Theoretical study of the properties of phosphonate

Journal of Molecular Structure (Theochem) 673 (2004) 79–86 www.elsevier.com/locate/theochem

Theoretical study of the properties of phosphonate T. Leyssens, D. Peeters* Universite´ catholique de Louvain, Laboratoire de Chimie Quantique, Baˆtiment Lavoisier, place Louis Pasteur 1, B-1348 Louvain-la-Neuve, Belgium Received 9 October 2003; revised 29 November 2003; accepted 1 December 2003

Abstract An ab initio study of the properties of the phosphonate functional group is presented in this paper. Methods like HF, DFT, MP2(4), QCISD are used to estimate structural and energetic behaviour and obtain charge distribution. The phosphonate radical and its positive and negative ion are considered as well as neutral and negatively charged organic radicals, in order to give a comparison between these situations. By the use of different properties, the influence of the phosphonate group on organic radicals is discussed and clarified. q 2004 Elsevier B.V. All rights reserved. Keywords: Phosphonic radical and ions; Phosphonate substituent; Functional properties; Substituent effects

1. Introduction Phosphorus compounds are important species in nowadays chemistry. They intervene in many chemical processes, namely in medicinal chemistry where phosphonate appears to be a bioisoster of carboxylic acids. Its importance led recently to the publication of a review compiling many interesting reactions [1]. Despite their importance, only some properties of such chemical functions are known. Thanks to significant studies of Denmark [2] and Anders [3], the effect of a phosphonic function on the stabilization of a negative charge in a is well documented. In a previous paper, [4] we studied the influence of the phosphonate substituent on the well-known Diels– Alder reaction by theoretical means. The main conclusion obtained from our analysis is that a very constant internal structure of the phosphonate function is observed the latter structure does not interfere significantly with the neutral neighbour groups. It is the aim of this paper to bring some further insight into the properties of the phosphonate group. The first question remains a methodological question as a basis set extension, or the introduction of electron correlation might sensibly modify the wave-function and induce a modification of the electron distribution, its properties, its geometry and further stabilize or destabilize the energy of the fragment. A second * Corresponding author. Tel.: þ 32-10-47-28-19; fax: þ 32-10-47-27-07. E-mail address: [email protected] (D. Peeters). 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2003.12.001

question consists in defining the best indices revealing the chemical nature and properties of the functional group. In order to get a better insight in the structure and properties of the phosphonate group, we intend to look first at the phosphonate radical and its ions. This will bring information on extreme situations encountered by the isolated functional group. In a second step, the functional group will be linked to various organic substrates such as CH3, CH2, C2H5, C4H5, and C6H5 in order to compare the structure and properties of the phosphonate group in current organic molecules to such extreme situations. Placing the various properties on the scale defined by the extremes and estimating the influence of each limiting structure may then quantify the substituent’s effects.

2. Methodological approach To avoid the problem of reliability of the theoretical approach, the results obtained are presented at various levels of sophistication regarding the chosen basis sets as well as the used methodology. All selected basis sets start at double zeta valence split and polarized level [6-31G(d,p)]. Diffuse and triple zeta functions were further added to complete the expansion [6-31þ þ G(d,p), 6-311G(d,p), 6-311þ þ G(d,p)]. The calculations were performed at Hartree-Fock Roothaan level as well as with the Density Functional Theory within the Becke’s three parameter functional (B3LYP) [5] methods

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using the GAUSSIAN series of programs [6]. Moeller Plesset (MP2) and quadratic CI (QCISD) computations were further used in order to check the sensitivity of our calculations on the nature of the two electron distribution. As radicals are present, some care has been taken to the quality of the wavefunctions. Firstly, the S2 operator’s eigenvalue was checked. All obtained values are close to 0.75, the expected value, and lie within 0.01. We may thus admit that this contamination is weak enough to be neglected. Further, the triple’s correction may be important with such species. At QCISD optimised level, single point calculations were performed in order to introduce such QCISD(T) corrections. The DFT approach should already mimic the effect of some electron correlation and the convergence of the results obtained by the various methods should comfort us in our interpretation. A PO3H2 group, whose hydrogen atoms are positioned in an orientation avoiding external hydrogen bonds, models the phosphonate. For all studied compounds, such conformation of the group was maintained in order to obtain constancy within the substituent and to allow for a better comparison of the observed effects. A full optimisation of each species, at any level of methodology, has always been performed and the various conformations of the phosphonate group explored. The energy properties of the substituents were principally studied through the use of isodesmic reactions [7]. This allows an easy comparison between stabilisation/ destabilisation effects due to structural or electronic factors. The electronic structures have been studied by an NAO, NBO analysis [8] and, when pertinent, by the Boys localisation method [9]. The localisation procedure (MLO) has the advantage of describing the electronic structure in a Lewis-like manner and allows a spatial partitioning of the electron density in localized fragments. This partitioning leads to defining local properties, such as group dipole moments for example. The conventional Mulliken population analysis was not retained as its charges are known to be unreliable, especially when diffuse and polarized basis sets are used.

