Phosphorus-carbon triple bond

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Introduction

Since the first phosphorus-carbon triple bond H-CºP was discovered in 1961 by Gier, the existence of the rare unsaturated organophosphorus compounds - in this study, the phosphaalkyne 1, the phosphaalkene 2 and the phosphacetylene 3 - has been sufficient to generate modest academic interest [5]. Though their syntheses have been characterised [4], the unsaturated molecules are unstable to oligomerisation at temperatures above -20oC and thus their storage and use are limited.

H3C-CºP

H2C=C=P-CH3

HCºC-P(H)-CH3

1

2

3

Phospha-1-propyne

Methyl ethylidene phospha-ketene

Methyl methylidyne phosphane

Table 1. Unsaturated organophosphorus molecules of interest denoted by IUPAC nomenclature.

However, parallels can be drawn with the enormously successful application of classical trivalent phosphine and acyclic 'phos' ligands such as PPh3 to homogeneous catalysis. Their catalytic operation relies on steric effects and changes in coordination-sphere electron density to steer reaction pathways, so availability of a wide range of Tolman cone angles and electron donation modes is desirable. Generally, large steric bulk used to stabilise the unsaturated phosphorus centre, for example with the use of trimethylsilyl, phenyl and imido groups [5], restrict this range and so the smaller unsaturated ligands, of which 1-3 are representative, demand further attention. Despite the low temperature restrictions and high reactivity they exhibit, they and their controlled oligomerisation products (e.g. phosphabarrelenes with Rh(I)) could enable novel kinetic control of a vast number of organic reactions intractable to conventional ligands [8,9,11,12]. They also form versatile synthons for novel unsaturated branches of alkali metal, Grignard and poor-metal functionality [13]. This crossdisciplinary approach draws on organometallic, organophosphorus and quantum mechanical theory to explore the properties of these unorthodox ligands.

Computational

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Pilot structures were created as isolated Cartesian cards for each of the molecules in Table 1 using GaussView03 and optimised via the Gaussian94 environment (keywords OPT+FREQ) using each of the computational theories: AM1 with its default basis set, and HF and B3LYP with the Pople-type STO-3G, 3-21G and 6-31G* basis sets for comparison. Absolute shielding constants were similarly obtained for these optimised structures (keyword NMR) using B3LYP and HF methods under a representative sample of basis sets. The resultant theoretical geometry (bond lengths, angles and dihedral angles for 1 only) and vibrational frequencies were then directly compared to experimental values [16, 18] to obtain estimates of correction factors and their uncertainties. For HF/6-31G*, B3LYP/6-31G* and AM1, this was repeated for the optimised structures for 2 and 3 after rotating the methyl group by 180o for comparison.

Molecule

Geometry

IR peaks

NMR peaks

Bond Lengths

Angles

Dihedrals

1H

13C

31P

1

5

4

1

6

3

2

1

2

7

5

2

1

3

2

5

2

1

Table2: Numbers of geometric and spectroscopic parameters included in the calculation of correctionfactors. †- no diffraction data available for comparison due to instability.

Equally, a suitable calculated reference shift is required to render each set of computed NMR shieldings comparable to experiment. The relevant 1H and 13C TMS shifts are given [14], though the 31P standard (85% w/w aqueous phosphoric acid) is a complex solvated system and is thus computationally inaccessible by direct quantum mechanical methods. However, at 85% w/w and higher, the concentration of conjugate bases in solution is negligible and the remaining structure of (H3PO4)2.2H2O dimers interacts weakly through a maximum of two hydrogen bonds per molecule [3]. The tetrahedral geometry and charge density of each phosphorus centre (P-O bond of 1.55 Å) is essentially similar to that averaged over all orientations in the gas phase. As a result, the NMR standard can be approximated acceptably by the isotropic 31P resonance of isolated H3PO4.

Results

Geometry

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Geometric correction factors reflect the length dependence of the interatomic potentials on the level of theory. Within error, all the methods used arrive at the experimentally measured geometry of 1 as shown in Table 2. Though a straightforward task with such a small molecule, where even simple VSEPR gives the same result, the methods have different levels of uncertainty. Note that the P lone pair precludes linear (2) and trigonal(3)P centres.

