Next Article in Journal
Third-Component-Regulated Choline Chloride–Monoethanolamine-Based Solvent Systems for Enhanced Valorization of Bamboo Toward Concurrent Bioethanol and Carbon Dot Production
Previous Article in Journal
Mechanochemical Preparation of Superabsorbent Materials from Okara and Itaconic Acid
Previous Article in Special Issue
Interference Structures in the High-Order Above-Threshold Ionization Spectra of Polyatomic Molecules in a Bicircular Laser Field
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Molecules
Volume 31
Issue 11
10.3390/molecules31111831
molecules-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Combined DFT Protocol for the Calculation of One-Bond 31P-31P Indirect Nuclear Spin–Spin Couplings

by
Svetlana A. Kondrashova
and
Shamil K. Latypov
*
Arbuzov Institute of Organic and Physical Chemistry, FRC Kazan Scientific Center of RAS, Kazan 420088, Tatarstan, Russia
*
Author to whom correspondence should be addressed.
Molecules 2026, 31(11), 1831; https://doi.org/10.3390/molecules31111831
Submission received: 7 April 2026 / Revised: 6 May 2026 / Accepted: 19 May 2026 / Published: 26 May 2026
(This article belongs to the Special Issue Exclusive Feature Papers on Molecular Structure, 2nd Edition)
Browse Figures
Versions Notes

Abstract

The comparative analysis of calculated and experimental one-bond 31P-31P indirect nuclear spin–spin couplings for a wide range of structures, including P-P bonds, has shown that, on the whole, it is possible to estimate 1JPP fairly accurately using even modest levels of theory. However, in order to reduce systematic errors, it is necessary to carry out a linear correction procedure specific to different groups of compounds. Certain difficulties may arise only for diphosphanes (R1R2P–PR1R2) that are in solution in fast (in NMR time scale) exchange of conformers with close populations. In practice, a relatively simple PBE0/6-31G(d)//PBE0/6-31G(d) combination is sufficient for calculating the 1JPP with practically reliable accuracy. The efficiency of the proposed protocol is demonstrated using the example of more subtle structural features—the isomeric structure. The proposed approach allowed for the absolute sign of 1JPP in a number of cases where it is unknown experimentally.

Graphical Abstract

1. Introduction

One of the important steps in the structure-property correlation is the establishment of fine structural details involving conformational, isomeric, and tautomeric equilibria. Such information is especially important in biochemical studies [1,2,3], as well as in the development of new catalysts [4,5,6,7]. Given the specifics of these processes, such structural information is particularly important, especially in solution.
In this regard, modern experimental high-resolution NMR methods are among the most informative. 2D correlation experiments designed to transfer coherence through various mechanisms (indirect and direct spin–spin interactions) in many cases allow one to obtain comprehensive information about the chemical structure (topology of a molecule) within even a single method [8].
However, situations sometimes arise where purely experimental approaches do not provide information on the structure, and additional NMR methods are required [9,10]. In such a situation, one can return to analyzing NMR spectral parameters, but at a different level. Namely, these parameters strongly depend on the electronic distribution in the molecule, and their analysis can help in establishing the structure. For example, quantum chemical calculations of chemical shifts for 1H, 13C, 15N, and 31P atoms are successfully used both for organic molecules [11,12,13,14,15,16,17,18], and in more difficult cases, for transition metal complexes [19,20,21,22,23]. In this regard, the spin–spin coupling constants (SSCC) look promising, especially in the analysis of the three-dimensional structure.
In terms of NMR theory, there should be a certain relationship between the SSCCs and the mutual orientation of the interacting nuclei. Some empirical correlations between SSCCs and structure have been known for a long time (for example, the Karplus-type dependence [24]) and have been successfully used to solve stereochemical problems [25,26]. In this regard, the use of SSCCs between heavier nuclei looks promising, since both their signs and absolute values can be very informative. However, there may be no empirical dependencies for such SSCCs. Therefore, the natural continuation of our work on the structure of organophosphorus compounds is an attempt to learn how to evaluate a fine NMR parameter—SSCCs at the phosphorus atom.
SSCCs are extremely important in the structural studies of molecules (e.g., determining configuration, conformation, tautomeric structure, and the nature of the chemical bond). However, this is a much more difficult task, since SSCCs are second-order molecular properties and are determined by a linear-response function that accounts for all excited states. Therefore, for example, it is believed that for the calculation of SSCC it is necessary to consider electron correlation, at least at the second-order perturbation theory level, to use special basic sets, to take into account solvent effects, vibrational corrections, and relativistic effects in the case of heavy nuclei [27,28,29]. All this requires substantial computational resources and specialized software products that are not widely available, making such methods practically inapplicable for relatively large molecules of practical interest.
At the same time, there are attempts to calculate the 1H-1H and 13C-13C SSCCs in certain systems within the framework of the density functional theory (DFT) [30,31,32,33,34,35,36]. In some cases, the authors were able to obtain calculated values with practically reliable accuracy.
Given that in practice we often deal with phosphorus-containing compounds, estimating spin–spin coupling constants involving a phosphorus atom is becoming particularly relevant. There are only a few examples of calculations of 31P-13C and 31P-31P SSCC [37,38,39,40]. Therefore, as a first step in this direction, we will try to consider the scopes and limitations in calculating 1JPP in the framework of DFT in organophosphorus systems.

