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**Unformatted text preview: **Lecture 09 9/26/11 Today in Chemistry 260/261 Lecture 9
9/26/2011
+ • Periodic trends:
• Atomic/ionic radii
• Ionization energy
• Electron affinity
• Electronegativity
• Valence bond model
• Hybrid atomic orbitals
• Resonance Later in Chemistry 260/261
• Reading: 6.1, 6.4
• Chemical bonding non-bonding atomic/
ionic radius Periodic Properties Atomic Size Atomic/Ionic Radius
bonding atomic/ionic radius
=1/2 bond length Ionization Energy
Amount of energy required to remove an electron from a gaseous atom X( g ) !! X + ( g ) + e#
"
Electron Affinity
Amount of energy released when a gaseous atom gains an electron X( g ) + e! "" X ! ( g )
# IN GENERAL
Atomic radius increases with increasing principle quantum number Electronegativity
Tendency of one atom to attract electrons from another atom to which it
is bonded Atomic Size Deviations of contracting size within a row are due to
shielding effect (filled subshells). 4f block
5d block
Zn/Ga At Z= 30, 4s/4p electrons are
well shielded by 3d electrons.
Full 3d is shielding well –
repelling more 5d elements not as big as expected
f electrons are very inefficient shielders
Zeff is thus larger than expected smaller atoms
LANTHANIDE CONTRACTION Atomic radius decreases with increasing nuclear charge in any given shell/subshell. Ionic Size Cations shrink
relative to the
corresponding
neutral atom
Anions expand
relative to the
corresponding
neutral atom
Effective nuclear
charge and e-–erepulsion
explain both
trends 1 Lecture 09 9/26/11 ConcepTest ConcepTest One of these spheres represents a K+ ion, the other a Cl- ion.
True or False: The red sphere is the K+ ion. One of these spheres represents a K+ ion, the other a Cl- ion.
True or False: The red sphere is the K+ ion. Of course True, same shielding (electron count) of a larger nuclei, will be more
contracted! Ionization Energy Ionization Energy Outermost electron removed
from atom to form cation X( g ) !! X + ( g ) + e#
" Koopman s approximation I.E. " !En = [Z (n)]
2 ! eff n 2p orbital is
higher in
energy than the
2s orbital (2p is
more shielded
than 2s) Generally, ionization energy increases with nuclear
charge… but there are some kinks.
Explanations must balance effective nuclear charge,
shielding/penetration, and e--e- repulsion. X( g ) !! X + ( g ) + e#
" 2 electrons begin being
paired in 2p ! more
e--e- repulsion as Z eff !, I.E. !
Frozen orbital approximation:
Assumes that the orbital energies are
the same before and after ionization
Relaxation effects (1-3 eV) included
in Hartree-Fock method
IP almost contant: increasing #
of d electrons shields 4s from
increasing Zeff (4S is ionized) Remember: Zeff for 2p < Zeff for 2s Second Ionization Energy Always takes a greater amount of energy to
remove a 2nd electron relative to the first ConcepTest Where on the periodic chart are the elements with the
smallest values of first ionization energy?
A B C E
D X + ( g ) !! X 2 + ( g ) + e#
" X( g ) !! X + ( g ) + e#
" I.E.1 < I.E.2 < I.E.3 < etc. LARGE jump when remove all electrons from upper most shell 2 Lecture 09 9/26/11 Electron Affinity ConcepTest Where on the periodic chart are the elements with the
smallest values of first ionization energy?
A B C E +/- Convention: In this class,
+ EA means a stable anion is formed Amount of energy released when a gaseous atom gains an electron
For halogens, the additional electron experiences a strong
Zeff, and has a half empty p orbital for an extra e- to enter X( g ) + e! "" X ! ( g )
# 5d block: 4f electrons don t shield very
well, therefore, strong Zeff D Of course A, it is tempting to get rid from just one
electron to get a noble gas configuration! Comparison of Trends All noble gases (Gr VIII) and most alkaline earth metals (Gr II) have EA < 0
(for noble gases e- enters n+1 shell, for alkaline earth metals e- enters p orbitals) Electronegativity
LINUS PAULING Although Ionization Energy
and Electron Affinity both
tend to increase across
periods, the patterns are not
exactly the same Tendency of one atom to attract electrons
from another atom to which it is bonded
ROBERT MULLIKEN !" Trends are shifted
All noble gases
(Gr VIII) and most alkaline
earth metals
(Gr II) have EA < 0 ( ! A " ! B = DAB " DA DB
2 2 ) 1/ 2 D is bond dissociation
energy I .E. + E. A.
