Protolysis and Complex Formation of Organophosphorus Compounds—Characterization by NMR-Controlled Titrations

Phosphonic acids, aminophosphonic acids, and phosphonocarboxylic acids are characterized by an advanced hyphenated technique, combining potentiometric titration with NMR spectroscopy. Automated measurements involving 13C, 19F and 31P nuclei lead to “pseudo 2D NMR” spectra, where chemical shifts or coupling constants are correlated with analytical parameters. Dissociation constants, stability constants, dynamic and specific chemical shifts are determined. Macroscopic and microscopic dissociation equilibria are discussed.


Introduction
NMR-controlled titration, also known as NMR titration, a useful tool combining NMR and analytical aspects, is based on fundamental observations in the dawn of NMR spectroscopy: "Early phosphorus NMR studies of condensed phosphates showed that raising the acidity of phosphate solutions increased the shielding of the phosphorus nucleus, causing a shift of the 31 P resonances to higher fields by several ppm" [1]. "Later studies on the short chain condensed phosphates exhibited that the pH variations of the chemical shifts and spin-coupling constants where, when measured to sufficient precision, sensitive functions of the molecular structure and the bonding". A first titration curve of H 3 PO 4 shown as δ P vs. pH was derived in this paper [2]. 13 C-NMR measurements on linear aliphatic acids revealed that COOH groups in C n H 2n+1 COOH (n = 0 to 4) exhibit higher chemical shifts δ C than COO − groups of corresponding anions C n H 2n+1 COO − . A characteristic downfield shift of δ C ranging from 5.1 to 4.7 ppm was observed for deprotonation by addition of tetramethylammonium hydroxide to carboxylic acids [3].
In subsequent years, those phenomena attracted the attention of numerous studies dealing with inorganic and organic phosphorus chemistry. A higher level of sophistication was achieved by combining the analytical theory of protolysis and complex formation for acids and bases with advanced NMR technologies and expanding the range of sensor nuclei to 1 H, 13 C, 15 N, 19 F, 31 P and spin active metal nuclei.
Further interests concentrated on phospha analogues of carboxylic acids, e.g., phosphonocarboxylic acids and geminal bisphosphonic acids. 31 P-and 13 C-NMR spectra of cyclohexyl-and phenylphosphonic acid showed that chemical shifts δ P and δ C including coupling constants n J PC (n = 1-4) of cyclohexanephosphonic acid and benzenephosphonic acid proved to be pH-dependent [17].
A key paper in understanding the NMR titration of geminal bisphosphonate structures described three asymmetric esters of chlodronic acid (HO) 2 2 . Proton coupled 31 P-NMR titration spectra revealed the coupling constants 2 J PP in a range between 15.6 and 17. 9 Hz. This significant parameter is not accessible for the symmetric ester HO(iPrO)(O)P-CCl 2 -P(O)(OiPr)OH since this compound gives rise to a dynamic deceptively simple spectrum ranging from singlet to triplet as a result of the parent symmetric [AM 6 X] 2 spin system [18]. 31 P-NMR measurements at 202.5 MHz showed that the chemical shift δ P of CH 3 C(OH)[P(O)(OH) 2 ] 2 (HEDP) is sensitive towards pH and the concentration of [(CH 3 ) 4 N] + when [(CH 3 ) 4 N]Cl was used as an ion buffer [19].
The determination of high pK values (pK > 13) and low pK values (pK < 1) required specific, advanced techniques for NMR titration. Comments on measurements at high and low pH were reported [19,20]. 1 H/ 31 P NMR pH indicator series were used to eliminate the glass electrode in NMR spectroscopic pK determinations, leading to "electrodeless titrations" [21]. Comprehensive guidelines for NMR measurements for the determination of high and low pK values were given in a IUPAC Technical Report. Those sophisticated and detailed instructions should be followed for accurate analytical and NMR measurements, data evaluation and subsequent publications [22].

Developing Technical Setups for Automated NMR Titrations
In general, NMR titrations for various nuclei were performed in single sample techniques, which proved to be rather laborious and time consuming. For practical reasons, the number of data points were limited in those early titration curves. Hence, attempts were made to develop the technology of automated NMR titrations.
An innovative set up was constructed, which permitted the acquisition of spectra from spinning 20 mm NMR tubes, adding a solution of base under efficient mixing while monitoring the pH. This apparatus worked together with the wide-bore magnet of a Bruker CXP-300 spectrometer, yielding approximately 80 titration points within a couple of hours. This technology was successfully used to titrate H 3 PO 4 vs. KOH and provided a smooth NMR titration curve [23].
Further progress for automated NMR titrations inside spinning 10 mm NMR tubes was described and the novel installation applied to monitor the complex formation between Tl(I) + and Cl − in aqueous solutions. A Bruker CXP-100 spectrometer was used, operating at 51.9 MHz for 205 Tl [24].
Very recently, an elegant low-cost construction was developed for a gravity-driven pH adjustment inside a 5 mm NMR tube. No hardware modifications of the NMR spectrometer were requested. This technique was applied to site-specific protein pK measurements [25]. It might be useful for future studies of organophosphorus compounds.
A different route to automated NMR titrations was chosen by the Düsseldorf group. We were intrigued by the technology of 2D NMR spectra and the graphical representation of such spectra by standard spectrometer software. Hence, a hyphenated technique was envisaged, replacing the f2 axis of 2D NMR spectra by analytical parameters.
Bypass constructions were developed in several generations of increasing accuracy. A 10 mm NMR tube was attached to a special homemade insert and used with a Bruker AM 200 SY NMR spectrometer operating at 81 MHz for 31 P NMR. This insert acted as bypass to a precision titration equipment. A series of pH dependent 1D NMR spectra were recorded and processed (using standard spectrometer software) to yield instructive "pseudo 2D NMR" spectra (e.g., in analogy to COSY spectra). Chemical shift δ P data were correlated with analytical data like pH or the degree of titration τ. The technical setup and two examples are shown in [26]. Phosphaalanine was used as an example where deprotonation and complex formation with Zn 2+ cations were observed by titrations vs. tetramethylammonium hydroxide (TMAOH) [26].
This equipment was used to characterize a series of aminomethylphosphine oxides (CH 3 ) 3-n (CH 2 NH 2 ) n PO (n = 1-3), adding n equivalents of HCl and back-titrating vs. NaOH. Ion-specific chemical shifts δ P and pK data were obtained for those aminomethylphosphine oxide bases. In addition, technical details of NMR, analytics, software concepts and programs used were described [27].
A brief overview of " 31 P NMR controlled titrations of Phosphorus-Containing Acids and Bases in Protolysis and Complex Formation" reported about the 81 MHz 31 P{ 1 H} NMR titration of phosphonoacetic acid [28]. The hardware and software concepts were shown.
In practice, 13 C-NMR titrations in single sample techniques proved to be very time consuming. Hence, it seemed advisable to use the technology described above for automated 50.29 MHz 13 C{ 1 H} or 13 C-NMR measurements. As practical examples, the pair of isomers 1-and 2-aminoethanephosphonic acids were titrated vs. NaOH. Within this context, CH 3 -CH(NH 2 )-PO 3 H 2 and the fluorinated analogue CF 3 -CH(NH 2 )-PO 3 H 2 were compared using 31 P{ 1 H} and 19 F{ 1 H} NMR titrations. Replacing the CH 3 by a CF 3 group reduces the basicity of the NH 2 function, which is reflected in δ P vs. τ and in the δ F vs. τ correlations [31].
The experimental set up described above requested individual titrations for each nucleus wanted. Hence, multinuclear studies (e.g., 1 H and 13 C and 31 P) demanded high spectrometer times.
At this stage, special probe heads were developed by Bruker for another hyphenated technique combining liquid chromatography with HR NMR. In our laboratory, a Bruker LC probe head LC-TXO-NMR was successfully introduced to a DRX 500 NMR spectrometer and used for advanced NMR titrations. It became routine to run consecutively 31 P{ 1 H}, 31 P, and 1 H-NMR spectra for each titration step, thus saving time, gaining higher sensitivity and reducing the necessary concentrations (and amounts) of titrands. Excellent spectra resulted with a high S/N ratio and high digital resolution in the chemical shift or frequency axis.
In addition, a special 19 F-LC probe head was available, combining 19  A comprehensive report about the technical designs of NMR and analytical components, software, data evaluation, error calculations and applications was written in 2002 and incorporated into the Bruker NMR Guide collection, freely accessible for Bruker spectrometer users [32] only. This detailed review is now open for free downloads to all interested readers: (a) https://www.theresonance.com/ nmr-controlled-titration-download-the-paper/, (b) https://www.bruker.com/fileadmin/user_upload/8-PDF-Docs/MagneticResonance/NMR/NMR_controlled_titration.pdf.
Within this context, a special computer program MultipleNMRGraphics was developed which is able to generate four characteristic "pseudo 2D NMR" plots, e.g., δ P vs. pH or δ P vs. τ either as contour or as stacked plots, in black-and-white or color design [33]. Those graphics have a lower storage demand than the previously used "pseudo 2D NMR" spectra generated by the routine Bruker spectrometer software.
Some examples relevant to phosphorous chemistry and organic chemistry dealt with in [32] are listed in Table 1: Table 1. Some examples for NMR-controlled titrations of phosphonic acids, phosphinic acids, and carboxylic acids as discussed in [32]. 1 A modification of our design for automated NMR titrations shown above was adjusted to the local conditions of a Bruker 250 MHz spectrometer and applied to study the complexation of Zn 2+ , Cd 2+ and Pb 2+ with diazacrown ethers substituted by phosphonate groups [34].
Particular attention was drawn towards microscopic dissociation constants going back to early studies on NH 2 -CH 2 -CH 2 -NH-CH 2 -COOH. 60 MHz and 100 MHz 1 H-NMR titrations evaluated the pH dependence of a singlet for the methylene group NH-CH 2 -COOH, while the ethylene function N-CH 2 -CH 2 -N appeared with the spectral character, changing from a deceptively simple singlet towards an AA BB ([AB] 2 ) system. The analytical formalism and microscopic dissociation constants were derived [35]. For deeper reading, an up-to-date and comprehensive survey on the theory and practice of proton microspeciation based on NMR-pH titrations is recommended [36].
As an example, S-2-amino-4-(methylphosphinoyl)butyric acid (S-phosphinothricine, GLUFOSINATE) HOOC-CH(NH 2 )-CH 2 -CH 2 -P(CH 3 )(O)OH was characterized by 31 P{ 1 H}-and 1 H-NMR titrations. Microscopic dissociation and intramolecular rotational equilibria were discussed [32,37]. Within this context, a program LAOTIT was developed, which is able to simulate series of pH-dependent second-order NMR spectra. A practical example for AFGMNQ 3 X spin systems of GLUFOSINATE in a pH range from 1 to 6 was shown in [37]. The ring-chain tautomerism and protolytic equilibria of an effectively three-basic 3-hydroxy-3-phosphonoisobenzofuranone was studied by 1 H-, 13 C{ 1 H}-and 31 P{ 1 H}-NMR-controlled titrations. A complex pattern of macroscopic and microscopic deprotonation steps leading from the starting H 3 L to the final L 3− (Scheme 1) was discussed.
derived [35]. For deeper reading, an up-to-date and comprehensive survey on the theory and practice of proton microspeciation based on NMR-pH titrations is recommended [36].
The ring-chain tautomerism and protolytic equilibria of an effectively three-basic 3-hydroxy-3phosphonoisobenzofuranone was studied by 1 H-, 13 C{ 1 H}-and 31 P{ 1 H}-NMR-controlled titrations. A complex pattern of macroscopic and microscopic deprotonation steps leading from the starting H3L to the final L 3-(scheme I) was discussed.
NMR-controlled titration was successfully used to analyze the mixture of diastereomers from 1phosphonopropane-1,2,3-tricarboxylic acid, HOOC-CH2-CH(COOH)-CH(COOH)-PO3H2 (PPTC). The genuine product from synthesis consisted of 64% of the RS/SR and 36% of the RR/SS forms. 31 P{ 1 H}-NMR-controlled titration revealed two diastereospecific titration curves which were individually identified by additional 1D and 2D NMR studies using 1 H, 31 P and 13 C nuclei. Dissociation constants and ion-specific chemical shifts δP were calculated for the pair of diastereomers [41][42][43]. It seems evident to use automated NMR titration for production control in research and industrial chemistry.

