Chemistry 3820 (Fall 2006)
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Chemistry 3820 - The Electronic Configuration of Atoms and Ions
Electronic configuration is very important as it can be used to explain and understand chemical
and physical properties, including periodic trends such as ionization energies and atomic/ionic
radii.
In order to find the electronic configuration of an atom, we need to know the energies of the
orbitals. Below is a plot of atomic orbital energy (E) against atomic number (Z) for the elements in
their ground state. NOTE: this is for elements only, NOT ions.
Energy
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
Note the following trends :
•
For single electron atoms (H; Z = 1) à E varies only with n (principal quantum no.)
•
For Z > 1 à E depends on both n and l (azumuthal (orbital shape: s, p, d, f) quantum no.)
•
The energy of ns and np decreases smoothly as Z increases
•
ns always lies lower in energy than np (e.g. 2p is higher in energy than 2s)
•
nd and nf show complex behaviour
•
The sequence Ens <Enp < End < Enf only holds for small and large Z.
•
At low Z, End and Enf do not cha nge much, but at higher Z, the energy of the nd or nf orbitals
drops precipitously (e.g. at Z = 19 for the 3d orbitals ).
We can rationalise these observations in terms of screening and effective nuclear charge.
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
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Chemistry 3820 (Fall 2006)
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The radial wave functions, radial distribution functions and boundary surface diagrams for a
variety of typical orbitals are shown below.
Radial wavefunctions ( Ψr )
1s
2
2
Radial Distribution Functions ( 4πr Ψr ) n l
1s
1 0
node
2s
2s
2 0
2p
2p
2 1
3s
3s
3 0
3p
3p
3 1
3d
3d
3 2
Note: 1s has no node, 2s has one node, 3s has two nodes, 4s has three nodes, …..
2p has no node, 3p has one node, 4p has two nodes, …..
3d has no node, 4d has one node, …..
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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Boundary Surface Diagrams
1s-orbital (g)
2p-orbitals (u)
3d-orbitals (g)
The dz2 and dx 2 -y2
orbitals are called
AXIAL orbitals because
they lie along the x/y/zaxes.
g = gerade (German)
u = ungerade (German)
g and u indicate parity,
which is the symmetry
of an object with
respect to inversion.
The dxy , dxz and dyz
orbitals are named
INTER-AXIAL orbitals
because they lie between
the x/y/z-axes
g = inversion centre
u = no inversion centre
4f-orbitals (u)
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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It is worth bearing in mind that since higher radial functions contain nodes (e.g. the 3p has one
node, 4p has two nodes, 5p has three nodes, 6p has four nodes, 4d has one node, 5d has two nodes,
5f has one node), the boundary surfaces for these orbitals are more complex (see examples below).
However, for simplicity, the basic 1s, 2p, 3d and 4f orbitals which contain no nodes, are usually
used to represent the s-, p-, d- and f-orbitals regardless of principal quantum number.
3p-orbitals
4d-orbitals
4p-orbitals
5d-orbitals
See http://winter.group.shef.ac.uk/orbitron for excellent pictures of boundary surfaces (and much
more).
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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Radial Distribution Functions versus Boundary Surface Diagrams – which one represents
the orbitals best?
The s-orbitals: s-orbitals are spherically symmetric and are well represented by their radial
wavefunctions and radial distribution functions. Note, however, that the small subsidiary maxima
for the 2s and 3s orbitals are not generally shown in boundary surface diagrams, although this can
be achieved by showing a cross section of a boundary surface, or a boundary surface with a slice
removed to reveal the inside.
Ψ2
or
4πr2 Ψ2
The d-orbitals: Unlike the s-orbitals, the p-, d- and f-orbitals are not spherical, so have both radial
and angular components to their wavefunctions. Neither Ψr2 or 4πr2 Ψr2 shows this, and as a result,
these orbitals are much better represented by their boundary surface diagrams. In addition, since
p-, d- and f-orbitals are not spherical, it is possible to view nodes in these orbitals when they are
displayed as boundary surface diagrams (unlike the spherical s-orbitals).
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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So how does all this relate to our plot of E vs Z ?
When building up the periodic table for elements with greater than one electron (i.e. not H or He+),
orbitals with the same n (principal q.n.) but different l (azimuthal q.n.) have different energies:
E2s ? E2p and E3s ? E 3p ? E3d etc.
This arises because electrons in orbitals which penetrate close to the nucleus experience more of
the nuclear charge (become lower in energy) , and at the same time, they partially screen less
penetrating orbitals from the nuclear charge.
It is instructive to look at the radial distribution functions for 1s, 2p, 2s, 3s, 3p and 3d orbitals:
Radial distribution functions (4π r2Ψ r2 )
Observations
•
The 1s-orbital clearly penetrates more
effectively than the 2s.
•
The 2s and 2p-orbitals look fairly similar in
terms of penetration. However, 2s actually
penetrates
more
effectively
than
2p,
because the inner minima lies in a region
where nuclear charge effects are strongest
{the electrostatic attraction between the
positively charged nucleus and an electron
is proportional to 1/r, so falls away rapidly
as r increases}.
•
In comparison, with the 2s-, 2p- and
3p-orbitals, the
3d-orbitals are poorly
penetrating and very well shielded from the
nuclear charge.
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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As a result of differing penetration towards the nucleus, electrons in many-electron atoms will
experience different effective nuclear charges, and the energy levels for atoms vary continuously
as Z increases (as is seen in the plot of E vs Z).
Values for effective nuclear charge (Z*) and screening constant (σ)
•
Atomic screening constants and values of Z* (effective nuclear charge) have been calculated
(using “self-consistent-field” (SCF) functions ); E. Clementi and D. L. Raimondi, J. Phys.
Chem., 1963, 38, 2686 & J. Phys. Chem., 1967, 47, 1300 – see below.
•
Alternatively, approximate values for Z* may be calculated using Slaters Rules. These are
very simple empirical rules that can be used to give an estimate of the effective nuclear charge
on any electron of any atom. We will not discuss these further in this course.
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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Back to the plot of E vs Z
The ns and np orbitals decrease in energy
smoothly as Z increases à this is because these
penetrating
orbitals
experience
a
steadily
increasing nuclear charge.
The 3d orbital has a ‘flat’ constant energy
region up to Z = 18 [Ar]. This is because it does
not
effectively
penetrate
the
Ar
core
(1s,2s,2p,3s,3p), so it is shielded from the
increasing nuclear charge by the inner ns and np
orbitals.
After argon (at potassium, Z = 19), electrons
can enter either the 4s or 3d-orbitals which
have comparable orbital penetration, and the
3d orbitals finally start to see their fair share of
the nuclear charge à a sharp drop in energy.
One outcome of the 3d orbitals refusing to drop in energy until Z = 18, is that it leads to a region
(the 1st row transition metals) where the 4s and 3d orbitals are very close in energy. Similar effects
can be seen for higher nd and nf orbitals
Now, lets have a look at the zoomed in part of the E vs Z plot, and discuss the electronic
configurations of transition metals (Remember: atoms, not ions).
Expansion shows that for K to Ca
à E4s < E3d
However, for Sc to Zn (1st row TMs) à E3d < E4p
Note: Regardless of the actual order (E 4s < E3d or E3d < E4p ), for Sc to Zn, the energies of the 4s
and 3d orbitals are very close.
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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The experimentally determined electronic configurations are shown below:
19 K
[Ar] 4s 1
37 Rb
[Kr] 5s 1
20 Ca
[Ar] 4s 2
38 Sr
[Kr] 5s 2
21 Sc
[Ar] 3d1 4s2
39 Y
[Kr] 4d1 5s2
71
Lu
[Xe] 4f14 5d1 6s2
22 Ti
[Ar] 3d2 4s2
40 Zr
[Kr] 4d2 5s2
72
Hf
[Xe] 4f14 5d2 6s2
23 V
[Ar] 3d3 4s2
41 Nb
[Kr] 4d4 5s1
73
Ta
[Xe] 4f14 5d3 6s2
24 Cr
[Ar] 3d5 4s1
42 Mo
[Kr] 4d5 5s1
74
W
[Xe] 4f14 5d4 6s2
25 Mn
[Ar] 3d5 4s2
43 Tc
[Kr] 4d5 5s2
75
Re
[Xe] 4f14 5d5 6s2
26 Fe
[Ar] 3d6 4s2
44 Ru
[Kr] 4d7 5s1
76
Os
[Xe] 4f14 5d6 6s2
27 Co
[Ar] 3d7 4s2
45 Rh
[Kr] 4d8 5s1
77
Ir
[Xe] 4f14 5d7 6s2
28 Ni
[Ar] 3d8 4s2
46 Pd
[Kr] 4d10
78
Pt
[Xe] 4f14 5d9 6s1
29 Cu
[Ar] 3d10 4s1
47 Ag
[Kr] 4d10 5s1
79
Au
[Xe] 4f14 5d10 6s1
30 Zn
[Ar] 3d10 4s2
48 Cd
[Kr] 4d10 5s2
80
Hg
[Xe] 4f14 5d10 6s2
K and Ca are [Ar]4s 1 and [Ar]4s 2 as expected, but for the 1st row transition metals, the order is not
as predicted (e.g. Sc = [Ar]4s 2 3d1 ). This is because complex interactions between the electrons
means that the 4s orbitals are generally filled before the 3d orbitals.
