³¹P NMR chemical shift of phosphine oxides measures the total strength of multiple anticooperative H-bonds formed between the P=O group and proton donors

Abstract

In this work, experimental ³¹P NMR chemical shifts of triphenylphosphine oxide are used to evaluate the strength of P=O⋯H–O hydrogen bonds. Complexes featuring either one or two H-bonds (1 : 1 and 1 : 2 complexes, respectively) formed between Ph₃P=O and 24 substituted phenols are investigated by low-temperature liquid-state NMR spectroscopy in CDF₃/CDF₂Cl solution. We demonstrate that the ³¹P NMR chemical shift changes upon complexation, ΔδP, correlate well with the total strength of all hydrogen bonds formed by the P=O group. This allows one to use ΔδP as a tool for estimating overall binding energies in compounds containing phosphine oxides. Additionally, using DFT calculations with implicit (PCM) and explicit (2–3 solvent molecules) solvation models we reached a semi-quantitative agreement between calculated and experimental ΔδP values. The anticooperativity effects in 1 : 2 complexes were estimated to be ca. 15–20% both in experiment and calculations.

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Introduction

In modern chemistry, various molecules containing the P=O functionality have demonstrated considerable practical utility due to the exceptional electron-donating ability of the P=O oxygen atom, allowing one to tune and enhance the properties of such molecules as participants in various non-covalent interactions: hydrogen bonding, halogen bonding and other σ-hole interactions, coordination bonding and others. For example, the presence of a proton-accepting P=O group was shown to facilitate the formation of effective hydrogen bond networks for proton transfer, as observed in various proton-conducting materials.^1–3 It is also able to impart superior mechanical and thermal properties to polymers.^4,5 Besides, the P=O group was employed in the design of a wide range of polymeric biomedical materials used in drug delivery, tissue engineering, dental applications, etc.^6,7 In particular, surface phosphorylation was used to increase the adhesion and biocompatibility of materials.^8,9 Interactions between phosphine oxides and the surfaces of nanoparticles^10,11 or quantum dots^12,13 are also utilized for their stabilization. In engineering applications, the introduction of the P=O moiety and the structural tunability around it were shown to occasionally improve properties such as flame retardation,^14,15 UV resistance,¹⁶ and mechanical strength.¹⁷ In catalysis, P=O-containing molecules have several applications, among which the most common ones are perhaps their usage as bifunctional ligands in cross-coupling reactions,^18–21 as chiral catalysts for asymmetric organocatalysis,^22,23 and as stabilization agents for peroxides formed at various stages of reaction.^24–27

One of the prominent fields in which materials involving P=O groups excel is extraction and separation.²⁸ The P=O group is considered one of the most effective functional groups in designing extractants for f-block elements, due to its strong coordination ability with highly charged metal ions.^29–31 Various compounds containing the P=O group—either phosphine oxides or phosphinic/phosphoric acids^29,32—have demonstrated high efficiency in selective extraction of various metals, including lanthanides and actinides, for reprocessing of metallurgical waste³³ and spent nuclear fuel.³⁴ Phosphine-oxide-based extractants are usually able to perform extraction in acidic media, which is linked to the high polarity of the P=O bond.^31,33 For example, the first extractant with high selectivity between Americium and Curium—two of the most challenging elements to separate chemically due to their similar properties—was a tridentate ligand with two P=O groups.³⁵

The P=O functionality is an excellent NMR and IR spectroscopic probe. In IR spectroscopy, changes in the stretching frequency of the P=O bond, Δν_P=O, were previously used to characterize the strength of hydrogen bonding in phosphine oxide complexes with proton donors.³⁶ In recent studies of R₃PO complexes with substituted phenols in organic solutions a non-linear relationship between hydrogen bond strength and the shift in P=O frequency was proposed.³⁷ Quantum chemical calculations revealed that the P=O vibrational frequency is affected by additional weak interactions with surrounding solvent molecules.^38,39

In NMR spectroscopy, it was shown that ³¹P NMR chemical shift, δP, is strongly affected by the geometry of hydrogen bonds involving the P=O group, as well as other structural and electronic parameters, reflecting the high sensitivity of δP to the surrounding environment,^40–42 including various weaker C–H⋯O interactions.⁴³ In a homologous series of complexes, the shift of the ³¹P NMR signal upon complexation was shown to correlate well with the hydrogen bond strength.^44,45 Similar correlations, obtained by quantum-chemical calculations, were also proposed for halogen-bonded complexes.⁴⁶ On a more qualitative level, experimental ³¹P NMR spectra were instrumental in proving the stoichiometry of self-associates formed by phosphinic, phosphoric and phosphonic acids: cyclic dimers and trimers,⁴⁷ cyclic tetramers⁴⁸ and cage-like tetramers.⁴⁹ The solid-state ³¹P NMR spectra of R₃PO molecules adsorbed on silica/zeolites were used to describe the translational mobility of guest molecules in the host matrix⁵⁰ and the acidity of the surface.⁵¹ Finally, no account on ³¹P NMR spectroscopy of phosphine oxides would be complete without mentioning the Gutmann–Beckett method,^52,53 in which triethylphosphine oxide (TEPO) is used as a spectroscopic probe to establish so-called Acceptor Numbers (ANs) as a measure of the electron-accepting ability of Lewis acids^54–56 or Brønsted acids.^57–60 The Gutmann–Beckett methodology, originally developed for liquid solutions, was later on extended to solids⁶¹ and to ionic liquids,⁶² and also the usage of Δν_P=O instead of δP was suggested.⁶³

One of the defining features of phosphine oxides is the ability of the P=O oxygen atom to simultaneously form multiple hydrogen bonds, a phenomenon for which phosphine oxides were previously called “ambidextrous hydrogen bond acceptors”.⁶⁴ This capability to interact with multiple proton donors at once enhances the versatility of phosphine oxides in molecular recognition and supramolecular assembly. Despite the experimental evidence confirming the formation of multiple hydrogen bonds with the same P=O group—both in solution and in the crystalline state^60,64–67—the previously established numerical correlations between ³¹P NMR spectra and the complexation energy were constructed only for 1 : 1 complexes (except for our recent computational work, ref. 39). Therefore, the primary objective of this work is to conduct both experimental and quantum chemical investigations to establish correlations between hydrogen bond energies and ³¹P NMR parameters of 1 : 2 phosphine oxide complexes with proton donors, as well as to explore the cooperativity effects within the pairs of mutually coupled hydrogen bonds in these complexes.

