CHEM 6343 - Advanced Computational Chemistry
Lab Report 9
Polarizability and Basis Set
Yunwen Tao∗
April 1, 2015
1
∗
Graduate Student in CATCO group, Southern Methodist University, yunwent[at]smu.edu
A Pople basis set example (From http://www.shodor.org/chemviz/basis/teachers/background.
html)
1
1
CHEM 6343 - Advanced Computational Chemistry
1
Brief Introduction
In this lab, we are going to modify exponent information in two given basis sets according
to Speckman’s paper2 , and to check the modifications to the value of dipole momentum
and polarizability.
According to Spackman, two basis sets 6-311++G(d,p) and cc-pVQZ will be modified
after the optimization work done by him. We will do 6 calculations in total in this lab.
The first two is done with Restricted Hartree-Fock with STO-3G and 6-31G(d,p) basis
sets. Then, another two calculations with 6-311++G(d,p) and cc-pVQZ basis set will be
finished. In the end, calculations with modified 6-311++G(d,p) and cc-pVQZ basis sets
will be conducted.
2
Computational Details and Methodology
2.1
General Introduction
Generally, the calculation is not difficult but deserves patience especially in the modification of exponent values in basis set information. We will use Polar keyword to calculate
polarizability in Gaussian.
2.2
Calculation Setting-up
In this section, we will give explicit input information for each calculation.
2.2.1
Calculation I - 1
%chk=water1.chk
# opt freq hf/sto-3g geom=connectivity polar
Title Card Required
0 1
O
H
H
-5.37533823 -0.80245471
-4.41533823 -0.80245471
-5.69579282 0.10248112
0.00000000
0.00000000
0.00000000
1 2 1.0 3 1.0
2
3
2
Mark A. Spackman, Accurate prediction of static dipole polarizabilities with moderately sized basis
sets, J. Phys. Chem., 1989, 93 (22), pp 7594-7603
2
CHEM 6343 - Advanced Computational Chemistry
2.2.2
Calculation I - 2
%chk=water2.chk
# opt freq hf/6-31G(d,p) geom=connectivity polar
Title Card Required
0 1
O
H
H
-5.37533823 -0.80245471
-4.41533823 -0.80245471
-5.69579282 0.10248112
0.00000000
0.00000000
0.00000000
1 2 1.0 3 1.0
2
3
2.2.3
Calculation II - 1
%chk=water3.chk
# gfinput opt freq hf/6-311++G(d,p) geom=connectivity polar
Title Card Required
0 1
O
H
H
-5.37533823 -0.80245471
-4.41533823 -0.80245471
-5.69579282 0.10248112
0.00000000
0.00000000
0.00000000
1 2 1.0 3 1.0
2
3
Here we use the keyword gfinput to print the information of basis set for later modifications.
Here we print out this part of information in output.
1 0
6 1.00
0.000000000000
0.8588500000D+04 0.1895150083D-02
0.1297230000D+04 0.1438590063D-01
0.2992960000D+03 0.7073200310D-01
0.8737710000D+02 0.2400010105D+00
0.2567890000D+02 0.5947970261D+00
0.3740040000D+01 0.2808020123D+00
SP 3 1.00
0.000000000000
S
3
CHEM 6343 - Advanced Computational Chemistry
0.4211750000D+02 0.1138890124D+00 0.3651139738D-01
0.9628370000D+01 0.9208111006D+00 0.2371529830D+00
0.2853320000D+01 -0.3274470358D-02 0.8197019412D+00
SP 1 1.00
0.000000000000
0.9056610000D+00 0.1000000000D+01 0.1000000000D+01
SP 1 1.00
0.000000000000
0.2556110000D+00 0.1000000000D+01 0.1000000000D+01
SP 1 1.00
0.000000000000
0.8450000000D-01 0.1000000000D+01 0.1000000000D+01
D 1 1.00
0.000000000000
0.1292000000D+01 0.1000000000D+01
****
2 0
S 3 1.00
0.000000000000
0.3386500000D+02 0.2549381454D-01
0.5094790000D+01 0.1903731086D+00
0.1158790000D+01 0.8521614860D+00
S 1 1.00
0.000000000000
0.3258400000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.1027410000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.3600000000D-01 0.1000000000D+01
P 1 1.00
0.000000000000
0.7500000000D+00 0.1000000000D+01
****
3 0
S 3 1.00
0.000000000000
0.3386500000D+02 0.2549381454D-01
0.5094790000D+01 0.1903731086D+00
0.1158790000D+01 0.8521614860D+00
S 1 1.00
0.000000000000
0.3258400000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.1027410000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.3600000000D-01 0.1000000000D+01
P 1 1.00
0.000000000000
0.7500000000D+00 0.1000000000D+01
****
2.2.4
Calculation II - 2
%chk=water4.chk
4
CHEM 6343 - Advanced Computational Chemistry
# gfinput opt freq hf/cc-pVQZ geom=connectivity polar
Title Card Required
0 1
O
H
H
-5.37533823 -0.80245471
-4.41533823 -0.80245471
-5.69579282 0.10248112
0.00000000
0.00000000
0.00000000
1 2 1.0 3 1.0
2
3
Also, in this one, we also print out the information of basis set.
