Chemistry Reference
In-Depth Information
2.8 Theoretical Methods
There have been extensive efforts put into the accurate calculation of PAs, gas phase
basicities and solution pK
a
values in recent years. Results vary depending on the level of
sophistication of the applied calculations, and the fit to experimental values varies with the
theoretical model employed. Although the calculated PA, gas phase basicity and pK
a
values
differ from the experimentally determined, these calculations appear reliable enough that
the major effects found in superbases can be clearly demonstrated. To generalize, more high
level the theory method the better the results, but it is not always, dependent on the system
under study. Large molecular systems need some trade-off between accuracy and compu-
tational effort (CPU time).
The proton affinity of a base is defined as the negative change of enthalpy (PA
¼D
H
prot
)
BH
þ
), while the absolute gas phase
basicity corresponds to the negative of the Gibbs free energy change, that is, GB
(H
þ
!
þ
associated with the protonation reaction B
ð
B
Þ¼
G
prot
. For estimation of PAs and GBs in the gas phase, high level Hartree-Fock (HF),
post-HF andDFT quantum-chemical calculations were employed. It has been found that the
quality of obtained geometry is not crucial if PAs are estimated by single-point calculations
at higher levels of theory, which is the approach generally used. For instance, ZPE(HF/6-
31G*)
D
þ
MP2/6-31
þ
G*//MP2/6-31
þ
G*; [37] ZPE
þ
MP2/6-311
þþ
G**//HF/6-311
þþ
G**; MP2(fc)/6-311
þ
G**//RHF/6-31G*; [71] BP86/TZVP//BP86/TZVP
þ
ZPE; [107]
B3LYP/6-311
þ
G(3df,3pd); [108] B3LYP/6-31
þ
G**//HF/6-31G**; [8] BP/DZVP [6] and
B3PW91/6-311
g(d,p)//B3PW91/6-31G* methods have been the most successful. For
larger molecular systems, a somewhat less accurate but computationally more efficient
model, the scaled Hartree-Fock (HF
SC
), scheme has been developed by Maksi
þþ
c et al.,based
on the linear correlation of experimental results and calculations [109]: APA(B)
¼
0.8924
10.4 kcal mol
1
.
High level computations such as CBS-QB3, CPCM/MP2/6-311
D
E
el(HF/6-31G*)
þ
þ
G**//CPCM/HF/6-
31
G** gave gas phase basicity and
absolute aqueous pK
a
values with chemical accuracy [110]. Unfortunately, these methods
are computationally too intensive to be applied to larger molecules. Maksi
þ
G* and CPCM/B3LYP/6-311
þ
G**//B3LYP/6-31
þ
c
[49] have used a computationally more economical model for pK
a
estimation, in which
solvation energies were calculated by IPCM/B3LYP/6-311
c and Kova
cevi
G**//HF/6-31G* method.
Then, the pK
a
values were estimated by a linear regression model of the experimental pK
a
data and calculated APA(solv). The correlation between APA(MeCN) calculated in
acetonitrile and the experimental pK
a
values for series of bases containing imino groups
is: pK
a
(MeCN)
imine
¼
þ
119.7. It should be noted that such linear
relations of pK
a
are valid for each computational level and each family of compounds
separately, hence they should be derived in each case [85,111-113].
0.4953, APA(MeCN)
¼
2.9 Concluding Remarks
In summary, guanidinophosphazenes belong to the most basic, experimentally deter-
minedclassofsuperbases,followedbyphosphazenes, proazaphosphatranes and guani-
dines. Amidines and classical proton sponges generally show less pronounced basicity.