For this purpose, here we focus on 1 : 1 and 1 : 2 hydrogen-bonded complexes composed of triphenylphosphine oxide (Ph₃PO) and substituted phenols as OH proton donors. See schematic structures of complexes in Fig. 1 and chemical structures of studied phenols in Fig. 2. Substituted phenols were chosen because they do not have a strong proton-accepting site and provide a decent variety of proton-donating abilities. The complexes were experimentally investigated using ¹H and ³¹P NMR spectroscopy in solution in a mixture of deuterated Freonic gases CDF₃/CDF₂Cl at 100 K. For each complex we used the value of ¹H NMR chemical shift of bridging protons to estimate the hydrogen bond energy, which was then correlated with the ³¹P NMR chemical shifts. The primary goal was to find a way to use changes in ³¹P chemical shifts upon complexation, ΔδP, to predict the strength of the complexes. Additionally, we conducted a series of DFT calculations to determine complexation energies ΔE and NMR parameters and compared the results with experimental data. In computations, the effects of P=O complexation with the neighboring solvent molecules via additional CH⋯O hydrogen bonds were explicitly considered.

Fig. 1 Chemical structures of (a) 1 : 1 and (b) 1 : 2 complexes formed by Ph₃PO with substituted phenols. The following set of parameters are considered in this work: the complexation energies, ΔE_1 : 1 and ΔE_1 : 2, the changes in ³¹P NMR chemical shifts, ΔδP_1 : 1 and ΔδP_1 : 2, and the changes in ¹H NMR chemical shifts for the OH group, ΔδH_1 : 1 and ΔδH_1 : 2.

Fig. 2 The set of OH proton donors considered in this work as partners in complexes with Ph₃PO.

Experimental and computational details

Sample preparation

Triphenylphosphine oxide (Ph₃PO), substituted phenols 1–24 and chloroform (CHCl₃) were purchased from companies listed in Table S1 in the SI and used without further purification. Ph₃PO (5.37 mg, 19.3 µmol) was dissolved in 1 mL of CHCl₃. Then the weighted amount of substituted phenol (or the corresponding volume for liquid substances) calculated according to the desired stoichiometric composition of the sample (1 : 1 or 1 : 2) was added. Subsequently, using an Eppendorf pipette 0.1 mL of the solution was transferred into a thick-walled NMR sample tube with a J. Young valve (Wilmad 522-LPV-7) and CHCl₃ was removed in vacuo. Finally, ca. 0.2 mL of the mixture of deuterated freonic gases CDF₃/CDF₂Cl, synthesized by a modified method of ref. 68, was added by vacuum transfer (at ca. 10⁻⁶ mbar), resulting in a Ph₃PO concentration of ca. 0.01 M. Prior to the addition to the sample the freonic mixture was additionally dried over alumina in a cold ethanol bath (ca. 140 K). The resulting composition of the sample was controlled by measuring NMR signal intensities of CH protons of Ph₃PO and phenols at room temperature. It should be noted that in some cases the composition of the sample at low temperature differs significantly from that initially prepared at room temperature due to the poor and varying solubility of phenols in Freons.

NMR measurements

All NMR measurements were performed at the Center of Magnetic Resonance in the Saint-Petersburg State University Research Park. The room-temperature and low-temperature (100 ± 1 K) liquid-state ¹H and ³¹P NMR spectra were recorded using a Bruker Avance III 500 MHz spectrometer (11.7 T, 499.91 MHz for ¹H, 202.4 MHz for ³¹P). For ¹H NMR spectra 30° pulses, an acquisition time of 2.6 s, a relaxation delay of 1 s, and 128 scans were used. For ³¹P NMR spectra 30° pulses, an acquisition time of 0.8 s, a relaxation delay of 2 s, and 256 scans were used. All ³¹P NMR spectra were recorded with broadband proton decoupling. ¹H NMR chemical shifts were calibrated to the TMS scale using the central signal of the CHClF₂ triplet as an internal secondary standard set to 7.21 ppm. The ³¹P NMR spectra were referenced to H₃PO₄ (85% in H₂O) using the unified scale, according to IUPAC recommendations.⁶⁹ The spectra were processed using MestReNova⁷⁰ and TopSpin software.⁷¹

Computational details

DFT calculations were carried out at the Computing Center of St. Petersburg State University Research Park. For individual compounds and complexes of Ph₃PO with proton donors 1–24 and/or explicit solvent molecules, the calculations of optimized geometries and harmonic vibration frequencies were performed using the Gaussian 16 software package⁷² at the PW6B95/def2-TZVPD level of theory.^73–76 The Grimme dispersion correction GD3 was included.⁷⁷ This level of theory was chosen because it follows the recent “best practice protocol” recommendations⁷⁸ and benchmarks,⁷⁹ combining a meta-hybrid generalized gradient approximation functional (mGGA) with a triple-ζ basis set and dispersion correction. In a large-scale benchmark study⁸⁰ PW6B95-D3 was found to be the most robust and accurate general-purpose hybrid-functional, based on its performance in the combined evaluation of basic molecular properties, reaction energies and non-covalent interactions.

