84.443/543 Advanced Inorganic Chemistry

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84.443/543Advanced Inorganic Chemistry
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Course Web Site

• http//faculty.uml.edu/ndeluca/84.334/
• Important links to
• course syllabus
• tentative class schedule

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The d orbitals
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Unusual Aspects of Inorganic Compounds

• The use of d orbitals enables transition metals
  to form quadruple bonds. Sigma (s) bonds can be
  formed using p orbitals, or the dz2 orbitals.

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Unusual Aspects of Inorganic Compounds

• Pi (p) bonds can be formed using the dxz and dyz
  orbitals.

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Unusual Aspects of Inorganic Compounds

• In addition, face-to-face overlap is possible
  between the dxy orbitals on each metal. This
  forms a delta (d) bond.

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Unusual Aspects of Inorganic Compounds

• The existence of d bonds is usually determined by
  measuring bond lengths and magnetic moments.

Re2Cl82- has a quadruple bond between the metal
atoms.
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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, 4-coordinate
  metal complexes need not be tetrahedral.

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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.

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Unusual Aspects of Inorganic Compounds

• Cluster compounds, in which there are metal-metal
  bonds can be formed. The structure of Mn2(CO)10
  has the two Mn atoms directly bonded to each
  other.

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Unusual Aspects of Inorganic Compounds

• Cage compounds lack a direct metal-metal bond.
  Instead, the ligands serve to hold the complex
  together.

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Unusual Aspects of Inorganic Compounds

• Organic molecules may bond to transition metals
  with s bonds or p bonds. If p bonded, some
  unusual sandwich compounds may result.

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Quantum Numbers
n principal quantum n 1, 2, 3, etc. Determines the major part of the energy of the electron
l angular momentum quantum 0,1,2n-1 Describes angular dependence and contributes to the energy
ml magnetic quantum -l0l Describes the orientation in space. (ex. px, py or pz)
ms Spin quantum 1/2 or -1/2 Describes orientation of the electrons magnetic moment in space
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Common Orbital Designations
s p d f
l 0 1 2 3
In the absence of a magnetic field, the p
orbitals (or d orbitals) are degenerate, and have
identical energy.
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Wave Functions of Orbitals

• Wave functions can be factored into two angular
  components (based on ? and f), and a radial
  component (based on r).

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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.

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The d-orbitals
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Radial Functions

• Radial functions are determined by the quantum
  numbers n and l, and are used to determine the
  radial wave probability function (4pr2R2).
• R is the radial function, and it describes the
  electron density at different distances from the
  nucleus. r is the distance from the nucleus.

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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.

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Radial Wavefunctions

• The radial wave functions for hydrogenic orbitals
  have some key features

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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.

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Radial Wavefunctions

• Key features
• 3. As n increases, the functions oscillate
  through zero, resulting in radial nodes.

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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 ?2, and the
  nodes result in regions of zero probability of
  finding an electron.

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Radial Nodes

• For a given orbital,
• the number of radial nodes n- l -1

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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.

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Radial Probability Functions

• Radial probability functions (4pr2?2 or 4pr2R2 )
  are the product of the blue and green functions
  graphed for a 1s orbital.

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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.

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Radial Probability Functions

• Note the zero probability at the nucleus (since
  r0). The most probable distance from the
  nucleus is the Bohr radius, ao 52.9 pm.

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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.

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Radial Probability Functions

• In a 1 electron atom, the 2s and 2p orbitals
  are degenerate. In multi-electron atoms, the 2s
  orbital is lower in energy than the 2p orbital.

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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.

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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.

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The d orbitals
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The f orbitals
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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.

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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. Hunds Rule requires that electrons in
  degenerate orbitals will have the maximum
  multiplicity (or highest total spin).

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Electron Configurations
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Electron Configurations

• Klechkowskys 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.

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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.

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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.

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Shielding

• Zeff Zactual S
• or
• Zeff Zactual s
• Where S or s is the shielding factor.
• Both the value of n and l (orbital type) play a
  significant role in determining the shielding
  factor.

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Slaters 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.

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Slaters 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

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Slaters 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

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Problem Zeff

• Use Slaters rules to estimate the effective
  nuclear charge of Cl and Mg.

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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.

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Ionization energy

• Ionization energy is the energy required to
  remove an electron from a mole of gaseous atoms
  or ions.
• An(g) energy ? A(n1)(g) e-
• Ionization energy increases going across a
  period, and sometimes decreases slightly going
  down a group.

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Ionization energy

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Ionization energy

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Ionization energy

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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.

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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) e- EA ?U
• The values of electron affinity are the same,
  with positive values for elements that readily
  accept an additional electron.

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Trends Electron Affinity
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Trends- Electron Affinity

• The electron affinity of fluorine is less
  negative than expected. This may be due to
  additional electron-electron repulsion when an
  electron is added to such a small atom.

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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.

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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.

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Atomic Radii
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Atomic Size
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Atomic Radii

• A close examination of the radii of elements in
  periods 5 and 6 shows values which defy the
  trends.

Group 4 (4B) Group 5 (5B) Group 11 (1B)
Zr 145 pm Nb 134 pm Ag 134 pm
Hf 144 pm Ta 135 pm Au 134 pm
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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.

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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.

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Ionic Radii

• Cations are always smaller than their neutral
  atom, since removal of an electron causes an
  increase in the effective nuclear charge.

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Ionic Radii

• Anions are always larger than their neutral
  atom, since additional electrons greatly decrease
  the effective nuclear charge.

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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.

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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.