Zlatko Mihalić MOLEKULARNO MODELIRANJE (2+1, 0+0)

Size: px
Start display at page:

Download "Zlatko Mihalić MOLEKULARNO MODELIRANJE (2+1, 0+0)"

Transcription

1 Zlatko Mihalić MOLEKULARNO MODELIRANJE (2+1, 0+0) Asistenti doc. dr. sc. Ivan Kodrin dr. sc. Igor Rončević Literatura A. R. Leach, Molecular Modelling, Principles and Applications, 2. izdanje, Longman, F. Jensen, Introduction to Computational Chemistry, 2. izdanje, Wiley C. J. Cramer, Essentials of Computational Chemistry: Theories and Models, 3. izdanje, Wiley Uvjet za potpis prisutvovanje testovima na kojima se rješavanjem zadatka na računalu provjerava praktično znanje iz modeliranja Ispit usmeni, uz prethodnu eventualnu provjeru praktičnog znanja na računala u slučaju neprolazne ocjene iz testova MM LITERATURA MM

2 POVIJESNI OSVRT We are perhaps not far removed from the time when we shall be able to submit the bulk of chemical phenomena to calculation. J. L. Gay-Lussac, All of chemistry, and with it crystallography, would become a branch of mathematical analysis which, like astronomy, taking its constants from observation, would enable us to predict the character of any new compound and possibly the source from which its formation might be anticipated. Ch. Babbage, The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the application of these laws leads to equations much too complicated to be soluble. P. A. Dirac, MM ŠTO JE TO RAČUNALNA KEMIJA? Computational chemistry attempts to model all aspects of real chemistry as closely as possible by using calculations rather than experiment. P. v. R. Schleyer, Computational chemistry is quantitative modeling of chemical phenomena by computerimplemented techniques. (...) Computational chemistry consists of those aspects of chemical research that are expedited or rendered practical by computers. K. B. Lipkowitz, D. B. Boyd, Computational chemistry sometimes involves application of computerized algorithms from quantum theory, but computational chemistry is certainly more than quantum chemistry. (...) Molecular mechanics, molecular dynamics, computer graphics, molecular modeling, and computer-assisted molecular design are other important aspects of computational chemistry. K. B. Lipkowitz, D. B. Boyd, (Reviews in Computational Chemistry) MM

3 ŠTO JE TO RAČUNALNA KEMIJA? Computational chemistry is a branch of theoretical chemistry that uses a digital computer to model systems of chemical interest. In this discipline, the computer itself is the primary instrument of research. Computational chemistry permits calculation of quantities which can be measured experimentally, such as molecular geometries of ground and excited states, heats of formation, and ionization potentials. Alternatively, quantities not readily accessible by existing experimental techniques, such as geometries of transition states and detailed structure of liquids, may be evaluated. Because of the increasing power and availability of computers, and the simultaneous development of well-tested and reliable theoretical methods, the use of computational chemistry as an adjunct to experimental research has increased rapidly. McGraw-Hill Science & Technology Encyclopedia. MM GRANE TEORIJSKE KEMIJE KVANTNA KEMIJA RAČUNALNA KEMIJA / MOLEKULARNO MODELIRANJE MATEMATIČKA KEMIJA (KEMIJSKA TEORIJA GRAFOVA) TEORIJSKA KEMIJSKA KINETIKA KEM(O)INFORMATIKA MM

4 TEORIJA MODEL RAČUNALNI EKSPERIMENT ZNANSTVENA TEORIJA tumačenje prirodnih pojava pomoću skupa općenitih pravila, većinom kvantitativne prirode (matematičke jednadžbe) posjeduje sposobnost predviđanja, podložna eksperimentalnoj provjeri teorijski (kvantni) kemičari MODEL jednostavnija aproksimacija općenitije teorije s naglaskom na primjenljivosti, često uključuje konstante dobivene eksperimentom nagli razvoj računala omogućuje numeričko rješavanja složenih ili analitički nerješivih jednadžbi RAČUNALNI EKSPERIMENT modeliranje kemijskih sustava na računalu - treći način pristupa prirodnim znanostima računalni kemičari MM OBJEKTI MODELIRANJA POJEDINAČNE MOLEKULE (STRUKTURA, SVOJSTVA, SPEKTRI,...) INTERAKCIJA NEKOLIKO MOLEKULA (MEĐUMOLEKULSKI KOMPLEKSI,...) KEMIJSKE REAKCIJE (BRZINE, RAVNOTEŽA, MEHANIZMI,...) MNOŠTVO MOLEKULA (KLASTERI, KONDENZIRANA FAZA,...) KEMIJSKE REAKCIJE U KONDENZIRANOJ FAZI (U OTOPINI, U KRISTALIMA,...) ORGANIZIRANI SUSTAVI (STRUKTURA I FUNKCIJA BIOLOŠKIH SUSTAVA) MM

5 SADRŽAJ KOLEGIJA 0. Uvod 1. Ploha potencijalne energije (PES) 2. Molekularna mehanika 3. Traženje stacionarnih točaka na PES (optimizacija) 4. Kvantna mehanika, Hartree-Fockov model 5. Konformacijska analiza 6. Orbitale 7. Kvalitativna molekularno-orbitalna teorija (QMOT) 8. Lokalizacija molekularnih orbitala 9. Post-HF metode: CI, MPn, CC 10. Sustavno pretraživanje plohe potencijalne energije MM SADRŽAJ KOLEGIJA 11. Analiza valne funkcije 12. Teorija funkcionala elektronske gustoće (DFT) 13. Utjecaj otapala na brzinu ravnotežu kemijskih reakcija 14. Računanje kinetičkih i termodinamičkih parametara 15. Izodezmičke reakcije 16. Prijelazna struktura i reakcijske staze 17. Spektroskopija i fotokemija 18. Molekularna dinamika 19. Višeslojni modeli (QM/MM prisup) 20. Molekularno uklapanje (docking) 21. Prikazi i programi MM

