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

Abstract

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.

1. 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 ³¹P 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 H₃PO₄ shown as δ_P vs. pH was derived in this paper [2]. ¹³C-NMR measurements on linear aliphatic acids revealed that COOH groups in C_nH_2n+1COOH (n = 0 to 4) exhibit higher chemical shifts δ_C than COO⁻ groups of corresponding anions C_nH_2n+1COO⁻. 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 ¹H, ¹³C, ¹⁵N, ¹⁹F, ³¹P and spin active metal nuclei.

The first NMR titration curves for phosphonoacetic acid HOOC-CH₂-PO₃H₂ using ¹³C and ³¹P NMR were reported as δ_C vs. pH and δ_P vs. pH functions. For the first time, a characteristic deprotonation sequence was established: HOOC-CH₂-PO₃H₂ → HOOC-CH₂-PO₃H⁻ → ⁻OOC-CH₂-PO₃H⁻ → ⁻OOC-CH₂-PO₃²⁻. In addition, ¹J_PC was related to the s-electron density around the central C-atom [4].

Several decades of creative work followed those early observations. Induced by synthetic, analytical, biological, or technical aspects, interests were concentrated on several classes of organophosphorus compounds. Particular attention was drawn towards analogues of amino acids, e.g., aminophosphonic acids and strong complexing agents like NTMP (N(CH₂PO₃H₂)₃) and EDTMP ((H₂O₃PCH₂)₂NCH₂CH₂N(CH₂PO₃H₂)₂), which are phospha analogues of the classical complexones NTA (N(CH₂COOH)₃) and EDTA ((HOOCCH₂)₂NCH₂CH₂N(CH₂COOH)₂). Dissociation constants, stability constants for protonation and metal complex formation were studied as quoted with a few selected key papers [5,6,7,8,9,10,11,12,13,14,15,16].

Further interests concentrated on phospha analogues of carboxylic acids, e.g., phosphonocarboxylic acids and geminal bisphosphonic acids. ³¹P- and ¹³C-NMR spectra of cyclohexyl- and phenylphosphonic acid showed that chemical shifts δ_P and δ_C including coupling constants ⁿJ_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(O)P-CCl₂-P(O)(OiPr)OH, (HO)₂(O)P-CCl₂-P(O)(OiPr)₂, and HO(iPrO)(O)P-CCl₂-P(O)(OiPr)₂. Proton coupled ³¹P-NMR titration spectra revealed the coupling constants ²J_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-CCl₂-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 [AM₆X]₂ spin system [18]. ³¹P-NMR measurements at 202.5 MHz showed that the chemical shift δ_P of CH₃C(OH)[P(O)(OH)₂]₂ (HEDP) is sensitive towards pH and the concentration of [(CH₃)₄N]⁺ when [(CH₃)₄N]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]. ¹H/³¹P 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].

1.1. 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 H₃PO₄ 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 ²⁰⁵Tl [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 ³¹P 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 Zn²⁺ cations were observed by titrations vs. tetramethylammonium hydroxide (TMAOH) [26].

This equipment was used to characterize a series of aminomethylphosphine oxides (CH₃)_3-n(CH₂NH₂)_nPO (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 “³¹P NMR controlled titrations of Phosphorus-Containing Acids and Bases in Protolysis and Complex Formation” reported about the 81 MHz ³¹P{¹H} NMR titration of phosphonoacetic acid [28]. The hardware and software concepts were shown.

Typical “pseudo 2D NMR” spectra correlating the chemical shift δ_P vs. the degree of titration τ were obtained for the pair of isomers 1- and 2-aminoethanephosphonic acids CH₃-CH(NH₂)-PO₃H₂ and NH₂-CH₂-CH₂-PO₃H₂ (α-Ala-P and β-Ala-P) and for diphosphaasparaginic acid H₂O₃P-CH(NH₂)-CH₂-PO₃H₂ (Asp-P₂). Macroscopic dissociation constants and ion-specific chemical shifts are reported. The p-aminophenylene-substituted phosphonic acid p-NH₂-C₆H₄-PO₃H₂ was compared [29]. Hardware and software concepts used in NMR titration were demonstrated. A subsequent UV-controlled titration revealed the microscopic dissociation scheme of p-NH₂-C₆H₄-PO₃H₂. Corresponding deprotonation patterns were discussed [30].

In practice, ¹³C-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 ¹³C{¹H} or ¹³C-NMR measurements. As practical examples, the pair of isomers 1- and 2-aminoethanephosphonic acids were titrated vs. NaOH. Within this context, CH₃-CH(NH₂)-PO₃H₂ and the fluorinated analogue CF₃-CH(NH₂)-PO₃H₂ were compared using ³¹P{¹H} and ¹⁹F{¹H} NMR titrations. Replacing the CH₃ by a CF₃ group reduces the basicity of the NH₂ 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., ¹H and ¹³C and ³¹P) 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 ³¹P{¹H}, ³¹P, and ¹H-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 ¹⁹F-LC probe head was available, combining ¹⁹F and ¹H-NMR techniques. The high field stability of the supercon magnet allowed measurements in H₂O solutions (without D₂O), thus avoiding the problems with “mixed” stability and dissociation constants resulting from D₂O/H₂O mixed solvents.

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.

NMR titrations using 200 MHz and 500 MHz spectrometers were described using geminal bisphosphonic acids, e.g., HEDP and Pamidronic acid, as model systems. The TXO-HPLC probe head improved the signal-to-noise ratio of “pseudo 2D NMR” spectra and reduced the concentration of titrand required by this procedure: The following concentrations for sensor nuclei are recommended: ¹H: 0.25–0.01 mol/L, ¹³C: 0.50–0.005 mol/L, ¹⁹F: 0.01–0.005 mol/L, ³¹P: 0.01–0.001 mol/L, and ¹¹³Cd: 0.25–0.1 mol/L. ¹¹³Cd NMR was used when studying protolytic and complex formation equilibria of (H₂O₃P-CH₂)₂NCH₂CH₂N(CH₂PO₃H₂)₂ (EDTMP).

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. Some examples for NMR-controlled titrations of phosphonic acids, phosphinic acids, and carboxylic acids as discussed in [32]. ¹⁾ Retro titration; ²⁾ Micro dissociation; ³⁾ Second-order ¹H-NMR spin systems.

