Using Software to Bridge the Gap
between Fundamental Science and
Engineering Applications
Jennifer Wilcox
Department of Chemical Engineering
Worcester Polytechnic Institute
ASEE New England Chapter Conference
March 18, 2006
MOTIVATION
• To introduce graduate and upper-level undergraduates to tools that will
allow them to bridge the gap between fundamental science (kinetic
model) and engineering applications (design equations).
• To help foster the intuitive side of an engineer through teaching first
principle concepts, which provide them with a molecular-scale and
mechanistic approach to problem solving in science.
• To use newly developed software, such as Gaussian03 and gOpenMol to
assist students in active and hands-on learning.
• To effectively use the software without it dictating the nature of the
course, i.e. to use the software purely as a supplement to learning.
METHODOLOGY
The class was broken up into the following 4 sections:
1.
During the first quarter students were introduced to quantum
mechanics, which serves as the foundation for many of the
calculations involved in molecular modeling.
Some example
problems included, particle in a 1-d box, harmonic oscillator,
perturbation theory, and the variational principle.
2.
In the second quarter students were introduced to the Gaussian
software package using WebMO as an interface. A server was set up
just for the class so that students could submit calculations from any
location that the internet was accessible. The Learning Through an
Example was assigned at this time.
METHODOLOGY cont.
3.
In the third quarter students were asked to take the tools of the
software from step 2, to apply to reactions provided. At this point they
learned kinetic tools rather than QM tools. These tools included the
Hard Sphere Collision Model, Transition State Theory and RRKM. The
Learning Through an Example Assignment was completed at this time.
4.
In the fourth quarter students were then asked to apply the tools
learned to a project associate with either their graduate research
project or their Major Qualifying Project (senior thesis). Images of
these projects serve as the backdrop of these slides.
Learning through an example
Six-week long assignment separated in five steps with one homework
assignment for each week, each step
At the end of the assignment, the students were given a take-home exam
which required them to compile all the assignments into a final draft in the
form of a manuscript.
Students were expected to learn the capabilities of the Gaussian98 software
package by means of a thorough structural, thermodynamic, and kinetic
investigation of an assigned reaction similar to,
H + F2 → HF + F
LTE Step 1
Ĥ  E
A variety of levels of theory were employed for the investigation
involving a wide range of method and basis set combinations:
B3LYP/LANL2DZ;
HF/6-31G;
MP2/6-31G;
MP2/6-311+G;
MP2/6-311+G(d,p);
QCISD/6-31G;
QCISD/6-311+G;
CCSD/6-31G;
QCISD/6-311+G
Students were required to choose two more levels of theory on their
own for further analysis and to organize the data using Excel.
LTE Steps 2 & 3
Step 2. Optimizations were performed at each level of theory, and for each
compound in the given reaction.
Results including the predicted geometry (e.g. equilibrium bond lengths,
angles, and dihedrals), energy, thermal correction including the zero point
energy, vibrational frequencies, rotational constants, and dipole moments
were recorded.
Using references such as the CRC Handbook of Chemistry and Physics, NIST
webbook, and individual reference papers (e.g. obtained via databases such
as Science Direct and SciFinder Scholar), each predicted chemical property
was compared to experiment where experimental data was available.
Step 3. Calculation of thermodynamic parameters such as reaction
enthalpies (ΔHrxn), entropies (ΔSrxn), Gibbs free energies (ΔGrxn), and
equilibrium constants (Keq) were determined for the given reaction at each
level of theory.
LTE Step 2
examples of students’ work
Theory
*This step allowed students
to observe the influence
of modified basis sets, i.e.
the addition of diffuse,
polarization, double, and
triple zeta.
Addition of polarization
functions improve the
predictions, diffuse
functions do not.