Teorijska i praktična znanja programiranja i modeliranja

Teorijska i praktična znanja programiranja i modeliranja Računarstvo Programsko inženjerstvo i informacijski sustavi Programsko inženjerstvo Software engineering... the application of engineering gto software..., IEEE Std 610.12 1990, pp.67 Teorijska i praktična

More information

RAČUNALNE METODE PRILAGOĐENE ISTRAŽIVANJU BIOKEMIJSKIH/BIOLOŠKIH SUSTAVA. Kolegij: Strukturna računalna biofizika

RAČUNALNE METODE PRILAGOĐENE ISTRAŽIVANJU BIOKEMIJSKIH/BIOLOŠKIH SUSTAVA. Kolegij: Strukturna računalna biofizika RAČUNALNE METODE PRILAGOĐENE ISTRAŽIVANJU BIOKEMIJSKIH/BIOLOŠKIH SUSTAVA Kolegij: Strukturna računalna biofizika Today the computer is just as important a tool for chemists as the test tube. Simulations

More information

Computational Modeling of Protein-Ligand Interactions

Computational Modeling of Protein-Ligand Interactions Computational Modeling of Protein-Ligand Interactions Steven R. Gwaltney Department of Chemistry Mississippi State University Mississippi State, MS 39762 Auguste Comte, 1830 Every attempt to refer chemical

More information

Computational Chemistry. An Introduction to Molecular Dynamic Simulations

Computational Chemistry. An Introduction to Molecular Dynamic Simulations Computational Chemistry An Introduction to Molecular Dynamic Simulations Computational chemistry simulates chemical structures and reactions numerically, based in full or in part on the fundamental laws

More information

TEORIJA SKUPOVA Zadaci

TEORIJA SKUPOVA Zadaci TEORIJA SKUPOVA Zadai LOGIKA 1 I. godina 1. Zapišite simbolima: ( x nije element skupa S (b) d je član skupa S () F je podskup slupa S (d) Skup S sadrži skup R 2. Neka je S { x;2x 6} = = i neka je b =

More information

Dependence of the total -electron energy on a large number of non-bonding molecular orbitals

Dependence of the total -electron energy on a large number of non-bonding molecular orbitals J. Serb. Chem. Soc. 69 (10) 777 782 (2004) UDC 54 724+537.872:519.17:54 12 JSCS 3204 Original scientific paper Dependence of the total -electron energy on a large number of non-bonding molecular orbitals

More information

ANALYSIS OF THE RELIABILITY OF THE "ALTERNATOR- ALTERNATOR BELT" SYSTEM

ANALYSIS OF THE RELIABILITY OF THE ALTERNATOR- ALTERNATOR BELT SYSTEM I. Mavrin, D. Kovacevic, B. Makovic: Analysis of the Reliability of the "Alternator- Alternator Belt" System IVAN MAVRIN, D.Sc. DRAZEN KOVACEVIC, B.Eng. BRANKO MAKOVIC, B.Eng. Fakultet prometnih znanosti,

More information

dopunska znanja(stcw) Trajanje semestar modul x trimestar

dopunska znanja(stcw) Trajanje semestar modul x trimestar 1 Kod kolegija Naziv kolegija BIL302 Fizikalna kemija Opći podaci Studijski program Dodiplomski studij Biotehnologija i istraživanje lijekova Godina održavanja 3. Semestar ( modul) održavanja Status kolegija

More information

Vladimir Šips ( )

Vladimir Šips ( ) Vladimir Šips (1928 2003) Vladimir Šips in memoriam This issue of the journal FIZIKA A (Zagreb) is dedicated to the memory of Professor Vladimir Šips.1 Vladimir Šips, together with Ivan Supek, founded

More information

Oracle Spatial Koordinatni sustavi, projekcije i transformacije. Dalibor Kušić, mag. ing. listopad 2010.

Oracle Spatial Koordinatni sustavi, projekcije i transformacije. Dalibor Kušić, mag. ing. listopad 2010. Oracle Spatial Koordinatni sustavi, projekcije i transformacije Dalibor Kušić, mag. ing. listopad 2010. Pregled Uvod Koordinatni sustavi Transformacije Projekcije Modeliranje 00:25 Oracle Spatial 2 Uvod

More information

EXAM INFORMATION. Radial Distribution Function: B is the normalization constant. d dx. p 2 Operator: Heisenberg Uncertainty Principle:

EXAM INFORMATION. Radial Distribution Function: B is the normalization constant. d dx. p 2 Operator: Heisenberg Uncertainty Principle: EXAM INFORMATION Radial Distribution Function: P() r RDF() r Br R() r B is the normalization constant., p Operator: p ^ d dx Heisenberg Uncertainty Principle: n ax n! Integrals: xe dx n1 a x p Particle

More information

On behaviour of solutions of system of linear differential equations

On behaviour of solutions of system of linear differential equations Mathematical Communications (997), 47 57 47 On behaviour of solutions of system of linear differential equations Božo Vrdoljak Abstract. The present paper deals with the existence, behaviour and approximation

More information

IZVEDBENI NASTAVNI PLAN

IZVEDBENI NASTAVNI PLAN Medicinski fakultet Sveučilišta u Rijeci Kolegij: Opća i anorganska kemija Voditelj: Suradnik: Katedra: Kemija i biokemija Studij: Preddiplomski studij sanitarnog inženjerstva Godina studija: I. godina

More information

Teoría del Funcional de la Densidad (Density Functional Theory)

Teoría del Funcional de la Densidad (Density Functional Theory) Teoría del Funcional de la Densidad (Density Functional Theory) Motivation: limitations of the standard approach based on the wave function. The electronic density n(r) as the key variable: Functionals

More information

Session 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education

Session 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education Session 1 Introduction to Computational Chemistry 1 Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools

More information

Chemistry 4560/5560 Molecular Modeling Fall 2014

Chemistry 4560/5560 Molecular Modeling Fall 2014 Final Exam Name:. User s guide: 1. Read questions carefully and make sure you understand them before answering (if not, ask). 2. Answer only the question that is asked, not a different question. 3. Unless

More information

KEMIJSKI ODSJEK. ZNANSTVENO-NASTAVNO OSOBLJE I STUDENTI 27 nastavnika 30 asistenata 21 znanstveni novak 600 studenata

KEMIJSKI ODSJEK. ZNANSTVENO-NASTAVNO OSOBLJE I STUDENTI 27 nastavnika 30 asistenata 21 znanstveni novak 600 studenata KEMIJSKI ODSJEK http://www.chem.pmf.hr/ 10.000 Zagreb, Horvatovac 102a Tel.: 01+4895500, Fax: 01+4829958 Pročelnik: prof.dr.sc. Nikola Kallay (do 1.10.2005) prof.dr.sc. Tomislav Cvitaš (od 1.10.2005) e-mail:

More information

Electron Correlation

Electron Correlation Electron Correlation Levels of QM Theory HΨ=EΨ Born-Oppenheimer approximation Nuclear equation: H n Ψ n =E n Ψ n Electronic equation: H e Ψ e =E e Ψ e Single determinant SCF Semi-empirical methods Correlation

More information

APPLICATION OF THOMAS-FERMI MODEL TO FULLERENE MOLECULE AND NANOTUBE UDC 547. Yuri Kornyushin

APPLICATION OF THOMAS-FERMI MODEL TO FULLERENE MOLECULE AND NANOTUBE UDC 547. Yuri Kornyushin FACTA UNIVERSITATIS Series: Physics, Chemistry and Technology Vol. 5, N o 1, 2007, pp. 11-18 DOI: 10.2298/FUPCT0701011K APPLICATION OF THOMAS-FERMI MODEL TO FULLERENE MOLECULE AND NANOTUBE UDC 547 Yuri

More information

CHEM3023: Spins, Atoms and Molecules

CHEM3023: Spins, Atoms and Molecules CHEM3023: Spins, Atoms and Molecules CHEM3006P or similar background knowledge is required for this course. This course has two parts: Part 1: Quantum Chemistry techniques for simulations of molecular

More information

Chem 1140; Molecular Modeling

Chem 1140; Molecular Modeling P. Wipf 1 Chem 1140 $E = -! (q a + q b )" ab S ab + ab!k

More information

CHEM 545 Theory and Practice of Molecular Electronic Structure. Anna I. Krylov. DON T PANIC.

CHEM 545 Theory and Practice of Molecular Electronic Structure. Anna I. Krylov.   DON T PANIC. CHEM 545 Theory and Practice of Molecular Electronic Structure Anna I. Krylov http://iopenshell.usc.edu/chem545/ DON T PANIC USC Fall 2014 Things to do: 1. Install IQmol (by this Thursday). http://iqmol.org/.

More information

DYNAMICS OF THE DUFFING OSCILLATOR WITH IMPACTS UDC: Slavka Mitić

DYNAMICS OF THE DUFFING OSCILLATOR WITH IMPACTS UDC: Slavka Mitić UNIVERSITY OF NIŠ The scientific journal FACTA UNIVERSITATIS Series: Working and Living Environmental Protection Vol. 1, No 2, 1997, pp. 65-72 Editor of series: Ljiljana Rašković, e-mail: ral@kalca.junis.ni.ac.yu

More information

Performance of Hartree-Fock and Correlated Methods

Performance of Hartree-Fock and Correlated Methods Chemistry 460 Fall 2017 Dr. Jean M. Standard December 4, 2017 Performance of Hartree-Fock and Correlated Methods Hartree-Fock Methods Hartree-Fock methods generally yield optimized geomtries and molecular

More information

Highly accurate quantum-chemical calculations

Highly accurate quantum-chemical calculations 1 Highly accurate quantum-chemical calculations T. Helgaker Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, Norway A. C. Hennum and T. Ruden, University

More information

Lecture 4: Band theory

Lecture 4: Band theory Lecture 4: Band theory Very short introduction to modern computational solid state chemistry Band theory of solids Molecules vs. solids Band structures Analysis of chemical bonding in Reciprocal space

More information

ATOMIC STRUCTURE. Atomic Structure. Atomic orbitals and their energies (a) Hydrogenic radial wavefunctions

ATOMIC STRUCTURE. Atomic Structure. Atomic orbitals and their energies (a) Hydrogenic radial wavefunctions ATOMIC STRUCTURE Atomic orbitals and their energies (a) Hydrogenic radial wavefunctions Bundet Boekfa Chem Div, Fac Lib Arts & Sci Kasetsart University Kamphaeng Saen Campus 1 2 Atomic orbitals and their

More information

ANALYSIS OF INFLUENCE OF PARAMETERS ON TRANSFER FUNCTIONS OF APERIODIC MECHANISMS UDC Života Živković, Miloš Milošević, Ivan Ivanov

ANALYSIS OF INFLUENCE OF PARAMETERS ON TRANSFER FUNCTIONS OF APERIODIC MECHANISMS UDC Života Živković, Miloš Milošević, Ivan Ivanov UNIVERSITY OF NIŠ The scientific journal FACTA UNIVERSITATIS Series: Mechanical Engineering Vol.1, N o 6, 1999 pp. 675-681 Editor of series: Nenad Radojković, e-mail: radojkovic@ni.ac.yu Address: Univerzitetski

More information

1 Rayleigh-Schrödinger Perturbation Theory

1 Rayleigh-Schrödinger Perturbation Theory 1 Rayleigh-Schrödinger Perturbation Theory All perturbative techniques depend upon a few simple assumptions. The first of these is that we have a mathematical expression for a physical quantity for which

