Bohr's atom model

Bohr’s atom model

electron(s)

The neon atom (Ne)

nucleus(10 protons,10 neutrons)

10+

K-shell

L-shell

K-shell: max. 2 electronsL-shell: max. 8 electronsM-shell: max. 18 electronsN-shell: max. 32 electrons

z

yx

pz

Schrödinger’s atom model

s-orbital

p-orbitals

z

xy r

r = Bohr radius

y

z

x

z

y

x

py px

P (L-shell)

distance from the nucleus

ptot

ProbabilityP to find anelectron fora s-orbital(K-shell)

distance from the nucleusin all directions

Radial probability to find an electron

proportionalto total probabilityto find an electron

1s,2s and 3s orbitals in hydrogen atoms

Diagram showing the position of an electron over time t (15'000 points) in the hydrogen (from right to left) 1s, 2s and 3s orbital. In the ground state the electron will remain in the 1s orbital.

Idem for one of the 2p and 3p orbitals.

z

x y

Boron atom

The boron atom: 5 electrons distributed among K- and L-shell

K-shell 2 s-orbital electrons

L-shell 2 s-orbital electrons

L-shell 1 P-orbital electron

distance from the nucleus

ProbabilityP to find anelectron

in z direction

Radial distribution along the z-axis of

Filling of orbitals

„Relationship“ between Bohr shells and Schrödinger orbitals: Each shell is decomposed into orbitalsK-shell: s-orbitalL-shell: s-orbital, 3 p-orbitalsM-shell: s-orbital, 3 p-orbitals, 5 d-orbitals etc.Shell designations by quantum numbers

Filling of shell’s

General rules:-Electrons are filled into orbitals in increasing order of their energy levels -An orbital can have maximum two electrons with opposite spin. -Every orbital of a subshell has to be filled at least with one electron before they can be occupied by pairs (Hund’s rule).

Energy

K-shell

s

d

sp

sp

sp

d

f

sp

d

f

L-shell M-shellN-shell O-shellMany exceptions to the rules!

z

yx

Silicon atom

Notation for orbital occupation: Prinicipal quantum number - letter for orbital type - number of electrons Electron distribution in silicon: 1s2 2s2 2p6 3s2 3p2

Filling scheme: total of 14 electrons

2 electrons into s orbital of K-shell

2 electrons into s orbital of L-shell

2 electrons into px orbital of L-shell

2 electrons into py orbital of L-shell

2 electrons into pz orbital of L-shell

2 electrons into s orbital of M-shell

1 electron into px ,py or pz orbital of L-shell

1 electron one of the two other p orbitals of L-shell

EN < 1.9: element gives up electrons, metallic character (except noble metals)EN > 2.1: element acquires electrons, non-metallic character1.9 > EN > 2.1: amphoteric character

Electronegativity

Electronegativity is a measure of the ability of an atom or molecule to attract respectively to give off an electron. Pauling's electronegativity scale is given in dimensionless units and ranges from 0 to 4:

Covalent bonds I

Covalent bonds: sharing of electrons between atoms = overlap of orbitals.Only between atoms with smallE (Electronegativity difference), perfect covalent bond only when E = 0 => between like atoms

2 p - orbitals of fluorinered: occupied by two electronsblue: occupied by one electron

Overlap of the two single occupied 2p-orbitals (= sharing of the single electrons)

Overlapping orbitals: molecular orbitals

Hybrid orbitals with axial symmetry: - bondsDirectionality is the major difference of covalent bonds compared to ionic bonds.

Most bonds are mixed in character. The covalent contribution is given by:

Example: Fluorine electron configuration: 1s22s2 p5

CC(%)= 100 - (16E + 3.5 E2)

Covalent bonds II

Example hybridization of s- and p- orbitals in diamondElectronconfiguration of carbon: 2s2p2

Hybridization (recombination) of orbitals of different types to form orbitals with new shape and orientation.

Overlap of 2sp3 orbitals results in the crystal structure of diamond:

1s2 2s2 2px1 2py

1 2pz0

Hybridization

1s2 2sp1 2sp1 2sp1 2sp1

+

2s2

=

2px1py

1pz0

empty

Hybrid 2sp3 - orbitals

Bonding between two carbon atoms through the overlap of two 2sp3

hybridized orbitals

2sp3

Example hybridization of s- and p- orbitals in graphite

Electronconfiguration of carbon: 2s2p2

1s2 2s2 2px1 2py

1 2pz0

2sp1 2sp1 2sp1 2pz11s2

+

2px1py

1pz02s2

=

Overlap of 2sp2 orbitals lead to hexagonal carbon sheets. The lonely 2pz

1 electrons overlap sideways and form - bonds. The hexagonal sheets are only hold together by very weak bonds.

