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.
Energy minimization methods - Molecular ModelingChandni Pathak
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).
PHARMACOHORE MAPPING AND VIRTUAL SCRRENING FOR RESEARCH DEPARTMENTShikha Popali
THE PHARMACOPHORE MAPPING AND VIRTUAL SCRRENING , THESE PRESENTATION INCLUDES THE DEATIL ACCOUNT ON PHARMACOPHORE, MAPPING, ITS IDENTIFIATION FEATURES, ITS CONFORMATIONAL SEARCH, INSILICO DRUG DESIGN, VIRTUAL SCREENING, PHARMACOPHORE BASED SCREENING
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.
Energy minimization methods - Molecular ModelingChandni Pathak
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).
PHARMACOHORE MAPPING AND VIRTUAL SCRRENING FOR RESEARCH DEPARTMENTShikha Popali
THE PHARMACOPHORE MAPPING AND VIRTUAL SCRRENING , THESE PRESENTATION INCLUDES THE DEATIL ACCOUNT ON PHARMACOPHORE, MAPPING, ITS IDENTIFIATION FEATURES, ITS CONFORMATIONAL SEARCH, INSILICO DRUG DESIGN, VIRTUAL SCREENING, PHARMACOPHORE BASED SCREENING
Quantum Mechanics in Molecular modelingAkshay Kank
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.
The screening of chemical libraries with traditional methods, such as high-throughput screening (HTS), is expensive and time consuming. Quantitative structure–activity relation (QSAR) modeling is an alternative method that can assist in the selection of lead molecules by using the information from
reference active and inactive compounds. This approach requires good molecular descriptors that are representative of the molecular features responsible for the relevant molecular activity.
Molecular Mechanics in Molecular ModelingAkshay Kank
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.
PREDICTION AND ANALYSIS OF ADMET PROPERTIES OF NEW.pptxMO.SHAHANAWAZ
Detail about PREDICTION AND ANALYSIS OF ADMET PROPERTIES OF NEW MOLECULES AND IT’S IMPORTANCE IN DRUG DISCOVERY, including DESCRIPTORS OF ADMET PREDICTION, DATASETS USED IN ADMET PREDICTION
MOLECULAR DOCKING AND DRUG RECEPTOR INTERACTION AGENT ACTING.pptxMO.SHAHANAWAZ
Point to point M.pharm CADD presentation on MOLECULAR DOCKING AND DRUG RECEPTOR INTERACTION AGENT ACTING, Dihydro Folate reductase Inhibiter (Methotrexate)
Quantum Mechanics in Molecular modelingAkshay Kank
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.
The screening of chemical libraries with traditional methods, such as high-throughput screening (HTS), is expensive and time consuming. Quantitative structure–activity relation (QSAR) modeling is an alternative method that can assist in the selection of lead molecules by using the information from
reference active and inactive compounds. This approach requires good molecular descriptors that are representative of the molecular features responsible for the relevant molecular activity.
Molecular Mechanics in Molecular ModelingAkshay Kank
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.
PREDICTION AND ANALYSIS OF ADMET PROPERTIES OF NEW.pptxMO.SHAHANAWAZ
Detail about PREDICTION AND ANALYSIS OF ADMET PROPERTIES OF NEW MOLECULES AND IT’S IMPORTANCE IN DRUG DISCOVERY, including DESCRIPTORS OF ADMET PREDICTION, DATASETS USED IN ADMET PREDICTION
MOLECULAR DOCKING AND DRUG RECEPTOR INTERACTION AGENT ACTING.pptxMO.SHAHANAWAZ
Point to point M.pharm CADD presentation on MOLECULAR DOCKING AND DRUG RECEPTOR INTERACTION AGENT ACTING, Dihydro Folate reductase Inhibiter (Methotrexate)
Building a mobile reaction lab notebook (ACS Dallas 2014)Alex Clark
Describes how a mobile app is being designed to capture chemical reactions at the planning stage, and to record experimental measurements. The app is designed with a data-pure approach to capturing the cheminformatic content of a reaction, which opens the door to a diverse variety of helpful functionality, such as calculation of green chemistry metrics.
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.
