Download Physical Chemistry 2nd Edition

Chapter 26
Computational Chemistry
Physical Chemistry 2nd Edition
Thomas Engel, Philip Reid
Objectives
• Discover the usage of numerical methods.
• Discussion is the Hartree-Fock molecular orbital
model.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Outline
1. The Promise of Computational Chemistry
2. Potential Energy Surfaces
3. Hartree-Fock Molecular Orbital Theory: A
Direct Descendant of the Schrödinger
Equation
4. Properties of Limiting Hartree-Fock Models
5. Theoretical Models and Theoretical Model
Chemistry
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Outline
6. Moving Beyond Hartree- Fock Theory
7. Gaussian Basis Sets
8. Selection of a Theoretical Model
9. Graphical Models
10. Conclusion
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.1 The Promise of Computational Chemistry
•
•
•
•
Sufficient accuracy can be obtained from
computational chemistry.
Approximations need to be made to realize
equations that can be solved.
No one method of calculation
is likely to be ideal for all
application.
Hartree-Fock theory leads to
ways to improve on it and to
a range of practical quantum
chemical models.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.2.1 Potential Energy Surfaces and Geometry
•
•
•
Energy minima give the equilibrium structures
of the reactants and products.
Energy maximum defines the transition state.
Reactants, products, and
transition states are all
stationary points on the
potential energy diagram.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.2.1 Potential Energy Surfaces and Geometry
•
In the one-dimensional case, 1st derivative of
the potential energy with respect to the
reaction coordinate is zero:
dV
0
dR
•
For many-dimensional case, each independent
coordinate, Ri, gives rise to 3N-6 second
derivatives:
2
V
Ri R3 N 6
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.2.1 Potential Energy Surfaces and Geometry
•
Stationary points where all second derivatives
are positive are energy minima:
 2V
 0 i  1,2,...,3N  6
2
i
where ζi = normal coordinates
•
Stationary points where all but one are positive
are saddle points:
 2V
0
2
 p
where ζi = reaction coordinate
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.2.2 Potential Energy Surfaces and Vibrational
Spectra
•
The vibrational frequency for a diatomic
molecule A-B is
1
v
2
•
k

k is the force constant which is defined as
d 2V R 
k
dR 2
•
And μ is the reduced mass.
m A mB

m A  mB
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.2.3 Potential Energy Surfaces and
Thermodynamics
•
•
The energy difference between the reactants
and products determines the thermodynamics
of a reaction.
The ratio is as follow,
n products
nreac tan ts
  E products  Ereac tan ts 

 exp  
kT

 
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.2.3 Potential Energy Surfaces and
Thermodynamics
•
•
The energy difference between the reactants
and transition state determines the rate of a
reaction.
The rate constant is given by the Arrhenius
equation and depends on the temperature:
 Etransitionstate  Ereac tan ts 
k  A exp 

kT


Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.3 Hartree-Fock Molecular Orbital Theory: A Direct
Descendant of the Schrödinger Equation
•
3 approximations need to realize a practical
quantum mechanical theory for multielectron
Schrödinger equation:
Ĥ  E
a) Born-Oppenheimer approximation
b) Hartree-Fock approximation
c) Linear combination of atomic orbitals
(LCAO) approximation
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL FORMULATION OF THE HARTREEFOCK METHOD
The Hartree-Fock and LCAO approximations, taken
together and applied to the electronic Schrödinger
equation, lead to a set of matrix equations now known
as the Roothaan-Hall equations:
Fc  Sc
where c = unknown molecular orbital coefficients
ε = orbital energies
S = overlap matrix
F = Fock matrix
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL FORMULATION OF THE HARTREEFOCK METHOD
For Fock matrix,
Fv  H core
v  J v  K v
where Hcore = core Hamiltonian
2
2

h
e
2


H core


r


v
  2me  40
nuclei

A
ZA 
v r dr
r 
Coulomb and exchange elements are given by
J v 
K v
P v  
basis function
 

1 basis
 
2 
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
P  v 
function


MATHEMATICAL FORMULATION OF THE HARTREEFOCK METHOD
P is called the density matrix
P  2
molecular orbitals
occupied

