2. Basis Set

3. ∞ Model chemistry: theoretical method and basis set …HF
MP2
CCSD
CCSD(T)
CCSDT …
Full CI
Minimal
Split-valence
Polarized
Diffuse
High angular momentum ∞
Exact solution
Goal: select the most accurate calculation that is computationally feasible for a given molecular system

5. Model Chemistries - three areas of consideration
Basis sets
Theoretical methods

6. Basis set Basis functions approximate orbitals of atoms in molecule
Linear combination of basis functions approximates total electronic wavefunction
Basis functions are linear combinations of gaussian functions
Contracted gaussians
Primitive gaussians

7. STOs v. GTOs Slater-type orbitals (J.C. Slater)
Represent electron density well in valence region and beyond (not so well near nucleus)
Evaluating these integrals is difficult
Gaussian-type orbitals (F. Boys)
Easier to evaluate integrals, but don’t represent electron density well
Overcome this by using linear combination of GTOs

10. Minimal basis set
One basis function for every atomic orbital required to describe the free atom
Most-common: STO-3G
Linear combination of 3 Gaussian-type orbitals fitted to one Slater-type orbital
CH4: H(1s); C(1s,2s,2px,2py,2pz)

17. More basis functions per atom
Split valence basis sets
Double-zeta: 2 “sizes” of basis functions for each valence atomic orbital
3-21G CH4: H(1s,1s'), C(1s,2s,2s',2px,2py,2pz,2px',2py',2pz')
Triple-zeta: 3 “sizes” of basis functions for each valence atomic orbital
6-311G CH4: H(1s,1s',1s''),
C(1s,2s,2s',2s'',2px,2py,2pz, 2px',2py',2pz',2px'',2py'',2pz'')

18. More basis functions per atom
Split valence basis sets
Double-zeta:
Triple-zeta:

19. 22
Total 36

20. Total 42 22

22. Ways to increase a basis set
Add more basis functions per atom
allow orbitals to “change size”
Add polarization functions
allow orbitals to “change shape”
Add diffuse functions for electrons with large radial extent
Add high angular momentum functions

23. Add polarization functions
Allow orbitals to change shape
Add p orbitals to H
Add d orbitals to 2nd row atoms
Add f orbitals to transition metals
6-31G(d) - d functions per heavy atoms
Also denoted: 6-31G*
6-31G(d,p) - d functions per heavy atoms and p functions to H atoms
Also deonoted: 6-31G**

29. Add diffuse functions “Large” s and p orbitals for “diffuse electrons”
Lone pairs, anions, excited states, etc.
6-31+G - diffuse functions per heavy atom
6-31++G - diffuse functions both per heavy atom and per H atom

31. High angular momentum functions
“Custom-made” basis sets
6-31G(2d) - 2d functions per heavy atom
G(3df,3pd)
Triple-zeta valence
Diffuse functions on heavy atoms, H atoms
3d, 1f functions per heavy atom; 3p, 1d functions per H atom

42. Minimal basis sets
A common naming convention for minimal basis sets is STO-XG, where X is an integer.
This X value represents the number of Gaussian primitive functions comprising a single basis function.
In these basis sets, the same number of Gaussian primitives comprise core and valence orbitals.
Minimal basis sets typically give rough results that are insufficient for research-quality publication,
but are much cheaper than their larger counterparts. Here is a list of commonly used minimal basis sets:
STO-2G
STO-3G
STO-6G
STO-3G* - Polarized version of STO-3G

43. Split-valence 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). The notation for these split-valence basis sets is typically X-YZg.
In this case, X represents the number primitive Gaussians comprising each core atomic orbital basis function.
The Y and Z indicate that the valence orbitals are composed of two basis functions each
Here is a list of commonly used split-valence basis sets:
3-21g
3-21g* - Polarized
3-21+g - Diffuse functions
3-21+g* - With polarization and diffuse functions
6-31g
6-31g*
6-31+g*
6-31g(3df, 3pd)
6-311g
6-311g*
6-311+g*
SV(P)
SVP

44. Double, triple, quadruple zeta basis sets
Basis sets in which there are multiple basis functions corresponding to each atomic orbital,
including both valence orbitals and core orbitals or just the valence orbitals, are called double, triple,
or quadruple-zeta basis sets. Here is a list of commonly used multiple zeta basis sets:
multiple zeta basis sets:
cc-pVDZ - Double-zeta
cc-pVTZ - Triple-zeta
cc-pVQZ - Quadruple-zeta
cc-pV5Z - Quintuple-zeta, etc.
aug-cc-pVDZ, etc. - Augmented versions of the
preceding basis sets with added diffuse functions
TZVPP - Triple-zeta
QZVPP - Quadruple-zeta