Correlation Consistent Bases

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In correlation consistent bases (in short: cc-bases "correlation-consistent basis sets") is, to the computational chemistry used basis sets . The basis sets developed by Thom H. Dunning, Jr. are designed to systematically converge post- Hartree-Fock calculations to the entire base set limit using empirical extrapolation techniques .

nomenclature

The common designation of these basic sets is: cc-pVNZ ( N = D, T, Q, 5, 6, ...)

The "cc-p" stands for correlation-consistent polarized (German: correlation-consistent polarized), the V indicates that it is valence-only basic sentences. " NZ " shows the number of zeta functions . It is therefore a cc basis with polarized valence-based double / triple / quadruple / ... zeta functions.

Examples

The cc bases are widely used and the current state of the art for correlated or post-Hartree-Fock calculations. Examples of cc basic sets are:

  • cc-pVDZ - Double-zeta
  • cc-pVTZ - Triple-zeta
  • cc-pVQZ - quadruple zeta
  • cc-pV5Z - quintuple zeta
  • aug-cc-pVDZ etc. - Extended versions of the previous basic sets with additional diffuse functions
  • cc-pCVDZ - Double-zeta with core correlation

extension

For the atoms of the third period (aluminum to argon), it has been found that additional functions are necessary, which is why the cc-pV (N + d) Z basis sets were developed. Even larger atoms require the use of pseudopotential-based basis sets, cc-pVNZ-PP, or the relativistically contracted Douglas-Kroll basis sets cc-pVNZ-DK.

While the Dunning basic sets are only used for valence-only calculations, they can be expanded to describe the correlation of the nuclear electrons with other functions. These core-valence basic sets (CV), cc-pCVXZ, can be used to form an approximation for the solution of the all-electron problem and are necessary for accurate calculations of geometry and core properties. The cc-pCVDZ basic set also has a tight- s function and a tight- p function, cc-pCVTZ also has 2s2p1d -tight functions, cc-pCVQZ has 3s3p2d1f and cc-pCV5Z also 4s4p3d2f1g -tight functions on.

In addition, the use of weighted core-valence basic rates (cc-pwCVXZ) has recently been recommended. These weighted basis sets aim to include the core-valence interaction, neglecting the core-core interactions, in order to obtain similarly accurate geometries as with the cc-pCVXZ basis sets, but at a lower cost.

In addition, diffuse functions can be added to the above-mentioned basic sets in order to enable a better description of anions and remote interactions (e.g. van der Waals forces ) or to enable calculations of electronic excitation states or field properties. Since it is well known how further augmented functions have to be set up, at least five different ones have been used in calculations in the specialist literature on the second hyperpolarizability . Due to the detailed construction of these basic sets, an extrapolation can be carried out for almost every energy problem.

Number of functions of selected basic sets

H-Hey Li-Ne Na-Ar
cc-pVDZ [2 s 1 p ] → 5 functions [3 s 2 p 1 d ] → 14 functions [4 s 3 p 1 d ] → 18 functions
cc-pVTZ [3 s 2 p 1 d ] → 14 functions [4 s 3 p 2 d 1 f ] → 30 functions [5 s 4 p 2 d 1 f ] → 34 functions
cc-pVQZ [4 s 3 p 2 d 1 f ] → 30 functions [5 s 4 p 3 d 2 f 1 g ] → 55 functions [6 s 5 p 3 d 2 f 1 g ] → 59 functions
aug-cc-pVDZ [3 s 2 p ] → 9 functions [4 s 3 p 2 d ] → 23 functions [5 s 4 p 2 d ] → 27 functions
aug-cc-pVTZ [4 s 3 p 2 d ] → 23 functions [5 s 4 p 3 d 2 f ] → 46 functions [6 s 5 p 3 d 2 f ] → 50 functions
aug-cc-pVQZ [5 s 4 p 3 d 2 f ] → 59 functions [6 s 5 p 4 d 3 f 2 g ] → 80 functions [7 s 6 p 4 d 3 f 2 g ] → 84 functions

To understand how the number of functions can be found out, cc-pVDZ is shown here using the example of hydrogen: Two s - ( l = 0) and one p -orbital ( l = 1) are used. The latter has three possible components ( m L = −1,0,1) for the orbital angular momentum along the z -axis, which are related to p x , p y and p z . So there are a total of 5 spatially different orbitals. Each orbital can contain two electrons with opposite spins.

Argon, on the other hand, has 3 s orbitals ( l = 0) and two sets of p orbitals ( l = 1). The orbitals used in cc-pVDZ are [1s, 2s, 2p, 3s, 3s ', 3p, 3p', 3d '], where' stands for the added polarization orbitals. A total of four s orbitals (4 basis functions), three sets of three p orbitals each (9 basis functions) and one set of five spatially different d orbitals (5 basis functions) follow . Simple addition leads to the 18 functions of the cc-pVDZ basic set for argon.

disadvantage

Caution should be exercised when extrapolating energy differences: the Hartree-Fock energy converges exponentially, while the correlation energy only converges polynomially.

Individual evidence

  1. ↑ a b Dunning, Thomas H .: Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen . tape 90 , no. 2 . J. Chem. Phys., 1989, pp. 1007-1023 , doi : 10.1063 / 1.456153 .
  2. ^ A b Jensen, Frank: Introduction to computational chemistry . Third ed. Chichester West Sussex, UK, ISBN 978-1-118-82599-0 , pp. 206-207 .
  3. ^ Jensen, Frank: Introduction to computational chemistry . Third ed. Chichester West Sussex, UK, ISBN 978-1-118-82599-0 , pp. 222 .
  4. ^ Jensen, Frank: Introduction to computational chemistry . Third ed. Chichester West Sussex, UK, ISBN 978-1-118-82599-0 , pp. 219 .

The basic sentences discussed here and others are discussed in the sources below with reference to the original articles: