84.443/543 Advanced Inorganic Chemistry. Course Web Site Important links to course syllabus tentative class

84.443/54384.443/543Advanced Advanced Inorganic Inorganic ChemistryChemistry

Course Web SiteCourse Web Site

http://faculty.uml.edu/ndeluca/84.334/

Important links toImportant links to course syllabuscourse syllabus tentative class scheduletentative class schedule

The d The d orbitalsorbitals

Unusual Aspects of Unusual Aspects of Inorganic CompoundsInorganic Compounds

The use of The use of dd orbitals enables transition orbitals enables transition metals to form quadruple bonds. Sigma metals to form quadruple bonds. Sigma ((σσ) bonds can be formed using ) bonds can be formed using pp orbitals, orbitals, or the dor the dzz2 2 orbitals.orbitals.


Pi (Pi (ππ) bonds can be formed using the d) bonds can be formed using the dxzxz and and ddyzyz orbitals. orbitals.


In addition, “face-to-face” overlap is In addition, “face-to-face” overlap is possible between the dpossible between the dxyxy orbitals on each orbitals on each metal. This forms a delta (metal. This forms a delta (δδ) bond.) bond.


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

[Re2Cl8]2- has a

quadruple bond between the metal atoms.


The coordination The coordination number for number for transition metals transition metals can be greater than can be greater than 4, with coordination 4, with coordination numbers of 6 being numbers of 6 being quite common. In quite common. In addition, 4-addition, 4-coordinate metal coordinate metal complexes need not complexes need not be tetrahedral.be tetrahedral.


When inorganic When inorganic compounds have compounds have tetrahedral tetrahedral geometry, it may be geometry, it may be quite different from quite different from organic compounds. organic compounds. P P44 has tetrahedral has tetrahedral geometry, but lacks geometry, but lacks a central atom.a central atom.


Cluster Cluster compounds, in compounds, in which there are which there are metal-metal bonds metal-metal bonds can be formed. can be formed. The structure of The structure of MnMn22(CO)(CO)10 10 has the has the two Mn atoms two Mn atoms directly bonded to directly bonded to each other.each other.


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


Organic molecules Organic molecules may bond to may bond to transition metals transition metals with with σσ bonds or bonds or ππ bonds. If bonds. If ππ bonded, some bonded, some unusual unusual “sandwich” “sandwich” compounds may compounds may result.result.

Quantum NumbersQuantum Numbersnn principal quantum #;principal quantum #;

n = 1, 2, 3, etc.n = 1, 2, 3, etc.Determines the major Determines the major part of the energy of part of the energy of the electronthe electron

ll angular momentum angular momentum quantum # = 0,1,2…quantum # = 0,1,2…n-1n-1

Describes angular Describes angular dependence and dependence and contributes to the contributes to the energyenergy

mmllmagnetic quantum # magnetic quantum #

= -= -ll…0…+…0…+llDescribes the Describes the orientation in space. orientation in space. (ex. p(ex. pxx, p, pyy or p or pzz))

mmssSpin quantum # = Spin quantum # = +1/2 or +1/2 or

-1/2 -1/2

Describes orientation Describes orientation of the electron’s of the electron’s magnetic moment in magnetic moment in spacespace

Common Orbital Common Orbital DesignationsDesignations

ss pp dd ff

ll 00 11 22 33

In the absence of a magnetic field, the p orbitals (or d orbitals) are degenerate, and have identical energy.

Wave Functions of Wave Functions of OrbitalsOrbitals

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

Angular FunctionsAngular Functions

The angular functions, based on The angular functions, based on ll and mand ml l , provide the probability of , provide the probability of finding an electron at various points finding an electron at various points from the nucleus. These functions from the nucleus. These functions provide the shape of the orbitals and provide the shape of the orbitals and their spatial orientation.their spatial orientation.

The d-orbitalsThe d-orbitals

Radial FunctionsRadial Functions

Radial functions are determined by Radial functions are determined by the quantum numbers n and the quantum numbers n and ll, and , and are used to determine the radial are used to determine the radial wave probability function (4wave probability function (4ππrr22RR22). ).