Method

HF

AM1

B3LYP

Expt.[16]

Basis

STO-3G

3-21G

6-31G*

STO-3G

3-21G

6-31G*

Lengths / Å

C-H

1.090

1.085

1.085

1.122

1.106

1.098

1.098

1.107

C-C

1.476

1.553

1.521

1.426

1.522

1.578

1.550

1.54

CºP

1.487

1.460

1.468

1.427

1.495

1.458

1.461

1.465

Angles / o

CH3

107.7

108.4

108.3

108.0

107.5

108.1

107.8

108.6

H-C-C

111.2

110.6

110.6

110.9

111.4

110.8

111.1

110.3

Dihedral / o

PºC-C

180.0

180.0

180.0

180.0

180.0

180.0

180.0

180.0

Table3: Calculated and experimental structures for molecule 1 with assignment, method of optimisation and basis set.

Whilst noting that for 2 and 3, B3LYP and 6-31G* methods will be slightly favoured by the use of B3LYP/6-31G* as a substitute for experimental data (Fig 2), the ab initio methods give increasingly and comparably precise structures, limited mostly just by basis size. Whilst AM1 only slightly underestimates the overall size of 1 by around 3%, its poor precision of up to ±4.5% suggests that its semi-empirical parameters expect greater binding, specifically in the molecule's CºP bond, than occurs naturally. Since the molecular sampling used to produce AM1 would have included significant numbers of CºC and CºN triple bonds, for example the analogous propyne (bond length 1.46 Å) and acetonitrile (1.16 Å), the CP triple bond length for AM1 can be expected to fall within this range. The ability of AM1 to give results consistent with the more accurate B3LYP/6-31G* for 2 and 3 increases as the CP bond order reduces to the more olefin-like C=P and alkane/amine-like C-P. This is also where AM1 is most successful for vibrational frequencies, noting the much larger error obtained for 1 than 2 and 3 in Fig 3.

In contrast to AM1, the quantum-mechanical rigour present in HF proves an advantage with regard to the precision in bond lengths for a compound as rare as 1., with HF/6-31G* yielding the most self-consistent scale over all three molecules. Even so, the significant static electron correlation accounted for in DFT provides further improvement, given that 1-3 are unsaturated systems with what we can expect to be correspondingly low-lying excited states. Indeed, even under STO-3G, the smallest basis, DFT predicts a much longer and more accurate CºP bond (1.522 Å) than HF (1.476 Å). B3LYP/STO-3G also returns the expected lengths for the P=C=C bonds in 2, 1.64 Å and 1.33 Å respectively [18], to within less than 0.005 Å.

The angular accuracy, such as that describing the deviation from the tetrahedral 109.5o in CH3 angles, is in general excellent across all methods. This is a result of the relative constancy of the correlation energy with respect to changes in bonding/torsional angles, where the pairing of electrons is unaffected; indeed the most accurate case was for HF/6-31G* where this is ignored save for a mean-field . Exceptions occur for the HF and B3LYP optimisation of 2 with STO-3G where the staggered (as opposed to eclipsed) methyl conformation is predicted to be the most stable. The inclusion of HF and the common basis set suggest that the ranges and flexibility of the STO-3G functions are insufficient to describe the larger steric repulsion exerted upon the methyl group by the phosphorus lone pair, relative to that from the ketene chain itself. Notably these functions also failed to predict the NMR-verified broken degeneracy of the methyl C-H bonds, with all other treatments indicating one of the three at least 0.002 Å shorter.

Infra-Red Spectra

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As stated, quantitative comparison with experiment is widely given by correction factors for vibrational frequencies [1], reflecting the combination of method and basis set. The correlation with previously reported values of the correction factors (Fig 1) is very good. It is evident from the average frequency uncertainties, which decrease strongly with a more complete basis set, that the concept of correction factors is best applied to HF theory, where the frequency errors are largely systematic in failing to account for electron correlation.

OPT + FREQ Method

HF

AM1

B3LYP

Expt.[16,18]

