Transcript Molecules
MOLECULES
BONDS • Ionic: closed shell (+) or open shell (-) • Covalent: both open shells neutral (“share” e) • Other (skip): van der Waals (He He)…Hydrogen bonds (in DNA, proteins, etc) ENERGY LEVELS • electronic • vibrational • rotational
P461 - Molecules 1
Ionic Bonds - NaCl
• First approximation. Both atoms are ions (no electron sharing) and bond due to EM force between two charged bodies
Na
bond
Cl
Atom valence ionization ~effZ radius Na 3s 5.1 eV 1.8 .17 nm Cl 3s 2 3p 5 13 eV 2.9 .07 nm Ar 3s 2 3p 6 16 eV 3.3 .07 nm
E
13 .
6 2
Z eff n
2 • Ar more tightly bound than Cl. But Cl “looks” like Ar. Has effective Z ~ 3
E
(
Cl
)
E
(
Cl
0 ) 3 .
8
eV need
: ( 5 .
1 3 .
8 )
eV Na
Cl
Na
Cl
P461 - Molecules 2
Ionic Bonds - NaCl
• There is an EM attraction between the two ions
U
4
e
2 0 1
R
1 .
4
eVnm R if R
0 .
9
nm
U
1 .
5
eV
• if |U| > (5.1-3.8) eV = 1.3 eV, then can have a bound NaCl molecule • but the two ions can’t get too close. Electron’s wave functions begin to overlap. Some states will become filled and Pauli exclusion forces to higher energy (large gap) • size of filled 2p about 0.05 nm • the nuclei will start to not be shielded from each other --> some ++ repulsion P461 - Molecules 3
Ionic vs Covalent
• As R >> 0.05 (size of 2p orbit), there is little overlap in the electron wave function between the Na and Cl ions ---> mostly ionic bond “94% ionic and 6% covalent (DH makes up numbers) • look at HFl molecule H ionization energy = 13.6 eV Fl electron affinity = 3.4 eV -----> need 10.2 eV in electrostatic energy
R
e
2 4 0 1
U
1 .
4
eVnm
10 .
2
eV
.
14
nm
• as the size of filled 2p in Fl about 0.05 nm and the nominal 1s in an H atom is 0.05 nm, the electrons are attached to both atoms --> covalent bond “10% ionic and 90% covalent” (DH made up numbers) • the nuclei will start to not be shielded from each other --> some ++ repulsion P461 - Molecules 4
Covalent Bonds - Diatomic Molecules • assume all valence electrons are shared • often S=0 lowest energy but not always (Oxygen is S=1) • if both atoms are the same then | y| 2 same if switch atom(1) and atom(2) --- electron densities around each atom are the same (even sort of holds if different atoms like CO) H(1s) <-- very far apart ---> H(1s) close together H(“1s”)H(“1s”) electron wavefunctions overlap -“shared” • two energy levels (S=0,1) which have | y ( 1 , 2 ) | 2 | y ( 2 , 1 ) | 2
E
R=infinity (atoms) bands 1s*1s P461 - Molecules Vib and rot 5
Covalent Bonds - Hydrogen • even if only 1 electron, bond is covalent • look first at ionized diatomic H
H
2 • have repulsive potential between 2 protons depends on R = p-p separation (about 0.11 nm)
V pp
e
2 4 0
R
• guess at a 3D solution for the wave function | y ( 1 , 2 ) | 2 | y ( 2 , 1 ) | 2 ( 1 , 2
spacial
• at large separation just two H atoms ) y y 1
S
( 1 , (
H
) 2 )
e
r
/
a
0
A
(
e
|
r
r
1 | /
a
0
e
|
r
r
2 | /
a
0 ) • two possibilities: symmetric and antisymmetric when the separation becomes small P461 - Molecules 6
Covalent Bonds - Hydrogen+ • symmetric wave function has lower energy • less curvature. 1 “node” vs 2 “nodes” (compare to particle in a box) • also greater shielding of protons from each other as higher probability for the electron to be between the two protons (antisymmetric goes to 0 at midpoint) • can extrapolate to R=0 --- symmetric becomes a 1S state of He and antisymmetric (with wavefunction=0 at orgin) becomes a 2P state
total E
V pp
E e
• determine this as a function of R internuclear separation. Find there is a minimum for symmetric but not for antisymmetric---> “covalent” bond P461 - Molecules 7
Energy Levels • for given electronic states (1s,3p, etc S=0, S=1) determine effective V(R) and see if a minium (bound state) exists • as NOT V(r) potential, Sch. Eq. Not separable into (THETA,PHI) parts • ---> L 2 not eigenfunction, L not good eigenvalue • but often phi symmetry --> L z m “good” • will then have H.O. vibrations around minimum R=nuclear separation
V
P461 - Molecules 8
Neutral Hydrogen Molecule
H
2 2 .
7
eV
H
H
H
4 .
7
eV
H
H
2 • more tightly bound with 2 electrons. Have: • additional shielding of protons (lower E) • e-e repulsion (higher E) • end up: R=0.07 nm (compared to about 0.09 nm with single electron) • the “size” of a H atom is about 0.05 nm and so the 1s wavefunctions of the 2 atoms are overlapping and need to use Fermi-Dirac statistics --> Pauli exclusion and a totally antisymmetric wavefunction y
if
(
e
1 ,
e
2 )
S
y
space
y
spin
y (
e
2 ,
e
1 ) 1 y
spin sym
, y
space antisym
if S
0 y
spin antisym
, y
space sym
P461 - Molecules 9
Neutral Hydrogen Molecule • the antisymmetric space has y0 when r1=r2 • gives: lower electron probability between protons • less shielding --> higher energy • in this case (and in most cases) have covalent bond when electrons are paired with “antiparallel” spin S=0
S=1
R pp E E e
2
E e
1
V pp
S=0
P461 - Molecules 10