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The following example of basis set input are followed by the printed output.
Si, Pople STO-3G minimal basis set. The value of the scale factor "0." means standard Pople scale factor.
14 3 1 0 3 2. 0. 1 1 3 8. 0. 1 1 3 4. 0. ******************************************************************************* ATOM X(AU) Y(AU) Z(AU) NO. TYPE EXPONENT S COEF P COEF D/F/G ******************************************************************************* 1 SI 1.280 1.280 1.280 1 S 4.078E+02 1.543E-01 0.000E+00 0.000E+00 7.428E+01 5.353E-01 0.000E+00 0.000E+00 2.010E+01 4.446E-01 0.000E+00 0.000E+00 2- 5 SP 2.319E+01-9.997E-02 1.559E-01 0.000E+00 5.390E+00 3.995E-01 6.077E-01 0.000E+00 1.753E+00 7.001E-01 3.920E-01 0.000E+00 6- 9 SP 1.479E+00-2.196E-01 1.059E-02 0.000E+00 4.126E-01 2.256E-01 5.952E-01 0.000E+00 1.615E-01 9.004E-01 4.620E-01 0.000E+00 ******************************************************************************* The adjoined gaussian exponent is underlined. |
The standard Pople scale factor is used for STO-nG basis set when the input scale factor is 0.0. If the input scale factor is 1.0, then the same exponents are attributed to all the atoms of the same row.
Si, Pople 6-21G split valence basis set
14 4 2 0 6 2. 1. 2 1 6 8. 1. 2 1 2 4. 1. 2 1 1 0. 1. ******************************************************************************* ATOM X(AU) Y(AU) Z(AU) NO. TYPE EXPONENT S COEF P COEF D/F/G ******************************************************************************* 1 SI 1.280 1.280 1.280 1 S 1.612E+04 1.959E-03 0.000E+00 0.000E+00 2.426E+03 1.493E-02 0.000E+00 0.000E+00 5.539E+02 7.285E-02 0.000E+00 0.000E+00 1.563E+02 2.461E-01 0.000E+00 0.000E+00 5.007E+01 4.859E-01 0.000E+00 0.000E+00 1.702E+01 3.250E-01 0.000E+00 0.000E+00 2- 5 SP 2.927E+02-2.781E-03 4.438E-03 0.000E+00 6.987E+01-3.571E-02 3.267E-02 0.000E+00 2.234E+01-1.150E-01 1.347E-01 0.000E+00 8.150E+00 9.356E-02 3.287E-01 0.000E+00 3.135E+00 6.030E-01 4.496E-01 0.000E+00 1.225E+00 4.190E-01 2.614E-01 0.000E+00 6- 9 SP 1.079E+00-3.761E-01 6.710E-02 0.000E+00 3.024E-01 1.252E+00 9.569E-01 0.000E+00 10- 13 SP 9.334E-02 1.000E+00 1.000E+00 0.000E+00 ******************************************************************************* The adjoined gaussian exponent is underlined |
Si, Pople 6-21G split valence basis set modified for crystalline calculation
14 4 2 0 6 2. 1. 2 1 6 8. 1. 2 1 2 4. 1. 0 1 1 0. 1. 0.1233392 1. 1. ******************************************************************************* ATOM X(AU) Y(AU) Z(AU) NO. TYPE EXPONENT S COEF P COEF D/F/G ******************************************************************************* 1 SI 1.280 1.280 1.280 1 S 1.612E+04 1.959E-03 0.000E+00 0.000E+00 2.426E+03 1.493E-02 0.000E+00 0.000E+00 5.539E+02 7.285E-02 0.000E+00 0.000E+00 1.563E+02 2.461E-01 0.000E+00 0.000E+00 5.007E+01 4.859E-01 0.000E+00 0.000E+00 1.702E+01 3.250E-01 0.000E+00 0.000E+00 2- 5 SP 2.927E+02-2.781E-03 4.438E-03 0.000E+00 6.987E+01-3.571E-02 3.267E-02 0.000E+00 2.234E+01-1.150E-01 1.347E-01 0.000E+00 8.150E+00 9.356E-02 3.287E-01 0.000E+00 3.135E+00 6.030E-01 4.496E-01 0.000E+00 1.225E+00 4.190E-01 2.614E-01 0.000E+00 6- 9 SP 1.079E+00-3.761E-01 6.710E-02 0.000E+00 3.024E-01 1.252E+00 9.569E-01 0.000E+00 10- 13 SP 1.233E-01 1.000E+00 1.000E+00 0.000E+00 ******************************************************************************* |
Si, Pople 3-21G split valence basis set
14 4
2 0 3 2. 1.
2 1 3 8. 1.
2 1 2 4. 1.
2 1 1 0. 1.
