From Electronic Structure Theory to
Simulating Electronic Spectroscopy
Marcel Nooijen
K. R. Shamasundar
University of Waterloo
Anirban Hazra
Hannah Chang
Princeton University
What is Calculated?
Vertical transitions, e.g. ethylene:
State
STEOM
[Nooijen]
E
Solutions to the problem set on angular momentum theory.
1. In this exercise you are asked to prove a number of relations in connection with angular
momentum theory. They are mentioned in the lecture notes. You should try to use the general
strategies tha
Solution set IV.
Most of the Szabo and Ostlund problems did not pose particular difficulties. I will discuss
two problems in detail that illustrate a general point.
S&O 2.27
Evaluate 0 aia j 0 ,
0 = a1a2 .aN vac
If j > N (not occupied in 0 , then the
Solution Set Oscillator.
1. You can use the commutation relations b, b = 1 , the definitions
1
1
b =
(q ip), b =
(q + ip ), where p = i , as well as the Hermiticty of p and q
q
2
2
in your proofs.
a.
1
1
1
i p
b =
q ip =
q *
*
2
2
2
1
1
( q +
Solution set 2: Chapter 1: Szabo and Ostlund
I will be brief in my solution set. I expect your home works to be more complete than my
solution set!
S&O 1.1:
r
r
Oei = e j O ji
j
a.
r
r r
r
r r
ek Oei = ek e jO ji = ek e j O ji = kjO ji = Oki
j
j
j
r r
Oa
Solution set III.
1. Szabo & Ostlund: 2.1, 2.2, 2.4, 2.5, 2.7. These problems are fairly straightforward and
I will not discuss them here.
2.
N!
N!
N!
i =1
j =1
i =1
p
AA = () pi Pi () j Pj =
N!
=
i =1
N!
k =1
N!
j =1
( )
pi + p j
( PPj )
i
,
() Pk = N
Solutions to problem set 1.
1.
Lx = ( ypz zp y ); Ly = ( zpx xpz );
Lx , Ly = ypz zp y , zpx xpz = ypx pz , z + xp y [ z , pz ]
= i ypx + i xp y = i Lz
Here we use for example that ypz , zpx = ypz zpx zpx ypz = ypx z , pz = i ypx : factors
that commute ca
NMR and ESR Spectroscopy
K. R. Shamasundar and M. Nooijen
University of Waterloo
Introduction
Nuclear Magnetic Resonance (NMR) spectroscopy and Electron Spin Resonance (ESR)
spectroscopy are two widely used spectroscopic techniques to infer structure and
Problem Set SO Chapter 2.
1. Szabo & Ostlund: 2.1, 2.2, 2.4, 2.5, 2.7. These problems are fairly straightforward and
I will not discuss them here.
2.
N!
N!
N!
i =1
j =1
i =1
p
AA = () pi Pi () j Pj =
N!
=
i =1
N!
k =1
N!
( )
pi + p j
j =1
( PPj )
i
,
()
On the Postulates of Quantum Mechanics
and their Interpretation.
Marcel Nooijen
University of Waterloo
One arrives at very implausible theoretical conceptions, if one attempts to maintain the
thesis that the statistical quantum theory is in principle capa
Derivation of Harmonic Oscillator form of Hamiltonian
for polyatomic molecules.
If we denote the coordinates of all the nuclei as the 3N components of a vector
r
R = ( x1 , y1 , z1 ,., x N , y N , z N )
(1)
we can expand the electronic energy (including n
On the Uniqueness of Molecular Orbitals and limitations of the MO-model.
The purpose of these notes is to make clear that molecular orbitals are a particular way to
represent many-electron wave functions. They are not unique and do not have an
unambiguous
Referee report on An efficient approach for the calculation of Franck-Condon
integrals of large molecules. By Diercksen and Grimme.
Dear Editor,
This paper discusses an interesting approach to the efficient calculation of FranckCondon integrals (FCIs) for