3. Analysis of the properties of the isolated phosphonate group and its ions Before discussing the results a general remark should be made first. As four different basis sets were used with four different methodologies, only the most pertinent results will be presented and discussed here after. Nevertheless unpublished data may be obtained on simple request to the authors. This restriction may be justified by the fact that all obtained results show similar tendencies in most computations. The introduction of diffuse functions in the basis sets modifies sensibly the results obtained, but the extension to a triple zeta basis leaves the computed properties almost unchanged. In the same order of ideas, even though

the energy changes, the structural data as well as the charge distribution are not really modified when comparing the DFT, MP2 and QCISD results. Hartree – Fock gives usually more dispersed results, which will not be further commented in this paper. 3.1. Structural data As an example of the above remarks, the structural results show that the geometries obtained are usually very close to each other for DFT, MP2 and QCISD computations. ˚ Bonds are slightly shorter for Hartree – Fock results (0.03 A in the mean). The results obtained within a method are very consistent whatever basis set being used. At triple zeta level, a very small shortening of the bonds is nevertheless ˚ for HF and DFT; 0.012 A ˚ for MP2 and observed (0.007 A QCISD). This effect appears for ions as well as for the radical. Table 1 reports the structural data for the radical and its ions obtained at QCISD level for a 6-311þ þ G(d,p) basis set, which should be the most accurate. As shown in the table, both PO bond lengths increase regularly as the ˚ for PO and 0.090 for number of electrons increases (0.045 A PO(H) in the mean), while the structure becomes pyramidal as the charge becomes negative. As shown by the valence and dihedral angles, the cation is fully planar while the anion turns to a very sharp geometry. 3.2. Energy and its properties Starting from these structural data, the vertical and adiabatic ionisation potential as well as the corresponding electron affinities may be obtained. Energy results are given in Table 2 for the optimised structures as well as for the ions frozen in the radical structures. The latter furnish the wellknown vertical properties, computed at the radical fixed geometries, and permit to deduce the Mulliken electronegativities from the conventional relation:

xM ¼

IE þ EA ðeV unitsÞ 2

ð1Þ

One may further rescale these results [10] to Pauling’s electronegativity by using relation (2)
 IE þ EA 2 0:615 ð2Þ xM ¼ 0:336 2 Table 1 ˚ , angles 8) Structure of the phosphonate radical and ions (distances A QCISD 6-311þþ G(d,p)

(PO3H2)þ

(PO3H2)8

(PO3H2)2

PO PO(H) OH OPO(H) POH OPO-O0 OPO-H

1.440 1.532 0.972 128.62 119.37 180.00 180.00

1.484 1.618 0.962 117.19 111.12 114.40 165.81

1.534 1.719 0.965 102.49 105.23 101.92 86.24

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Table 2 Energy of phosphonate and its ions at optimised and frozen (f) geometry (in hartree) Method

Basis

Cation

Cation (f)

Radical

Anion (f)

Anion

DFT

6-31þþ G(d,p) 6-311þþ G(d,p) 6-31þþ G(d,p) 6-311þþ G(d,p) 6-31þþ G(d,p) 6-311þþ G(d,p)

2567.9525 2568.0385 2566.8873 2567.0146 2566.8957 2567.0184

2567.9014 2567.9869 2566.8392 2566.9661 2566.8448 2566.9670

2568.2611 2568.3481 2567.1770 2567.3036 2567.1910 2567.3134

2568.3215 2568.4097 2567.2220 2567.3485 2567.2374 2567.3595

2568.3573 2568.4458 2567.2637 2567.3898 2567.2778 2567.3998

MP2 QCISD

Following Jaffe´’s approach, the fit of these vertical energies by a quadratic relation: E ¼ aq þ bq 2

The relaxation energies obtained for the ions are appreciable as the structural reorganisation decreases the energy by about 1.4 eV for the cation and 1.0 eV for the anion.

