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This document discusses various methods for energy minimization in molecular modeling, including non-derivative methods like the simplex method and sequential univariate method, as well as first derivative methods like steepest gradient and conjugate gradient. The goal of energy minimization is to determine the lowest energy conformation of a molecule by systematically adjusting atomic coordinates. Non-derivative methods require only energy evaluations but may need many steps, while derivative methods use gradient and Hessian information to converge more efficiently in fewer steps.

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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).

energy minimization

The document discusses energy minimization methods in computational chemistry. It explains that energy minimization aims to find the lowest energy confirmation of a molecule by varying its intramolecular degrees of freedom. This corresponds to stable molecular states. Several algorithms are used for energy minimization, including steepest descent, conjugate gradient, and Newton-Raphson methods. The goal is to locate minima on the multidimensional energy surface in the fewest computational steps.

Molecular modelling

Molecular modelling techniques help scientists visualize molecules and discover new drug compounds. They use computational methods to mimic molecular behavior without physical experiments. Molecular modelling includes molecular mechanics, which calculates molecular energies and motions using parameters like potential energy surfaces and force fields, and quantum mechanics, which provides nuclear positions and distributions based on electron and nuclear interactions using equations like the Schrodinger equation. Key steps in molecular modelling for drug design include generating lead molecules, minimizing molecular energies, analyzing conformations, and developing pharmacophore models of receptor sites.

Energy minimization

THE ENERGY MINIMIZATION, FOR THE STUDENTS OF M.PHARM, B.PHARM AND OTHERS USEFUL FOR ACADEMIC TOO. THE PRESENT DATA IS MOST USEFUL FOR PHARMACY PURPOSE.

7.local and global minima

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 minimum energies within a small region, and global minima, which represent the absolute lowest energy structure 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. Non-derivative minimization methods like the simplex method require only energy evaluations but may need many steps.

Energy minimization

Introduction
2.Potential energy surface
3.Basics of energy minimization
Energy Minimization Algorithms
1.Steepest Descent
2.Conjugate Gradient

Seminar energy minimization mettthod

The document discusses various energy minimization methods used to optimize molecular geometries and find low energy conformations. It describes molecular mechanics force fields and parameters used in energy minimization. Common energy minimization methods include first-order methods like steepest descent and conjugate gradient, as well as second-order Newton-Raphson methods. Examples are given of minimizing the energies of small organic molecules like lactic acid and drug molecules glyburide and repaglinide using conjugate gradient minimization.

Molecular modelling

MM is the excellent strategical tool in the world of computational Chemistry. I tried my best to
compile overall aspects.

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).

energy minimization

The document discusses energy minimization methods in computational chemistry. It explains that energy minimization aims to find the lowest energy confirmation of a molecule by varying its intramolecular degrees of freedom. This corresponds to stable molecular states. Several algorithms are used for energy minimization, including steepest descent, conjugate gradient, and Newton-Raphson methods. The goal is to locate minima on the multidimensional energy surface in the fewest computational steps.

Molecular modelling

Molecular modelling techniques help scientists visualize molecules and discover new drug compounds. They use computational methods to mimic molecular behavior without physical experiments. Molecular modelling includes molecular mechanics, which calculates molecular energies and motions using parameters like potential energy surfaces and force fields, and quantum mechanics, which provides nuclear positions and distributions based on electron and nuclear interactions using equations like the Schrodinger equation. Key steps in molecular modelling for drug design include generating lead molecules, minimizing molecular energies, analyzing conformations, and developing pharmacophore models of receptor sites.

Energy minimization

THE ENERGY MINIMIZATION, FOR THE STUDENTS OF M.PHARM, B.PHARM AND OTHERS USEFUL FOR ACADEMIC TOO. THE PRESENT DATA IS MOST USEFUL FOR PHARMACY PURPOSE.

7.local and global minima

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 minimum energies within a small region, and global minima, which represent the absolute lowest energy structure 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. Non-derivative minimization methods like the simplex method require only energy evaluations but may need many steps.

Energy minimization

Introduction
2.Potential energy surface
3.Basics of energy minimization
Energy Minimization Algorithms
1.Steepest Descent
2.Conjugate Gradient

Seminar energy minimization mettthod

The document discusses various energy minimization methods used to optimize molecular geometries and find low energy conformations. It describes molecular mechanics force fields and parameters used in energy minimization. Common energy minimization methods include first-order methods like steepest descent and conjugate gradient, as well as second-order Newton-Raphson methods. Examples are given of minimizing the energies of small organic molecules like lactic acid and drug molecules glyburide and repaglinide using conjugate gradient minimization.

Molecular modelling

MM is the excellent strategical tool in the world of computational Chemistry. I tried my best to
compile overall aspects.

Molecular modeling in drug design

Molecular Modeling methods # QUANTUM MECHANICS # Drug Design #
PHARMACOPHORE MODELING # MOLECULAR DOCKING #

Conformational analysis

This document discusses methods for conformational analysis of molecules, which is needed to identify a molecule's lowest energy conformation. It describes systematic search methods that systematically explore all torsion angles combinations but are limited by computational time. It also describes model-building methods that construct conformations by joining molecular fragments. Available technologies for conformational analysis include software tools from Accelrys, Molecular Networks, OpenEye, Schrodinger, and Tripos.

Molecular modelling for M.Pharm according to PCI syllabus

THE MOLECULAR MODELLING IS THE MOST IMPORTANT TOPIC FOR CHEMISTRY STUDENTS , HENCE THE THEORY OF MOLECULAR MODELLING IS COVER IN THIS PRESNTATION . HOPE THIS MATTER SAISFY ALL AS WE HAVE TRIED TO ATTEMPT ALL TH TOPICS OF IT.

Homology modelling

Prediction of the three dimensional structure of a given protein sequence i.e. target protein from the amino acid sequence of a homologous (template) protein for which an X-ray or NMR structure is available based on an alignment to one or more known protein structures

Denovo Drug Design

1) De novo drug design involves generating new drug molecules from scratch based on the 3D structure of the target receptor.
2) It uses molecular modeling tools to modify lead compounds to better interact with the receptor's binding site.
3) The process involves defining interaction sites on the receptor, generating potential drug molecules, scoring them based on their fit with the receptor, and using search algorithms to refine candidates.

