The nuclear Overhauser effect (NOE) is an incoherent cross-relaxation process between two nuclear spins within approximately 5 angstroms of each other. The intensity of the NOE is proportional to r-6, where r is the distance between the spins, meaning it decays very quickly with increasing distance. NOE experiments can provide distance restraints for structure determination of biological macromolecules like proteins.
Labile & inert and substitution reactions in octahedral complexesEinstein kannan
The first part includes a definition of labile and inert. lability and inertness on the basis of VB theory and CFT and also factors affecting inertness and lability of the complexes.
And also the second part includes Substitution Reactions in Octahedral Complexes like mechanisms and their evidence.
i have worked on the application of suzuki coupling reaction. For general awareness and fun, i have made this presentation. I hope people in such field and interest will enjoy.
Labile & inert and substitution reactions in octahedral complexesEinstein kannan
The first part includes a definition of labile and inert. lability and inertness on the basis of VB theory and CFT and also factors affecting inertness and lability of the complexes.
And also the second part includes Substitution Reactions in Octahedral Complexes like mechanisms and their evidence.
i have worked on the application of suzuki coupling reaction. For general awareness and fun, i have made this presentation. I hope people in such field and interest will enjoy.
CONTENTS
INTRODUCTION
CONCEPTS OF WALSH DIAGRAM
APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur Donald Walsh FRS The introducer of walsh diagram (8 August 1916-23 April 1977) was a British chemist, professor of chemistry at the University of Dundee . He was elected FRS in 1964. He was educated at Loughborough Grammar School.
Walsh diagrams were first introduced in a series of ten papers in one issue of the Journal of the Chemical Society . Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken .
IMPORTANT NAMED REACTIONS in Organic synthesis with Introduction, General Mechanism, and their synthetic application covering more than 20 named reactions in it.
CONTENTS
INTRODUCTION
CONCEPTS OF WALSH DIAGRAM
APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur Donald Walsh FRS The introducer of walsh diagram (8 August 1916-23 April 1977) was a British chemist, professor of chemistry at the University of Dundee . He was elected FRS in 1964. He was educated at Loughborough Grammar School.
Walsh diagrams were first introduced in a series of ten papers in one issue of the Journal of the Chemical Society . Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken .
IMPORTANT NAMED REACTIONS in Organic synthesis with Introduction, General Mechanism, and their synthetic application covering more than 20 named reactions in it.
We know that the molecules vibrate with characteristic frequencies. These frequencies match to the IR region of electromagnetic radiation, and Molecular vibrations are nothing but the relative motions of atoms with respect to each other.
Thus molecular vibrations actually define the energy states of the molecules.Group theory can help us to identify which molecular vibrations can really exist.
Study of Parametric Standing Waves in Fluid filled Tibetan Singing bowlSandra B
I completed a Summer Project (May-July 2015) in Physics entitled "Study of
Parametric Standing Waves in Fluid filled Tibetan Singing bowl" under the
guidance of Dr. S. Shankaranarayanan at Indian Institute of Science Education
and Research (IISER-TVM). The project was to theoretically analyze and solve the
non-linear equations for the patterns of wave formed on the surface of Tibet
Singing Bowl for ideal and viscous fluid.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
1. NOE
•Transferring magnetization through scalar coupling is a
“coherent” process. This means that all of the spins are doing
the same thing at the same time.
•Relaxation is an “incoherent” process, because it is caused by
random fluxuations that are not coordinated.
•The nuclear Overhauser effect (NOE) is in incoherent process
in which two nuclear spins “cross-relax”. Recall that a single
spin can relax by T1 (longitudinal or spin-latice) or T2
(transverse or spin-spin) mechanisms. Nuclear spins can also
cross-relax through dipole-dipole interactions and other
mechanisms. This cross relaxation causes changes in one spin
through perturbations of the other spin.
•The NOE is dependent on many factors. The major factors
are molecular tumbling frequency and internuclear distance.
The intensity of the NOE is proportional to r-6 where r is the
distance between the 2 spins.
2. Qualitative Description
Two nuclear spins within about 5 Å will
interact with each other through
space. This interaction is called
cross-relaxation, and it gives rise to
the nuclear Overhauser effect
(NOE).
Two spins have 4 energy levels, and the
transitions along the edges
correspond to transitions of one or
the other spin alone. W2 and W0 are
the cross-relaxation pathways,
which depend on the tumbling of
the molecule.
