Chemistry Reference
In-Depth Information
where the two-electron integrals are written in the charge density
notation:
ð
dr
1
dr
2
x
l
ð
r
2
Þx
s
ð
r
2
Þ
r
12
ðx
n
x
m
jx
l
x
s
Þ¼
x
n
ð
r
1
Þx
m
ð
r
1
Þ
ð
7
:
43
Þ
Under appropriate simplifying assumptions in the matrix elements
above, all LCAO approximations that can be derived from HF theory,
such as H
€
€
uckel, Pople's complete neglect of differential
overlap (CNDO), intermediate neglect of differential overlap (INDO),
and so on, are easily obtained.
uckel, extended H
7.3 MOLECULAR SELF-CONSISTENT-FIELD
CALCULATIONS
The AOs used as a basis in quantum chemical calculations are the
STOs and GTOs introduced in Chapter 3. Calculations are affected
by errors arising (i) from the very nature of the basis set (we saw
that STOs are definitely superior to GTOs) and (ii) from the insuffi-
ciency of the basis set, the so-called truncation errors. We now briefly
review the different types of bases most used in today molecular
calculations.
A minimal basis set involves those AOs which are occupied in the
ground state of the constituent atoms. An extended set includes
polarization functions, namely those AOs that are unoccupied in the
ground state of the atoms, say 3d and 4f AOs for C, N, O, F and 2p
and3dAOsforH.
In general, we speak of single zeta (SZ) for a minimal set, double zeta
(DZ) when each AO is described by two functions, triple zeta (TZ) when
each AO is described by three functions, and so on. When polarization
functions (P) are included, we have correspondingly DZP, TZP or DZPP,
TZPP (Van Duijneveldt-Van de Rijdt and Van Duijneveldt, 1982), de-
pending onwhether the polarization functions are only on the heavy atom
or on the H atom as well.
GTO bases are often of the redundant Cartesian type:
G
uvw
ð
r
Þ¼
Nx
u
y
v
z
w
exp
ð
cr
2
Þ
ð
7
:
44
Þ