Some Comments on Macroscopic Protolytic Equilibria-Dissociation and Stability Constants
Organophosphorus compounds studied by potentiometric or NMR-controlled titrations may be described by two numerical indices: a, the number of acidic functions (e.g., P(O)OH, C(O)OH, etc.) and b, the number of basic functions (e.g., NH2, NHR, NR2, etc.). The minimal protonated species corresponds to the n-valent base L -a having a anionic centers and b neutral base centers in ( 0 N)b-R-(O -)a. Total protonation leads to the n-valent acid HnL b+ (n = a + b) having a neutral centers and b cationic acid centers in ( + HN)b-R-(OH 0 )a.
NMR-controlled titration was successfully used to analyze the mixture of diastereomers from 1-phosphonopropane-1,2,3-tricarboxylic acid, HOOC-CH 2 -CH(COOH)-CH(COOH)-PO 3 H 2 (PPTC). The genuine product from synthesis consisted of 64% of the RS/SR and 36% of the RR/SS forms. 31 P{ 1 H}-NMR-controlled titration revealed two diastereospecific titration curves which were individually identified by additional 1D and 2D NMR studies using 1 H, 31 P and 13 C nuclei. Dissociation constants and ion-specific chemical shifts δ P were calculated for the pair of diastereomers [41][42][43]. It seems evident to use automated NMR titration for production control in research and industrial chemistry.