2 spins I and S
aa n1(***)
(***) n2 ab
bb n4(*)
WS
(1)
WS
(2)
WI
(1)
WI
(2)
ba n3(*)
W2
W0
3. dn1/dt = -WS
(1)n1-WI
(1)n1–W2n1 + WS
(1)n2+WI
(1)n3+W2n4
… etc for n2,3,4
using: Iz= n1-n3+n2-n4 Sz= n1-n2+n3-n4 2IzSz= n1-n3-n2+n4
One gets the ‘master equation’ or Solomon equation
dIz/dt = -(WI
(1)+WI
(2)+W2+W0)Iz – (W2-W0)Sz –(WI
(1)-WI
(2))2IzSz
dSz/dt = -(WS
(1)+WS
(2)+W2+W0)Sz – (W2-W0)Iz – (WS
(1)-WS
(2))2IzSz
d2IzSz/dt = -(WI
(1)+WI
(2)+ WS
(1)+WS
(2))2IzSz - (WS
(1)-WS
(2))Sz - (WI
(1)-WI
(2))Iz
(WI
(2)+W2+W0) auto relaxation rate of Iz or rI
(1)+WI
(WS
(1)+WS
(2)+W2+W0) auto relaxation rate of Rz or rR
(W-W) cross relaxation rate s20IS
Terms with 2IzSz can be neglected in many circumstances
unless (W(1)-WI/S
I/S
(2)) (D-CSA ‘cross correlated relaxation’ etc …)
4. Spectral densities J(w)
W0 µ gI
2 gS
2 rIS
-6 tc / [ 1 + (wI - wS)2tc
2]
W2 µ gI
2 gS
-6 tc / [ 1 + (wI + wS)2tc
2 rIS
2]
WS µ gI
2 rIS
2 gS
-6 tc / [ 1 + wS
2tc
2]
WI µ gI
2 rIS
2 gS
-6 tc / [ 1 + wI
2]
2tc
• Since the probability of a transition depends on the different
frequencies that the system has (the spectral density), the
W terms are proportional the J(w).
• Also, since we need two magnetic dipoles to have dipolar
coupling, the NOE depends on the strength of the two
dipoles involved. The strength of a dipole is proportional to
rIS
-3, and the Ws will depend on rIS
-6:
for proteins only W0 is of importance W I,S,2 <<
• The relationship is to the inverse sixth power of rIS, which
means that the NOE decays very fast as we pull the two
nuclei away from each other.
• For protons, this means that we can see things which are at
most 5 to 6 Å apart in the molecule (under ideal conditions…).
5. d(Iz – Iz0)/dt = - rI (Iz–Iz0) - sIS (Sz–Sz0)
d(Sz – Sz0)/dt = - sIS (Iz–Iz0) - rS (Sz–Sz0)
Note that in general there is no simple
mono-exponential T1 behaviour !!
6. Steady State NOE Experiment
For a ‘steady state’ with Sz saturation Sz=0
d(IzSS – Iz0)/dt = - rI (IzSS–Iz0) - sIS (0–Sz0) = 0
IzSS = sIS/rI Sz0 + Iz0
for the NOE enhancement
h=(IzSS-Iz0)/ Iz0= sIS/rI Sz0/Iz0
7. NOE difference
Ultrahigh quality NOE spectra: The upper spectrum shows the NOE enhancements observed when
H 5 is irradiated. The NOE spectrum has been recorded using a new technique in which pulsed
field gradients are used; the result is a spectrum of exceptional quality. In the example shown here,
it is possible to detect the enhancement of H10 which comes from a three step transfer via H6 and
H9.
One-dimensional NOE experiments using pulsed field gradients, J. Magn. Reson., 1997, 125, 302.
8. Transient NOE experiment
Solve the Solomon equation
With the initial condition
Iz(0)=Iz0 Sz(0)=-Sz0
For small mixing times tm
the ‘linear approximation’ applies:
d(Iz(t)– Iz0)/dt = -r(Iz(t)–Iz0) - s(Sz–Sz0) ~ 2 sSz0
IISISValid for trand ts<< 1
mS mIS (i.e. S is still inverted and very little transfer from S)
h(t) = (Iz(t) - Iz0)/ Iz0 = 2stmm IS
m
The NOE enhancement is proportional to sIS !
9. Longer mixing times
a system of coupled differential equations can be solved
by diagonalization or by numerical integration
Multi-exponential solution: the exponentials are the
Eigenvalues of the relaxation matrix
10. NOESY
The selective S inversion is replaced
with a t1evolution period
Sz(0)=cosWSt1Sz0, Iz(0)=cosWIt1Iz0
(using the initial rate appx.)
Sz(tm)=sIStmIz0 + rStmSz0 (a)
+cosWIt1[sIStm]Iz0 (b)
+cosWSt1[rStm-1]Sz0 (c)
11. NOE vs. ROE
Enhancement
NOE goes through zero wtc
NOE
~10 kDa ~33kDa Small peptides
~1 kDa
12. ROESY
90
t1
tm
" wSL << wo, w * tc << 1
• The analysis of a 2D ROESY is pretty much the same than
for a 2D NOESY, with the exception that all cross-peaks are
the same sign (and opposite sign to peaks in the diagonal).
Also, integration of volumes is not as accurate…
90s
tm
13. t Approaches to Identifying NOEs
• 15N- or 13C-dispersed
(heteronuclear)
3D
1H
13C
1H
1H
15N
1H
1H
15N
1H
13C
1H
13C
1H
13C
1H
15N
1H
15N
4D
2D 1H 1H
3D 1H 1H 1H
• 1H-1H (homonuclear)