The document discusses energy minimization in molecular modeling. It explains that energy minimization aims to find the lowest energy conformation of a molecule by exploring different conformations and determining which has the smallest steric energy. There are local minima, which are relative energy minima within a small region, and global minima, which represent the absolute lowest energy state when considering the entire molecule. Molecular mechanics is preferred over quantum mechanics for energy minimization due to its ability to model larger molecules more accurately. Multiple local minima can be combined to approximate the global minimum for complex molecules with many degrees of freedom.

1. 1
Energy Minimization
Local Minima
&
Global Minima
Abhijeet Kadam
TSEC
BioTechnology

2. 2
Energy Minimization
● Once a model is constructed – we explore
conformations
● Two types of conformations
– Lowest energy structure is the str of intrest
– Other different conformations to represent the
structure

3. 3
Energy Minimization
● The lowest energy conformation is the set of bond lengths and angles that
gives the smallest steric energy.
● In other words, bonds find a compromise among competing forces to determine
the lowest energy conformation.
● The goal of molecular mechanics is to determine the lowest energy
conformation of a molecule. The process is called energy minimization
● Knowing the stable conformers of a molecule is important because it allows us
to understand its properties and behavior based on its structure.

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Energy Minimization
● Local minima – relative
● Global minima - absolute

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Local minima
● This is a relative minimum
● Confimed in a smaller place, i.e. with limited
amount of atoms
● Has same neighbourhood which can be (not
be) a part of global energy calculations

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Global minima
● This is the absolute minima
● Includes the entire energy balance of a
molecule
● It is a overall value of a set or function of a
energy calculation

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Energy Minimization
● Theoritically – QM calculations are enough for
energy calculations
● But it is not possible to be accurate in QM
– As it has number of atoms in consideration
– And that includes as many wave functions
– Also the inaccuracy in approximation is a problem
● Hence Molecular mechanics is preffered over
QM

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Energy Minimization
● Molecules have
– Number of degree of freedom
– And multiple global minimas
– Hence difficult for larger molecules
● So, we can take multiple local minimas and join
the results to get a global minima

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After a number of
steps, a local or global
minimum on the
potential energy
surface is reached
xnew - the value of the geometry at the next step
Xold - refers to the geometry at the current step
correction - some adjustment made to the geometry
General Formula:

10. 10
Criteria to start minimization
1. Starting set of atomic coordinates
2. Parameters for various terms of the potential energy function
3. Description of molecular topology
Energy Minimization – The Problem
E = f(x)
E - function of coordinates Cartesian /internal
At minimum the first derivatives are zero and
the second derivatives are all positive
Derivatives of the energy with respect to the coordinates provide information about the shape
of energy surface and also enhances the efficiency of the minimization.

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Non Derivative Methods
– Require energy evaluation only and may require many energy evaluations
–– Simplex Method
Simplex is a geometrical figure with M+1 interconnected vertices, where M is the dimensionality of the
energy function
It does not rely on the calculation of the gradients at all.
As a result, it is the least expensive in CPU time per step.
However, it also often requires the most steps.

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