## 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.

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: ÒtachlisÓ (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...)