Examples	NMR	Remarks
Phosphonic acids
CH3P(O)(OH)2	31P{1H}
LiOOC-CH2-P(O)(OLi)2	31P{1H}	1)
(HO)2(O)P-CH2-CH2-P(O)(OH)2	13C{1H}
CH3-C(OH)[P(O)(OH)2]2, HEDP, etidronic acid	31P{1H}
NH2-CH2-CH2-C(OH)(P(O)(OH)2)2, pamidronic acid	31P{1H}
HOOC-CH2-CH(COOH)-CH(COOH)-P(O)(OH)2, PPTC	31P{1H}
Phosphinic acids
(CH3)2P(O)OH	31P{1H}
HOOC-CH2-CH2-P(CH3)(O)OH	13C{1H}, 1H	2)
HO(O)(CH3)P-CH2-CH2-P(CH3)(O)OH	13C{1H}
HO(O)(CH3)P-CH2-CH2-C(H)(NH2)COOH	1H	2, 3)
Carboxylic acids
CH3COOH	13C{1H}
CH(CH3)2-CH2-CH(NH2)-C(O)-NH-CH(CH3)-COOH, peptide Leu-Ala	13C{1H}
CH2=CF-CH2-C(CH3)(NH2)-COOH	19F

:

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 Zn²⁺, Cd²⁺ and Pb²⁺ with diazacrown ethers substituted by phosphonate groups [34].

Particular attention was drawn towards microscopic dissociation constants going back to early studies on NH₂-CH₂-CH₂-NH-CH₂-COOH. 60 MHz and 100 MHz ¹H-NMR titrations evaluated the pH dependence of a singlet for the methylene group NH-CH₂-COOH, while the ethylene function N-CH₂-CH₂-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(NH₂)-CH₂-CH₂-P(CH₃)(O)OH was characterized by ³¹P{¹H}- and ¹H-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 AFGMNQ₃X 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 ¹H-, ¹³C{¹H}- and ³¹P{¹H}-NMR-controlled titrations. A complex pattern of macroscopic and microscopic deprotonation steps leading from the starting H₃L to the final L³⁻ (Scheme 1) was discussed.

The OPIUM program enabled the simultaneous evaluation of potentiometric, ³¹P{¹H}- and ¹H-NMR titrations using the four individual ¹H signals from the ABCD system [38]. Macroscopic dissociation constants, pK₁ = 0.445 ± 0.008, pK₂ = 5.792 ± 0.003, pK₃ = 6.486 ± 0.002. δ_H, δ_C, and δ_P of H₃L (0.2510 mol/L in D₂O) and L³⁻ (0.1919 mol/L in 1 mol/L KOD), were determined. For details of the complex equilibrium system, see [39,40].

NMR-controlled titration was successfully used to analyze the mixture of diastereomers from 1-phosphonopropane-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. ³¹P{¹H}-NMR-controlled titration revealed two diastereospecific titration curves which were individually identified by additional 1D and 2D NMR studies using ¹H, ³¹P and ¹³C 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.

1.2. 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 (⁰N)_b-R-(O⁻)_a. Total protonation leads to the n-valent acid H_nL^b+ (n = a + b) having a neutral centers and b cationic acid centers in (⁺HN)_b-R-(OH⁰)_a.

Protonation equilibria of the n-valent base are described by Equation (1):

$${\mathrm{iH}}^{+}+{\mathrm{L}}^{-\mathrm{a}}\stackrel{}{\rightleftharpoons }{\mathrm{H}}_{\mathrm{i}}{\mathrm{L}}^{\mathrm{i}-\mathrm{a}}\mathrm{i}=1\mathrm{to}\mathrm{n}$$

(1)

and by brutto-stability constants following Equation (2):

$${\mathsf{\beta }}_{\mathrm{i}}=\frac{[{\mathrm{H}}_{\mathrm{i}}{\mathrm{L}}^{\mathrm{i}-\mathrm{a}}]}{{[{\mathrm{H}}^{+}]}^{\mathrm{i}}[{\mathrm{L}}^{-\mathrm{a}}]}\mathrm{i}=1\mathrm{to}\mathrm{n}{\mathsf{\beta }}_0=1$$

(2)

Stepwise dissociation equilibria of the n-valent acid are described by Equation (3):

$${\mathrm{H}}_{\mathrm{n}+1-\mathrm{i}}{\mathrm{L}}^{\mathrm{b}+1-\mathrm{i}}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{H}}_{\mathrm{n}-\mathrm{i}}{\mathrm{L}}^{\mathrm{b}-\mathrm{i}}\mathrm{i}=1\mathrm{to}\mathrm{n}$$

(3)

while corresponding dissociation constants K_i are given by Equation (4):

$${\mathrm{K}}_{\mathrm{i}}=\frac{[{\mathrm{H}}^{+}][{\mathrm{H}}_{\mathrm{n}-\mathrm{i}}{\mathrm{L}}^{\mathrm{b}-\mathrm{i}}]}{[{\mathrm{H}}_{\mathrm{n}+1-\mathrm{i}}{\mathrm{L}}^{\mathrm{b}+1-\mathrm{i}}]}\mathrm{i}=1\mathrm{to}\mathrm{n}$$

(4)

Stoichiometric stability constants and stoichiometric dissociation constants are connected by Equations (5) and (6):

$${\mathrm{pK}}_{\mathrm{i}}=\lg {\mathsf{\beta }}_{\mathrm{n}+1-\mathrm{i}}-\lg {\mathsf{\beta }}_{\mathrm{n}-\mathrm{i}}\mathrm{i}=1\mathrm{to}\mathrm{n}$$

(5)

$$\lg {\mathsf{\beta }}_{\mathrm{i}}={\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{i}}\mathrm{p}{\mathrm{K}}_{\mathrm{n}+1-\mathrm{j}}\mathrm{i}=1}\mathrm{to}\mathrm{n}$$

(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_iL^i–a are derived from Equation (7):

$${\mathrm{x}}_{\mathrm{i}}=\frac{{10}^{\lg {\mathsf{\beta }}_{\mathrm{i}}-\mathrm{i}\cdot \mathrm{p}\mathrm{H}}}{{\displaystyle \sum _{\mathrm{j}=0}^{\mathrm{n}}{10}^{\lg {\mathsf{\beta }}_{\mathrm{j}}-\mathrm{j}\cdot \mathrm{p}\mathrm{H}}}}\mathrm{i}=0\mathrm{to}\mathrm{n}$$

(7)

