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Frozen-core Calculations

By default, calculations with CFOUR are carried with all electrons and all orbitals correlated. Frozen-core calculations (with valence electrons correlation alone) can be performed with


or by explicitly specifying the orbitals to be dropped from the correlation treatment via

DROPMO=n1-n2 ...n3>n4...

The numbers supplied with the DROPMO keyword (separated by a dash) specify the orbitals to be dropped, whereby n3>n4 means that all orbitals from n3 through n4 inclusive are dropped. Note that the orbitals are numbered in ascending order from the most stable to the most unstable.

For UHF-type calculations, the appropriate orbitals (which are not identical) are deleted for both spin cases.

In ROHF-type calculations, the definition of the frozen-core orbitals depend on whether standard or semi-canonical orbitals are used, as the transformation to the semi-canonical representation is carried out with the full set of orbitals (this for example is done differently in MOLPRO, where just the correlated orbitals are transformed to a semi-canonical representation; therefore, there are slight differences in ROHF-CCSD(T) energies obtained with CFOUR and MOLPRO when freezing orbitals).

Dropped orbitals are allowed for energy as well as analytic first and second derivative calculations, though the implementation for analytic derivative is currently not the most efficient.

General Remarks

Correlated calculations are often performed with only a subset of the molecular orbitals included in the correlation treatment.

Common choices are:

  • all-electron (ae) calculations involving all electrons and all

(occupied as well as virtual) orbitals in the correlation treatment;

  • frozen-core (fc) calculations considering only the valence

electrons in the correlated calculations in the sense that only the occupied valence orbitals together with all virtual orbitals are included in the correlation treatment.

Besides these two common choices, any other choice in principle is also possible, though often less meaningful.


The default is to perform all-electron (ae) calculations, while with the keyword


a standard frozen-core (fc) calculation is invoked (note that some care is required for heavier elements, alkaline as well as alkaline earth elements concerning the appropriate definition of the core orbitals).

Standard frozen cores

Using the FROZEN_CORE=ON keyword, the following definitions for the core are applied:

H, HE: no core orbitals
Li-Ne: 1 core orbital
Na-Ar: 5 core orbitals
K-Zn: 9 core orbitals
Ga-Kr: 14 core orbitals
Rb-Cd: 18 core orbitals
In-Xe: 23 core orbitals

  1. Recommendation

In general, frozen-core calculations should be performed with so-called valence basis sets, while all-electron calculations necessitate the use of so-called core-polarized basis sets. In the case of the correlation-consistent basis-sets of Dunning, the cc-pVXZ sets are well suited for fc calculations, while the cc-pCVXZ sets are the appropriate choice for ae calculations.


The information about the dropped molecular orbitals is stored on the following JOBARC records. Record NUMDROPA contains the total number of dropped orbitals, while the records MODROPA and MODROPB contain the indices of the corresponding alpha and beta molecular orbitals to be dropped (ordered in ascending order according to the orbital energies).

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Page last modified on August 19, 2011, at 12:19 AM
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CFOUR is partially supported by the U.S. National Science Foundation.