CHEM 602
Special Topics in Physical Chemistry
Spring 2003 Curriculum
Mon and Wed 19.00-20.30
Room 1505
Background theory of physical methods relating to characterization of
molecular structure and bonding. Topics covered will include X-ray
crystallography, powder diffraction; Multi-nuclear nmr; magnetic
measurements and esr spectroscopy; ir, Raman, uv-visible spectroscopies;
mass spectrometry; surface and elemental analysis and computational
methods applied to inorganic systems.
The course will be given in seven two-week modules. Each should
a)
cover fundamental background of the techniques discussed
b)
include some details of hardware/software used
(and if available at HKUST)
c)
what results/information can be obtained giving clear
worked examples
d)
discuss the limitations /experimental difficulties involved.
Each module will have one assignment which reinforces the concepts and
examples given and may involve some searching of research literature. The
aim of the course is to be straightforward and of practical benefit to the
students research and understanding of literature, seminars etc.
Proposed Schedule:
Week 1-2
Dr. Williams
Overview and X-ray crystallography
Weeks 3-4
Dr. Williams/ Yen Surface and Elemental Analysis
Weeks 5-6
Dr. Lin
Computational Methods
Weeks 7-8
Dr. Jia
Multinuclear NMR
Weeks 9-10 Dr. Li
IR-Raman UV-visible Spectroscopies
Weeks 11-12 Dr. Yang
Mass Spectrometry
Weeks 13-14 Dr. Leung
Magnetism and ESR
Week 15
Presentations for Review
Students
CHEM 602: Special Topics in Physical Chemistry
Grading Scheme
Attendance/participation
15%
Assignments
60%
Term presentation & paper
30%
You will be graded on your top 6 of 7 assignments from the seven
modules.
The term paper will be written by those taking the course for credit and
an oral Power-point presentation by small groups (including all attending
and auditing students !!)
Course Text:
There are two good text books which cover much of the course content:
1.
Physical Methods for Chemists by Drago
2.
Structure Elucidation for Inorganic Chemisty
by Rankin, Ebsworth et al
Unfortunately the former is now out of print and the second is too expensive.
We will try to obtain 1-2 copies of each for your reference and place on library
reserve.
CHEM 602
Special Topics in Physical Methods
Overview

This course is intended to cover topics which are complementary to those
normally used for Organic molecular characterization.

CHEM 602 will concentrate on topics that have special relevance to
Organometallic and Metal-ligand complexes, as well as metallo-organic polymers
and inorganic solids.
(This doesn't mean they cannot be applied to organic
molecules, e.g. X-ray crystallography, ir, uv spectroscopies are very important)

However before meeting these tools it is instructive to review the four main
characterization techniques used by organic chemists:
13
1.
C and 1H NMR (nuclear magnetic resonance)
Can yield the likely molecular structure with skilled interpretation and sufficient
resolution and possibly 2D or advanced pulse techniques. It should be emphasized
this is an indirect method. Also useful for molecular structure in solution and
information on molecular dynamics, through variable temperature measurements.
Usefulness / Limitations for Inorganic Compounds:
Clearly for many soluble organometallic and metal complexes these methods are still
of great value, but are less likely to give the full or correct structure.
Presence of more nmr silent nuclei leads to loss of information. In addition many
metal containing species are paramagnetic and the method may break down. Many
inorganic solids are insoluble and although solid state nmr may be possible, resolution
and information is lost.
These reasons lead to studies by single crystal X-ray diffraction, magnetic or esr
studies or by multi-nuclear nmr involving other spin active nuclei, eg
29
Si,
27
Al,
195
Pt etc.
31
P, 19F,
119
Sn,
Since many of these have wide chemical shift ranges and
coupling constants some useful information can often be gained. Frequently there is
problem due to lower sensitivity or peak broadening.
2.
High resolution mass spectrometry
Gives confirmation of likely molecular formula, since exact molecular ion eg [C15H22
N] can be distinguished from others of same mass unit eg [C14H20O] etc.