- Markov Chain
Random movements, one follow another
- Importance sampling
To sample many points in the region where the Boltzmann factor is large and few elsewhere
- Ergodicity (ensemble average)
Such an average over all possible quantum states of a system
- Detailed Balance
Excess gibbs free energy models,MARGULES EQUATION
,REDLICH-KISTER EQUATION,VAN LAAR EQUATION
,WILSON AND “NRTL” EQUATION
,UNIversal QUAsi Chemical equation
International Journal of Engineering Research and DevelopmentIJERD Editor
• Electrical, Electronics and Computer Engineering,
• Information Engineering and Technology,
• Mechanical, Industrial and Manufacturing Engineering,
• Automation and Mechatronics Engineering,
• Material and Chemical Engineering,
• Civil and Architecture Engineering,
• Biotechnology and Bio Engineering,
• Environmental Engineering,
• Petroleum and Mining Engineering,
• Marine and Agriculture engineering,
• Aerospace Engineering
Atmosphere Clouds Model Algorithm for Solving Optimal Reactive Power Dispatch...ijeei-iaes
In this paper, a new method, called Atmosphere Clouds Model (ACM) algorithm, used for solving optimal reactive power dispatch problem. ACM stochastic optimization algorithm stimulated from the behavior of cloud in the natural earth. ACM replicate the generation behavior, shift behavior and extend behavior of cloud. The projected (ACM) algorithm has been tested on standard IEEE 30 bus test system and simulation results shows clearly about the superior performance of the proposed algorithm in plummeting the real power loss.
Loss Reduction by Optimal Placement of Distributed Generation on a Radial feederIDES Editor
Due to the increasing interest on renewable sources
in recent times, the studies on integration of distributed
generation to the power grid have rapidly increased. In order
to minimize line losses of power systems, it is crucially
important to define the location of local generation to be placed.
Proper location of DGs in power systems is important for
obtaining their maximum potential benefits. This paper
presents analytical approaches to determine the optimal
location to place a DG on radial systems to minimize the power
loss of the system. Simulation results are given to verify the
proposed analytical approaches.
SIMULTANEOUS OPTIMIZATION OF STANDBY AND ACTIVE ENERGY FOR SUB-THRESHOLD CIRC...VLSICS Design
Increased downscaling of CMOS circuits with respect to feature size and threshold voltage has a result of
dramatically increasing in leakage current. So, leakage power reduction is an important design issue for
active and standby modes as long as the technology scaling increased. In this paper, a simultaneous active
and standby energy optimization methodology is proposed for 22 nm sub-threshold CMOS circuits. In the
first phase, we investigate the dual threshold voltage design for active energy per cycle minimization. A
slack based genetic algorithm is proposed to find the optimal reverse body bias assignment to set of noncritical paths gates to ensure low active energy per cycle with the maximum allowable frequency at the
optimal supply voltage. The second phase, determine the optimal reverse body bias that can be applied to
all gates for standby power optimization at the optimal supply voltage determined from the first phase.
Therefore, there exist two sets of gates and two reverse body bias values for each set. The reverse body bias
is switched between these two values in response to the mode of operation. Experimental results are
obtained for some ISCAS-85 benchmark circuits such as 74L85, 74283, ALU74181, and 16 bit RCA. The
optimized circuits show significant energy saving ranged (from 14.5% to 42.28%) and standby power
saving ranged (from 62.8% to 67%).
SIMULTANEOUS OPTIMIZATION OF STANDBY AND ACTIVE ENERGY FOR SUB-THRESHOLD CIRC...VLSICS Design
Increased downscaling of CMOS circuits with respect to feature size and threshold voltage has a result of
dramatically increasing in leakage current. So, leakage power reduction is an important design issue for
active and standby modes as long as the technology scaling increased. In this paper, a simultaneous active
and standby energy optimization methodology is proposed for 22 nm sub-threshold CMOS circuits. In the
first phase, we investigate the dual threshold voltage design for active energy per cycle minimization. A
slack based genetic algorithm is proposed to find the optimal reverse body bias assignment to set of noncritical
paths gates to ensure low active energy per cycle with the maximum allowable frequency at the
optimal supply voltage. The second phase, determine the optimal reverse body bias that can be applied to
all gates for standby power optimization at the optimal supply voltage determined from the first phase.
Therefore, there exist two sets of gates and two reverse body bias values for each set. The reverse body bias
is switched between these two values in response to the mode of operation. Experimental results are
obtained for some ISCAS-85 benchmark circuits such as 74L85, 74283, ALU74181, and 16 bit RCA. The
optimized circuits show significant energy saving ranged (from 14.5% to 42.28%) and standby power
saving ranged (from 62.8% to 67%).