Unless specified in the text, the polarizable continuum model (PCM, ε = 40)⁸¹ was used for implicit solvent effects. All structures were checked for the absence of imaginary harmonic vibrational frequencies. For each complex several chemically reasonable starting geometries were tested, which differed by the relative orientations of Ph₃P=O and proton donors pre-positioned to form hydrogen bonds with the P=O group and preoptimized at the B3LYP/6-311++G(d,p) level of theory. In all cases, in the final optimized structures the CH⋯O and the OH⋯O hydrogen bonds stayed intact. The structures with the lowest electronic energies were selected for further analysis. For more on that see Fig. 8 and the corresponding text.

The complexation energies for 1 : 1 complexes (ΔE_1 : 1) were calculated as the difference between the full electronic energies of the complex and its constituting fragments in their relaxed geometries: ΔE_1 : 1 = E_{complex 1 : 1} – (E_Ph3PO + E_{free proton donor}). In a similar way, the complexation energies for 1 : 2 complexes (ΔE_1 : 2) were defined as ΔE_1 : 2 = E_{complex 1 : 2} – (E_Ph3PO + 2·E_{free proton donor}). In case if explicit solvent molecules were used in the calculation, the expressions for complexation energies were modified accordingly. Namely, all energy values were taken for complexes of the corresponding species with the required number of solvent molecules. For example, ΔE_1 : 2 = E_{complex 1 : 2+CHF3} + 2·E_CHF3 − E_{Ph3PO+3×CHF3} − 2·E_{free proton donor}, see one of the following subsections for more details. The complexation energies were calculated without correction for the basis set superposition error (BSSE).

For each species optimized at the abovementioned level of theory, the set of NMR parameters were calculated using the GIAO approach at the WP04/pcSseg-2 level of theory. The pcSseg-2 basis set was extensively benchmarked for nuclear shielding calculations for a wide set of atoms.⁸² The WP04 functional was previously shown to perform especially well for ¹H NMR chemical shifts.⁸³ The NMR shielding constants σ_free were calculated for isolated proton donors (for ¹H) or isolated Ph₃PO (for ³¹P) in their relaxed geometries. The NMR shielding constants σ_complex were computed for the same moieties in 1 : 1 and 1 : 2 complexes. Changes in ¹H and ³¹P NMR chemical shifts upon complexation, ΔδH_1 : 1 (or ΔδH_1 : 2) and ΔδP_1 : 1 (or ΔδP_1 : 2), were calculated as Δδ = σ_free – σ_complex.

Results

NMR spectra

Triphenylphosphine oxide spectra in solution. The low-field parts of ¹H and ³¹P NMR spectra of Ph₃PO solution in a CDF₃/CDF₂Cl mixture at 100 K are shown in blue at the top of Fig. 3. In the ¹H NMR spectrum there are no signals in the range 9.5–14.2 ppm, which is convenient for studying hydrogen-bonded complexes, due to the absence of interfering signals. The ³¹P NMR signal of “free” Ph₃PO appears at 33.25 ppm.

Fig. 3 The low-field parts of the ¹H and ³¹P NMR spectra of Ph₃PO complexes with substituted phenols in CDF₃/CDF₂Cl at 100 K. Insets for spectra of Ph₃PO with phenols 9, 16, 18, and 24 are taken from separately measured samples, see Fig. S2–S5 in the SI.

Hydrogen-bonded complexes. Fig. 3 shows in black the low-field parts of ¹H and ³¹P NMR spectra of samples containing solutions of Ph₃PO with phenols 1–24 in CDF₃/CDF₂Cl at 100 K. At this temperature a slow proton and molecular exchange regime is reached and resolved signals of several species are visible. Firstly, in some ³¹P NMR spectra a signal is visible corresponding to free Ph₃PO; the position of this signal is indicated by the dashed blue line. Apart from this, in the majority of spectra two separate signals are visible, corresponding to complexes of different compositions (stoichiometry). We assign these signals to 1 : 1 and 1 : 2 complexes. This assignment is based on the following. The signals of 1 : 1 complexes were identified by studying NMR spectra of additional samples at different Ph₃PO/phenol ratios: when the concentration of substituted phenol is decreased this signal remains the only one in the spectrum. Fig. S1 in the SI gives an example of a series of such measurements for the Ph₃PO complex with 4-chlorophenol 7. The stoichiometry of 1 : 2 complexes was identified by comparing the relative integrated intensities of signals in the ¹H and ³¹P spectra, as shown in Fig. S1 in the SI.

For the Ph₃PO complex with phenols 9, 16, 18 and 24 it is hard to find conditions for simultaneous observation of 1 : 1 and 1 : 2 complexes, so it is done for separate samples, see Fig. S2–S5 in the SI.

In cases of 2,6-disubstituted phenols with bulky substituents (1, 2, and 23) and in several other cases (10, 15, and 20) we were unable to obtain convincing spectra with resolved signals, which could be assigned to 1 : 2 complexes. In most of cases this was at least partially due to the low solubility of these phenols at low temperatures. Besides, steric hindrance imposed by two ortho-substituents might preclude the formation of stable 1 : 2 complexes (for more on this, see the Discussion). Moreover, for 2,6-disubstituted phenols 1 and 2 the observed ¹H and ³¹P signals keep shifting when the composition of the samples is changed, indicating a fast exchange regime between free species and weakly H-bonded complexes, see Fig. S6 and S7 in the SI. For this reason, as the closest approximation to the spectra of 1 : 1 complexes we took ¹H NMR spectra of the samples with the lowest amounts of 1 (2), and ³¹P NMR spectra of the samples with the ratio of Ph₃PO and 1 (2) closest to 1 : 1. We felt that this is more appropriate than to discard these data entirely.