R is the radial function, and it R is the radial function, and it describes the electron density at describes the electron density at different distances from the nucleus. different distances from the nucleus. r is the distance from the nucleus. r is the distance from the nucleus.

Radial FunctionsRadial Functions

Radial functions are used to Radial functions are used to determine the probablity of finding determine the probablity of finding an electron in a specific subshell at a an electron in a specific subshell at a specified distance from the nucleus, specified distance from the nucleus, summed over all angles.summed over all angles.

Radial WavefunctionsRadial Wavefunctions

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


Key features:Key features:

1. All 1. All ss orbitals orbitals have a finite have a finite amplitude at the amplitude at the nucleus.nucleus.

2. All orbitals 2. All orbitals decay decay exponentially at exponentially at sufficiently sufficiently great distances great distances from the from the nucleus.nucleus.


Key features:Key features:

3. As n 3. As n increases, the increases, the functions functions oscillate oscillate through zero, through zero, resulting in resulting in radial nodesradial nodes..

Radial NodesRadial Nodes

Radial nodes represent the point at Radial nodes represent the point at which the wave function goes from a which the wave function goes from a positive value to a negative value. positive value to a negative value. They are significant, since the They are significant, since the probability functions depend upon probability functions depend upon ΨΨ22, and the nodes result in regions , and the nodes result in regions of zero probability of finding an of zero probability of finding an electron.electron.

Radial NodesRadial Nodes

For a given orbital, For a given orbital,

the number of radial nodes= n- the number of radial nodes= n- ll -1 -1

p orbitalsp orbitals

The radial wave The radial wave functions of functions of pp orbitals show a zero orbitals show a zero amplitude at the amplitude at the nucleus.nucleus.

The result is The result is thatthat

p p orbitals are less orbitals are less penetrating than penetrating than ss orbitals.orbitals.

Radial Probability Radial Probability FunctionsFunctions

Radial Radial probability probability functions (4functions (4ππrr22ΨΨ22 or 4or 4ππrr22RR22 ) are ) are the product of the product of the blue and the blue and green functions green functions graphed for a 1s graphed for a 1s orbital.orbital.


The orange line The orange line represents the represents the probability of probability of finding an finding an electron in a 1s electron in a 1s orbital as a orbital as a function of function of distance from distance from the nucleus.the nucleus.


Note the Note the zero probability zero probability at the nucleus at the nucleus (since r=0). (since r=0). The The most probable most probable distance from distance from the nucleus is the nucleus is the Bohr radius, the Bohr radius, aaoo = 52.9 pm. = 52.9 pm.


The The probability falls probability falls off rapidly as the off rapidly as the distance from the distance from the nucleus increases. nucleus increases.

For a 1s For a 1s orbital, the orbital, the probability is near probability is near zero at a value of zero at a value of r = 5ar = 5aoo..


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


On average, the On average, the electrons in the 2s electrons in the 2s orbital will be farther orbital will be farther from the nucleus from the nucleus than those in the 2p than those in the 2p orbital. Yet, orbital. Yet, electrons in the 2s electrons in the 2s orbital have a higher orbital have a higher probability of being probability of being near the nucleus due near the nucleus due to the inner to the inner maximum.maximum.


The net result The net result is that the energy is that the energy of electrons in the of electrons in the 2s orbital are 2s orbital are lower than that of lower than that of electrons in the 2p electrons in the 2p orbitals.orbitals.

The The dd orbitalsorbitals

The The ff orbitals orbitals

The Aufbau PrincipleThe Aufbau Principle

The loss of degeneracy in multi-The loss of degeneracy in multi-electron atoms or ions results in electron atoms or ions results in electron configurations that cannot electron configurations that cannot be predicted based solely on the be predicted based solely on the values of quantum numbers.values of quantum numbers.

The aufbau (building up) The aufbau (building up) principle provides rules for principle provides rules for obtaining electron configurations.obtaining electron configurations.

The Aufbau PrincipleThe Aufbau Principle

1.1. The lowest values of n and The lowest values of n and ll are filled are filled first to minimize energy.first to minimize energy.