Notable exceptions are Cr ([Ar]4s 1 3d5 ) and Cu ([Ar]4s1 3d10 ). These two elements are different
because half filled and filled shells have particular stability (quantum mechanical energy excha nge
effects).
However, there are other exceptions such as Nb ([Kr]4d4 5s1 ), Ru, Rh and Pt, that cannot be
explained so easily. These anomalies demonstrate that it is not possible to accurately predict the
electronic configuration of transition elements with simple rules.
So far, we have only been looking at the electronic structure of transition metal atoms, and the
situation is clearly relatively complex due to the similar energies of ns and (n-1)d orbitals.
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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For transition metal cations or transition metal complexes, the
situation is much simpler:
• All valence electrons are in (n-1)d orbitals
THIS IS
VERY
IMPORTANT
• There are no electrons in ns orbitals
4s is always higher in energy than 3d!
The result is that TM cations always have the electronic configuration: ns 0 (n-1)dx
The ability to work out the number of d-electrons is crucial to understanding the behaviour of
transition metal complexes, so it is crucial for Chemistry 3820 and 4000! Therefore, you should
take the time to practice working out the electronic configuration of transition metal ions such as
TiII, FeIII, ZnII, RuVII, PtII, MoIII, TiIV, VIV, RhI, PtIV, etc.
Examples:
OC
Ni
Ph3P
PPh3
Ph3 P
Rh
Cl
H2O
CO
H2O
Ti
OH2
OH2
RhI = d8
Fe
OC
TiIII = d1
Note that this is a very unusual oxidation state, and is only
possible with ligands such as CO. However, it is included
to illustrate, that you only need to worry about d-electrons,
regardless of whether the metal carries a formal positive
charge, is neutral or carries a negative charge.
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
2-
CO
OH2
PPh3
Ni0 = d10
3+
OH2
PPh3
CO
CO
Fe2- = d10
Chemistry 3820 (Fall 2006)
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Atomic Radii (J. Chem. Ed. 1988, 65, 17.)
(metallic radii for metals, covalent radii for non-metals)
Main Group
•
Size increases sharply at the start of each period (at the alkali metals) à due to very low Z*
(see Clementi, Raimonti Z* table).
•
For the alkali metals, size increases with atomic number à the valence electrons are located
further from the nucleus (see radial distribution functions).
•
For 2nd and 3rd periods (Lià F and Naà Cl), size decreases as Z* increases.
Transition metals
•
General trend 1 = size decreases across the transition metals (more slowly than for the pblock).
Exceptions = Mn, (Cu + Zn), (Pd + Ag + Cd), (Au, Hg) – see also Eu and Yb à can you
correlate these observations with any particular electronic configuration ?
© 2006 - Dr. Paul G. Hayes – University of Lethbridge
Chemistry 3820 (Fall 2006)
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General trend 2 = 1st Row transition metals are smaller than 2nd and 3rd row transition metals.
= 2nd and 3rd row transition metals are approximately the same size, so exhibit
fairly similar properties and chemistry. Explanation: the 3rd row TMs are
smaller than expected due to the Lanthanide contraction.
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1st Ionization Energies
[A(g) à A+(g) + e-]
Ionization energy correlates strongly with atomic radius (large radius = low IE) à for electrons
located further from the nucleus (atoms with large radii), there is less electrostatic attraction
between the electron and the nucleus, so the electron is easier to remove (smaller IE).
For the transition metals, IE increases across the transition series. This ties in with the observed
oxidation state preferences (early TMs prefer the 3+ oxidation state, late TMs prefer 2+). Also
consider correlations between maximum oxidation states and ∆Hvap.
© 2006 - Dr. Paul G. Hayes – University of Lethbridge