The Study of HOMO Energy for Showing the Basicity and the n(C=O) Stretching Bands Obtained by the Semi-empirical and ab initio Methods in Phosphorus Ylides

Shun-ichi MITOMO, Sumio TOKITA and Manabu SENO


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1 Introduction

An ylide can be defined as a substance in which a carbanion is attached directly to a heteroatom(X) carrying a high degree of positive charge - represented by the general formula I.


Ylides have two main canonical structures: X+ - Y- and X = Y, whose relative contributions depend on the nature of the heteroatom and substituents. Phosphorus ylides employed in this study have a general structure often written as a hybrid.[II]


The structural requirement for a phosphorus ylide is that it contains an anionic carbon attached to a phosphorus atom which carries a high degree of positive charge. Thus, ylides have electronically unique characteristics because of the specific structures and are known to be electron donors[1 - 13].
The kinetics of the charge-transfer complex composed of TCNQ as the acceptor and phosphorus ylides (ylides 1-3) was reported. As the basicity on the ylide carbon (anionic carbon) of phosphorus ylides is controlled by substituents on ylide carbon, the correlation between pKa of the phosphorus ylide as the donor and the formation of the phosphorus ylide-TCNQ charge-transfer complex was studied. The linear relationship between the reaction rate in the formation of charge-transfer complexes and pKa of the ylides was reported[13].
Although a vast number of basicity measurements in acetonitrile have been carried out, the reliability is still not good. Basicity data obtained by different authors often lack consistency and gaps exist[18]. And then, studies related to the pKa of the ylides[14 - 19] are still not sufficient.
Exact quantitative basicity data are very important in applying bases in various fields of chemistry and in designing new bases with desired properties. Thus, it is most necessary to discuss a new approach by the semi-empirical and ab initio methods for showing pKa of the ylides.
In this paper, it is reported that the HOMO energies obtained by the semi-empirical and ab initio methods[20 - 23], can be adopted instead of pKa as a new method for showing the basicity of ylides in organic reactions.
Since the n(C=O) stretching bands are important as means to investigate the electronic structure of the ylide molecule[24, 25], those were calculated by the AM1, PM3, and MNDOD methods (by WinmopacVer3.0) and the HF/3-21G and 6-31G methods (by Spartanf04) in this study. These results were compared with the observed n(C=O) stretching bands in ylide molecules. Furthermore, the relationships between the HOMO energy, pKa, the substituent constant (s(p))[26], and the n(C=O) stretching bands were also reported.

2 Results and discussion

2. 1 The relationship between pKa and the HOMO energies in phosphorus ylides

The charge-transfer complexes were formed by the reaction of Ph3P=CH-C(=O)-C6H4-R(R=OMe(ylide 1), R=H(ylide 2), and R=NO2(ylide 3)) and TCNQ.[III]


We already found that there is a linear relationship between the rate constant, log k and pKa[13]. When the linear relationship is represented by the form log k = m(pKa) + c, the values of m and c are 0.43 and -1.77 at 50 °C, 0.43 and -1.87 at 40 °C, and 0.43 and -1.99 at 30 °C, respectively. This result indicates that the electron density of the donor molecule plays an important role in the formation of charge-transfer complexes. The substituent effect was also examined by the Hammett method[13]. In this case, the range of reaction constants (r) is from -1.06 to -1.17. The result shows that the rate constant increases when increasing the electron density at the reaction site.
In order to investigate the relationship between the HOMO energy and the degree of electron density in ylides, the HOMO energies in ylides 1-3 were computed by three methods (AM1, PM3, and MNDOD), as shown in Table 1. The same calculations for Ph3P=CH-C(=O)-OMe(ylide 4), Ph3P=C(Cl)-C(=O)-OMe(ylide 5), and ylides 6-9 were also carried out for comparison. These results are also shown in Table 1.
A linear relationship was not found between the HOMO energies obtained by the PM3 and MNDOD methods and pKa. The plot of the HOMO energy obtained by the AM1 method and pKa is shown in Figure 1 and a linear relationship was found. A linear relationship between the HOMO energy obtained by the AM1 method and s(p) was also found, as shown in Figure 2.
In addition, HOMO energies obtained by the HF/3-21G and 6-31G methods are shown in Table 1. Linear relationships were found between HOMO energies obtained by these methods, pKa, and s(p). The plots of HOMO energy obtained by the HF/6-31G method and both of pKa and s(p) are shown in Figures 3, 4, respectively. The HOMO energy agrees with the change of pKa caused by substituents.
The plot of the HOMO energy obtained by the AM1 method and the rate constant, log k at different temperatures is shown in Figure 5. In addition, a linear relation between the rate constant of the Wittig reaction, log k(Wittig) and the HOMO energy obtained by the same method was found, as shown in Figure 6. From these results, it is clarified that as there are close relationships between pKa, s(p), and HOMO energies obtained by the AM1, HF/3-21G, and HF/6-31G methods, thus HOMO energies can be used instead of pKa as a new method for considering the electron donation of ylides 1-3 in organic reactions.