Molecular docking

Molecular docking is a computer modeling technique used to predict the preferred orientation of one molecule to another when bound to form a stable complex. It involves fitting potential drug molecules into the active site of a protein receptor in order to identify which molecules may bind strongly. There are different approaches to molecular docking including rigid docking which treats molecules as rigid bodies, and flexible docking which accounts for conformational changes in ligands. The goal of docking is to find binding orientations that minimize the total energy of the system and maximize intermolecular interactions in order to predict effective drug candidates.

Quantum Mechanics in Molecular modeling

This slides gives you the information related to computer aided drug design and its application in drug discovery. Also you learn the Quantum mechanics related to the molecular mechanics. Theory related to molecular modeling and how the molecular modeling helps in drug discovery.

De novo drug design

1. Structure-based drug design relies on knowledge of the three-dimensional structure of the biological target obtained through methods such as x-ray crystallography. Candidate drugs that are predicted to bind with high affinity and selectivity to the target can be designed.
2. Structure-based drug design approaches include receptor-based drug design, which involves "building" ligands within the constraints of the binding pocket, and ligand-based drug design.
3. De novo drug design is a receptor-based approach that uses the target's 3D structure to design new molecules without existing leads. It involves building ligands that complement the active site properties through manual or automated methods.

molecular docking its types and de novo drug design and application and softw...

This ppt deals with all the aspects related to molecular docking ,its types(rigid ,flexible and manual) and screening based on it and also deals with de novo drug design , various softwares available for docking methodologies and applications for molecular docking in new drug design

Structure based drug design

The document discusses structure-based drug design (SBDD). It first provides background on drug design and SBDD. It then describes some key aspects of SBDD, including using the 3D structure of the biological target obtained from techniques like X-ray crystallography and NMR spectroscopy. It also discusses ligand-based and receptor-based drug design approaches. The document then outlines the typical steps involved in SBDD, including target selection, ligand selection, target preparation, docking, evaluating results, and discusses some molecular docking techniques and scoring functions used to predict binding.

MOLECULAR DOCKING.pptx

Molecular docking is a method to predict how two molecules, such as a ligand and a protein, will interact and bind to one another. The key steps in molecular docking include preparing the protein and ligand, analyzing the binding site, docking the ligand to the protein, scoring the docked poses, and validating the docking results. Molecular docking can be used for applications like hit identification in drug discovery and lead optimization.

Quantitative Structure Activity Relationship

This document discusses quantitative structure-activity relationships (QSAR) modeling techniques. It introduces 2D-QSAR which uses molecular descriptors to correlate structure and activity. It also discusses 3D-QSAR techniques like CoMFA and CoMSIA which use 3D molecular fields/properties and statistical methods like PLS to model activity. These techniques are useful for drug design, virtual screening, and predicting absorption, distribution, metabolism, excretion properties.

Homology Modelling

Homology modeling is a technique used to predict the 3D structure of a protein from its amino acid sequence by comparing it to proteins with similar sequences whose structures are already known. It involves searching a database for template structures, aligning the target sequence to the template, building a model by transferring 3D coordinates from the template to the target sequence, and validating the resulting model. Homology modeling works best when the sequence identity between the target and template is over 30% since protein structure is more conserved than sequence over evolution.

Molecular docking

Molecular docking involves determining the optimal orientation of two biological molecules to maximize their interaction and minimize their total energy. It is important for understanding protein-protein interactions and rational drug design. Docking programs represent molecule surfaces and match them to find orientations, evaluating via scoring functions like shape complementarity, empirical potentials, or knowledge-based potentials derived from protein structures. Common techniques include representing surfaces as spheres or alpha shapes, and optimization methods like Monte Carlo, molecular dynamics, or genetic algorithms to introduce flexibility.

Docking

Molecular docking is a method for predicting how two molecules, such as a ligand and its protein target, will interact and fit together in three dimensions. Docking has become an important tool in drug discovery for identifying potential binding conformations between drug candidates and protein targets. The key steps in a typical docking workflow involve selecting the receptor and ligand molecules, then using software to computationally predict the orientation of binding and evaluate the fit through scoring functions. Popular molecular docking software packages include AutoDock, GOLD, and Glide. Applications of docking include virtual screening in drug discovery and lead optimization.

Structure based in silico virtual screening

The document discusses structure-based in-silico virtual screening protocols. It describes virtual screening as using computer methods to discover new ligands based on a target protein's biological structure. The main goal is to reduce the enormous chemical space of potential compounds to a manageable number with the highest likelihood of becoming drug candidates. Molecular docking is a key method, involving sampling potential ligand positions in the protein's binding site and scoring the interactions. The document also discusses force field, empirical, and knowledge-based scoring functions used to evaluate docking poses. Applications mentioned include designing Hsp90 inhibitors for cancer treatment and identifying novel BACE1 inhibitors.

Molecular Mechanics in Molecular Modeling

In this slide you learn about the computational chemistry and its role in designing a drug molecule. Also learn concept about the molecular mechanics and its application to Computer Aided Drug Design. difference between the Quantum mechanics and Molecular Mechanics.

De Novo Drug Design

This document discusses de novo drug design, which involves designing novel drug structures based on the receptor structure without using existing ligands. It describes various algorithms and methods for de novo drug design, including outside-in and inside-out methods, active site analysis, whole molecule fitting, site point connection, fragment connection, sequential buildup, and random connection/disconnection methods. Each method has advantages and disadvantages for suggesting potential drug molecules.

ENERGY MINIMIZATION METHODS.pptx

The document discusses various energy minimization methods used in molecular modeling. It explains that the goal of energy minimization is to find a conformation with the lowest possible energy by making small adjustments to bond angles and lengths. It describes several common algorithms for energy minimization, including steepest descent, conjugate gradient, and Newton-Raphson methods. The document also discusses importance of energy minimization in modeling protein-ligand and protein-protein docking.

Virtual screening ppt

Molecular modelling encompasses theoretical and computational methods used to model molecular behavior. It involves computational drug design, computational biology, and materials science. Virtual screening is a computational technique used in drug discovery to search small molecule libraries and identify structures most likely to bind to targets like drug receptors and enzymes. Virtual screening can dock small molecules into known protein structures and automatically evaluate large libraries to find potential drug candidates. It has advantages of being reliable, cost-effective, time-saving, and increasing success rates. Virtual screening methods include ligand-based, structure-based, and hybrid approaches.