ð3Þ

allows also to obtain the hardness ðhÞ of the species by evaluating the b coefficient. ! 1 ›2 E IE 2 EA ¼b ¼ h¼ ðeV unitsÞ ð4Þ 2 ›q2 2

3.3. The charge distribution The charge reorganisations appearing during the ionisation processes are given in Table 4. A Natural Analysis is reported at DFT and MP2 level for 6-31þ þ G(d,p) computations. Both methods give coherent results. They show for the radical a fairly positive phosphorus atom whose electrons are shifted towards the oxygen atoms. Each oxygen carries a 2 1 charge, but the presence of hydrogen atoms reduces this charge on the hydroxyl groups to 2 0.5. The ionisation processes may be decomposed in a vertical ionisation followed by the relaxation process. Most of the charge transfer affects the phosphorus atom but also the singly linked oxygen atom. The loss of an electron during the vertical ionisation affects equally both atoms for 63% of the charge. The two remaining oxygen atoms carry about the 30% of the resulting charge. The relaxation of the geometry further modifies the charge distribution as the lost charge increases on the phosphorus atom redirecting the electrons to the other atoms that tend to retrieve their initial charge. The addition of an electron essentially affects the phosphorus atom while the OH functions are almost unaffected. In this case, the geometry relaxation has no further effect on the charge distribution.

As charged species are considered in this discussion, the presence of diffuse orbitals in the basis sets will sensibly lower the energy. This modifies the energy gap between the radical and its ions and increases the electronegativity but decreases the hardness of the species. Such tendency is marked in Table 3 which reports the results for the various methods and basis sets. One should notice here that the 6-31þ þ G(d,p) values are usually very close to 6311þ þ G(d,p) results, confirming the prominence of diffuse orbitals over the triple zeta extension. At this level, our recommended values will be QCISD/ 6-311þ þ G(d,p) results including the triple’s correction, which give a relatively low electronegativity combined to a fairly soft group. Single point MP4/6-311þ þ G(d,p) computations give an electronegativity of 1.53 with an unchanged hardness of 3.91 confirming these recommended values. In comparison, the electronegativity/ hardness of the isolated hydrogen and phosphorus atom are respectively 2.14/6.0 and 1.49/5.06 using QCISD/6-31þ þ G(d,p).

Table 3 Pauling’s electronegativity and hardness of phosphonate with various methodologies (Relation (3)) 6-31þ þG(d,p)

6-31G(d,p)

HF DFT MP2 QCISD QCISD(T) MP4a a

6-311þ þ G(d,p)

6-311G(d,p)

a

b

a

b

a

b

a

b

1.30 1.50 1.32 1.38 1.34 1.30

4.99 4.38 4.31 4.39 4.32 4.26

1.44 1.71 1.54 1.59 1.56 1.53

4.76 4.07 3.98 4.08 4,00 3.92

1.35 1.58 1.37 1.43 1.39 1.35

4.96 4.32 4.26 4.35 4.27 4.20

1.45 1.73 1.54 1.59 1.56 1.53

4.76 4.08 3.98 4.08 3.99 3.91

The results are obtained with MP4 (SDTQ) single point calculations using MP2 geometry.

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Table 4 Natural Atomic Charges at 6-31þ þG(d,p) level for PO3H2

DFT P O O( –H) H MP 2 P O O( –H) H

Cation

Cation (f)

Radical

Anion (f)