2. Result and Discussion

To assess the scopes and limitations of theoretical calculations, almost all known types of structures, including P-P bonds for which experimental coupling constants 1JPP are available, were used as models (Figures S1–S4). This set represents a wide range of possible classes of organophosphorus compounds, with 1JPP values from −700 to 800 Hz (Table S1). To find an approximation applicable to relatively large molecules, we started our analysis within the DFT framework using a relatively simple combination (PBE0/6-31G(d)//PBE0/6-31G(d) (the “level 1//level 2” notation means: “level 1” at spin–spin constant calculation stage and “level 2” at the geometry optimization stage)) that has proven itself well in the analysis of chemical shifts in organic systems.
According to calculations, a certain correlation is observed between the calculated and the experimental data (Figure 1a). Importantly, in the vast majority of cases, both the absolute values of the constants and their signs are reproduced quite well. In a number of cases, when the original source lacked information about the sign of the experimental 1JPP, its sign in the analysis was taken in accordance with the calculation (Table S1).
In general, three correlations can be clearly identified (Figure 1a, green, black, and blue circles). There are also several points that deviate noticeably from these correlations (Figure 1b, orange circles) (70–75). These points correspond to diphosphanes of the R1R2P–PR1R2 type. It will be shown later that there is no clear conformational preference for them, and they are most likely in a conformational exchange.
The first pronounced correlation (Figure 1a, green, Group 1) with large negative values of 1JPP (−670 to −526 Hz) is due to systems in which phosphorus atoms participate in a double bond (compounds with coordination numbers of P(2)). The correlation line has a slope of about 1, but the calculation overestimates the experimental values by about 155 Hz for all compounds of this type.
The second correlation that stands out extends from about the middle of the ranges to extremely large positive values of 1JPP (from −250 to 815 Hz, Figure 1a, blue, Group 3). This group includes systems containing at least one phosphorus atom with coordination numbers of P(4) or P(6), and are characterized by the presence of strongly electronegative atoms directly bonded to it. These are mono and doubly oxidized (sulfidized) diphosphine derivatives (R2(E)PPR2, R2(E)PP(E)R2, E=O, S), HnMe3−nPPF5, and cationic bis-chelate complex 61. For these systems, according to calculations (in vacuum), the forms with an anti-orientation of the P=E (E=O, S) groups are significantly more stable than gauche- (Table S2); therefore, only 1JPP for this conformer was considered in the analysis. The correlation line for them deviates strongly from the diagonal (slope of approximately 0.7). For these systems, there is a noticeable underestimation of the 1JPP, which becomes larger as the absolute (positive) values increase.
The remaining data fall on the third correlation in the central part (Figure 1a, black, Group 2), and the 1JPP covers a wide range from −665 to −55 Hz. Compounds in this group are characterized by single bonds between the phosphorus atoms, which have coordination numbers 2, 3, 4, and 5. The slope of the correlation line is close to 1, and only a slight overestimation (at about 36 Hz) is observed throughout the range.
Thus, there are three fairly good correlations between the calculated (PBE0/6-31G(d)//PBE0/6-31G(d)) and experimental 1JPP. However, they differ depending on the type of P-P fragment. This may be due to limitations of the approximation (simplicity of the basis set, type of functional, etc.), which can lead to systematic errors in calculations that differ for different types of systems. In an attempt to obtain a unified correlation, we tested a number of computational approximations.
First, we tried to use a more flexible basis set with the addition of a diffuse function both at the geometry optimization stage and when calculating the NMR parameters (PBE0/6-31G+(d)//PBE0/6-31G+(d)). In this case, the slopes of the correlation lines are approximately the same as in the initial protocol. However, unexpectedly, the correlation coefficients decrease somewhat for each group (Figure 2a, Table S1).
Next, a combination was examined that proved to be effective for NMR 31P shifts [18], in which the shielding is calculated using a more flexible triple-ζ quality basis set (PBE0/6-311G(2d,2p)//PBE0/6-31+G(d)). In this case, three separate correlation lines are also observed, but their slopes differ noticeably from those in the initial approach (Figure 2b). Significant changes are observed for the central (Group 2, slope 1.4 vs. 1.0) and right (Group 3, slope 1.0 vs. 0.7) correlation lines, while there are practically no changes for the left one (Group 1, slope 1.1 vs. 1.1) (Figure 2b, Table S1). It should also be noted that for each of the correlation lines, the R2 decreases, although the opposite was expected.
Since a simple approach based on the use of more flexible basis sets did not lead to the desirable unification of correlation dependencies, and, moreover, revealed unexpected effects, a more detailed analysis of the influence of parameters on the calculation results was carried out on a narrower representative “training” set of 15 compounds (18 data points, 1, 11–12, 14–16, 20, 26, 30, 45, 51, 54–55, 62, and 65, Figure 3), for which 3 dependencies are also observed, as for the entire set of model compounds (Figure S5).
First of all, the possible influence of the solvent was evaluated within the framework of the polarizable continuum model (PCM) [41] (PBE0/6-31G(d)(PCM)//PBE0/6-31G(d)(PCM)). For this purpose, a fairly polar acetone was used as a model solvent in the calculations. In this case, the correlation worsens for Group 1 and Group 2, while almost no changes are expected for Group 3 compared with the initial level (Figure 4, Table S3).
At the same time, the use of a more flexible basis set at both stages of the calculation (PBE0/6-311+G(2d)//PBE0/6-311+G(2d), Table S3) does not lead to an improvement in the correlation, although the slopes become approximately the same as for the PBE0/6-311G(2d,2p)//PBE0/6-31+G(d) level.
In order to establish at which stage (optimization or calculation of constants) the effect of changing the slope of the correlation lines appears when using a more flexible basis set, calculations were carried out with a step-by-step strengthening of the basis set at the SSCC calculation while maintaining optimization at the PBE0/6-31+G(d) level. The evaluation showed that in the series of basis sets 6-31(2d), 6-311(d), and 6-311(2d), it is the transition to the triple-ζ quality basis set that leads to a significant change in the slopes of all correlation lines, although they remain separate, as in the initial approximation (Figure S6).
Using a specially developed basis set for the SSCC calculations with an increased flexibility in the core region also does not lead to significant changes. Namely, when using the pcJ-2 basis set obtained by adding tight s, p, d, and f functions to the standard polarization-consistent basis sets pc-n [42], a picture is very similar to that observed when using PBE0/6-311G(2d,2p) (Table S3). That is, first of all, the effects of triple splitting of the pcJ-2 basis set are activated. The correlation coefficients are also worse than for the initial approximation for all three groups of compounds (Figure 4).
The type of functional can also influence the calculated NMR parameters. So, when using other standard hybrid functionals (B3LYP, B97-2), the changes for Group 2 and Group 3 are not minor compared to the original approach (Figure 5, Table S3). In Group 1 (with P=P), R2 is significantly lower (0.919 and 0.893 vs. 0.984; Figure 5, Table S3).
Pure-GGA functionals (BLYP, BP86, PBE), which are often recommended in the literature (e.g., KT-3 [43]), were also tested. For Group 3, virtually no changes were observed, for Group 2 the correlation worsened somewhat, but for Group 1 (with P=P), a noticeable deterioration in the correlation was noted compared to the initial level (0.790, 0.841 and 0.864 vs. 0.984, Figure 5, Table S3).
Next, the influence of more subtle parameters of the functional on the 1JPP calculation was considered. In particular the dependence of the 1JPP on the percentage of the HF exact exchange contribution to the functional was estimated. Calculations were performed using the PBE functional with a systematic increase in the proportion of the HF exact exchange contribution: PBE (0%), PBE0 (25%) and PBE50 (50%) (Table 1). Thus, for the systems in the Group 1, with an increase of the HF contribution, the slope of the correlation line increases sharply (Figure 6) and for PBE50, the 1JPP takes on extreme values (up to 2280 Hz, Table 1). For the Group 3, the slope of the correlation line becomes closer to 1. For the Group 2, the slope decreases only slightly (0.98, Figure 6). Thus, for systems with a P=P fragment, an extremely strong dependence on the proportion of HF exact exchange contribution is observed.
The observed effect indicates the exceptional importance of the correct choice of a functional for the SSCCs calculations. In this context, it is interesting to evaluate another popular functional with the same 50% HF contribution—BHandHLYP. This also leads to a similar “error” for systems with the P=P fragment (Table 1), while for the other two groups, no significant changes are observed (Figure 5, Table S3). Thus, even the proportion of the HF exact exchange contribution to the hybrid functional may, in some cases, lead to unrealistic results.
This “error” may be related to the so-called triplet instability discovered in HF calculations of 1JPP [44]. The following arguments go some way to suggesting that these breakdowns in accuracy may be related to this. First, the specific ΔETS dependence: in the classical case, the lowest triplet state should be below the singlet ground state [44]. In our case, although the triplet state is not lower than the ground state, ΔETS systematically decreases with the increase in the proportion of the HF exact exchange contribution for the compounds of the Group 1 (e.g., for 11 ΔETS is about 30.0 (PBE), 26.8 (PBE0), 23.5 (PBE50) kcal/mol), but for compounds from the Groups 2 and 3 the opposite picture is observed (Table S4). Second, specific effects on JSD/FC terms, involving triplet perturbation operators [45]. In our case, with the increase in the HF contribution, the SD and FC components for compounds of Group 1 suffer the most (Table S5). Moreover, the magnitude of the “error” correlates with the percentage of the HF exact exchange contribution.
A clear explanation of the identified anomalies requires a separate detailed analysis, which may become the subject of further research. However, based on the main objective of this work—to find a tool for practical assessments—it is possible to recommend the use of hybrid functionals in which the proportion of the HF exact exchange contribution is significantly less than 50%.

2.1. Practical Aspects and Recommendations

Testing a number of standard approaches in the calculation of the 1JPP within the framework of the DFT method did not allow us to identify a unified correlation for all of the above-mentioned systems. Moreover, unexpected effects related to the flexibility of the basis sets and the contribution of exact HF exchange to the functional were discovered, examples of which had not previously been observed for 1JPP. Thus, we concluded that, for now, the question of finding a protocol to unify correlation dependencies remains open. At the same time, the obtained results allow us to estimate the 1JPP with good accuracy within a certain series of compounds. From a practical point of view, the dependencies obtained indicate the possibility of using reliable protocols, but with an appropriate correction specific to each group.
If we analyze the revealed correlation dependencies in more detail, it becomes clear that for calculating the 1JPP, the best agreement with the experiment is achieved at the PBE0/6-31G(d)//PBE0/6-31G(d) level (Table 2). At the same time, across different types of systems, there are three correlation lines, each with a systematic error. To obtain a good quantitative estimate of the 1JPP, such errors can be minimized by performing a linear correction procedure [46,47] according to Equation (1) using regression analysis parameters for the corresponding type of model systems:
Jcorrected = (J − Intercept)/Slope
where J is the calculated 1JPP, and intercept and slope are scaling factors.
Thus, the application of this procedure allows one to obtain 1JPP, which can be quantitatively compared with experimental data (Figure 7). It can be seen that the best accuracy is achieved for compounds in the central part (Group 2), for which the error is minimal (RMSE = 13 Hz). For P=P type compounds (Group 1), the accuracy is somewhat lower (RMSE = 17 Hz). The lowest accuracy is expected for compounds from Group 3 (RMSE = 27 Hz) (Table 2).

2.2. Systems with Conformational Exchange

As shown above, for diphosphanes of the R1R2P–PR1R2 type (70–75), the calculated 1JPP values are in poor agreement with the correlation in the central region. According to calculations for these compounds, the conformers resulting from rotation around the P-P bond are close in energy (Table S6), and as a result, the NMR parameters in solution can be exchange-averaged. The calculated values for these rotamers differ by up to 150 Hz, while experimental values for 1JPP lie in between. Considering the complexity of theoretically estimating the population of the corresponding forms, comparison of experimental 1JPP values with those calculated for one conformation may be incorrect, which explains the observed deviation.
For example, for compound 74, according to calculations, the 1JPP is −109.6 and −222.4 Hz for trans and gauche forms, respectively (Figure 8). In this case, the energy difference is small, and the equilibrium can be easily changed by the solvent. Therefore, even a small shift in equilibrium can significantly change the observed 1JPP. Thus, in such systems, the limitations in estimating the 1JPP are not due to the weakness of the theoretical approximation used to calculate 1JPP, but to the difficulty in predicting the population of forms in solution.

