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Pseudopotentials


 

Huzinaga style Model Potentials

There are two forms of pseudopotential which can be used in Cadpac - the first is due to Huzinaga et. al. , the second is the Hay-Wadt form. (Note editions of Cadpac earlier than Cadpac6.0 only had the Huzinaga form). The Huzinaga version exists only for the transition elements. The precise form of potential is that called 'Model Potentials' by Huzinaga and co-workers. A full definition of the form and parameters of these potentials for the transition elements can be found in,

Y. Sakai, E. Miyoshi, M. Klobukowski and S. Huzinaga, J. Comp. Chem., 8 (1987) 226

Y. Sakai, E. Miyoshi, M. Klobukowski and S. Huzinaga, J. Comp. Chem., 8 (1987) 256

The actual parameters incorporated into Cadpac were obtained from a tape kindly supplied by Dr Y Sakai, thereby eliminating the very real possibility of transcription errors.

The potentials are simple to use. Consider the following dataset for CuF2.

TITLE
COPPER FLUORIDE with Huzinaga model potentials
ATOMS
    COPPER 29  0     0     0
    MP
    LIBRARY CUVAL1
    END
    FLUORINE  9   3.3 0.0 0.0
    LIBRARY FSTO3G
    END
    FLUORINE  9  -3.3 0.0 0.0
    LIBRARY FSTO3G
    END
END
CHARGE 1
OPTIMISE
START
SECDER
START
FINISH
This would perform a geometry optimisation on CuF2+ followed by a force constant calculation. There are two forms of model potential in the library for each atom. The simplest uses a valence shell of just 3D and 4S electrons; a slightly more complicated version has the valence shell 3P, 3D and 4S (or the equivalent for second and third transition series). The first of these two forms is indicated by the line

MP

in the dataset. The valence basis functions are taken from the library set indicated CUVAL1.

This is in fact a minimal basis set. Expanded out it would be

1 S 5
1           8.36994    0.0942563
2           2.09394   -0.1987078
3           0.89379   -0.1089926
4           0.10244    0.5912877
5           0.03639    0.5066644
2 D 5
1          38.42241    0.0441537
2           9.91260    0.2423669
3           3.12112    0.4533707
4           0.95779    0.4312863
5           0.26013    0.2111950
This is probably too rigid a contraction and it would be better to use a double-zeta type valence basis set. Double- zeta basis sets are not explicitly in the library but can be easily constructed by uncontracting the minimal set , for example giving
MP
1 S 4
1           8.36994    0.0942563
2           2.09394   -0.1987078
3           0.89379   -0.1089926
4           0.10244    0.5912877
2 S 1
1           0.03639    0.5066644
3 D 4
1          38.42241    0.0441537
2           9.91260    0.2423669
3           3.12112    0.4533707
4           0.95779    0.4312863
4 D 1
1           0.26013    0.2111950
Although it is a little inconvenient for the user, it was felt that it would be better just to include the minimal contractions in the library as these were obtained straight from the tape and thus constitute a definitive, error free, record of the exponents and contraction coefficients. If it is wished to use less strict contractions, such as the double- zeta example given, then it is advisable to copy the minimal basis from the library and edit it as shown.

The entire dataset equivalent to the job above , but with a double-zeta basis set would be,

TITLE
COPPER FLUORIDE with Huzinaga model potentials
ATOMS
    COPPER 29  0     0     0
    MP
1 S 4
1           8.36994    0.0942563
2           2.09394   -0.1987078
3           0.89379   -0.1089926
4           0.10244    0.5912877
2 S 1
1           0.03639    0.5066644
3 D 4
1          38.42241    0.0441537
2           9.91260    0.2423669
3           3.12112    0.4533707
4           0.95779    0.4312863
4 D 1
1           0.26013    0.2111950
    END
    FLUORINE  9   3.3 0.0 0.0
    LIBRARY FDZ
    END
    FLUORINE  9  -3.3 0.0 0.0
    LIBRARY FDZ
    END
END
CHARGE 1
OPTIMISE
START
SECDER
START
FINISH
The alternative form of the Huzinaga model potential, including the outermost P shell in the valence set is denoted