Each protolytic species H_iL^i–a present in the equilibrium contributes specific NMR parameters δ(H_iL^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):

$$\mathsf{\delta }={\displaystyle \sum _{\mathrm{i}=0}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{i}}\cdot {\mathsf{\delta }}_{{\mathrm{H}}_{\mathrm{i}}{\mathrm{L}}^{\mathrm{i}-\mathrm{a}}}}\mathrm{i}=0\mathrm{to}\mathrm{n}$$

(8)

A gradient called the deprotonation shift Δ_i [ppm] is given by Equation (9):

$${\mathsf{\Delta }}_{\mathrm{i}}={\mathsf{\delta }}_{{\mathrm{H}}_{\mathrm{n}-\mathrm{i}}{\mathrm{L}}^{\mathrm{b}-\mathrm{i}}}-{\mathsf{\delta }}_{{\mathrm{H}}_{\mathrm{n}+1-\mathrm{i}}{\mathrm{L}}^{\mathrm{b}+1-\mathrm{i}}}\mathrm{i}=1\mathrm{to}\mathrm{n}$$

(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):

$$\mathsf{\tau }=\frac{{\mathrm{n}}_{\mathrm{T}\mathrm{i}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}}}{{\mathrm{n}}_{\mathrm{T}\mathrm{i}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}}}$$

(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, HNO₃, HClO₄). n_Titrand corresponds to the molar amount of a n-basic acid H_nL.

Details of the basic principles and experimental equipment with hardware and software are described in [31,32] and in references given herein.

2. 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. (CH₃)₃Si-CH₂-CH₂-SO₃Na, while δ_P [ppm] was virtually referenced towards external H₃PO₄. Coupling constants ⁿJ_XY are given in [Hz].

2.1. Phosphonic Acids

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

2.1.1. Methanephosphonic Acid 1

The results from a proton-coupled ³¹P-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. Specific chemical shifts δ_C, δ_P and coupling constants ¹J_PC and ²J_PH of methanephosphonic acid 1 were obtained by ¹³C{¹H}-, ³¹P{¹H}-, and ³¹P-NMR-controlled titrations in H₂O. Δ_i = δ(H_n-iL) − δ(H_n+1-iL) or Δ_i = ⁿJ_PC(H_n-iL) − ⁿJ_PC(H_n+1-iL), 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].

	1 in H2O
Method	13C{1H}		31P{1H}	31P		31P{1H}
Exp.	a)		b)	c)		d)
Species	δC	1JPC	δP	δP	2JPH	δP
	[ppm]	[Hz]	[ppm]	[ppm]	[Hz]	[ppm]
H2L	14.27	135.92	33.03	33.03	−17.65	31.76
HL−	15.53	133.82	24.79	24.79	−16.52	24.94
L2−	16.61	129.95	21.08	21.08	−15.52	20.94
Gradients	δC	1JPC	δP	δP	2JPH	δP
Δ1	1.26	−2.10	−8.24	−8.24	1.13
Δ2	1.08	−3.87	−3.71	−3.71	1.00
pKi
pK1	2.27		2.06	2.00		2.33
pK2	7.85		7.66	7.68		7.78

. The deprotonation of both P-OH functions induces a decrease in chemical shifts δ_P and a decrease in the absolute values of ²J_PH.

pK_i values found are consistent with results from potentiometric titrations of CH₃P(O)(OH)₂ [46].

2.1.2. Phenylphosphonic Acid 2

Chemical shifts δ_P for protolytic species H₂L, HL⁻, and L²⁻ of phenylphosphonic acid 2 together with dissociation constants pK₁ and pK₂ are listed in

Table 3. Specific chemical shifts δ_P [ppm], gradients [ppm] and dissociation constants pK_i from ³¹P{¹H}-NMR-controlled titration of phenylphosphonic acid 2 vs. TMAOH and NaOH. Exp.: C_Titrator: a) 0.09894 mol/L TMAOH. b) 0.09925 mol/L NaOH. C_Titrand: a) 0.02 mol/L 3. b) 0.008 mol/L 2. Shifts and gradients given in ppm.

	Phenylphosphonic Acid 2
	vs. TMAOH	vs. NaOH
	a)	b)
δP(H2L)	18.39	17.77
δP(HL−)	13.77	13.75
δP(L2−)	11.69	11.72
Δ1	−4.62	−4.02
Δ2	−2.08	−2.03
pK1	1.74	1.86
pK2	7.28	7.16

. The deprotonation of both P-OH groups leads to characteristic high field shifts for δ_P as indicated by negative gradients Δ₁ and Δ₂.

Higher concentrations are required for ¹³C{¹H}-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.

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-PO₃²⁻, 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 ⁿJ_PC (n = 1 to 4). Particularly indicative is ¹J_PC from the ipso-carbon C1, which reaches a minimum at total deprotonation. Numerical results for compound 2 are listed in

Table 4. Specific chemical shifts δ_C [ppm] and coupling constants ⁿJ_PC (n = 1 to 4) [Hz] for the ¹³C{¹H}-NMR-controlled titration of phenylphosphonic acid 2 vs. KOH. pK₁ = 1.75. pK₂ = 6.92. Experimental data: C_Titrand: a) 0.237 mol/L 2. C_Titrator: 4.53 mol/L KOH.

	δC and nJPC for Species			Gradients
Parameters	H2L	HL−	L2−	Δ1	Δ2
δC C1	133.66	138.15	143.83	+4.48	+5.69
δC C2/6	133.68	133.45	133.43	−0.24	−0.02
δC C3/5	131.99	131.59	130.95	−0.40	−0.64
δC C4	135.66	134.03	131.98	−1.58	−2.06
1JPC	183.48	177.02	167.32	−6.46	−9.70
2JPC	10.51	9.72	8.79	−0.79	−0.93
3JPC	14.84	13.90	12.65	−0.94	−1.25
4JPC	3.08	2.91	2.74	−0.17	−0.17

:

Laborious and time-consuming single sample ³¹P{¹H}- and ¹³C{¹H}-NMR studies on phenylphosphonic acid 2 were performed, where δ_P, δ_C, and ⁿJ_PC data are consistent with findings derived from the automated titrations presented in this paper [17].

2.2. Comparison of Aliphatic and Aromatic Aminophosphonic Acids

α-Aminoethylphosphonic acid (α-Ala-P) 3 [29,44], β-aminoethylphosphonic acid (β-Ala-P, CILIATIN) 4 [29], and p-aminophenylphosphonic acid 5 [29,30,43] shown in Scheme 3 will be studied as examples in the following section.

