Date: 1/23/03
Property: Calculated energy of protonation of PZ3 (DFT, B3LYP Functional, 6-31++G** Basis Set. ZPE correction included) Calculations were done using the Gaussian98 Program
Reference: Unpublished data from the Giering/Prock Group.
Calculations:Gaussian 98, Revision A.6, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1998.
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Summary:
Energy (calc) = (256±2) - (3.24±0.08)cd + (11.1±0.7)Ear - (4.4±0.6)i
n = 24 s = 2.424 r2 = 0.989 outliers - none
%cd = 65 %q = 0 %Ear = 28 %pp = 0 %i = 7
General Comments:
Data:
|
PZ3 |
Energy of protonation (kcal/mol) |
cd |
q
|
Ear
|
pp |
'i' |
|
PH3 |
185.7 |
17.00 |
87 |
0.0 |
3.7 |
3 |
|
PH2F |
177.1 |
22.30 |
93 |
0 |
6.9 |
2 |
|
PH2(OMe) |
196.5 |
17.30 |
94 |
0.3 |
3.4 |
2 |
|
PH2Me |
202.2 |
14.20 |
97 |
0.0 |
2.5 |
2 |
|
PHF2 |
166.1 |
27.70 |
98 |
0 |
10.0 |
1 |
|
PH2Cl |
178.6 |
25.30 |
99 |
1.4 |
4.2 |
2 |
|
PH(OMe)2 |
203.6 |
17.60 |
100 |
0.6 |
3.1 |
1 |
|
PH2Et |
204.6 |
13.40 |
102 |
0.0 |
2.5 |
2 |
|
PH2(CF3) |
173.7 |
22.30 |
103 |
0.0 |
6.2 |
2 |
|
PF3 |
146.1 |
33.00 |
104 |
0.0 |
13.2 |
0 |
|
PH2(p-MeOC6H4)* |
214.5 |
14.80 |
106 |
1.0 |
0.0 |
2 |
|
PH2(p-MeC6H4) |
209.1 |
15.20 |
106 |
1.0 |
2.7 |
2 |
|
PH2(p-HC6H4) |
206.3 |
15.80 |
106 |
1.0 |
2.7 |
2 |
|
PH2(p-FC6H4) |
203.3 |
16.60 |
106 |
1.0 |
2.7 |
2 |
|
PH2(p-CF3C6H4) |
198.9 |
18.2 |
106 |
1.0 |
0.0 |
2 |
|
PHMe2 |
215.6 |
11.40 |
107 |
0.0 |
1.2 |
1 |
|
P(OMe)3 |
214.2 |
17.90 |
107 |
1.0 |
2.8 |
0 |
|
PHCl2 |
172.6 |
33.70 |
112 |
2.8 |
4.8 |
1 |
|
PH2Cy |
210.5 |
11.80 |
115 |
0.0 |
2.5 |
2 |
|
PHEt2 |
220.1 |
9.90 |
117 |
0.0 |
1.2 |
1 |
|
PMe3 |
226.0 |
8.55 |
118 |
0.0 |
0.0 |
0 |
|
PH2(t-Bu) |
209.5 |
11.30 |
119 |
0.0 |
2.5 |
2 |
|
PCl3 |
166.0 |
42.00 |
124 |
4.1 |
5.3 |
0 |
|
PEt3 |
232.7 |
6.30 |
132 |
0.0 |
0.0 |
0 |
Graphical Analysis:
Interpretation of Graphs:
• Plot of data versus cd for PH2(p-XC6H4)(Graph A): The data form a reasonably good line with a slope = -(2.3±0.7).
• Slope of the PH2R line (Graph A): The slope of the line defined by these points is not quite parallel to the line defined by the PH2(p-XC6H4). This suggests that there might be a small steric effect. It turns out that the steric effect is statistically insignificant.
• Point of intersection of the 2 lines in graph A.
The lines are separated and intersect at a very positive value of cd. This indicates a significant Ear effect.
• Plot of Energy of Protonation versus 'i' for PZ3-iPhi (Graph B). These are linear with the exception of the PH3-iFi family where we observe some curvature (Graph D)
• Outliers: None
• Steric threshold: None that is obvious.
Statistical Analysis:
We began the analysis using all the data and a five parameter fit. The resulting regression equation is
Energy (calc) = 274 - 3.35cd - 0.139q + 12.0Ear + 0.023pp - 5.34 i
|
Predictor |
Coef |
Stdev |
t-ratio |
p |
|
Constant |
273.95 |
10.51 |
26.06 |
0.000 |
|
cd |
-3.3549 |
0.2972 |
-11.29 |
0.000 |
|
q |
-0.13853 |
0.07771 |
-1.78 |
0.091 |
|
Ear |
11.970 |
1.810 |
6.61 |
0.000 |
|
pp |
0.0231 |
0.5726 |
0.04 |
0.968 |
|
i |
-5.3416 |
0.7891 |
-6.77 |
0.000 |
s = 2.288 r2 = 0.991 r2 (adj) = 0.989
We dropped pp as a parameter on the basis of its small 't-ratio' and large 'p-value'. The resulting regression equation is
Energy (calc) = 274 - 3.34cd - 0.138q + 11.9Ear - 5.34 i
|
Predictor |
Coef |
Stdev |
t-ratio |
p |
|
Constant |
273.801 |
9.611 |
28.49 |
0.000 |
|
cd |
-3.34354 |
0.09490 |
-35.23 |
0.000 |
|
q |
-0.13796 |
0.07439 |
-1.85 |
0.079 |
|
Ear |
11.9047 |
0.7723 |
15.41 |
0.000 |
|
i |
-5.3428 |
0.7675 |
-6.96 |
0.000 |
s = 2.351 r2 = 0.991 r2 (adj) = 0.988
On the basis of its small 't-ratio' and large 'p-value' we dropped q as a parameter. The resulting and final regression equation is
Energy (calc) = 256 - 3.24cd + 11.1Ear - 4.37 i
|
Predictor |
Coef |
Stdev |
t-ratio |
p |
|
Constant |
256.220 |
1.678 |
152.70 |
0.000 |
|
cd |
-3.23715 |
0.08008 |
-40.42 |
0.000 |
|
q |
||||
|
Ear |
11.1186 |
0.6839 |
16.26 |
0.000 |
|
i |
-4.3693 |
0.5931 |
-7.37 |
0.000 |
s = 2.424 r2 = 0.989 r2 (adj) = 0.988
%cd = 65 %q = 0 %Ear = 28 %pp = 0 %i = 7
Stereoelectronic Profiles:
Discussion:
It is remarkable and satisfying that the calculated values of the energy of protonation of PZ3 are well described by the QALE model. In the following Graph we show a plot of the statistical fit versus the quantum mechanically calculated values.
The conclusion is that somewhere buried in the quantum mechanics are the meanings of the QALE parameters.
The results of the QALE analysis are reasonable. The energy of protonation increases as the electron donor ability of PZ3 increases (smaller cd). The energy of protonation decreases as the number of the P-H bonds increases, which we associate with an unfavorable change in hybridization of the phosphorus upon protonation.