2.3. Showcasing Examples

Having established the optimal protocol for evaluating the 1JPP on a wide range of different model compounds, we will now attempt to apply it to calculate the 1JPP for more complex bi- and tri-cyclic strained structures (Figure 9).
For example, for compounds 76 and 77 with two and four phosphorus atoms, which belong to Group 2, the agreement between the 1JPP calculated according to the proposed protocol and the experimental one is excellent (Figure 9, Table S7). Good agreement is also observed for the tricyclic structure 78, which belongs to Group 3 (Figure 9, Table S7). For tricyclic hexaphosphane (Mes*P6Mes*, 79, Group 2), the agreement for the two constants is excellent (<2.6 Hz), while for 1J(PC-PD) the agreement is somewhat poorer (Figure 9, Table S7). Overall, despite the rather complex picture of the connections in these cyclic systems, the calculation allows us to predict the 1JPP with good accuracy and in a fairly wide range.
From this perspective, it is interesting to see how this protocol will allow the 1JPP to be predicted when more subtle structural features such as the isomeric structure are changed. In this regard, the example of triphospha[3]ferrocenophanes (80a–e) [48] is indicative; in solution, they exist in both cis and trans forms, and their ratio depends on the substituent on the phosphorus atom (Figure 10). Overall, the results are in fairly good agreement with the experiment (Figure 10), although in some cases the differences are somewhat larger than for relatively simple model compounds. It is important that the trend in 1JPP is reproduced unambiguously when hydrogen at the phosphorus atom is replaced by halogen in both isomeric forms (Figure 10). However, as we move to heavier halogens, the discrepancy between the calculation and experiment increases (up to 76 Hz for I). This is most likely due to the relativistic effects of a heavy I atom on the NMR parameters of neighboring nuclei [49,50], and in this case, a fully relativistic level of theory may be required. But the most important fact is that the calculations predict a significant difference in the 1JPP between the isomeric forms (350–360 Hz vs. 165–170 Hz), which is fully consistent with the experiment. Thus, the proposed approach can be reliably used in practice to identify the isomeric structure of phosphorus-containing systems.

3. Experimental Section

Calculational Details

The quantum chemical calculations have been carried out within the framework of the density functional theory (DFT) [51] with the Gaussian 03 [52] (Revision B.04) and the Gaussian 16 [53] (Revision A.03) software packages by using using a variety of functionals (PBE0 [54], PBE [55], PBE50 [56], B3LYP [57,58], B97-2 [59], BLYP [60,61,62], BP86 [60,63], BHandHLYP [64]) and a number of families of basis sets (Pople’s [63,64,65,66,67,68,69,70,71,72], Jensen’s [42]). To take into account the medium effects, calculations were also carried out in the framework of Polarizable Continuum Model [41] (denoted as “PCM”) with acetone as solvent. Wherever possible, geometry optimization was started from X-ray structure. For most of the compounds the calculations were carried out for all possible conformers/isomers and results for the lowest energy forms were used in analysis.
The SSCC was calculated in the framework of the GIAO method [73].
The pcJ-2 basis set was downloaded from the EMSL basis set library for the Gaussian package [74,75,76]. The Gaussian 03 calculations were carried out on a PC with an Intel Core i7-3970X CPU, 3.5 GHz. Calculations with the pcJ-2 basis set were carried out with the Gaussian 16 on 20 CPUs, Intel Xeon ES-2650 2.20 GHz.

4. Conclusions

Thus, it is possible to estimate indirect SSCCs 1JPP fairly accurately using even modest levels of theory. Certain difficulties may arise only for diphosphanes of the R1R2P–PR1R2 type that in solution are in fast (in NMR time scale) exchange of conformers with close populations.
In practice, a relatively simple PBE0/6-31G(d)//PBE0/6-31G(d) combination is sufficient for calculating the SSCCs 1JPP. To obtain estimates with practically reliable accuracy in order to reduce systematic errors, it is necessary to carry out a linear correction procedure specific to different groups of compounds.
The effectiveness of the proposed protocol is demonstrated by the example of SSCCs 1JPP estimates for relatively complicated systems, as well as for the analysis of finer structural features—the isomeric structure.
The proposed approach allowed the absolute sign of 1JPP to be determined in a number of cases where it is unknown experimentally.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/molecules31111831/s1, Figure S1: The structure of model compounds from Group-1 (1–15); Figure S2: The structure of model compounds from Group-2 (16–49); Figure S3: The structure of model compounds from Group-3 (50–69) (DCHA=dicyclohexylamine). Figure S4: The structure of model compounds in conformational exchange (70–75); Table S1: Experimental and calculated 1JPP (Hz) for all model compounds except for systems with conformational exchange (1–69 [77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125]); Table S2: Experimental and calculated 1JPP (Hz) for different forms (with corresponded energy difference ΔE) of the model compounds 50–69; Figure S5: Correlation of calculated (PBE0/6-31G(d)//PBE0/6-31G(d)) vs. experimental 1JPP for (a) all model compounds and (b) the “training” set (except for systems with conformational exchange); Table S3: Experimental and calculated 1JPP (Hz) for model compounds of the “training” set (1, 11–12, 14–16, 20, 26, 30, 45, 51, 54–55, 62, 65). Figure S6: Correlation of calculated vs. experimental 1JPP for the “training” set compounds: PBE0/6-31G(2d)//PBE0/6-31+G(d) (a), PBE0/6-311G(d)//PBE0/6-31+G(d) (b) and PBE0/6-311G(2d)//PBE0/6-31+G(d) (c) levels; Table S4: Energy differences between triplet and singlet states (ΔETS, kcal/mol) for some model compounds from three groups (2, 11, 14, 20, 45, 51, 62, 65); Table S5: Experimental and calculated contribution to FC, SD and PSO components of the 1JPP (Hz) for some model compounds from three groups (2, 11, 14, 20, 45, 51, 62, 65); Table S6: Experimental and calculated 1JPP (Hz) for gauche and trans forms (with corresponded energy difference ΔE) of the model compounds 70–75 [126,127,128]; Table S7: Experimental and calculated 1JPP (Hz) for compounds 76–79 [129,130].

