Download - Density Functional Theory
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DIAGRAM
Simulation chemical structures
Calculation vibrational wavenumbers,
intensities and normal modes of vibrations
Simulation of vibrational spectra by
applying quantum chemical calculations
Yields useful information on molecular
potential energy surfaces and force constants
Computational Methods Of Theoretical Chemistry
THEORETICAL METHODS
MOLECULAR MECHANICS QUANTUM MECHANICS
Ab initio quantum chemical method
Ab initio followed by empirical scalingof force constants
DENSITY FUNCTIONAL
THOERY
MOLLERPLESSET
HARTREE FOCK
SemiempiricalQuantum Chemical
Method
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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
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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 spectra6
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
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H =E
Quantum Chemical Methods
SEMI EMPIRICAL METHODSIt 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 assignments8
AB INITIO METHODS
Derived directly from theoretical principlesDoes not use experimental data other than the
values of the fundamental physical constants Uses exact Hamiltonian
MeritsAb initio methods includes treatment of
electron correlationLead to calculations of molecular geometriesSpectroscopic properties are very close to
experimental data.Efficient to predict the properties of molecule
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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
AB INITIO METHODS
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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
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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 areMinimal basis sets Ex: STO-2G, STO-3G, STO-6G, STO-3G*Split valence Basis setsEx: 3-21G, 6-31G 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 incompletenessIncomplete implementation of electronic
correlation
Neglect of anharmonicity effect in theoretical treatment
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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 ScalingSelective scaling
Using the number of scale factors, the observedfrequencies are reproduced reasonably well
Employs different scale factors for different coordinates
Scaled Quantum chemical Calculations
FLOW CHART OF COMLETE SQM PROCEDURE
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