Under the conditions used – no more than 1 : 2 molar ratio of phosphine oxide to phenol – there was no detectable formation of 1 : 3 complexes. It should be mentioned, however, that during the course of the experiments for 4-fluorophenol (4), phenol (5), 2,4-dichlorophenol (15), 2-chlorophenol (16), 2-bromophenol (18), 2-iodophenol (20), and 2,6-dichloro-4-nitrophenol (23) we tested higher relative concentrations and noticed that the excess phenol tends to precipitate at low temperatures. This might indicate that for these particular phenols the formation of 1 : 3 complexes is suppressed either by steric reasons or by the low solubility of the phenol, which is true for the majority of studied phenols in the CDF₃/CDF₂Cl mixture (note that already 1 : 2 complexes are rarely in majority or even entirely absent, as for 15, 20, and 23).

In ¹H NMR spectra there are no OH signals that could be assigned to free (uncomplexed) phenols with one notable exception. In the ³¹P NMR spectrum of the sample containing Ph₃PO and 2-nitrophenol 6 the position of the signal of the P=O group is unchanged, indicating that there is no clearly detectable complexation between the species. Thus, the corresponding ¹H NMR signal at 11.11 ppm is likely due to the formation of an intramolecular hydrogen bond between –OH and –NO₂ groups of 6. In the Discussion section the corresponding data point will be omitted from the construction of various correlations. In all other cases the OH chemical shifts of 1 : 1 species in the range 10.5–13.5 ppm are characteristic of medium–strong hydrogen bonds with Ph₃PO. The further downfield the signal appears, the stronger the corresponding hydrogen bond.⁸⁴ The OH signals of 1 : 2 complexes are shifted upfield with respect to the signals of 1 : 1 complexes, which is indicative of anticooperative coupling of two hydrogen bonds,⁸⁵ competing for the electron density at the central oxygen atom, RO–H⋯O(P)⋯H–OR. In turn, ³¹P NMR signals shift further to the low field as the number of hydrogen bonds and/or their strength increases. Therefore, it could be suggested that while OH chemical shifts are markers of the strength of each hydrogen bond individually, the ³¹P NMR chemical shift of phosphine oxide could be a marker of the total (combined) strength of all hydrogen bonds formed with the P=O group. This hypothesis will be examined in detail in the Discussion. The numerical values of ¹H and ³¹P NMR chemical shifts of 1 : 1 and 1 : 2 complexes (δH_1 : 1, δH_1 : 2, δP_1 : 1 and δP_1 : 2, respectively) and their changes upon complexation with respect to free individual species (ΔδP_1 : 1 and ΔδP_1 : 2) are collected in Table 1.

Table 1 The experimental ¹H and ³¹P NMR chemical shifts of 1 : 1 and 1 : 2 complexes formed between Ph₃PO and substituted phenols in CDF₃/CDF₂Cl at 100 K. Chemical shifts δH_1 : 1, δH_1 : 2, δP_1 : 1, and δP_1 : 2 in ppm. Changes in NMR chemical shifts upon complexation ΔδP_1 : 1 and ΔδP_1 : 2 in ppm. Complexation energies (estimated using eqn (1) as described in the text), ΔE_1 : 1, ΔE_1 : 2 in kJ mol⁻¹

No.	Proton donor	Complexes 1 : 1				Complexes 1 : 2
		δH1 : 1	δP1 : 1	ΔδP1 : 1	−ΔE1 : 1	δH1 : 2	δP1 : 2	ΔδP1 : 2	−ΔE1 : 2
1	2,6-Dibromophenol	10.77	35.31	2.06	27.29	—	—	—	—
2	2,6-Dichlorophenol	10.92	35.23	1.98	27.90	—	—	—	—
3	4-Methylphenol	10.88	35.03	1.78	27.75	10.03	38.30	5.05	48.43
4	4-Fluorophenol	11.03	35.22	1.97	28.38	10.11	39.41	6.16	49.10
5	Phenol	11.10	35.04	1.79	28.66	10.23	38.84	5.59	50.06
6	2-Nitrophenol	11.11	33.29	0.04	28.70	—	—	—	—
7	4-Chlorophenol	11.25	35.47	2.22	29.30	10.27	39.92	6.67	50.43
8	4-Bromophenol	11.28	35.40	2.15	29.43	10.28	39.91	6.66	50.49
9	2-Methoxyphenol	11.29	34.96	1.71	29.45	10.30	39.35	6.10	50.66
10	4-Iodophenol	11.33	35.51	2.26	29.65	—	—	—	—
11	3-Bromophenol	11.43	35.59	2.34	30.03	10.39	40.42	7.17	51.38
12	3-Chlorophenol	11.46	35.56	2.31	30.16	10.40	40.40	7.15	51.54
13	3-Cyanophenol	11.69	35.90	2.65	31.15	10.56	40.96	7.71	52.85
14	3-Nitrophenol	11.81	35.88	2.63	31.63	10.78	41.50	8.25	54.68
15	2,4-Dichlorophenol	12.04	35.38	2.13	32.61	—	—	—	—
16	2-Chlorophenol	12.06	35.14	1.89	32.69	10.85	40.27	7.02	55.27
17	4-Cyanophenol	12.07	35.87	2.62	32.72	10.90	41.31	8.06	55.66
18	2-Bromophenol	12.09	35.01	1.76	32.81	11.00	40.37	7.12	56.53
19	2,3,4,5,6-Pentafluorophenol	12.12	36.56	3.31	32.94	11.05	40.64	7.39	56.95
20	2-Iodophenol	12.13	34.76	1.51	32.97	—	—	—	—
21	4-Nitrophenol	12.45	36.23	2.98	34.33	11.22	42.03	8.78	58.37
22	2-Cyanophenol	12.59	35.71	2.46	34.92	11.27	41.83	8.58	58.78
23	2,6-Dichloro-4-nitrophenol	12.68	34.77	1.52	35.27	—	—	—	—
24	2-Chloro-4-nitrophenol	13.40	36.31	3.06	38.28	11.80	42.63	9.38	63.23

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QC calculations

To find out how much solvation influences the observed correlation between ³¹P NMR chemical shift and hydrogen bond strength, we have performed a series of quantum-chemical calculations including implicit and explicit solvent models. The full set of considered structures is schematically shown in Fig. S8 in the SI, while here we will focus primarily on the most relevant cases.