Author Contributions

Conceptualization, S.K.L. and S.A.K.; methodology, S.K.L.; software, S.K.L.; validation, S.K.L. and S.A.K.; formal analysis, S.K.L. and S.A.K.; investigation, S.K.L. and S.A.K.; resources, S.K.L.; data curation, S.K.L. and S.A.K.; writing—original draft preparation, S.K.L. and S.A.K.; writing—review and editing, S.K.L. and S.A.K.; visualization, S.A.K.; supervision, S.K.L.; project administration, S.K.L.; funding acquisition, S.K.L. The manuscript was written with the participation of all authors. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Supplementary Information available. Structures of all model compounds with experimental 1JPP, all calculation results, and some comments.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Fontana, C.; Widmalm, G. Primary structure of glycans by NMR spectroscopy. Chem. Rev. 2023, 123, 1040–1102. [Google Scholar] [CrossRef]
  2. Alderson, T.R.; Kay, L.E. NMR spectroscopy captures the essential role of dynamics in regulating biomolecular function. Cell 2021, 184, 577–595. [Google Scholar] [CrossRef] [PubMed]
  3. Contreras, R.H.; Barone, V.; Facelli, J.C.; Peralta, J.E. Advances in Theoretical and Physical Aspects of Spin-Spin Coupling Constants. Annu. Rep. NMR Spectrosc. 2003, 51, 167–260. [Google Scholar] [CrossRef]
  4. Raugei, S.; DuBois, D.L.; Rousseau, R.; Chen, S.; Ho, M.H.; Bullock, R.M.; Dupuis, M. Toward molecular catalysts by computer. Acc. Chem. Res. 2015, 48, 248–255. [Google Scholar] [CrossRef]
  5. Liu, T.; Wang, X.; Hoffmann, C.; DuBois, D.L.; Bullock, R.M. Heterolytic Cleavage of Hydrogen by an Iron Hydrogenase Model: An Fe-H···H-N Dihydrogen Bond Characterized by Neutron Diffraction. Angew. Chem. Int. Ed. 2014, 53, 5300–5304. [Google Scholar] [CrossRef]
  6. Zheng, A.; Liu, S.B.; Deng, F. 31P NMR chemical shifts of phosphorus probes as reliable and practical acidity scales for solid and liquid catalysts. Chem. Rev. 2017, 117, 12475–12531. [Google Scholar] [CrossRef] [PubMed]
  7. Rocchigiani, L.; Bochmann, M. Recent advances in gold (III) chemistry: Structure, bonding, reactivity, and role in homogeneous catalysis. Chem. Rev. 2020, 121, 8364–8451. [Google Scholar] [CrossRef]
  8. Derome, A.E. Modern NMR Techniques for Chemistry Research; Pergamon: Cambridge, UK, 1988. [Google Scholar]
  9. Kaupp, M. Calculation of NMR and EPR Parameters: Theory and Applications; Kaupp, M., Buhl, M., Malkin, V.G., Eds.; Wiley-VCH: Weinheim, Germany, 2004. [Google Scholar]
  10. De Dios, A.C.; Jameson, C.J. Recent advances in nuclear shielding calculations. Annu. Rep. NMR Spectrosc. 2012, 77, 1–80. [Google Scholar] [CrossRef]
  11. Bagno, A.; Rastrelli, F.; Saielli, G. Prediction of the 1H and 13C NMR Spectra of α-D-Glucose in Water by DFT Methods and MD Simulations. J. Org. Chem. 2007, 72, 7373–7381. [Google Scholar] [CrossRef]
  12. Rosselli, S.; Bruno, M.; Maggio, A.; Bellone, G.; Formisano, C.; Mattia, C.A.; Di Micco, S.; Bifulco, G. Two New Flavonoids from Bonannia Graeca: A DFT-NMR Combined Approach in Solving Structures. Eur. J. Org. Chem. 2007, 2007, 2504–2510. [Google Scholar] [CrossRef]
  13. Bifulco, G.; Riccio, R.; Gaeta, C.; Neri, P. Quantum Mechanical Calculations of Conformationally Relevant 1H and 13C NMR Chemical Shifts of N-, O-, and S-Substituted Calixarene Systems. Chem. Eur. J. 2007, 13, 7185–7194. [Google Scholar] [CrossRef]
  14. Claramunt, R.M.; López, C.; Santa María, M.D.; Sanz, D.; Elguero, J. The Use of NMR Spectroscopy to Study Tautomerism. Prog. Nucl. Magn. Reson. Spectrosc. 2006, 49, 169–206. [Google Scholar] [CrossRef]
  15. Lodewyk, M.W.; Siebert, M.R.; Tantillo, D.J. Computational Prediction of 1H and 13C Chemical Shifts: A Useful Tool for Natural Product, Mechanistic, and Synthetic Organic Chemistry. Chem. Rev. 2011, 112, 1839–1862. [Google Scholar] [CrossRef] [PubMed]
  16. Bifulco, G.; Dambruoso, P.; Gomez-Paloma, L.; Riccio, R. Determination of Relative Configuration in Organic Compounds by NMR Spectroscopy and Computational Methods. Chem. Rev. 2007, 107, 3744–3779. [Google Scholar] [CrossRef] [PubMed]
  17. Di Micco, S.; Chini, M.G.; Riccio, R.; Bifulco, G. Quantum Mechanical Calculation of NMR Parameters in the Stereostructural Determination of Natural Products. Eur. J. Org. Chem. 2010, 2010, 1411–1434. [Google Scholar] [CrossRef]
  18. Latypov, S.K.; Polyancev, F.M.; Yakhvarov, D.G.; Sinyashin, O.G. Quantum chemical calculations of 31P NMR chemical shifts: Scopes and limitations. Phys. Chem. Chem. Phys. 2015, 17, 6976–6987. [Google Scholar] [CrossRef]
  19. Kondrashova, S.A.; Polyancev, F.M.; Ganushevich, Y.S.; Latypov, S.K. DFT approach for predicting 13C NMR shifts of atoms directly coordinated to nickel. Organometallics 2021, 40, 1614–1625. [Google Scholar] [CrossRef]
  20. Latypov, S.K.; Kondrashova, S.A.; Polyancev, F.M.; Sinyashin, O.G. Quantum chemical calculations of 31P NMR chemical shifts in nickel complexes: Scope and limitations. Organometallics 2020, 39, 1413–1422. [Google Scholar] [CrossRef]
  21. Payard, P.A.; Perego, L.A.; Grimaud, L.; Ciofini, I. A DFT protocol for the prediction of 31P NMR chemical shifts of phosphine ligands in fi rst-row transition-metal complexes. Organometallics 2020, 39, 3121–3130. [Google Scholar] [CrossRef]
  22. Kondrashova, S.A.; Latypov, S.K. DFT Approach for Predicting 13C NMR Shifts of Atoms Directly Coordinated to Pd. Organometallics 2023, 42, 1951–1962. [Google Scholar] [CrossRef]
  23. Kondrashova, S.A.; Latypov, S.K. Combined DFT protocol for the calculation of 31P NMR shifts in platinum complexes. Dalton Trans. 2026, 55, 1781–1791. [Google Scholar] [CrossRef]
  24. Karplus, M. Contact electron-spin coupling of nuclear magnetic moments. J. Chem. Phys. 1959, 30, 11–15. [Google Scholar] [CrossRef]
  25. Contreras, R.N.H.; Peralta, J.E. Angular dependence of spin-spin coupling constants. Prog. Nucl. Magn. Reson. Spectrosc. 2000, 37, 321–425. [Google Scholar] [CrossRef]
  26. Marshall, J.L. Carbon-Carbon and Carbon-Proton NMR Couplings: Applications to Organic Stereochemistry and Conformational Analysis; VCH Pub: New York, NY, USA, 1983. [Google Scholar]
  27. Krivdin, L.B.; Contreras, R.H. Recent advances in theoretical calculations of indirect spin-spin coupling constants. Annu. Rep. NMR Spectrosc. 2007, 61, 133–245. [Google Scholar] [CrossRef]
  28. Helgaker, T.; Jaszuński, M.; Pecul, M. The quantum-chemical calculation of NMR indirect spin-spin coupling constants. Prog. Nucl. Magn. Reson. Spectrosc. 2008, 53, 249–268. [Google Scholar] [CrossRef]
  29. Rusakov, Y.Y.; Krivdin, L.B. Modern quantum chemical methods for calculating spin-spin coupling constants: Theoretical basis and structural applications in chemistry. Russ. Chem. Rev. 2013, 82, 99–130. [Google Scholar] [CrossRef]
  30. Bally, T.; Rablen, P.R. Quantum-chemical simulation of 1H NMR spectra. 2. Comparison of DFT-based procedures for computing proton-proton coupling constants in organic molecules. J. Org. Chem. 2011, 76, 4818–4830. [Google Scholar] [CrossRef]
  31. Kutateladze, A.G. Structure Revision of Decurrensides A-E Enabled by the RFF Parametric Calculations of Proton Spin-Spin Coupling Constants. J. Org. Chem. 2016, 81, 8659–8661. [Google Scholar] [CrossRef]