Anion

2.49 20.83 20.93 0.61 2.46 20.79 20.93 0.60

2.28 20.72 20.85 0.58 2.28 20.70 20.86 0.57

1.93 21.00 21.00 0.53 1.97 21.02 21.01 0.53

1.42 21.20 21.09 0.48 1.40 21.19 21.09 0.49

1.46 21.22 21.09 0.47 1.45 21.22 21.09 0.47

This phenomenon may also be analysed by describing the electronic structure by means of localized orbitals. The electron reorganisation will now be deduced from the distribution of the centroı¨ds of charges obtained from a Boys localisation procedure. The valence centroı¨ds are presented in Fig. 1 for the ions and radical. The patterns obtained for the ions show clearly that the charge is associated with the phosphorus lone pair, which disappears for the cation and is clearly located on the phosphorus atom for the anion. This behaviour will further control the centroı¨ds distribution along the oxygen atoms. The most conventional Lewis-like electronic structure is obtained for the negative ion. Four centroı¨ds surround the P atom describing three single bonds and a lone pair. The singly linked oxygen forms one single bond completed by three lone pairs leading to a strong ionic situation confirmed by the 2 1.2 NAO charge on this oxygen. The cation loses the lone pair located on the P atom enhancing its positive charge. As a consequence, this local electronic deficiency induces a shift from the lone pairs, which move towards the phosphorus atom, (leaving finally one single lone pair well

defined on the singly linked oxygen). The same trends appear for the OH oxygens that shift a lone pair into the bond region. This distribution is represented in a schematic way in Fig. 1. While a conventional Lewis structure is obtained for the anion, in the cation the increase of positive charge carried by the P atom, pulls the lone pairs into the PO bond, increasing their bond strength. The drastic reduction of the electron distribution by the use of centroı¨ds brings nevertheless an interestingly simple picture as the PO bond may be represented in the anion by the conventional single bond/Triple lone pair of a semi polar situation, but at the opposite in the limiting situation of the cation a triple bond/ single lone pair fits as well. This observation is of course coherent with the bond length variation presented in Table 1. Concerning the structure obtained for the radical, one observes here the usual description where ðn þ 1Þ a centroı¨ds mimic the anion electron pair distribution, while the n b centroı¨ds distribute such as the cation’s centroı¨ds. This qualitative description shows that in the simplified representation of the tetrahedral octet surrounding an atom, when the ionic character is high, this tetrahedron responds easily to the polarisation by neighbouring atoms and may lead to a single, double or triple bond description as mentioned previously by D.G. Gilheany [11].

4. Phosphonate as substituent in current organic molecules After studying the isolated phosphonate and its ions, we shall now turn to discussing the behaviour of the phosphonate group as a substituent linked to various types of carbon atoms. The chosen radicals belong to important families of chemical compounds:

Fig. 1. Centroı¨ds of the phosponate radical and its ions. Centroids in black (for the radical: b in white).

T. Leyssens, D. Peeters / Journal of Molecular Structure (Theochem) 673 (2004) 79–86

Alkyl radicals CH3 and C2H5 describe situations where the inductive effect prevails. The C2H3 vinyl radical will bring conjugation with p electrons into the discussion. The butadienyl 1 and 2 radicals may bring information about the extension of the conjugation over four p electrons. A CH2 radical allows discussing the well-known stabilisation for anions when one compares the neutral species to a negatively charged one. Finally the phenyl radical introduces the aromatic effects into the discussion. The different effects the substituent may induce, will be approached mainly by analysing the structural, electronic and energetic results obtained using the previously described methodology. 4.1. The structural data The PO bond lengths are given in Table 5 for the studied compounds with various methodologies and basis sets. As can be seen, the obtained structural data show a remarkable ˚ , while both constancy. The PO bond remains close to 1.49 A ˚ even though in conjugated single bonds are close to 1.63 A ˚ ). systems, one of those bonds shortens a little bit (1.62 A This shows the substituent is scarcely dependent on the nature of the linked carbon atom. Comparing these data to the corresponding value of the isolated group, they are close to the neutral radical, although a little bit shorter [12], suggesting the group becomes slightly positive, i.e. electron donating. In the case of a CH2 substituted anion, the bond lengths obtained are 1.535 and 1.679 (to be compared to 1.55 and 1.74 for the phosphonate anion) showing

