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2
Computational Methods Of Theoretical Chemistry 
3 
Simulation chemical structures 
Calculation vibrational wavenumbers, intensities 
and normal DIAGRAM 
modes of vibrations 
Simulation of vibrational spectra by applying 
quantum chemical calculations 
Yields useful information on molecular potential 
energy surfaces and force constants
THEORETICAL METHODS 
MOLECULAR MECHANICS QUANTUM MECHANICS 
Ab initio quantum 
chemical method 
Ab initio followed by 
empirical scaling 
of force constants 
DENSITY 
FUNCTIONAL 
THOERY 
MOLLER 
PLESSET 
Semiempirical 
Quantum Chemical 
HARTREE 
FOCK 
Method 
4
Classical approach 
Does not use molecular Hamiltonian 
operator and wave function 
It views the molecule as atoms held by 
bonds 
Expresses energy in terms of internal 
degrees of freedom 
Using NCA, appropriate frequency 
assignment can be performed 
5
With the increase of complexity, molecular mechanics no 
longer suitable for large molecules 
Larger deviation between theoretical and experimental 
frequencies 
Unable to predict intensities 
Impossible to simulate IR and Raman spectra 
6
Quantum Chemical Methods 
Uses the laws of quantum mechanics rather than 
classical physics 
Energy and related properties of the molecule 
obtained by solving Schrodinger equation 
There are different QCMs, characterized by their 
mathematical approximation to its solution. 
1.Semi empirical methods 
2. Ab- inito method 
7 
H y =Ey
SEMI EMPIRICAL METHODS 
It uses simpler Hamiltonian rather than the correct 
one 
Use parameters whose values are adjusted to fit with 
experimental data. 
Provides fairly good theoretical results 
Demerits with the Vibration prediction using 
empirical forces: 
sufficient accuracy is not obtained 
depends on the choice of force constants 
leads to wrong vibrational assignments 
8
AB INITIO METHODS 
Derived directly from theoretical principles 
Does not use experimental data other than the values 
of the fundamental physical constants 
Uses exact Hamiltonian 
Merits 
Ab initio methods includes treatment of electron 
correlation 
Lead to calculations of molecular geometries 
Spectroscopic properties are very close to experimental 
data. 
Efficient to predict the properties of molecule 
9
AB INITIO METHODS 
Hartree Fock self 
consistant field 
•Simulation of the 
infrared and 
Raman intensities 
•Simulation of 
vibrational spectra 
•Large deviation 
between the 
calculated and 
observed frequency 
at the HF-SCF level 
•This is due to 
neglect of electron 
correlation and 
anharmonicity 
Moller–Plesset 
Perturbation theory 
•Which treats electron 
correlation as a 
perturbation of the 
Fock operator. 
Disadvantages 
•It does not use 
variational method. 
•The estimate of the 
correlation energy can 
be too large. 
Density Functional 
Theory 
•Calculates molecular 
energy from electron 
density 
•Deliver force field of 
high accuracy 
•Its lower 
computational 
requirements allow it 
to tackle larger poly 
atomic molecules 
10
DFT allows all properties to be determined 
by electron density ,n(r), as a function of 
three variables r = (x,y,z) 
DFT offers an elegant formulation of N-particles 
quantum mechanics, conceptual 
simplicity and computational efficiency 
Extends limitations of accuracy from 
approximation to unknown energy terms 
11
Finite number of atomic orbitals centered 
at each atomic nucleus within the molecule 
Initially, these atomic orbitals were Slater 
Type Orbital (STO), which corresponded to 
a set of functions which decayed 
exponentially with distance from the nuclei 
STOs could in turn be approximated as 
linear combinations of Gaussian 
orbitals(G) 
Types are 
Minimal basis sets 
12
Polarized basis sets 
* - Addition of polarized function ‘d ̕ 
**- Addition of polarized function ‘p ̕ 
6-31G(d) or 6-31G* 
6-31G(d, p) or 6-31G** 
Diffuse functions 
+ - Diffuse functions added to heavy atoms 
++ - Diffuse functions added to light atoms 
Exchange and correlation functional 
B3LYP - Becke’s three parameter exchange 
functional + Correlation functional of Lee, Yang and 
Parr. 
13
Drawbacks of Ab Initio Methods 
The calculated frequencies are higher than their 
experimental counterpart 
Over estimation of force constant is due to, 
Basis set incompleteness 
Incomplete implementation of electronic 
correlation 
Neglect of anharmonicity effect in theoretical 
treatment 
14
Scaled Quantum chemical Calculations 
15 
Introduces empirical adjustment at two levels 
molecular geometry, force constant 
The procedure empirical correction of Ab initio method– 
Scaling 
Scale factors depends on the usage of both method and 
basis set (6-31G, 6-31G*, 6-311+G**) 
Types of Scaling applied for correcting the Ab initio force 
field 
Uniform Scaling 
Selective scaling 
Using the number of scale factors, the observed 
frequencies are reproduced reasonably well 
Employs different scale factors for different coordinates
FLOW CHART OF COMLETE SQM 
PROCEDURE 
16

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Density Functional Theory

  • 1.