  32. Klepach, T.; Zhang, W.; Carmichael, I.; Serianni, A.S. 13C-1H and 13C-13C NMR J-couplings in 13C-labeled N-acetyl-neuraminic acid: Correlations with molecular structure. J. Org. Chem. 2008, 73, 4376–4387. [Google Scholar] [CrossRef]
  33. Del Bene, J.E.; Alkorta, I.; Elguero, J. Probing 1J(C-F) and nJ(F-F) Spin- Spin Coupling Constants for Fluoroazines: An Ab Initio Theoretical Investigation. J. Phys. Chem. A 2010, 114, 2637–2643. [Google Scholar] [CrossRef] [PubMed]
  34. San Fabián, J.; García De La Vega, J.M.; Suardíaz, R.; Fernández-Oliva, M.; Pérez, C.; Crespo-Otero, R.; Contreras, R.H. Computational NMR coupling constants: Shifting and scaling factors for evaluating 1JCH. Magn. Reson. Chem. 2013, 51, 775–787. [Google Scholar] [CrossRef]
  35. Deng, W.; Cheeseman, J.R.; Frisch, M.J. Calculation of nuclear spin-spin coupling constants of molecules with first and second row atoms in study of basis set dependence. J. Chem. Theory Comput. 2006, 2, 1028–1037. [Google Scholar] [CrossRef]
  36. Helgaker, T.; Jaszuński, M.; Świder, P. Calculation of NMR spin-spin coupling constants in strychnine. J. Org. Chem. 2016, 81, 11496–11500. [Google Scholar] [CrossRef] [PubMed]
  37. Del Bene, J.E.; Alkorta, I.; Sanchez-Sanz, G.; Elguero, J. 31P−31P spin-spin coupling constants for pnicogen homodimers. Chem. Phys. Lett. 2011, 512, 184–187. [Google Scholar] [CrossRef]
  38. Pecul, M.; Urbańczyk, M.; Wodyński, A.; Jaszuński, M. DFT calculations of 31P spin-spin coupling constants and chemical shift in dioxaphosphorinanes. Magn. Reson. Chem. 2011, 49, 399–404. [Google Scholar] [CrossRef] [PubMed]
  39. Forgeron, M.A.; Gee, M.; Wasylishen, R.E. A Theoretical Investigation of One-Bond Phosphorus- Phosphorus Indirect Nuclear Spin- Spin Coupling Tensors, 1J(31P, 31P), Using Density Functional Theory. J. Phys. Chem. A 2004, 108, 4895–4908. [Google Scholar] [CrossRef]
  40. Wrackmeyer, B. Density functional theory (DFT) calculations of indirect nuclear spin-spin coupling constants 1J(31P, 13C) in λ3-phosphaalkynes. Z. Naturforsch. B 2003, 58, 1041–1044. [Google Scholar] [CrossRef]
  41. Miertus, S.; Scrocco, E.; Tomasi, J. Electrostatic interaction of a solute with a continuum. A direct utilization of AB initio molecular potentials for the prevision of solvent effects. Chem. Phys. 1981, 55, 117–129. [Google Scholar] [CrossRef]
  42. Jensen, F. The optimum contraction of basis sets for calculating spin-spin coupling constants. Theor. Chem. Acc. 2010, 126, 371–382. [Google Scholar] [CrossRef]
  43. Ukhanev, S.A.; Fedorov, S.V.; Rusakov, Y.Y.; Rusakova, I.L.; Krivdin, L.B. Computational protocols for the 19F NMR parameters. Part 2: Fluorobenzenes. J. Fluor. Chem. 2023, 266, 110093. [Google Scholar] [CrossRef]
  44. Lutnæs, O.B.; Helgaker, T.; Jaszuński, M. Spin-spin coupling constants and triplet instabilities in Kohn-Sham theory. Mol. Phys. 2010, 108, 2579–2590. [Google Scholar] [CrossRef]
  45. Vaara, J. Theory and computation of nuclear magnetic resonance parameters. Phys. Chem. Chem. Phys. 2007, 9, 5399–5418. [Google Scholar] [CrossRef] [PubMed]
  46. Pierens, G.K. 1H and 13C NMR scaling factors for the calculation of chemical shifts in commonly used solvents using density functional theory. J. Comput. Chem. 2014, 35, 1388–1394. [Google Scholar] [CrossRef] [PubMed]
  47. Konstantinov, I.A.; Broadbelt, L.J. Regression formulas for density functional theory calculated 1H and 13C NMR chemical shifts in toluene-d8. J. Phys. Chem. A 2011, 115, 12364–12372. [Google Scholar] [CrossRef]
  48. Borucki, S.; Kelemen, Z.; Maurer, M.; Bruhn, C.; Nyulászi, L.; Pietschnig, R. Stereochemical alignment in triphospha [3]ferrocenophanes. Chem. Eur. J. 2017, 23, 10438–10450. [Google Scholar] [CrossRef]
  49. Komorovsky, S.; Jakubowska, K.; Świder, P.; Repisky, M.; Jaszuński, M. Nmr spin-spin coupling constants derived from relativistic four-component DFT theory—Analysis and visualization. J. Phys. Chem. A 2020, 124, 5157–5169. [Google Scholar] [CrossRef]
  50. Batista, P.R.; Ducati, L.C.; Autschbach, J. Dynamic and relativistic effects on Pt-Pt indirect spin-spin coupling in aqueous solution studied by ab initio molecular dynamics and two- vs four-component density functional NMR calculations. J. Chem. Phys. 2024, 160, 114307. [Google Scholar] [CrossRef]
  51. Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140, A1133. [Google Scholar] [CrossRef]
  52. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Montgomery, J.A., Jr.; Vreven, T.; Kudin, K.N.; Burant, J.C.; et al. Gaussian 03, Revision B.04; Gaussian, Inc.: Pittsburgh, PA, USA, 2003. [Google Scholar]
  53. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Petersson, G.A.; Nakatsuji, H.; et al. Gaussian 16, Revision A.03; Gaussian, Inc.: Wallingford, CT, USA, 2016. [Google Scholar]
  54. Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158–6170. [Google Scholar] [CrossRef]
  55. Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865–3868, Erratum in Phys. Rev. Lett. 1997, 78, 1396. https://doi.org/10.1103/PhysRevLett.78.1396. [Google Scholar] [CrossRef]
  56. Bernard, Y.A.; Shao, Y.; Krylov, A.I. General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: Theory, implementation, and benchmarks. J. Chem. Phys. 2012, 136, 204103. [Google Scholar] [CrossRef]
  57. Becke, A.D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648–5652. [Google Scholar] [CrossRef]
  58. Stephens, P.J.; Devlin, F.J.; Chabalowski, C.F.; Frisch, M.J. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force field methods. J. Phys. Chem. A 1994, 98, 11623–11627. [Google Scholar] [CrossRef]
  59. Wilson, P.J.; Bradley, T.J.; Tozer, D.J. Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials. J. Chem. Phys. 2001, 115, 9233–9242. [Google Scholar] [CrossRef]
  60. Becke, A.D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A At. Mol Opt. Phys. 1988, 38, 3098–3100. [Google Scholar] [CrossRef]
  61. Lee, C.; Yang, W.; Parr, R.G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B Condens. Matter Mater. Phys. 1988, 37, 785–789. [Google Scholar] [CrossRef]
  62. Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Results obtained with the correlation energy density functional of Becke and Lee, Yang and Parr. Chem. Phys. Lett. 1989, 157, 200–206. [Google Scholar] [CrossRef]
  63. Perdew, J.P. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B 1986, 33, 8822–8824. [Google Scholar] [CrossRef]
  64. Becke, A.D. A new mixing of Hartree-Fock and local density-functional theories. J. Chem. Phys. 1993, 98, 1372–1377. [Google Scholar] [CrossRef]
  65. Hehre, W.J.; Ditchfield, R.; Pople, J.A. Self-Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian-Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56, 2257–2261. [Google Scholar] [CrossRef]
  66. Clark, T.; Chandrasekhar, J.; Spitznagel, G.W.; Schleyer, P.V.R. Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21+G basis set for first-row elements, Li-F. J. Comput. Chem. 1983, 4, 294–301. [Google Scholar] [CrossRef]
  67. Francl, M.M.; Pietro, W.J.; Hehre, W.J.; Binkley, J.S.; Gordon, M.S.; DeFrees, D.J.; Pople, J.A. Self-consistent molecular orbital methods. XXIII. A polarization-type basis set for second-row elements. J. Chem. Phys. 1982, 77, 3654–3665. [Google Scholar] [CrossRef]