2.2.1. 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. Macroscopic and microscopic dissociation species of aminophosphonic acids.

Dissociation Species
Macroscopic	Microscopic
H3L+	+NH3-R-PO3H2
H2L	+NH3-R-PO3H−	NH2-R-PO3H2
HL−	+NH3-R-PO32−	NH2-R-PO3H−
L2−		NH2-R-PO32−

below:

If R is aliphatic (e.g., in 3 and 4), the deprotonation takes place following route a): ⁺NH₃-R-PO₃H₂ → ⁺NH₃-R-PO₃H⁻ → ⁺NH₃-R-PO₃²⁻ → NH₂-R-PO₃²⁻. But if R is aromatic (e.g., in 5. R = p-C₆H₄-), the deprotonation dominantly will follow b): ⁺NH₃-R-PO₃H₂ → ⁺NH₃-R-PO₃H⁻ → NH₂-R-PO₃H⁻ → NH₂-R-PO₃²⁻. Consistent conclusions are supported by a combination of potentiometric titrations and ³¹P{¹H}-NMR-controlled titrations as shown for examples 3 to 5, and in addition by ¹³C{¹H}-NMR-controlled titrations for examples 3 and 4. Owing to its low solubility, 5 was not suitable for ¹³C{¹H}-NMR-controlled titrations.

Macroscopic dissociation constants pK_i of 3 and 4 are listed in

Table 6. Macroscopic dissociation constants pK_i of compounds α-Ala-P 3 and β-Ala-P 4 obtained by ¹³C{¹H}- and ³¹P{¹H}-NMR-controlled titrations and by potentiometric titrations [4a]. Note: pK₃ − pK₂ > 3 and pK₂ − pK₁ > 3 for compounds 3 and 4. Exp.: 3: C_Titrand: a) 0.0867 mol/L 3 + 0.0834 mol/L HNO₃. b) and c) 0.005 mol/L 3 + 0.00476 HNO₃ + 0.0917 mol/L NaNO₃. C_Titrator: a) 3.98 mol/L NaOH. b) and c): 0.100 mol/L NaOH. 4: C_Titrand: d) 0.139 mol/L 4 + 0.139 mol/L HNO₃. e) 0.010 mol/L 4 + 0.010 mol/L HNO₃. f) 0.010 mol/L 4 + 9.747 mmol/L HNO₃. g) 0.005 mol/L 4 + 0.005 mol/L HNO₃ + 0.100 mol/L TMACl. C_Titrator: d) 0.98 mol/L NaOH. e): 0.0991 mol/L TMAOH. f): 0.0993 mol/L NaOH. g): 0.099 mol/L TMAOH.

	3			4
	13C{1H} a	31P{1H} b	Pot. c	13C{1H} d	31P{1H} e	31P{1H} f	Pot. g
	NaOH	NaOH	NaOH	NaOH	TMAOH	NaOH	TMAOH
pK1	0.70	0.31	0.3	1.02	1.22	1.26	1.14
pK2	5.72	5.63	5.58	6.38	6.23	6.24	6.34
pK3	10.64	10.21	10.28	11.50	11.06	11.08	11.06

. pK_i data of compounds 4 and 5 were discussed in [44,45,48,49,50].

Specific chemical shifts δ_P and gradients Δ for compounds 3 to 5 obtained by ³¹P{¹H}-NMR-controlled titrations are given in

Table 7. Specific chemical shift δ_P [ppm] and gradients Δ [ppm] for compounds 3 to 5 [44]. *) Not iterated. Experimental details for 3 and 4 are given in Table 6. Titrator: a) NaOH; b) TMAOH; c) for 5 were used: C_Titrand = 1.6953 mol/L 5 and 3.6935 mol/L TMAOH. Titrator = 0.09993 mol/L HCl.

	3	4		5
	31P{1H} a	31P{1H} b	31P{1H} a	31P{1H} c
Species	δP	δP	δP	δP
H3L+	15 *	22.9	23.4	13 *
H2L	14.92	19.29	19.36	12.16
HL−	13.08	16.80	16.81	15.29
L2−	22.25	19.39	19.72	12.70
Gradients
Δ1	−0.08	−3.61	−4.04	−0.84
Δ2	−1.84	−2.49	−2.55	+3.13
Δ3	+9.17	+2.59	+3.91	−2.59

:

The deprotonation of the P-OH groups led to high field shifts for δ_P connected with negative gradients. The final deprotonation of the NH₃⁺ 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 H₂L, HL⁻ and L²⁻ species of 3 and 4 were mentioned in [5,45]. In addition, δ_P of H₃L⁺ was accessible for 4 but not for 3.

¹³C{¹H}-NMR-controlled titrations of compounds 4 and 5 led to specific chemical shifts δ_C, coupling constants ¹J_PC, and gradients Δ as listed in

Table 8. Specific chemical shifts δ_C [ppm], coupling constants ¹J_PC [Hz], and corresponding gradients Δ 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. ¹J_PC shows a minimum for species HL⁻ of 3 and 4. ²J_PC was not resolved for compounds 3 and 4.

	3 in H2O			4 in H2O
Species	δC(C1)	1JPC	δC(C2)	δC(C1)	1JPC	δC(C2)
H3L+	46.80	151.5	16.0	27.50	137.4	37.09
H2L	47.70	143.8	16.43	28.73	131.4	38.22
HL−	49.07	134.5	17.23	29.47	124.8	39.28
L2−	48.15	138.0	19.79	35.45	126.5	39.76
Gradients
Δ1	+0.9	−8.7	+0.43	+1.23	−6.0	+1.13
Δ2	+1.37	+9.3	+0.80	+0.74	−6.6	+1.04
Δ3	−0.92	+3.5	+2.55	+5.98	+1.3	+0.47

:

NMR was used to monitor the complex formation of aminophosphonic acids with biorelevant cations in homogeneous solutions. An instructive example is the ³¹P{¹H}-NMR-controlled titration of CILIATIN/Mg²⁺ vs. NaOH where the formation of [MgL] and [MgHL]⁺ was monitored [44].

2.2.2. Aromatic p-Aminophenylphosphonic Acid 5

The deprotonation of PO₃H⁻ in aliphatic aminophosphonic acids 3 and 4 is affiliated with a high field shift (gradients Δ₂ are negative), while the deprotonation of the ammonium function ⁺NH₃ leads to a low field shift (gradients Δ₃ are positive).

