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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