Energy Minimization Using Gromacs

The document discusses performing molecular dynamics simulations using GROMACS to minimize the energy of a protein structure. It describes converting protein data files, setting up the simulation box, running the simulation with tools like grompp and mdrun, and analyzing the results by visualizing trajectories and the minimized protein structure.

Molecular dynamics and Simulations

Molecular dynamics (MD) simulations allow atoms and molecules to interact over time, representing a virtual experiment. MD was used to give dynamics to SUMO proteins in solution. The SUMO protein was divided into fragments which were given random conformations using CYANA. These conformations were then converted to GROMACS format and molecular dynamics simulations were performed using GROMACS. The simulations involved energy minimization to relieve strain, followed by production runs. Various analysis tools were then used to analyze the results.

Molecular modeling in drug design

Molecular Modeling methods # QUANTUM MECHANICS # Drug Design #
PHARMACOPHORE MODELING # MOLECULAR DOCKING #

Conformational analysis

This document discusses methods for conformational analysis of molecules, which is needed to identify a molecule's lowest energy conformation. It describes systematic search methods that systematically explore all torsion angles combinations but are limited by computational time. It also describes model-building methods that construct conformations by joining molecular fragments. Available technologies for conformational analysis include software tools from Accelrys, Molecular Networks, OpenEye, Schrodinger, and Tripos.

Molecular modelling for M.Pharm according to PCI syllabus

THE MOLECULAR MODELLING IS THE MOST IMPORTANT TOPIC FOR CHEMISTRY STUDENTS , HENCE THE THEORY OF MOLECULAR MODELLING IS COVER IN THIS PRESNTATION . HOPE THIS MATTER SAISFY ALL AS WE HAVE TRIED TO ATTEMPT ALL TH TOPICS OF IT.

Homology modelling

Prediction of the three dimensional structure of a given protein sequence i.e. target protein from the amino acid sequence of a homologous (template) protein for which an X-ray or NMR structure is available based on an alignment to one or more known protein structures

Denovo Drug Design

1) De novo drug design involves generating new drug molecules from scratch based on the 3D structure of the target receptor.
2) It uses molecular modeling tools to modify lead compounds to better interact with the receptor's binding site.
3) The process involves defining interaction sites on the receptor, generating potential drug molecules, scoring them based on their fit with the receptor, and using search algorithms to refine candidates.

Molecular docking

Molecular docking is a computer modeling technique used to predict the preferred orientation of one molecule to another when bound to form a stable complex. It involves fitting potential drug molecules into the active site of a protein receptor in order to identify which molecules may bind strongly. There are different approaches to molecular docking including rigid docking which treats molecules as rigid bodies, and flexible docking which accounts for conformational changes in ligands. The goal of docking is to find binding orientations that minimize the total energy of the system and maximize intermolecular interactions in order to predict effective drug candidates.

Quantum Mechanics in Molecular modeling

This slides gives you the information related to computer aided drug design and its application in drug discovery. Also you learn the Quantum mechanics related to the molecular mechanics. Theory related to molecular modeling and how the molecular modeling helps in drug discovery.

De novo drug design

1. Structure-based drug design relies on knowledge of the three-dimensional structure of the biological target obtained through methods such as x-ray crystallography. Candidate drugs that are predicted to bind with high affinity and selectivity to the target can be designed.
2. Structure-based drug design approaches include receptor-based drug design, which involves "building" ligands within the constraints of the binding pocket, and ligand-based drug design.
3. De novo drug design is a receptor-based approach that uses the target's 3D structure to design new molecules without existing leads. It involves building ligands that complement the active site properties through manual or automated methods.

molecular docking its types and de novo drug design and application and softw...

This ppt deals with all the aspects related to molecular docking ,its types(rigid ,flexible and manual) and screening based on it and also deals with de novo drug design , various softwares available for docking methodologies and applications for molecular docking in new drug design

Structure based drug design

The document discusses structure-based drug design (SBDD). It first provides background on drug design and SBDD. It then describes some key aspects of SBDD, including using the 3D structure of the biological target obtained from techniques like X-ray crystallography and NMR spectroscopy. It also discusses ligand-based and receptor-based drug design approaches. The document then outlines the typical steps involved in SBDD, including target selection, ligand selection, target preparation, docking, evaluating results, and discusses some molecular docking techniques and scoring functions used to predict binding.

MOLECULAR DOCKING.pptx

Molecular docking is a method to predict how two molecules, such as a ligand and a protein, will interact and bind to one another. The key steps in molecular docking include preparing the protein and ligand, analyzing the binding site, docking the ligand to the protein, scoring the docked poses, and validating the docking results. Molecular docking can be used for applications like hit identification in drug discovery and lead optimization.

Quantitative Structure Activity Relationship

This document discusses quantitative structure-activity relationships (QSAR) modeling techniques. It introduces 2D-QSAR which uses molecular descriptors to correlate structure and activity. It also discusses 3D-QSAR techniques like CoMFA and CoMSIA which use 3D molecular fields/properties and statistical methods like PLS to model activity. These techniques are useful for drug design, virtual screening, and predicting absorption, distribution, metabolism, excretion properties.

Homology Modelling

Homology modeling is a technique used to predict the 3D structure of a protein from its amino acid sequence by comparing it to proteins with similar sequences whose structures are already known. It involves searching a database for template structures, aligning the target sequence to the template, building a model by transferring 3D coordinates from the template to the target sequence, and validating the resulting model. Homology modeling works best when the sequence identity between the target and template is over 30% since protein structure is more conserved than sequence over evolution.

Molecular docking

Molecular docking involves determining the optimal orientation of two biological molecules to maximize their interaction and minimize their total energy. It is important for understanding protein-protein interactions and rational drug design. Docking programs represent molecule surfaces and match them to find orientations, evaluating via scoring functions like shape complementarity, empirical potentials, or knowledge-based potentials derived from protein structures. Common techniques include representing surfaces as spheres or alpha shapes, and optimization methods like Monte Carlo, molecular dynamics, or genetic algorithms to introduce flexibility.