Bond Length
(Å)
Vibrational
Frequency
(cm-1)
DCl
D2
Dipole
Moment
(Debye)
DCl
Rotational
Constant
(GHz)
DCl
D2
DCl
D2
B3LYP/LANL2DZ
1.3149
0.7435
1943
3153
1.80
5.11
30.28
HF/6-31G
1.2953
0.7297
2097
3289
1.87
5.27
31.44
HF/STO-6G
1.3112
0.7105
2097
3886
1.77
5.14
33.16
MP2/6-31G
1.3174
0.7376
1970
3206
1.88
5.10
30.77
MP2/6-311+G
1.3269
0.7376
1943
3149
1.89
5.02
30.77
MP2/6-311+G(d,p)
1.2731
0.7383
2214
3206
1.44
5.46
30.71
MP2/6-31+G*
1.2810
0.7375
2177
3206
1.53
5.39
30.77
MP2/6-311(3df,3pd)
1.272
0.7367
2190
3195
1.17
5.47
30.84
QCISD/6-31G
1.3262
0.7462
1901
3089
1.88
5.03
30.06
QCISD/6-311+G
1.3262
0.7465
1875
3018
1.71
5.03
30.04
QCISD/6-311+G**
1.2758
0.7435
2183
3126
1.33
5.43
30.28
QCISD/6-311++G**
1.2762
0.7435
2181
3126
1.32
5.43
30.29
CCSD/6-31G
1.3261
0.7462
1901
3089
1.88
5.03
30.06
CCSD/6-311+G
1.3365
0.7465
1876
3018
1.89
4.95
30.04
CCSD/cc-pVDZ
1.2905
0.7609
2144
3100
1.16
5.31
28.91
CCSD(T)/6-311G**
1.2772
0.7435
2174
3127
1.46
5.42
30.28
CCD/aug-cc-pVDZ
1.2897
0.7610
2151
3084
1.16
5.32
28.90
CCD/cc-pVTZ
1.2748
0.7421
2172
3127
1.18
5.44
30.39
Experimental
1.2746
0.7420
2145
3116
N/A
5.44
30.44
LTE Step 3
examples of students’ work
F2 + H → HF +
F
*Students were required
to find a level of theory
that predicted the reaction
enthalpy to within 2
kcal/mol to experiment
and the equilibrium
constant to within an order
of magnitude.
Theory
B3LYP/LANL2DZ
ΔHrxn
ΔSrxn
ΔGrxn
(kcal/mol) (cal/mol*K) (kcal/mol)
-91.61
1.841
-92.16
Keq
3.87(+67)
HF/6-31G
-121.20
1.904
-121.7
2.01(+89)
MP2/6-31G
-82.76
1.677
-83.26
1.16(+61)
MP2/6-311+G
-91.99
1.586
-92.46
6.48(+67)
MP2/6-311+G(d,p)
-103.8
1.787
-104.3
3.44(+76)
QCISD/6-31G
-84.52
1.578
-84.99
2.14(+62)
QCISD/6-311+G
-94.24
1.510
-94.69
2.82(+69)
CCSD/6-31G
-84.65
1.577
-85.12
2.68(+62)
CCSD/6-311+G
-94.44
1.513
-94.89
3.91(+69)
CCSD/aug-cc-pVDZ
-104.4
1.798
-104.9
9.08(+76)
CCSD(T)/6-311G**
-98.96
1.607
-99.44
8.56(+72)
QCISD(T)/6-311G**
-98.92
1.612
-99.40
7.92(+72)
Experimental
-98.27
3.596
-99.34
7.20(+72)
LTE Step 4
Calculation of kinetic parameters such as activation energies and rate
constants were determined for the given reaction at selected levels of
theory. The following steps were involved in determining an overall rate
expression:
•calculation of a potential energy surface (ab initio-derived energies were
plotted using MatLab),
•determination of a saddle point corresponding to a transition structure
linking reactants to products of the reaction path of interest, frequency
calculation at the predicted transition structure to ensure there exists one
and only one negative frequency,
•evaluation of rotational, vibrational, and translational partition functions
for preexponential factor calculation, and
•use of transition state theory (TST) at varying temperatures for the final
expression.
A tunneling correction by Gonzalez-Lafont was used in
conjunction with TST.
LTE Step 4
examples of students’ work
•SPEs of the F2 + H → HF + F reaction
were calculated at the QCISD(T)/6-311G**
level of theory, with a total of 208 points.
•SPEs of the D2 + Cl → DCl + D reaction
Were calculated at the CCD/aug-cc-pVDZ
Level of theory, with a total of 165 points.
LTE Step 5
• The rate expression for the reaction was calculated as a function of
temperature in both directions.