ci ci
i
The cost of a calculation rises rapidly with the size
of the basis set:
1
v      r1 v r1   r2  r2 dr1dr2
 r12 
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.4 Properties of Limiting Hartree-Fock Models
•
1.
2.
3.
4.
For computation, it is expected to have errors
in:
Relative energies
Geometries
Vibrational frequencies
Properties such as dipole moments
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.4.1 Reaction Energies
•
•
Hartree-Fock models is compare with
homolytic bond dissociation energies.
For example in methanol,
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.4.1 Reaction Energies
•
The poor results seen for homolytic bond
dissociation reactions do not necessarily carry
over into other types of reactions as long as the
total number of electron pairs is maintained.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.4.2 Equilibrium Geometries
•
•
•
Systematic discrepancies are also noted in
comparisons involving limiting Hartree-Fock and
experimental.
They are geometries and bond distances.
The reason is that limiting Hartree-Fock bond
distances is shorter than experimental values.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.4.3 Vibrational Frequencies
•
•
The error in bond distances for limiting HartreeFock models calculated frequencies are larger
than experimental frequencies.
The reason is that the Hartree-Fock model does
not dissociate to the proper limit of two radicals
as a bond is stretched.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.4.4 Dipole Moments
•
Electric dipole moments are compared, the
calculated values are larger than experimental
values.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.5 Theoretical Models and Theoretical Model
Chemistry
•
•
Limiting Hartree-Fock models do not provide
results that are identical to experimental
results.
Theoretical model chemistry is a detailed
theory starting
from the electronic
Schrödinger equation
and ending with a
useful scheme.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.6 Moving Beyond Hartree-Fock Theory
•
Improvements will increase the cost of a
calculation.
• 2 approaches to improve Hartree-Fock theory:
1. Increases the flexibility by combining it with
wave functions corresponding to various excited
states.
2. Introduces an explicit term in the Hamiltonian
to account for the interdependence of electron
motions.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.6.1 Configuration Interaction Models
•
Improvements will increase the cost of a
calculation.
• 2 approaches to improve Hartree-Fock theory:
1. Increases the flexibility by combining it with
wave functions corresponding to various excited
states.
2. Introduces an explicit term in the Hamiltonian
to account for the interdependence of electron
motions.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.6.2 Møller-Plesset Models
•
Møller-Plesset models are based on HartreeFock wave function and ground-state energy E0
as exact solutions.
Hˆ  Hˆ 0  Vˆ
where Vˆ = small perturbation
λ = dimensionless parameter
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL FORMULATION OF MØLLER-PLESSET
MODELS
Substituting the expansions into the Schrödinger
equation and gathering terms in λn yields
Hˆ 0  E 0 0
Hˆ  1  Vˆ  E 0  1  E 1
0
0
0
Hˆ 0  2   Vˆ 1  E 0  2   E 1 1  E 2 0
...
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL FORMULATION OF MØLLER-PLESSET
MODELS
Multiplying each by ψ0 and integrating over all
space yields the following expression for the nthorder (MPn) energy:
E 0    ... 0 Hˆ 0 d 1d 2 ...d n
E 1   ... 0Vˆ 0 d 1d 2 ...d n
E 2    ... 0 Hˆ  1d 1d 2 ...d n
...
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL FORMULATION OF MØLLER-PLESSET
MODELS
In this framework, the Hartree-Fock energy is the
sum of the zero- and firstorder Møller-Plesset
energies:


E 0   E 1   ... 0 Hˆ  Vˆ  1d 1d 2 ...d n
The first correction, E(2) can be written as follows
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL FORMULATION OF MØLLER-PLESSET
MODELS
The integrals (ij || ab) over filled (i and j) and empty (a
and b) molecular orbitals account for changes in
electron–electron interactions as a result of electron
promotion,
ij ab  ij ab  ij ja
in which the integrals (ij | ab) and (ib | ja) involve
molecular orbitals rather than basis functions.
The two integrals are related by a simple
transformation,
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.6.3 Density Functional Models
•
•
Density functional theory is based on the
availability of an exact solution for an idealized
many-electron problem.
The Hartree-Fock energy may be written as
E HF  ET  EV  E J  EK
where ET = kinetic energy
EV = the electron–nuclear potential energy
EJ = Coulomb
EK = interaction energy
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.6.3 Density Functional Models
•
For idealized electron gas problem:
E DFT  ET  EV  E J  E XC
where EXC = exchange/correlation energy
•
Except for ET, all components depend on the
total electron density, p(r):
 r   2
orbitals

i
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
 i r 
2
MATHEMATICAL FORMULATION OF DENSITY
FUNCTIONAL THEORY
Within a finite basis set (analogous to the LCAO
approximation for Hartree Fock models), the
components of the density functional energy, EDFT,
can be written as follows:
 h 2e 2 2 
ET      r 
 v r dr

v
 2me

basis functions
nuclei


Z Ae 2
2
EV     v    r 
 v r dr

v
A

 4  0 r  RA
basis functions
1
E J       v   v  
2  v  
basis functions
E XC   f  r ,  r ...dr
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL FORMULATION OF DENSITY
FUNCTIONAL THEORY
Better models result from also fitting the gradient
of the density. Minimizing EDFT with respect to the
unknown orbital coefficients yields a set of matrix
equations, the Kohn-Sham equations, analogous to
the Roothaan-Hall equations
Fc  Sc
Here the elements of the Fock matrix are given by
XC
Fv  H core