Some Comments on Macroscopic Protolytic Equilibria-Dissociation and Stability Constants
Organophosphorus compounds studied by potentiometric or NMR-controlled titrations may be described by two numerical indices: a, the number of acidic functions (e.g., P(O)OH, C(O)OH, etc.) and b, the number of basic functions (e.g., NH 2 , NHR, NR 2 , etc.). The minimal protonated species corresponds to the n-valent base L −a having a anionic centers and b neutral base centers in Total protonation leads to the n-valent acid H n L b+ (n = a + b) having a neutral centers and b cationic acid centers in ( Protonation equilibria of the n-valent base are described by Equation (1): and by brutto-stability constants following Equation (2): Stepwise dissociation equilibria of the n-valent acid are described by Equation (3): Molecules 2019, 24, 3238 6 of 26 while corresponding dissociation constants K i are given by Equation (4): Stoichiometric stability constants and stoichiometric dissociation constants are connected by Equations (5) and (6): This paper will use stoichiometric variables (containing concentrations instead of activities) in abbreviated forms: pK i -macroscopic acid dissociation constant; pk i -microscopic acid dissociation constant; pK w -ion product of water. pH stands for the concentration-based pH = −lg(c H ). Glass electrodes were calibrated by blank titration. The more complex situation of activities and activity-based parameters exceeds the scope of this paper and hence will not be discussed at this stage.
The molar fractions x i of protolytic species H i L i-a are derived from Equation (7): Each protolytic species H i L i-a present in the equilibrium contributes specific NMR parameters δ(H i L i-a ) in an exchange reaction, which is rapid on the NMR timescale. Effectively, only one signal is observed when monitoring NMR during the course of titrations. A dynamically averaged chemical shift δ follows Equation (8): A gradient called the deprotonation shift ∆ i [ppm] is given by Equation (9): This gradient defines the change of chemical shift for each deprotonation step. Signs and magnitudes of gradients are used to elucidate the deprotonation and protonation pathways of multifunctional acids, bases and ligands as shown in examples below.
As deduced above, the dynamically averaged chemical shift δ is a function of pH. Experimentally, the pH of solutions may be varied by titration with a strong univalent base or a strong univalent acid. While the experiment directly provides the well-known titration curve pH = f(V Titrator ), it is more convenient to calculate the inverse function V Titrator = f(pH) with suitable computer programs. Within this paper, a reduced parameter τ, commonly called degree of titration, will be used to describe the status of a titration process. τ is a ratio defined by Equation (10): The sign of τ is positive if n Titrator corresponds to the molar amount of a strong monovalent base (e.g., NaOH, KOH, TMAOH), but is negative for a strong monovalent acid (HCl, HNO 3 , HClO 4 ). n Titrand corresponds to the molar amount of a n-basic acid H n L.
Details of the basic principles and experimental equipment with hardware and software are described in [31,32] and in references given herein.