• The equilibrium constant was reexamined for validation. All kinetic (k1
and k-1) and thermodynamic (Keq) predictions were compared to
experimental values where available.
• The NIST kinetic database served as a reference for this comparison.
LTE Step 5
examples of students’ work
*The trouble with this reaction
is that the hydrogen atom
is actually approaching at an
angle and we’ve assumed
a linear TS.
40
20
TST
HSCM
Garrett et al.
Baulch et al.
0
ln k (cm³/mol*s)
-20
Comparison of Arrhenius Parameters for the reaction, F2 + H → HF + F
Temp Range (K)
225 - 2000
294 - 565
224 - 493
298.15 - 505
298.15 - 2500
A (cm3/mol*s)
8.43(12)
1.21(14)
3.98(13)
3.02(13)
4.96(15)
Ea (kcal/mol)
1.4
2.4
0.95
2.13
5.24
298.15 - 2500
2.55(12)
4.68
Reference
Cohen et al.
Albright et al.
Homann et al.
Zelenov et al.
Present work (HSCM)
Present work (TST)
QCISD(T)/6-311G**
-40
Comparison of Arrhenius Parameters for the reaction, HF + F → F2 + H
-60
-80
-100
-120
-140
Temp Range (K)
300 - 1000
298.15 - 500
298.15 - 2500
A (cm3/mol*s)
2.43(14)
1.33(13)
2.31(14)
Ea (kcal/mol)
99.76
101.0
103.39
298.15 - 2500
6.53(11)
103.81
-160
0
0.001
0.002
1/T (K -1)
0.003
0.004
Reference
Garrett et al.
Baulch et al.
Present work (HSCM)
Present work (TST)
QCISD(T)/6-311G**
LTE Step 5
examples of students’ work
TST
HSCM
Allison et al.
Miller and Gordon
Westenberg and de Hass
34
32
28
3
ln k (cm /mol*s)
30
Comparison of Arrhenius Parameters for the Reaction, HCl + H → Cl + H2
Temp Range (K)
291 - 1192
1000 - 1500
600 - 1000
400 - 600
200 - 650
199 - 502
195 - 497
195 - 373
200 - 1000
200 - 1000
A (cm3/mol*sec)
2.999(13)
3.114(13)
2.318(13)
1.223(13)
7.95(12)
1.09(13)
2.3(13)
8.974(12)
7.94(12)
1.00(13)
Ea (kcal/mol)
5.10
4.84
4.25
3.49
3.40
3.50
3.50
3.1
4.39
3.51
298.15 - 2500
5.015(13)
4.39
298.15 - 2500
6.134(14)
4.67
Reference
Adusei and Fontijn
Allision et al.
Allison et al.
Allison et al.
Baulch et al.
Miller and Gordon
Westenberg and de Hass
Clyne and Stedman
Lendvay et al.
Ambidge et al.
Present work (TST)
CCSD/6-311G(3df,3pd)
Present work (HSCM)
26
24
22
20
0
0.001
0.002
0.003
-1
1/T (K )
HCl + H → Cl + H2
0.004
EVALUATION OF SUCCESS
• The results of the Learning Through an Example exercise has resulted in
two manuscript submissions to the Journal of Molecular Structure
(THEOCHEM).
• Students from the class have incorporated the tools learned into their
research. Some examples are,
-Electrochemical water-gas shift reactions on platinum and ruthenium
catalysts
Application: fuel cell chemistry
-Adsorption mechanisms of MTBE, Chloroform, and 1,4-dioxane with
ions
Application: separation of contaminants from groundwater using
zeolites
-Mechanism development of sulfur’s role in poisoning palladium
Application: hydrogen separation using Pd membranes
CONCLUSIONS – FUTURE PLANS
Students provided helpful feedback for improving the class in the
future:
•Seek additional funding to add computational strength to the class
server; often times calculations were backed up even though the
levels of theory were minimal.
•In the future provide more focus to the levels of theory considered
in the Learning Through an Example assignment so that a smaller, but
more effective list is employed.
Additional future plans:
•Consider other kinetic techniques such as variational TST
•Fix different degrees of freedom within the TS to consider nonlinear
orientations.