Introduction
Reaction Coordinates and Potential Energy
Scan,
Population Analysis
Prepared by: Ben Joseph R. Cuyacot
Introduction
Reaction Coordinates and Potential
Energy Scan
Prepared by: Ben Joseph R. Cuyacot
The most important and basic types of calculations in
computational chemistry
• the optimization and
• the frequency calculations.
These methods offer the essential factors for
thermodynamic and kinetic information to
characterize a chemical reaction.
The first step always choose an appropriate
computational method since the surface of the
Potential Energy Surface (right) is highly dependent
on the method.
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In chemistry, a reaction coordinate is
“representation” of progress along a reaction
pathway. It is usually a geometric parameter that
changes during the conversion of one or more
molecular entities.
In computational chemistry usually is very complex
to study the entire surface, also considering that
not all points are interesting. For this reason and
for the simplicity of working on 2D the required
points for a reaction are the minima, maxima and
saddle points which will no make our Reaction
Coordinates.
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In chemistry, a reaction coordinate is an abstract
coordinate which represents progress along a
reaction pathway. It is usually a geometric
parameter that changes during the conversion of
one or more molecular entities.
In computational chemistry usually is very complex
to study the entire surface, also considering that
not all points are interesting. for this reason and
for the simplicity of working on 2D the required
points for a reaction are the minima, maxima and
saddle points which will make our Reaction
Coordinates.
An important fact to model a chemical reaction is
to draw “approximate” PES (2 RC) of the system
with the objective to start with better structures.
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Characterizing the PES
Minima represents stable or quasi-stable species, i.e.
reactants and products with finite lifetime.
Saddle point represents a maximum along only one direction
(that of the reaction coordinate) and is a minimum along all
other directions. In other words, a saddle point represents a
transition state along the reaction coordinate.
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An important fact to model a chemical reaction is
to draw “approximate” PES (2 RC) of the system
with the objective to start with better structures.
Step 1: Optimizations of Initial Geometries (i.e.
Reactants and Products)
• Frequency Calculation
Step 2: TS Characterization
• Scan
• Frequency Calculation
• Confirmation (IRC, etc)
Task
➢model the reaction of this dimerization.
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STEPS:
1. Optimize Reactants and
Products
2. Explore PES by
performing a Scan
3. Performed an
Optimization (TS)
calculation on the TS
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STEPS:
1. Optimize Reactants and
Products
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STEPS:
1. Optimize Reactants and Products
commands:
$ module add gaussian:09.E1
$ g09 input.com > output.log
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STEPS:
1. Optimize Reactants and
Products
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STEPS:
2. Explore PES by performing
a Scan
commands:
$ module add gaussian:09.E1
$ g09 input.com > output.log
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STEPS:
2. Explore PES by performing
a Scan
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STEPS:
3. Performed an
Optimization (TS) calculation
on the TS
commands:
$ module add gaussian:09.E1
$ g09 input.com > output.log
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STEPS:
3. Performed an
Optimization (TS) calculation
on the TS
Task
> model the reaction of this classic SN2 reaction.
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STEPS:
1. Optimize Reactants and
Products
2. Explore PES by
performing a Scan
3. Performed an
Optimization (TS)
calculation on the TS
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Population Analysis
Population analysis is the study of charge distribution within molecules.
What does a population analysis deliver
• Determination of the distribution of electrons in a molecule
• Describing the shape of orbitals
• Derivation of atomic charges and dipole ( multiple ) moments
Methods of calculation
• Based on the wave function ( Mulliken, NBO)
• Based on the electron density (Atoms in Molecules)
• Fitted to the electrostatic potential (CHELPG, MK)
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Mulliken Population Analysis
Advantages
• Available in nearly every software program (most popular method) for molecular modeling.
• Fast and simple method for determination of electron distribution and atomic charged
Disadvantages
• Strong dependence of the results from the level of theory (basis set or kind of calculation)
Example: Li-charge in LiF
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Population basis set q(Li,RHF) q(Li,B3LYP)
Mulliken STO-3G
6-31G
6-311G(d)
+0.227
+0.743
+0.691
+0.078
+0.593
+0.558
Lӧwdin population analysis
Advantages
• Sought to improve upon the Mulliken method
• More stable than Mulliken with changes in basis set.
Disadvantages
• More computationally expensive
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Natural Bond Orbital Analysis
NBO classifies atomic orbitals into two distinct groups: NAOs, NBOs. NAOs are made up of basis
sets of single atoms (core, valence and Rydberg) and the NBOs are a combination of basis set
atomic orbitals of two atoms.
Two parts of the methods
• NPA ! Natural population analysis to identify the population numbers
• NBO ! Analysis of the bond order based on the electron population obtained by NPA
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Natural Bond Orbital Analysis
Advantages
• Smaller dependence on the basis set
• better reproducibility for different molecules
• Orientates itself at the formalism for Lewis formulas
Disadvantages
• More computationally expensive
• tends to predict larger charged.
• best used for comparing differences rather than absolute atomic charges.
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AIM (Atoms in Molecules)
The population analysis using Atoms in Molecules theory is requested by keyword AIM in a Gaussian
input file. Atoms in Molecules theory bases its calculations on the calculated electron density. The
existence of critical points defines the existence of a bond between two nuclei in AIM.
Advantages
• Almost no dependence on the level of basis sets.
Disadvantages
• For a low level of theory mostly inappropriate
• Instability during calculation runs
• relatively computationally expensive.
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Task
1. Draw HF molecule, optimize the geometry and generate G09
input.
2. Use pop=(full) Pop=Full for Mulliken and Pop=NBO
After Pop command, add a space and type ”FormCheck”
3. Run the calculation
Visualizing the orbitals
1. Open the *FChk file in Avogadro
2. Click on Extensions ! Create Surface
3. Select ”Molecular Orbital” as surface type
4. Choose the MO you want to visualize and calculate
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You should be able to see something like these that shows the HOMO
and LUMO of HF molecules
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End
Prepared by: Ben Joseph R. Cuyacot