# A note on Karlsruhe’s def2 basis sets

During most molecular bonding, it is the valence electrons which principally take part in the bonding. In recognition of this fact, it is common to represent valence orbitals by more than one basis function (each of which can in turn be composed of a fixed linear combination of primitive Gaussian functions).

Basis sets in which there are multiple basis functions corresponding to each valence atomic orbital are called valence double, triple, quadruple-zeta, and so on, basis sets (“zeta” or “ζ” was commonly used to represent the exponent of an STO basis function). Since the different orbitals of the split have different spatial extents, the combination allows the electron density to adjust its spatial extent appropriate to the particular molecular environment.

Some of the various valence adaptations of Karlsruhe basis sets are

• def2-SV(P) – Split valence with polarization functions on heavy atoms (not hydrogen)
• def2-SVP – Split valence polarization
• def2-SVPD – Split valence polarization with diffuse functions
• def2-TZVP – Valence triple-zeta polarization
• def2-TZVPD – Valence triple-zeta polarization with diffuse functions
• def2-TZVPP – Valence triple-zeta with two sets of polarization functions
• def2-TZVPPD – Valence triple-zeta with two sets of polarization functions and a set of diffuse functions
• def2-QZVP – Valence quadruple-zeta polarization
• def2-QZVPD – Valence quadruple-zeta polarization with diffuse functions
• def2-QZVPP – Valence quadruple-zeta with two sets of polarization functions
• def2-QZVPPD – Valence quadruple-zeta with two sets of polarization functions and a set of diffuse functions

(from Wikipedia “Basis set (chemistry)“)

### Correspondence with Pople basis sets

The components of the def2- basis sets are shown below.

H     0
S    3   1.00
13.0107010              0.19682158D-01
1.9622572              0.13796524
0.44453796             0.47831935
S    1   1.00
0.12194962             1.0000000
****

(The term “SV” stands for “split valence”)

The def2-SV(P) basis assigns four bases to hydrogen atoms. In terms of Pople’s basis sets system, this number of bases corresponds to the 6-31G basis set (as well as to the 6-31+G, 6-31G*, and 6-31+G*).

### Corresponding Pople’s basis sets

def2-SVP　　･･･　6-31G(d,p), 6-31+G(d,p) (5 basis for H atom; 4s1p)
def2-SVPD　 ･･･　6-31G(2df,p) (6 basis for H atom; 4s2p)
def2-TZVP 　 ･･･　6-311G(d,p) (6 basis for H atom; 5s1p)
def2-TZVPD   ･･･　no match(?) (7 basis for H atom; 5s2p)
def2-TZVPP   ･･･　6-311G(2df,2pd) (8 basis for H atom; 5s2p1d)