  68. Frisch, M.J.; Pople, J.A.; Binkley, J.S. Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets. J. Chem. Phys. 1984, 80, 3265–3269. [Google Scholar] [CrossRef]
  69. Krishnan, R.; Binkley, J.S.; Seeger, R.; Pople, J.A. Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys. 1980, 72, 650–654. [Google Scholar] [CrossRef]
  70. McLean, A.D.; Chandler, G.S. Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z = 11–18. J. Chem. Phys. 1980, 72, 5639–5648. [Google Scholar] [CrossRef]
  71. Spitznagel, G.W.; Clark, T.; von Ragué Schleyer, P.; Hehre, W.J. An evaluation of the performance of diffuse function-augmented basis sets for second row elements, Na-Cl. J. Comput. Chem. 1987, 8, 1109–1116. [Google Scholar] [CrossRef]
  72. Ditchfield, R.; Hehre, W.J.; Pople, J.A. Self-Consistent Molecular-Orbital Methods. IX. An. Extended Gausian-Type Basis for Molecular-Orbital Studies of Organic Molecules. J. Chem. Phys. 1971, 54, 724–728. [Google Scholar] [CrossRef]
  73. Hansen, A.E.; Bouman, T.D. Localized orbital/local origin method for calculation and analysis of NMR shieldings. Applications to 13C shielding tensors. J. Chem. Phys. 1985, 82, 5035–5047. [Google Scholar] [CrossRef]
  74. Pritchard, B.P.; Altarawy, D.; Didier, B.; Gibson, T.D.; Windus, T.L. A New Basis Set Exchange: An Open, Up-to-date Resource for the Molecular Sciences Community. J. Chem. Inf. Model. 2019, 59, 4814–4820. [Google Scholar] [CrossRef]
  75. Feller, D. The Role of Databases in Support of Computational Chemistry Calculations. J. Comput. Chem. 1996, 17, 1571–1586. [Google Scholar] [CrossRef]
  76. Schuchardt, K.L.; Didier, B.T.; Elsethagen, T.; Sun, L.; Gurumoorthi, V.; Chase, J.; Li, J.; Windus, T.L. Basis Set Exchange: A Community Database for Computational Sciences. J. Chem. Inf. Model. 2007, 47, 1045–1052. [Google Scholar] [CrossRef]
  77. Niecke, E.; Rüger, R.; Lysek, M.; Pohl, S.; Schoeller, W.W. Diaminodiphosphenes—Synthesis, Crystal Structure and Bonding Properties. Angew. Chem. Int. Ed. Engl. 1983, 22, 639–654. [Google Scholar] [CrossRef]
  78. Jutzi, P.; Meyer, U.; Krebs, B.; Dartmann, M. Bis(Pentamethylcyclopentadienyl)Diphosphene—A Molecule with Fluxional Structure and Reactive PC Bond. Angew. Chem. Int. Ed. Engl. 1986, 25, 919–921. [Google Scholar] [CrossRef]
  79. Cowley, A.H.; Knueppel, P.C.; Nunn, C.M. Silyl-Substituted Diphosphenes. Synthesis, Structure, and Modes of Decomposition. Organometallics 1989, 8, 2490–2492. [Google Scholar] [CrossRef]
  80. Cowley, A.H.; Kilduff, J.E.; Pakulski, M.; Stewart, C.A. An Unsymmetrically Substituted Diphosphene: NMR Spectroscopic Data Pertinent to the Phosphorus-Phosphorus Double Bond. J. Am. Chem. Soc. 1983, 105, 1655–1656. [Google Scholar] [CrossRef]
  81. Sasamori, T.; Tsurusaki, A.; Nagahora, N.; Matsuda, K.; Kanemitsu, Y.; Watanabe, Y.; Furukawa, Y.; Tokitoh, N. Synthesis and Properties of 9-Anthryldiphosphene. Chem. Lett. 2006, 35, 1382–1383. [Google Scholar] [CrossRef]
  82. Smit, C.N.; van der Knaap, T.A.; Bickelhaupt, F. Stable Unsymmetrical Diphosphenes. Tetrahedron Lett. 1983, 24, 2031–2034. [Google Scholar] [CrossRef]
  83. Schwedtmann, K.; Hennersdorf, F.; Bauzá, A.; Frontera, A.; Fischer, R.; Weigand, J.J. Isolation of Azadiphosphiridines and Diphosphenimines by Cycloaddition of Azides and a Cationic Diphosphene. Angew. Chem. Int. Ed. 2017, 56, 6218–6222. [Google Scholar] [CrossRef]
  84. Smith, R.C.; Urnezius, E.; Lam, K.-C.; Rheingold, A.L.; Protasiewicz, J.D. Syntheses and Structural Characterizations of the Unsymmetrical Diphosphene DmpPPMes* (Dmp = 2,6-Mes2C6H3, Mes* = 2,4,6-tBu3C6H2) and the Cyclotetraphosphane [DmpPPPh]2. Inorg. Chem. 2002, 41, 5296–5299. [Google Scholar] [CrossRef]
  85. Escudie, J.; Couret, C.; Ranaivonjatovo, H.; Lazraq, M.; Satge, J. Synthesis of two stable diphosphenes with a new stabilizing substituent. Phosphorus Sulfur Silicon Relat. Elem. 1987, 31, 27–31. [Google Scholar] [CrossRef]
  86. Yoshifuji, M.; Shibayama, K.; Inamoto, N.; Matsushita, T.; Nishimoto, K. Isolation of Some Sterically Protected Unsymmetrical Diphosphenes: Nature of the Phosphorus-Phosphorus Double Bond. J. Am. Chem. Soc. 1983, 105, 2495–2497. [Google Scholar] [CrossRef]
  87. Niecke, E.; Kramer, B.; Nieger, M. Synthesis, Structure, and Reactivity of Diphosphenes Having a Cis-Configuration. Angew. Chem. Int. Ed. Engl. 1989, 28, 215–217. [Google Scholar] [CrossRef]
  88. Donath, M.; Hennersdorf, F.; Weigand, J.J. Recent Highlights in Mixed-Coordinate Oligophosphorus Chemistry. Chem. Soc. Rev. 2016, 45, 1145–1172. [Google Scholar] [CrossRef]
  89. Surgenor, B.A.; Bühl, M.; Slawin, A.M.Z.; Woollins, J.D.; Kilian, P. Isolable Phosphanylidene Phosphorane with a Sterically Accessible Two-Coordinate Phosphorus Atom. Angew. Chem. Int. Ed. 2012, 51, 10150–10153. [Google Scholar] [CrossRef]
  90. Ellis, B.D.; Macdonald, C.L.B. Phosphorus(I) Iodide:  A Versatile Metathesis Reagent for the Synthesis of Low Oxidation State Phosphorus Compounds. Inorg. Chem. 2006, 45, 6864–6874. [Google Scholar] [CrossRef]
  91. Cowley, A.H.; Cushner, M.C. Exchange Reactions in (CH3)3PPCF3, Phosphinidene Analog of a Wittig Reagent. Inorg. Chem. 1980, 19, 515–518. [Google Scholar] [CrossRef]
  92. Lamande, L.; Munoz, A. Reactivity of Conjugated Bases of Hydridophosphoranes Synthesis of New Phosphoranes Involving P-P Bonds. Tetrahedron 1990, 46, 3527–3534. [Google Scholar] [CrossRef]
  93. Kovacs, I.; Matern, E.; Fritz, G. Zum Einfluß Der Substituenten R = Ph, NEt2, iPr Und tBu in Triphosphanen, (R2P)2PSiMe3, Und Phosphiden, Li(THF)2[(R2P)2P], Auf Die Bildung Und Eigenschaften von Phosphinophosphiniden-Phosphoranen. Z. Anorg. Allg. Chem. 1996, 622, 935–941. [Google Scholar] [CrossRef]
  94. Beil, A.; Gilliard, R.J.; Grützmacher, H. From the Parent Phosphinidene–Carbene Adduct NHCPH to Cationic P4-Rings and P2-Cycloaddition Products. Dalton Trans. 2016, 45, 2044–2052. [Google Scholar] [CrossRef]
  95. Burford, N.; Cameron, T.S.; Ragogna, P.J.; Ocando-Mavarez, E.; Gee, M.; McDonald, R.; Wasylishen, R.E. Phosphine Ligand Exchange at a Phosphine Lewis Acceptor:  The First Structural Characterization of Homoleptic Phosphinophosphonium Salts. J. Am. Chem. Soc. 2001, 123, 7947–7948. [Google Scholar] [CrossRef]
  96. Karaçar, A.; Freytag, M.; Thönnessen, H.; Jones, P.G.; Bartsch, R.; Schmutzler, R. Preparation and Structures of 1-Dimethylamino-2-Bis(Dimethylamino)- and 1-Chloro-2-Bis(Diethylamino)-1-Phospha-2-Phosphonium Acenaphthene: The First Examples of the 1,2-Dihydro-1,2-Diphospha-Acenaphthene Ring System. J. Organomet. Chem. 2002, 643–644, 68–80. [Google Scholar] [CrossRef]
  97. Solan, D.; Timms, P.L. The Thermal Dissociation of Diphosphoros Tetrafluoride and the Formation of Tetraphosphorus Hexafluoride. Chem. Commun. 1968, 23, 1540–1541. [Google Scholar] [CrossRef]
  98. Bäudler, M.; Makowka, B.; Langerbeins, K. Beiträge zur Chemie des Phosphors, 156 [1, 2]. 1,2-Di-tert-butyl-cyclotriphosphan,(t-BuP)2PH, und 1,2,3-Tri-tert-butyl-cyclotetraphosphan,(t-BuP)3PH/Contributions to the Chemistry of Phosphorus, 156 [1,2]1,2-Di-tert-butyl-cyclotriphosphane,(t-BuP)2PH, and 1,2,3-Tri-tert-butyl-cyclotetraphosphane,(t-BuP)3PH. Z. Naturforschung B 1985, 40, 1274–1276. [Google Scholar]