The aromatic p-aminophenylphosphonic acid 5 exhibits a different pattern: while gradient Δ₂ is positive, Δ₃ is negative (Scheme 4).

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 ¹³C{¹H}-NMR-controlled titration should lead to specific chemical shifts and coupling constants ⁿJ_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 ¹³C{¹H}-NMR spectra of 5 is not sufficient to perform evaluable ¹³C{¹H}-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 C₆H₅PO₃H₂ 2 and C₆H₅NH_2*HCl 6 were compared. The following macroscopic pK_i data were found by potentiometric titration and listed in

Table 9. Dissociation constants of compounds p-aminophenylphosphonic acid 5, phenylphosphonic acid 2, and anilinium hydrochloride 6.

	5	2	6
pK1	0.44	1.88	4.68
pK2	3.95	7.15
pK3	7.56

:

Those data point towards a dominating deprotonation sequence for 5 following ⁺NH₃-R-PO₃H₂ → ⁺NH₃-R-PO₃H⁻ → NH₂-R-PO₃H⁻ → NH₂-R-PO₃²⁻. But is it justified to exclude the alternative route ⁺NH₃-R-PO₃H₂ → ⁺NH₃-R-PO₃H⁻ → ⁺NH₃-R-PO₃²⁻ → NH₂-R-PO₃²⁻? Evaluating the macroscopic dissociation constants of 5 shows that between pH = 1.5 and pH = 10, only three macroscopic species exist: H₂L, HL⁻, and L²⁻. 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 NH₂-R-PO₃H⁻ and ⁺NH₃-R-PO₃²⁻ in a ratio of 9:1. Thus, the results from the UV/VIS-controlled titration of 5 [30] confirm the dominance of NH₂-R-PO₃H⁻ as previously assumed for the macroscopic deprotonation sequence derived from the ³¹P{¹H}-NMR-controlled titration of 5 [44].

2.3. Phosphonocarboxylic Acids HOOC-(CH₂)_n-PO₃H₂ 7a to 7d (n = 0 to 3)

Phosphonocarboxylic acids HOOC-(CH₂)_n-PO₃H₂ gave rise to potentiometrically [4,44] and NMR-controlled titrations [4,28,31,44]. Those neutral acids of type H₃L deprotonate dominantly in a sequence: HOOC-(CH₂)_n-PO₃H₂ → ⁻OOC-(CH₂)_n-PO₃H⁻ → ⁻OOC-(CH₂)_n-PO₃²⁻. Corresponding dissociations constants for compounds shown in Scheme 5 are listed in

Table 10. Dissociation constants of phosphonocarboxylic acids HOOC-(CH₂)_n-PO₃H₂ (n = 0 to 3) 7a to 7d [8,44]. Experimental data: ^a) C_Titrand: 0.153 mol/L FOSCARNET (trisodium phosphonoformate hexahydrate), C_Titrator: 2.002 mol/L HNO₃, retro titration; ^b) C_Titrand: 0.220 mol/L 7b, C_Titrator: 0.980 mol/L NaOH. ^c) C_Titrand: 0.200 mol/L 7c, C_Titrator: 3.986 mol/L NaOH. ^d) C_Titrand: 0160 mol/L 7d, C_Titrator: 3.986 mol/L NaOH.

	HOOC-(CH2)n-PO3H2
	7a	7a [4]	7b	7c	7c [4]	7d
	n = 0 a	n = 0	n = 1 b	n = 2 b	n = 2	n = 3 b
pK1	0.78	1.7 ± 0.1	1.22 ± 0.166	2.58 ± 0.013	2.26 ± 0.04	2.276 ± 0.006
pK2	3.60	3.59 ± 0.02	4.942 ± 0.004	4.633 ± 0.004	4.63 ± 0.02	4.776 ± 0.004
pK3	7.57	7.56 ± 0.02	8.099 ± 0.003	7.738 ± 0.003	7.75 ± 0.02	7.969 ± 0.003

below:

¹³C{¹H}-NMR-controlled titrations yielded the specific chemical shift δ_C and coupling constants ⁿJ_PC (n = 1 to 3) of phosphonocarboxylic acids HOOC-(CH₂)_n-PO₃H₂ (n = 0 to 3) 7a to 7d as listed in

Table 11. (a). Specific chemical shifts δ_C [ppm] and coupling constants ⁿJ_PC [Hz] of phosphonocarboxylic acids HOOC-(CH₂)_n-PO₃H₂ (n = 0 to 3) 7a to 7d. For experimental data, see preceding Table 10. Remarks: n. r. = not resolved; (b). Gradients Δ_i of specific chemical shifts δ_C [ppm] and coupling constants ⁿJ_PC [Hz] of phosphonocarboxylic acids HOOC-(CH₂)_n-PO₃H₂ (n = 0 to 3) 7a to 7d. For experimental data, see preceding Table 10.

(a)
7	n	Species	δC(C1)	δC(C2)	δC(C3)	δC(C4)	1JPC	2JPC	3JPC	4JPC
a	0	H3L	176.8				246.6
		H2L−	178.7				236.7
		HL2−	181.8				231.8
		L3−	187.3				220.0
b	1	H3L	172.91	37.68			128.6	n. r.
		H2L−	175.44	39.30			117.8	n. r.
		HL2−	178.85	41.64			119.2	n. r.
		L3−	181.74	43.50			112.6	n. r.
c	2	H3L	179.25	30.09	24.51		138.5	3.6	17.3
		H2L−	180.68	31.40	25.91		135.1	3.2	17.8
		HL2−	185.01	34.27	27.50		133.0	4.1	18.7
		L3−	186.71	35.61	28.99		130.3	3.6	19.8
d	3	H3L	180.38	36.67	20.44	28.19	135.2	4.0	17.4	n. r.
		H2L−	181.12	37.46	21.58	29.74	133.5	3.8	17.2	n. r.
		HL2−	185.86	41.45	23.13	30.46	132.5	3.9	17.7	n. r.
		L3−	186.41	42.01	24.08	31.92	130.1	3.4	17.9	n. r.
(b)
7	n	Gradients	δC(C1)	δC(C2)	δC(C3)	δC(C4)	1JPC		2JPC	3JPC
a	0	Δ1	+1.9				−9.9
		Δ2	+3.1				−4.9
		Δ3	+5.5				−11.8
b	1	Δ1	+2.53	+1.62			−10.8
		Δ2	+3.41	+2.34			+1.4
		Δ3	+2.89	+1.86			−6.6
c	2	Δ1	+1.43	+1.31	+1.40		−3.4		−0.3	0.5
		Δ2	+4.33	+2.87	+1.59		−2.1		0.9	0.9
		Δ3	+1.70	+1.34	+1.49		−2.7		−0.5	1.1
d	3	Δ1	+0.74	+0.79	+1.14	1.56	−1.7		−0.2	−0.2
		Δ2	+4.74	+3.99	+1.55	0.72	−1.0		0.1	0.5
		Δ3	+0.55	+0.56	+0.95	1.46	−2.4		−0.5	0.2

a. Gradients are given in Table 11b. Note: The deprotonation of P-OH groups and of C-OH led to a low field shift for all carbon atoms. Some chemical shifts and coupling constants ¹J_PC of 7a and 7c were obtained and discussed in an early key paper [4].