Docking

Molecular docking is a method for predicting how two molecules, such as a ligand and its protein target, will interact and fit together in three dimensions. Docking has become an important tool in drug discovery for identifying potential binding conformations between drug candidates and protein targets. The key steps in a typical docking workflow involve selecting the receptor and ligand molecules, then using software to computationally predict the orientation of binding and evaluate the fit through scoring functions. Popular molecular docking software packages include AutoDock, GOLD, and Glide. Applications of docking include virtual screening in drug discovery and lead optimization.

Structure based in silico virtual screening

The document discusses structure-based in-silico virtual screening protocols. It describes virtual screening as using computer methods to discover new ligands based on a target protein's biological structure. The main goal is to reduce the enormous chemical space of potential compounds to a manageable number with the highest likelihood of becoming drug candidates. Molecular docking is a key method, involving sampling potential ligand positions in the protein's binding site and scoring the interactions. The document also discusses force field, empirical, and knowledge-based scoring functions used to evaluate docking poses. Applications mentioned include designing Hsp90 inhibitors for cancer treatment and identifying novel BACE1 inhibitors.

Molecular Mechanics in Molecular Modeling

In this slide you learn about the computational chemistry and its role in designing a drug molecule. Also learn concept about the molecular mechanics and its application to Computer Aided Drug Design. difference between the Quantum mechanics and Molecular Mechanics.

De Novo Drug Design

This document discusses de novo drug design, which involves designing novel drug structures based on the receptor structure without using existing ligands. It describes various algorithms and methods for de novo drug design, including outside-in and inside-out methods, active site analysis, whole molecule fitting, site point connection, fragment connection, sequential buildup, and random connection/disconnection methods. Each method has advantages and disadvantages for suggesting potential drug molecules.

ENERGY MINIMIZATION METHODS.pptx

The document discusses various energy minimization methods used in molecular modeling. It explains that the goal of energy minimization is to find a conformation with the lowest possible energy by making small adjustments to bond angles and lengths. It describes several common algorithms for energy minimization, including steepest descent, conjugate gradient, and Newton-Raphson methods. The document also discusses importance of energy minimization in modeling protein-ligand and protein-protein docking.

Virtual screening ppt

Molecular modelling encompasses theoretical and computational methods used to model molecular behavior. It involves computational drug design, computational biology, and materials science. Virtual screening is a computational technique used in drug discovery to search small molecule libraries and identify structures most likely to bind to targets like drug receptors and enzymes. Virtual screening can dock small molecules into known protein structures and automatically evaluate large libraries to find potential drug candidates. It has advantages of being reliable, cost-effective, time-saving, and increasing success rates. Virtual screening methods include ligand-based, structure-based, and hybrid approaches.

Molecular modeling in drug design

Molecular modeling in drug design

Conformational analysis

Conformational analysis

Molecular modelling for M.Pharm according to PCI syllabus

Molecular modelling for M.Pharm according to PCI syllabus

Homology modelling

Homology modelling

Denovo Drug Design

Denovo Drug Design

Molecular docking

Molecular docking

Quantum Mechanics in Molecular modeling

Quantum Mechanics in Molecular modeling

De novo drug design

De novo drug design

molecular docking its types and de novo drug design and application and softw...

molecular docking its types and de novo drug design and application and softw...

Structure based drug design

Structure based drug design

MOLECULAR DOCKING.pptx

MOLECULAR DOCKING.pptx

Quantitative Structure Activity Relationship

Quantitative Structure Activity Relationship

Homology Modelling

Homology Modelling

Molecular docking

Molecular docking

Docking

Docking

Structure based in silico virtual screening

Structure based in silico virtual screening

Molecular Mechanics in Molecular Modeling

Molecular Mechanics in Molecular Modeling

De Novo Drug Design

De Novo Drug Design

ENERGY MINIMIZATION METHODS.pptx

ENERGY MINIMIZATION METHODS.pptx

Virtual screening ppt

Virtual screening ppt

Energy Minimization Using Gromacs

The document discusses performing molecular dynamics simulations using GROMACS to minimize the energy of a protein structure. It describes converting protein data files, setting up the simulation box, running the simulation with tools like grompp and mdrun, and analyzing the results by visualizing trajectories and the minimized protein structure.

Molecular dynamics and Simulations

Molecular dynamics (MD) simulations allow atoms and molecules to interact over time, representing a virtual experiment. MD was used to give dynamics to SUMO proteins in solution. The SUMO protein was divided into fragments which were given random conformations using CYANA. These conformations were then converted to GROMACS format and molecular dynamics simulations were performed using GROMACS. The simulations involved energy minimization to relieve strain, followed by production runs. Various analysis tools were then used to analyze the results.

12 Global Brands & Local Markets

Global brands face challenges in expanding to new markets that have different cultures. While products that succeeded in Western markets in the past could sometimes be easily adapted to other countries, today's globalism requires understanding local differences. Companies must ensure their offerings are culturally appropriate for target markets. Both product-focused and culture-focused research are needed to understand consumers, but each has advantages and limitations. Successful companies coordinate globally while allowing local responsiveness in areas like product delivery and marketing.

Vocabulary

This document discusses various applications of derivatives including position, velocity, and acceleration which are the first and second derivatives of position functions. It also covers related rates, absolute and relative extrema found using derivatives, critical numbers where the derivative equals zero, concavity determined by the second derivative, and optimization problems which use derivatives to find unknown values.

Building a mobile reaction lab notebook (ACS Dallas 2014)

This document discusses building a mobile electronic lab notebook focused on chemical reactions called the Green Lab Notebook. It would allow users to draw chemical structures, balance reactions, and calculate quantities, yields, and green metrics. Key features include digitally capturing reaction data, prioritizing computer-friendly data structures and intuitive workflows, and linking to external databases for solvent data, sustainable feedstocks, and curated green reaction transforms. The goal is to facilitate recording, analyzing, and promoting the reuse of experimental reaction data in a sustainable chemistry context.

2.molecular modelling intro

This document discusses the history and concepts of molecular modelling in drug design. It describes how early drug design involved trial and error methods to find biologically active molecules through random screening. The development of X-ray crystallography in the 1970s allowed visualization of 3D molecular structures, advancing drug design. Molecular modelling uses computer techniques based on chemistry and experimental data to analyze molecules and predict properties. The first generation of rational drug design used quantitative structure-activity relationships based on 2D structures. The second generation involves molecular modelling to simulate molecular interactions and design molecules meeting biological requirements through direct and indirect approaches as well as database searches and 3D computer-aided drug design.