Table 1. The HOMO energies (eV) in ylides 1-10, pKa, and substituent constant s(p)
ylide 1ylide 2ylide 3ylide 4ylide 5
Methods
AM1-8.367-8.494-8.924-8.658-8.560
PM3-8.041-8.079-8.446-8.214-7.883
MNDOD-8.150-8.109-8.458-8.296-7.888
pKa6.76.04.28.8
s (p)-0.26800.778
ylide 6ylide 7ylide 8ylide 9ylide10
Methods
AM1-8.674-8.743-8.022-8.442-8.243
PM3-8.026-8.298-8.037-8.055-7.763
MNDOD-8.218-8.319-8.101-8.113-7.881
pKa
s (p)0.5020.660-0.6-0.320
ylide 1ylide 2ylide 3
Methods
HF/3-21G-7.59-7.70-8.14
HF/6-31G-7.45-7.60-8.04
pKa6.76.04.2
s (p)-0.26800.778
Ph3P=CH-C(=O)-C6H4-R
  R=OMe (ylide 1), R=H (ylide 2), R=NO2 (ylide 3)
ylide 4 Ph3P=CH-C(=O)-OMe
ylide 5 Ph3P=C(Cl)-C(=O)-OMe
Ph3P=CH-C(=O)-C6H4-R
  R=COMe (ylide 6), R=CN (ylide 7), R=NH2 (ylide 8), R=OH (ylide 9)
ylide 10 Ph3P=C(Cl)-C(=O)-C6H5

By comparing Ph3P=CH-C(=O)-C6H5 (ylide 2) and Ph3P=C(Cl)-C(=O)-C6H5 (ylide 10), the effect on electronic structure of introducing a Cl atom in ylides was investigated. The HOMO energy and pKa of ylide 10 substituted by Cl atom is also shown in Table 1. The substitution of a Cl atom for hydrogen in ylide 2 leads to higher HOMO energies in all methods. Thus, it is shown that the electron donation on carbon atom of ylide 10 is increased by the Cl atom and its basicity is higher than that of ylide 2.


Figure 1. Relationship between HOMO(AM1) and pKa


Figure 2. Relationship between HOMO(AM1) and s(p)


Figure 3. Relationship between HOMO(6-31G) and pka


Figure 4. Relationship between HOMO(6-31G) and s(p)


Figure 5. Relationship between log k and HOMO(AM1) at different temperatures


Figure 6. Relationship between log k(Wittig) and HOMO(AM1)

2. 2 Comparison of the n(C=O) stretching bands in Ph3P=CH-C(=O)-C6H4-R (R=OMe(ylide 1), R=H (ylide 2), R=NO2 (ylide 3)) and corresponding phosphonium salts 11-13

Three resonance structures of Ph3P=CH-C(=O)-C6H4-R[II] shown below have been presented [25]:


The n(C=O) stretching bands in the corresponding salts shifted to higher frequency (135-189 cm-1) in comparison with those of phosphorus ylides[25]. This result indicates that the contribution of resonance structure IIb is large in ylides. In addition, the n(C=O) stretching bands of ylides in the charge-transfer complexes shifted to high frequency (30-60 cm-1)[13]. This shift shows the interaction with TCNQ and the ylide bond. Hence, it is noted that the n(C=O) stretching band is a very important factor concerning the electronic structure of ylides.
The n(C=O) stretching bands in ylides 1-3 and corresponding phosphonium salts 11-13 were computed by three methods (AM1, PM3, and MNDOD), and these results are shown in Table 2. The n(C=O) stretching bands in phosphorus ylides shifted to lower frequency compared with those of phosphonium salts in all calculation methods.
In addition, the n(C=O) stretching bands in Ph3P=CH-C(=O)-OMe(ylide 4) and Ph3P=C(Cl)-C(=O)-OMe (ylide 5) were computed by three methods(AM1, PM3, and MNDOD) and these results are also shown in Table 2. The n(C=O) stretching bands in phosphorus ylides 4-5 were located at the middle of ylides 1-3 and salts 11-13 in both observed and calculated n(C=O) stretching bands. Thus, it is shown that the degree of electron donation in ylides 4-5 is less when compared with ylides 1-3. The differences between the n(C=O) stretching bands in ylides and correponding salts and means of those are shown in Table 3. The mean of these differences for observed n(C=O) stretching bands was 144 cm-1. Those for the n(C=O) stretching bands obtained by the PM3 and MNDOD methods were 98, 93 cm-1, respectively.
The differences between the n(C=O) stretching bands obtained by the semi-empirical methods in ylides and corresponding salts were smaller than the observed result. It is suggested that the n(C=O) stretching bands obtained by calculations can't reflect the unusual electronic structure of ylide molecules. In other words, the results obtained by the semi-empirical methods cannot give the correct change of polarity of the C=O group in ylide molecules.

2. 3 Relationships between pKa, the substituent constant (s (p)), the HOMO energy, and the n(C=O) stretching band

The n(C=O) stretching bands in simple carbonyl compounds 14-15 and amine imides 16-17 having the C=O group were investigated in order to compare with ylides 1-3 and 4-5[27, 28]. The n(C=O) stretching bands in Ph-C(=O)-Me (compound 14), Ph-O-C(=O)-O-Me (compound 15), (p-NO2-C6H4-CH2)Me2N+-N-C(=O)-CH3 (amine imide 16), and (PhCH2)Me2N+N-C(=O)-Ph (amine imide 17) were calculated by the AM1, PM3, and MNDOD methods and these results are shown in Table 4.
The calculated n(C=O) stretching bands in amine imides 16-17 appeared at lower frequency by about 100 cm-1 than those of compounds 14-15, and the observed n(C=O) stretching bands in amine imides 16-17 showed a similar low frequency shift compared to those of compound 14-15. The PM3 method showed the smallest value for the mean of (calculated - observed) n(C=O) stretching band. The n(C=O) stretching bands in phosphorus ylides 6-9 were computed by three methods (AM1, PM3, and MNDOD) and these results are shown in Table 5.
The n(C=O) stretching band obtained by the MNDOD method did not change with s(p). The plot of the n(C=O) stretching band obtained by the PM3 method and s(p) was divided into two groups and the good linear relationship was not found, as shown in Figure 7. The linear relationship between the n(C=O) stretching band obtained by the AM1 method and pKa was found, as shown in Figure 8. The linear relationship between the n(C=O) stretching band and s(p) was also found, as shown in Figure 9. Then, the linear relationship between the n(C=O) stretching band and the HOMO energy obtained by the AM1 method in ylides 1-3 and 6-9 was found, as shown in Figure 10.
The AM1 method was the best for the estimation of n(C=O) stretching bands in semi-empirical methods. The result obtained by the AM 1 method reflects clearly the change of the electronic structure of ylide molecules caused by the substitutent. The linear relationship between the observed n(C=O) stretching band and the HOMO energy obtained by the AM1 method in phosphorus ylides 1-3 was found, as shown in Figure 11.
The HOMO energies and the n(C=O) stretching bands in ylides 1-3 were also computed by the HF/3-21G and HF/6-31 methods in order to perform precise calculations. These results are shown in Table 1 and Table 6, respectively. The ratios of observed band and those calculated using the HF/3-21G and 6-31G methods were 0.90-0.91 and 0.86-0.87, respectively.


