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Basis sets (Read 12490 times)
Gerrit-Jan Linker
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Basis sets
28.02.08 at 11:33:07
 
Basis sets
 
A basisset in chemistry is a set of functions used to create the molecular orbitals, which are expanded as a linear combination of such functions with the weights or coefficients to be determined. Usually these functions are atomic orbitals, in that they are centered on atoms, but functions centered in bonds or lone pairs have been used as have pairs of functions centered in the two lobes of a p orbital.  
 
Different Atomic basis sets are available:

  • STO: Slater Type Orbitals
    In the STO-NG method the 1s, 2s and 2p Slater functions are expanded in a set of N primitive Gaussians where N=1,2,..., 6 corresponding to STO-1G, STO-2G, ..., STO-6G
  • GTO: Gaussian Type Orbitals
    • Primary weakness of GTO functions is that their radial derivative vanishes at the nucleas. It is common to combine two or three or more GTO's into a contracted GTO or CGTO.
    • Gaussians have no cusp at the nucleus. Several Gaussian-type primitives are contracted to appoximate the cusp.

  • STO-3G
    These bases are constructed by least-squares fitting GTOs to STOs which have been optimized for various electronic states of the atom. When three GTOs are employed to fit each STO, a STO-3G basis is formed.
  • minimal basis
    • In a minimal basis the number of STO orbitals is equal to the number of core and valence AOs in the atom.
    • In the minimal basisset a basisfunction is an AO obtained from atomic calculation and kept fixed in the molecular calculations.

  • extended basis
    • In a extended basis a basis function is a linear combination of several basis functions. The coefficients in this combination can vary in the molecular calculation. In this way it is possible to achieve good description of the AOs in an isolated atom and a good description of MOs in a molecule.
    • Basis functions of different spatial extent are combined to describe a valence orbital. These basis sets provide greater flexibility.

  • DZ: Double zeta basis sets
    Each orbital is expressed as the sum of 2 STO's. Twice as many STO or CGTO's are used as there are core and valence AO's.
  • TZ: Triple zeta basissets.
    Three times as many STO's or CGTO's are used as there are core and valence AO's.
  • Split valence basis sets
    Improving the minimal basis set where extra functions are used for each valence atomic orbital. Doubling functions on the core orbitals may not be so useful as we do in double zeta.  
  • ANO: Atomic natural orbital basis sets
    Generally contracted basissets.
    ANO basis sets are formed by contracting Gaussian functions so as to reproduce the natural orbitals obtained from correlated (usually using a configuration interaction with single and double excitation (CISD) level wavefunction) calculations on atoms.
  • Even tempered basissets.
     
    Split valence basis sets are denoted K-LMG where K, L and M are integers:
    K=number of gaussians summed to describe the inner shell orbital
    L=number of gaussian functions that comprise the first STO of the double zeta.
    M=number of gaussian functions summed in the second STO.

 
See also:
Basis set (chemistry)
http://en.wikipedia.org/wiki/Basis_set_(chemistry)
Background Reading for Basis Sets
http://www.shodor.org/chemviz/basis/teachers/background.html
Molcas basissets
http://www.teokem.lu.se/molcas/basis/64/list.html
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« Last Edit: 11.09.09 at 22:01:08 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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Re: Basis sets
Reply #1 - 06.03.08 at 11:03:44
 
Minimum basisset
 
A minimum basis set is one in which, on each atom in the molecule, a single basis function is used for each orbital in a Hartree-Fock calculation on the free atom.
 
The most common addition to minimal basis sets is probably the addition of polarization functions, denoted by an asterisk, *. Two asterisks, **, indicate that polarization functions are also added to light atoms (hydrogen and helium). These are auxiliary functions with one additional node. For example, the only basis function located on a hydrogen atom in a minimal basis set would be a function approximating the 1s atomic orbital. When polarization is added to this basis set, a p-function is also added to the basis set.
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« Last Edit: 06.03.08 at 11:05:26 by Gerrit-Jan Linker »  

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Re: Basis sets
Reply #2 - 06.03.08 at 11:12:15
 
STO-nG basisset
 
The most common minimal basis set is STO-nG, where n is an integer. This n 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.  
 