Triphenylphosphine oxide. Calculated structures of Ph₃PO without explicit solvation, as well as with one, two or three solvent molecules (CHF₃) in the aprotic medium (ε = 40) are shown in Fig. 4. The directions in which CH⋯O hydrogen bonds with solvent molecules are formed correspond to the directions of lone pair localization, better described by sp³ hybridization of oxygen (Ph₃P⁺–O⁻), than sp² hybridization (Ph₃P=O). This matches the distribution of electron localization function (ELF) previously described for (CH₃)₃PO.³⁹

Fig. 4 The optimized structures of Ph₃PO in an aprotic medium (ε = 40) without explicit solvent molecules (a) and with one (b), two (c) and three (d) solvent molecules.

Triphenylphosphine oxide complexes with phenols. Fig. 5 and 6 show optimized structures of 1 : 1 and 1 : 2 complexes with and without solvent molecules on the examples of complexes with 3-chlorophenol 12. Optimized structures of other complexes are qualitatively similar and collected in the SI as sets of xyz coordinates.

Fig. 5 The optimized structures of 1 : 1 complexes of Ph₃PO with 3-chlorophenol 12 in an aprotic medium (ε = 40) without explicit solvent molecules (a) and with one (b) or two (c) solvent molecules.

Fig. 6 The optimized structures of 1 : 2 complexes of Ph₃PO with 3-chlorophenol 12 in an aprotic medium (ε = 40) without (a) and with one (b) explicit solvent molecule.

The structures of all complexes exhibit several similarities: the intermolecular OHO hydrogen bonds are nearly linear and formed along one of the lone pairs of the oxygen atom of Ph₃PO, while solvent molecules fill other vacancies around the PO group. Note that in the case of 1 : 2 complexes without the solvent molecule the dihedral angle between two OHO hydrogen bonds (more precisely, the angle between two PO(H)O planes) is close to 120°, which also corresponds to the localization of lone pairs characteristic of sp³ hybridization of the PO oxygen.

As it will be justified in the Discussion, as the main complexation reaction we have considered the reaction schematically shown in Fig. 7. Here, the oxygen atom of Ph₃PO in its “free” state forms three hydrogen bonds with CHF₃ solvent molecules, which are being substituted one by one with phenols upon formation of 1 : 1 and 1 : 2 complexes. Addition of each subsequent solvent molecule is energetically favorable due to the formation of an extra CH⋯O hydrogen bond. Moreover, replacing any solvent molecule with phenols 1–24 is also energetically favorable mainly because the newly formed OH⋯O hydrogen bonds are stronger than the replaced CH⋯O ones. This is demonstrated in Fig. S9 as an energy diagram on the example of 2-chloro-4-nitrophenol 24. The calculations indicate that for the smaller phenols (with the possible exception of 2,6-disubstituted one) there is sufficient space around the P=O group for a third phenol molecule to replace the remaining CHF₃ solvent molecule and to form a third OH⋯O hydrogen bond; as an example, see the structure of the 1 : 3 complex with phenol 24 below Fig. S9. The third OH⋯O bond remains stronger than the CH⋯O bond it replaces, and the complex gains additional stability. However, the 1 : 3 complexes were not considered in this work, as their experimental counterparts were not detected.

Fig. 7 Reaction of formation of 1 : 1 and 1 : 2 complexes between Ph₃PO and ROH including explicit solvation of Ph₃PO by CHF₃ molecules.

In all cases the complexes were also surrounded by a polarizable medium. Other possible reactions are listed in Fig. S10 in the SI, and they will be briefly mentioned in the Discussion as well.

The full electronic energy values and the NMR shielding constants for all species considered are included in Tables S2–S4 in the SI. For convenience, using the data for the species shown in Fig. 7, we have prepared a separate table (Table 2) containing changes in electronic energies (ΔE_1 : 1 and ΔE_1 : 2) and the corresponding changes in NMR observables (ΔδH_1 : 1, ΔδH_1 : 2, ΔδP_1 : 1, and ΔδP_1 : 2) along the complexation reaction. In this way, Table 2 is analogous to the experimental table (Table 1).

Table 2 Calculated parameters of hydrogen-bonded complexes formed by Ph₃PO with proton donors 1–24 (in all cases in the aprotic medium ε = 40): the changes in ¹H and ³¹P NMR chemical shifts upon complexation (ΔδH_1 : 1, ΔδH_1 : 2, ΔδP_1 : 1 and ΔδP_1 : 2) in ppm, complexation energy, ΔE_1 : 1 and ΔE_1 : 2, in kJ mol⁻¹