SIMULTANEOUS OPTIMIZATION OF STANDBY AND ACTIVE ENERGY FOR SUB-THRESHOLD CIRC...VLSICS Design
Increased downscaling of CMOS circuits with respect to feature size and threshold voltage has a result of dramatically increasing in leakage current. So, leakage power eduction is an important design issue for active and standby modes as long as the technology scaling increased. In this paper, a simultaneous active and standbyrgy optimization methodology is proposed for 22 nm sub-threshold CMOS circuits. In thefirst phase, we investigate the dual threshold voltage design for active energy per cycle minimization. A slack based genetic algorithm is proposed to find the optimal reverse body bias assignment to set of noncritical paths gates to ensure low active energy per cycle with the maximum allowable frequency at the optimal supply voltage. The second phase, determine the optimal reverse body bias that can be applied to
all gates for standby power optimization at the optimal supply voltage determined from the first phase. Therefore, there exist two sets of gates and two reverse body bias values for each set. The reverse body bias is switched between these two values in response to the mode of operation. Experimental results are obtained for some ISCAS-85 benchmark circuits such as 74L85, 74283, ALU74181, and 16 bit RCA. The optimized circuits show significant energy saving ranged (from 14.5% to 42.28%) and standby power saving ranged (from 62.8% to 67%).
SIMULTANEOUS OPTIMIZATION OF STANDBY AND ACTIVE ENERGY FOR SUB-THRESHOLD CIRC...VLSICS Design
Increased downscaling of CMOS circuits with respect to feature size and threshold voltage has a result of dramatically increasing in leakage current. So, leakage power reduction is an important design issue for active and standby modes as long as the technology scaling increased. In this paper, a simultaneous active and standby energy optimization methodology is proposed for 22 nm sub-threshold CMOS circuits. In the first phase, we investigate the dual threshold voltage design for active energy per cycle minimization. A
slack based genetic algorithm is proposed to find the optimal reverse body bias assignment to set of noncritical
paths gates to ensure low active energy per cycle with the maximum allowable frequency at the optimal supply voltage. The second phase, determine the optimal reverse body bias that can be applied to all gates for standby power optimization at the optimal supply voltage determined from the first phase.
Therefore, there exist two sets of gates and two reverse body bias values for each set. The reverse body bias is switched between these two values in response to the mode of operation. Experimental results are obtained for some ISCAS-85 benchmark circuits such as 74L85, 74283, ALU74181, and 16 bit RCA. The optimized circuits show significant energy saving ranged (from 14.5% to 42.28%) and standby power
saving ranged (from 62.8% to 67%)
CEM Workshop Lectures (5/11): Best Practices in RCS PredictionAbhishek Jain
Above lecture can be downloaded from www.zeusnumerix.com
Computational Electromagnetics Workshop Lecture 5 of 11. The lecture is designed such that it can be read independently. It covers the basics of electromagnetics, issues that can happen with the mesh, how to post-process the results and analysis. The general advice is given for setting up the simulation and use of boundary conditions.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Multi-objective whale optimization based minimization of loss, maximization o...IJECEIAES
Huge need in electricity causes placement of Distribution Generation (DG)s like Photovoltaics (PV) systems in distribution side for enhancing the loadability by improving the voltage stability and minimization of loss with minimum cost. Many optimal placements of DG have done in focus of minimum loss and improving voltage profile. This Whale optimization is a new optimization technique framed with mathematics of spiral bubble-net feeding behavior of humpback whales for solving a power system multi-objective problem considering cost of the power tariff and DG. Here main objectives are minimizing loss and cost with maximization of voltage stability index. IEEE 69 power system data is used for solution of the proposed method.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
1. Presented by Guided by
Mr. Pradeep V. Kore Mr.
M. Pharm. ( II Sem ) M. Pharm.
Department of Pharmaceutical Chemistry
JSPM’s Charak College of Pharmacy & Research,
Gat No. 720(1/2), Wagholi, Pune-Nagar road,
Wagholi-412 207.
1 1
3. INTRODUCTION
In computational chemistry energy minimization (also called
energy optimization or geometry optimization) methods are
used to compute the equilibrium configuration of molecules
and solids.
Energy minimizatiom methods can precisely locate minimum
energy confirmation by mathematically “homing in” on the
energy function minima (one at a time).