Grds international conference on pure and applied science (5)

The document proposes a new hybrid conjugate gradient method called SW-A that combines the WYL and AMRI conjugate gradient methods. It presents the algorithm for SW-A and evaluates its performance on 18 standard unconstrained optimization test functions compared to WYL and AMRI in terms of number of iterations and CPU time. The results show that SW-A is able to solve all test problems while WYL solves 97% and AMRI solves 95%, demonstrating the effectiveness of the new hybrid method.

Grds international conference on pure and applied science (6)

Medical Conferences, Pharma Conferences, Engineering Conferences, Science Conferences, Manufacturing Conferences, Social Science Conferences, Business Conferences, Scientific Conferences Malaysia, Thailand, Singapore, Hong Kong, Dubai, Turkey 2014 2015 2016
Global Research & Development Services (GRDS) is a leading academic event organizer, publishing Open Access Journals and conducting several professionally organized international conferences all over the globe annually. GRDS aims to disseminate knowledge and innovation with the help of its International Conferences and open access publications. GRDS International conferences are world-class events which provide a meaningful platform for researchers, students, academicians, institutions, entrepreneurs, industries and practitioners to create, share and disseminate knowledge and innovation and to develop long-lasting network and collaboration.
GRDS is a blend of Open Access Publications and world-wide International Conferences and Academic events. The prime mission of GRDS is to make continuous efforts in transforming the lives of people around the world through education, application of research and innovative ideas.
Global Research & Development Services (GRDS) is also active in the field of Research Funding, Research Consultancy, Training and Workshops along with International Conferences and Open Access Publications.
International Conferences 2014 – 2015
Malaysia Conferences, Thailand Conferences, Singapore Conferences, Hong Kong Conferences, Dubai Conferences, Turkey Conferences, Conference Listing, Conference Alerts

Higher-Order Conjugate Gradient Method (HCGM) For Solving Continuous Optimal ...

In this paper, we considered the role of penalty when the higher-order conjugate gradient method
(HCGM) was used as a computational scheme for the minimization of penalised cost functions for optimal
control problems described by linear systems and integral quadratic costs. For this family of commonly
encountered problems, we find out that the conventional penalty methods require very large penalty constants
for good constants satisfaction. Numerical results shows that, as the penalty constant tend to infinity, the
convergence rate of the method becomes poor. To circumvent the poor convergence rate of the penalty method,
the HCGM was often considered as a good substitute to accelerate the convergence.

Hmm

Hidden Markov Models (HMM) are a machine learning method that uses probabilistic models and state machines to model sequential problems where the underlying or "hidden" states cannot be directly observed, only the outputs. An HMM has a set of states, transition probabilities between states, output symbols emitted from the states, and emission probabilities. It is useful for problems like speech recognition where the hidden states are phonemes but only acoustic signals can be observed.

Gromacs Tutorial

This document provides instructions for using GROMACS to simulate the solvation of a spider toxin peptide. It describes downloading files, setting up directories, converting file formats, building simulation boxes using editing and generation tools, and setting up energy minimization parameters. The goal is to study the peptide structure and interactions with water and ions using molecular dynamics simulations. Questions about structural stability, positions of charged residues, and the role of water will be explored.

Molecular modelling

Electrostatic Potential Models
The electrostatic potential is the energy of interaction
of a point positive charge (an electrophile) with the
nuclei and electrons of a molecule. Negative
electrostatic potentials indicate areas that are prone to
electrophilic attack. For example, a negative
electrostatic potential of benzene shows that
electrophilic attack should occur onto the p system,
while the corresponding electrostatic potential for
pyridine shows that an electrophile should attack the
nitrogen in the s plane.

Functions And Graphs Part 1

The document provides instructions for finding the first and second derivatives of a function F(x) given its graph. To find the first derivative, the student must take the derivative of F(x) and sketch its graph, labeling any roots, y-intercepts, and maxima/minima. The second derivative can be found from either the original function or its graph. No calculators are allowed.

Parallel algorithms for solving linear systems with block-fivediagonal matric...

D. Belousov, E. Akimova: Parallel algorithms for solving linear systems with block-fivediagonal matrices on multi-core CPU

Molecular mechanics

Molecular mechanics uses classical mechanics to model molecular systems by calculating the potential energy. It can study small molecules as well as large biological systems with many thousands to millions of atoms. Molecular mechanics represents atoms as spheres and bonds as springs, with interactions described by classical potentials. It has been used to calculate properties like binding constants, protein folding kinetics, and to design binding sites.

Topic 1 intro to derivatives

This document provides an introduction to derivatives. It has four main goals: 1) introduce risk and the role of derivatives in managing risk, 2) discuss general finance terms, 3) introduce three major classes of derivatives (forwards, futures, options), and 4) introduce how these securities are analyzed and the major traders. It defines derivatives as financial instruments whose value depends on underlying variables. The document discusses the basics of risk, positions (long/short), commissions, bid-ask spreads, and market efficiency. It provides an example of Disney using earthquake bonds to transfer risk from shareholders to bondholders.

Global optimization

The document discusses various optimization methods for solving different types of optimization problems. It begins by defining a general optimization problem and then describes several specific problem types including linear programming (LP), integer programming (IP), mixed-integer linear programming (MILP), nonlinear programming (NLP), and mixed-integer nonlinear programming (MINLP). It provides examples and discusses solution methods like the simplex algorithm, branch and bound, and decomposition approaches.

Optimization Methods in Finance

Non-linear optimization applications in finance including volatility estimation with ARCH and GARCH models, line search methods, Newton's method, steepest descent method, golden section search method, and conjugate gradient method.

勾配法

This document discusses gradient descent optimization methods. It begins by explaining where gradient methods are used, such as in regression and machine learning problems. It then introduces several gradient descent algorithms - steepest descent, momentum, Nesterov's accelerated gradient, and others. It provides explanations of how each algorithm works. The document ends by performing benchmarks comparing the algorithms on MNIST data and a regression problem, finding that quasi-Newton and Adam methods tend to work best. In summary, it outlines common gradient descent optimization algorithms and compares their performance on sample problems.