No.	Proton donor	Complexes 1 : 1 + 2 × CHF3			Complexes 1 : 2 + 2 × CHF3
		δH1 : 1	ΔδP1 : 1	−ΔE1 : 1	δH1 : 2	ΔδP1 : 2	−ΔE1 : 2
a Iodine element is not included in the pcSseg-2 basis set used in this work.
1	2,6-Dibromophenol	3.55	5.86	33.17	2.98	8.75	63.87
2	2,6-Dichlorophenol	3.48	5.37	31.91	3.06	9.09	57.55
3	4-Methylphenol	5.23	3.17	27.86	5.29	6.61	44.78
4	4-Fluorophenol	5.04	3.45	29.43	5.35	7.51	46.42
5	Phenol	5.23	3.31	28.01	5.35	6.99	45.27
6	2-Nitrophenol	5.92	4.86	37.30	5.50	9.31	63.25
7	4-Chlorophenol	5.26	3.40	30.70	5.49	7.42	47.95
8	4-Bromophenol	5.27	3.39	31.15	5.49	7.94	48.35
9	2-Methoxyphenol	5.08	3.41	29.08	5.00	7.33	51.52
10	4-Iodophenol^a	—	—	—	—	—	—
11	3-Bromophenol	5.30	3.82	30.92	5.51	7.78	49.04
12	3-Chlorophenol	5.24	4.03	30.64	5.49	7.54	48.58
13	3-Cyanophenol	5.63	4.45	32.15	5.59	8.63	49.96
14	3-Nitrophenol	5.46	4.40	33.38	5.65	9.13	50.77
15	2,4-Dichlorophenol	5.76	4.34	35.59	5.73	9.80	54.84
16	2-Chlorophenol	5.56	3.28	32.59	5.67	8.84	52.32
17	4-Cyanophenol	5.65	3.96	33.48	5.78	9.15	51.27
18	2-Bromophenol	5.42	4.26	33.15	5.68	9.30	53.51
19	2,3,4,5,6-Pentafluorophenol	5.97	4.11	41.56	4.55	8.86	67.30
20	2-Iodophenol^a	—	—	—	—	—	—
21	4-Nitrophenol	5.92	4.27	35.42	5.82	10.21	52.66
22	2-Cyanophenol	5.92	4.15	35.42	5.91	10.17	55.66
23	2,6-Dichloro-4-nitrophenol	4.70	6.28	36.95	3.42	9.37	67.18
24	2-Chloro-4-nitrophenol	6.47	4.79	40.21	6.23	11.70	60.16

---

As a side note it should be mentioned that for some 1 : 1 complexes we have obtained more than one stable structure. These structures differ in relative orientations of phenyl rings in Ph₃P=O and phenol: π-stacking lowers the complexation energy by ca. 10 kJ mol⁻¹, as shown schematically in Fig. 8. As an example, Fig. S11a and S10b in the SI illustrate two structures of the Ph₃PO complex with 2,4-dichlorophenol 15 in the presence of two CHF₃ molecules, while Fig. S11c in the SI shows the energy difference between the structures with and without the π-stacking for all complexes in which this phenomenon was observed. Throughout this work we always used the structures with the lowest energy.

Fig. 8 Structure stabilization by π-stacking between the substituted phenol ring and one of the aromatic rings of Ph₃PO.

Discussion

In the following, we attempt to construct and discuss the relationships between the energy of complexation and the experimental ¹H and ³¹P NMR chemical shifts of 1 : 1 and 1 : 2 hydrogen-bonded complexes formed by Ph₃PO and substituted phenols 1–24. We also discuss the construction of an appropriate computational model, which is able to quantitatively reproduce the experimental findings, mainly by evaluating implicit and explicit solvation effects on the calculated parameters. Additionally, we study and discuss the anticooperativity of hydrogen bonds in the case of 1 : 2 complexes.

Experimental correlations between δH, ΔδP and ΔE

Fig. 9a shows the experimental correlations between δH and ΔδP for the 1 : 1 complexes (green circles) and the 1 : 2 complexes (red circles). At first glance, the two data sets seem to follow independent trends (the solid curves shown in Fig. 9a will be explained below). However, the situation changes if one converts the experimental ¹H NMR chemical shifts, δH, into the complexation energy, ΔE, using the linear equation previously proposed by T. Schaefer in ref. 86 for intramolecular O–H⋯O hydrogen bonds formed within ortho-substituted phenols:

–ΔE (in kJ mol⁻¹) = 4.18·(δH − δH_free) (in ppm) + 1.67 (1)

where δH_free is the OH chemical shift of a “free” (uncomplexed) phenol. Here, we used δH_free = 4.64 ppm, experimentally measured for unsubstituted phenol 5 in solution in CDCl₃ at room temperature (see Fig. S12 in the SI). For 1 : 1 complexes, the ΔE_1 : 1 values calculated using eqn (1) range from ∼26 kJ mol⁻¹ to ∼40 kJ mol⁻¹. For 1 : 2 complexes, the ΔE_1 : 2 values, determined as the sum of energies of two hydrogen bonds, each calculated using eqn (1), range from ∼48 kJ mol⁻¹ to ∼70 kJ mol⁻¹. The ΔE_1 : 1 and ΔE_1 : 2 values are added to Table 1, while the resulting ΔE(ΔδP) plot is shown in Fig. 9b.

Fig. 9 The experimental correlations between ΔδP and (a) δH and (b) ΔE (estimated using eqn (1)) for the 1 : 1 complexes (green circles) and the 1 : 2 complexes (red circles) formed between Ph₃PO with substituted phenols based on the NMR experimental data set listed in Table 1.

At this point it seems appropriate to say a couple of words about the applicability and validity of eqn (1). Over the last several decades there were at least a dozen of experimental and theoretical publications dedicated to the construction of correlations between hydrogen bond strength and bridging proton NMR chemical shifts, see examples in ref. 87–91. Somewhat surprisingly, in all of these works a linear relationship was established/proposed. Depending on the type of the hydrogen bond (OHO, OHN, FHF, etc.) and the set of studied complexes, various slopes and free terms were listed. Based on this collection of works, the following could be summarized: for medium strong hydrogen bonds formed between OH acids and organic proton acceptors the downfield shift of the ¹H NMR signal by 1 ppm typically corresponds to ca. 4–7 kJ mol⁻¹ of hydrogen bond strengthening. In turn, the free term, which logically should be zero in an ideal case, tends to be relatively small, correcting the results by a couple of kJ mol⁻¹. For more on this, see ref. 81. There are no publications perfectly matching the set of complexes considered here. Two of the close matches are our previous works, ref. 45 and 39, where based on theoretical calculations for trimethylphosphine oxide complexes with various organic acids the slope of ca. 6 kJ mol⁻¹ ppm⁻¹ was proposed. Nevertheless, in the spirit of this essentially experimental work we decided to rely on the experimental results reported in ref. 83 and given by eqn (1), which has an additional advantage of dealing specifically with hydrogen bonds involving phenolic OH groups. Previously, eqn (1) was also successfully applied to the study on phenol complexes with C=O acceptors.⁸²

