Chimica | MOLECULAR QUANTUM MECHANICS

cod. 0522300037

MOLECULAR QUANTUM MECHANICS

	0522300037
	DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI"
	EQF7
	CHEMISTRY
	2020/2021

CURRICULUM BIOMOLECULAR CHEMISTRY

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2016
	PRIMO SEMESTRE

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
CHIM/02	7	56	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
CHIM/02	2	24	EXERCISES	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
CHIM/02	3	36	LAB	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

	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.

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
	REVIEW OF PERTURBATIVE AND VARIATIONAL METHODS. BORN-OPPENHEIMER APPROXIMATION. FORCE FIELDS. STRETCH POTENTIAL, BENDING, BENDING OUT OF PLANE, TORSION. MORSE POTENTIAL. MINIMUM LINEAR SQUARES IN MATRIX FORM. NORMAL COORDINATES. INTERNAL AND CARTESIAN COORDINATES. RIGHT INVERSE MATRIX. WILSON'S GF METHOD, DETERMINATION OF NORMAL CO2 COORDINATES. APPLICATIONS OF GROUP THEORY TO THE CLASSIFICATION OF NORMAL MODES. HESSIAN MATRIX. STEEPEST-DESCENT AND QUASI-NEWTON ENERGY OPTIMIZATION METHODS. HÜCKEL METHOD. BOND ORDER, ATOMIC CHARGES; RELATIONSHIP BETWEEN BOND ORDER AND BOND LENGTHS. GROUP DEFINITION. MULTIPLICATION TABLE. SYMMETRY OPERATORS. POINT SYMMETRY GROUPS. GENERATORS. DETERMINATION OF THE SYMMETRY GROUP OF A MOLECULE. CLASSES. REPRESENTATIONS AND SIMILARITY TRANSFORMATIONS. CHARACTER TABLES AND THEIR USE. IRREDUCIBLE REPRESENTATIONS. REDUCTION PROCESS. SELECTION RULES FOR MATRIX ELEMENTS. THE HARTREE-FOCK METHOD. COULOMB AND EXCHANGE OPERATORS. SLATER ORBITALS, GAUSSIANS, GIAO. 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. THE CI METHOD. THE MP2 METHOD. DENSITY FUNCTIONAL THEORY. HOHENBERG-KOHN THEOREMS AND KOHN-SHAM EQUATIONS. QUANTUM CHEMICAL TOPOLOGY: QTAIM, ELF. FERMI AND COULOMB HOLES. VIRIAL THEOREM; EHRENFEST THEOREM; HELLMANN-FEYNMANN THEOREM MULTIPOLAR EXPANSION; DIPOLE AND QUADRUPOLE. TENSORIAL 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 THE GAUGE. TIME DEPENDENT PERTURBATION THEORY. FERMI GOLDEN RULE. RELATIONSHIP BETWEEN INTEGRATED ABSORBANCE AND DIPOLE FORCE. ROTATOR FORCE. THE COUPLET IN CHIROOTTIC SPECTROSCOPY: THE EXCITONIC MODEL. MOLECULAR RESPONSE THEORY POLARIZATION OF ELECTRIC DIPOLE AND OPTICAL ACTIVITY TENSOR. RAMSEY FORMALISM FOR THE NUCLEAR SHIELDING. MAGNETISABILITY. AVERAGE VALUES OF SECOND-RANK TENSORS. DEFINITION OF CURRENT DENSITY INDUCED BY A UNIFORM AND CONSTANT EXTERNAL MAGNETIC FIELD. CLASSIC RELATIONSHIPS BETWEEN FIRST-ORDER CURRENT DENSITY AND MAGNETIZABILITY AND NUCLEAR MAGNETIC SHIELDING. RING CURRENTS. NICS. INTENSITY OF BINDING CURRENT. DISTRIBUTION OF THE AVERAGE FREE PATHS. TRANSPORT PROPERTIES IN GASES. THE DISTRIBUTION OF RELATIVE VELOCITIES. COLLISION THEORY AND KINETIC CONSTANT OF A BIMOLECULAR REACTION. RS, LOC AND ADLOC MODELS. POTENTIAL ENERGY SURFACE FOR THE H2 + H REACTION. TRANSITION STATE THEORY IN A MICROCANONICAL AND CANONICAL APPROACH. MARCUS' MODEL, HAMMOND'S POSTULATE, THE BELL-EVANS-POLANYI PRINCIPLE. EARLY AND LATE TRANSITION STATES. O’FERRALL JENKS PLOT. THE LABORATORY WILL REQUEST TO PUT THEORETICAL KNOWLEDGE INTO PRACTICE THROUGH THE BASIC USE OF CALCULATION AND VISUALIZATION SOFTWARE (AVOGADRO, JMOL, GAUSSVIEW, GAUSSIAN), TO RATIONALIZE MOLECULAR STRUCTURE AND REACTIVITY, AND DICHROISM AND INFRARED ABSORPTION SPECTRA, WHICH WILL BE RECORDED IN THE LABORATORY.

