Transcript Unusual Aspects of Inorganic Compounds

84.443/543
Advanced Inorganic
Chemistry
The d
orbitals
Unusual Aspects of Inorganic
Compounds

The use of d orbitals enables transition metals to form
quadruple bonds. Sigma (σ) bonds can be formed using
p orbitals, or the dz2 orbitals.
Unusual Aspects of Inorganic
Compounds

Pi (π) bonds can be formed using the dxz and dyz orbitals.
Unusual Aspects of Inorganic
Compounds

In addition, “face-to-face” overlap is possible between the
dxy orbitals on each metal. This forms a delta (δ) bond.
Unusual Aspects of Inorganic
Compounds

The existence of δ bonds is usually determined by
measuring bond lengths and magnetic moments.
[Re2Cl8]2- has a
quadruple bond
between the metal
atoms.
Unusual Aspects of Inorganic
Compounds

The coordination
number for transition
metals can be greater
than 4, with coordination
numbers of 6 being quite
common. In addition, 4coordinate metal
complexes need not be
tetrahedral.
Unusual Aspects of Inorganic
Compounds

When inorganic
compounds have
tetrahedral geometry, it
may be quite different
from organic
compounds. P4 has
tetrahedral geometry, but
lacks a central atom.
Unusual Aspects of Inorganic
Compounds

Cluster compounds, in
which there are metalmetal bonds can be
formed. The structure of
Mn2(CO)10 has the two
Mn atoms directly
bonded to each other.
Unusual Aspects of Inorganic
Compounds

Cage compounds lack a
direct metal-metal bond.
Instead, the ligands serve
to hold the complex
together.
Unusual Aspects of Inorganic
Compounds

Organic molecules may
bond to transition metals
with σ bonds or π bonds.
If π bonded, some
unusual “sandwich”
compounds may result.
Quantum Numbers
n
principal quantum #;
n = 1, 2, 3, etc.
Determines the major part of
the energy of the electron
l
angular momentum quantum Describes angular
# = 0,1,2…n-1
dependence and contributes
to the energy
ml magnetic quantum #
Describes the orientation in
space. (ex. px, py or pz)
ms Spin quantum # = +1/2 or
Describes orientation of the
electron’s magnetic moment
in space
= -l…0…+l
-1/2
Common Orbital Designations
l
s
p
d
f
0
1
2
3
In the absence of a magnetic field, the p
orbitals (or d orbitals) are degenerate, and have
identical energy.
Wave Functions of Orbitals

Wave functions can be
factored into two angular
components (based on θ
and φ), and a radial
component (based on r).
Angular Functions

The angular functions, based on l and ml ,
provide the probability of finding an electron at
various points from the nucleus. These
functions provide the shape of the orbitals and
their spatial orientation.
The d-orbitals
Radial Functions

Radial functions are determined by the quantum
numbers n and l, and are used to determine the
radial wave probability function (4πr2R2).
R is the radial function, and it describes the
electron density at different distances from the
nucleus. r is the distance from the nucleus.
Radial Functions

Radial functions are used to determine the
probablity of finding an electron in a specific
subshell at a specified distance from the nucleus,
summed over all angles.
Radial Wavefunctions

The radial wave
functions for
hydrogenic orbitals
have some key
features:
Radial Wavefunctions
Key features:
1. All s orbitals have a
finite amplitude at
the nucleus.
2. All orbitals decay
exponentially at
sufficiently great
distances from the
nucleus.
Radial Wavefunctions
Key features:
3. As n increases, the
functions oscillate
through zero,
resulting in radial
nodes.
Radial Nodes

Radial nodes represent the point at which the
wave function goes from a positive value to a
negative value. They are significant, since the
probability functions depend upon Ψ2, and the
nodes result in regions of zero probability of
finding an electron.
Radial Nodes