Clearly this tool must be used in conjunction with nmr above to give the molecular
structure. They are complementary methods.
Usefulness / Limitations for Inorganic Compounds:
The method is only of use for volatile substances and unless care is taken fragile or
reactive molecules may be destroyed by the ionization process. Organometallics and
metal complexes may be studied, and even molecular clusters.
The isotope
distribution patterns for certain elements are characteristic and can help. In general
solids are less practical for study and cannot be directly investigated in their native
state, though SIMS can look at solid 'fragments'.
3.
X-ray Crystallography
Single crystal structure determination is the best and most direct method of structure
elucidation. In most organic compounds it is quite unambiguous and even H atoms
can be located with confidence. It has the bonus of giving accurate geometrical
information useful for conformational analysis and bonding studies. Furthermore
absolute configuration can be obtained for chiral compounds, either by using Copper
X-rays or a heavy atom derivative or salt. However organic chemists are notoriously
lazy to grow suitable crystals !! (need ca. 0.1mm minimum dimension)
Usefulness / Limitations for Inorganic Compounds:
Already outstanding for organic compounds, X-ray crystallography is perhaps the
most important characterization tool for organometallic and coordination chemists.
This is because of the difficulties inherent in nmr being indirect method. The higher
complexity possible for inorganic compounds, the more silent nuclei and the wide
range of geometries and stereochemistries possible mean even compounds for which
structural connectivities are well established may still be subjected to X-ray structure
determination.
For inorganic solids crystallography is a key technique, though for fine powders, the
crystal size may be too small. The related method of powder X-ray diffraction may
then be used. X-ray structure analysis can ususally determine ab initio which elements
are present since it is a direct method in 'seeing' location of electron density. One
limitation is that some heavy atom compounds have high absorption leading to lower
structural accuracy and more difficulties in dtermining H atom locations. Also larger
metal complexes or clusters often pack space inefficiently leading to co-crystallization
with solvent or water molecules which are 'disordered' or partial occupancy. These
can also decrease the quality of a structure determination and can also mean many
crystals 'die' through solvent loss before being analyzed.
4.
Combustion Analysis (CHN)
Still often required by journals for publication of 'pure' substances a 'CHN' analysis
actually gives limited structural information and for example cannot distinguish
isomers and of course is almost meaningless for mixtures.
Usefulness / Limitations for Inorganic Compounds:
Again may be applied to certain organometallic compounds and solids with
confidence, but care should be taken over complete combustion with high C materials,
and of course by their nature inorganic materials may have little C, H or N !! Air
sensitive compounds must be properly handled before analysis for obvious reasons.
Other elements than C H or N can be analyzed but typically this is done by variety of
methods. In this course we will compare and contrast several of these such as X-ray
Fluorescence, EDAX (Energy dispersive Analysis of X-rays) which is an attachment
of the scanning Electron Microscope and XPS (X-ray Photoelectron Spectroscopy) a
tool of surface analysis. Methods such as Atomic absorption spectroscopy will also
be briefly reviewed.
Topic 1.

X-ray Crystallography
Basis of the Technique
Most important is single crystal X-ray structure determination. In this a single crystal
is oriented in a monochromatic X-ray beam.
The X-rays are produced by electrons hitting a metal target, Usually Mo or Cu.
Only characteristic X-rays with a particular wavelength are then used for the
experiment Mo-K 0.71Å (or Cu-K 1.54Å).
A small fraction > 0.1% of these X-rays are scattered by the electron clouds in the
crystal. Scattering occurs in all directions, though with different probabilities.
Since the crystal is an ordered 3D repeat pattern of electron density this gives rise to
reinforcement of the scattered X-rays in certain directions through constructive
interference.
If the positions of the diffracted beams are measured they can be used to reconstruct
the 'unit cell'. The unit cell is the smallest parallel sided box which stacked together
repetitively in 3D forms the whole crystal.