Results and Discussion
In the following sections, a few examples will be shown for automated NMR-controlled titrations using hardware and software concepts described above. Chemical shifts δ C [ppm] quoted below were referenced vs. (CH 3 ) 3 Si-CH 2 -CH 2 -SO 3 Na, while δ P [ppm] was virtually referenced towards external H 3 PO 4 . Coupling constants n J XY are given in [Hz].

Phosphonic Acids
Methanephosphonic acid 1 and phenylphosphonic acid 2 shown in Scheme 2 were chosen from [31,44], which will be presented below: The sign of τ is positive if nTitrator corresponds to the molar amount of a strong monovalent base (e.g., NaOH, KOH, TMAOH), but is negative for a strong monovalent acid (HCl, HNO3, HClO4). nTitrand corresponds to the molar amount of a n-basic acid HnL.
Details of the basic principles and experimental equipment with hardware and software are described in [31,32] and in references given herein.

Results and Discussion
In the following sections, a few examples will be shown for automated NMR-controlled titrations using hardware and software concepts described above. Chemical shifts δC [ppm] quoted below were referenced vs. (CH3)3Si-CH2-CH2-SO3Na, while δP [ppm] was virtually referenced towards external H3PO4. Coupling constants n JXY are given in [Hz].

Methanephosphonic Acid 1
The results from a proton-coupled 31 P-NMR-controlled titration of methanephosphonic acid 2 vs. NaOH are shown as a contour plot in Figure 1. A quartet structure from the parent A3X spin system of the P-CH3 fragment is recognized. Numerical results are given in Table 2. The deprotonation of both P-OH functions induces a decrease in chemical shifts δP and a decrease in the absolute values of 2 JPH.

Methanephosphonic Acid 1
The results from a proton-coupled 31 P-NMR-controlled titration of methanephosphonic acid 2 vs. NaOH are shown as a contour plot in Figure 1. A quartet structure from the parent A 3 X spin system of the P-CH 3 fragment is recognized. Numerical results are given in Table 2. The deprotonation of both P-OH functions induces a decrease in chemical shifts δ P and a decrease in the absolute values of 2 J PH .

Phosphonic Acids
Methanephosphonic acid 1 and phenylphosphonic acid 2 shown in Scheme 2 were chosen from [31,44], which will be presented below:

Methanephosphonic Acid 1
The results from a proton-coupled 31 P-NMR-controlled titration of methanephosphonic acid 2 vs. NaOH are shown as a contour plot in Figure 1. A quartet structure from the parent A3X spin system of the P-CH3 fragment is recognized. Numerical results are given in Table 2. The deprotonation of both P-OH functions induces a decrease in chemical shifts δP and a decrease in the absolute values of 2 JPH.   Figure 1. 1 H-coupled 31 P-NMR-controlled titration of methanephosphonic acid 1 vs. NaOH. Note: quartet fine structure from X-part of AX 3 system of P-CH 3 fragment. X-axis: δ P [ppm]. Y-axis: degree of titration τ. Table 2. Specific chemical shifts δ C , δ P and coupling constants 1 J PC and 2 J PH of methanephosphonic acid 1 were obtained by 13 C{ 1 H}-, 31 P{ 1 H}-, and 31 , respectively. i = 1 to n. n = 2. Experimental data: C Titrand : a) 0.269 mol/L. b) 0.01220 mol. c) 0.0095 mol/L. C Titrator : a) 4.82 mol/L KOH. b) 0.0971 mol/L NaOH. c) 0.0971 mol/L NaOH. d) Early data from results from titration vs. KOH [45].  Chemical shifts δ P for protolytic species H 2 L, HL − , and L 2− of phenylphosphonic acid 2 together with dissociation constants pK 1 and pK 2 are listed in Table 3. The deprotonation of both P-OH groups leads to characteristic high field shifts for δ P as indicated by negative gradients ∆ 1 and ∆ 2 .  Higher concentrations are required for 13 C{ 1 H}-NMR-controlled titrations as shown for the titration of phenylphosphonic acid 2 vs. KOH in Figure 2: The deprotonation of each of the two P-OH functions led to a strong low field shift for the ipso-C1 carbon. For the remaining carbons high field shifts are observed, an effect decreasing in the order para-C4 > meta-C3/5 > ortho-C2/5.

in H 2 O
Semi-empirical calculations with VAMP 4.4 using parameter set AM1 showed that the electron density at C1 increases with deprotonation in the order PhPO3H2 < PhPO3H -< Ph-PO3 2-, while the electron density of C4 decreases in this order [44,47]. In addition, the deprotonation of P-OH led to a decrease for all n JPC (n = 1 to 4). Particularly indicative is 1 JPC from the ipso-carbon C1, which reaches a minimum at total deprotonation. Numerical results for compound 2 are listed in Table 4:  The deprotonation of each of the two P-OH functions led to a strong low field shift for the ipso-C1 carbon. For the remaining carbons high field shifts are observed, an effect decreasing in the order para-C4 > meta-C3/5 > ortho-C2/5.
Semi-empirical calculations with VAMP 4.4 using parameter set AM1 showed that the electron density at C1 increases with deprotonation in the order PhPO 3 H 2 < PhPO 3 H − < Ph-PO 3 2− , while the electron density of C4 decreases in this order [44,47]. In addition, the deprotonation of P-OH led to a decrease for all n J PC (n = 1 to 4). Particularly indicative is 1 J PC from the ipso-carbon C1, which reaches a minimum at total deprotonation. Numerical results for compound 2 are listed in Table 4: Laborious and time-consuming single sample 31 P{ 1 H}-and 13 C{ 1 H}-NMR studies on phenylphosphonic acid 2 were performed, where δ P , δ C , and n J PC data are consistent with findings derived from the automated titrations presented in this paper [17].

Aliphatic Aminophosphonic Acids
Aminophosphonic acids NH2-R-PO3H2, such as examples 3 to 5, exist as betainic forms + NH3-R-PO3H -in solid and in solution state. Protolytic equilibria of aminophosphonic acids are described by macroscopic and microscopic formalisms as shown in Table 5 below: Table 5. Macroscopic and microscopic dissociation species of aminophosphonic acids.

Aliphatic Aminophosphonic Acids
Aminophosphonic acids NH 2 -R-PO 3 H 2 , such as examples 3 to 5, exist as betainic forms + NH 3 -R-PO 3 H − in solid and in solution state. Protolytic equilibria of aminophosphonic acids are described by macroscopic and microscopic formalisms as shown in Table 5 below: Table 5. Macroscopic and microscopic dissociation species of aminophosphonic acids.
Specific chemical shifts δ P and gradients ∆ for compounds 3 to 5 obtained by 31 P{ 1 H}-NMR-controlled titrations are given in Table 7: The deprotonation of the P-OH groups led to high field shifts for δ P connected with negative gradients. The final deprotonation of the NH 3 + group gave rise to a low field shift for δ P. This effect is stronger in α-aminophosphonic acid 4 than in β-aminophosphonic acid 5. Earlier results for chemical shifts δ P of H 2 L, HL − and L 2− species of 3 and 4 were mentioned in [5,45]. In addition, δ P of H 3 L + was accessible for 4 but not for 3. Table 6. Macroscopic dissociation constants pK i of compounds α-Ala-P 3 and β-Ala-P 4 obtained by 13    13 C{ 1 H}-NMR-controlled titrations of compounds 4 and 5 led to specific chemical shifts δ C , coupling constants 1 J PC , and gradients ∆ as listed in Table 8:  [Hz], and corresponding gradients ∆ for α-aminoethanephosphonic acid (α-Ala-P) 3 and β-aminoethanephosphonic acid (β-Ala-P, CILIATIN) 4. Spin enumerations: 3: C2-C1(N)-P; 4: (N)C2-C1-P. 1 J PC shows a minimum for species HL − of 3 and 4. 2 J PC was not resolved for compounds 3 and 4.

