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3 Fundamentals of the Analysis Tools
(4) Diffuse basis set
Addition of diffuse functions is expressed by insertion of the sign + or ++ between
split valence and G such as, e.g., 6-311 + G(d, p), 6-311 + G(2d, p), and 6-311 +
+G(3df, 3pd), etc. Notations of diffuse basis sets are bit complicated, and implications
of those are as follows:
6-311 + G(d, p): For the valence orbitals of atoms larger than Li, quadruple zeta
of valence s and p functions and single zeta of d functions. For the valence orbital of
H atom, triple zeta of s function and single zeta of p functions.
6-311 + G(2d, p): For the valence orbitals of atoms larger than Li, quadruple zeta
of valence s and p functions and double zeta of d functions. For the valence orbital
of H atom, triple zeta of s function and single zeta of p functions.
6-311 ++G(3df, 3pd): For the valence orbitals of atoms larger than Li, quadruple
zeta of valence s and p functions, and triple zeta of d functions, and single zeta of f
functions. For the valence orbital of H atom, quadruple zeta of s function, triple zeta
of p functions, and single zeta of d functions.
*In the above, all the inner-shell orbitals are expanded by six GTO’s.
Although the computation time largely increases by using a diffuse basis set,
this kind of basis set well describes the electronic structure of anionic molecule,
supermolecule, molecule with lone pairs, or rather high excited state of molecules,
since electrons in these species are rather liberated from the original molecule.
Some others:
(5) cc-PVNZ; correlation consistent basis set (Dunning 1989)
(cc-P = correlation consistent polarized; V = valence orbitals only; N = D, T, Q,
and so on, where D = double, T = triple, Q = quadruple; Z = zeta).
This basis set includes polarization functions from the first. Inclusion of diffuse
orbitals is represented by putting prefix “aug-” like “aug-cc-PVDZ”.
(6) Effective core potential (ECP)
This is not exactly the basis set for all the electrons particularly in heavy atoms whose
inner core electrons are replaced with a certain potential form. There are several kinds
of ECP’s such as CEP-31G (compact effective potential plus 31G), LanL2DZ (Los
Alamos national laboratory ECP plus DZ), SDD (Stuttgart/Dresden ECP), and so
on. One can also use the ECP called RECP including the relativistic effect inherent
in the heavy atoms.
Q3: Is there restrictions for the optimization of molecular structure?
A3: All the calculation methods cannot necessarily perform molecular structure
optimization. For instance, the Hückel and the extended Hückel methods cannot
perform the geometrical optimization, since they afford only the simple MO energies
without inclusion of the interelectron interactions.
The optimization of molecular structure is possible by the usage of HF, post-HF,
DFT, and MM methods. Broadly speaking, the post-HF or the DFT method can
3 Fundamentals of the Analysis Tools
(4) Diffuse basis set
Addition of diffuse functions is expressed by insertion of the sign + or ++ between
split valence and G such as, e.g., 6-311 + G(d, p), 6-311 + G(2d, p), and 6-311 +
+G(3df, 3pd), etc. Notations of diffuse basis sets are bit complicated, and implications
of those are as follows:
6-311 + G(d, p): For the valence orbitals of atoms larger than Li, quadruple zeta
of valence s and p functions and single zeta of d functions. For the valence orbital of
H atom, triple zeta of s function and single zeta of p functions.
6-311 + G(2d, p): For the valence orbitals of atoms larger than Li, quadruple zeta
of valence s and p functions and double zeta of d functions. For the valence orbital
of H atom, triple zeta of s function and single zeta of p functions.
6-311 ++G(3df, 3pd): For the valence orbitals of atoms larger than Li, quadruple
zeta of valence s and p functions, and triple zeta of d functions, and single zeta of f
functions. For the valence orbital of H atom, quadruple zeta of s function, triple zeta
of p functions, and single zeta of d functions.
*In the above, all the inner-shell orbitals are expanded by six GTO’s.
Although the computation time largely increases by using a diffuse basis set,
this kind of basis set well describes the electronic structure of anionic molecule,
supermolecule, molecule with lone pairs, or rather high excited state of molecules,
since electrons in these species are rather liberated from the original molecule.
Some others:
(5) cc-PVNZ; correlation consistent basis set (Dunning 1989)
(cc-P = correlation consistent polarized; V = valence orbitals only; N = D, T, Q,
and so on, where D = double, T = triple, Q = quadruple; Z = zeta).
This basis set includes polarization functions from the first. Inclusion of diffuse
orbitals is represented by putting prefix “aug-” like “aug-cc-PVDZ”.
(6) Effective core potential (ECP)
This is not exactly the basis set for all the electrons particularly in heavy atoms whose
inner core electrons are replaced with a certain potential form. There are several kinds
of ECP’s such as CEP-31G (compact effective potential plus 31G), LanL2DZ (Los
Alamos national laboratory ECP plus DZ), SDD (Stuttgart/Dresden ECP), and so
on. One can also use the ECP called RECP including the relativistic effect inherent
in the heavy atoms.
Q3: Is there restrictions for the optimization of molecular structure?
A3: All the calculation methods cannot necessarily perform molecular structure
optimization. For instance, the Hückel and the extended Hückel methods cannot
perform the geometrical optimization, since they afford only the simple MO energies
without inclusion of the interelectron interactions.
The optimization of molecular structure is possible by the usage of HF, post-HF,
DFT, and MM methods. Broadly speaking, the post-HF or the DFT method can