*******************************************************************************
ATOM X(AU) Y(AU) Z(AU) NO. TYPE EXPONENT S COEF P COEF D/F/G
*******************************************************************************
1 SI 1.280 1.280 1.280
1 S
9.107E+02 6.608E-02 0.000E+00 0.000E+00
1.373E+02 3.862E-01 0.000E+00 0.000E+00
2.976E+01 6.724E-01 0.000E+00 0.000E+00
2- 5 SP
3.667E+01-1.045E-01 1.134E-01 0.000E+00
8.317E+00 1.074E-01 4.576E-01 0.000E+00
2.216E+00 9.514E-01 6.074E-01 0.000E+00
6- 9 SP
1.079E+00-3.761E-01 6.710E-02 0.000E+00
3.024E-01 1.252E+00 9.569E-01 0.000E+00
10- 13 SP
9.334E-02 1.000E+00 1.000E+00 0.000E+00
*******************************************************************************
|
Si, Pople 3-21G split valence + polarization basis set
14 5 2 0 3 2. 1. 2 1 3 8. 1. 2 1 2 4. 1. 2 1 1 0. 1. 2 3 1 0. 1. ******************************************************************************* ATOM X(AU) Y(AU) Z(AU) NO. TYPE EXPONENT S COEF P COEF D/F/G ******************************************************************************* 1 SI 1.280 1.280 1.280 1 S 9.107E+02 6.608E-02 0.000E+00 0.000E+00 1.373E+02 3.862E-01 0.000E+00 0.000E+00 2.976E+01 6.724E-01 0.000E+00 0.000E+00 2- 5 SP 3.667E+01-1.045E-01 1.134E-01 0.000E+00 8.317E+00 1.074E-01 4.576E-01 0.000E+00 2.216E+00 9.514E-01 6.074E-01 0.000E+00 6- 9 SP 1.079E+00-3.761E-01 6.710E-02 0.000E+00 3.024E-01 1.252E+00 9.569E-01 0.000E+00 10- 13 SP 9.334E-02 1.000E+00 1.000E+00 0.000E+00 14- 18 D 4.500E-01 0.000E+00 0.000E+00 1.000E+00 ***************************************************************************** |
Si, user defined basis set derived from Pople 6-21G
14 4 0 0 6 2. 1. 16115.9 0.00195948 2425.58 0.0149288 553.867 0.0728478 156.340 0.24613 50.0683 0.485914 17.0178 0.325002 0 1 6 8. 1. 292.718 -0.0027809 0.0044383 69.8731 -0.0357146 0.0326679 22.3363 -0.114985 0.134721 8.15039 0.0935634 0.328678 3.13458 0.603017 0.449640 1.22543 0.418959 0.261372 0 1 2 4. 1. 1.07913 -0.376108 0.067103 0.302422 1.25165 0.956883 0 1 1 0. 1. 0.123 1. 1. ******************************************************************************* ATOM X(AU) Y(AU) Z(AU) NO. TYPE EXPONENT S COEF P COEF D/F/G ******************************************************************************* 1 SI 1.280 1.280 1.280 1 S 1.612E+04 1.959E-03 0.000E+00 0.000E+00 2.426E+03 1.493E-02 0.000E+00 0.000E+00 5.539E+02 7.285E-02 0.000E+00 0.000E+00 1.563E+02 2.461E-01 0.000E+00 0.000E+00 5.007E+01 4.859E-01 0.000E+00 0.000E+00 1.702E+01 3.250E-01 0.000E+00 0.000E+00 2- 5 SP 2.927E+02-2.781E-03 4.438E-03 0.000E+00 6.987E+01-3.571E-02 3.267E-02 0.000E+00 2.234E+01-1.150E-01 1.347E-01 0.000E+00 8.150E+00 9.356E-02 3.287E-01 0.000E+00 3.135E+00 6.030E-01 4.496E-01 0.000E+00 1.225E+00 4.190E-01 2.614E-01 0.000E+00 6- 9 SP 1.079E+00-3.761E-01 6.710E-02 0.000E+00 3.024E-01 1.252E+00 9.569E-01 0.000E+00 10- 13 SP 1.230E-01 1.000E+00 1.000E+00 0.000E+00 ****************************************************************************** |
| Si Basis set | AO | exponent | Total energy bulk silicon | SCF cycles | Million. biel integrals | CPU integrals | CPU total |
|
sto-3g |
9 | 0.1315 |
-5.713207531E+02 |
8 |
0.11 | 2.46 | 3.22 |
|
3-21 |
13 | 0.09334 |
-5.748914299E+02 |
9 |
0.86 | 26.38 | 28.70 |
|
3-21+d |
18 | 0.09334 |
-5.749481876E+02 |
9 |
2.04 | 53.19 | 57.70 |
|
6-21 |
13 | 0.09334 |
-5.778250380E+02 |
10 |
0.92 | 30.04 | 32.75 |
|
6-21mod |
13 | 0.1233 |
-5.778265558E+02 |
9 |
0.58 | 12.80 | 14.75 |
|
free.out |
13 | 0.123 |
-5.778265813E+02 |
9 |
0.58 | 12.81 | 14.74 |
The table shows for bulk Silicon how the value of the exponent of the lowest exponent
gaussian influence the computational resources and the total energy, when all other
computational parameters are fixed. The crystalline basis functions are the Bloch
functions, built with localized functions, the AOs. The diffuse functions, very
important to describe the tails of the electron density in a molecular systems,
are useless in an infinite system, increase the computational cost, but do not
improve the wave function.
Crystalline atomic basis sets are built starting from an atomic basis set
optimized for molecules, and reoptimizing the exponent of the most diffuse
GTF.
