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2/17/11
1
Introduction to Energy Minimization
BIOL 7110 / CHEM 8901 / BIOL 4105 / CHEM 4804
February 17, 2011
The semiharmonic restraint
K = 10 kcal/(mol•Å
2
) and k
box
= 10Å.
Used as the “box” restraint in Oscar
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2
The semiharmonic restraint
K = 10 kcal/(mol•Å
2
) and k
box
= 10Å.
This is an example of a onedimensional energy surface.
Onedimensional potential energy surface: nbutane
E(
φ
) (kcal/mol)
E(
φ
) = 2.5 + (7/6)*cos(
φ
) + 0.5*cos(2
φ
) + (11/6)*cos(3
φ
)
φ
(deg)
2/17/11
3
TwoDimensional
Energy Surfaces
Energy Minimization:
• a conformational search algorithm
• an optimization algorithm
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4
Conformational Searches
Goal:
To find the lowest energy structure
Approach:
Calculate energy for different conformations
Question:
How to vary the conformation?
Different search algorithms have different rules
Optimization of the Structure
Assumption: the optimal structure is the structure that has the
lowest energy
as calculated by the potential energy function
.
The energy surface is very complex, even for small molecules. The development
of optimization algorithms is an area of major ongoing research efforts.
The conformational energy surface
is a 3Ndimensional surface.
Optimization problem is confounded by the multiple minimum problem
.
2/17/11
5
Search Algorithm #1
Sample problem:
What is the lowest point on Mars?
Search strategy 1:
Grid Search
This is a reasonable strategy for this problem, because:
• you can cover the surface completely with
a grid of reasonable fineness
• it’s a 2D search surface
• The continuous function h(x,y) is well behaved
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This note was uploaded on 09/22/2011 for the course BIOL 7110 taught by Professor Steveharvey during the Spring '11 term at Georgia Institute of Technology.
 Spring '11
 SteveHarvey

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