Coming back to the ΔE(ΔδP) plot shown in Fig. 9b, now the data points for 1 : 1 and 1 : 2 complexes could be simultaneously and reasonably well fit by a single power function:

–ΔE (in kJ mol⁻¹) = 22.2·ΔδP^0.45 (in ppm) (2)

Here it should be mentioned that the solid curves in Fig. 9a correspond to the same equation (eqn (2)) with the appropriate scaling of the ordinate using eqn (1). In short, the fit shown in Fig. 9b suggests that the ³¹P NMR chemical shift of Ph₃PO is a marker of the overall strength of all hydrogen bonds formed with the P=O group. A caution should be exercised, however, when interpreting ΔδP values for 1 : 1 complexes alone, due to significant scattering of the data points. All the hydrogen bond energies of 1 : 1 complexes are relatively close to each other within the 25–35 kJ mol⁻¹ range and the chemical shifts are scattered over the 1.5–3.5 ppm region. The overall cloud of data points is somewhat elongated along the correlation curve and the general upward trend is well reproduced by the calculations (see below), but the scattering of experimental data points is clear. As a result, not much could be concluded about the relative hydrogen bond energies for a random pair of 1 : 1 complexes from their ³¹P NMR chemical shifts, besides the rough estimate that both hydrogen bonds are around 30 kJ mol⁻¹. The situation is somewhat better for 1 : 2 complexes. While the range of hydrogen bond energies is twice as wide, the ΔδP ranges three times larger, so that the data points are better stretched along the correlation curve, giving more confidence in the curve itself and in the resulting estimates of hydrogen bond energies.

Previously the functional dependence of type ΔE = α·ΔδP^β was found computationally for hydrogen-bonded complexes of trimethylphosphine oxide ((CH₃)₃PO, TMPO) with stoichiometries 1 : 1⁴⁵ and 1 : 2³⁹ and also for various halogen-bonded complexes of TMPO.⁴⁶ It could be expected that for other phosphine oxides, such as popular thiethylphosphine oxide (TEPO), a similar functional dependence would be observed, with some variations in coefficients α and β reflecting different spans of ³¹P NMR chemical shifts and bond energies available for TEPO. We find it too early to speculate about the exact α and β values for other phosphine oxides prior to the experiments/calculations.

It is intriguing to check the possibility of reproducing quantitatively the results shown in Fig. 9b using quantum-chemical calculations. Clearly, the ³¹P NMR chemical shift is quite sensitive to hydrogen bonds formed by the P=O group. Thus, it could be argued that in the case of weakly CH–proton donating solvents, such as CHF₃, a careful account for specific solvent–solute interactions is required to achieve the quantitative match. We explore this in the following section.

Quantum-chemical correlations between ΔE and ΔδP

The set of optimized structures described in Results allows one to consider complexation between Ph₃PO and substituted phenols in vacuum or in a polarizable continuum (Fig. S10a in the SI), as well as additionally explicitly taking into account solvent molecules forming CH⋯O hydrogen bonds with P=O oxygen: two solvent molecules (if sp² hybridization dominates, Fig. S10b in the SI) or three solvent molecules (if sp³ hybridization dominates, Fig. 7). Using the data from Tables S2–S4 in the SI, for each of these models one could generate −ΔE(ΔδP) plots, which are shown in Fig. S13a–c in the SI and Fig. 11, respectively, superimposed with experimental data points (several data points in Fig. 11 are shown as open symbols for the reason that will be explained in one of the following paragraphs). In all cases, the general trends are qualitatively consistent with the experiment: ΔδP increases with increasing overall ΔE for the majority of compounds. Quantitatively, clearly, both implicit and explicit solvent models consequently and significantly improve the quality of the match between theory and experiment. Going from vacuum to PCM and then subsequently adding two or three explicit solvent molecules brings the calculated data points closer and close to the experimental ones. Table 3 illustrates the decrease in the mean absolute error for both ΔE and ΔδP in the 1 : 1 and 1 : 2 complexes of Ph₃PO with substituted phenols. The sequential improvement of the computational data is additionally visualized in Fig. S14 and S15 in the SI, where the mismatches between experimental and calculated hydrogen bond energies and ³¹P NMR chemical shifts are shown as histograms for all four complexation reactions. Finally, in TOC graphics we attempted to depict it as an arrow hitting the target closer and closer to the bull's eye.

Table 3 Mean absolute error in ΔE (in kJ mol⁻¹) and ΔδP (in ppm) values for 1 : 1 and 1 : 2 complexes of Ph₃PO with substituted phenols, obtained using various solvation models

Solvent model	1 : 1 complexes		1 : 2 complexes
	Error in ΔδP	Error in ΔE	Error in ΔδP	Error in ΔE
Gas phase	8.9	37.6	14.6	73.0
Polarizable medium (ε = 40)	4.4	21.2	6.0	41.1
Aprotic medium with 2 solvent molecules	3.2	2.0	0.9	5.2
Aprotic medium with 3 solvent molecules	1.9	1.8	1.3	3.6

---

For the best-performed model (polarizable continuum and three explicit solvent molecules) we have plotted a direct comparison between calculated and experimental ³¹P NMR chemical shifts (Fig. 10a) and hydrogen bond energies (Fig. 10b). In both cases there is a decent slightly non-linear correlation. The largest scattering of data points is observed for the ΔδP of 1 : 1 complexes, especially for those with 2,6-disubstituted phenol (open symbols in Fig. 10).

Fig. 10 Correlation between experimental and calculated parameters for 1 : 1 complexes (green symbols) and the 1 : 2 complexes (red symbols): (a) ³¹P NMR chemical shifts, (b) hydrogen bond energies. Dashed lines are guides to the eye. Open symbols correspond to 2,6-disubstituted phenols.