More information

Conceptual Chemistry West Linn High School

Conceptual Chemistry West Linn High School Conceptual Chemistry West Linn High School Unit I: Branches of Science, Metric, Sci. Method, Density Unit II: Matter, Change, Chemical Formulas and Equations Ch. 1, 6 Unit III: Periodic Table and Atomic

More information

Preliminary Program for PHD students- English language

Preliminary Program for PHD students- English language Mathematics and Computer Aided Modeling in Sciences Intensive School Novi Sad Preliminary Program for PHD students- English language Time Friday, 05/27/2011 9:00 -- 11:00 Registration 11:00-11:30 Opening

More information

Mathematics and Computer-Aided Modeling in Sciences Intensive School Novi Sad Preliminary Program for PHD students- English language

Mathematics and Computer-Aided Modeling in Sciences Intensive School Novi Sad Preliminary Program for PHD students- English language Mathematics and Computer-Aided Modeling in Sciences Intensive School Novi Sad Preliminary Program for PHD students- English language Time Friday, 05/27/2011 9:00 11:00 Registration 11:00 11:30 Opening

More information

DEVELOPMENT OF MATHEMATICAL MODELS TO PREDICT THE EFFECT OF INPUT PARAMETERS ON FEED RATE OF A RECIPROCATORY TUBE FUNNEL FEEDER

DEVELOPMENT OF MATHEMATICAL MODELS TO PREDICT THE EFFECT OF INPUT PARAMETERS ON FEED RATE OF A RECIPROCATORY TUBE FUNNEL FEEDER http://doi.org/10.24867/jpe-2018-01-067 JPE (2018) Vol.21 (1) Jain, A., Bansal, P., Khanna, P. Preliminary Note DEVELOPMENT OF MATHEMATICAL MODELS TO PREDICT THE EFFECT OF INPUT PARAMETERS ON FEED RATE

More information

Heidelberg Molecular Modelling Summer School The Challenges of Transition Metal Systems

Heidelberg Molecular Modelling Summer School The Challenges of Transition Metal Systems Heidelberg Molecular Modelling Summer School The Challenges of Transition Metal Systems Dr Rob Deeth Inorganic Computational Chemistry Group University of Warwick UK verview Is molecular modelling of TM

More information

Let a system undergo changes from a state 1 to state 2.

Let a system undergo changes from a state 1 to state 2. ME 410 Day 11 Topics First Law of Thermodynamics Applied to Combustion Constant olume Combustion Constant ressure Combustion Enthalpy of Formation Heating alues of Fuels 1. The First Law of Thermodynamics

More information

MO Calculation for a Diatomic Molecule. /4 0 ) i=1 j>i (1/r ij )

MO Calculation for a Diatomic Molecule. /4 0 ) i=1 j>i (1/r ij ) MO Calculation for a Diatomic Molecule Introduction The properties of any molecular system can in principle be found by looking at the solutions to the corresponding time independent Schrodinger equation

More information

Gustavus Adolphus College. Lab #5: Computational Chemistry

Gustavus Adolphus College. Lab #5: Computational Chemistry CHE 372 Gustavus Adolphus College Lab #5: Computational Chemistry Introduction In this investigation we will apply the techniques of computational chemistry to several of the molecular systems that we

More information

An Introduction to Quantum Chemistry and Potential Energy Surfaces. Benjamin G. Levine

An Introduction to Quantum Chemistry and Potential Energy Surfaces. Benjamin G. Levine An Introduction to Quantum Chemistry and Potential Energy Surfaces Benjamin G. Levine This Week s Lecture Potential energy surfaces What are they? What are they good for? How do we use them to solve chemical

More information

one ν im: transition state saddle point

one ν im: transition state saddle point Hypothetical Potential Energy Surface Ethane conformations Hartree-Fock theory, basis set stationary points all ν s >0: minimum eclipsed one ν im: transition state saddle point multiple ν im: hilltop 1

More information

INTRODUCTION TO LOW FREQUENCY LOCAL PLASMONS IN BULK EXTRINSIC SEMICONDUCTORS UDC 538.9; Yuri Kornyushin

INTRODUCTION TO LOW FREQUENCY LOCAL PLASMONS IN BULK EXTRINSIC SEMICONDUCTORS UDC 538.9; Yuri Kornyushin FACTA UNIVERSITATIS Series: Physics, Chemistry and Technology Vol. 2, N o 5, 2003, pp. 253-258 INTRODUCTION TO LOW FREQUENCY LOCAL PLASMONS IN BULK EXTRINSIC SEMICONDUCTORS UDC 538.9; 621.315.5 Yuri Kornyushin

More information

DESIGN AND IMPLEMENTATION OF OBJECT-ORIENTED COMPUTER SOFTWARE TO SOLVE SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

DESIGN AND IMPLEMENTATION OF OBJECT-ORIENTED COMPUTER SOFTWARE TO SOLVE SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS DESIGN AND IMPLEMENTATION OF OBJECT-ORIENTED COMPUTER SOFTWARE TO SOLVE SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS Atsa am, D. D., Department of Mathematics/Statistics/Computer

More information

General Chemistry I & Lab

General Chemistry I & Lab General Chemistry I & Lab Course Text/Materials Chang, Raymond. General Chemistry: The Essential Concepts, 6th edition, McGraw-Hill, 2010, ISBN: 9780077354718 [Students may find used, new, or rental copies

More information

ATOM atomov - indivisible

ATOM atomov - indivisible Structure of matter ATOM atomov - indivisible Greek atomists - Democrite and Leukip 300 b.c. R. Bošković - accepts the concept of atom and defines the force J. Dalton - accepts the concept of atom and

More information

Chem 3502/4502 Physical Chemistry II (Quantum Mechanics) 3 Credits Spring Semester 2006 Christopher J. Cramer. Lecture 17, March 1, 2006

Chem 3502/4502 Physical Chemistry II (Quantum Mechanics) 3 Credits Spring Semester 2006 Christopher J. Cramer. Lecture 17, March 1, 2006 Chem 3502/4502 Physical Chemistry II (Quantum Mechanics) 3 Credits Spring Semester 2006 Christopher J. Cramer Lecture 17, March 1, 2006 (Some material in this lecture has been adapted from Cramer, C. J.

