MOLECULAR QUANTUM MECHANICS

Chimica MOLECULAR QUANTUM MECHANICS

0522300037
DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI"
EQF7
CHEMISTRY
2022/2023

OBBLIGATORIO
YEAR OF COURSE 1
YEAR OF DIDACTIC SYSTEM 2016
AUTUMN SEMESTER
CFUHOURSACTIVITY
756LESSONS
224EXERCISES
336LAB
ExamDate
MECCANICA QUANTISTICA MOLECOLARE21/02/2023 - 09:00
MECCANICA QUANTISTICA MOLECOLARE21/02/2023 - 09:00
Objectives
KNOWLEDGE AND UNDERSTANDING. THE COURSE AIMS AT PROVIDING THE PHYSICAL AND CHEMICAL PRINCIPLES GOVERNING THE PROPERTIES AND THE REACTIVITY OF ORGANIC MOLECULES AND TO DEVELOP AWARENESS OF THE FUNDAMENTALS OF COMPUTATIONAL CHEMISTRY.
APPLYING KNOWLEDGE AND UNDERSTANDING. THE NUMERICAL EXERCISES WILL ALLOW TO BECOME FAMILIAR WITH PROGRAMS ALREADY AVAILABLE AND TO ADDRESS INDEPENDENTLY THE COMPUTATIONAL STUDY OF MOLECULAR STRUCTURE AND CHEMICAL REACTIONS OF MEDIUM COMPLEXITY.
MAKING JUDGMENTS. THE STUDENT WILL BE ABLE TO CRITICALLY DISCUSS THE VALIDITY OF THE RESULTS OBTAINED IN DISCUSSIONS PROMOTED BY THE TEACHER IN THE LABORATORY GROUP.
COMMUNICATION SKILLS. THE COURSE WILL ENABLE STUDENTS TO ACQUIRE THE APPROPRIATE TERMINOLOGY TO DESCRIBE THE COMPUTATIONAL ANALYSIS OF THE MOLECULAR STRUCTURE AND REACTION INTERMEDIATES, ALSO BY READING ARTICLES PUBLISHED IN INTERNATIONAL JOURNALS.
Prerequisites
BASIC KNOWLEDGE OF CLASSICAL MECHANICS, STATISTICAL THERMODYNAMICS, CALCULUS AND LINEAR ALGEBRA. REFERENCE QUANTUM HAMILTONIANS WITH EXACT SOLUTIONS.
Contents
PERTURBATIVE AND VARIATIONAL METHODS.
BORN-OPPENHEIMER APPROXIMATION.
FORCE FIELDS. POTENTIAL FOR STRETCHING, BENDING,TORSION. MORSE POTENTIAL.
NORMAL COODINATES. INTERNAL AND CARTESIAN COORDINATES.
STEEPEST-DESCENT AND QUASI-NEWTON ENERGY OPTIMIZATION METHODS.

TIME DEPENDENT PERTURBATION THEORY.
FERMI GOLDEN RULE.
RELATIONSHIP BETWEEN INTEGRATED ABSORBANCE AND DIPOLE STRENGTH.

GROUP DEFINITION. MULTIPLICATION TABLE. SYMMETRY OPERATORS.
POINT GROUP SYMMETRY. GENERATORS. DETERMINATION OF THE SYMMETRY GROUP OF A MOLECULE.
CLASSES. REPRESENTATIONS AND TRANSFORMATIONS OF SIMILARITY. CHARACTER TABLES AND THEIR USE. IRREDUCIBLE REPRESENTATIONS. REDUCTION PROCESS. APPLICATIONS OF GROUP THEORY TO THE CLASSIFICATION OF NORMAL MODES.
SELECTION RULES FOR MATRIX ELEMENTS.

HÜCKEL'S METHOD. BOND ORDER, ATOMIC CHARGES; RELATIONSHIP BETWEEN BINDING ORDER AND BINDING LENGTHS.
THE HARTREE-FOCK METHOD.
COULOMB AND EXCHANGE OPERATORS.
SLATER, GAUSSIAN, GIAO ORBITALS.
THE HARTREE-FOCK-ROOTHAN METHOD.
THE SCF PROCEDURE.
CONDON-SLATER RULES.
LOCALIZED MOLECULAR ORBITALS.
LIMITATIONS OF THE HARTREE-FOCK MODEL.
STATIC AND DYNAMIC CORRELATION ENERGY.
BASICS ON CORRELATED CALCULATIONS.
DENSITY FUNCTIONAL THEORY.
HOHENBERG-KOHN THEOREMS AND KOHN-SHAM EQUATIONS.
QUANTUM CHEMICAL TOPOLOGY: QTAIM.

