Ateneo - UPO

Introduction to theoretical chemistry. Fundamentals of molecular quantum mechanics techniques, introduction to computational methods and their implementation.
Applications of the theory to problems of chemical interest.
The course is completed by a module on classical and Montecarlo molecular dynamics (8h, Prof. M. Cossi)

Suggested textbooks are:
-- A. Szabo and N. S. Ostlund, “Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory,” Dover Publications, New York, 1996
-R. McWeeny “Methods of Molecular Quantum Mechanics. 2nd Ed.” Academic Press, London, 1992
- T. Helgaker, P. Jørgensen, and J. Olsen"Molecular Electronic Structure Theory". John Wiley & Sons, LTD, Chichester, (2000)
- F. Jensen, “Introduction to Computational Chemistry”, 3rd Edition Feb. 2017, Wiley;
- J.H. Jensen, “Molecular Modeling Basics”, 2010, CRC Press Taylor&Francis Group.

Students will benefit of handouts as well as exercises and supplementary material.

The course aims at the knowledge of the mathematical and physical principles of the different calculation methods, in reference to their classical or quantum nature. Develop the ability to identify in the scientific literature the particular computational method applied to a problem of chemical interest. A more advanced objective is the development of the ability to autonomously propose a computational method suitable for a specific type of chemical system, managing to identify the most convenient calculation program, indicating the quantity and type of computational resources necessary.
Communication skills: acquire and know how to use the appropriate chemical vocabulary in relation to the topics and theoretical methods presented in the course.

A good knowledge of the Physical-Chemistry I and II, Physics I and II, and Mathematics I and II courses is essential.

Lectures.
Tutorials, Case study and problem solving.

At the beginning of each lesson, the subject of the previous lesson will be summarized, involving the students in identifying the most complex points of the discussion.
To verify that students are following the topics during the course, exercises will be carried out, even with the use of the computer, to apply a theoretical method suitable to answer questions of chemical interest on different real systems.

The exam includes a written test and possibly an oral exam. The written test includes problems regarding the topics covered in the three theoretical parts of the program (introduction and fundamental concepts; approximate calculation methods in molecular quantum mechanics and
calculation methods in classical mechanics). The oral test will serve to demonstrate complete mastery of the course topics in knowing how to demonstrate the various theorems and methods covered. The overall evaluation will take into account the answers to the theoretical problems and questions and any oral exam.

1. references to quantum mechanics (operators, wave functions and related properties, eigenvectors and eigenvalues, probabilistic interpretation of QM, notation
bra-ket), time-dependent Schrödinger equation and separation of variables for time-independent Hamiltonians, phase factors, molecular Hamiltonian and definition of atomic units.
2. Born-Huang expansion of the molecular wave function and related molecular Schrödinger equation, demonstration of the origin of non-adiabatic couplings and
discussion of the limits of the adiabatic and Born-Oppenheimer approximation. Proof of the Hellmann-Feynmann theorem.
3. The electronic problem: - single electron functions, distinction in atomic and molecular orbitals, correlated and uncorrelated probabilities, Hartree products, and Slater determinants. Description of exchange correlation and Fermi hole. Slater-Condon rules.
4. The Hartree-Fock equations: proof using the Lagrange multiplier method, formal aspects of the exchange and Coulomb operators and their physical interpretation. Diagonalization of multipliers and canonical HF equations. Introduction of a basic set. Proof of the Roothaan equations, analysis of the terms of the Fock operator on the basis of atomic orbitals and outline of the computational problems on the computation of bielectronic integrals. Molecular basis sets: Slater orbitals, Gaussian expansions, nomenclature and details on Pople and Dunning bases.
Discussion of the properties of the HF-Roothan equations, dependence on the one-body density matrix and definition of the iterative algorithm. Orthogonalizations
symmetric and canonical. Linear dependence problems and possible solutions. Koopmans theorem for IP and EA. The Brillouin theorem.
5 Introduction to the concept of electronic correlation and its definition according to Lowdin, distinction between static and dynamic correlation, definition of electronic configuration determinants and notes on the CI method. Definition of restricted and unrestricted determinants, spin operators and calculation of eigenvalues ​​on a single determinant and excited configurations
6. Definition of Configuration state functions (CSF) The method of Configuration interaction (CI): introduction, formal development of the wave function, calculation of the number of determinants, linear variational method and structure of the full-CI matrix. Correlation energy in intermediate normalization and dependence on double excitation coefficients. Dependence of double excitation coefficients on single and triple excitations. The size consistency problem
7. The perturbation theory and the Moeller-Plesset approach. Calculation of energy and wave function at various orders. Computational considerations and performances of the MP2 method.
8. The theory of density functional: definition of functional and functional derivative and calculation of some examples. Hoemberg and Kohn theorems. The Kohn-Sham method. effective potential formulation, correlation and exchange potential term, variational formulation and Kohn-Sham equations. Approximations to the exchange and correlation functional: LDA, GGA, hybrid and range separation functionals. Performance of the functionals depending on the molecular properties to be simulated.
9. The calculation of excited electronic states: the CIS, TDHF and TDDFT approaches and their performances. Notes on how to select dft functionals and basis sets .
10. Presentation of the PCM formulation to model solvents as a polarizable continuum dielectric medium .

Knowledge and understanding: to acquire solid theoretical knowledge of the computational methods presented during the course, together with the understanding of their historical evolution; to learn the mathematical foundation necessary to justify and describe in detail the theoretical relationships involved in the main equations; to be able to underline the advantages and disadvantages of applying different fundamental theories to chemical problems.
Applying knowledge and understanding: ability to propose the most suitable computational method for answering various chemical questions, based on the lessons learned during the course and motivate the proposal using theoretical concepts.
Communication skills: Acquire and properly use the basics of the technical lexicon typical of computational chemistry, with respect to the context; be able to expose and argue topics and applicative examples similar to those proposed during the course.
Making judgements: critically analyze the computational approaches adopted for a specific chemical problem, even in comparison to recent literature.