Chemistry Reference
In-Depth Information
the first dipole-allowed transition from a valence shell of
l
quantum number
l
v
generally involves orbitals with
l
-quantum number
l
v
þ
1. Basis sets of SV(P)
or similar quality are often the first choice for TDDFT applications to large
systems, especially if only the lowest states are of interest and/or if diffuse exci-
tations are quenched due, e.g., to a polar environment. The popular 6-31G*
basis set
205,206
has essentially the same size as SV(P) but performed slightly
worse in our example above.
Adding a single set of
p
-type polarization functions to hydrogen atoms
produces the SVP basis set.
204
These functions describe mainly C-H
s
-type
excitation in molecules, which usually occur in the far ultraviolet (UV) and
are rarely studied by most scientists. Going from SV(P) to SVP has no signifi-
cant effect in our example. Such an observation may be different for molecules
containing strongly polarized hydrogen element or hydrogen bridge bonds,
however.
The aug-SV(P) is an SV(P) basis set augmented by a
set of pri-
mitive Gaussians with small exponents, often called ''diffuse functions'' (from
Dunning's aug-cc-pVDZ
203
). The effect of diffuse augmentation is a moderate
downshift of less than 0.1 eV for the first two singlet excitation energies, as
shown in Table 3. This behavior is typical of lower valence excited states hav-
ing a similar extent as the ground state. The naphthalene example also shows
that diffuse functions can have a significant effect on higher excitations. An
extreme case is the 1
1
A
u
state, which is an excitation into the 10
a
u
orbital hav-
ing the character of a 3
s
Rydberg state (any state with principal quantum num-
ber higher than HOMOs) of the entire molecule. The excitation energy of this
state is lowered by more than 1 eV upon diffuse augmentation.
While polarization functions are necessary for a qualitatively correct
description of transition dipole moments, additional diffuse polarization func-
tions can account for radial nodes in the first-order KS orbitals, which further
improves computed transition moments and oscillator strengths. These bene-
fits are counterbalanced with a significant increase of the computational cost
involved: In our example, the aug-SV(P) basis increased the computation time
by about a factor of 4. For molecules with more than 30-40 atoms, most exci-
tations of interest are valence excitations, and the use of diffuse augmentation
may become prohibitively expensive because the large spatial extent of these
functions confounds integral prescreening.
½
1
s
1
p
1
d
Triple-Zeta Basis Sets
For large molecules where the use of diffuse augmentation is prohibi-
tive, an alternative is to use triple-zeta valence (TZV) basis sets. The
TZVP (def-2-TZVP
207
) basis set corresponds to
½
5
s
3
p
2
d
1
f
on C and
½
on H. It also includes a second set of polarization functions on nonhy-
drogen atoms and provides a description of the valence electrons that is
3
s
1
p
