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 FINISHThis 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 0.2111950This 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 0.2111950Although 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 FINISHThe 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 FINISHThe 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 0.2208893and 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 0.2208893Notation 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)
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 FINISHAs 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 FINISHNote that the valence set corresponding to this potential is call NIECP2. Similar naming conventions hold for the other elements.