Commonly used minimal basis sets of this type are:
STO-3G
STO-4G
STO-6G
STO-3G* - Polarized version of STO-3G
STO-3G** - Polarisation functions also added for light atoms
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Re: Basis sets
Reply #3 - 06.03.08 at 11:19:49
 
X-YZG / split valence basissets
 
The notation for the split-valence basis sets arising from the group of John Pople is typically X-YZg.  
-X represents the number of primitive Gaussians comprising each core atomic orbital basis function.  
-Y and Z indicate that the valence orbitals are composed of two basis functions each, the first one composed of a linear combination of Y primitive Gaussian functions, the other composed of a linear combination of Z primitive Gaussian functions.  
 
In this case, the presence of two numbers after the hyphens implies that this basis set is a split-valence double-zeta basis set.  
 
Split-valence triple- and quadruple-zeta basis sets are also used, denoted as X-YZWg, X-YZWVg, etc.  
 
Here is a list of commonly used split-valence basis sets of this type:
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*
 
Example H 6-31G**:
H: 1s1
Core shell: none
Valence shell: 1s -> Nr Basisfunctions=2, Nr Primitives=3+1
Diffuse function: p -> Nr Basisfunctions=1, Nr Primitives=1
Total:  
s: 2 basisfunctions, 4 primitives
p: 1 basisfunction, 1 primitive
 
Example C 6-31G**:
C 1s22s22p2
Core shell: 1s -> Nr Basisfunctions=1, Nr Primitives=6
Valence shell: 2s+2p -> Nr Basisfunctions=2, Nr Primitives=3+1
Diffuse function: d -> Nr Basisfunctions=1, Nr Primitives=1
Total:
s: 3 basisfunctions, 10 primitives
p: 2 basisfunctions, 4 primitives
d: 1 basisfunction, 1 primitive
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« Last Edit: 22.02.12 at 13:08:05 by Gerrit-Jan Linker »  

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Molcas ANO Basis sets
Reply #4 - 18.09.08 at 09:15:14
 
Molcas ANO Basis sets
 

  • ANO-DK3:
    Reference state: atomic ground states
    Relativistic effects: The scalar relativistic third-order Douglas-Kroll(DK3) method
    Primitive functions: Optimized by the total energy minimization in DK3-SCF              
    Contraction: Taken from the DK3-SCF orbital coefficients  
     
    References:
    http://www.teokem.lu.se/molcas/basis/64/ANO-DK3.txt
    Takashi Tsuchiya, Minori Abe, Takahito Nakajima and Kimihoko Hirao, J. Chem. Phys., 115, 4463 (2001)
  • ANO-L: Large ANO basissets
    Basic primitive: Duijneveldt
    Basis is augmented with diffuse functions optimised with SDCI and other methods.
     
    References:
    http://www.teokem.lu.se/molcas/basis/64/ANO-L.txt
    P.-O. Widmark, P.-A. Malmqvist, and B. O. Roos
    Theor. Chim. Acta 77, 291 (1990)
  • ANO-RCC: Large ANO basissets.
    For some atoms this basisset is the same as ANO-L. They are contracted using the Douglass Kroll Hamiltonian and should only be used in calculations where scalar relativistic effects are included.
     
    References:
    P.-O. Widmark, P.-A. Malmqvist, and B. O. Roos
    Theor. Chim. Acta 77, 291 (1990)
    http://www.teokem.lu.se/molcas/basis/64/ANO-RCC.txt
  • ANO-S: Small ANO basis sets
    These basissets have been constructed by averaging over several electronic configurations: ground state and one or more of the following: valence excited states, ground state for the anion and ground state for the cation.
     
    References:
    K. Pierloot, B. Dumez, P.-O. Widmark and B. O. Roos
    Theor. Chim. Acta 90, 87 (1995)
    http://www.teokem.lu.se/molcas/basis/64/ANO-S.txt

See also:
Molcas 6.4. basissets
http://www.teokem.lu.se/molcas/basis/64/list.html
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« Last Edit: 18.09.08 at 15:34:17 by Gerrit-Jan Linker »  

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One-particle basis, N-particle basis
Reply #5 - 26.12.09 at 10:49:01
 
One-particle basis, N-particle basis
 
A one-particle basis (one-electron basis) refers to the basis set. This limits the description of the one-electron functions; the Molecular Orbitals.
 
The size of the many electron basis (N-particle basis) refers to the number of Slater determinants. This limits the description of electron correlation.
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Basisset exchange portal
Reply #6 - 10.02.11 at 16:52:57
 
Basisset exchange portal
 
https://bse.pnl.gov/bse/portal
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