IB Maths. Graphs of a funtion and its derivative

This document discusses how to draw sketches of the graphs of the first and second derivatives of a given function. It includes graphs of a quadratic function and its derivatives, asking the reader to identify each function. Additional resources like worksheets are provided to help readers practice drawing derivative graphs and solving related puzzles.

Energy Minimization Using Gromacs

Energy Minimization Using Gromacs

Molecular dynamics and Simulations

Molecular dynamics and Simulations

12 Global Brands & Local Markets

12 Global Brands & Local Markets

Vocabulary

Vocabulary

Building a mobile reaction lab notebook (ACS Dallas 2014)

Building a mobile reaction lab notebook (ACS Dallas 2014)

2.molecular modelling intro

2.molecular modelling intro

Grds international conference on pure and applied science (5)

Grds international conference on pure and applied science (5)

Grds international conference on pure and applied science (6)

Grds international conference on pure and applied science (6)

Higher-Order Conjugate Gradient Method (HCGM) For Solving Continuous Optimal ...

Higher-Order Conjugate Gradient Method (HCGM) For Solving Continuous Optimal ...

Hmm

Hmm

Gromacs Tutorial

Gromacs Tutorial

Molecular modelling

Molecular modelling

Functions And Graphs Part 1

Functions And Graphs Part 1

Parallel algorithms for solving linear systems with block-fivediagonal matric...

Parallel algorithms for solving linear systems with block-fivediagonal matric...

Molecular mechanics

Molecular mechanics

Topic 1 intro to derivatives

Topic 1 intro to derivatives

Global optimization

Global optimization

Optimization Methods in Finance

Optimization Methods in Finance

勾配法

勾配法

IB Maths. Graphs of a funtion and its derivative

IB Maths. Graphs of a funtion and its derivative

7-150202040705-conversion-gate02.pdf

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.

6.ab initio qm

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.

Introduction to finite element method

Finite element method have many techniques that are used to design the structural elements like automobiles and building materials as well. we use different design software to get our simulated results at ansys, pro-e and matlab.we use these results for our real value problems.

12 l1-harmonic methodology

Structural harmonic analysis is a technique used to determine the steady-state response of a linear structure to loads that vary sinusoidally over time. Any sustained cyclic load will produce a sustained cyclic response in the structural system. Harmonic response analysis allows predicting the sustained dynamic behavior of structures to verify designs can overcome resonance, fatigue, and other harmful effects of forced vibrations. The analysis calculates the structure's response at different frequencies to identify peak responses and review stresses at peak frequencies.

Computational methodologies

Computational chemistry uses mathematical and computing methods to simulate chemical processes. It can predict molecular properties, structures, interactions and reaction pathways without expensive experiments. The main computational methods are ab initio, semi-empirical, density functional theory, molecular mechanics and molecular dynamics. Geometry optimization finds the lowest energy conformation of a molecule using algorithms to minimize the potential energy surface. It is important for understanding how structure influences properties and reactivity.

IEEE APE

1. The document presents a generalized averaging technique for analyzing power conversion circuits that goes beyond traditional state space averaging methods.
2. It describes using a Fourier series representation over a sliding time window to approximate waveforms in power electronics circuits. The Fourier coefficients become state variables to develop an averaged model.
3. An example of applying this technique to a series resonant converter is provided. The waveforms are approximated using fundamental frequency terms, resulting in a time-invariant model that captures transient behavior better than steady-state models.

paper term SUMMARY powerpoint.pptx

TWO-STAGE SYSTEM IDENTIFICATION APPROACH FOR THREE DIMENSIONAL STRUCTURE SYSTEMS SUMMARY " hASAN kATKHUDA PAPER"

Lecture on Introduction to finite element methods & its contents

The document provides an overview of the Finite Element Method (FEM) course being taught. It discusses:
1. What FEM is and its common application areas like structural analysis, heat transfer, fluid flow.
2. The main steps in FEM including discretization, selecting interpolation functions, developing element matrices, assembling the global matrix, imposing boundary conditions, and solving equations.
3. Different element types like 1D, 2D, and 3D elements and the use of isoparametric formulations.
4. The history of FEM and how it has evolved from being used on mainframe computers to PCs.

Placement and algorithm.

Placement is the process of determining the locations of circuit devices on a chip. It is a critical step that affects performance, routability, heat distribution, and power consumption. There are different types of placement like standard cell placement and building block placement. Placement algorithms aim to optimize objectives like minimizing total area and wire length. Simulated annealing is a commonly used iterative placement algorithm that models the physical annealing process to arrive at a low-cost solution. Other algorithms include partitioning-based approaches and cluster growth.

Modern power system planning new

Summary of Modern power system planning part one
"The Forecasting of Growth of Demand for Electrical Energy"
the main topic of this chapter is the analysis of the various techniques required for utility planning engineers to optimally plan the expansion of the electrical power system.

Lecture3

Lecture 3: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.

Computational chemistry

Computational chemistry uses computers to simulate chemical systems and solve equations that model their properties. It is considered a third pillar of scientific investigation, along with theory and experiment. There are several computational methodologies including quantum mechanics, molecular mechanics, and molecular dynamics. Computational chemistry software can be used to optimize molecular geometries, map potential energy surfaces, perform conformational analyses, and calculate many other molecular properties and reaction kinetics. These methods have improved significantly with increasing computer power over the past few decades.

Finite Element Methods

The document discusses various numerical methods for analyzing mechanical components under applied loads, including the finite element method. It describes weighted residual methods like the Galerkin method and collocation method which approximate solutions by minimizing residuals. The variational or Rayleigh-Ritz method selects displacement fields to minimize total potential energy. The finite element method divides a structure into small elements and applies these methods to obtain approximate solutions for displacements and stresses at discrete points.

Introduction_to_exament_Methods.pdf

This document outlines the course structure and content for ECE 2408 Theory of Structures V. The course introduces finite element methods for structural analysis. It covers matrix analysis of structures, force and deformation methods, and the use of finite element analysis software. The document compares analytical and finite element analysis methods and explains the key steps in finite element modeling and analysis, including discretization, deriving element stiffness matrices, assembling the global stiffness matrix, applying boundary conditions, and solving for displacements, strains and stresses. The course aims to provide students with skills in using finite element analysis for structural design and problem solving.

