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

1 Introduction

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

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 1	ylide 2	ylide 3	ylide 4	ylide 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
pKa	6.7	6.0	4.2	8.8
s (p)	-0.268	0	0.778

	ylide 6	ylide 7	ylide 8	ylide 9	ylide10
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)	0.502	0.660	-0.6	-0.320

	ylide 1	ylide 2	ylide 3
Methods
HF/3-21G	-7.59	-7.70	-8.14
HF/6-31G	-7.45	-7.60	-8.04
pKa	6.7	6.0	4.2
s (p)	-0.268	0	0.778

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

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

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 method	calculated	observed	mean of (calcd - obs)
Compounds	n(C=O) band	n(C=O) band	n(C=O) band
ylide 1	1965	1503	440
ylide 2	1967	1527
ylide 3	1975	1540
phosphonium salt 11	2011	1652	355
phosphonium salt 12	2027	1662
phosphonium salt 13	2029	1689
ylide 4	2007	1621	386
ylide 5	2044	1642

PM3 method	calculated	observed	mean of (calcd - obs)
Compounds	n(C=O) band	n(C=O) band	n(C=O) band
ylide 1	1845	1503	333
ylide 2	1847	1527
ylide 3	1860	1540
phosphonium salt 11	1938	1652	286
phosphonium salt 12	1953	1662
phosphonium salt 13	1956	1689
ylide 4	1909	1621	276
ylide 5	1903	1642

MNDOD method	calculatied	observed	mean of (calcd - obs)
Compounds	n(C=O) band	n(C=O) band	n(C=O) band
ylide 1	2024	1503	507
ylide 2	2025	1527
ylide 3	2025	1540
phosphonium salt 11	2117	1652	450
phosphonium salt 12	2117	1662
phosphonium salt 13	2118	1689
ylide 4	2028	1621	394
ylide 5	2023	1642

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)

	AM1		Experiment
Compounds	calculated	(mean)	observed	(mean)
	Dn(C=O) band		Dn(C=O) band
The difference (11) - (1)	46	(53)	149	(144)
The difference (12) - (2)	60		135
The difference (13) - (3)	54		149

	PM3		MNDOD
Compounds	calculated	(mean)	calculated	(mean)
	Dn(C=O) band		Dn(C=O) band
The difference (11) - (1)	93	(98)	93	(93)
The difference (12) - (2)	106		92
The difference (13) - (3)	96		93

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         method	calculated	observed	the mean of
	n(C=O) band	n(C=O) band	(calcd - obs)
Compounds			n(C=O) band
compound 14	2038	1680	352
compound 15	2121	1775
amine imide 16	1919	1580	337
amine imide 17	1904	1570

PM3         method	calculated	observed	the mean of
	n(C=O) band	n(C=O) band	(calcd - obs)
Compounds			n(C=O) band
compound 14	1955	1680	232
compound 15	1964	1775
amine imide 16	1867	1580	292
amine imide 17	1859	1570

MNDOD method	calculated	observed	the mean of
	n(C=O) band	n(C=O) band	(calcd - obs)
Compounds			n(C=O) band
compound 14	2081	1680	372
compound 15	2117	1775
amine imide 16	2038	1580	462
amine imide 17	2032	1570

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)

Methods	ylide 6	ylide 7	ylide 8	ylide 9
AM1	1975	1971	1962	1964
PM3	1861	1857	1854	1855
MNDOD	2024	2024	2024	2025
s (p)	0.502	0.660	-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

Methods	3-21G	6-31G
Compounds	n(C=O) band	n(C=O) band	ratio of	ratio of
			obs/calcd(3-21G)	obs/calcd(6-31G)
ylide 1	1658	1747	0.907	0.860
ylide 2	1689	1759	0.904	0.868
ylide 3	1694	1799	0.909	0.856

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

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.

References