More information

"Let me tell you the secret that has led me to my goal. My strength lies solely in my tenacity." -Louis Pasteur-

Let me tell you the secret that has led me to my goal. My strength lies solely in my tenacity. -Louis Pasteur- CHEMISTRY 101 Hour Exam III December 4, 2014 Adams/Esbenshade Name Signature Section "Let me tell you the secret that has led me to my goal. My strength lies solely in my tenacity." -Louis Pasteur- This

More information

Hartree, Hartree-Fock and post-hf methods

Hartree, Hartree-Fock and post-hf methods Hartree, Hartree-Fock and post-hf methods MSE697 fall 2015 Nicolas Onofrio School of Materials Engineering DLR 428 Purdue University nonofrio@purdue.edu 1 The curse of dimensionality Let s consider a multi

More information

MUSICAL COMPOSITION AND ELEMENTARY EXCITATIONS OF THE ENVIRONMENT

MUSICAL COMPOSITION AND ELEMENTARY EXCITATIONS OF THE ENVIRONMENT Interdisciplinary Description of Complex Systems (-2), 22-28, 2003 MUSICAL COMPOSITION AND ELEMENTARY EXCITATIONS OF THE ENVIRONMENT Mirna Grgec-Pajić, Josip Stepanić 2 and Damir Pajić 3, * c/o Institute

More information

Sveučilište u Zagrebu Fakultet prometnih znanosti Diplomski studij. Umjetna inteligencija - Genetski algoritmi 47895/47816 UMINTELI HG/

Sveučilište u Zagrebu Fakultet prometnih znanosti Diplomski studij. Umjetna inteligencija - Genetski algoritmi 47895/47816 UMINTELI HG/ Sveučilište u Zagrebu Fakultet prometnih znanosti Diplomski studij Umjetna inteligencija - Genetski algoritmi 47895/47816 UMINTELI HG/2008-2009 Genetski algoritam Postupak stohastičkog pretraživanja prostora

More information

Computational Chemistry I

Computational Chemistry I Computational Chemistry I Text book Cramer: Essentials of Quantum Chemistry, Wiley (2 ed.) Chapter 3. Post Hartree-Fock methods (Cramer: chapter 7) There are many ways to improve the HF method. Most of

More information

BOOKS BY IVAN GUTMAN

BOOKS BY IVAN GUTMAN BOOKS BY IVAN GUTMAN 1. A. Graovac, I. Gutman, N. Trinajstić TOPOLOGICAL APPROACH TO THE CHEMISTRY OF CONJUGATED MOLECULES Springer, Berlin, 1977, pp. X+123. 2. I. Gutman, O. E. Polansky MATHEMATICAL CONCEPTS

More information

Intro to ab initio methods

Intro to ab initio methods Lecture 2 Part A Intro to ab initio methods Recommended reading: Leach, Chapters 2 & 3 for QM methods For more QM methods: Essentials of Computational Chemistry by C.J. Cramer, Wiley (2002) 1 ab initio

More information

Simulacije dinamičkih sustava u programskom jeziku Python

Simulacije dinamičkih sustava u programskom jeziku Python Simulacije dinamičkih sustava u programskom jeziku Python Vladimir Milić Sveučilište u Zagrebu Fakultet strojarstva i brodogradnje Zagreb, 19. siječnja 2017. Vladimir Milić Nastupno predavanje Zagreb,

More information

The Hartree-Fock approximation

The Hartree-Fock approximation Contents The Born-Oppenheimer approximation Literature Quantum mechanics 2 - Lecture 7 November 21, 2012 Contents The Born-Oppenheimer approximation Literature 1 The Born-Oppenheimer approximation 2 3

More information

A COMPARATIVE EVALUATION OF SOME SOLUTION METHODS IN FREE VIBRATION ANALYSIS OF ELASTICALLY SUPPORTED BEAMS 5

A COMPARATIVE EVALUATION OF SOME SOLUTION METHODS IN FREE VIBRATION ANALYSIS OF ELASTICALLY SUPPORTED BEAMS 5 Goranka Štimac Rončević 1 Original scientific paper Branimir Rončević 2 UDC 534-16 Ante Skoblar 3 Sanjin Braut 4 A COMPARATIVE EVALUATION OF SOME SOLUTION METHODS IN FREE VIBRATION ANALYSIS OF ELASTICALLY

More information

VISOKOTLAČNI FAZNI PRIJELAZI U BINARNIM POLUVODIČIMA

VISOKOTLAČNI FAZNI PRIJELAZI U BINARNIM POLUVODIČIMA Sveučilište u Zagrebu Prirodoslovno-matematički fakultet Fizički odsjek Igor Lukačević VISOKOTLAČNI FAZNI PRIJELAZI U BINARNIM POLUVODIČIMA Doktorska disertacija predložena Fizičkom odsjeku Prirodoslovno-matematičkog

More information

Microscopical and Microanalytical Methods (NANO3)

Microscopical and Microanalytical Methods (NANO3) Microscopical and Microanalytical Methods (NANO3) 06.11.15 10:15-12:00 Introduction - SPM methods 13.11.15 10:15-12:00 STM 20.11.15 10:15-12:00 STS Erik Zupanič erik.zupanic@ijs.si stm.ijs.si 27.11.15

More information

Chemistry: The Central Science Brown LeMay Bursten Murphy Woodward Twelfth Edition

Chemistry: The Central Science Brown LeMay Bursten Murphy Woodward Twelfth Edition Chemistry: The Central Science Brown LeMay Bursten Murphy Woodward Twelfth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit

More information

Electron Correlation - Methods beyond Hartree-Fock

Electron Correlation - Methods beyond Hartree-Fock Electron Correlation - Methods beyond Hartree-Fock how to approach chemical accuracy Alexander A. Auer Max-Planck-Institute for Chemical Energy Conversion, Mülheim September 4, 2014 MMER Summerschool 2014

More information

Lab 3: Solubility of Organic Compounds

Lab 3: Solubility of Organic Compounds Lab 3: Solubility of rganic Compounds bjectives: - Understanding the relative solubility of organic compounds in various solvents. - Exploration of the effect of polar groups on a nonpolar hydrocarbon

More information

( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r)

( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r) Born Oppenheimer Approximation: Ĥ el ( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r) For a molecule with N electrons and M nuclei: Ĥ el What is E el (R)? s* potential surface Reaction Barrier Unstable intermediate

More information

On Theoretical Evaluation of Equilibrium Thermodynamics and Kinetics of the Water Dimer and of the Second Virial Coefficient of Steam"

On Theoretical Evaluation of Equilibrium Thermodynamics and Kinetics of the Water Dimer and of the Second Virial Coefficient of Steam CROATICA CHEMICA ACTA CCACAA 58 (3) 295-304 (1985) CCA-1582 YU ISSN 0011-1643 UDC 541.123.11 OriginaL Scientific Paper On Theoretical Evaluation of Equilibrium Thermodynamics and Kinetics of the Water

More information

COUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI

COUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI COUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI Marta Włoch, a Jeffrey R. Gour, a and Piotr Piecuch a,b a Department of Chemistry,Michigan State University, East Lansing, MI 48824 b

More information

CR 0 AT IC A CHEM I CA ACT A 54 (1981) Isospectral and Subspectral Molecules

CR 0 AT IC A CHEM I CA ACT A 54 (1981) Isospectral and Subspectral Molecules CR 0 AT IC A CHEM I CA ACT A 54 (1981) S. S. D' Amato, B. M. Gimarc, and N. Trinajstic C. D. Godsil and I. Gutman A. Bezjak, I. Smit, and V. Alujevic s. Ursic I. Gutman Isospectral and Subspectral Molecules

More information

Welcome!! Chemistry 328N Organic Chemistry for Chemical Engineers. Professor: Grant Willson

Welcome!! Chemistry 328N Organic Chemistry for Chemical Engineers. Professor: Grant Willson Welcome!! - 50750 Organic Chemistry for Chemical Engineers Professor: Grant Willson Teaching Assistants: Ji yeon Kim, Jai Hyun Koh, Paul Meyer, Qingjun Zhu http://willson.cm.utexas.edu January 19,2016

More information

Ab initio proučavanje neadijabatskih efekata kod malih molekula

Ab initio proučavanje neadijabatskih efekata kod malih molekula Ab initio proučavanje neadijabatskih efekata kod malih molekula Marko Mitić Fakultet za fizičku hemiju, Univerzitet u Beogradu Seminar iz fizike/astrofizike Departman za fiziku, PMF, Novi Sad 15. april

More information

Evaluate Scientific Models for Atomic Structure

Evaluate Scientific Models for Atomic Structure Evaluate Scientific Models for Atomic Structure Directions: Answer all parts of each question below. Make sure your answers are in complete sentences and are concise, including ONLY necessary details.

More information

Cyclical Surfaces Created by a Conical Helix

Cyclical Surfaces Created by a Conical Helix Professional paper Accepted 23.11.2007. TATIANA OLEJNÍKOVÁ Cyclical Surfaces Created by a Conical Helix Cyclical Surfaces Created by a Conical Helix ABSTRACT The paper describes cyclical surfaces created

More information

Additional background material on the Nobel Prize in Chemistry 1998

Additional background material on the Nobel Prize in Chemistry 1998 Additional background material on the Nobel Prize in Chemistry 1998 The Royal Swedish Academy of Sciences has decided to award the 1998 Nobel Prize in Chemistry with one half to Professor WALTER KOHN,

More information

Montgomery County Community College CHE 131 Chemistry for Technology I 4-3-3

Montgomery County Community College CHE 131 Chemistry for Technology I 4-3-3 Montgomery County Community College CHE 131 Chemistry for Technology I 4-3-3 COURSE DESCRIPTION: A general course in physical-inorganic and organic chemistry. Emphasis will be placed on the theoretical

More information

The Basics of Theoretical and Computational Chemistry

The Basics of Theoretical and Computational Chemistry Bernd M. Rode, Thomas S. Hofer, and Michael D. Kugler The Basics of Theoretical and Computational Chemistry BICENTENNIA BICENTBNN I AL. WILEY-VCH Verlag GmbH & Co. KGaA V Contents Preface IX 1 Introduction

More information

Detaljni izvedbeni nastavni plan za kolegij: Uvod u bioanorgansku kemiju

Detaljni izvedbeni nastavni plan za kolegij: Uvod u bioanorgansku kemiju Detaljni izvedbeni nastavni plan za kolegij: Uvod u bioanorgansku kemiju Akademska godina: 2018/2019 Studij: Preddiplomski sveučilišni studij Biotehnologija i istraživanje lijekova Kod kolegija: BIL 106

More information

Multi-reference Density Functional Theory. COLUMBUS Workshop Argonne National Laboratory 15 August 2005

Multi-reference Density Functional Theory. COLUMBUS Workshop Argonne National Laboratory 15 August 2005 Multi-reference Density Functional Theory COLUMBUS Workshop Argonne National Laboratory 15 August 2005 Capt Eric V. Beck Air Force Institute of Technology Department of Engineering Physics 2950 Hobson

More information

Calculations of band structures

Calculations of band structures Chemistry and Physics at Albany Planning for the Future Calculations of band structures using wave-function based correlation methods Elke Pahl Centre of Theoretical Chemistry and Physics Institute of

More information

Density Functional Theory

Density Functional Theory Chemistry 380.37 Fall 2015 Dr. Jean M. Standard October 28, 2015 Density Functional Theory What is a Functional? A functional is a general mathematical quantity that represents a rule to convert a function

More information

Chemistry, Physics and the Born- Oppenheimer Approximation

Chemistry, Physics and the Born- Oppenheimer Approximation Chemistry, Physics and the Born- Oppenheimer Approximation Hendrik J. Monkhorst Quantum Theory Project University of Florida Gainesville, FL 32611-8435 Outline 1. Structure of Matter 2. Shell Models 3.

