Diffuse basis functions for split valence basis sets
The theoretical description of
negatively charged species is particularly challenging for ab initio MO theory. This is due to the fact that the excess
negative charge spreads outward to a much larger degree than is typically the
case for uncharged or positively charged molecules. The description of such a diffuse charge
distribution is not very well possible with the typical split
valence basis sets discussed before. Addition of very diffuse basis functions
(with correspondingly small orbital exponents) cures this problem to a
certain extend as it allows the description of electron density relatively far
from the nucleus.^{12,13} Diffuse basis functions are
typically added as an additional set of uncontracted Gaussian functions of the
same angular momentum as the valence electrons. To reflect the addition of
diffuse basis functions on all non-hydrogen atoms, a +-sign is added to the
standard basis set notation. If diffuse s-type functions are also added to the
basis set of hydrogen atoms, a second +-sign is appended. Using carbon as an
example, the combination of the 3-21G basis set with one set of diffuse
sp-functions yields the improved "3-21+G" basis set:
C 0
S 3 1.00
.1722560000D+03 .6176690000D-01
.2591090000D+02 .3587940000D+00
.5533350000D+01 .7007130000D+00
SP 2 1.00
.3664980000D+01
-.3958970000D+00 .2364600000D+00
.7705450000D+00
.1215840000D+01 .8606190000D+00
SP 1 1.00
.1958570000D+00
.1000000000D+01 .1000000000D+01
SP 1
1.00
.4380000000D-01
.1000000000D+01 .1000000000D+01
It can clearly be seen that the orbital exponent of the diffuse SP shell is significantly smaller than that of the outer valence shell (0.0438 vs. 0.1959). The same diffuse functions developed for the small 3-21G basis set are also used with larger double and triple zeta basis sets. Recommended exponents^{13} for the first row atoms and hydrogen are: 0.0360 (H), 0.0074 (Li), 0.0207 (Be), 0.0315 (B), 0.0438 (C), 0.0639 (N), 0.0845 (O), and 0.1076 (F). These values were obtained through minimizing the energy for a small set of hydrides at the UHF/6-21+G level of theory.
%Kjob L301 #P HF/3-31+G GFInput GFPrint methanol basis set 0,1 C1 O2 1 r2 H3 1 r3 2 a3 H4 1 r4 2 a4 3 d4 r2=1.20 r3=1.0 r4=1.0 a3=120. a4=120. d4=180. |
Kjob command kills the job after checking the input The GFInput (“Gaussian Function Input”) output generation keyword causes the current basis set to be printed in a form suitable for use as general basis set input, and can thus be used in adding to or modifying standard basis sets. GFPrint command: This output generation keyword prints the current basis set in tabular form. |
A word on theoretical studies of
negatively charged species appears in place at this point.
Numerous negatively charged species do not represent stable species in
the gas phase with respect to spontaneous loss of an electron. That MO
calculations can be done at all on these species is simply due to the use of a
limited basis set. It is therefore suggested to always verify in calculations
on negatively charged species that the energy of the anionic system is lower
than the energy of the neutral system obtained after vertical neutralization.
This does not guarantee that the negatively charged system represents a bound
state, but certainly makes this more likely. A point in case is the
formaldehyde radical anion. This molecule can be optimized at the UHF/3-21G
level of theory and gives a result which is in line with expectation for ketyl
radical anions: the C-O bond is longer than in formaldehyde (1.319Å vs.
1.207Å), most of the negative charge is located at the oxygen atom and most of
the spin density is located on carbon. Comparison of the total energy of the
radical anion (-113.132324 hartree) with that of neutral formaldehyde after
vertical neutralization (-113.203973 hartree) shows, however, that the
formaldehyde radical anion does not represent a bound species in the gas phase.
The same result is obtained at other levels of theory.
The use of diffuse basis functions
in calculations of neutrals has usually little consequences. As can be seen in
Table I, the C-O bond length becomes slightly longer on inclusion of diffuse
basis functions. This can easily be understood as a consequence of removal of
some electron density from the internuclear region further away from the
molecules. The addition of diffuse functions does, however, significantly
increase the computational effort. For methanol, we have 26 basis functions and
42 primitives for the 3-21G, but 34 basis functions and 50 primitives for the
3-21+G basis set. The computational cost is further increased as SCF
convergence is more difficult to achieve with diffuse basis functions.
last changes: 01.04.2008, AS questions & comments to: axel.schulz@uni-rostock.de