Basis

STO-3G

3-21G

6-31G*

STO-3G

3-21G

6-31G*

Compound 1

ν / cm-1

C-CºP sym. stretch

879.7

768.3

806.0

925.9

794.3

731.2

761.1

750.0

CH3 sym. bend

1712.8

1577.9

1548.0

1412.5

1559.5

1457.3

1423.8

1366.9

CH3 dgn. bend

1814.4

1638.6

1611.6

1362.0

1663.1

1530.4

1491.4

1437.5

C-CºP asym. stretch

1999.5

1670.6

1743.5

1861.1

1776.2

1562.4

1606.7

1558.7

CH3 sym. stretch

3537.7

3187.2

3205.7

3125.7

3266.4

3026.7

3031.9

2910.3

CH3 dgn. stretch

3708.4

3247.5

3274.5

3023.0

3418.1

3083.6

3095.6

2966.0

Compound 2

ν / cm-1

P-CH3 stretch

865.9

659.1

711.3

771.6

766.3

608.5

643.2

653

C=P stretch

939.2

796.7

844.6

950.8

839.6

744.0

781.5

869

CH2 wag

1107.2

1084.9

1040.0

1042.3

935.1

917.5

881.0

950

CH3 sym. bend

1683.4

1475.4

1477.0

1329.8

1513.7

1360.5

1341.7

1255

C=C stretch

2188.6

1967.6

1969.5

2030.9

1956.0

1823.0

1819.4

1715

CH3 asym. twist

3742.3

3289.6

3278.1

3089.1

3473.2

3146.7

3128.2

2970

CH3 asym. stretch

3747.1

3317.4

3313.7

3101.6

3476.3

3177.6

3164.5

2970

Compound 3

ν / cm-1

P-H stretch

3035.5

2361.6

2346.0

2369.9

2345.4

2222.9

2379.7

2025

CºC stretch

2635.2

2355.1

2592.1

2276.7

2726.1

2187.3

2159.0

2280

Table4: Calculated and experimental (±2%)infrared frequencies for the molecules1-3, with assignment, method of optimisation and basis set.

In AM1, correlation is partially compensated for, albeit in a holistic manner via re-parametrisation for enthalpies and ionisation potentials, rather than explicit correction terms so its variability is somewhat greater on average. Although DFT provides a much better approximation to the electron correlation than HF or AM1, (hence the B3LYP factors approaching unity), errors for the factors on 2 are much larger than AM1, since B3LYP counters the ubiquitous HF overestimates sufficiently at low frequency, but not at high frequency. The overall result is that despite being much more accurate, these particular B3LYP spectral peaks fall on either side of the true values for 2 and so a universal conversion factor is poorly defined compared to the case of 1 or 3.

Given that the average frequency correction factors are remarkably insensitive to the methyl conformation in 2 and 3 (Fig.4), the overestimated frequencies for the STO-3G methods (Fig. 3) cannot be attributed to the rotational preference of the methyl groups, but are instead typical of this minimal basis for all molecules (with the smallest literature factor of 0.83 [14]). The small difference in stability of staggered and eclipsed forms of 2 and 3 reflects the free rotation about the P-CH3 axis, with a monotonically increasing rms error of 70-150 cm-1 toward higher frequencies (though lower frequencies have larger percentage error).

However the normal modes associated with individual functional groups can be affected by the methyl rotation. In 2, the P-CH3 stretch is significantly worsened, confirming the prediction of a predominantly eclipsed structure as the most stable. The overall picture is more complex since the multiple bond stretch predictions actually benefit from the rotation, together with a reduction in error for P=C stretch, whilst the P-H stretch and methyl bending descriptions mildly deteriorate.

Though, like many of the normal modes considered, the P-H and CºC fall closely together for 3, (experimentally more separate at 2025 cm-1 and 2280 cm-1 [18]), the gap between these two peaks is relatively constant (<5 cm-1 difference) under rotation for most treatments. Still, for AM1 the gap increases by 44 cm-1 from the staggered (optimum) conformation to the eclipsed one. The relationship between C-P bond order and frequency depends on the relative fragment masses as well as the ionic bonding contribution, plus the coupling in normal modes (e.g. the similar C=C and C=P stretches in 2) [6]. It is seen that the increased gap between the CºC and P-H frequencies results from AM1's neglect of two factors: the fact that the analogy between CP and CC bonding weakens as the bond order decreases, as well as the tendency of sp3 phosphorus to be more basic than sp3 carbon.

In terms of IR spectral intensities, none of the methods calculated a spectral profile entirely consistent with the experimental assignments for 1. B3LYP and HF fail to assign any notable intensity to the P=C=C symmetric stretch in 1. Whilst AM1 does, with 17% intensity relative to its largest peak, it omits the comparably large CH3 degenerate bends (18% rel. intensity for HF and B3LYP). HF and B3LYP reliably predict the most evident peaks for 2, but the P=C stretch and CH3 symmetric bend are heavily underestimated (appearing at less than 10% relative intensity), despite being sustained in the experimental IR. For both methods, methyl rotation only mildly affected the intensity of the related CH3 asymmetric stretch.