2.3.1. Compound 7c: ¹³C{¹H}-NMR-Controlled Titration of 3-Phosphonopropionic Acid HOOC-CH₂-CH₂-PO₃H₂ 7c.

3-Phosphonopropionic acid 7c was chosen as an example to show practical results from ¹³C{¹H}-NMR-controlled titrations (see Figure 3a,b below). The deprotonation of C-OH and of both P-OH functions induces low field shifts for C1, C2, and C3. Hence, the corresponding gradients are negative. Lorentzian deconvolution of ¹³C{¹H} signals yielded ⁿJ_PC, where absolute values follow the sequence: ¹J_PC >> ³J_PC > ²J_PC. See Table 11a,b above.

The 81 MHz ³¹P{¹H}-NMR-controlled titration of 3-phosphonopropionic acid 7c vs. NaOH yielded Figure 3c. The deprotonation sequence reported in [4] corresponds to: HOOC-CH₂-CH₂-PO₃H₂ → HOOC-CH₂-CH₂-PO₃H⁻ → ⁻OOC-CH₂-CH₂-PO₃H⁻ → ⁻OOC-CH₂-CH₂-PO₃²⁻. Deprotonation at PO₃H₂ or PO₃H⁻ is affiliated with high field shifts of δ_P, while deprotonation at HOOC induces a low field shift for δ_P.

Specific chemical shifts δ_P for 7c and corresponding anions together with gradients are listed in

Table 12. Gradients Δ_i of specific chemical shifts δ_P [ppm] of 7c. Experimental data: C_Titrand: 0.010 mol/L of 7c. C_Titrator: 0.10 mol/L TMAOH.

Shifts	δP	Error
H3L	29.93	±0.25
H2L−	24.56	±0.02
HL2−	25.88	±0.01
L3−	22.06	±0.01
Gradients
Δ1	−5.37
Δ2	+1.32
Δ3	−3.82

.

2.3.2. ^19. F-NMR-Controlled Retro Titrations of Lithium Salts LiOOC-CH_2-nF_n-PO₃Li₂ 8a and 8b

The trilithium salts LiOOC-CH_2-nF_n-PO₃Li₂ (8a and 8b; n = 1 and 2, Scheme 6) were used for retro titrations vs. HNO₃, since the parent mono- and difluorophosphonoacetic acids 8c and 8d were not available for ¹⁹F-NMR- and ³¹P{¹H}-NMR titrations. Corresponding dissociation constants pK_i of 8c and 8d were calculated as listed in

Table 13. Dissociation constants of fluorinated phosphonocarboxylic acids HOOC-CH_2-nF_n-PO₃H₂ (8c and 8d; n = 1 and 2) obtained by the retro titration of LiOOC-CH_2-nF_n-PO₃Li₂ (8a and 8b; n = 1 and 2) vs. HClO₄. Experimental data: C_Titrand: 0.85 mol/L 8a or 8b resp. C_Titrator: 0.3928 mol/L HClO₄. No ion buffer.

	HOOC-CH2-nFn-PO3H2
	8c n = 1	8d n = 2
	[44]	[44]	[52]
pK1	1.05	0.52	1.30
pK2	3.43	2.22	1.95
pK3	7.08	6.36	6.16

, while chemical shifts δ_F and δ_P and coupling constants ²J_PF are given in

Table 14. Chemical shifts δ_F [ppm], coupling constants ²J_PF [Hz] and corresponding gradients of fluorinated phosphonocarboxylic acids HOOC-CH_2-nF_n-PO₃H₂ (8c and 8d, n = 1 and 2) obtained by ¹⁹F-NMR-controlled titrations vs. HNO₃ of LiOOC-CH_2-nF_n-PO₃Li₂ (8c and 8d, n = 1 and 2). For experimental data, see Table 13. δ_F is virtually referenced to δ_F(CF³⁵Cl₂³⁷Cl) = 0 ppm.

HOOC-CH2-nFn-PO3H2
	8c	8d	8c	8d
	n = 1	n = 2	n = 1	n = 2
	19F		19F
Species	δF	δF	2JPF	2JPF
H3L	−38.27	44.24	67.8	76.5
H2L−	−38.72	50.24	65.5	88.6
HL2−	−29.31	53.05	70.3	92.8
L3−	−27.15	55.24	63.4	82.0
Gradients
Δ1	−0.45	+6.00	−2.3	+12.1
Δ2	−9.41	+2.81	+4.8	+4.2
Δ3	−8.16	+2.19	−6.9	−10.8

. As expected, the introduction of fluorine into the skeleton of the parent phosphonoacetic acid led to lower pK₁ and pK₂ values. The deprotonation of P-OH groups induces a low field shift for δ_F in fluorinated phosphonic acids 8c and 8d.

2.3.3. 2,4-Diphosphonobutane-1,2-Dicarboxylic Acid (DPBDC) 9

Strong practical interests focused on polyfunctional phosphonocarboxylic acids, e.g., phosphonosuccinic acid (PBS), 1-phosphonopropane-1,2,3-tricarboxylic acid (PPTC), and 2-phosphonobutane-1,2,4-tricarboxylic acid (PBTC), which gave rise to analytical and NMR studies of protolytic and complex formation equilibria [42,43,44,53].

The following section will deal with 2,4-diphosphonobutane-1,2-dicarboxylic acid (DPBDC) 9 to demonstrate the potential of automated NMR titrations. Dissociation constants of this 6-valent acid DPBDC 9 were obtained from precision potentiometric [53] and by ¹³C{¹H}-NMR-controlled titrations vs. NaOH [44].