The positions of the diffracted X-ray beams are dependent on the
orientation of the crystal and the size and shape of its unit cell.
The diffracted beams have different intensities and these can be measured and
integrated by a CCD detector.
The intensities of the diffracted beams (once corrected for certain
effects) are related to the electron density distribution in the unit cell.
In principle mathematical analysis of the intensity pattern can yield the electron
density distribution and since electrons are associated with atomic positions, the
molecular structure is revealed.
This gives both accurate and precise 3D atomic coordinates and thus
molecular structure and connectivity
bond lengths, angles and torsions
molecular packing or polymer architectures
absolute or relative stereochemical configurations
phase transitions, vibrational information etc
Note the need for a 'single' crystal in which the unit cells are aligned in one
orientation. Its size should be 0.1-0.5 mm dimension and good quality. Obtaining
this may be the most difficult and time consuming part of the technique !
With modern diffractometer the diffracted X-ray data is typically measured in 3-6 hrs
by taking successive diffraction images from slightly different crystal orientations.
With modern computational methods the atomic positions are found and refined
within 1 hr to give the molecular structure. Often the most time consuming part is
deciding a 'labelling scheme' to describe each atom position !
So far this sounds simple enough - what about the Phase
problem and difficult things like space groups and R-values?
Step 1.
Growing and Selecting a Crystal
Crystals represent ordered 3D packing arrangements of molecules, ions, atoms or
combinations of these.
In general these ordered arrangements are energetically favored over random
(amorphous) packing of the same entities. Thus almost all pure substances can be
crystallized if suitable growth conditions are found.
Note however a particular crystal may not be the most stable packing arrangement
and many compounds can be found as Polymorphs if a sufficiently large number of
crystallization conditions are attempted.
For organic molecules and soluble inorganic complexes the
following methods of crystal growth are most common.
1.
Cooling a Saturated Solution
useful for very hydrocarbon soluble 'greasy' compounds
2.
Solvent Layer Diffussion (my preferred method if possible)
dissolve in a good solvent and let excess of a poor one diffuse in
eg CH2Cl2/hexane EtOH/Et2O
3.
dmso/water
Solvent Vapour Diffusion
similar to layer diffusion but the second solvent condenses into
solution from the vapor phase eg EtOAc/Et2O
4.
Evaporation
a common traditional method but not advised since leaves sticky mess
Other crystallization methods:
include Sublimation, Freezing (for RT liquid), Hydrothermal, Cooling/Pulling
from a Melt or Flux. Many of these are more useful for inorganic species or
slow formation of insoluble phases.
Ideal Crystal Size
The crystal should completely fit into X-ray beam which is 0.8mm diameter.
In general larger crystals give stronger diffraction, unless there is severe
absorption. Limiting size is 2/ where  is the absorption coefficient. Most
organics have low coefficients.
Ideal Crystal Quality
The shape of crystal should be regular, with parallel edges, and if possible
shape should be isotropic, so i.e. a 'chunky' cube is better than a thin plate.
Ideally crystal should be optically transparent, without major cracks, steps
occlusions or other flaws. 'Twinning' can be examined using polarizing filters.
Mounting of Crystals
Crystal is mounted using epoxy glue on end of a glass fiber which is set in a
brass pin. The pin is then locked into a Goniometer head, which allows xyz
translation of crystal to centre of diffractometer and alignment in the X-ray
beam.
Special care must be taken with air-sensitive crystals and those that lose
solvent. These can be mounted under inert atmosphere or in mother solvent in
a small quartz capillary tube, which is then sealed.
Typically at HKUST all X-ray diffraction data is measured at 100K so further
crystal deterioration during experiment is unlikely.
X-ray Crystallography Lecture 1. Multi-choice Revision
X-ray Diffraction
1.
X-ray crystallography excellent direct technique for molecular structure
determination,
2.
a)
only for organics
b)
only for inorganics
c)
both for organic and inorganic molecular solids.
