Syllabus
Permutations, their properites and algorithms for their generation mp
Normal mp 1 1 2003-02-07T14:12:00Z 2003-02-07T14:13:00Z 1 gfhghgg 1 1 9.3821 21
/* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";}
@page Section1
{size:595.3pt 841.9pt; margin:70.85pt 70.85pt 70.85pt 70.85pt; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1
{page:Section1;}
-->
Permutations, their properites and algorithms for their generation
Group of all permutations of normal'>n elements and its properties
Young tableaux, irreducible representations, computation of characters
Young operators, decomposition of the tensor space of orbital products according to irreps
Application in quantum chemistry: construction of spin-adapted antisymmetrized wave functions
The general linear group and their subgroups
Generators of Lie groups and the corresponding Lie algebras
Irreducible representations of the unitary group, Gel'fand basis, connection to the symmetric group
Matrix elements of generators in the Gel'fand basis
Connection to second quantisation, isomorphism between excitation operators and unitary group generators
Formalism for spin ½ particles: Weyl tableaux, Paldus tableaux, hamiltonian matrix elements
Graphical Unitary Group Approach: distinct row table and
Shavitt graph
Practical implementation of the CI method: direct CI, use of point group symmetry
Other CI formulations, contracted CI technique, size-extensivity corrections
General ROHF and CASSCF methods
Introduction to spin adapted coupled clusters method
Annotation
This course is intended for advanced undergraduates and Ph.D. students of quantum chemistry, who would like to know more about post-Hartree-Fock methods. We will first deal with basis properties of the symmetric (permutation) group, which has its own application in quantum chemistry and is deeply connected with the unitary group.
Then we will introduce Lie groups and algebras and show application of their theory to the computation of matrix elements of the CI hamiltonian for many electron system.