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   Next: Concluding Remarks Up: Results and Discussion Previous: Geometries
Proton Affinities
Total energies calculated by different quantum approaches are listed
in Table V.
Direct comparison of absolute total energies calculated by different methods
used in this work is only possible among the results obtained by the same
program. For ab initio, as expected,
the inclusion of six d-type polarization functions
(in the DH6D basis set), compared with five pure d-type functions (in the
DH5D basis set)
lowers the calculated energy. Using six cartesian d-type gaussians
is equivalent to using the set of five pure functions of d-type augmented with
a 3s-type (i.e.,
The effect of adding Becke-Perdew corrections to the LSD energy can be
examined for DGauss and deMon calculations. It is known that LSD approximation
tends to grossly overestimate correlation energy (frequently as much as 100%)
while it underestimates electron exchange energy by as much as 10% DMol uses five d-type functions) while DGauss and deMon use six cartesian gaussians as d-type functions. Judging from ab initio results, this difference should not have any substantial impact on the calculated proton affinities.
The changes in the ground state electronic energies on protonation,
The DH5D and DH6D basis sets are far from optimal for calculations
of proton affinities since they do not include diffuse s and p-type
functions
Table VI collects zero point energies (ZPE) derived from calculated
vibrational frequencies by eq 2, and the temperature-dependent portion
of vibrational enthalpies,
The magnitudes of calculated ZPE's in our series of molecules
are ordered as:
DMol
Proton affinities were calculated from eq 4. The values of calculated
gas phase proton affinities together with the experimental values
are collected in Table VII. The errors in experimental values are roughly
2 kcal/mol for affinities within 167-204 kcal/mol range and the error
gets much larger outside this range due to the lack of adequate reference
proton affinities
The proton affinities calculated within the
LSD approximation are substantially smaller than
the experimental values. For our series of molecules, LSD underestimates
It seems that for this particular series of molecules it does not matter if gradient corrections were applied perturbationally to the LSD energy (at LSD optimized geometry) or if they were introduced in a self-consistent way during geometry optimization. This may, however, be fortuitous due to the fact that C--X bonds are slightly shorter and X--H and C--H slightly longer than for the corresponding NLSD calculations. It may provide for some cancellation of errors which results in similar overall values of affinities.
Next: Concluding Remarks Up: Results and Discussion Previous: Geometries Computational Chemistry Thu Oct 30 00:15:06 EST 1997 |
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| Modified: Thu Oct 30 17:00:00 1997 GMT |
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) function.
This energy change is negligible for our RHF calculations
(on average 0.00060 hartree, i.e., 
0.38 kcal/mol), however,
this change is roughly 10 times larger
(on average 0.0059 hartree, i.e., 
, to the calculated proton affinity.
This should be expected since
the parent and the protonated molecule have the same number of ``heavy''
atoms whose basis sets contain d-type functions and they differ only
in the number of hydrogen atoms.
.
Both, the exchange and the correlation energy, are negative but typically
the magnitude of electron exchange energy is of several orders of magnitude
larger than the correlation energy for the same system. Therefore, the
magnitude of the 10% correction to the exchange energy is typically
larger than the magnitude of the correlation energy. For this reason,
NLSD corrected energies are lower than the corresponding LSD energies.
. It is dramatically pronounced in the calculated energies
for anions. However, they were chosen here for comparison with DFT
calculations.
Inclusion of diffuse functions is absolutely required 
for meaningful calculations of electronic energy for anions by ab initio
methods..
To illustrate the effect of diffuse functions, we performed
RHF and MP2 calculations for formate anion,
and the corresponding neutral acid with DH6D basis set
augmented with diffuse s-type and p-type functions
on oxygen atoms. As expected, this led to a substantial lowering of
electronic energy for the formate anion, while the effect was much
smaller for the neutral acid, i.e., the 
,
computed from eq 3 for the molecules studied.
All values of 
can also be safely
omitted in proton affinity calculations since the largest contributions
to 
must be accounted for in proton affinity calculations.
Also, systematic over- or under-estimation of frequencies will
bias the value of ZPE in the same direction.
Moreover, it should be noted that ZPE in our case is calculated
within the harmonic approximation. Experimental frequencies available
in the literature for our series of molecules are not
corrected for anharmonicity, and therefore,
direct comparisons with experimental values of ZPE were
not attempted.
.
The MP2 calculated frequencies are in much better agreement with
experiment, though in general they are also slightly higher
than measured harmonic frequencies 
basis set for formic acid,
and the corresponding anion, produced ZPE's very similar to
the DH6D basis set. The major contribution to error in proton affinities
of anions calculated with basis sets lacking diffuse functions is therefore
from the electronic energies.
.
.
This trend in RHF calculations is mainly due to
the overestimated 
kcal/mol, 
kcal/mol)
then those from MP2 calculations
( 
kcal/mol when
the result obtained with diffuse basis functions was used for formate)
and much better
than the ones from RHF calculations ( 
kcal/mol).