X-rays are part of electro-magnetic radiation spectrum. They are high
energy photons with
3.
a)
 = 0.01 -100Å.
b)
 = 0.01 -100m.
c)
 = 0.01 -100mm.
In X-ray diffraction experiments we use monochromatic X-rays. Their
production involves:
4.
a)
electrons bombarding a metal target
b)
atomic ionization yielding 'characteristic' X-rays.
c)
constructing the equipment to select only one wavelength
A single crystal in X-ray beam gives a diffraction pattern. This is due to
small fraction of X-rays being scattered by electrons in the xtal.
a)
X-rays are only scattered in some directions due to the atomic
positions
b)
X-rays are scattered in all directions, but for some directions have
reinforced scattering due to constructive interference
c)
X-rays are scattered by the atomic nuclei not electrons.
5.
The Bragg condition implies that the direction of the scattered beams
depends on the 3D repeating nature of the crystal.
6.
a)
Direction of diffracted beams depends on size of Unit Cell
b)
Direction of diffracted beams depends on shape of Unit Cell
c)
Direction of diffracted beams depends on orientation of Unit Cell
The intensities of the diffracted beams come about from the relative inphase scattering behavior of all electrons in the unit cell and
a)
Are different for each diffraction spot.
b)
Are dependent on the atomic positions within the Unit Cell.
c)
Always increase if crystal is larger.
Summary
Measuring _______ and _________ of diffracted X-rays can yield the
___ cell and the _______ density within it.
Since electrons are associated with ______ positions (core electrons)
we can then re-construct all molecules within the unit cell giving the
'Crystal Structure'.
Crystals
7.
Crystals
a)
Are 3D ordered arrays of atoms, molecules, ions or combinations
of these.
b)
They can be pharmaceuticals, natural products, organometallic
complexes, coordination polymers or solid state oxides or metal
alloys.
c)
8.
Are always difficult to grow !
Single crystals
a)
are important since we need all unit cells in our diffracting
sample to be aligned.
9.
b)
must have parallel edges and be optically transparent
c)
are better since married crystals are more troublesome !
Crystals of a particular size are needed. Larger ones do not fit in X-ray
beam and smaller ones are usually too small to give a strong enough
diffraction pattern.
10.
a)
Size required is 0.1 - 0.5 mm
b)
Size required is 100 - 500 m
c)
Size required is 1.0 - 5.0 mm
For
the
following
compounds
choose
a
suitable
(different)
crystallization technique.
a)
Ferrocene
e)
LaAlO3
b) Lysozyme
c) p-Nitroaniline
d) D-Mannose
Choose from:
Controlled Aqueous Evaporation / Organic Layer diffusion / Sublimation /
Flux / Cooling MeOH solution
CHEM 602
Lecture 2. X-ray Crystallography
Topic: Crystal Symmetry
Some knowledge of crystal symmetry important since we will create a model
of electron density within the unit cell. However what we will mathematically
model is the symmetry unique part of this - what is called the asymmetric unit.
In this Lecture we will meet the following concepts, which you must be clear
about
1.
Pattern
simple or complex repeat of structure or entities in 2D or 3D
2.
Lattice
set of identical points from a repeating pattern - a mathematical abstraction
3.
Unit Cell
smallest parallel sided box which can stack to make up entire crystal
formed by connecting nearest set of lattice points by shortest vectors
4.
Cell Parameters
Edge lengths a, b, c (Å) and angles ,  and  Volume V (Å3)
5.
Crystal System
e.g. monoclinic
indicates the shape of unit cell and implies internal symmetry
6.
Asymmetric Unit
the symmetry unique part of the pattern - a simple fraction of the unit cell
7.
Crystallographic Symmetry Elements
Pure Translation
e.g. move 2 cells along a axis, or body diagonal
Point Symmetry
e.g. mirror, 3-fold axis
Mixed Symmetry elements
e.g. screw axis, glide plane
Q.
What point symmetries are allowed ?
8.
Fractional Coordinates
Allow us to consider atomic positions within the unit cell.
9.