Contents

REVIEW OF PERTURBATIVE AND VARIATIONAL METHODS.
BORN-OPPENHEIMER APPROXIMATION.
FORCE FIELDS. STRETCH POTENTIAL, BENDING, BENDING OUT OF PLANE, TORSION. MORSE POTENTIAL.
MINIMUM LINEAR SQUARES IN MATRIX FORM.
NORMAL COORDINATES. INTERNAL AND CARTESIAN COORDINATES.
RIGHT INVERSE MATRIX. WILSON'S GF METHOD, DETERMINATION OF NORMAL CO2 COORDINATES. APPLICATIONS OF GROUP THEORY TO THE CLASSIFICATION OF NORMAL MODES.
HESSIAN MATRIX.
STEEPEST-DESCENT AND QUASI-NEWTON ENERGY OPTIMIZATION METHODS.
HÜCKEL METHOD. BOND ORDER, ATOMIC CHARGES; RELATIONSHIP BETWEEN BOND ORDER AND BOND LENGTHS.
GROUP DEFINITION. MULTIPLICATION TABLE. SYMMETRY OPERATORS.
POINT SYMMETRY GROUPS. GENERATORS. DETERMINATION OF THE SYMMETRY GROUP OF A MOLECULE.
CLASSES. REPRESENTATIONS AND SIMILARITY TRANSFORMATIONS. CHARACTER TABLES AND THEIR USE. IRREDUCIBLE REPRESENTATIONS. REDUCTION PROCESS.
SELECTION RULES FOR MATRIX ELEMENTS.

THE HARTREE-FOCK METHOD.
COULOMB AND EXCHANGE OPERATORS.
SLATER ORBITALS, GAUSSIANS, GIAO.
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.
THE CI METHOD.
THE MP2 METHOD.
DENSITY FUNCTIONAL THEORY.
HOHENBERG-KOHN THEOREMS AND KOHN-SHAM EQUATIONS.
QUANTUM CHEMICAL TOPOLOGY: QTAIM, ELF.
FERMI AND COULOMB HOLES.

VIRIAL THEOREM; EHRENFEST THEOREM; HELLMANN-FEYNMANN THEOREM
MULTIPOLAR EXPANSION; DIPOLE AND QUADRUPOLE.
TENSORIAL 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 THE GAUGE.
TIME DEPENDENT PERTURBATION THEORY.
FERMI GOLDEN RULE.
RELATIONSHIP BETWEEN INTEGRATED ABSORBANCE AND DIPOLE FORCE.
ROTATOR FORCE.
THE COUPLET IN CHIROOTTIC SPECTROSCOPY: THE EXCITONIC MODEL.
MOLECULAR RESPONSE THEORY
POLARIZATION OF ELECTRIC DIPOLE AND OPTICAL ACTIVITY TENSOR.
RAMSEY FORMALISM FOR THE NUCLEAR SHIELDING.
MAGNETISABILITY. AVERAGE VALUES OF SECOND-RANK TENSORS.
DEFINITION OF CURRENT DENSITY INDUCED BY A UNIFORM AND CONSTANT EXTERNAL MAGNETIC FIELD.
CLASSIC RELATIONSHIPS BETWEEN FIRST-ORDER CURRENT DENSITY AND MAGNETIZABILITY AND NUCLEAR MAGNETIC SHIELDING.
RING CURRENTS. NICS. INTENSITY OF BINDING CURRENT.

DISTRIBUTION OF THE AVERAGE FREE PATHS.
TRANSPORT PROPERTIES IN GASES.
THE DISTRIBUTION OF RELATIVE VELOCITIES.
COLLISION THEORY AND KINETIC CONSTANT OF A BIMOLECULAR REACTION.
RS, LOC AND ADLOC MODELS.
POTENTIAL ENERGY SURFACE FOR THE H2 + H REACTION. TRANSITION STATE THEORY IN A MICROCANONICAL AND CANONICAL APPROACH. MARCUS' MODEL, HAMMOND'S POSTULATE, THE BELL-EVANS-POLANYI PRINCIPLE. EARLY AND LATE TRANSITION STATES. O’FERRALL JENKS PLOT.

