Post on 25-Dec-2015
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IntroductionIntroduction
What is Computational Chemistry? Use of computer to help solving chemical
problemsChemical Problems
Computer Programs
Physical Models
Math formulas
Physical & Chemical Properties
Chemical Systems Geometrical Arrangements of the nuclei
(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)– Spherical coordinate (r,,)– Internal coordinate (r,a,d)
x
y
z
1
x1
y1
z1
r
z
r1
r2a
Fundamental Forces The interaction between particles can be
described in terms of either forces (F) or potentials (V)
r
VrF
)( VdrrF )(
r
r
V
Force Particle Relative strength
Range
Gravitational Mass particles 10-40
Electromagnetic Charged particle 1
Week Interaction Quarks & Leptons 0.001 <10-15
Strong Interaction Quarks 100 <10-15
r
VrF
)(
r
qqCrV jielecijelec )(
r
mmCrV jigravijgrav )(
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
+
-
+-
V = Vw/s + Vpn + Vee + Vpp
E r
Potential Energy Surfaces
Product
Reactant
Potential energy depends on many structural variables
r1r2
degree
E
0 60 120 180 240 300 360
Cl
Cl
Cl
Cl
Cl
Cl
Important Features of PES Equilibrium molecular structures correspond to the
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 Quantum Mechanic
maF H
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
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
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 semi-empirical 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