Simulated annealing presentation

Simulated annealing is a local search algorithm inspired by the annealing process in metallurgy. It is used to find optimal solutions to complex problems by simulating the cooling of materials in a heat bath. The algorithm starts with a random solution and explores neighboring solutions, accepting worse solutions with a probability based on temperature. The temperature is slowly decreased, limiting acceptance of worse solutions over time to converge to a global optimum. Practical issues include developing an effective cost function and proper cooling schedule to ensure convergence. Simulated annealing has applications in optimization problems like the traveling salesman problem.

Voltage Stability Improvement by Reactive Power Rescheduling Incorporating P...

In this paper, reactive power rescheduling is done to keep the voltage stable. Due to system
disturbances the active as well as reactive power flows changes. Generators being always connected to the
system reactive power rescheduling of generators can be effectively done. Therefore it is selected as the
suitable method for voltage control. The voltage and reactive power management is studied from the
generator’s point of view to minimize generator reactive power loss. To reduce the reactive losses
optimization procedure is used. The simulations are done using MATLAB.

Conformational_Analysis.pptx

Conformational analysis, molecular modelling technique, b.pharm 8th semester, unit 5, computer aided drug design

A Research on Optimal Power Flow Solutions For Variable Loa

This document discusses research on using optimization techniques to solve the optimal power flow problem under variable load conditions. It proposes combining the continuation method with an interior point algorithm to track optimal power flow solutions as the load parameter is increased. This would allow analyzing system behavior near the maximum loadability limit. The research aims to study optimal power flow behavior near limits, evaluate the proposed methodology's efficiency, and analyze critical bus indices and sensitivity of maximum load to reactive power injections. Results show the proposed approach can track solutions continuously for load increases where no new operational limits become active.

ME-314- Control Engineering - Week 03-04

ME-314 Introduction to Control Engineering is a course taught to Mechanical Engineering senior undergrads. The course is taught by Dr. Bilal Siddiqui at DHA Suffa University. This lecture is about modeling electrical and mechanical systems (transnational and rotational) in frequency domain.

Differential Evolution Based Optimization Approach for Power Factor Correction

In radial distribution systems, the voltages at buses
reduces when moved away from the substation, also the losses
are high. The reason for decrease in voltage and high losses is
the insufficient amount of reactive power, which can be
provided by the shunt capacitors. For this purpose, in this
paper, two stage methodologies are used. In first stage, the
load flow of pre-compensated distribution system is carried
out using ‘Dimension reducing distribution load flow
algorithm’. In the second stage, Differential Evolution (DE)
technique is used to determine the optimal location and size
of the capacitors. The above method is tested on IEEE 69 bus
system. In this paper a new method is proposed to improve the
power factor of those buses having low power factor (less than
0.8lag) to unity power factor simultaneously by placing the
capacitors.

7-150202040705-conversion-gate02.pdf

7-150202040705-conversion-gate02.pdf

6.ab initio qm

6.ab initio qm

Introduction to finite element method

Introduction to finite element method

12 l1-harmonic methodology

12 l1-harmonic methodology

Computational methodologies

Computational methodologies

IEEE APE

IEEE APE

paper term SUMMARY powerpoint.pptx

paper term SUMMARY powerpoint.pptx

Lecture on Introduction to finite element methods & its contents

Lecture on Introduction to finite element methods & its contents

Placement and algorithm.

Placement and algorithm.

Modern power system planning new

Modern power system planning new

Lecture3

Lecture3

Computational chemistry

Computational chemistry

Finite Element Methods

Finite Element Methods

Introduction_to_exament_Methods.pdf

Introduction_to_exament_Methods.pdf

Simulated annealing presentation

Simulated annealing presentation

Voltage Stability Improvement by Reactive Power Rescheduling Incorporating P...

Voltage Stability Improvement by Reactive Power Rescheduling Incorporating P...

Conformational_Analysis.pptx

Conformational_Analysis.pptx

A Research on Optimal Power Flow Solutions For Variable Loa

A Research on Optimal Power Flow Solutions For Variable Loa

ME-314- Control Engineering - Week 03-04

ME-314- Control Engineering - Week 03-04

Differential Evolution Based Optimization Approach for Power Factor Correction

Differential Evolution Based Optimization Approach for Power Factor Correction

Verb forms tenses class 9 cbse

Structures and form of all tenses with examples and related workbook exercises. Apt for cbse class 9.

Genome rearrangement

1. The document describes an experiment analyzing genome rearrangement between two pig chromosomal genomes using the SPRING tool.
2. The SPRING tool was used to input and analyze two pig chromosome Y sequences, retrieving locally collinear blocks (LCBs) that identify conserved genomic regions between the sequences.
3. The results show the LCB number and coordinates identified in each sequence, with the total LCBs covering 13.92% of one genome and 29.19% of the other.

Genome comparision

The document describes an experiment to analyze genomes using comparison tools. The aim is to compare genomes to find conserved and divergent sequences. Two tools are described: Genome VISTA and GenomeBlast, which allow uploading or entering genome sequences to compare regions and find orthologs between species. The protocol retrieves a genome from NCBI, uses Genome VISTA to submit it for comparison, and would show results of similar regions found between the query genome and other species.

Tutorial to Swiss PDB Viewer

The document describes predicting the secondary structure of two protein sequences and the secondary structure composition of protein O13837. The results show that sequence 1 is predicted to have mostly alpha helices and sequence 2 is predicted to have a mix of alpha helices and beta strands. Less than 50% coils are predicted for both sequences. The secondary structure prediction for protein O13837 shows a mix of alpha helices and beta strands.

CoMFA CoMFA Comparative Molecular Field Analysis)

Comparative Molecular Field Analysis (CoMFA) is a 3D QSAR technique that derives correlations between biological activity of molecules and their 3D shape, electrostatic, and hydrogen bonding characteristics. It involves aligning molecules, placing probes in a 3D grid around them, calculating interaction energies, and using PLS analysis to generate a regression equation and contour maps showing regions where certain properties enhance or reduce binding affinity. CoMFA is useful for predicting properties of untested molecules, optimizing lead compounds, and generating hypotheses about receptor binding sites, with hundreds of applications in drug design, particularly ligand-protein interactions.

