facilitate the nucleophilic attack to 3576

dx.doi.org/10.1021/jp111855x |J. Phys. Chem. B 2011, 115, 3571–3577

The Journal of Physical Chemistry B the central phosphorus atom from water molecules, and thus accelerate the hydrolyses of the thiomonophosphate anions. The protonation equilibria and the hydrolytic properties of the series of thiomonophosphates that were obtained in this work will be able to provide useful information and benchmarks about protonation properties, acid
base properties, and pH-Rate profiles for the hydrolyses of various thiophosphate derivatives.

’ AUTHOR INFORMATION

ARTICLE

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Corresponding Author

*E-mail: [email protected].

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