  99. Burford, N.; Ragogna, P.J.; McDonald, R.; Ferguson, M.J. Phosphine Coordination Complexes of the Diphenylphosphenium Cation: A Versatile Synthetic Methodology for P−P Bond Formation. J. Am. Chem. Soc. 2003, 125, 14404–14410. [Google Scholar] [CrossRef]
  100. Vogt, R.; Jones, P.G.; Schmutzler, R. Darstellung, Struktur Und Eigenschaften von Harnstoffverbrückten Cyclischen Phosphoniumsalzen Mit Phosphor-Phosphor-, Phosphor-Arsen-, Phosphor-Antimon-und Phosphor-Zinn-Bindung. Chem. Ber. 1993, 126, 1271–1281. [Google Scholar] [CrossRef]
  101. Wolf, R.; Finger, M.; Limburg, C.; Willis, A.C.; Wild, S.B.; Hey-Hawkins, E. Reactivity of cyclooligophosphanes: Synthesis and structural characterisation of cyclo-1, 4-(BH3)2(P4Ph4CH2) and cyclo-1, 2-(BH3)2(P5Ph5). Dalton Trans. 2006, 6, 831–837. [Google Scholar] [CrossRef]
  102. Avens, L.R.; Wolcott, R.A.; Cribbs, L.V.; Mills, J.L. Some Perfluoroalkyl-Substituted Tripnicogens and Their Hydrolysis to Yield Chiral Dipnicogens. Inorg. Chem. 1989, 28, 200–205. [Google Scholar] [CrossRef]
  103. Bresien, J.; Schulz, A.; Villinger, A. A Tricyclic Hexaphosphane. Chem. Eur. J. 2015, 21, 18543–18546. [Google Scholar] [CrossRef]
  104. Schwedtmann, K.; Holthausen, M.H.; Sala, C.H.; Hennersdorf, F.; Fröhlich, R.; Weigand, J.J. [(ClImDipp)PP(Dipp)][GaCl4]: A Polarized, Cationic Diphosphene. Chem. Commun. 2016, 52, 1409–1412. [Google Scholar] [CrossRef]
  105. Miluykov, V.; Bezkishko, I.; Zagidullin, A.; Sinyashin, O.; Lönnecke, P.; Hey-Hawkins, E. Cycloaddition Reactions of 1-Alkyl-3,4,5-triphenyl-1,2-diphosphacyclopenta-2,4-dienes. Eur. J. Org. Chem. 2009, 2009, 1269–1274. [Google Scholar] [CrossRef]
  106. Cui, J.; Li, Y.; Ganguly, R.; Kinjo, R. Reactivity Studies on a Diazadiphosphapentalene. Chem. Eur. J. 2016, 22, 9976–9985. [Google Scholar] [CrossRef]
  107. Jutzi, P.; Meyer, U. Photochemie von pentamethylcyclopentadienyl-substituierten Diphosphenen und Phosphaarsenen. J. Organomet. Chem. 1987, 333, C18–C20. [Google Scholar] [CrossRef]
  108. Walter, M. Polyphosphine Heterocycles. J. Am. Chem. Soc. 1964, 86, 2306–2307. [Google Scholar] [CrossRef]
  109. Yogendra, S.; Chitnis, S.S.; Hennersdorf, F.; Bodensteiner, M.; Fischer, R.; Burford, N.; Weigand, J.J. Condensation Reactions of Chlorophosphanes with Chalcogenides. Inorg. Chem. 2016, 55, 1854–1860. [Google Scholar] [CrossRef]
  110. Issleib, K.; Thorausch, P.; Meyer, H. NMR-daten Substituierter 1,2-diphospholane Sowie Des 1,5-diphosphabicyclo[3.3.0]Octans Und Seiner P-derivate. Org. Magn. Reson. 1977, 10, 172–174. [Google Scholar] [CrossRef]
  111. Okruszek, A.; Stec, W.J.; Harris, R.K. The Axial/Equatorial Preference of the Diphenylphosphino Group Bonded to the Phosphorus of a 2-oxo-1,3,2-dioxaphosphorinanyl Ring. Org. Magn. Reson. 1977, 9, 497–498. [Google Scholar] [CrossRef]
  112. Fluck, E.; Binder, H. Darstellung von verbindungen MIT PP—und PPP—gerüsten. Inorg. Nucl. Chem. Lett. 1967, 3, 307–313. [Google Scholar] [CrossRef]
  113. Hägele, G.; Harris, R.K.; Nichols, J.M. Nuclear Magnetic Resonance Spectra of Symmetrical Phosphorus Compounds. Part V.1H Nuclear Magnetic Resonance Spectrum of P,P′-Dimethyl-P,P′-Di-t-Butyldiphosphine P,P′-Disulphide, an [ARtXn]2Spin System. J. Chem. Soc. Dalton Trans. 1973, 1, 79–82. [Google Scholar] [CrossRef]
  114. Harris, R.K.; Hayter, R.G. Nuclear Magnetic Resonance Studies Of Compounds Related To Tetramethyldiphosphine Disulphide. Can. J. Chem. 1964, 42, 2282–2291. [Google Scholar] [CrossRef]
  115. Aime, S.; Harris, R.K.; McVicker, E.M.; Fild, M. Multinuclear Magnetic Resonance Studies. Part 2. Diphosphanes and Dithioxodi-λ5-Phosphanes. J. Chem. Soc. Dalton Trans. 1976, 21, 2144–2153. [Google Scholar] [CrossRef]
  116. Appel, R.; Milker, R. Synthese von Tetramethyldiphosphan-oxid-sulfid. Chem. Ber. 1977, 110, 3201–3204. [Google Scholar] [CrossRef]
  117. Haynes, R.K.; Lam, W.W.L.; Williams, I.D.; Yeung, L.L. The First Examples of Enantiomerically Pure Diphosphane Dioxides—(RP, RP)-and (SP, SP)-1, 2-Di-ter-butyl-1, 2-diphenyldiphosphane 1, 2-Dioxides, and (RP)-and (SP)-1-tert-Butyl-1, 2, 2-triphenyldiphosphane 1, 2-Dioxides. Chem. Eur. J. 1997, 3, 2052–2057. [Google Scholar] [CrossRef]
  118. Finer, E.G.; Harris, R.K. Variations in Sign for the Coupling Constants between Directly-Bonded Phosphorus Nuclei. Chem. Commun. 1968, 2, 110. [Google Scholar] [CrossRef]
  119. Harris, R.K.; Woplin, J.R.; Stec, W. Nuclear Magnetic Resonance Coupling Constants for a Bis(Dioxaphosphorinanyl). J. Chem. Soc. D. 1970, 21, 1391–1392. [Google Scholar] [CrossRef]
  120. Luo, H.; McDonald, R.; Cavell, R.G. A Cationic, Macrocyclic, Six-Coordinate Phosphorus(V) Compound Containing a Mixed Valence PIII-PV-PIII Linear Chain. Angew. Chem. Int. Ed. 1998, 37, 1098–1099. [Google Scholar] [CrossRef]
  121. Harris, R.K.; Katritzky, A.R.; Musierowicz, S.; Ternai, B. Phosphorus and Proton Magnetic Resonance Spectra of Esters of Pyrophosphoric and Hypophosphoric Acid and Some Derivatives. J. Chem. Soc. A 1967, 37–40. [Google Scholar] [CrossRef]
  122. Roesky, H.W.; Djarrah, H. Preparation of a Spirocyclic Phosphorane with a PV-PV Bond. Inorg. Chem. 1982, 21, 844–845. [Google Scholar] [CrossRef]
  123. Rudolph, R.W.; Schultz, C.W. Phosphorus-Phosphorus Bond. I. Complexes Containing Highly Connected Phosphorus Atoms, HnMe3-nPPF5. Directly Bonded Phosphorus-Phosphorus Coupling Constant. J. Am. Chem. Soc. 1971, 93, 1898–1903. [Google Scholar] [CrossRef]
  124. Ruflin, C.; Fischbach, U.; Grützmacher, H.; Levalois-Grützmacher, J. Tetrakis(Trimethysilyl)Hypophosphate P2O2(OTMS)4: Synthesis, Reactivity and Application as Flame Retardant. Heteroat. Chem. 2007, 18, 721–731. [Google Scholar] [CrossRef]
  125. Falius, H.; Murray, M. NMR Investigations on Fluorophosphate Anions Containing a PP Bond. J. Magn. Res. (1969) 1973, 10, 127–129. [Google Scholar] [CrossRef]
  126. McFarlane, H.C.E.; McFarlane, W.; Nash, J.A. Phosphorus–Phosphorus Nuclear Spin Coupling in Tetraorganobiphosphines and Some of Their Derivatives. J. Chem. Soc. Dalton Trans. 1980, 2, 240–244. [Google Scholar] [CrossRef]
  127. Cavell, R.G.; Dobbie, R.C. Preparation and properties of some bis (trifluoromethyl)-phosphorus and-arsenic derivatives containing P–P, P–As, and As–As bonds. J. Chem. Soc. A Inorg. Phys. Theor. 1968, 1406–1410. [Google Scholar] [CrossRef]
  128. Baudler, M.; Heumüller, H. Beiträge Zur Chemie Des Phosphors. 74. 1,1-Diphenyldiphosphan Und Monophenyldiphosphan Durch Reaktion von Diphosphan Mit Tetraphenyldiphosphan Bzw. 1,2-Diphenyldiphosphan. Z. Anorg. Allge. Chemie. 1977, 437, 73–77. [Google Scholar] [CrossRef]
  129. Zagidullin, A.; Ganushevich, Y.; Miluykov, V.; Krivolapov, D.; Kataeva, O.; Sinyashin, O.; Hey-Hawkins, E. Reactions of 1-Alkyl-1,2-Diphospholes with 1,3-Dipoles: Diphenyldiazomethane and Nitrones. Org. Biomol. Chem. 2012, 10, 5298. [Google Scholar] [CrossRef]
  130. Baudler, M.; Warnau, M.; Koch, D. Beiträge Zur Chemie Des Phosphors, 81: 1,2,5,6-Tetraphosphabicyclo[3.3.0]Octan. Chem. Ber. 1978, 111, 3838–3842. [Google Scholar] [CrossRef]
