The correlation consistent (cc) basis sets are popular in high-accuracy wavefunction based quantum chemistry, partly due to their regular energy convergence characteristics allowing for a systematic pathway for increasing the accuracy of a calculation and enabling convenient complete basis set extrapolation techniques. The cc basis sets are:
- Energy optimized. They are not fit to given experimental data.
- Generally contracted for the functions describing the occupied orbitals (the HF wavefunction).
- Modular. Additional functions can be added to address specific chemical problems.
- Based on spherical (rather than Cartesian) orbitals.
Decoding the abbreviations
Correlation consistent polarised valence n zeta basis sets are usually abbreviated as cc-pVnZ. However, many basis sets within the correlation consistent family also have abbreviations based upon this "parent". Some of the more common ones are:
- aug-cc-pVnZ: These basis sets augment the parent set with an extra diffuse function in each orbital angular momentum. This can be useful for the description of electron affinities and intermolecular interactions, amongst others.
- d-aug-cc-pVnZ: Doubly augmented with diffuse functions. Applications might include diffuse Rydberg states.
- cc-pCVnZ: These basis sets possess additional functions for the description of core-valence effects. Standard cc basis sets should only be used for correlating valence electrons with wavefunction based methods (i.e., with the frozen core approximation). Note, the cc-pCVnZ sets are only designed for outer-core correlation, electrons below the next to largest noble gas core should still be frozen. E.g., 1s electrons for Na-Ar should remain frozen.
- cc-pwCVnZ: These weighted core-valence basis sets emphasise the correlation of core-valence pairs as opposed to core-core pairs. In general this leads to faster convergence of spectroscopic properties and should be used in preference to cc-pCVnZ.
- cc-pV(n+d)Z: These basis sets for the second row atoms Na–Ar include an extra set of tight d functions. This greatly improves the performance of the basis sets and should always be used for these atoms. Note, there are no cc-pCV(n+d)Z bases as the core-valence sets already include tight d functions.
- cc-pVnZ-DK: These all-electron basis sets have been developed for use with Douglas-Kroll-Hess Hamiltonians (for the calculation of scalar relativistic effects). They should not be used without a DKH Hamiltonian.
- cc-pVnZ-X2C: These all-electron basis sets have been developed for use with eXact-2-Component Hamiltonians (for the calculation of scalar relativistic effects). They should not be used without an X2C Hamiltonian.
- cc-pVnZ-PP: These basis sets have been designed to be used with specific pseudopotentials (also known as ECPs) replacing the inner-core electrons. These are typically the small-core relativistic PPs of the Stuttgart-Köln variety.
- cc-pVnZ-F12: These basis sets are designed to be used specifically with explicitly correlated (F12) methods. In addition to F12 specific polarizing functions, these sets also have additional functions to prevent the HF basis set error becoming larger than the basis set incompleteness error in the F12 correlation energy.
- seg-cc-pVnZ: These basis sets have been re-contracted to use a segmented contraction scheme, which may be more efficient in some quantum chemistry codes. The underlying primitive exponents are the same as in the non-seg set.
Auxiliary basis sets
Integral approximation techniques, such as density fitting in, e.g., DF-MP2, or the resolution of the identity in F12 methods, require auxiliary basis sets that are specifically matched to a given AO basis set. These auxiliary sets are often suffixed in the following manner:
- aug-cc-pVnZ/JKFit: For use in density fitting of Fock and exchange matrices in, e.g., the DF-HF method.
- aug-cc-pVnZ/MP2Fit: For use in density fitting of two-electron integrals in, e.g., the DF-MP2 method (sometimes referred to as RI-MP2).
- aug-cc-pVnZ/OptRI: For use in the resolution of the identity approximation of many-electron integrals in F12 methods.
- aug-cc-pVnZ/OptRI+: For use in the resolution of the identity approximation of many-electron integrals in F12 methods, adds a small number of additional functions to the OptRI auxiliary sets to maximise the CABS singles correction.
These auxiliary sets should not be used as standard AO basis sets.
Trivia
There is an academic family tree showing some of the links between people involved in the development of correlation consistent basis sets.
On a recent holiday, I cycled through a small village with a correlation-consistent basis set related name:
