25.2.4 Keyword for frozen core approximation

Orbitals for the frozen core approximation in post-HF and post-KS calculations can be specified in the data group $freeze in four alternative formats which might be usefull for different types of applications.

In the most explicit format the indices of the frozen orbitals are spefied per irreducible representation:

$freeze
 a1g     1-2
 t1u     1

In general, these can be occupied orbitals for a frozen core and/or virtual orbitals for anti-core orbitals that should be excluded from calculations of correlation and/or excitation energies.

A more compact definition of the number of frozen occupied and virtuals orbitals is possible with the implicit option:

$freeze
 implicit core=5 virt=2

This will freeze the 5 energetically lowest occupied and 2 highest virtual orbitals (alpha and beta count as one in UHF cases). Note that for degenerate orbitals each degenerate component is counted.

Since version 7.7 two additional options are available to determine the number of frozen core orbitals automatically.

With the format

$freeze
  fpc=-3.0  fpv=50.0

all orbitals with energies below \(-3.0\) Hartree or above 50.0 Hartree will be frozen. If the option fpv is left out, only orbitals below \(-3.0\) Hartree will be frozen. If both options are used that have to be specified on the same line. The values should be chosen such that the energy gaps between frozen and non-frozen orbitals are sufficiently large. This is in particular important for the calculation of reaction energies and potential energy curves or surfaces to ensure that a consistent number of orbitals and, as much as possible, also orbitals of the same shape are frozen for products and educts or all structures.

Alternatively, the option

$freeze
   defcore

can be used to request a default frozen core. The number of frozen core orbitals will then be determined from the atomic symbols and charges according to the table below. It corresponds approximately, although not strictly to a freezing point of \(-3\) Hartree. Dummy atoms or atoms with charges below 3.2 au will be ignored in when determination of the default frozen core. If atomic charges are modified with charge option in the $atoms data group, the size of the suggest default core should be checked carefully. Additional information about the number of core orbitals included per atom can be obtained by adding two or more question marks in the line with $freeze.

Note that this scheme will likely not work for systems that mix atoms with charges just below the next larger core is used with such that are just above such a value as e.g. Co and Ni. In such cases alternative freezing points can be set for the the option fpc.

Limitations:

• Freezing of virtual orbitals is not supported by mpgrad and not by the by F12 methods implemented in ccsdf12, ricc2, and pnoccsd.

• The calculation of gradients in mpgrad does not support frozen occupied or virtuals orbitals.

• For the limitations regarding frozen orbitals GW calculations see Sec. 14

Default core orbitals:

Be–Mg

(2) [He] core: \(1s^2\)

Al–Co

(10) [Ne] core: \(1s^2 2s^2 2p^6\)

Ni–Kr

(18) [Ar] core: \(1s^2 2s^2 2p^6 3s^2 3p^6\)

Rb–Rh

(28) [Ni] core: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10}\)

Pd–Cd

(30) [Zn] core: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2\)

In–Ba

(36) [Kr] core: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6\)

La–Ir

(46) [Pd] core: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10}\)

Pt–Hg

(62) [Pd] \(4f^{14} 5s^2\) core: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2\)

Tl–Ra

(68) [Pd] \(4f^{14} 5s^2 5p^6\) core: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2 5p^6\)

Ac–Lr

(78) [Pt] core: \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2 5p^6 5d^{10}\)