General and Symmetry Generated Positions
e.g. Coordinates x,y,z move to -x, y+1/2, -z upon 2-fold screw operation.
10.
Lattice Planes and Indices
Important to the diffraction phenomenon - a family of lattice planes include all
lattice points. Indices hkl indicate how a family of lattice planes intercept the
cell edges - allow us to index the diffraction pattern.
CHEM 602 X-ray Crystallography
Lecture 3
From X-ray Diffraction Pattern to Crystal Structure
The positions of diffracted X-rays derive from the unit cell and their relative
intensities relate to the electron density distribution within that cell.
On other handouts we will see why in detail.
Geometry of Diffraction
First refer to the Bragg condition for diffraction to see the geometric part.
Lattice planes hkl in the crystal scatter in-phase for beams diffracted at angle
2 to the incident beam. The geometry is that of reflection, however note that
reflection occurs at all angles 2. Diffraction only occurs at special angles 2.
If we place atoms at the lattice points then they scatter in phase with each other
for these 2 directions.
Intensity of Diffraction
The intensity of the diffraction maxima now depends on the electron density
distribution between the set of lattice planes hkl. The scattered waves in
general are not all in-phase. However the resultant scattering effect is a wave
addition which includes the amplitude and the phase angle. The former is
based on the atomic number and the latter on the position in the cell.
The resultant scattering for all electrons in the unit cell for a particular hkl
plane is called the structure factor F. This is a summed wave that contains
both amplitude (Intensity) and phase information.
Step 1.
Measurement of Diffracted Beams
Now done using CCD - X-rays hit phosphor screen, which produces visible
photons. Travel along fibre optic to the 4K s-conductor chip and converted to
electrical signal.
The CCD area detector measures many diffraction spot
simultaneously.
Remember also the position of diffracted beams also depends on crystal
orientation. In practice to get the full diffraction pattern measured we
incrementally move the crystal.
Full data set takes 3-6 hrs, depends on
exposure for each position. Weak crystals could be done in 24hrs.
Interesting to note that large cells have more spots per area and so dont take
longer than small unit cells.
In the past each spot had to be measured
separately so large structures took much longer for data collection.
Step 2.
Data Reduction
Software now does data reduction, averaging etc to treat symmetry equivalent
and duplicate data. Coorection of Lorentz and polarization effects. Also
absorption due to different path lengths through crystal is corrected. The data
must also be 'indexed' to a unit cell and the likely symmetry of the crystal
system is determined.
The output from data reduction include 3 things for each
diffraction maximum:
the indices h,k,l
the structure factor amplitude Fo
and the esd (error) in Fo.
Incidentally the error in Fo is used to derive errors in positions, so ultimately
we get our bond length esds etc from this information.
Step 3.
Space Group Determination
In principle we cannot mathematically solve the electron density in the cell
without knowledge of the space group. Certainly we cannot refine a model of
it in a stable way without appropriate use of symmetry within the cell.
The space group tells us how the different asymmetric units within the unit cell
are organized by symmetry.
Analysis of missing data - called 'systematic absences', gives information about
the space group. They are sets of allowed diffraction positions which have zero
intensity.
Example if reflections hk0 h = 2n+1 are absent (such as 320, 550, -100) then
an a-glide plane perpendicular to c-axis is indicated, as in space group Pbca.
Actually the systematic absences just tell us about the type of translational
symmetry elements present.
These are either
i)
Lattice centering
ii)
Glide planes (mirror + translation)
iii)
Screw axes (rotation + translation)
Although there are 230 space groups only 15-20 are common, so knowledge of
crystal system and the absences can usually give us just one or two choices.
From this we can usually get a solution quite quickly.
Note: Space group symbols e.g. P21/c will be explained on a separate handout.
Step 4.
Solving the Structure
If we know all Fhkl then we can directly compute electron density which is a
Fourier transform of the structure factors.