More information

UČNI NAČRT PREDMETA / COURSE SYLLABUS Numerical linear algebra. Študijska smer Study field. Samost. delo Individ. work Klinične vaje work

UČNI NAČRT PREDMETA / COURSE SYLLABUS Numerical linear algebra. Študijska smer Study field. Samost. delo Individ. work Klinične vaje work Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS Numerična linearna algebra Numerical linear algebra Študijski program in stopnja Study programme and level Univerzitetni študijski program Matematika

More information

COMPUTATION OF WIRE AND JUNCTION CAPACITANCE IN VLSI STRUCTURES

COMPUTATION OF WIRE AND JUNCTION CAPACITANCE IN VLSI STRUCTURES COMPUTATION OF WIRE AND JUNCTION CAPACITANCE IN VLSI STRUCTURES F. Straker, s. Selberherr Abteilung fur Physikalische Elektronik Institut flir allgemeine Elektrotechnik und Elektronik Technische Universitat

More information

Kinetics of the Thermal Degradation of n-propylbenzene in a Micro Flow Reactor by Gas Chromatography*

Kinetics of the Thermal Degradation of n-propylbenzene in a Micro Flow Reactor by Gas Chromatography* CROATICA CHEMICA ACTA CCACAA 45 (4) 525-530 (1973) YU ISSN 0011-1643 547.535.1 CCA-795 Original Scientific Paper Kinetics of the Thermal Degradation of n-propylbenzene in a Micro Flow Reactor by Gas Chromatography*

More information

3.1 Hydrogen Spectrum

3.1 Hydrogen Spectrum 3.1 Hydrogen Spectrum Light is electromagnetic radiation that can be produced at different energy levels. High energy light has a short wavelength (λ) and a high frequency (ƒ, ν) (gamma rays, x-rays, ultraviolet).

More information

Advanced Electronic Structure Theory Density functional theory. Dr Fred Manby

Advanced Electronic Structure Theory Density functional theory. Dr Fred Manby Advanced Electronic Structure Theory Density functional theory Dr Fred Manby fred.manby@bris.ac.uk http://www.chm.bris.ac.uk/pt/manby/ Course overview This is a course about density functional theory (DFT)

More information

Methoxyphenyl-substituted derivatives of indolo[3,2-b]carbazole: structure. properties relationship

Methoxyphenyl-substituted derivatives of indolo[3,2-b]carbazole: structure. properties relationship Methoxyphenyl-substituted derivatives of indolo[3,2-b]carbazole: structure properties relationship Jurate Simokaitiene, Egle Stanislovaityte, Juozas V. Grazulevicius *, Vygintas Jankauskas, Rong Gu, Wim

More information

Product Function Matrix and its Request Model

Product Function Matrix and its Request Model Strojarstvo 51 (4) 293-301 (2009) M KARAKAŠIĆ et al, Product Function Matrix and its Request Model 293 CODEN STJSAO ISSN 0562-1887 ZX470/1388 UDK 6585122:00442 Product Function Matrix and its Request Model

More information

MATHEMATICAL MODELING OF DIE LOAD IN THE PROCESS OF CROSS TUBE HYDROFORMING

MATHEMATICAL MODELING OF DIE LOAD IN THE PROCESS OF CROSS TUBE HYDROFORMING Journal for Technology of Plasticity, Vol. 40 (2015), Number 1 MATHEMATICAL MODELING OF DIE LOAD IN THE PROCESS OF CROSS TUBE HYDROFORMING Mehmed Mahmić, Edina Karabegović University of Bihać, Faculty

More information

MORRISON AND BOYD ORGANIC CHEMISTRY 7TH EDITION PDF

MORRISON AND BOYD ORGANIC CHEMISTRY 7TH EDITION PDF MORRISON AND BOYD ORGANIC CHEMISTRY 7TH EDITION PDF ==> Download: MORRISON AND BOYD ORGANIC CHEMISTRY 7TH EDITION PDF MORRISON AND BOYD ORGANIC CHEMISTRY 7TH EDITION PDF - Are you searching for Morrison

More information

MATEMATIČKA FIZIKA III Smer: (Teorijska) i eksperimentalna fizika Semestar: 7 Fond: 3+2 Ispit:P+U

MATEMATIČKA FIZIKA III Smer: (Teorijska) i eksperimentalna fizika Semestar: 7 Fond: 3+2 Ispit:P+U 1. MATEMATIČKA FIZIKA III Smer: (Teorijska) i eksperimentalna fizika Semestar: 7 Fond: 3+2 Ispit:P+U KVANTNO-MEHANIČKI METODI I PRIMENA SIMETRIJE............2 nedelje Simetrijski adaptirana stanja, fizički

More information

Chemistry Instrumental Analysis Lecture 34. Chem 4631

Chemistry Instrumental Analysis Lecture 34. Chem 4631 Chemistry 4631 Instrumental Analysis Lecture 34 From molecular to elemental analysis there are three major techniques used for elemental analysis: Optical spectrometry Mass spectrometry X-ray spectrometry

More information

Strojarstvo Preddiplomski Preddiplomski - 6. semestar Izborni

Strojarstvo Preddiplomski Preddiplomski - 6. semestar Izborni OBRAZAC 1. Vrednovanje sveucilišnih studijskih programa preddiplomskih, diplomskih i integriranih preddiplomskih i diplomskih studija te strucnih studija Tablica 2: Opis predmeta 1. OPĆE INFORMACIJE 1.1.

