Introduction to Computational Quantum Chemistry
Lesson 8: Population analysis
Martin Novák & Pankaj Lochan Bora
Population Analysis
November8,2016 1/12
Importance
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
• Creating orbital shape
• 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)
Martin Novák & Pankaj Lochan Bora
Population Analysis
□       SP        -        =       5 -oc\o November8,2016 2/12
Mulliken Population Analysis
Advantages o Most popular method
• Available in nearly every software program for molecular modeling.
• Fast and simple method for determination of electron distribution and atomic charged
Disadvantage
• Strong dependance of the results from the level of theory (basis set or kind of calculation)
Example: Li-charge in LiF
Population	basis set	q(l_i,RHF)	q(l_i,B3LYP)
Mulliken	STO-3G 6-31G 6-311G(d)	+0.227 +0.743 +0.691	+0.078 +0.593 +0.558
Martin Novák & Pankaj Lochan Bora
Population Analysis
November8,2016 3/12
Lowdin population analysis
Advantages
• Sought to improve upon the Mulliken method
• More stable than Mulliken with changes in basis set. Disadvantage
o More computationally expensive
Martin Novák & Pankaj Lochan Bora
Population Analysis
□       SP        -        =       5 -oc\o November8,2016 4/12
Natural Bond Orbital Analysis
Martin Novák & Pankaj Lochan Bora
Population Analysis
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
Martin Novák & Pankaj Lochan Bora
Population Analysis
□       SP        -        =       5 -oc\o November8,2016 6/12
Advantages
• Smaller dependence on the basis set
o 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.
Population Analysis
November 8, 2016 7/12
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.
Advantage:
• Almost no dependence on the level of basis sets. Disadvantage:
a For a low level of theory mostly inappropriate
• Unstability during calculation runs
• relatively computationally expensive.
Population Analysis
November8,2016 8/12
Practical task
• Draw HF molecule, optimize the geometry and generate G09 input.
• Use pop=(nbo,savenbo) for NBO or Pop=Full for Mulliken
• After Pop command, add a space and type "FormCheck"
• Run the calculation
Martin Novák & Pankaj Lochan Bora
Population Analysis
□       SP        -        =       5 -oc\o November8,2016 9/12
Visualizing the orbitals
o Open the *FChk file in Avogadro
• Click on Extensions -> Create Surface
o Select "Molecular Orbital" as surface type
• Choose the MO you want to visualize and calculate
Martin Novák & Pankaj Lochan Bora
Population Analysis
□       SP        -        =       5 -oc\o November 8, 2016 10/12
You should be able to see something like these that shows the HOMO and LUMO of HF molecules
Martin Novák & Pankaj Lochan Bora
Population Analysis
November 8, 2016 11/12