MULTIPOLAR EXPANSION; DIPOLE AND QUADRUPOLE.
TENSORY NOTATION AND EINSTEIN CONVENTION.
PERTURBATION THEORY APPLIED TO TWO WEAKLY INTERACTING MOLECULES.
DIPOLE-DIPOLE INTERACTION.
DISPERSION FORCES, LONDON EQUATION.
MULTIPOLE INTERACTION HAMILTONIAN.
THE PROBLEM OF THE ORIGIN OF GAUGE.
FORCE OF THE ROTATOR.
THE COUPLET IN CHIROOPTIC SPECTROSCOPIES: THE EXCITONIC MODEL.
POLARIZABILITY OF ELECTRIC DIPOLE AND OPTICAL ACTIVITY TENSOR.
BASICS ON MOLECULAR MAGNETIC PROPERTIES.

COLLISION THEORY AND KINETIC CONSTANT OF A BIMOLECULAR REACTION.
RS, LOC AND ADLOC MODELS.
SURFACE OF POTENTIAL ENERGY FOR THE H2 + H REACTION. TRANSITION STATE THEORY IN THE MICROCANONICAL AND CANONICAL APPROACH. THE MARCUS MODEL, THE HAMMOND POSTULATE, THE BELL-EVANS-POLANYI PRINCIPLE.

THE LABORATORY WILL REQUIRE TO PUT THEORETICAL KNOWLEDGE INTO PRACTICE THROUGH THE BASIC USE OF CALCULATION AND VISUALIZATION SOFTWARE (AVOGADRO, JMOL, GAUSSVIEW, GAUSSIAN), TO RATIONALIZE STRUCTURE AND MOLECULAR REACTIVITY, AND SPECTRA REGISTERED IN THE LABORATORY.
Teaching Methods
CLASSROOM LECTURES FOR A TOTAL OF 7 CFU; PRACTICAL QUANTUM MECHANICAL APPLICATIONS AND LABORATORY EXPERIENCES FOR A TOTAL OF 6 CFU.
Verification of learning
THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS VERIFIED BY PASSING AN EXAM WITH EVALUATION IN THIRTIES.
THE ORAL EXAM CAN BE ACCESSED ONLY AFTER SUBMITTING AND DISCUSSING THE REPORTS ON THE EXERCISES, PARTLY DURING THE COURSE AND PARTLY AT THE END OF THE COURSE.
THE DISCUSSION OF THE RELATIONSHIPS, BOTH IN GROUPS AND INDIVIDUALLY WILL SERVE TO DEMONSTRATE SKILLS IN THE USE OF QUANTUM AND COMPUTATIONAL CHEMISTRY METHODS CONCERNING THE TOPICS OF THE TEACHING PROGRAM. THE VOTE ASSIGNED TO THE REPORTS AND TO AN ORAL PRESENTATION TO BE MADE ON A TOPIC ASSIGNED AT THE END OF THE COURSE WILL BE MEDIATED WITH THE VOTE OF THE ORAL EXAMINATION TO OBTAIN THE FINAL VOTE.

THE ORAL TEST CONSISTS OF AN INTERVIEW WITH QUESTIONS AND DISCUSSION ON THE THEORETICAL AND METHODOLOGICAL CONTENTS, ALSO INHERENT TO THE EXERCISES, INDICATED IN THE TEACHING PROGRAM, AND ITS PURPOSE IS THE ASSESSMENT OF THE LEVEL OF KNOWLEDGE AND UNDERSTANDING, AS WELL AS THE VERIFICATION OF THE EXPOSURE CAPACITY USING THE APPROPRIATE TERMINOLOGY.
Texts
REFERENCE TEXTBOOKS
1) L. PIELA, IDEAS OF QUANTUM CHEMISTRY
2) P. ATKINS, MOLECULAR QUANTUM MECHANICS

FURTHER READING
1) MCWEENY, SYMMETRY
2) SZABO OSTLUND, MODERN QUANTUM CHEMISTRY
3) I.N. LEVINE, QUANTUM CHEMISTRY
4) BARROW, INTRODUCTION TO MOLECULAR SPECTROSCOPY
5) F. JENSEN, INTRODUCTION TO COMPUTATIONAL CHEMISTRY
6) P. POLAVARAPU, CHIROPTICAL SPECTROSCOPY
7) HOUSTON, CHEMICAL KINETICS AND REACTION DYNAMICS
More Information
NOTES OR RESEARCH ARTICLES WILL BE MADE AVAILABLE FOR SELECTED TOPICS.
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