The goal of energy minimization is to find a route (consisting
of variation of the intramolecular degrees of freedom) from an
initial confirmation to nearest minimum energy confirmation
using the smallest number of calculations possible.
5/9/2012 3
4. In molecular modeling we are interested in minimum points on
the energy surface.
Minimum energy arrangments of the atoms corresponds to
stable states of the system:
Any movement away from a minimum gives a configuration
with higher energy.
There may be a very large number of minima on energy
surface. The minimum with very lowest energy is known as the
Global Energy Minimum.
5/9/2012 4
6. What can energy minimization do?
It can repair distorted geometries by moving atoms to release
internal constraints, as shown below:
In this example, the CZ of a phenylanalnine ring was artificially
stretched out, which lead to bonds much too long.
Fig: Phenylanalnine
5/9/2012 6
7. By first invoking an energy computation, the C-terminal Oxygen
(OXT) is added to the residue. Note that the residue must also be
protonated, and in this case an N-terminal blocking group (HHT)
is added. Then the energy computation can be done:
The direction in which atoms should be displaced in order to
reach a lowe energy state are shown by dotted lines. A
minimal deplacement appears in dark blue, while a big
deplacement appear in red (blue-green-red gradient).
5/9/2012 7
8. After an energy minimization (200 cycles of Steepest
Descent), the geometry is repaired, and all the force vectors are
dark blue, which means a minimum has been reached.
Fig: Repaired geometry structure
5/9/2012 8
9. Energy minimising procedures
1) Conformational energy searching
2) Energy minimisation
3) Minimisation algorithms
5/9/2012 9
10. Conformational energy searching
Energy is a function of the degrees of freedom in a molecule:
bonds, angles, dihedrals.
Conformational energy searching is used to find all of the
energetically preferred conformations of a molecule.
This is mathematically equivalent to locating all of the minima of
the energy function of the molecule.
The possible conformations for a molecule lie on an n-dim.
Lattice, with n being the number of degrees of freedom.
5/9/2012 10
11. Systematic energy sampling is thus technically impossible for
almost all molecules in question, due to the high large number
of required sampling points.
Need for methods to speed up energy minima localisation.
5/9/2012 11
13. Minimisation algorithms are designed to head down-hill towards
the nearest minimum.
Remote minima are not detected, because this would require some
period of up-hill movement.
Minimisation algorithms monitor the energy surface along a series
of incremental steps to determine a down-hill direction.
5/9/2012 13
14. •The local shape of the energy surface around a given conformation
en route to a minimum is often assumed to be quadratic so as to
simplify the mathematics.
•An energy minimum can be characterised by a small change in
energy between steps and/or by a zero gradient of the energy
function
5/9/2012 14
15. Approximation of the quadratic energy function
Approximation of the quadratic energy function is given by
aTaylor series:
f(x)= f(P) – bx + 1/2Ax2
P- is the current point
x -an arbitrary point on the energy surface
b- is the gradient at
P, A- is the
Hessian matrix
(the second partial derivatives) at P. A and b can be viewed
as parameters that fit the idealised quadratic form to the actual
energy surface.
5/9/2012 15
16. Minimisation algorithms
Simplex algorithm
- Not a gradient minimization method.
- Used mainly for very crude, high energy starting structures.
Steepest descent minimiser
- Follows the gradient of the energy function (b) at each step.
This results in successive steps that are always mutually
perpendicular, which can lead to backtracking.
- Works best when the gradient is large (far from a minimum).
- Tends to have poor convergence because the gradient becomes
smaller as a minimum is approached.
5/9/2012 16
17. Conjugate gradient and Powell minimiser
Remembers the gradients calculated from previous steps to help
reduce backtracking.
Generally finds a minimum in fewer steps than Steepest
Descent.
May encounter problems when the initial conformation is far
from a minimum.
5/9/2012 17
18. Newton-Raphson and BFGS minimiser
- Predicts the location of a minimum, and heads in that direction.
- Calculates (Newton-Raphson) or approximates (BFGS) the second
derivatives in A.
- Storage of the A term can require substantial amounts of
computer memory
- May find a minimum in fewer steps than the gradient-only
methods.
- May encounter serious problems when the initial conformation is
far from a minimum.
5/9/2012 18
19. Types of minima:
weak strong
strong local local
local minimum minimum
f(x) minimum strong
global
minimum
feasible region x
which of the minima is found depends on the starting point
such minima often occur in real applications
5/9/2012 19