The calculated data points in Fig. 11 (PCM + three solvent molecules) could be fitted with the following equation:

–ΔE (in kJ mol⁻¹) = 15.0·ΔδP^0.57 (in ppm) (3)

Fig. 11 The calculated ΔE(ΔδP) correlation constructed for the 1 : 1 complexes (green stars) and the 1 : 2 complexes (red stars) for the complexation reaction shown in Fig. 7 (see the numerical data in Table 2). The experimental data points are shown as crosses for comparison. The dashed and solid curves correspond to eqn (2) and (3), respectively. Note: “PCM + 3 solvent molecules” in the legend refers to the initial state of Ph₃PO subsequently forming hydrogen bonds with phenols. In other words, the P=O group is forming three hydrogen bonds at all times, as shown in Fig. 7.

To construct this correlation, we have excluded from the fitting the data points for the complexes of Ph₃PO with 2,6-disubstituted phenols (1, 2, 19 and 23; open symbols in Fig. 11). These data points look like clear outlier, though by looking at the optimized structures it is hard to pinpoint which particular geometric feature might be responsible for that.

Chemical intuition suggests that it could have something to do with the interference of intramolecular H-bonds with ortho-substituents and steric hinderances; we leave this question for future studies. The deviation of eqn (3) from eqn (2) and the corresponding deviations of calculated data points from the experimental ones seem to be systematic, but at the moment it is hard to tell what would decrease these deviations: improvements in chemical modelling (inclusion of motion averaging or further solvation effects) or improvements in computational modelling (usage of more advanced functionals and/or basis sets). In any case, the match between calculated and experimental data is fine and it seems reasonable to conclude that Ph₃P=O in solution tends to form three hydrogen bonds whenever possible, occupying all electron-donating sites on the oxygen atom, thus indicating a significant P⁺–O⁻ character of the P=O bond. Finally, we note that in calculations the correlation between ΔδP and ΔE for 1 : 1 complexes is less subjected to the scattering of the data points and the increase of ΔδP could be interpreted as the increase in hydrogen bond strength with more confidence.

Anticooperativity of H-bonds in 1 : 2 complexes

When two hydrogen bonds are formed between a single P=O group and two proton donors, these interactions exhibit anticooperativity, meaning that strengthening (shortening) of one bond weakens (lengthens) the other one, as both bonds compete for the electron density of the same oxygen atom. In our study, the mutual influence of two hydrogen bonds in 1 : 2 complexes manifests itself as the reduction in the strength of each bond compared to the strength of a single hydrogen bond in 1 : 1 complexes. (Nevertheless, the algebraic sum of the strengths of the two hydrogen bonds in 1 : 2 complexes is greater than that of a single hydrogen bond in 1 : 1 complexes) This is illustrated in Fig. 12, which shows the correlation between the H-bond energy values for 1 : 1 and 1 : 2 complexes (ΔE_1 : 1 and ΔE_1 : 2, respectively). All data points (both calculated and experimental ones) lie below the “no cooperativity” line ΔE_1 : 2 = 2·ΔE_1 : 1, demonstrating a 15–20% reduction of individual bond energy.

Fig. 12 Correlation between hydrogen bond energy in 1 : 2 complexes, ΔE_1 : 2, and the hydrogen bond energy in 1 : 1 complexes, ΔE_1 : 1. The dashed line indicates the boundary between cooperativity and anticooperativity regions.

If two phenols would form a chain-like complex with Ph₃PO, the anticooperativity would switch to cooperativity, as was previously shown in ref. 92 on the example of 2-OH and 2,3-di-OH substituted phenol in complexes with (n-Bu)₃PO. In this case adding a second hydrogen bond to a chain nearly doubles the strength of the bond with phosphine oxide, while further additions have diminishing effects. This highlights that hydrogen bond interactions are highly context-dependent: while P=O-centered complexes exhibit competitive weakening due to shared electron density, linear chains can exhibit cooperative reinforcement.

Conclusions

Let us summarize the key findings of this work. We began by experimentally investigating 1 : 1 and 1 : 2 hydrogen-bonded complexes formed between Ph₃P=O and 24 substituted phenols using low-temperature liquid-state NMR spectroscopy.

Despite the noticeable scattering of the experimental data points (especially for 1 : 1 complexes), the full data set strongly suggests that there is a monotonous interdependence between the change of the ³¹P NMR chemical shift upon complexation and the combined strength of the hydrogen bonds formed with the P=O group. The larger the ΔδP, the smaller the relative error in hydrogen bond energy estimations. For example, all studied 1 : 1 complexes cluster around 25–35 kJ mol⁻¹ hydrogen bond energy and are hard to distinguish one from another based on ΔE or ΔδP. In contrast, the data points for 1 : 2 complexes are stretched over wider ranges of both ΔE and ΔδP and could be interpreted with more confidence.

These findings could be seen as experimental evidence of the effect previously predicted computationally.³⁹ The proposed correlation could be used to solve the reverse spectroscopic problem: estimating the complexation energy from experimental ³¹P NMR chemical shift. The H-bond anticooperativity effects in 1 : 2 complexes were estimated to be ca. 15% of the individual H-bond energy. Furthermore, we demonstrated that advanced solvation models including both implicit and explicit solvents are necessary to achieve a semi-quantitative match between calculated and experimental ³¹P NMR parameters. We concluded that in solution Ph₃P=O tends to form three hydrogen bonds, where solvent molecules form CH⋯O hydrogen bonds, occupying all vacant spots, left around the P=O moiety after its complexation with phenols.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5cp03320a.

Acknowledgements

This work was financially supported by the Russian Science Foundation (RSF) grant no. 23-13-00095. NMR measurements were performed at the Center for Magnetic Resonance of St. Petersburg State University Research Park. The authors are grateful to Mikhail Vovk for conducting the low-temperature measurements. Quantum-chemical calculations were performed at the Computing Center of St. Petersburg State University Research Park.

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