in H 2 O 4 in H 2 O
Species

Aromatic p-Aminophenylphosphonic Acid 5
The deprotonation of PO 3 H − in aliphatic aminophosphonic acids 3 and 4 is affiliated with a high field shift (gradients ∆ 2 are negative), while the deprotonation of the ammonium function + NH 3 leads to a low field shift (gradients ∆ 3 are positive).

Aromatic p-Aminophenylphosphonic Acid 5
The deprotonation of PO3H -in aliphatic aminophosphonic acids 3 and 4 is affiliated with a high field shift (gradients 2 are negative), while the deprotonation of the ammonium function + NH3 leads to a low field shift (gradients 3 are positive).
The aromatic p-aminophenylphosphonic acid 5 exhibits a different pattern: while gradient 2 is positive, 3 is negative (scheme IV). But is it sufficient to assume a simple first-order macroscopic dissociation scheme for compound 5? Deeper insight might be obtained from the microscopic dissociation scheme. In principle 13  But is it sufficient to assume a simple first-order macroscopic dissociation scheme for compound 5? Deeper insight might be obtained from the microscopic dissociation scheme. In principle 13 C{ 1 H}-NMR-controlled titration should lead to specific chemical shifts and coupling constants n J PC indicative for microscopic dissociations species of 5. But p-aminophenylphosphonic acid 5 is less soluble in water than the aliphatic aminophosphonic acids 3 and 4. The S/N-ratio of 13 C{ 1 H}-NMR spectra of 5 is not sufficient to perform evaluable 13 C{ 1 H}-NMR-controlled titrations.
In this situation, UV/VIS-controlled titration, which allows for lower concentrations suitable for conclusive measurements, will help to study both the macroscopic and the microscopic dissociation equilibrium of 5 [30]. In addition, the parent compounds C 6 H 5 PO 3 H 2 2 and C 6 H 5 NH 2* HCl 6 were compared. The following macroscopic pK i data were found by potentiometric titration and listed in Table 9: Table 9. Dissociation constants of compounds p-aminophenylphosphonic acid 5, phenylphosphonic acid 2, and anilinium hydrochloride 6. Those data point towards a dominating deprotonation sequence for 5 following + NH 3 -R-PO 3 H 2 → + NH 3 -R-PO 3 H − → NH 2 -R-PO 3 H − → NH 2 -R-PO 3 2− . But is it justified to exclude the alternative route + NH 3 -R-PO 3 H 2 → + NH 3 -R-PO 3 H − → + NH 3 -R-PO 3 2− → NH 2 -R-PO 3 2− ? Evaluating the macroscopic dissociation constants of 5 shows that between pH = 1.5 and pH = 10, only three macroscopic species exist: H 2 L, HL − , and L 2− . The UV/VIS-controlled titration of 5 [30] showed that the maximum concentration for macroscopic HL − is reached at pH = 5.75, consisting of two microdissociation species NH 2 -R-PO 3 H − and + NH 3 -R-PO 3 2− in a ratio of 9:1. Thus, the results from the UV/VIS-controlled titration of 5 [30] confirm the dominance of NH 2 -R-PO 3 H − as previously assumed for the macroscopic deprotonation sequence derived from the 31 P{ 1 H}-NMR-controlled titration of 5 [44].