¹³C{¹H}-technique yielded Figure 4a–d. The spin enumeration used in subsequent tables and figures is given in Scheme 7:

Results for those six carbon atoms C1*, C2*, and C1 to C4 will be presented as (δ,τ))-contour plots in four separate spectral ranges shown in Figure 4a–d. Numerical results including specific chemical shifts δ_C and coupling constants ⁿJ_PC of DPBDC are listed in

Table 15. Dissociation constants of 2,4-diphosphonobutane-1,2-dicarboxylic acid (DPBDC) as obtained from ¹³C{¹H}-NMR-controlled and potentiometric titrations vs. NaOH. * Concentrations given in mol/L.

	13C{1H} NMR [44]	Potentiometric [44]	Potentiometric [53]
pK1	1.07	0.6	1.806 ± 0.066
pK2	2.73	2.42	2.250 ± 0.021
pK3	4.82	4.32	4.078 ± 0.005
pK4	7.05	6.46	6.562 ± 0.004
pK5	8.95	8.18	8.664 ± 0.006
pK6	11.62	10.75	12.839 ± 0.007
CTitrand	0.262 (DPBDC) *	0.0050 (DPBDC) *	0.01119 (DPBDC) *
CTitrator	3.986 (NaOH) *	0.0975 (NaOH) *	0.09863 (TMAOH) *
CIon buffer	0	0.1 (NaCl) *	0.09863 (TMANO3) *

and

Table 16. Specific chemical shifts δ_C [ppm], coupling constants ⁿJ_PC [Hz] and gradients Δ_i [ppm] of 2,4-diphosphonobutane-1,2-dicarboxylic acid DPBDC 9. For experimental data, see Table 15.

	C1	C2			C3	C4			C1*		C2*
Species	δC	δC	1JPC	3JPC	δC	δC	1JPC	3JPC	δC	3JPC	δC
H6L	38.29	52.19	124.2	18.4	27.26	25.11	134.0	4.7	177.23	17.5	177.53
H5L−	38.70	52.42	116.8	18.2	27.51	25.56	132.4	5.1	177.82	15.9	178.66
H4L2−	39.38	52.98	116.9	17.3	29.09	26.34	131.3	6.3	178.85	12.5	179.18
H3L3−	41.78	54.06	116.7	16.8	30.95	26.15	131.3	9.0	181.69	6.4	180.70
H2L4−	43.28	54.66	115.9	16.6	29.98	26.54	130.3	9.9	183.46	4.3	181.53
HL5−	43.26	55.04	115.8	15.9	30.99	27.51	128.3	9.4	184.08	5.3	182.53
L6−	42.70	55.01	111.7	16.3	29.87	28.65	127.7	-	184.82	18.9	186.15
Gradients
Δ1	+0.41	+0.23	−7.4	−0.2	+0.25	+0.45	−1.6	+0.4	+0.59	−1.6	+1.13
Δ2	+0.68	+0.56	+0.1	−0.9	+1.58	+0.78	−1.1	+1.2	+1.03	−3.4	+0.52
Δ3	+1.40	+1.08	−0.2	−0.5	+1.86	−0.19	0.0	+2.7	+2.84	−6.1	+1.52
Δ4	+1.50	+0.60	−0.8	−0.2	−0.97	+0.39	−1.0	+0.9	+1.77	−2.1	+0.83
Δ5	−0.02	+0.38	−0.1	−0.7	+1.01	+0.97	−2.0	−0.5	+0.62	+1.0	+1.00
Δ6	−0.56	−0.03	−4.1	+0.4	−1.12	+1.14	−0.6	-	+0.74	+13.6	+3.62

.

Some Comments on DPBDC 9

A complicated example for NMR-controlled titration which needs some discussion is 2,4-diphosphonobutane-1,2-dicarboxylic acid DPBDC 9. Measurements and data evaluation were performed according to the state of technique. But it is not possible to explain all the parameters found for compound 9 by comparison with data from analogous structural elements of HOOC-(CH₂)n-PO₃H₂ (n = 1 to3) 7b to 7d, H₂O₃P-(CH₂)₃-PO₃H₂, and phosphonopolycarboxylic acids 10 to 12 shown in Scheme 8:

In a starting phase, 1D and 2D NMR techniques involving ¹H-, ¹H{³¹P}-, ¹³C-, ¹³C{¹H}-, and C,H-COSY spectra were combined to assign the carbons C1*, C2*, C1 to C4 and phosphonate functions P2* and P4*.

For ¹³C{¹H}-NMR-controlled titration, the deprotonation steps may be divided into three sections (see Table 15 and Figure 4a,d). For τ = 0 to 2 deprotonation PO₃H₂ → PO₃H⁻ takes place, first at P2* and then at P4*. In the second section for τ = 2 to 4, the carboxylic units C1* and C2* are deprotonated. Finally for τ = 4 to 6 the deprotonation PO₃H⁻ → PO₃²⁻ takes place at P2* and P4*.

(1) Comments on Chemical Shifts δ_C 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 δ_C C1* and C2* (see Figure 4a), while carbons C1 to C4 exhibit specific non-monotonous trends (see Figure 4b,d).

Since gradient Δ₆ for δ_C (C1*) > Δ₅ for δ_C (C1*), the final sixth deprotonation steps is affiliated with P2*. This conclusion is confirmed by Δ₆ for δ_C (C2*) >> Δ₅ for δ_C (C1*). Hence, the fifth deprotonation step of 9 is due to PO₃H⁻ → PO₃²⁻ of P4*. Dynamic chemicals shifts δ_C of C1* span a range from 177.5 to 184.61 ppm, while δ_C of C2* is found from 178 to 185.1, as shown in Figure 4a.

A tentative explanation may be found using Δ₃ for δ_C (C1*) > Δ₄ for δ_C (C1*) and Δ₃ for δ_C (C2*) < Δ₄ for δ_C (C1*). These findings imply that the carboxylic function C1* is more acidic than C*2.

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 H₆L corresponds to 52.2 ppm, while the totally deprotonated form L⁶⁻ is found at 55 ppm. Deprotonation at C1* and C2* is characterized again by Δ₃ of δ_C (C2) > Δ₄ of δ_C (C2).

Chemical shifts δ_C of C3 span a range of 38.4 to 43.3 ppm. Surprisingly, the final deprotonation HL⁵⁻ → L⁶⁻, due to PO₃H⁻ → PO₃²⁻ 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 (Δ₆ = −0.56 Hz) connected to deprotonation at a PO₃H⁻ unit.