AM1 predicts all experimental peaks for 2 with adequate relative intensity; notably methyl rotation to the unstable conformation favourably increases the absorption magnitude of the P-CH3 and C=C stretches by very large factors of 3 and 5 (see Fig 5) as well as those of the CH3 modes. For 3, AM1 only shows the P-H bond stretch when it is eclipsed with the rotated methyl group. This appears at 21% intensity, roughly equal to the CºC stretch at 24%. HF gives the P-H stretch at a strikingly large 73% relative intensity in contrast with the barely detectable CºC stretch at 7%. This is exaggerated further for B3LYP with 57% P-H and 2% C=C. Again, for the ab initio methods there is little effect on intensity from methyl rotations at frequencies above 1100 cm-1.

NMR Shifts

The calculated 31P NMR values appropriate to each level of theory are shown in Table 5. Since NMR chemical shifts use additive references rather than absolute ones (i.e. TMS and H3PO4 are merely accessible standards), it is more informative to represent the accuracy of each calculation method by a mean error (i.e. shift to high/low field) and its standard deviations, instead of correction factors.

Theoretical NMR reference shift / ppm

OPT method

HF/

STO3G

HF/

3-21G

HF/

6-31G*

AM1

B3LYP/

6-31G*

NMR method

HF/

STO-3G

HF/

3-21G

HF/

6-31G*

HF/

STO3G

HF/

3-21G

HF/

6-31G*

B3LYP/

6-31G*

B3LYP/

6-31G*

31P H3PO4

503.89

468.287

429.617

510.71

417.05

373.94

328.354

378.476

13C TMS [14]

249.4

214.67

201.73

245.65

211.52

198.1

188.06

189.75

1H TMS [14]

33.47

33.84

32.9

32.87

33.11

32.19

31.79

32.18

Table 5: Reference NMR shielding constants including(31P)H3PO4calculated by combining different computational methods.

Experimental NMR chemical shift / ppm

31P

13C

1H

1[17]

P

-60

CH3

170.8

CH3

1.49

CP

15.6

2[18]

P

42

C=P

250.4

P-C(H)H2

5.46

H2C

95.2

P-C(H)H2

1.49

CH3

10.4

H2C=C

1.35

3[18]

P

-115

HCºCP

80.8

P-H

3.96

CH3

4.6

CºC-H

2.71

HCºCP

92

CH3

1.35

Table 6: Summary of experimental NMR chemical shifts for 1-3 relative to H3PO4 and TMS,and the corresponding nuclear assignments.

For large systems such as C47H51NO14, HF/6-31G* has been shown to produce a 13C chemical shift RMS error of as low as 6.4 ppm [19]. In this study, combined optimisation and NMR HF/6-31G* and B3LYP/6-31G* are the two most successful methods over all the chemical shifts (Fig 6) despite much smaller molecules. The exception of the overestimated HF/6-31G* 31P shift of 1is corrected by use of an AM1 optimisation, though this is not a better technique in general. Use of the less geometrically accurate AM1 optimisation instead of the ab-initio structure appears to move indiscriminately all 31P resonances to high field, by a inordinate 25-75 ppm. As a result of the poor AM1 geometry, this also fails to yield the correct 13C NMR shifts, though this appears less acute for 2 and 3 where there are smaller partial charges on P. For proton NMR the AM1 displacement to lower shifts almost disappears, since the changes in the hydrogen environments average out. However these non-equivalent environments cause the deviation in error to increase; the broken degeneracy of methyl C-H bonds means that 2 and 3 have increasingly large 1H spread, which is not significantly ameliorated by methyl rotation

Despite the well-known tendency of DFT calculations to overestimate the paramagnetic contribution to NMR shifts, in this case the de-shielding for B3LYP/6-31G* is relatively minor, with less than 5 ppm mean error for 13C, and 0.5 ppm for 1H, over all molecules. The similar large errors and spread of the data for STO-3G (particularly 1) show that even moderately accurate structures used as input for a small basis NMR will be subject to a significant error on the NMR output. Judging from the methods using AM1 optimisations, it can be seen conversely that the effect of a larger NMR basis set is to dramatically decrease both error and spread, above STO-3G for 1H and 13C and above 3-21G for 31P.

Methyl rotation of 2 causes a minor shift to low field for 31P and significant worsening of error for 13C and 1H values, whereas for 3 the results are comparable to or slightly more accurate than the most stable conformer. On rotation of 3, although the accuracy of 13C NMR shifts slightly decreased by about -0.5 ppm for the larger basis NMR methods, the corresponding RMS error clearly decreased by up to 3 ppm.