HOOC-(CH 2 ) n -PO
Specific chemical shifts δP for 7c and corresponding anions together with gradients are listed in Table 12.   The trilithium salts LiOOC-CH 2-n F n -PO 3 Li 2 (8a and 8b; n = 1 and 2, Scheme 6) were used for retro titrations vs. HNO 3 , since the parent mono-and difluorophosphonoacetic acids 8c and 8d were not available for 19 F-NMR-and 31 P{ 1 H}-NMR titrations. Corresponding dissociation constants pK i of 8c and 8d were calculated as listed in Table 13, while chemical shifts δ F and δ P and coupling constants 2 J PF are given in Table 14. As expected, the introduction of fluorine into the skeleton of the parent phosphonoacetic acid led to lower pK 1 and pK 2 values. The deprotonation of P-OH groups induces a low field shift for δ F in fluorinated phosphonic acids 8c and 8d. Scheme VI. Trilithium salts LiOOC-CH2-nFn-PO3Li2 8a and 8b and free acids HOOC-CH2-nFn-PO3H2 8c and 8d.
(1) Comments on Chemical Shifts δC of Carbon Atoms in DPBDC 9 The deprotonation of PO3H2, PO3H -and COOH functions in DPBDC 9 leads to a monotonous down field shift for δC C1* and C2* (see Figure 4a), while carbons C1 to C4 exhibit specific nonmonotonous trends (see Figure 4b,d).
Similar arguments for the relative acidity of C1* and C2* may be derived from the chemical shift δC of the skeleton carbon C2 (see Figure 4b). δC (C2) of H6L corresponds to 52.2 ppm, while the totally deprotonated form L 6-is found at 55 ppm. Deprotonation at C1* and C2* is characterized again by 3 of δC (C2) > 4 of δC (C2).
(1) Comments on Chemical Shifts δ C of Carbon Atoms in DPBDC 9 The deprotonation of PO 3 H 2 , PO 3 H − and COOH functions in DPBDC 9 leads to a monotonous down field shift for δ C C1* and C2* (see Figure 4a), while carbons C1 to C4 exhibit specific non-monotonous trends (see Figure 4b,d).
Similar arguments for the relative acidity of C1* and C2* may be derived from the chemical shift δ C of the skeleton carbon C2 (see Figure 4b). δ C (C2) of H 6 L corresponds to 52.2 ppm, while the totally deprotonated form L 6− is found at 55 ppm. Deprotonation at C1* and C2* is characterized again by ∆ 3 of δ C (C2) > ∆ 4 of δ C (C2).
Chemical shifts δ C of C3 span a range of 38.4 to 43.3 ppm. Surprisingly, the final deprotonation HL 5− → L 6− , due to PO 3 H − → PO 3 2− of P2* reduces δ C (C3) from 43.26 to 42.70 ppm. This is the first observation (within this context) of a negative gradient (∆ 6 = −0.56 Hz) connected to deprotonation at a PO 3 H − unit.
Those unexpected observations for chemical shifts δc in 9 and conformational aspects will be mentioned in the following section on coupling constants n JPC as well.
Those unexpected observations for chemical shifts δc in 9 and conformational aspects will be mentioned in the following section on coupling constants n JPC as well.
(2) Comments on Coupling Constants nJPC (n = 1 to 3) of DPBDC 9 The vicinal coupling 3 JPC (P2*C1*) is remarkably sensitive towards the protonation state (see Figure 5): For the protolytic species H6L to H2L 4-of 9, a decrease in 3 JPC (P2*C1*) from 17.5 Hz down to a minimum of 4.3 Hz is observed, followed by an increase from 5.3 Hz to 18.6 Hz due to HL 5-and finally L 6-. Between pH = 7 and 8, a maximum of the protolytic species H2L 4-is expected, while HL 5dominates around pH = 9. Those observations indicate changes of the dihedral angle of P2*-C2-C1-C1* possibly involving hydrogen bridges as indicated by scheme IX below: Scheme IX. Tentative hydrogen bridges for protolytic species H3L 3-to HL 5-.