For a given orbital,
the number of radial nodes= n- l -1
p orbitals
The radial wave
functions of p orbitals
show a zero amplitude at
the nucleus.
The result is that
p orbitals are less
penetrating than s
orbitals.
Radial Probability Functions
Radial probability
functions (4πr2Ψ2 or
4πr2R2 ) are the
product of the blue
and green functions
graphed for a 1s
orbital.
Radial Probability Functions
The orange line
represents the
probability of
finding an electron
in a 1s orbital as a
function of distance
from the nucleus.
Radial Probability Functions
Note the zero
probability at the
nucleus (since r=0).
The most
probable distance
from the nucleus is
the Bohr radius, ao =
52.9 pm.
Radial Probability Functions
The probability
falls off rapidly as
the distance from
the nucleus
increases.
For a 1s orbital,
the probability is
near zero at a value
of r = 5ao.
Radial Probability Functions
In a 1 electron atom,
the 2s and 2p orbitals are
degenerate. In multielectron atoms, the 2s
orbital is lower in energy
than the 2p orbital.
Radial Probability Functions
On average, the
electrons in the 2s orbital
will be farther from the
nucleus than those in the
2p orbital. Yet, electrons
in the 2s orbital have a
higher probability of
being near the nucleus
due to the inner
maximum.
Radial Probability Functions
The net result is that
the energy of electrons in
the 2s orbital are lower
than that of electrons in
the 2p orbitals.
The d
orbitals
The f orbitals
The Aufbau Principle
The loss of degeneracy in multi-electron
atoms or ions results in electron configurations
that cannot be predicted based solely on the
values of quantum numbers.
The aufbau (building up) principle provides
rules for obtaining electron configurations.
The Aufbau Principle
1. The lowest values of n and l are filled first to
minimize energy.
2. The Pauli Exclusion Principle requires that
each electron in an atom must have a unique
set of quantum numbers.
3. Hund’s Rule requires that electrons in
degenerate orbitals will have the maximum
multiplicity (or highest total spin).
Electron Configurations
Electron Configurations
Klechkowsky’s Rule states that filling
proceeds from the lowest available value of
n + l.
When two combinations have the same sum
of n + l, the orbital with a lower value of n is
filled first.
Electron Configurations
The electron configurations of Cr and Cu in
the first row of the transition metals defy all
rules, as do many of the lower transition
elements.
Shielding
The energy of an orbital is related to its
ability to penetrate the area near the nucleus,
and its ability to shield other electrons from the
nucleus.
The positive charge affecting a specific
electron is called the effective nuclear charge, or Zeff.
Shielding
Zeff = Zactual – S
or
Zeff = Zactual – σ
Where S or σ is the shielding factor.
Both the value of n and l (orbital type) play a
significant role in determining the shielding
factor.
Slater’s Rules
1. The electronic structure of atoms is written in
groupings:
(1s)(2s, 2p)(3s, 3p)(3d)(4s, 4p)(4d)(4f )
2. Electrons in higher groupings do not shield
those in lower groups.
Slater’s Rules- Calculation of S
3. For ns or np electrons:
a) electrons in the same ns and np as the
electron being considered contribute .35,
except for 1s, where .30 works better.
b) electrons in the n-1 group contribute .85
c) electrons in the n-2 group or lower (core
electrons) contribute 1.00
Slater’s Rules- Calculation of S
4. For nd or nf electrons:
a) electrons in the same nd or nf levelas the
electron being considered contribute .35
b) electrons in the groups to the left contribute
1.00
Problem: Zeff

Use Slater’s rules to estimate the effective
nuclear charge of Cl and Mg.
Periodic Trends
Zeff increases across a period. This is due to
the addition of protons in the nucleus,
accompanied by ineffective shielding for the
added electrons. As a result, the valence
electrons experience a greater nuclear charge on
the right side of the periodic table.
Ionization energy
Ionization energy is the energy required to
remove an electron from a mole of gaseous
atoms or ions.
An+(g) + energy  A(n+1)(g) + eIonization energy increases going across a
period, and sometimes decreases slightly going
down a group.
Ionization energy
Ionization energy
Ionization energy
Electron Affinity
Electron affinity has several definitions.
Originally, it was defined as the energy released
when an electron is added to a mole of gaseous
atoms or ions.
A(g) + e-  A-(g) + energy
Under this definition, the elements in the
upper right part of the periodic table (O, F) have
relatively high (and positive) electron affinities.
Electron Affinity
Your text still uses this basic definition, but
defines electron affinity as the energy change for
the reverse process.
A-(g)  A(g) + eEA = ∆U
The values of electron affinity are the same,
with positive values for elements that readily
accept an additional electron.
Electron Affinity
There are no real trends in electron affinity.
The affinities of group IA metals are slightly
positive, near zero for group IIA, and then
increase in groups IIIA and IVA. They drop
(but remain positive) for group VA, and then
increase through group VIIA. The values are
negative for the noble gases.
Atomic Radii
The determination of atomic radii is difficult.
The method used depends upon the nature of
the elemental structure (metallic, diatomic, etc.).
As a result, comparisons across the table are not
straightforward.
In general, size decreases across a period due
to the increase in effective nuclear charge, and
increases going down a group due to increasing
values of n.
Atomic
Radii
Atomic Radii
A close examination of the radii of elements in
periods 5 and 6 shows values which defy the trends.
Group 4 (4B)
Zr = 145 pm
Group 5 (5B)
Nb = 134 pm
Group 11 (1B)
Ag = 134 pm
Hf = 144 pm
Ta = 135 pm
Au = 134 pm
Atomic Radii
There is a large decrease in atomic size
between La (169pm) and Hf (144 pm). This is
due to the filling of the f orbitals of the
Lanthanide series. As a result, the elements Hf
and beyond appear to be unusually small.
The decrease in size is called the lanthanide
contraction, and is simply due to the way elements
are listed on the table.
Ionic Radii
Determining the size of ions is problematic.
Although crystal structures can be determined
by X-ray diffraction, we cannot determine where
one ion ends and another begins.
Ionic Radii
Cations are always smaller than their neutral atom,
since removal of an electron causes an increase in the
effective nuclear charge.
Ionic Radii
Anions are always larger than their neutral atom,
since additional electrons greatly decrease the effective
nuclear charge.
Ionic Radii
For isoelectronic
cations, the more
positive the
charge, the smaller
the ion.
For isoelectronic
anions, the lower
the charge, the
smaller the ion.
Ionic Radii
Determining ionic radii is extremely difficult.
Ionic size varies with ionic charge, coordination
number and crystal structure. Past approaches
involved assigning a “reasonable” radius to the
oxide ion.
Calculations based on X-ray data and electron
density maps provide results where cations are
14pm larger and anions 14pm smaller than
previously found.