2. 2. The Pauli Exclusion Principle The Pauli Exclusion Principle requires that each electron in an atom requires that each electron in an atom must have a unique set of quantum must have a unique set of quantum numbers.numbers.

3.3. Hund’s Rule requires that electrons in Hund’s Rule requires that electrons in degenerate orbitals will have the degenerate orbitals will have the maximum multiplicity (or highest total maximum multiplicity (or highest total spin).spin).

Electron ConfigurationsElectron Configurations


Klechkowsky’s Rule states that Klechkowsky’s Rule states that filling proceeds from the lowest filling proceeds from the lowest available value of n + available value of n + ll. .

When two combinations have When two combinations have the same sum of n + the same sum of n + ll, the orbital , the orbital with a lower value of n is filled first.with a lower value of n is filled first.


The electron configurations of The electron configurations of Cr and Cu in the first row of the Cr and Cu in the first row of the transition metals defy all rules, as do transition metals defy all rules, as do many of the lower transition many of the lower transition elements.elements.

ShieldingShielding

The energy of an orbital is The energy of an orbital is related to its ability to penetrate the related to its ability to penetrate the area near the nucleus, and its ability area near the nucleus, and its ability to shield other electrons from the to shield other electrons from the nucleus.nucleus.

The positive charge affecting a The positive charge affecting a specific electron is called the specific electron is called the effective nuclear chargeeffective nuclear charge, or Z, or Zeffeff..

ShieldingShielding

ZZeffeff = Z = Zactualactual – S – S

oror

ZZeffeff = Z = Zactualactual – – σσ

Where S or Where S or σσ is the shielding factor. is the shielding factor.

Both the value of n and Both the value of n and ll (orbital (orbital type) play a significant role in type) play a significant role in determining the shielding factor.determining the shielding factor.

Slater’s RulesSlater’s Rules

1. The electronic structure of atoms is 1. The electronic structure of atoms is written in groupings: written in groupings:

(1s)(2s, 2p)(3s, 3p)(3d)(4s, 4p)(4d)(4f )(1s)(2s, 2p)(3s, 3p)(3d)(4s, 4p)(4d)(4f )

2. Electrons in higher groupings do 2. Electrons in higher groupings do not shield those in lower groups.not shield those in lower groups.

Slater’s Rules- Slater’s Rules- Calculation of SCalculation of S

3. For ns or np electrons:3. For ns or np electrons:

a) electrons in the same ns and np as a) electrons in the same ns and np as the the electron being considered electron being considered contribute .35, contribute .35, except for 1s, except for 1s, where .30 works better.where .30 works better.

b) electrons in the n-1 group b) electrons in the n-1 group contribute .85contribute .85

c) electrons in the n-2 group or lower c) electrons in the n-2 group or lower (core (core electrons) contribute 1.00electrons) contribute 1.00

Slater’s Rules- Slater’s Rules- Calculation of SCalculation of S

4. For nd or nf electrons:4. For nd or nf electrons:

a) electrons in the same nd or nf a) electrons in the same nd or nf levelas the levelas the electron being electron being considered contribute .35considered contribute .35

b) electrons in the groups to the b) electrons in the groups to the left contribute left contribute 1.001.00

Problem: ZProblem: Zeffeff

Use Slater’s rules to estimate the Use Slater’s rules to estimate the effective nuclear charge of Cl and effective nuclear charge of Cl and Mg.Mg.

Periodic TrendsPeriodic Trends

ZZeffeff increases across a period. increases across a period. This is due to the addition of protons This is due to the addition of protons in the nucleus, accompanied by in the nucleus, accompanied by ineffective shielding for the added ineffective shielding for the added electrons. As a result, the valence electrons. As a result, the valence electrons experience a greater electrons experience a greater nuclear charge on the right side of nuclear charge on the right side of the periodic table.the periodic table.

Ionization energyIonization energy

Ionization energy is the energy Ionization energy is the energy required to remove an electron from a required to remove an electron from a mole of gaseous atoms or ions.mole of gaseous atoms or ions.