Covalent bonds III

-bond

2sp2

2pz1

Van der Waals bonds

Ionization I

fluor atom

sodium atom

Most stable electron configuration: s2p6 in the outermost shell = Noble gas configurationAtoms can get this configuration by loosing or acquiring electrons, becoming charged ions by this process

positive ions:

negative ions:

cations

anions

negative fluor anion

positive sodium cation

Tendency for ionization ionization potential electron configuration

s2p6: most stable configuration, “noble gas” configuration => high ionization potential

Tendency to give off an electron increases when:

- no other electron was added or subtracted before - the valence shell of the ion gets closer to a s2p6

configuration - the electron is in a low energy orbital, far from the nucleus

Examples:

Element electron configuration 1st ionization potential

Lithium 1s22s1 5.39 eVCaesium 1s22s2 p63s2p6 d104s2 p6d10 5s2p66s1 3.89 eV

Neon 1s22s2p6 21.56 eVKrypton 1s22s2p63s2p6 d104s2 p6 14.00 eV

Ability to acquire a valence electron: Electron affinity. Positive affinities =release of energy

Example Electron affinity

Chlorine 1s22s2 p63s2p5 3.61 eV

Ionization II

Ionic bonding I

- Large electronegativity difference E between two atoms => complete transfer of electrons from one atom to the other.

- Opposite charge of the atoms => Coulomb attraction = ionic bond with gain of cohesive energy.

Energetics of sodium chloride formation from the gaseous elements

+ 5.14 eV

Ionization energy

Cl -

Gas

Na++ e -

Gas

Na +

+ 3.61 eV

Electron affinity

+ 7.9 eV Cohesive energy

Na

Gas

e - + Cl

Gas

Gas

Cl - + Na +

Gas

Na + Cl -

Crystal

Energy budget

- 5.14 eV

+ 3.61 eV

+7.90 eV

Total: + 6.37eV

Ionic bonding II

Attractive and repulsive forces between a fixed cation located at the origin and an anion approaching from the right:

Force

Distance R between cation and anion (Å)

(arb. units)

Repulsive forceA exp(-R/B) C/Rn

Born potential

Coulomb forceq2R

Total force

Ftot = q2R + C/Rn

REq

Equilibrium distance REq: F = 0 => bond length

The configuration for which attractiveand repulsive forces between atomscancel each other is the minimum energy configuration. The distance between the center of one atom to thecenter of the other is called bond length.

Ionic bonding III

When two or more anions are in the surrounding of a cation, the forces at the cation position will cancel each other. In most cases this will occur only at one single position, but it is also possible (b) that the forces cancel each other at more than one location. There is a equal likelyhood to find the cation in positions B or D.

Direction in which the force is acting

Atomic and ionic radii I

RA

RCL= RA +RC

Electron distribution around atoms and ions are not perfectly spherical, but are assumed so in the ionic model.Assumption:

bond length = sum of radii of spherical atoms or ions

anion radius RA cation radius Rc+ = ionic bond length L

Atomic and ionic radii II

Ca

RO

O

Determination of ion radii:

RCaLMgO= RO +RMg

- Fixing the radius of one ion e.g. oxygen anion RO e.g. O-2

- Measuring cation - oxygen bond length L in different oxides with similar structure, e.g.

A set of radii is only valid for the same coordination number. Standard ionic radii:Shannon and Prewitt (1969, revised by Shannon 1976) based onthe radius of VIO2- taken as 1.4Å.

=> ionic radius of Mg = LMgO - RO

Mg-O bond length in MgO

Ca-O bond length in CaO

=> ionic radius of Ca = LCaO - RO

Mg

RMg

RO

O

LMgO= RO +RMg

Electron density I

What is the absolute (numerical) value of a specific ionic radius?Section of the electron density contours in NaCl, determined by x-ray diffraction. The contour indicate a certain electron "concentration". The contours close to the nuclei are not shown, they would be too close together. Ionic radii correspond to distance between electron density maxima (= center of atoms) and minima on a line connecting neighboring ions.

rCl rNa

bondlength

Electron density contours in LiF, determined by x-ray diffraction.Ionic radii in tables deviate slightly from the actual values, because the anion radius is taken as a fixed value.

Interatomic distance

F Lix

x

electrondensity

Minimum density

F- (Shannon & Prewitt)

Li+ (Shannon & Prewitt)

F Li

x

Electron density II

Metallic bonds

Metallic bonding is characteristic among elements in ± the left part of the periodic table.Each atom gives off its valence electrons. The valence electronscan move freely, forming an „electron gas“ between the positively charged nuclei.

+ + + + +

+ + + + +

+ + + + +

Schematic example of metallic sodium:

free electrons

Van der Waals bonds

Non-metallic elements like nitrogen, oxygen and fluorine form molecules with no extra electrons remaining in the valence shell for further bonding. In the fluorine molecule, the two atoms of the molecule share the their single valence electrons, which are located in the single occupied valence orbitals. Fluorine is a gas at high temperature. At low temperature, the electrons of neighboring molecules influence each other. Negative and positive charges are not longer homogeneously distributed. The molecules are polarized. Positive and negative ends of neighboring molecule attract each other and form bonds (named after the physicist Van der Waals)

Orbital model of the fluorine atom

+- +-

+ -+ -

Polarization of the fluorinemolecules and formationof Van der Waals bondsat low temperature

Hydrogen bonds

The polarization of the charge distribution in molecules such as O2 , N2 or F2 is not permanent and is only strong enough at low temperature to create bonds between the molecules. Bonds between hydrogen and atoms like oxygen or nitrogen lead to a permanent polarization of the resulting molecule. The hydrogen atom will be attracted by other positively charged ions and form a hydrogen bond.

OHH

O

H

H

OH

H

Hydrogen bonds betweenwater molecules

Structure of ice II (box: unit cell)Some of the hydrogen bonds are shownas stippled lines