Molecules 31 01831 g001
Figure 1. Correlation of calculated (PBE0/6-31G(d)//PBE0/6-31G(d)) vs. experimental 1JPP for model compounds, with the exception of systems with conformational exchange (a) and for systems in conformational exchange (b).
Figure 1. Correlation of calculated (PBE0/6-31G(d)//PBE0/6-31G(d)) vs. experimental 1JPP for model compounds, with the exception of systems with conformational exchange (a) and for systems in conformational exchange (b).
Molecules 31 01831 g001
Molecules 31 01831 g002
Figure 2. Correlation of calculated vs. experimental 1JPP for all model compounds (except for systems with conformational exchange): PBE0/6-31+G(d)//PBE0/6-31+G(d) (a) and PBE0/6-311G(2d,2p)//PBE0/6-31+G(d) (b) levels (the designations are the same as in Figure 1).
Figure 2. Correlation of calculated vs. experimental 1JPP for all model compounds (except for systems with conformational exchange): PBE0/6-31+G(d)//PBE0/6-31+G(d) (a) and PBE0/6-311G(2d,2p)//PBE0/6-31+G(d) (b) levels (the designations are the same as in Figure 1).
Molecules 31 01831 g002
Molecules 31 01831 g003
Figure 3. “Training” set of model compounds.
Figure 3. “Training” set of model compounds.
Molecules 31 01831 g003
Molecules 31 01831 g004
Figure 4. R2 dependence of on basis set for three groups of the “training” set (the PBE0 functional was used in all cases).
Figure 4. R2 dependence of on basis set for three groups of the “training” set (the PBE0 functional was used in all cases).
Molecules 31 01831 g004
Molecules 31 01831 g005
Figure 5. R2 dependence on the functionals when calculating the SSCCs 1JPP for three groups of the “training” set (in all cases, the 6-31G(d) basis set and the PBE0/6-31G(d)) geometry was used).
Figure 5. R2 dependence on the functionals when calculating the SSCCs 1JPP for three groups of the “training” set (in all cases, the 6-31G(d) basis set and the PBE0/6-31G(d)) geometry was used).
Molecules 31 01831 g005
Molecules 31 01831 g006
Figure 6. Correlation of calculated vs. experimental 1JPP for the “training” set, depending on the type of functional: PBE (a), PBE0 (b), and PBE50 (c) (in all cases the 6-31G(d) basis set and the PBE0/6-31G(d)) geometry was used, the designations are the same as in Figure 1).
Figure 6. Correlation of calculated vs. experimental 1JPP for the “training” set, depending on the type of functional: PBE (a), PBE0 (b), and PBE50 (c) (in all cases the 6-31G(d) basis set and the PBE0/6-31G(d)) geometry was used, the designations are the same as in Figure 1).
Molecules 31 01831 g006
Molecules 31 01831 g007
Figure 7. Correlation of calculated (corrected, PBE0/6-31G(d)//PBE0/6-31G(d) level) vs. experimental 1JPP for all model compounds (the designations are the same as in Figure 1).
Figure 7. Correlation of calculated (corrected, PBE0/6-31G(d)//PBE0/6-31G(d) level) vs. experimental 1JPP for all model compounds (the designations are the same as in Figure 1).
Molecules 31 01831 g007
Molecules 31 01831 g008
Figure 8. Schematical representation of energy diagrams for trans and gauche isomers of compound 74 in vacuum and acetone, and corresponding calculated (PBE0/6-31G(d)//PBE0/6-31G(d)) and experimental 1JPP.
Figure 8. Schematical representation of energy diagrams for trans and gauche isomers of compound 74 in vacuum and acetone, and corresponding calculated (PBE0/6-31G(d)//PBE0/6-31G(d)) and experimental 1JPP.
Molecules 31 01831 g008
Molecules 31 01831 g009
Figure 9. Structure of compounds 76–79 with experimental (green) and calculated (black, corrected, PBE0/6-31G(d)//PBE0/6-31G(d)) 1JPP (Hz) (Mes* = 2,4,6-Tri-tert-butylphenyl).
Figure 9. Structure of compounds 76–79 with experimental (green) and calculated (black, corrected, PBE0/6-31G(d)//PBE0/6-31G(d)) 1JPP (Hz) (Mes* = 2,4,6-Tri-tert-butylphenyl).
Molecules 31 01831 g009
Molecules 31 01831 g010
Figure 10. Structure of the triphospha[3]ferrocenophanes (80a–e) and schematic of the possible diastereomers with the experimental and calculated 1JPP (Hz, PBE0/6-31G(d)//PBE0/6-31G(d), corrected).
Figure 10. Structure of the triphospha[3]ferrocenophanes (80a–e) and schematic of the possible diastereomers with the experimental and calculated 1JPP (Hz, PBE0/6-31G(d)//PBE0/6-31G(d), corrected).
Molecules 31 01831 g010
Table 1. Experimental and calculated 1JPP for the “training” set (basis set in the calculation of SSCCs is 6-31G(d), geometry optimization is the same for all levels—PBE0/6-31G(d)).
Table 1. Experimental and calculated 1JPP for the “training” set (basis set in the calculation of SSCCs is 6-31G(d), geometry optimization is the same for all levels—PBE0/6-31G(d)).
Comp.Exp.Calculated 1JPP, Hz
PBE0PBEPBE50BHandHLYP
1−670.0−558.1−635.91377.5529.9
11−574.3−478.4−557.9185.017.8
12−573.7−462.9−573.62279.9837.3
14−548.7−450.4−545.82205.2734.6
15−526.0−418.1−475.8−21.6−416.2
16−665.0−631.4−646.4−608.8−643.7
20−436.4−419.1−437.0−394.6−418.6
26−347.0−325.2−357.4−285.4−305.2
30−309.5−276.9−261.6−280.9−277.7
−222.4−181.6−190.9−167.5−175.5
−157.5−125.3−132.7−114.9−123.4
45−131.1−102.5−122.0−81.7−90.8
−93.0−60.6−77.6−42.5−51.9
51−243.0−198.9−264.3−177.8−187.4
54−118.0−117.3−177.2−51.6−64.0
55−18.7−56.5−114.86.2−2.6
62583.0385.0292.4483.6499.4
65715.0479.2367.0586.4625.2
R2 (Group 1)0.98370.86380.04300.1459
R2 (Group 2)0.99860.99110.99700.9987
R2 (Group 3)0.99960.99970.99910.9992
The experimental values are shown in green, and the largest “errors” are shown in red.
Table 2. Empirical scaling factors obtained by the linear regression analysis of the calculated and experimental 1JPP for corresponding groups of models, R2 and RMSE.
Table 2. Empirical scaling factors obtained by the linear regression analysis of the calculated and experimental 1JPP for corresponding groups of models, R2 and RMSE.
Level of Theory InterceptSlopeR2RMSE a
PBE0/6-31G(d)//
PBE0/6-31G(d)		Group 1155.01.100.81417.0
Group 234.51.000.98913.1
Group 3−37.10.710.99527.1
PBE0/6-31+G(d)//
PBE0/6-31+G(d)		Group 118.50.890.74920.5
Group 240.21.070.97420.9
Group 3−64.30.690.99431.1
PBE0/6-311G(2d,2p)//
PBE0/6-31+G(d)		Group 114.71.100.73921.1
Group 253.61.460.96225.2
Group 3−79.90.990.99040.5
a RMSE—Root Mean Square Error (Hz).
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Kondrashova, S.A.; Latypov, S.K. Combined DFT Protocol for the Calculation of One-Bond 31P-31P Indirect Nuclear Spin–Spin Couplings. Molecules 2026, 31, 1831. https://doi.org/10.3390/molecules31111831

AMA Style

Kondrashova SA, Latypov SK. Combined DFT Protocol for the Calculation of One-Bond 31P-31P Indirect Nuclear Spin–Spin Couplings. Molecules. 2026; 31(11):1831. https://doi.org/10.3390/molecules31111831

Chicago/Turabian Style

Kondrashova, Svetlana A., and Shamil K. Latypov. 2026. "Combined DFT Protocol for the Calculation of One-Bond 31P-31P Indirect Nuclear Spin–Spin Couplings" Molecules 31, no. 11: 1831. https://doi.org/10.3390/molecules31111831

APA Style

Kondrashova, S. A., & Latypov, S. K. (2026). Combined DFT Protocol for the Calculation of One-Bond 31P-31P Indirect Nuclear Spin–Spin Couplings. Molecules, 31(11), 1831. https://doi.org/10.3390/molecules31111831

Article Metrics

Back to TopTop