Figure 7. Relationship between the n(C=O) stretching band(PM3) and s(p)


Figure 8. Relationship between the n(C=O) stretching band(AM1) and pKa


Figure 9. Relationship between the n(C=O) stretching band(AM1) and s(p)


Figure 10. Relationship between the n(C=O) stretching band(AM1) and HOMO(AM1)


Figure 11. Relationship between the n(C=O) stretching band(obs) and HOMO(AM1)


Figure 12. Relationship between the n(C=O) stretching band(obs) and HOMO(6-31G)


Figure 13. Relationship between the n(C=O) stretching band(6-31G) and pKa


Figure 14. Relationship between the n(C=O) stretching band(6-31G)) and s(p)


Figure 15. Relationship between the n(C=O) stretching band(6-31G) and HOMO(6-31G)

Table 2. The n(C=O) stretching bands obtained by the AM1, PM3, and MNDOD methods, those observed, and the means of (calcd - obs) n(C=O) stretching bands in ylides 1-3, phosphonium salts 11-13, and ylides 4-5 (cm-1)
AM1 methodcalculatedobservedmean of (calcd - obs)
Compoundsn(C=O) bandn(C=O) bandn(C=O) band
ylide 119651503440
ylide 219671527
ylide 319751540
phosphonium salt 1120111652355
phosphonium salt 1220271662
phosphonium salt 1320291689
ylide 420071621386
ylide 520441642
PM3 methodcalculatedobservedmean of (calcd - obs)
Compoundsn(C=O) bandn(C=O) bandn(C=O) band
ylide 118451503333
ylide 218471527
ylide 318601540
phosphonium salt 1119381652286
phosphonium salt 1219531662
phosphonium salt 1319561689
ylide 419091621276
ylide 519031642
MNDOD methodcalculatiedobservedmean of (calcd - obs)
Compoundsn(C=O) bandn(C=O) bandn(C=O) band
ylide 120241503507
ylide 220251527
ylide 320251540
phosphonium salt 1121171652450
phosphonium salt 1221171662
phosphonium salt 1321181689
ylide 420281621394
ylide 520231642
ylide 4 Ph3P=CH-C(=O)-OMe, ylide 5 Ph3P=C (Cl)-C(=O)-OMe
Ph3P+-CH2-C(=O)-C6H4-R
  R=OMe (phosphonium ), R=H (phosphonium salt 12), R=NO2 (phosphonium salt 13)

Table 3. The differences between the calculated n(C=O) stretching bands in ylides and corresponding salts, and means in the semi-empirical methods and Experiment (cm-1)
AM1Experiment
Compoundscalculated(mean)observed(mean)
Dn(C=O) bandDn(C=O) band
The difference (11) - (1)46(53)149(144)
The difference (12) - (2)60135
The difference (13) - (3)54149
PM3MNDOD
Compoundscalculated(mean)calculated(mean)
Dn(C=O) bandDn(C=O) band
The difference (11) - (1)93(98)93(93)
The difference (12) - (2)10692
The difference (13) - (3)9693

Table 4. The n(C=O) stretching bands obtained by the AM1, PM3, and MNDOD methods, those observed and the means of (calcd - obs) n(C=O) stretching bands in carbonyl compounds 14-15 and amine imides 16-17 (cm-1)
AM1         methodcalculatedobservedthe mean of
n(C=O) bandn(C=O) band(calcd - obs)
Compoundsn(C=O) band
compound 1420381680352
compound 1521211775
amine imide 1619191580337
amine imide 1719041570
PM3         methodcalculatedobservedthe mean of
n(C=O) bandn(C=O) band(calcd - obs)
Compoundsn(C=O) band
compound 1419551680232
compound 1519641775
amine imide 1618671580292
amine imide 1718591570
MNDOD methodcalculatedobservedthe mean of
n(C=O) bandn(C=O) band(calcd - obs)
Compoundsn(C=O) band
compound 1420811680372
compound 1521171775
amine imide 1620381580462
amine imide 1720321570
compound 14 Ph-C(=O)-Me, compound 15 Ph-O-C(=O)-O-Me
amine imide 16
(p-NO2-C6H4-CH2)Me2N+N-C(=O)-Me
amine imide 17
(PhCH2)Me2N+N-C(=O)-Ph

