Transcript Computer Simulation for Chemistry and Chemical Engineering

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Introduction
What is Computational Chemistry?
 Use of computer to help solving chemical
problems
Chemical Problems
Math formulas
Physical Models
Computer Programs
Physical & Chemical
Properties
Chemical Systems
 Geometrical Arrangements of the nuclei
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(atoms/molecules)
Relative Energies
Physical & Chemical Properties
Time dependence of molecular structures
and properties
Molecular interactions
System Description
 Fundamental Units
– elementary units (quarks/electrons/nuetron …)
– atoms/Molecules
– Macromolecules/Surfaces
– Bulk materials
 Starting Condition
 Interaction
 Dynamical Equation
Molecular Structure
 Arrangement of nuclei/groups of nuclei
 Coordination Systems
– Cartesian coordinate (x,y,z)
– Sphericalz coordinate (r,,)
– Internal coordinate (r,a,d)
a
z
z1
1
r2
r
r1

x1
x
y1
y
Fundamental Forces
 The interaction between particles can be
described in terms of either forces (F) or
potentials (V)
V
F (r )  
r
 F (r )dr  V
r
V
r
Force
Gravitational
Electromagnetic
Week Interaction
Strong Interaction
Particle
Relative
Range
strength
10-40

Charged particle
1

Quarks & Leptons
0.001
<10-15
100
<10-15
Mass particles
Quarks
V
F (r )  
r
mi m j
qi q j
Vgrav (rij )  C grav
Velec (rij )  Celec
r
r
Potential Energy Surface (PES)
 The concept of potential energy surfaces is
central to computational chemistry
 The challenge for computational chemistry
is to explore potential energy surfaces with
methods that are efficient and accurate
enough to describe the chemistry of
interest
Potential Energy Curve
 Potential Energy between two atoms
-
+
+
E
V = Vw/s + Vpn + Vee + Vpp
r
Potential Energy Surfaces
 Potential energy depends on many
structural variables
Product
r1
Reactant
r2
Cl
Cl
Cl
Cl
E
0
60
120 180 240 300 360
degree
Important Features of PES
 Equilibrium molecular structures correspond to the
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positions of the minima in the valleys on a PES
Energetics of reactions can be calculated from the
energies or altitudes of the minima for reactants and
products
A reaction path connects reactants and products
through a mountain pass
A transition structure is the highest point on the lowest
energy path
Reaction rates can be obtained from the height and
profile of the potential energy surface around the
transition structure
 The shape of the valley around a minimum
determines the vibrational spectrum
 Each electronic state of a molecule has a
separate potential energy surface, and the
separation between these surfaces yields the
electronic spectrum
 Properties of molecules such as dipole moment,
polarizability, NMR shielding, etc. depend on the
response of the energy to applied electric and
magnetic fields
Classical & Quantum Mechanics
 Newtonian Mechanic
F  ma
 Quantum Mechanic
Hˆ   
Types of Molecular Models
 Wish to model molecular structure,
properties and reactivity
 Range from simple qualitative descriptions
to accurate, quantitative results
 Costs range from trivial to months of
supercomputer time
 Some compromises necessary between
cost and accuracy of modeling methods
Plastic molecular models
 Assemble from standard parts
 Fixed bond lengths and coordination geometries
 Good enough from qualitative modeling of the
structure of some molecules
 Easy and cheap to use
 Provide a good feeling for the 3 dimensional
structure of molecules
 No information on properties, energetics or
reactivity
Molecular mechanics
 Ball and spring description of molecules
 Better representation of equilibrium geometries than
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plastic models
Able to compute relative strain energies
Cheap to compute
Lots of empirical parameters that have to be carefully
tested and calibrated
Limited to equilibrium geometries
Does not take electronic interactions into account
No information on properties or reactivity
Cannot readily handle reactions involving the making
and breaking of bonds
Semi-empirical
molecular orbital methods
 Approximate description of valence electrons
 Obtained by solving a simplified form of the
Schrödinger equation
 Many integrals approximated using empirical
expressions with various parameters
 Semi-quantitative description of electronic
distribution, molecular structure, properties and
relative energies
 Cheaper than ab initio electronic structure methods,
but not as accurate
Ab Initio Molecular Orbital Methods
 More accurate treatment of the electronic
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distribution using the full Schrödinger equation
Can be systematically improved to obtain
chemical accuracy
Does not need to be parameterized or calibrated
with respect to experiment
Can describe structure, properties, energetics
and reactivity
Expensive
Molecular Modeling Software
 Many packages available on numerous
platforms
 Most have graphical interfaces, so that
molecules can be sketched and results
viewed pictorially
 Will use a few selected packages to
simplify the learning curve
 Experience readily transferred to other
packages
Modeling Software (cont’d)
 Chem3D
– molecular mechanics and simple semiempirical methods
– available on Mac and Windows
– easy, intuitive to use
– most labs already have copies of this, along
with ChemDraw
Modeling Software, cont’d
 Gaussian 03
– semi-empirical and ab initio molecular orbital
calculations
– available on Mac (OS 10), Windows and Unix
(we will probably use all three versions,
depending on which classroom we are in)
 GaussView
– graphical user interface for Gaussian
Modeling Software, cont’d
 Software for marcomolecular modeling and
molecular dynamics will be determined
later (depends on what is freely available
and is capable of meeting our needs)
Force Field Methods
 Stretching Energy
 Bending Energy
 Torsion Energy
 Van der Waals Energy
 Electrostatic Energy
– Charges/dipoles
– multipoles/polarizabilities
 Cross terms
Molecular Mechanics
 PES calculated using empirical potentials
fitted to experimental and calculated data
 composed of stretch, bend, torsion and
non-bonded components
E = Estr + Ebend + Etorsion + Enon-bond
 e.g. the stretch component has a term for
each bond in the molecule
Bond Stretch Term
 many force fields use just a quadratic term, but the
energy is too large for very elongated bonds
Estr =  ki (r – r0)2
 Morse potential is more accurate, but is usually not
used because of expense
Estr =  De [1-exp(-(r – r0)]2
 a cubic polynomial has wrong asymptotic form, but a
quartic polynomial is a good fit for bond length of
interest
Estr =  { ki (r – r0)2 + k’i (r – r0)3 + k”i (r – r0)4 }
 The reference bond length, r0, not the same as the
equilibrium bond length, because of non-bonded
contributions
Angle Bend Term
 usually a quadratic polynomial is sufficient
Ebend =  ki ( – 0)2
 for very strained systems (e.g. cyclopropane) a
higher polynomial is better
Ebend =  ki ( – 0)2 + k’i ( – 0)3
+ k”i ( – 0)4 + . . .
 alternatively, special atom types may be used for
very strained atoms
Torsional Term
 most force fields use a single cosine with
appropriate barrier multiplicity, n
Etors =  Vi cos[n( – 0)]
 some use a sum of cosines for 1-fold (dipole), 2-
fold (conjugation) and 3-fold (steric)
contributions
Etors =  { Vi cos[( – 0)] + V’i cos[2( – 0)]
+ V”i cos[3( – 0)] }
Non-Bonded Terms
 Lennard-Jones potential
– EvdW =  4 ij ( (ij / rij)12 - (ij / rij)6 )
– easy to compute, but r -12 rises too rapidly
 Buckingham potential
– EvdW =  A exp(-B rij) - C rij-6
– QM suggests exponential repulsion better, but
is harder to compute
 tabulate  and  for each atom
– obtain mixed terms as arithmetic and
geometric means
– AB = (AA + BB)/2; AB = (AA BB)1/2
Applications