More information

The temperature dependence of the disproportionation reaction of iodous acid in aqueous sulfuric acid solutions

The temperature dependence of the disproportionation reaction of iodous acid in aqueous sulfuric acid solutions J. Serb. Chem. Soc. 67(5)347 351(2002) UDC 542.9:546.155+535.243:536.5 JSCS-2955 Original scientific paper The temperature dependence of the disproportionation reaction of iodous acid in aqueous sulfuric

More information

OA07 ANNEX 4: SCOPE OF ACCREDITATION IN CALIBRATION

OA07 ANNEX 4: SCOPE OF ACCREDITATION IN CALIBRATION OA07 ANNEX 4: SCOPE OF ACCREDITATION IN CALIBRATION Table of contents 1 TECHNICAL FIELDS... 2 2 PRESENTING THE SCOPE OF A CALIBRATION LABOORATORY... 2 3 CONSIDERING CHANGES TO SCOPES... 6 4 CHANGES WITH

More information

Chemistry 11. Unit 10 Organic Chemistry Part III Unsaturated and aromatic hydrocarbons

Chemistry 11. Unit 10 Organic Chemistry Part III Unsaturated and aromatic hydrocarbons Chemistry 11 Unit 10 Organic Chemistry Part III Unsaturated and aromatic hydrocarbons 2 1. Unsaturated hydrocarbons So far, we have studied the hydrocarbons in which atoms are connected exclusively by

More information

Strojarstvo Preddiplomski Preddiplomski - 4. semestar Obvezni

Strojarstvo Preddiplomski Preddiplomski - 4. semestar Obvezni OBRAZAC 1. Vrednovanje sveucilišnih studijskih programa preddiplomskih, diplomskih i integriranih preddiplomskih i diplomskih studija te strucnih studija Tablica 2: Opis predmeta 1. OPĆE INFORMACIJE 1.1.

More information

Some Observations on the Topological Resonance Energy of Benzenoid Hydrocarbons*

Some Observations on the Topological Resonance Energy of Benzenoid Hydrocarbons* CROATICA CHEMICA ACTA CCACAA 55 (4) 375-382 (1982) YU ISSN 0011-1643 UDC 539.19:547.53 CCA-1342 Original Scientific Paper Some Observations on the Topological Resonance Energy of Benzenoid Hydrocarbons*

More information

AN INTRODUCTION TO QUANTUM CHEMISTRY. Mark S. Gordon Iowa State University

AN INTRODUCTION TO QUANTUM CHEMISTRY. Mark S. Gordon Iowa State University AN INTRODUCTION TO QUANTUM CHEMISTRY Mark S. Gordon Iowa State University 1 OUTLINE Theoretical Background in Quantum Chemistry Overview of GAMESS Program Applications 2 QUANTUM CHEMISTRY In principle,

More information

DIPOLE MOMENTS IN ORGANIC CHEMISTRY

DIPOLE MOMENTS IN ORGANIC CHEMISTRY DIPOLE MOMENTS IN ORGANIC CHEMISTRY PHYSICAL METHODS IN ORGANIC CHEMISTRY B. I. lonin and B. A. Ershov NMR Spectroscopy in Organic Chemistry, 1970 V. I. Minkin, O. A. Osipov, and Yu. A. Zhdanov Dipole

More information

Degeneracy in One Dimensional Quantum Systems: Dynamically Shifted Oscillator

Degeneracy in One Dimensional Quantum Systems: Dynamically Shifted Oscillator Degeneracy in One Dimensional Quantum Systems: Dynamically Shifted Oscillator Pirooz Mohazzabi1*, G. Clark Alexander2 1 2 Department of Mathematics and Physics, University of Wisconsin-Parkside, Kenosha,

More information

The Radial Electron Density in the Hydrogen Atom and the Model of Oscillations in a Chain System

The Radial Electron Density in the Hydrogen Atom and the Model of Oscillations in a Chain System July, 01 PROGRESS IN PHYSICS Volume 3 The Radial Electron Density in the Hydrogen Atom and the Model of Oscillations in a Chain System Andreas Ries Universidade Federal de Pernambuco, Centro de Tecnologia

More information

Equilibrium/Acids and Bases

Equilibrium/Acids and Bases Adult Basic Education Science Equilibrium/Acids and Bases Prerequisite: Chemistry 3102A Credit Value: 1 Chemistry Concentration Chemistry 1102 Chemistry 2102A Chemistry 2102B Chemistry 2102C Chemistry

More information

CLASSIFICATION OF CONIC SECTIONS IN P E 2 (R) Jelena Beban-Brkić and Marija Šimić Horvath

CLASSIFICATION OF CONIC SECTIONS IN P E 2 (R) Jelena Beban-Brkić and Marija Šimić Horvath RAD HAZU. MATEMATIČKE ZNANOSTI Vol. 18 = 519 (2014): 125-143 CLASSIFICATION OF CONIC SECTIONS IN P E 2 (R) Jelena Beban-Brkić and Marija Šimić Horvath Abstract. This paper gives a complete classification

More information

Course Project. Physics I with Lab

Course Project. Physics I with Lab COURSE OBJECTIVES 1. Explain the fundamental laws of physics in both written and equation form 2. Describe the principles of motion, force, and energy 3. Predict the motion and behavior of objects based

More information

EXAM INFORMATION. Radial Distribution Function: B is the normalization constant. d dx. p 2 Operator: Heisenberg Uncertainty Principle:

EXAM INFORMATION. Radial Distribution Function: B is the normalization constant. d dx. p 2 Operator: Heisenberg Uncertainty Principle: EXAM INFORMATION Radial Distribution Function: P() r RDF() r Br R() r B is the normalization constant., p Operator: p ^ d dx Heisenberg Uncertainty Principle: n ax n! Integrals: xe dx n1 a x p Particle

More information