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the influence of the negative charge that partially delocalises over the phosphonate functional group. 4.2. The energetic behaviour The best way to discuss the influence of a substituent on a carbon chain rests on a comparison with thermoneutral reactions. Ideally isodesmic reactions are thermoneutral. Stabilising or destabilising effects will justify the deviation from this neutrality. In this work we considered a set of such reactions whose results are given in Table 6 using the 6-31þ þ G(d,p) basis set, that includes the necessary diffuse orbitals. Some of these reactions are redundant as they may be deduced from others by the use of thermochemical cycles. They are nevertheless given for sake of clarity, presenting in a simple way the various effects, which could appear by shifting the substituent from one radical onto another. Looking at the single-point MP4 results (obtained using the MP2 geometry), which should be the most reliable, one notices that the overall effects are small. Reaction ‘a’ brings some stabilisation by extending an inductive effect from CH3 to C2H5 but reaction ‘b’ retrieves the same order of magnitude showing that no mesomeric effect appears when the phosphonate group is put in a conjugative position close to the p electrons of the vinyl radical. When the function is linked to a phenyl radical (reaction c), a small extra stabilisation occurs bringing a global stabilisation of 3.0 kcal/mol. A comparable stabilisation is obtained when the phosphonate is linked to a butadiene at position 1 and 2. This shows that the direct interaction between phosphonate and the double bond (vinyl) is almost non-existent, but extra stabilisation appears when phosphonate is brought in presence of delocalisable p electrons (phenyl, butadienyl). This suggest, as will be

Table 5 ˚) Some structural data of the phosphonate substituent (in A

PCH3 PCH2 PC2H3

PC2H5 PC6H5

PO PO(H) PO PO(H) PO PO(H) PO PO(H) PO PO(H)

PC4H51

PO PO(H)

PC4 H52

PO PO(H)

DFT 6-31þ þG(d,p)

MP 6-31þ þG(d,p)

DFT 6-31G(d,p)

MP 6-31G(d,p)

1.490 1.631 1.493 1.626 1.488 1.620 1.636 1.491 1.632 1.488 1.621 1.637 1.489 1.620 1.638 1.488 1.619 1.638

1.495 1.631 1.496 1.628 1.493 1.620 1.637 1.496 1.632 1.493 1.621 1.638 1.493 1.620 1.639 1.493 1.620 1.639

1.486 1.628 1.490 1.624 1.485 1.619 1.633 1.488 1.629 1.485 1.620 1.634 1.486 1.619 1.635 1.485 1.618 1.635

1.489 1.628 1.491 1.625 1.488 1.618 1.633 1.491 1.629 1.488 1.619 1.634 1.488 1.619 1.634 1.488 1.618 1.635

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Table 6 Isodesmic reaction energies of phosphonate substituted molecules (kcal/mol) [MP4, MP2 and DFT/6-31þ þ G(d,p)] DE Isodesmic Reaction (a) H2O3PCH3 þ C2H6 ! H2O3PC2H5 þ CH4 (b) H2O3PCH3 þ C2H4 ! H2O3PC2H3 þ CH4 (c) H2O3PCH3 þ C6H6 ! H2O3PC6H5 þ CH4 (d) H2O3PCH3 þ C4H6 ! H2O3PC4H5 (1) þ CH4 (e) H2O3PCH3 þ C4H6 ! H2O3PC4H5 (2) þ CH4 (f) H2O3PC2H5 þ C2H4 ! H2O3PC2H3 þ C2H6 (g) H2O3PC2H5 þ C6H6 ! H2O3PC6H5 þ C2H6 (h) H2O3PC2H5 þ C4H6 ! H2O3PC4H5(1) þ C2H6 (i) H2O3PC2H5 þ C4H6 ! H2O3PC4H5(2) þ C2H6

MP4 21.65 21.29 22.99 23.02 22.75 0.36 21.34 21.37 21.10

MP2 21.60 21.25 22.70 22.68 22.43 0.35 21.10 21.08 20.84

DFT 20.33 20.64 0.56 21.73 0.57 0.31 20.90 21.40 0.90

Table 7 Isodesmic reaction energies of phosphonate on carbon centered anions (kcal/mol) [DFT, MP2 and MP4 /6-31þþ G(d,p)] DE Isodesmic reaction 2 (1) H2O3PCH3 þ CH2 3 ! H2O3PCH2 þ CH4 2 (2) H2O3PCH28 þ CH3 ! H2O3PCH2 2 þ CH38 (3) H2O3PCH3 þ CH38 ! H2O3PCH28 þ CH4 2 (4) H2O3PC2H5 þ C2H2 5 ! H2O3PC2H4 þ C2H6 2 (5) H2O3PC2H48 þ C2H2 5 ! H2O3PC2H4 þ C2H58 (6) H2O3PC2H5 þ C2H58 ! H2O3PC2H48 þ C2H6