2 Electronegativity
follows roughly the
pattern : low in lower
left hand corner, high in
upper right hand corner This Week in Chemistry 260/261 Chapter 6:
• Born-Oppenheimer Approximation
• Valence Bond Theory
• Adjustment of Valence Bond Theory to achieve better bonding description
• VB based approach:
bonding through overlap of orbitals
ground state, structure properties
intuitive + • MO based approach:
( ad hoc aufbau) , bonding, antibonding and non bonding
energy level
computational efficient Chemical bonding 3 Lecture 09 9/26/11 Quantum View of Chemical Bonds • Quantum Mechanics successfully predicts atomic properties (sizes, energy levels,
spectra, etc.)
• Want to extend it to molecules, intermolecular interactions, chemical reactivity, etc.
• Next logical step would be to solve the Schrödinger equation for a molecule of
interest
• Even more difficult than for multi-electron atoms
• e--e- repulsion
• Dependence on nuclear coordinates
• Need to make further approximations Valence Bond Theory: Basics How to solve the Schrödinger equation beyond single atoms? • Valence Bond Theory - Localized Orbitals
• Molecular Orbital Theory - Delocalized Orbitals
• As orbitals overlap
Electrons spend time around both nuclei
Electrons are attracted to both nuclei
Bond is formed
• Overlap , bond strength Valence Bond Theory Bond will occur between 2 atoms when:
1. An orbital from one atom occupies the same space as an orbital from the
other atom – overlap
2. Total number of electrons in the overlapping orbitals is no more than two • Both H and He have 1s orbital occupied
H : 1s1 & He: 1s2
• H2 :1s1+1s1 : 2e- in same space
• He2 :1s2+1s2 : 4e- in same space
(no unpaired electrons in He)
NOT bonded
Yes bonded The Sigma (σ) Bond Simplest chemical bond: H-H
Ψ built from the merging of H 1s orbitals, we can expect the overall
distribution to be the mathematical sum of these shapes
1s(A)
s(A)
!1(1) ! 1s(B)
(2)
A B 1s(B) ! (1, 2) = ! A (1)! B ( 2) 1s(A) 1s(B) ! (1, 2) = ! A ( 2)! B (1) .. but we cannot keep track of either electron ! H-H (1, 2) = ! A (1)! B (2) + ! A (2)! B (1) good first approximation - though, it is
not true that electrons do not interact Next, we apply the VB description to specific types of bonding: +
A VB wave function with cylindrical symmetry around the internuclear axis is called a
σ bond (imagine splitting the center of a sphere and extending the difference
between the two points.
" = !1A ( )!1B (2)+ !1A (2)!1B ( )
s1
s
s
s1
! 1AS
! 1BS All VB wave functions are constructed in a similar way, by
using atomic orbitals available on the participating atoms.
In general for an A-B
bond in VB theory: ! A-B (1, 2) = ! A (1)! B ( 2) + ! A ( 2)! B (1) 4 Lecture 09 9/26/11 σ vs. π bonds A VB Description of N2 σ bond
Cylindrical symmetry about internuclear axis
N
N
N
" p z = !2p1z ( )!2p2z (2)+ !2p1z (2)!2p2z ( )
1N
1 Descriptions similar to those used for H2 can be used for molecules built from
atoms that contribute more than one electron to the bonding.