J

F
v
v
v
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL FORMULATION OF DENSITY
FUNCTIONAL THEORY
FXC is the exchange/correlation part, the form of
which depends on the particular
exchange/correlation functional used. Note that
substitution of the Hartree-Fock exchange, K, for
FXC yields the Roothaan-Hall equations.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.6.4 Overview of Quantum Chemical Models
•
An overview of quantum chemical models.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.7 Gaussian Basis Sets
•
•
•
LCAO approximation requires the use of a finite
number of well-defined functions centered on
each atom.
Early numerical calculations
use nodeless
Slater-type orbitals (STOs),
If the AOs are expanded
in terms of Gaussian functions,
g ijk r   Nx y z e
i
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
j
k r 2
26.7.1 Minimal Basis Sets
•
•
•
The minimum number is the number of
functions required to hold all the electrons of
the atom while still maintaining its overall
spherical nature.
This simplest representation or minimal basis
set involves a single (1s) function for hydrogen
and helium.
In STO-3G basis set,
basis functions is expanded
in terms of three
Gaussian functions.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.7.2 Split-Valence Basis Sets
•
Minimal basis set is bias toward atoms with
spherical environments.
• A split-valence basis set represents core
atomic orbitals by one set of functions and
valence atomic orbitals by two sets of functions:
 for lithium to neon
 for sodium to argon
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.7.3 Polarization Basis Sets
•
•
Minimal (or split-valence) basis set functions are
centered on atoms rather than between atoms.
The inclusion of polarization functions can
be thought about either in terms of hybrid
orbitals.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.7.4 Basis Sets Incorporating Diffuse Functions
•
•
Calculations involving anions can pose problems
as highest energy electrons may only be loosely
associated with specific atoms (or pairs of
atoms).
In these situations, basis sets may need to be
supplemented by diffuse functions.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8 Selection of a Theoretical Model
•
Hartree-Fock models have proven to be
successful in large number of situations and
remain a mainstay of computational chemistry.
• Correlated models can be divided into 2
categories:
1. Density functional models
2. Møller-Plesset models
• Transitionstate geometry optimizations are
more time-consuming than equilibrium
geometry optimizations, due primarily to guess
of geometry.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.1 Equilibrium Bond Distances
•
•
Hartree-Fock double bond lengths are shorter
than experimental distances.
Treatment of electron correlation involves the
promotion of electrons from occupied molecular
orbitals to unoccupied molecular orbitals.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.2 Finding Equilibrium Geometries
•
•
•
An equilibrium structure corresponds to the
bottom of a well on the overall potential energy
surface.
Equilibrium structures that cannot be detected
are referred to as reactive intermediates.
Geometry optimization does not guarantee that
the final geometry will have a lower energy
than any other geometry of the same molecular
formula.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.3 Reaction Energies
•
Reaction energy comparisons are divided into
three parts:
1. Bond dissociation energies
2. Energies of reactions relating structural isomers
3. Relative proton affinities.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.4 Energies, Enthalpies, and Gibbs Energies
•
•
•
Quantum chemical calculations account for
thermochemistry by combining the energies of
reactant and product molecules at 0 K.
Residual energy of vibration is ignored.
We would need 3 corrections:
1. Correction of the internal energy for finite
temperature.
2. Correction for zero point vibrational energy.
3. Corrections of entropy.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.5 Conformational Energy Differences
•
•
Hartree-Fock models overestimate differences
by large amounts.
Correlated models also typically overestimate
energy differences but magnitudes of the errors
are much smaller than those seen for HartreeFock models.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.6 Determining Molecular Shape
•
•
The problem of identifying the lowest energy
conformer in simple molecules is when the
number of conformational degrees of freedom
increases.
Sampling techniques will need to replace
systematic procedures for complex molecules,
thus Monte Carlo methods is used.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.7 Alternatives to Bond Rotation
•
Single-bond rotation is the most common
mechanism for conformer interconversion.
• 2 other processes are known:
1. Inversion is associated with pyramidal
nitrogen or phosphorus and involves a planar
transition state.
2. Pseudorotation is associated with trigonal
bipyramidal phosphorus and involves a squarebased-pyramidal
transition state.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.8 Dipole Moments
•
•
Dipole moments from the two Hartree-Fock
models are larger than experimental values due
to behavior of the limiting Hartree-Fock model.
Recognize that electron promotion from
occupied to unoccupied molecular orbitals takes
electrons from “where they are” to “where they
are not”.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.9 Atomic Charges: Real or Make Believe?
•
Charge distributions assess overall molecular
structure and stability.
•
Mulliken population analysis can be used to
formulate atomic charges.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
MATHEMATICAL DESCRIPTION OF THE MULLIKEN
POPULATION ANALYSIS
The Mulliken population analysis starts from the
definition of the electron density, ρ(r), in the
framework of the Hartree-Fock model:
 r  
basis functions
 