confirmed below by the charge distribution analysis, that phosphonate is able to polarize conjugated p electrons and that this polarisation induces the observed extra-stabilisation. Considering now the effect of phosphonate on a CH3 radical or anion, Table 7 presents the results of isodesmic reactions obtained in the same context as above. Once more, one arrives at the conclusion that no significant effect appears when the substituent shifts on an alkyl radical (reaction 3 and 6). On the contrary, reactions 1 and 2 show the impressive stabilisation obtained when a negative charge is introduced on the a position. 4.3. The charge distribution The charge distribution obtained by a Natural Population Analysis is given in Table 8 for the atoms of the phosphonate group. These charges were obtained with the diffuse basis set at DFT level. For the OH part a single entry is given as the charges of both oxygen and hydrogen atoms are the same up to the second decimal. The results show a remarkable constancy of oxygen and hydrogen charges inside the functional group. This clearly shows that these atoms are not affected by the nature of the linked carbon skeleton. Even the phosphorus atom, which is directly connected to the carbon, does not change significantly. If mesomeric effects were present, the charges would be affected by the hybridisation of the carbon atom. As this is not the case, one may conclude that no such effect appears. A comparison with Table 4 shows that the oxygen and hydrogen atoms carry charges close to those of the neutral

DFT 242.99 240.82 22.16 246.45 243.20 23.25

MP2 244.83 244.94 0.11 247.44 246.29 21.14

MP4 244.67 244.21 20.46 247.16 245.50 21.66

radical. Only the phosphorus atom presents a larger positive charge that compares in all cases to the isolated cation. This clearly shows that the phosphorus atom is the only electron releasing atom in the group and that it carries the whole of the transferred charge. This will be associated to an inductive effect where the linked carbon withdraws the electronic charge in its s(P– C) bond as shown by the last line of Table 8. It has been observed that the charges obtained are almost independent of the methodology used. This is shown in Table 9 by comparing MP2 and DFT results. To complete our information, the last column of Table 9 presents the charge carried by the corresponding hydrogen atom of the related hydrocarbon. It appears from this point of view that the phosphonate group behaves essentially like an hydrogen atom, even though it is much more voluminous. Admitting the relative constancy of the phosphonate group, we may nevertheless consider now the polarisation it induces upon a carbon skeleton. Fig. 2 presents the NPA Table 8 Natural Charges of the phosphonate atoms in reference molecules [DFT/ 631þþ G(d,p)]

P O O(H) H Total a

PCH2

PCH3

PC2H5

PC2H3

PC6H5a

C4H51

C4H52

2.30 21.08 21.03 0.54 0.24

2.37 21.10 21.04 0.54 0.27

2.38 21.10 21.04 0.53 0.27

2.36 21.09 21.03 0.53 0.28

2.40 21.08 21.03 0.53 0.32

2.36 21.09 21.03 0.53 0.28

2.38 21.09 21.03 0.54 0.30

Using a 6-31G(d,p) basis set with a 6-31þ þG(d,p) geometry.

T. Leyssens, D. Peeters / Journal of Molecular Structure (Theochem) 673 (2004) 79–86 Table 9 Natural Charges of the phosphonate group with various methods [631þ þG(d,p)]

CH2 CH3 C2H5 C2H3 C4H51 C4H52

MP2

DFT

H(DFT)

0.24 0.28 0.29 0.29 0.29 0.32

0.24 0.27 0.27 0.28 0.28 0.30

0.23 0.27 0.27 0.26 0.26 0.24

charges of the carbon atoms of the substituted and original reference molecules. The polarisation of the ethyl radical shows that the increased charge is due to a polarisation of the a carbon’s s C –H and C –C bonds. This carbon, becoming more negative, tends to the stabilizing situation presented by a CH2 2 anion. The b carbon is in this case almost unaffected. For unsaturated species, the charges clearly show the polarisation of the carbons as the a carbon enhances its charge while that of the b carbon decreases when we compare it to the reference situation. Comparing the ethyl and vinyl radical, shows that both vinylic carbon atoms have an even more pronounced polarisation, indicating the deformation of the p bond, whose easily polarisable electrons are moved towards the a carbon. The same trends appear in the dienes with a comparable polarisation of the substituted double bond. The same polarisation, compared to the reference molecule, is observed for the diene 1 where a slight polarisation is observed on the second double bond. When substitution is at position 2, the same behaviour as in the ethylene case is encountered, but the second double bond seems unaffected by the substitution. To explain this polarisation, one may evaluate the group dipole moment by computing local properties through the use of localized orbitals. Such orbitals can only be obtained if their occupation numbers are integers. This is of course the case in a mono determinantal wave function such as Hartree – Fock orbitals, but also in DFT theory, using the Kohn – Sham orbitals. Table 10 reproduces the dipole moments obtained with the DFT orbitals for the molecules in the first column