For N2, consider the electron configuration of the N atoms:
N z-axis [He]2s 22p1 2p1 2p1
x
y
z N [He]2s 22p1 2p1 2p1
x
y
z ! 2pz orbitals 2px and 2py
orbitals π bond
Nodal plane along the inter-nuclear
axis
(e- density above and below plane) Each N atom p orbital has one
unpaired electron which can pair
with a p electron from the other atom N1
2p z N
N
N
" p x = !2p1x ( )!2p2x (2)+ !2p1x (2)!2p2x ( )
1N
1 (1)! (2)+ ! (2)! (1)
N2
2p z N1
2p z N2
2p z the merging of two orbitals that approach
side-by-side (z is the bonding axis):
N
N
N
!2p1x ( )!2p2x (2)+ !2p1x (2)!2p2x ( )
1N
1 N1
N2
N1
N2
! 2 py (1) ! 2 py ( 2 ) + ! 2 py ( 2 ) ! 2 py (1) N
N
N
" p y = !2p1y ( )!2p2y (2)+ !2p1y (2)!2p2y ( )
1N
1 NN
The VB model of N2 consists
of one σ and two π bonds Bond strength is related to the
orbital overlap:
Overlap , bond strength Each bond involves 2p
orbitals on the two atoms Overlap for σ bond > π bond
∴ σ bond stronger than π bond Two adjustments of VB theory solve these problems. Promotion and Hybridization of Atomic orbitals 1. Promotion Inability of plain VB theory to
account for the number of bonds
that atoms can form
e.g. tetravalence of carbon C : [He] s 2 2p1 2p1
2
x
y
According to VB theory, C is only
capable of making two bonds, since
it has only 2 unpaired electrons 1. Promote a valence electron to an empty atomic orbital more unpaired
electrons that can form bonds
2p ΔE is small: relieves e--e- repulsions in 2s
Energy required by promotion is more than
recovered by the atom s ability to form four bonds 2s the four C unpaired electrons can then pair with 4 H 1s electrons to form CH4
Promotion implies the presence of three σ bonds of one type (C2p-H1s
overlap) and a fourth, distinctly different type (C2s-H1s overlap).
It is well-known, however, that the
four C-H bonds in methane are
equivalent in terms of both their
chemical and physical properties… The four C-H bonds in methane are
equivalent in terms of both their
chemical and physical properties and Two adjustments of VB theory improve
agreement with experimental observations:
tetrahedral coordination. 2. Hybridization
Second adjustment of VB theory addresses this problem
Quantum mechanics allows the same electron distribution to be described in different
ways…
We can describe electron distribution in CH4 as arising from four different mixtures
of s and p orbitals.
These mixtures (more formally, linear combinations) are called hybrid orbitals Hybrid Orbitals
2. Hybridization sp3 Linear combinations Linear combinations that give rise to
four equivalent hybrid orbitals
1
h1 = 2s + 2p x + 2p y + 2p z
2
1
h2 = 2s ! 2p x ! 2p y + 2p z
2
1
h3 = 2s + 2p x ! 2p y ! 2p z
2
1
h4 = 2s ! 2p x + 2p y ! 2p z
2 A linear combination of N functions result in N hybrid functions.
The LCs are of functions on the same atom. [ [ [ A linear combination of two functions f and g is given by c1f + c2g , where c1 and c2 are
numerical coefficients. [ Each hybrid orbital
has a lobe pointing
toward the corner
of a tetrahedron
Note there are four
coefficients in h1-h4
which are either
+1/2 or -1/2.
Equal contribution
from each orbital involved s p3 5 Lecture 09 9/26/11 The sp3 Hybrid Orbitals Hybridization in Alkenes H H
CC H 120° H C : [He] s12p1 2p1 2p1
2
x
y
z p z Linear combinations that give rise to
three equivalent hybrid orbitals
#
, 1)
1&
'2p y !
h1 =
$2s + *
*
'
3$
!
+ 2(
%
" h2 = ed
in
π bo nd #
, 3)
, 1)
1&
'
*
'
$2s + *
* 2 '2p x - * 2 '2p y !
3$
!
+
(
+
(
%
" h3 = us #
, 3)
, 1)
1&
*
'
*
'
$2s - *
'2p x - * 2 '2p y !
3$
!
+ 2(
+
(
%
"
Normalization factor Hybridization in Alkynes H Linear combinations that give rise to two
equivalent hybrid orbitals 1
[2s + 2pz ]
h1 =
2 CC H2O with VB theory H
180° 1
[2s ! 2pz ]
h2 =
2 C : [He] s12p1 2p1 2p1
2
x
y
z The hybridization of N atomic orbitals always results
in the formation of N hybrid orbitals used in π bond O-H ! bond is sp3 + s
character H O 104° H the bonding in H2O with VB theory Other Hybridizations sp3d
The hybridization of N atomic orbitals always results
in the formation of N hybrid orbitals
We can use VB theory to explain VSEPR theory
number shape hybridization 2 linear sp 3 trigonal planar sp2 4 tetrahedral sp3 5 trigonal bipryramidal sp3d 6 octahedral sp3d2 These pure schemes with equal contribution from each orbital
are not the only possibilities: it is possible to form hybrid
orbitals with optimized proportions of atomic orbitals. increase p
sp
decrease s
180° sp2
120° 6 ...

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