Discussion

The differences in electron density and bonding, and the related spectroscopic alterations and contrasting reactivity of 2 and 3 are perhaps surprising, given that theyare isomers. The σ-component of CP bonding is polar, but the π-parts are relatively apolar, due to the relatively similar electronegativities of carbon (2.1-2.2) and phosphorus (2.4-2.5). On formation of a second π-bond, the lone pair of 1 is less reactive than that of 2, having been held even closer to the phosphorus centre (as shown by the larger improvement of the STO-3G frequency description of the adjacent bonds relative to other basis sets) and its PºC bond is very short. Its π orbital and phosphorus lone pair are clearly separated in ionisation energy [5], and few PºC complexes are known with η1 PŠM donation [10]. For P=C compounds the η1 and η2 complexes are more similar in energy, and equilibria may occur [5]. In both cases a 31P NMR shift to high field and longer CP bond upon π-complexation to the η2 form could be expected due to σ-donation and π*-acceptance. This correlates well with the observation that chemical shifts decrease linearly with the electron population in the P(3s) orbital [6], as overestimated by the AM1 optimised geometry. As well as chemical shifts in this work, B3LYP is known to be particularly effective at the description of ionisation potentials. This is in accordance with the low error (<1eV) encountered for quasi-degenerate transition metal systems in previous studies using a partial LANL2DZ basis [7].

In this manner, complexes of a transition metal, such as Rh(I), of 1-3 in η1 and η2 forms could be optimised using a mix (such as Gaussian keyword GEN PSEUDO=READ) of the necessarily larger basis set LANL2DZ for Rh and 6-31G* for C, P, H. The corresponding ligand optimisation would act as input, whilst varying the only the bond angles on the phosphorus centre to accommodate the metal atom. As transition metals lie outside the parametrisation of AM1, this would be obtained for B3LYP and HF only. Spectroscopic calculations based on these coordinated ligands would form an effective comparison with the present study into the free ligands.

It is clear that neglect of perturbations, such as intermolecular interactions, may give rise to systematic theoretical errors. Moreover, the inaccuracy in 31P chemical shifts from the use of ideal gas H3PO4, instead of aqueous solution phase, as a reference is estimated to be 2-5 ppm by comparison with experimental conditions [15]. However this is less than the difference in spread of the corresponding 31P experimental and calculated shieldings, >8 ppm, for the three molecules 1-3 and thus not the predominant source of 31P NMR error in this study. Alternatively, a better-characterised secondary reference such as H-CºP could have been specified, though this would have superimposed any inaccuracy of the triple bond description (as opposed to that of a more common phosphate group) onto all other compounds treated with the same method [6].

Notably, the small data sets (Table 2) strongly limit the statistical precision of the results - this also restricts the generality of the trends that can be drawn to only those organophosphorus compounds very similar in their chemical functionality to 1-3. However, it can be said that the trends are likely to extend to larger such compounds, which are perhaps more stable (for example longer-chain or conjugated species) and thus more widely useful, in spite of their poorer computational accessibility.

Conclusions

Of all the methods used, the standard B3LYP/6-31G* clearly gives the most accurate geometric and spectroscopic data, reflecting its small exchange correlation errors and use of a moderately large basis set. In a similar manner to B3LYP, Hartree-Fock theory was also found to have satisfactory correlation for all geometric and spectroscopic experimental values, on the condition that a large basis was used. It is recommended for species where self-interaction may become problematic for density functional methods. Despite 1-3 only incorporating main block elements, use of AM1, which was developed with more common organic molecules, showed poor, inconsistent results. Though AM1 geometric optimisation appeared to provide occasional correction to NMR chemical shifts, the only use of AM1 that can be consistently encouraged for unsaturated organophosphorus compounds is to calculate the relative IR activities of normal modes, as this could aid future interpretation of experimental IR spectra. Rotation of methyl dihedral angles by 180o from the most stable conformers (staggered in 2, eclipsed for 3) showed mixed alterations to the spectroscopic calculations, notably improvement of AM1 IR spectral profiles for 2 and more accurate 13C NMR shifts in 3.

Further topics for study include the relationship of the above trivalent compounds, particularly 2, to their pentavalent equivalents such as the famous Wittig reagents which have become essential to olefin chemistry [12]. Oligomerisation studies from multiple CP and PP bonding will be necessary to probe the range of possible catalysts. This study into the geometric and spectroscopic properties of 1-3 should offer some footing and predictive power to future research into the unsaturated organophosphorus compounds, and clear direction for computational analysis of their transition metal complexes has been given.

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