Using Software to Bridge the Gap between Fundamental Science and

Engineering Applications

Jennifer WilcoxDepartment 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

A variety of levels of theory were employed for the investigation involving a wide range of method and basis set combinations:

B3LYP/LANL2DZ; MP2/6-311+G; QCISD/6-311+G;HF/6-31G; MP2/6-311+G(d,p); CCSD/6-31G;MP2/6-31G; QCISD/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.

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 Steps 2 & 3

LTE Step 2examples of students’ work

*This step allowed studentsto observe the influenceof modified basis sets, i.e. the addition of diffuse, polarization, double, and triple zeta.

Addition of polarizationfunctions improve thepredictions, diffuse functions do not.

LTE Step 3examples of students’ work

F2 + H → HF + F

*Students were requiredto 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.

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 4examples 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 5examples of students’ work

*The trouble with this reactionis that the hydrogen atomis actually approaching at an angle and we’ve assumeda linear TS.

LTE Step 5examples of students’ work

Comparison of Arrhenius Parameters for the Reaction, HCl + H _ Cl + H 2

Temp Range (K) A (cm 3/mol*sec) Ea (kcal/mol) Reference 291 - 1192 2.999(13) 5.10 Adusei and Fontijn

1000 - 1500 3.114(13) 4.84 Allision et al .

600 - 1000 2.318(13) 4.25 Allison et al .

400 - 600 1.223(13) 3.49 Allison et al . 200 - 650 7.95(12) 3.40 Baulch et al.

199 - 502 1.09(13) 3.50 Miller and Gordon

195 - 497 2.3(13) 3.50 Westenberg and de Hass

195 - 373 8.974(12) 3.1 Clyne and Stedman

200 - 1000 7.94(12) 4.39 Lendvay et a l.

200 - 1000 1.00(13) 3.51 Ambidge et al.

298.15 - 2500 5.015(13) 4.39 Present work (TST)

CCSD/6-311G(3df,3pd) 298.15 - 2500 6.134(14) 4.67 Present work (HSCM)

HCl + H → Cl + H2

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 palladiumApplication: 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 nonlinearorientations.