Table 5. The n(C=O) stretching bands obtained by the AM1, PM3, and MNDOD methods in ylides 6-9 (cm-1)
Methodsylide 6ylide 7ylide 8ylide 9
AM11975197119621964
PM31861185718541855
MNDOD2024202420242025
s (p)0.5020.660-0.6-0.320
Ph3P=CH-C(=O)-C6H4-R
  R=COMe (ylide 6), R=CN (ylide 7), R=NH2 (ylide 8), R=OH (ylide 9)

Table 6. The n(C=O) stretching bands obtained by the HF/3-21G and 6-31G methods (cm-1) and the ratios of observed bands and those calculated in ylides 1-3
Methods3-21G6-31G
Compoundsn(C=O) bandn(C=O) bandratio ofratio of
obs/calcd(3-21G)obs/calcd(6-31G)
ylide 1165817470.9070.860
ylide 2168917590.9040.868
ylide 3169417990.9090.856

The result obtained by the HF/6-31G method was found to be better than that obtained by the HF/3-21G method. Linear relationships between the observed n(C=O) stretching bands and the HOMO energies obtained by the HF/3-21G and 6-31G methods in phosphorus ylides 1-3 were found, and the result obtained by the HF/6-31G method is shown in Figure 12. Linear relationships were found between the n(C=O) stretching bands and HOMO energies obtained by these methods, pKa, and s(p). The plots of n(C=O) stretching band and both of pKa and s(p) are shown in Figures 13, 14, respectively. The plot of the n(C=O) stretching band and HOMO energy is also shown in Figure 15.
Since the ratio of the observed n(C=O) stretching band and that calculated using the HF/6-31G method was 0.86 - 0.87, the n(C=O) stretching band in ylides can be estimated from the HOMO energy obtained by this method and this ratio. Thus, the HOMO energy is useful to estimate the n(C=O) stretching bands in ylides.
As a consequence, the n(C=O) stretching bands obtained by the AM1, HF/3-21G, and HF/6-31G methods are closely related to s (p), pKa, and the HOMO energy. Especially, it is clarified that the HOMO energy is an important parameter when considering the n(C=O) stretching bands in ylides.

3 Conclusion

The electron donation of ylides is a very important factor in the formation of charge-transfer complexes and organic reactions. The basicity, pKa is already used as the parameter when choosing donors in the formation of charge-transfer complexes.
Data related to pKa of ylides are not enough. Especially, we pay attention to the HOMO energies obtained by the semi-empirical and ab initio methods instead of pKa. Linear relationships between pKa and the HOMO energies obtained by the AM1, HF/3-21G, and HF/6-31G methods were found. Linear relationships between the HOMO energies obtained by these methods and s(p) were also found. It is clarified that the HOMO energies in ylides are useful to elucidate the change of pKa caused by substituents and can be used when choosing donors in various chemical reactions. Therefore, the semi-empirical and ab initio methods play a role in the determination of pKa of donors in organic reactions.
The n (C=O) stretching bands in the charge-transfer complex are very important to investigate the interaction with TCNQ and the ylide carbon. Linear relationships between the n(C=O) stretching bands and the HOMO energies obtained by the AM1, HF/3-21G, and HF/6-31G methods were found. The HF/6-31G method was found to be better than the HF/3-21G method in ab initio methods. Since the ratio of the observed n(C=O) stretching band and that calculated using the HF/6-31G method was 0.86 - 0.87, the n(C=O) stretching band in ylides can be estimated from the HOMO energy obtained by this method and this ratio. It is found from these results that the HOMO energy is useful to estimate the n(C=O) stretching bands in ylides.
It is worthy of attention that close relations were found between pKa, s(p), the n(C=O) stretching band, and the HOMO energy in the ylide molecules.

We are most grateful to Dr. Shinji Tsuchiya for bringing the ylides to our attention and for his support with various aspects of this work.

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