  • 2. 2
  • 3. Computational Methods Of Theoretical Chemistry 3 Simulation chemical structures Calculation vibrational wavenumbers, intensities and normal DIAGRAM modes of vibrations Simulation of vibrational spectra by applying quantum chemical calculations Yields useful information on molecular potential energy surfaces and force constants
  • 4. THEORETICAL METHODS MOLECULAR MECHANICS QUANTUM MECHANICS Ab initio quantum chemical method Ab initio followed by empirical scaling of force constants DENSITY FUNCTIONAL THOERY MOLLER PLESSET Semiempirical Quantum Chemical HARTREE FOCK Method 4
  • 5. Classical approach Does not use molecular Hamiltonian operator and wave function It views the molecule as atoms held by bonds Expresses energy in terms of internal degrees of freedom Using NCA, appropriate frequency assignment can be performed 5
  • 6. With the increase of complexity, molecular mechanics no longer suitable for large molecules Larger deviation between theoretical and experimental frequencies Unable to predict intensities Impossible to simulate IR and Raman spectra 6
  • 7. Quantum Chemical Methods Uses the laws of quantum mechanics rather than classical physics Energy and related properties of the molecule obtained by solving Schrodinger equation There are different QCMs, characterized by their mathematical approximation to its solution. 1.Semi empirical methods 2. Ab- inito method 7 H y =Ey
  • 8. SEMI EMPIRICAL METHODS It uses simpler Hamiltonian rather than the correct one Use parameters whose values are adjusted to fit with experimental data. Provides fairly good theoretical results Demerits with the Vibration prediction using empirical forces: sufficient accuracy is not obtained depends on the choice of force constants leads to wrong vibrational assignments 8
  • 9. AB INITIO METHODS Derived directly from theoretical principles Does not use experimental data other than the values of the fundamental physical constants Uses exact Hamiltonian Merits Ab initio methods includes treatment of electron correlation Lead to calculations of molecular geometries Spectroscopic properties are very close to experimental data. Efficient to predict the properties of molecule 9
  • 10. AB INITIO METHODS Hartree Fock self consistant field •Simulation of the infrared and Raman intensities •Simulation of vibrational spectra •Large deviation between the calculated and observed frequency at the HF-SCF level •This is due to neglect of electron correlation and anharmonicity Moller–Plesset Perturbation theory •Which treats electron correlation as a perturbation of the Fock operator. Disadvantages •It does not use variational method. •The estimate of the correlation energy can be too large. Density Functional Theory •Calculates molecular energy from electron density •Deliver force field of high accuracy •Its lower computational requirements allow it to tackle larger poly atomic molecules 10
  • 11. DFT allows all properties to be determined by electron density ,n(r), as a function of three variables r = (x,y,z) DFT offers an elegant formulation of N-particles quantum mechanics, conceptual simplicity and computational efficiency Extends limitations of accuracy from approximation to unknown energy terms 11
  • 12. Finite number of atomic orbitals centered at each atomic nucleus within the molecule Initially, these atomic orbitals were Slater Type Orbital (STO), which corresponded to a set of functions which decayed exponentially with distance from the nuclei STOs could in turn be approximated as linear combinations of Gaussian orbitals(G) Types are Minimal basis sets 12
  • 13. Polarized basis sets * - Addition of polarized function ‘d ̕ **- Addition of polarized function ‘p ̕ 6-31G(d) or 6-31G* 6-31G(d, p) or 6-31G** Diffuse functions + - Diffuse functions added to heavy atoms ++ - Diffuse functions added to light atoms Exchange and correlation functional B3LYP - Becke’s three parameter exchange functional + Correlation functional of Lee, Yang and Parr. 13
  • 14. Drawbacks of Ab Initio Methods The calculated frequencies are higher than their experimental counterpart Over estimation of force constant is due to, Basis set incompleteness Incomplete implementation of electronic correlation Neglect of anharmonicity effect in theoretical treatment 14
  • 15. Scaled Quantum chemical Calculations 15 Introduces empirical adjustment at two levels molecular geometry, force constant The procedure empirical correction of Ab initio method– Scaling Scale factors depends on the usage of both method and basis set (6-31G, 6-31G*, 6-311+G**) Types of Scaling applied for correcting the Ab initio force field Uniform Scaling Selective scaling Using the number of scale factors, the observed frequencies are reproduced reasonably well Employs different scale factors for different coordinates
  • 16. FLOW CHART OF COMLETE SQM PROCEDURE 16