THE LABORATORY WILL REQUEST TO PUT THEORETICAL KNOWLEDGE INTO PRACTICE THROUGH THE BASIC USE OF CALCULATION AND VISUALIZATION SOFTWARE (AVOGADRO, JMOL, GAUSSVIEW, GAUSSIAN), TO RATIONALIZE MOLECULAR STRUCTURE AND REACTIVITY, AND DICHROISM AND INFRARED ABSORPTION SPECTRA, WHICH WILL BE RECORDED IN THE LABORATORY.

	Teaching Methods
	CLASSROOM LECTURES FOR A TOTAL OF 9 CFU; PRACTICAL QUANTUM MECHANICAL APPLICATIONS AND LABORATORY EXPERIENCES FOR A TOTAL OF 3 CFU.

	Verification of learning
	THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS VERIFIED BY PASSING AN EXAM. SUFFICIENCY IS GRANTED WITH 18/30. THE EXAM IS ACCESSED ONLY AFTER HAVING DELIVERED AND DEFENDED THE LABORATORY EXPERIENCE REPORTS. THE EXAM INCLUDES A PRACTICAL TEST AND AN ORAL TEST. THE PRACTICAL TEST IS PROPAEDEUTIC TO THE ORAL TEST AND CONSISTS OF A TEST OF USE OF QUANTUM CHEMISTRY METHODS CONCERNING THE TOPICS OF THE TEACHING PROGRAM. THE TEST IS CARRIED OUT BEFORE THE ORAL TEST AND IS CONSIDERED PASSED WITH THE MINIMUM SCORE OF 18/30. GENERALLY, THE PRACTICAL TEST HAS A DURATION OF 120 MINUTES AND IS AIMED TO VERIFY THE ABILITY TO CORRECTLY APPLY THEORETICAL KNOWLEDGE AND THE ABILITY TO UNDERSTAND THE PROBLEMS PROPOSED. THE ORAL TEST CONSISTS OF AN INTERVIEW WITH QUESTIONS AND DISCUSSION ON THEORETICAL AND METHODOLOGICAL CONTENT, EVEN INHERENT TO LABORATORY TESTS AND PRACTICAL EXERCISES, INDICATED IN THE TEACHING PROGRAM, AND HAS THE PURPOSE OF ASSESSING THE LEVEL OF KNOWLEDGE AND KNOWLEDGE REACHED BY THE STUDENT, AS WELL AS VERIFYING THE EXPOSURE CAPACITY BY USING THE APPROPRIATE TERMINOLOGY.

Verification of learning

THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS VERIFIED BY PASSING AN EXAM. SUFFICIENCY IS GRANTED WITH 18/30. THE EXAM IS ACCESSED ONLY AFTER HAVING DELIVERED AND DEFENDED THE LABORATORY EXPERIENCE REPORTS. THE EXAM INCLUDES A PRACTICAL TEST AND AN ORAL TEST.
THE PRACTICAL TEST IS PROPAEDEUTIC TO THE ORAL TEST AND CONSISTS OF A TEST OF USE OF QUANTUM CHEMISTRY METHODS CONCERNING THE TOPICS OF THE TEACHING PROGRAM. THE TEST IS CARRIED OUT BEFORE THE ORAL TEST AND IS CONSIDERED PASSED WITH THE MINIMUM SCORE OF 18/30. GENERALLY, THE PRACTICAL TEST HAS A DURATION OF 120 MINUTES AND IS AIMED TO VERIFY THE ABILITY TO CORRECTLY APPLY THEORETICAL KNOWLEDGE AND THE ABILITY TO UNDERSTAND THE PROBLEMS PROPOSED.
THE ORAL TEST CONSISTS OF AN INTERVIEW WITH QUESTIONS AND DISCUSSION ON THEORETICAL AND METHODOLOGICAL CONTENT, EVEN INHERENT TO LABORATORY TESTS AND PRACTICAL EXERCISES, INDICATED IN THE TEACHING PROGRAM, AND HAS THE PURPOSE OF ASSESSING THE LEVEL OF KNOWLEDGE AND KNOWLEDGE REACHED BY THE STUDENT, AS WELL AS VERIFYING THE EXPOSURE CAPACITY BY USING THE APPROPRIATE TERMINOLOGY.

	Texts
	REFERENCE TEXTBOOKS 1) L. PIELA, IDEAS OF QUANTUM CHEMISTRY 2) P. POLAVARAPU, CHIROPTICAL SPECTROSCOPY 3) HOUSTON, CHEMICAL KINETICS AND REACTION DYNAMICS 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