Structure factors contain amplitude and phase information. In our X-ray
diffraction experiment we only measure the relative intensities of the diffracted
beams. These relate to F amplitudes but not their phases. So getting the e.d.
pattern is not a direct thing - this is known as the Phase Problem.
It is overcome by first obtaining a rough or partial solution of where the atoms
are. The calculated phases from these correct positions will be enough to give
interpretable e.d. maps for the missing or incorrect electrons when combined
with the real Fo amplitudes.
The initial solution is done nowadays by 'black box' routines called direct
methods, which are computationally exhaustive. They rely on fact that e.d.
distributions are always positive (no negative holes) and that the phase of a
Fhkl is actually related to the phases of all other Fhkl which add to the same
integer values !
A lot of complex probability theory is involved but the idea is to start with a
small set of defined phases and keep building up consistent sets of phases by
adding more and more hkl.
A consistent set with a good Figure of Merit is then used to calculate a rough
electron density map. If this looks like a chemical solution we proceed further.
If not we keep looking for other solutions !!
Step 5.
Refining the Structure
We then refine the structure by adjusting atomic positions and thermal
vibrations. This causes calculated F amplitudes Fc to be changed and the
program by least squares minimizes the differences to observed structure
factors Fo.
In successive cycles of refinement Fo-Fc (or their squares) are
reduced by applying values of the least squares parameters.
As the model gets better the phases get more and more correct and so the
calculated e.d. maps are better. This allows us to locate all missing atoms,
including eventually H atoms, or reassign atom types if necessary.
The adjustable parameters of structure refinement are
Overall scale factor
(overall Fc and Fo must sum to be equal)
Atomic coordinates (x,y,z)
(for each non-H atom)
Thermal parameters U
(anisotropic 6 values for each non-H)
So for every atom in structure have 9 parameters to adjust. To determine these
well by the l.s. method need at least 10 Fo per parameter. So for each atom in
structure need to measure about 100 diffraction data.
In practice this means we need to measure hkl to 2 = 55o for Mo-K or to
140o (a complete 'sphere') for Cu-K.
Step 6. Assessing the Structure
Three factors can be used to see if resulting structure is of good quality. All
three should be studied rather than one alone.
1.
R-Value
This is a sum  Fo-Fc/Fo for all hkl.
It implies your calculated model of e.d. matches that which gave rise to the
diffraction data. Good R-value usually about 5% (0.05). Note: wR2 now used
is based on differences in F2 not F, so is higher - even can be 0.2.
2.
Residual Electron Density
At the end of the structure refinement you have adjusted all parameters to
minimize the R-value. There is nothing more to do. However you can now
calculate two electron density maps from the atomic positions (phases) and the
observed and calculated F amplitudes.
The resulting 'difference map' between these should not contain significant
peaks or holes implying you have not missed any atoms in your model or added
ones that are not there, or are of the correct type.
For heavy atom structures you may find +/-1.0-2.0 eÅ-3 near those atoms
due to absorption effects.
For organics however the residual should be ca. +/-0.25eÅ-3 in ideal case.
3.
Bond Length Esds
If the model is well determined and self-consistent the esds of the bond lengths
should be small. This implies l.s. refinement of the atomic positions proceeded
smoothly. Sometimes esds are higher due to disorder and other factors outside
of your control. Note that esds involving heavy atoms are usually smaller, e.g.
moving a Pb atom affects the structure factors more than moving an O atom.
Step 7.
Results
In our final class we will look at the results: in principle the atomic positions
give geometric information which is usually tabulated.
Output includes
structure summary,
atomic coordinates and thermal parameters (xyz and U's),
bond lengths, angles and torsions.
H atoms are often treated separately since they are not refined in the l.s. process
but simply added in geometrically sensible positions.
By analysis with graphics programs we can get molecular plots and examine
intermolecular contacts, H-bonds etc as well.
Our result can also be compared with the ever growing databases of structures.
Cambridge Structural Database
for organics and organometallics
ICSD (Karlsruhe)
for inorganics
PSD (Brookhaven)
for proteins/ biopolymers