AAn+n+(g) + energy (g) + energy A A(n+1)(n+1)(g) + e(g) + e--

Ionization energy increases going Ionization energy increases going across a period, and sometimes across a period, and sometimes decreases slightly going down a decreases slightly going down a group.group.




Electron AffinityElectron Affinity

Electron affinity has several Electron affinity has several definitions. Originally, it was defined as definitions. Originally, it was defined as the energy the energy releasedreleased when an electron is when an electron is added to a mole of gaseous atoms or added to a mole of gaseous atoms or ions.ions.

A(g) + eA(g) + e-- A A--(g) + energy(g) + energy

Under this definition, the elements Under this definition, the elements in the upper right part of the periodic in the upper right part of the periodic table (O, F) have relatively high (and table (O, F) have relatively high (and positive) electron affinities.positive) electron affinities.


Your text still uses this basic Your text still uses this basic definition, but defines electron definition, but defines electron affinity as the energy affinity as the energy changechange for the for the reverse process.reverse process.

AA--(g) (g) A(g) + e A(g) + e-- EA = ∆UEA = ∆U

The values of electron affinity The values of electron affinity are the same, with positive values are the same, with positive values for elements that readily accept an for elements that readily accept an additional electron.additional electron.

Trends – Electron AffinityTrends – Electron Affinity

Trends- Electron AffinityTrends- Electron Affinity

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


There are no real trends in There are no real trends in electron affinity. The affinities of electron affinity. The affinities of group IA metals are slightly positive, group IA metals are slightly positive, near zero for group IIA, and then near zero for group IIA, and then increase in groups IIIA and IVA. increase in groups IIIA and IVA. They drop (but remain positive) for They drop (but remain positive) for group VA, and then increase through group VA, and then increase through group VIIA. The values are negative group VIIA. The values are negative for the noble gases.for the noble gases.

Atomic RadiiAtomic Radii

The determination of atomic radii is The determination of atomic radii is difficult. The method used depends difficult. The method used depends upon the nature of the elemental upon the nature of the elemental structure (metallic, diatomic, etc.). As a structure (metallic, diatomic, etc.). As a result, comparisons across the table are result, comparisons across the table are not straightforward.not straightforward.

In general, size decreases across a In general, size decreases across a period due to the increase in effective period due to the increase in effective nuclear charge, and increases going nuclear charge, and increases going down a group due to increasing values down a group due to increasing values of n.of n.

Atomic Atomic RadiiRadii

Atomic SizeAtomic Size


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

Group 4 Group 4 (4B)(4B)

Group 5 Group 5 (5B) (5B)

Group 11 Group 11 (1B)(1B)

Zr = 145 Zr = 145 pmpm

Nb = 134 Nb = 134 pmpm

Ag = 134 Ag = 134 pmpm

Hf = 144 Hf = 144 pmpm

Ta = 135 Ta = 135 pmpm

Au = 134 Au = 134 pmpm


There is a large decrease in atomic There is a large decrease in atomic size between La (169pm) and Hf (144 size between La (169pm) and Hf (144 pm). This is due to the filling of the pm). This is due to the filling of the ff orbitals of the Lanthanide series. As a orbitals of the Lanthanide series. As a result, the elements Hf and beyond result, the elements Hf and beyond appear to be unusually small. appear to be unusually small.

The decrease in size is called the The decrease in size is called the lanthanide contractionlanthanide contraction, and is simply due , and is simply due to the way elements are listed on the to the way elements are listed on the table.table.

Ionic RadiiIonic Radii

Determining the size of ions is Determining the size of ions is problematic. Although crystal problematic. Although crystal structures can be determined by X-structures can be determined by X-ray diffraction, we cannot determine ray diffraction, we cannot determine where one ion ends and another where one ion ends and another begins.begins.


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


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

Ionic RadiiIonic Radii For For

isoelectronic isoelectronic cations, the cations, the more positive more positive the charge, the the charge, the smaller the ion.smaller the ion.

For For isoelectronic isoelectronic anions, the anions, the lower the lower the charge, the charge, the smaller the ion.smaller the ion.


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.

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84.443/543 Advanced Inorganic Chemistry. Course Web Site Important links to course syllabus tentative class