Quantum Chemistry

Lecturer: Gershom (Jan M.L.) Martin, x2533, Email: comartin@wicc.weizmann.ac.il
Summary | Evaluation | Reading List | Course Outline | Back to schedule | Martin group

Course abstract

The course will discuss the "hows and whys" of modern methods in computational quantum chemistry. Topics include: relationship between molecular energy surface and molecular properties; Hartree-Fock theory; electron correlation and its chemical manifestations; many-body perturbation theory; configuration interaction; coupled cluster theory; density functional techniques; basis set convergence and "quality control" of quantum chemical calculations.

The concepts involved will be illustrated with application case studies from the recent literature.

The main goal of the course is to empower students to critically read the ever-expanding quantum chemistry literature, to effectively apply computational methods on their own or collaborate with specialists in the area; and to intelligently interpret the results. While the main emphasis lies on qualitative concepts, rather than mathematical "drudgery", some mathematics cannot be avoided.

It is strongly recommended that students previously took the courses "Quantum mechanics for chemists" and "Mathematics for chemists" or undergraduate courses with similar content. Some basic knowledge of group theory will also be helpful.

Method of evaluation

Student paper.

Recommended reading

F. Jensen, Introduction to Computational Chemistry (Wiley, 1999). Additions and Corrections are available on the WWW. This will probably become the "official" textbook of the course. It is fairly comprehensive and rather inexpensive: if you're going to buy one book on the subject, this would be my recommendation. Lecture Notes in Quantum Chemistry I and II, Lecture Notes in Chemistry 52 and 64 (Springer, Berlin, 1992 and 1995). These books are in the Chemistry Library and have been put in the "Reserved for Courses" closet. Ask the librarian for assistance.

Course outline

  • Unit 0: statement of purpose
  • Unit 1: connection between molecular potential energy surface (PES) and physico-chemical properties
  • what is a molecule quantum-mechanically speaking? Molecular Schroedinger equation
  • Born-Oppenheimer approximation
  • electronic Schroedinger equation
  • nuclear motion Schroedinger equation => spectroscopy
  • Statistical thermodynamics: bridge between properties for 1 molecule and for 1 mol (i.e. macroscopic quantity)
  • fundamentals of molecular spectroscopy
  • diatomic molecule
  • polyatomic molecule (some elements of the theory)
  • Unit 2: the independent-particle approximation
  • Hartree-Fock theory: basis of everything else despite its many flaws
  • introduction of a finite basis set
  • why (almost) everybody uses atom-centered Gaussian basis functions
  • esoterica like bond-centered functions, etc.
  • contracted and uncontracted basis sets
  • basis sets in molecules, how they differ from atoms
  • polarization functions
  • diffuse functions
  • the issue of Basis Set Superposition Error (BSSE)
  • analytical energy derivatives
  • geometry optimization
  • the logic of a practical calculation: the SCF method
  • direct SCF methods
  • spatial and spin symmetry
  • some remarks about exploiting and imposing spatial symmetry
  • unrestriced Hartree-Fock (UHF) and the spin contamination problem
  • remark on RHF/UHF instability
  • restricted open-shell Hartree-Fock
  • Unit 3: electron correlation
  • what is electron correlation? Why is it important?
  • chemical consequences of electron correlation for
  • reaction energies
  • molecular structure
  • vibrational frequencies
  • reaction barrier heights
  • other properties
  • form of the exact wave function => full configuration interaction (FCI)
  • types of electron correlation and concomitant basis set requirements
  • nondynamical correlation
  • dynamical correlation in atoms
  • radial correlation
  • angular correlation
  • dynamical correlation in molecules
  • inner-shell versus valence correlation
  • natural orbitals: an extension of the orbital concept
  • Unit 4: approximate electron correlation methods
  • why exact solution is not practical option for most molecules
  • limited configuration interaction
  • the size extensivity problem
  • multiconfigurational SCF methods, including CASSCF
  • multireference configuration interaction (MRCI) and related methods
  • many-body perturbation theory
  • coupled cluster theory
  • general discussion
  • CCSD(T), best general-purpose single-reference electron correlation method to date
  • Methods based on Brueckner orbitals
  • Unit 5: modern basis sets for correlated calculations
  • atomic natural orbital (ANO) basis sets
  • correlation consistent basis sets
  • diffuse functions in correlated calculations
  • basis sets for inner-shell correlation
  • BSSE in correlated calculations
  • reasons to avoid some commonly used basis sets
  • what with heavier elements (e.g. transition metals)
  • Unit 6: density functional theory (an implicit electron correlation treatment)
  • the Hohenberg-Kohn theorem and the Kohn-Sham equations
  • some exchange-correlation functionals
  • local density approximation
  • gradient-corrected functionals
  • hybrid functionals including Hartree-Fock exchange: B3LYP and B3PW91
  • basis set convergence in DFT calculations
  • Unit 7: “tachlis” (brass tacks)
  • some modern quantum chemical computer programs: GAUSSIAN 94, ACES II, MOLPRO 96, SPARTAN, ...
  • practical strategies for calculations
  • case studies from the literature
  • Unit 8: capita selecta (e.g. effective core potentials, population analysis, chemical reactivity indices: the Fukui function, semiempirical methods,x...)