Fig. 2. Charge distribution on the carbon atoms of the substituted and reference molecules [DFT/ 6-31þ þG(d,p)].

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Table 10 Dipole moment of the molecule and the phosphonate substituent [Debye Units, DFT/B3LYP 6-31þ þG(d,p)]

PO3H28 PO3H2 – C2H5 PO3H2 – C2H3 PO3H2 – C4H5 1 PO3H2 – C4H5 2

Molecule

PO3H2

1.40 1.79 2.22 1.88

1.20 2.37 2.60 2.62 2.52

and for the substituent PO3H2 in the second. The PO3H2 radical is given for comparison in the first row of the table. Results show that the dipole moment is fairly increased. This is essentially due to the increase of the positive charge on the phosphorus atom. This positive charge modifies the dipole moment of the substituent, which interacts with the s and even more readily the polarisable p electrons of the carbon skeleton inducing the observed changes. 5. Conclusion In this paper we have studied the structure of the phosphonate group and analysed its effect on various carbon skeletons. Although study is going on, the behaviour of phosphonate on carbanions merits an extensive complementary study, some characteristics of this phosphorus-containing functional group are introduced in this paper. The importance of diffuse functions in the basis-set and of correlation is clearly observed, which is obviously related to the fact that this third period functional group contains highly polar bonds. It is therefore preferable to use at least MP2 calculations on this type of functional groups, even though the size of molecular systems grows quickly. The structural changes for the isolated phosphonate group, going from the positive ion, to the radical, to the negative ion, follow VSEPR rules for a highly ionic entity, as indicated by its charge distribution. Once placed on an organic radical, the phosphonate group presents a high structural constancy from one radical to another, eliminating conjugation between a p carbon frame and the phosphonate assembly. This absence of conjugation is confirmed by the constancy of the charge distribution within the phosphonate group. Furthermore does the charge distribution indicate the phosphonate group to be a weak donor group, polarising the carbon skeleton it is attached to. The p electrons of double bonds are polarised. Using this description the phosphonate group behaves like a huge hydrogen-like atom, having a low electronegativity, being highly ionic inside, and therefore polarising the adjacent carbon frame. The energetic properties show also the absence of conjugation, but stabilisation of delocalised p electrons. In the latter case, p delocalised electrons polarise over all concerned centres leading to a small global stabilisation of these organic structures.

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As shown, the phosphonate group behaves internally as a highly ionic, highly polarisable group, acting mostly by electrostatic interactions (charges, dipole interactions, etc.). Its influence on a negative charge at the a position is impressive, but is relatively poor on neutral organic groups. Nevertheless a clear polarization of p delocalised electrons is observed, strong enough to induce a fair reactivity in Diels– Alder reactions. Further research is done on this stabilisation of an adjacent negative charge as well as a more detailed study of the influence on neutral organic radicals and chemical reactions. These results will be discussed in coming papers.

[3] [4] [5] [6]

Acknowledgements The authors are indebted to the Belgian National Fund for Scientific Research (F.N.R.S.) for its financial support to this research. They would like also to thank the F.N.R.S. for its support to access computational facilities (FRFC project No 2.4556.99 ‘Simulations nume´riques et traitement des donne´es’). References [1] P. Savignac, B. Iorga, Modern Phosphonate Chemistry, CRC Press, Boca Raton, 2003. [2] S.E. Denmark, C.J. Cramer, J. Org. Chem. 55 (1990) 1806–1813. C.J. Cramer, S.E. Denmark, P.C. Miller, R.L. Dorow, K.A. Swiss, S.R. Wilson, J. Am. Chem. Soc. 116 (1994) 2437–2447. M. Kranz, S.E. Denmark, J. Org. Chem. 60 (1995) 5867–5877. M. Kranz, S.E.

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