S
S
S
S
S
P
P
P
1 0
8 1.00
0.000000000000
0.6142000000D+05 0.1555184099D-03
0.9199000000D+04 0.1184405834D-02
0.2091000000D+04 0.6248769097D-02
0.5909000000D+03 0.2559127665D-01
0.1923000000D+03 0.8775669353D-01
0.6932000000D+02 0.2307291002D+00
0.2697000000D+02 0.4428043050D+00
0.1110000000D+02 0.3336804620D+00
7 1.00
0.000000000000
0.9199000000D+04 -0.7858278867D-05
0.5909000000D+03 -0.4745929019D-03
0.1923000000D+03 -0.2159162994D-02
0.6932000000D+02 -0.2375420471D-01
0.2697000000D+02 -0.1019215293D+00
0.1110000000D+02 -0.4532285868D+00
0.4682000000D+01 -0.4847930118D+00
1 1.00
0.000000000000
0.1428000000D+01 0.1000000000D+01
1 1.00
0.000000000000
0.5547000000D+00 0.1000000000D+01
1 1.00
0.000000000000
0.2067000000D+00 0.1000000000D+01
3 1.00
0.000000000000
0.6342000000D+02 0.3132750252D-01
0.1466000000D+02 0.2166542485D+00
0.4459000000D+01 0.8352428422D+00
1 1.00
0.000000000000
0.1531000000D+01 0.1000000000D+01
1 1.00
0.000000000000
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CHEM 6343 - Advanced Computational Chemistry
0.5302000000D+00 0.1000000000D+01
1 1.00
0.000000000000
0.1750000000D+00 0.1000000000D+01
D 1 1.00
0.000000000000
0.3775000000D+01 0.1000000000D+01
D 1 1.00
0.000000000000
0.1300000000D+01 0.1000000000D+01
D 1 1.00
0.000000000000
0.4440000000D+00 0.1000000000D+01
F 1 1.00
0.000000000000
0.2666000000D+01 0.1000000000D+01
F 1 1.00
0.000000000000
0.8590000000D+00 0.1000000000D+01
G 1 1.00
0.000000000000
0.1846000000D+01 0.1000000000D+01
****
2 0
S 3 1.00
0.000000000000
0.8264000000D+02 0.2295075779D-01
0.1241000000D+02 0.1755401181D+00
0.2824000000D+01 0.8647035510D+00
S 1 1.00
0.000000000000
0.7977000000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.2581000000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.8989000000D-01 0.1000000000D+01
P 1 1.00
0.000000000000
0.2292000000D+01 0.1000000000D+01
P 1 1.00
0.000000000000
0.8380000000D+00 0.1000000000D+01
P 1 1.00
0.000000000000
0.2920000000D+00 0.1000000000D+01
D 1 1.00
0.000000000000
0.2062000000D+01 0.1000000000D+01
D 1 1.00
0.000000000000
0.6620000000D+00 0.1000000000D+01
F 1 1.00
0.000000000000
0.1397000000D+01 0.1000000000D+01
****
3 0
S 3 1.00
0.000000000000
0.8264000000D+02 0.2295075779D-01
0.1241000000D+02 0.1755401181D+00
0.2824000000D+01 0.8647035510D+00
S 1 1.00
0.000000000000
P
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CHEM 6343 - Advanced Computational Chemistry
0.7977000000D+00 0.1000000000D+01
1 1.00
0.000000000000
0.2581000000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.8989000000D-01 0.1000000000D+01
P 1 1.00
0.000000000000
0.2292000000D+01 0.1000000000D+01
P 1 1.00
0.000000000000
0.8380000000D+00 0.1000000000D+01
P 1 1.00
0.000000000000
0.2920000000D+00 0.1000000000D+01
D 1 1.00
0.000000000000
0.2062000000D+01 0.1000000000D+01
D 1 1.00
0.000000000000
0.6620000000D+00 0.1000000000D+01
F 1 1.00
0.000000000000
0.1397000000D+01 0.1000000000D+01
****
S
2.2.5
Calculation III - 1
%chk=water3_modify.chk
# opt freq hf/gen geom=connectivity polar
Title Card Required
0 1
O
H
H
-5.37533823 -0.80245471
-4.41533823 -0.80245471
-5.69579282 0.10248112
0.00000000
0.00000000
0.00000000
1 2 1.0 3 1.0
2
3
1 0
6 1.00
0.000000000000
0.8588500000D+04 0.1895150083D-02
0.1297230000D+04 0.1438590063D-01
0.2992960000D+03 0.7073200310D-01
0.8737710000D+02 0.2400010105D+00
0.2567890000D+02 0.5947970261D+00
0.3740040000D+01 0.2808020123D+00
SP 3 1.00
0.000000000000
0.4211750000D+02 0.1138890124D+00 0.3651139738D-01
0.9628370000D+01 0.9208111006D+00 0.2371529830D+00
S
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CHEM 6343 - Advanced Computational Chemistry
0.2853320000D+01 -0.3274470358D-02 0.8197019412D+00
1 1.00
0.000000000000
0.9056610000D+00 0.1000000000D+01 0.1000000000D+01
SP
1 1.00
0.000000000000
0.2556110000D+00 0.1000000000D+01 0.1000000000D+01
S 1 1.00
0.000000000000
0.6800000000D-01 0.1000000000D+01 0.1000000000D+01
D 1 1.00
0.000000000000
0.0165000000D+01 0.1000000000D+01
****
2 0
S 3 1.00
0.000000000000
0.3386500000D+02 0.2549381454D-01
0.5094790000D+01 0.1903731086D+00
0.1158790000D+01 0.8521614860D+00
S 1 1.00
0.000000000000
0.3258400000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.1027410000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.6800000000D-01 0.1000000000D+01
P 1 1.00
0.000000000000
0.07300000000D+00 0.1000000000D+01
****
3 0
S 3 1.00
0.000000000000
0.3386500000D+02 0.2549381454D-01
0.5094790000D+01 0.1903731086D+00
0.1158790000D+01 0.8521614860D+00
S 1 1.00
0.000000000000
0.3258400000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.1027410000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.6800000000D-01 0.1000000000D+01
P 1 1.00
0.000000000000
0.07300000000D+00 0.1000000000D+01
****
SP
2.2.6
Calculation III - 2
%chk=water4_modify.chk
# opt freq hf/gen geom=connectivity polar
Title Card Required
8
CHEM 6343 - Advanced Computational Chemistry
0 1
O
H
H
-5.37533823 -0.80245471
-4.41533823 -0.80245471
-5.69579282 0.10248112
1 2 1.0 3 1.0
2
3
S
S
S
S
S
P
P
P
P
D
D
1 0
8 1.00
0.000000000000
0.6142000000D+05 0.1555184099D-03
0.9199000000D+04 0.1184405834D-02
0.2091000000D+04 0.6248769097D-02
0.5909000000D+03 0.2559127665D-01
0.1923000000D+03 0.8775669353D-01
0.6932000000D+02 0.2307291002D+00
0.2697000000D+02 0.4428043050D+00
0.1110000000D+02 0.3336804620D+00
7 1.00
0.000000000000
0.9199000000D+04 -0.7858278867D-05
0.5909000000D+03 -0.4745929019D-03
0.1923000000D+03 -0.2159162994D-02
0.6932000000D+02 -0.2375420471D-01
0.2697000000D+02 -0.1019215293D+00
0.1110000000D+02 -0.4532285868D+00
0.4682000000D+01 -0.4847930118D+00
1 1.00
0.000000000000
0.1428000000D+01 0.1000000000D+01
1 1.00
0.000000000000
0.5547000000D+00 0.1000000000D+01
1 1.00
0.000000000000
0.2067000000D+00 0.1000000000D+01
3 1.00
0.000000000000
0.6342000000D+02 0.3132750252D-01
0.1466000000D+02 0.2166542485D+00
0.4459000000D+01 0.8352428422D+00
1 1.00
0.000000000000
0.1531000000D+01 0.1000000000D+01
1 1.00
0.000000000000
0.5302000000D+00 0.1000000000D+01
1 1.00
0.000000000000
0.1750000000D+00 0.1000000000D+01
1 1.00
0.000000000000
0.3775000000D+01 0.1000000000D+01
1 1.00
0.000000000000
9
0.00000000
0.00000000
0.00000000
CHEM 6343 - Advanced Computational Chemistry
0.1300000000D+01 0.1000000000D+01
1 1.00
0.000000000000
0.4440000000D+00 0.1000000000D+01
F 1 1.00
0.000000000000
0.2666000000D+01 0.1000000000D+01
F 1 1.00
0.000000000000
0.8590000000D+00 0.1000000000D+01