MPP

for example

TITLE
COPPER  OXIDE with smaller core Huzinaga potential
VARIABLES
R 3.505
T 75 D
END
SYMMETRY
CNV 2
END

ATOMS
COPPER 29  POL    R   T   0
MPP
LIBRARY CUVAL2
END
O 8 0 0 0
LIBRARY ODZ
END
END
OPTIMISE
START
FINISH
The valence basis sets in this case are called CUVAL2 etc. This is again a minimal contraction. It corresponds to
1 S 6
1         314.08700   -0.0236046
2          13.10480    0.1206648
3           2.09401   -0.1933212
4           0.89383   -0.1771614
5           0.10244    0.6125991
6           0.03639    0.4938715
1 P 4
1         143.79000   -0.0777300
2          30.24590   -0.3009129
3           2.89393    0.6802534
4           0.91170    0.4058118
1 D 5
1          38.42240    0.0546633
2           9.91260    0.2341039
3           3.12112    0.4409421
4           0.95779    0.4415061
5           0.26013    0.2208893
and again it will be better to use a more flexible valence shell, which can be obtained by uncontracting the library set. Eg
1 S 5
1         314.08700   -0.0236046
2          13.10480    0.1206648
3           2.09401   -0.1933212
4           0.89383   -0.1771614
5           0.10244    0.6125991
2 S 1
1           0.03639    0.4938715
3 P 3
1         143.79000   -0.0777300
2          30.24590   -0.3009129
3           2.89393    0.6802534
4 P 1
1           0.91170    0.4058118
5 D 4
1          38.42240    0.0546633
2           9.91260    0.2341039
3           3.12112    0.4409421
4           0.95779    0.4415061
6 D 1
1           0.26013    0.2208893
Notation for the basis sets for other transition elements follows that for Cu given above.

It is possible to add single or double sets of polarisation functions to the valence basis sets. Suitable exponents are given in the papers by Sakai et. al. referenced above.

All of the types of energy, geometry optimisation, force constant and property calculations in Cadpac can make use of model potential basis sets. If doing calculations on the third transition series it will be necessary to specify the nuclear masses if you wish to calculate frequencies, as there are no default values for the isotope masses in the current program for these nuclei.

For an example of the potentials in use in Cadpac see, Chemical Physics Letters vol 163 page 151 (1989)

Hay-Wadt style pseudopotentials

It is also possible to use the alternative Hay-Wadt potentials. These exist for more atoms than the Huzinaga model potentials, but have the restriction that the implementation in Cadpac cannot do analytic force constants (it is also much slower than the Huzinaga potentials)

The Hay-Wadt potentials exist in forms with a large and a small core. The form with the larger core is denoted

ECP1

that with the smaller core is denoted

ECP2

as an example here is the copper oxide case given previously, but this time with the potential ECP1 and the corresponding valence set, denoted CUECP1

TITLE
COPPER  OXIDE with Hay-Wadt pseudopotenials
VARIABLES
R 3.505
T 75 D
END
SYMMETRY
CNV 2
END

ATOMS
COPPER 29  POL    R   T   0
ECP1
LIBRARY CUECP1
END
O 8 0 0 0
LIBRARY ODZ
END
END
OPTIMISE
START
FINISH
As an example of the Hay-Wadt potential with the smaller core,
TITLE
NI(CO)4
SYMMETRY
TD
END
VARIABLES
A  2.00491138
B  3.29886631
END
ATOMS
NI 28 0 0 0
ECP2
LIBRARY NIECP2
END
C 6 A A A
LIBRARY CDZ
END
O 8 B B B 
LIBRARY ODZ
END
END
OPTIMISE
START
FINISH
Note that the valence set corresponding to this potential is call NIECP2. Similar naming conventions hold for the other elements.
 


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