Energy minimization methods - Molecular Modeling

Methods to minimize the energy of molecules during drug designing - Computational chemistry. According to the PCI syllabus, B.Pharm 8th Sem - Computer-Aided Drug Design (CADD).

1. MOLECULAR MODELING ENERGY MINIMIZATION METHODS Prepared by: Chandni Pathak (180821101075) 8th Sem, B.Pharm Parul Institute of Pharmacy

2. Contents Molecular Modeling Energy Minimization Basic Steps of EM EM techniques

3. MOLECULAR MODELING Molecular Modeling is a group of computerized techniques which are being used to predict molecular and biological properties or to analyze molecular systems using the basic principles of theoretical chemistry in conjunction with or without available experimental data.

4. ENERGY MINIMIZATION The main objective of molecular mechanics is to find the lowest energy conformation of a molecule and this process is termed as Energy minimization or Geometry optimisation method. Definition :- It is the process of finding an arrangement in space of a collection of atoms where, according to some computational model of chemical bonding, the net interatomic force on each atom is acceptably close to zero and the position on the Potential Energy Surface (PES) is a stationary point.

5. Potential Energy Surface (PES) It is a plot of the mathematical relationship between the molecular structure and its energy .

6. ENERGY MINIMIZATION In short, it is a procedure that attempts to minimize the potential energy of the system to the lowest possible point. The system makes several changes in the atom position through rotation and calculates energy in every position. This process is repeated many times to find the position with lowest energy until an overall minimum energy is attained. In every move the energy is kept lowered, otherwise the atom will return to its original position. The one full round of an atom rotation is called minimization step or iteration.

7. ENERGY MINIMIZATION EM is used for : Locating a stable conformation Locating Global and Local minima Locating a saddle point

8. 4 MAIN STEPS: Computation of the potential energy of the starting geometry Alterations of the atomic positions of each atom and computing the energy of the entire molecule If the energy of the new conformer is less than the starting one, adopt this conformation and proceed for next alteration otherwise retain the first one Repeat the process till there is no more decrease in the potential energy

9. TECHNIQUES OF GEOMETRY OPTIMIZATION Steepest descent Newton-Raphson method Conjugate gradient Quasi-Newton Raphson or variable matrix method Downhill Simplex

10. Steepest Descent Method Simplest method for Geometry Optimization Also called as Gradient Descent Method. Optimization algorithm for obtaining local minimum of a multi-dimensional function. The energy minimization methodology needs to involve identification of the point closest to the starting structure.

11. Steepest Descent Method Simplest technique which uses the first derivative (dE/dX i = 0). R i+1 = R i - 𝞪F i Where, i = iteration number R i = Old coordinates R i+1 = New coordinates F i = Force (energy gradient) on the atoms at step ‘i’ and ‘𝛂’, a constant, determining the extent to which force is applied

12. Steepest Descent Method This method converges rapidly when first derivatives are large, i.e. the geometry is far away from the minimum. The method slows down considerably when it comes close to a minimum. Near the minimum, its progress is so slow that it almost never reaches the bottom.

13. B. Newton - Raphson minimization methods In this method, inverse of the second derivative matrix (Hessian) is used. The method can be implemented in full or partial [Block diagonal (BDNR)] matrix form. The method is the most computationally expensive per step of all the methods utilized to perform EM. Advantage :- The minimization could converge in one or two steps. Disadvantage :- This method requires the calculation of the second derivatives.

14. C. Conjugate Gradient Method It is a first order minimization technique. It uses for both the current gradient and the previous search direction to drive the minimization. The number of computing cycles required for a conjugated gradient calculation is approximately proportional to the number of atoms (N, and the time per cycle is proportional to N 2 . Require fewer energy evaluations and gradient calculations Convergence characterizations are better than the steepest gradient.

15. D. Quasi - Newton Raphson Method These methods avoid the difficult evaluation of the generalized inverse of the Hessian matrix. Consequently, these methods are faster ones. DFP (Davidson, Fletcher and Powell) and BFGS (Broyden, Fletcher, Goldfard and Shanno) methods are representatives of this class.

16. F. Downhill Simplex Method It is a robust and non-derivative-based method which probably is one of the easiest method to implement. It requires only function evaluation.

17. REFERENCE https://www.slideshare.net/PavanBadgujar/seminar-energy-minimization-mettthod https://vlab.amrita.edu/?sub=3&brch=277&sim=1491&cnt=1 A textbook of drug design and development by M.R. Yadav and P.R. Murumkar

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