****
2 0
S 3 1.00
0.000000000000
0.8264000000D+02 0.2295075779D-01
0.1241000000D+02 0.1755401181D+00
0.2824000000D+01 0.8647035510D+00
S 1 1.00
0.000000000000
0.7977000000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.2581000000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.8989000000D-01 0.1000000000D+01
P 1 1.00
0.000000000000
0.2292000000D+01 0.1000000000D+01
P 1 1.00
0.000000000000
0.8380000000D+00 0.1000000000D+01
P 1 1.00
0.000000000000
0.2920000000D+00 0.1000000000D+01
D 1 1.00
0.000000000000
0.2062000000D+01 0.1000000000D+01
D 1 1.00
0.000000000000
0.6620000000D+00 0.1000000000D+01
F 1 1.00
0.000000000000
0.1397000000D+01 0.1000000000D+01
****
3 0
S 3 1.00
0.000000000000
0.8264000000D+02 0.2295075779D-01
0.1241000000D+02 0.1755401181D+00
0.2824000000D+01 0.8647035510D+00
S 1 1.00
0.000000000000
0.7977000000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.2581000000D+00 0.1000000000D+01
S 1 1.00
0.000000000000
0.8989000000D-01 0.1000000000D+01
P 1 1.00
0.000000000000
0.2292000000D+01 0.1000000000D+01
P 1 1.00
0.000000000000
D
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CHEM 6343 - Advanced Computational Chemistry
0.8380000000D+00 0.1000000000D+01
1 1.00
0.000000000000
0.2920000000D+00 0.1000000000D+01
D 1 1.00
0.000000000000
0.2062000000D+01 0.1000000000D+01
D 1 1.00
0.000000000000
0.6620000000D+00 0.1000000000D+01
F 1 1.00
0.000000000000
0.1397000000D+01 0.1000000000D+01
****
P
3
Data
In this section, we listed all data for number of basis functions, primitive gaussians, total
dipole moments and polarizabilities.
Table 1: Data for number of basis functions, primitive gaussians, total energy and dipole
moment.
Basis set
STO-3G
6-31G(d,p)
6-311++G(d,p)
Modified 6-311++G(d,p)
cc-pVQZ
Modified cc-pVQZ
Basis function #
Primitive Gaussian #
Total energy (a.u.)
Dipole moment (Debye)
7
25
36
33
115
106
21
42
54
51
163
149
-74.9659011708
-76.0236149302
-76.0534234741
-76.0245014252
-76.0655184122
-76.0655088433
1.7094
2.1485
2.1968
2.0615
1.9660
1.9658
Table 2: Data for polarizability in the unit of Bohr3
Basis set
STO-3G
6-31G(d,p)
6-311++G(d,p)
Modified 6-311++G(d,p)
cc-pVQZ
Modified cc-pVQZ
Experimental data
αxx
αyy
αzz
0.040
2.931
5.502
7.230
6.074
6.072
10.399
5.506
6.769
7.421
8.941
8.184
8.183
11.231
2.565
4.906
5.853
7.905
7.234
7.233
10.788
11
CHEM 6343 - Advanced Computational Chemistry
4
Conclusion
In this lab, we could easily see that Modified 6-311++G(d,p) did the best job in calculating polarizability although it has nearly 30% error. Because the modification to
6-311++G(d,p) explicitly includes altering the exponents if the d polarization function
for oxygen and the p polarization function for hydrogen as well as changing a diffuse sp
function for oxygen to a diffuse s function and altering the exponents of this s function for
both oxygen and hydrogen. The resulting basis set is called 6-31G(+sd,+sp). However,
it seems that for cc-pVQZ basis set which is quite larger than 6-311++G(d,p), after the
modification, the properties and energies calculated do not change so much. Maybe the
reason is that larger basis sets have more basis functions, and changing just a few of them
can not matter so much.
12