The document discusses quantum mechanics and ab initio methods. It explains that the Schrodinger equation is the basic wave equation used in quantum mechanics to describe particle behavior. Ab initio methods refer to solving the Schrodinger equation without approximations, which is the highest level of quantum mechanics. There are two approaches to ab initio - calibrated uses a fixed basis set and calibrates calculations, while converged uses improving basis sets until results converge. Ab initio is based on the self-consistent field method and Hartree-Fock approximation to calculate energies and new orbitals iteratively until self-consistency is achieved.

1. 1
Quantum Mechanics
Ab-Initio
Abhijeet Kadam
TSEC
BioTechnology

2. 2
Schrodinger equation
● The Schrodinger equation is the name of the basic non-relativistic
wave equation used in one version of quantum mechanics to describe
the behaviour of a particle in a field of force.
● Non-relativistic quantum mechanics refers to the mathematical
formulation of quantum mechanics applied in the context of Galilean
relativity, more specifically quantizing the equations of classical
mechanics by replacing dynamical variables by operators.
● In quantum mechanics, the analogue of Newton's law (F = ma) is
Schrödinger's equation for a quantum system.
● It is not a simple algebraic equation, but in general a linear partial
differential equation, describing the time-evolution of the system's
wave function (also called a "state function").
●

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Ab-Initio
● Schrodinger equation + Approximations = Semiempirical QM
● Schrodinger equation – Approximations = Ab-Initio QM
● Ab-Initio is the Highest level of Quantum Mechanics
● 2 approaches
– Calibrated – Pople and coworkers
– Converged – Chemical Physicist

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Calibrated
● Full exact equations without approximations
● Basic set is fixed
● Calculations are calibrated
● Errors measured on average error w.r.t.
Experiment
● More practical and used routinely

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Converged
● Sequence of calculations
● With improving/changing basic sets till
convergence is reached
● Error measured w.r.t. sensitivity of results to
further refinement in basic set
● Used for small molecules and test cases

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Ab-Initio
● Based on self-consistant feild (SCF)
● Electron-electron replusion noted the most
● Uses Hartree-Fock approximation
– determination of the wave function and the energy of
a quantum many-body system in a stationary state.
● Treats single electron at a time w.r.t others
● Self consistency acheived by iterations

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● Energy calculations from SCF are used to
calculate a new set of orbitals
● And again used for new repulsion energy
● Processes repeated till convergence accurred
and self-consistency is acheived

8. 8
● Higher the number of basic set of orbitals – more
sophesticated ab-initio and slower
● Standard ab-initio
– Good results for ground state molecular geometry
– Good Energy distribution
– Good charge distribution
● Most popular ab-initio methord – Gaussian and
Hondo series