Transcript Ab Initio Quantum Chemistry: Thermochemistry and Kinetics

New Approaches for Teaching the
Chemical Principles of Engineering
Phil Westmoreland
University of Massachusetts Amherst
[email protected]
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
What are the chemical principles of
engineering?
• Principles that underlie the useful properties of atoms, molecules,
macromolecules, continuum ensembles, materials
• Is it chemistry? Is it physics? Is it biology?
• Biochemistry? Physical chemistry? Chemical physics?
• Physical organic chemistry? Biophysical chemistry?
• Quantum mechanics? Statistical mechanics?
• Semiconductor physics? Organic semiconductors?
• I don’t care! These are all “molecular sciences”.
• Student need to master these principles - and can.
• Molecular modeling and computer visualization helps greatly!
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
ChE is the engineering profession
that focuses on applying chemistry.
• Phase and reaction equilibria
– Bond and interaction energies
– Ideal-gas thermochemistry
– Thermochemistry and
equations of state for real
gases, liquids, solids, mixtures
– Adsorption and solvation
• Reaction kinetics
– Rate constants, products
– Metabolic pathways
• Transport properties
– Interaction energies, dipole
– µ, kthermal, DAB
• Analytical information
– Spectroscopy: Frequencies,
UV / Vis /IR absorptivity
– GC elution times
– Mass spectrometric ionization
potentials and cross-sections,
fragmentation patterns
– NMR shifts
• Protein folding and misfolding,
docking, ADME, drug discovery
• Mechanical properties of hard
and soft condensed matter
• Electronic & optical properties
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Yes, ChE is the engineering profession
that focuses on applying chemistry.
• But mechanical engineers use many properties that
are molecular in origin.
– Basic thermochemistry: ∆fHº, Cpº, Sº
– P-V-T relations
– Strength of materials
• So do civil and environmental engineers
– Chemical and biological treatment
– Air, water, soil properties
– Effects of environment on materials
• And likewise electrical and computer engineers
– Band gap as collective HOMO-LUMO differences.
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
We all need to understand the chemical principles
of engineering because we all need properties.
• Maybe accurate, precisely known numbers.
– Necessary for accurate design, costing, safety analysis.
– Cost and time for calculation may be secondary.
• Maybe “just” accurate trends and estimates.
–
–
–
–
Often more valuable.
Correlate with data to get high-accuracy predictions.
Use to identify relationships between structure and properties.
Enormous value for product and process development,
operations, and troubleshooting.
• Great data are best, but we must understand enough
theory to predicting unmeasured properties.
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
1. Most property predictions are by correlations,
wholly empirical or theory-based.
• Arrhenius
kinetics
• Ideal gas law
• Ideal gas
mixtures
(P=xiP= Pi):
• Ideal solutions
• Activity
coefficients
Ken Jolls, www.public.iastate.edu/~jolls/gibbsPics/pvtn.jpg
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
2. Property correlations require a grasp of
underlying principles.
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
3. Molecular visualization helps develop this grasp.
Compare the
descriptions:
i-Pr
H3 C
N
(C33N3H43)FeCl2,
a liganded
di(methyl imide
xylenyl) aniline ...
Fe
N
i-Pr
Cl
Cl
N
i-Pr
H3 C
i-Pr
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
See functionality with the 3-D structure.
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
A key tool for describing molecular biology…
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Such as enzymatic docking.
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
5. For getting and using quantitative correlations
properly, use the appropriate theory.
Continuum Mechanics
1m
100 m
0.1 m
10 nm
Statistical Mechanics
Length
1 nm
Quantum Mechanics
10 ns
1 ps
Time
1 hr
(After Maroudas, 2002)
Molecular and material structure
Electronic structure theory
(Computational quantum
chemistry)
"Ab initio":
Wavefunction methods
Density-functional theory
Molecular simulations
Monte Carlo simulations
Quantum MD,
Car-Parrinello
Molecular dynamics,
molecular mechanics
Semi-empirical MO theory
Basis sets
Statistical
mechanics
Potential energy
functions
Thermochemistry, kinetics, transport, materials properties, VLE, solutions
6. We can use these computational tools to help us
teach about theory and applications.
The educational principle:
• Easy visualization and successful predictions motivate
students to study useful underlying theories.
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Example: Sketch ethylene; Calculate optimized
structure/frequencies/thermo; Compare to data.
Electron
density
HOMO;
LUMO
Calculations and graphics at HF/3-21G* with
MacSpartan Plus (Wavefunction Inc.).
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Then they’ll tackle “How” -- the needed theory.
• Maxwell-Boltzmann and Bose-Einstein statistics.
• Ideal-gas thermochemistry for Cpº and Sº, broken down
into additive translation, rotation, vibration:

q(V,T )
 ln q(V,T ) 
S  N 1  ln
T

 N 

V 
T



 ln qtransqrotqvibrqelec  
S(molar )  R  ln qtransqrotqvibr qelec e   T

V 
T


 Strans  Srot  Svibr  Selec
• Compare with group additivity correlations.
• [Can develop transition-state theory quickly, logically.]
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Get bond lengths, bond angles, frequencies from
analogies -- or from quantum chemistry.
• Efficiently explain the underlying quantum
chemistry.
• Easiest to think of a small, covalently bonded
molecule like H2 or CH4 in vacuo.
With energies,
• Most simply, the goal of electronic structure
w e can optimize
calculations is energy.
molecular structure
Energy E
[from
• However, usually we want
x
EH ]
energy of an optimized
x
structure and the energy’s
variation with structure.
x
Position r
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
For quantum mechanics, a Hamiltonian operator is
used for translational + kinetic energy.
• Obtain a Hamiltonian function for a wave using the
Hamiltonian operator:
h2 2
H 
  U(x, y, z)
8m
to obtain:
ih (q ,t)
E  H (q,t) 
2
t
where  is the “wavefunction,” an eigenfunction
of the equation
• Born recognized that 2 is the probability density function
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
H-atom eigenfunctions y correspond to
hydrogenic atomic orbitals.
l=0
m=0
z
l=1
m=-1
m=0
l=2
m=+1
n=1
1s
n=2
2s
2px
2py
2pz
n=3
3s
3px
3py
3pz
m=-2,-1,0,1,2
3d orbitals (5)
y
x
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Construct each MO yi by LCAO.
• Lennard-Jones (1929) proposed treating
molecular orbitals as linear combinations
of atomic orbitals (LCAO):

y i   Ci i
i 1
• Linear combination of s orbital on one atom with s or p
orbital on another gives s bond:
• Linear combination of p orbital on one atom with p orbital
on another gives  bond:
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Simulate the real functionality with gaussians.
• Start with a function that describes hydrogenic orbitals
well.
3
– Slater functions are “best”; e.g.,
– Gaussian functions are better; e.g.,
• No s cusp at r=0
• However, all analytical integrals
– Linear combinations of
gaussians; e.g., STO-3G
• 3 Gaussian “primitives” to simulate
a STO
• (“Minimal basis set”)
1s (r ; 1 ) 
1
exp(1 r )

3/ 4
2 
gs r ;      exp( r 2 )

True STO
3 gaussian
functions
r
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Then explain Hartree-Fock, density functional
theory, compound methods, and then...
Improved electron correlation 
H-F MP2
MP4 QCISD(T) ... Full CI
STO-3G
3-21G
More
complete 6-31G(d)
basis
sets 6-311G(d,p)

6-311+G(d,p)
Infinite basis
set
Exact
solution
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
7. Use them to solve some small, real problems
that reinforce the point.
• Heat of combustion for dimethyloxirane safety.
• Rate constant for simple reaction like C2H4+OH.
• Heat of solvation for small molecules in various
solvents.
• Fit Lennard-Jones parameters for simple potential.
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Safety / reactor engineering example:
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
Simplest properties are interaction energies:
Here, the van der Waals well for an Ar dimer.
100.00
50.00


0.00
0
2
4
6
8
-50.00
-100.00
-0.2 kcal/mol = -0.8 kJ/mol
Basis set:
aug-cc-pVDZ;
Method:
HF
MP2
MP3
10
MP4D
MP4DQ
MP4SDQ
CCSD
CCSD(T)
L-J 12-6
-150.00
Ar-Ar, angstroms
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
In conclusion,
We can use these tools effectively to teach the
chemical principles our students will need.
• Build on students’ chemistry education and their prior
use of properties to solve problems.
• Refresh their recognitions of molecule types using
sketching / visualization codes.
• Have them predict structures and properties.
• With them motivated, build the underlying theory.
• Have them obtain properties for use.
"Chemistry and life sciences in a new vision of chemical engineering," Chemical
Engineering Education, 35(4), 248-255 (2001).
http://www.et.byu.edu/~rowley/WebModules/modules.htm
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.
“New Approaches for Teaching the Chemical Principles of Engineering.” New England Section Conf., March 17-18, 2006.