Pv r v r 
v
Summing over basis functions and integrating over
all space leads to an expression for the
total number of electrons, n:
basis functions
  r dr   
v
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Pv r v r  
basis functions
 
v
Pv S v  n
MATHEMATICAL DESCRIPTION OF THE MULLIKEN
POPULATION ANALYSIS
where Sμv are elements of the overlap matrix:
S v    r v r dr
It is possible to equate the total number of
electrons in a molecule to a sum of products of
density matrix and overlap matrix elements as
follows:
basis functions
 
Pv S v 
v
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
basis functions

P  2
basis functions
 
v
Pv S v  n
MATHEMATICAL DESCRIPTION OF THE MULLIKEN
POPULATION ANALYSIS
According to Mulliken’s scheme, the gross electron
population for basis function is given by
q  P 
basis functions
 
Pv S v
v
Atomic electron populations, qA, and atomic
charges, QA, follow, where ZA is the atomic
basis function
number of atom A:
on atom A
qA 

QA  Z A  q
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
q
26.8.10 Transition-State Geometries and Activation
Energies
•
Transition-state theory states that all reactants
have the same energy, or that none has energy
in excess of that needed to reach the transition
state.
•
Hartree-Fock models overestimate the
activation energies by large amounts.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.8.11 Finding a Transition State
•
•
There is less effort (energy) by passing through
a “valley” between two “mountains” (pathway
B).
Saddle point referred to a maximum and
minimum in the transition state.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9 Graphical Models
•
Molecular orbitals, electron density and
electrostatic potential can be defined a isovalue
surface or isosurface:
f x, y, z   constant
•
Most common graphical models are on
electron density surfaces and electrostatic
potential.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.1 Molecular Orbitals
•
Molecular orbitals, ψ, are written as
i 
•
basis functions

ci
Highest energy occupied molecular orbital
(HOMO) holds the highest energy electrons
and is attack by electrophiles, while lowest
energy unoccupied molecular orbital (the
LUMO) provides the lowest energy space for
additional electrons and attack by nucleophiles.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.2 Orbital Symmetry Control of Chemical Reactions
•
HOMO and LUMO (frontier molecular
orbitals) could be used to rationalize why
some chemical reactions proceed easily
whereas others do not.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.3 Electron Density
•
Electron density ρ(r) is written in terms of
•
Depending on the value, isodensity surfaces can
either serve to locate atoms to delineate
chemical bonds or to indicate overall molecular
size and shap.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.4 Where Are the Bonds in a Molecule?
•
•
An electron density surface can be used to
know the location of bonds in a molecule.
Electron density surfaces is also use as the
description of the bonding in transition states
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.5 How Big Is a Molecule?
•
•
The size of a molecule can be defined according
to the amount of space that it takes up in a
liquid or solid.
The electron density provides an alternate
measure of how much space molecules actually
take up.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.6 Electrostatic Potential
•
The electrostatic potential,εp, is defined as
p 
nuclei

A
•
basis function
 r v r 
e2 Z A
   Pv 
dr
40 RAP  v
rp
*
Note that electrostatic potential represents a
balance between repulsion of the point charge
by the nuclei and attraction of the point charge
by the electrons.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.7 Visualizing Lone Pairs
•
•
The octet rule dictates that each main-group
atom in a molecule will be surrounded by eight
valence electrons.
A comparison between electrostatic potential
surfaces for ammonia in both the observed
pyramidal and unstable trigonal planar
geometries.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.8 Electrostatic Potential Maps
•
Most commonly used property map is the
electrostatic potential map.
•
It gives the value of the electrostatic potential
at locations on a particular surface.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.8 Electrostatic Potential Maps
•
Electrostatic potential maps are used to
distinguish between molecules in which charge
is localized from those where it is delocalized.
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
26.9.10 Conclusions
•
Inability of the calculations to deal highly reactive
molecules that
1. difficult to synthesize
2. with reaction transition states
•
1.
2.
3.
Limitations of quantum chemical calculations are:
Practical and numerical results not match
Important quantities cannot be yield
Calculations apply strictly to isolated molecules (gas
phase)
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Example 27.1
a. Are the three mirror planes for the NF3
molecule in the same or in different classes?
b. Are the two mirror planes for H2O in the same or
in different classes?
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd
Solution
a. NF3 belongs to the C3v group, which contains
1
2
ˆ
ˆ
ˆ
the rotation operators C3 , C3  C3  , and Cˆ33  E and the
vertical mirror planes  v 1,  v 2, and  v 3 . These
operations and elements are illustrated by this
figure:
Chapter 26: Computational Chemistry
Physical Chemistry 2nd Edition
© 2010 Pearson Education South Asia Pte Ltd