The situation is even more complex for the chemical shift δ_C of C2 covering a range from 27.4 to 30.9 ppm (Figure 4d). Two negative gradients are observed: Δ₄ = −0.97 ppm for H₃L³⁻ → H₂L⁴⁻ due to deprotonation at C2* and Δ₆ = −1.12 ppm for HL⁵⁻ → L⁶⁻ induced by deprotonation at P2*. For simpler compounds CH₃-(CH₂)_n-COOH (n = 0 to 3) and HOOC-(CH₂)_n-COOH (n = 1 to 3), solely positive gradients were described [54].

In addition, we did not observe negative gradients for compounds 7b to 7d and 10 (PBC), but in 11 (PPTC) and in 12 (PBTC) [43].

The major RR/SS diastereomer of PPTC 11 exhibited a negative gradient Δ₅ (C1) = −0.44 ppm for the final deprotonation step PO₃H⁻ → PO₃²⁻ at P3*. An upfield shift occurred, since δc (C1) of HL⁴⁻ = 42.17 ppm and δc (C1) of L⁵⁻ = 41.73 ppm. This effect might be due to opening of hydrogen bridges and conformational changes. In contrast here to is the minor RR/SS diastereomer of PPTC, it does not show a negative gradient Δ₅ (C1) [42,44].

Weaker negative gradients Δ₅ = −0.22 ppm are observed for chemical shifts δ_C of both carbons C1 and C3 in PBTC 12. The final deprotonation PO₃H⁻ → PO₃²⁻ at P2* is affiliated with following data: δc (C1) of HL⁴⁻ = 43.54 ppm, δc (C1) of L⁵⁻ = 43.32 ppm, and δc (C3) of HL⁴⁻ = 32.60 ppm, δc (C3) of L⁵⁻ = 32.60 ppm. In contrast hereto carbons C2 and C4 in PBTC 12 exhibit positive gradients Δ₅.

Those unexpected observations for chemical shifts δc in 9 and conformational aspects will be mentioned in the following section on coupling constants ⁿJ_PC as well.

(2) Comments on Coupling Constants nJPC (n = 1 to 3) of DPBDC 9

The vicinal coupling ³J_PC (P2*C1*) is remarkably sensitive towards the protonation state (see Figure 5):

For the protolytic species H₆L to H₂L⁴⁻ of 9, a decrease in ³J_PC (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 HL⁵⁻ and finally L⁶⁻. Between pH = 7 and 8, a maximum of the protolytic species H₂L⁴⁻ is expected, while HL⁵⁻ dominates around pH = 9. Those observations indicate changes of the dihedral angle of P2*-C2-C1-C1* possibly involving hydrogen bridges as indicated by Scheme 9 below:

A corresponding bridge -C1-P-O---H---O-P-C2- was discussed for the HL³⁻ species of ethane-1,2-bisphosphonic acid [44].

²J_PC (P2*C1), ²J_PC (P2*C3), ²J_PC (P2*C2*), and ²J_PC (P4*C3) were not resolved in ¹³C{¹H}-NMR spectra obtained by NMR-controlled titrations.

³J_PC (P2*C4) shows a monotonous increase from 4.7 Hz to a maximum of 9.9 Hz for the sequence H₆L to H₂L⁴⁻ followed by a decrease to 9.4 Hz for HL⁵⁻. This observation points towards an increase in the dihedral angle in P2*-C2-C3-C4.

³J_PC (P4*C2) is less sensitive towards deprotonation but larger than ³J_PC (P2*C4) and found in a range from 18.4 to 16.3 Hz possibly indicating a tendency towards trans-conformation of the fragment P4*-C4-C3-C2. For comparison, ³J_PC in HOOC-(CH₂)₃-PO₃H₂ 7d appeared in a corresponding range from 17.2 to 17.9 Hz.

¹J_PC (P2*C2), ranging from 124.2 to 111.7 Hz, is markedly smaller than ¹J_PC (P4*C4), which is observed from 134.0 to 127.7 Hz. A ¹J_PC, pH diagram is given in Figure 6 below:

¹J_PC (P2*C2) is very indicative and selective for the deprotonation of the phosphonic functions PO₃H₂ → PO₃H⁻ and PO₃H⁻ → PO₃²⁻. It indicates that the first deprotonation (pK₁ = 1.07) of DPBDC 9 takes place at P2* with a strong gradient Δ₁ ¹J_PC (P2*C2) = −7.4 Hz. The final deprotonation (pK₆ = 11.62) is affiliated with P2* as well as indicated by Δ₆ ¹J_PC (P2*C2) = −4.1 Hz. This assignment leaves pK₂ = 2.73 and pK₅ = 8.95 to the deprotonation of P4*. Deprotonation at the carboxylic groups (pK₃ = 4.62) and pK₄ = 7.05) does not significantly affect ¹J_PC (P2*C2) and ¹J_PC (P4*C4).

Results on ¹J_PC (P2*C2) of 9 are consistent with observations on phosphonosuccinic acid 10, where ¹J_PC (P2*C2) is found in a range from 133.7 to 112.1 Hz. Strong gradients Δ₁ = −17.1 Hz and Δ₄ = −4.5 Hz are affiliated with the deprotonation of P2*, while deprotonations of C1* and C2* do not significantly influence ¹J_PC (P2*C2).

3. Conclusions

Automated NMR-controlled titrations efficiently combine ¹H, ¹³C-, ¹⁹F-, and ³¹P-NMR spectroscopy with potentiometric titrations to determine dissociation constants, specific chemicals shifts and coupling constants. Results are presented in two-dimensional plots, where NMR parameters (chemical shifts, coupling constants) are correlated with analytical parameters (pH, degree of titration τ). High digital resolution and high S/N are achieved in time- and material-saving measurements. These hyphenated techniques are powerful instruments to identify the structure and purity of research and industrial compounds. Limitations of accuracy due to the nature of glass electrodes occur at very low and very high pH values, obscuring the lower and higher pK_i values. In those situations, single sample NMR methods are recommended. ¹³C{¹H}-NMR-controlled titrations may be used for conformational analysis. For more complicated structures, additional studies using pH-dependent high-resolution ¹H- and ¹H{³¹P}-NMR spectra, X-ray diffraction of selected salts and molecular modelling of acids and anions are needed to solve details of conformational problems. The latter topics are laborious and beyond the scope of this paper.

4. Experimental

Details of the hardware and software used in NMR-controlled titration together with references for this field are described in [31,32]. Most model compounds were obtained from external sources listed under the acknowledgements.