MATLAB Bioinformatics tool box

The document provides an overview of the MATLAB Bioinformatics Toolbox. It allows for sequence analysis including alignment and searching, microarray data analysis and visualization, phylogenetic analysis, and mass spectrometry data preprocessing and visualization. Specific functions covered include sequence manipulation and statistical analysis, microarray normalization and clustering, phylogenetic tree creation and editing, and mass spectrometry spectrum analysis. Several extensions to the toolbox are also mentioned, including tools for CGH data analysis, general sequence analysis and evolution functions, efficient microarray analysis functions, and a graphical preprocessing tool for mass spectrometry data.

Global alignment

The document discusses global sequence alignment and the Needleman-Wunsch algorithm. Global alignment finds the optimal alignment of two sequences over their entire lengths by allowing gaps. It uses a dynamic programming approach to fill a matrix to find the highest scoring alignment based on matches, mismatches and gap penalties. The algorithm allows obtaining an alignment score that accounts for the total number of matches and mismatches as well as gap penalties.

Probiotics

This document provides an overview of probiotics, focusing on the bacteria Lactobacillus and Bifidobacterium. It discusses the history of probiotics, why they are important for human health, examples of foods containing probiotics, and their mechanisms of action. The document also covers commercial probiotic strains, genetically engineered probiotics, prebiotics, and Indian probiotic manufacturers.

Verb forms tenses class 9 cbse

Verb forms tenses class 9 cbse

Genome rearrangement

Genome rearrangement

Genome comparision

Genome comparision

Tutorial to Swiss PDB Viewer

Tutorial to Swiss PDB Viewer

CoMFA CoMFA Comparative Molecular Field Analysis)

CoMFA CoMFA Comparative Molecular Field Analysis)

MATLAB Bioinformatics tool box

MATLAB Bioinformatics tool box

Global alignment

Global alignment

Probiotics

Probiotics

- 1. Energy Minimization -Non-Derivative Methods -First Derivative Methods Pinky Sheetal V 1801110004 M.Tech Bioinformatics Background Image Courtesy: 3dciencia.com visual life sciences
- 2. Contents • Introduction • Criteria to start minimization • Energy Minimization –The Problem • Non Derivative Methods • Simplex Method • Sequential univariate method • First Derivative Methods • Steepest Gradient • Conjugate Gradient Method • References
- 3. Introduction • 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 [1] • Knowing the stable conformers of a molecule is important because it allows us to understand its properties and behavior based on its structure [2]
- 4. After a number of steps, a local or global minimum on the potential energy surface is reached General Formula: 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 In all these methods, a numerical test is applied to the new geometry to decide if a minimum is reached. For example, the slope may be tested to see if it is zero within some numerical tolerance. If the criterion is not met, then the formula is applied again to make another change in the geometry. [2]
- 5. 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 [3] 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. [5] – A Hessian matrix is a square matrix of second derivatives of a function. [4]
- 6. 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. [5]
- 7. • To implement the simplex algorithm it is first necessary to generate the vertices of the initial simplex. • The initial configuration of the system corresponds to just one of these vertices. The remaining points can be obtained by adding a constant increment to each coordinate in turn. The energy of the system is calculated at the new point, giving the function value for the relevant vertex. [5] • The point with the highest energy of the three is noted. Then, this point is reflected through the line segment connected the other two (to move away from the region of high energy). • If the energy of point A is the highest out of the three points A, B and C, then A is reflected through line segment BC to produce point D. • In the next step, the two original lowest energy points (B and C) along with the new point D are analyzed. The highest energy point of these is selected, and that point is reflected through the line segment connecting the other two. The process continues until a minimum is located. [2]
- 8. • The sequential univariate method is a non-derivative method that is considered more appropriate as it systematically cycles through the coordinates in turn • For each coordinate, two new structures are generated by changing the current coordinate. • The energies of these two structure are calculated. • A parabola is then fitted through the 3 points corresponding to the two distorted structures and the original structure. • The minimum point in this quadratic function is determined and the coordinate is then changed to the position of the minimum [5]
- 9. Derivative Methods • The direction of the first derivative of the energy (the gradient) indicates where the minimum lies, and the magnitude of the gradient indicates the steepness of the local slope. • The energy of the system can be lowered by moving each atom in response to the force acting on it; the force is equal to minus the gradient. • Second derivatives indicate the curvature of the function, information that can be used to predict where the function will change direction ( pass through a minimum or some other stationary point) • When discussing derivative methods it is useful to write the function[5] a Taylor as series expansion about the point Xk • Therefore first order methods use the first derivatives (gradients), second order uses both first and second derivative. The simplex method can thus be considered as a zeroth-order method as it does not use any derivatives.
- 10. Steepest Descent • In the steepest descents method, the Hessian is just approximated as a constant, γ • γ as an effective force constant and is calculated at the beginning of the first step to give a specified step size. [1] γ is a constant • In this method, the gradients at each point still must be calculated, but by not requiring second derivatives to be calculated. • The method is much faster per step than the Newton-Raphson method. • However, because of the approximation, it is not as efficient and so more steps are generally required to find the minimum. [2]
- 11. Conjugate Gradient Method • Conjugate gradient is a variation of the steepest descents method. The calculation of the gradient is improved by using information from previous steps. [1] • The gradients of the current geometry are first computed. The direction of the largest gradient is determined after the gradient of current geometry is computed. • The geometry is minimized along this one direction (this is called a line search). Then, a direction orthogonal to the first one is selected (a “conjugate” direction). The geometry is minimized along this direction. • This continues until the geometry is optimized in all the directions. • Pure steepest descents algorithms always take 90° turns after each stage, which may move the first minimization stage away from the optimal value. • If the initial steepest descents finds the minimum along the initial direction. The next best direction to look for the overall minimum is not necessarily perpendicular to the initial path. • Conjugate gradients is a good general purpose technique. [2] Figure: potential energy surface for the two variables
- 12. References 1. https://www.uzh.ch/oci/efiles/OCPkb/EnergyMinNotes.pdf 2. http://www.coursehero.com/file/2883095/38037emin/ 3. http://ocikbws.uzh.ch/education/molecular_science/mm/minimization.html 4. http://www.gromacs.org/Documentation/Terminology/ 5. A R Leach, Molecular Modelling Principles and Applications, Pearson Education Second Edition 6. http://i572-molecular-modeling.wikispaces.com/file/view/opt_lecture.pdf
- 13. Thank you