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Konfigurasi elektronik atom multi-elektron

Apakah makna konfigurasi 2p2 ?

n = 2; l = 1; ml = -1, 0, +1; ms = ± 1/2

Penataan elektron yang sesuai

microstatesbeda energi karena tolakan antar elektron (inter-electronic repulsions)

Konfigurasi elektronik atom multi-elektron pasangan RS

Russell-Saunders (or LS) coupling

Untuk tiap elektron 2p n = 2; l = 1

ml = -1, 0, +1ms = ± 1/2

Untuk tiap atom multi-elektronL = total orbital angular momentum quantum numberS = total spin angular momentum quantum number

Spin multiplicity = 2S+1

ML = ∑ml (-L,…0,…+L)MS = ∑ms (S, S-1, …,0,…-S)

• ML/MS menyatakan microstates • L/S menyatakan states (kumpulan microstates)• Group microstates dengan energi yang sama disebut terms

Menentukan microstates untuk p2

Spin multiplicity = 2S + 1

Menentukan harga L, ML, S, Ms untuk terms yang berbeda

1S

2P

Mengklasifikasikan microstates p2

Spin multiplicity = # columns of microstates

Next largest ML is +1,so L = 1 (a P term)

and MS = 0, ±1 for ML = +1,2S +1 = 3

3P

One remaining microstate ML is 0, L = 0 (an S term)

and MS = 0 for ML = 0,2S +1 = 1

1S

Largest ML is +2,so L = 2 (a D term)

and MS = 0 for ML = +2,2S +1 = 1 (S = 0)

1D

Largest ML is +2,so L = 2 (a D term)

and MS = 0 for ML = +2,2S +1 = 1 (S = 0)

1D

Next largest ML is +1,so L = 1 (a P term)

and MS = 0, ±1 for ML = +1,2S +1 = 3

3P

ML is 0, L = 0 2S +1 = 1

1S

Energy of terms (Hund’s rules)

Lowest energy (ground term)Highest spin multiplicity

3P term for p2 case

If two states havethe same maximum spin multiplicity

Ground term is that of highest L

3P has S = 1, L = 1

before we did:

p2

ML & MS

MicrostateTable

States (S, P, D)Spin multiplicity

Terms3P, 1D, 1S

Ground state term3P

the largest ML Lspin multiplicity = Σcolumnsor 2S+1, S the largest MS

single e- (electronic state) multi-e- (atomic state)

For metal complexes we need to considerd1-d10

d2

3F, 3P, 1G, 1D, 1S

For 3 or more electrons, this is a long tedious process

But luckily this has been tabulated before…

Transitions between electronic terms will give rise to spectra

Remember what we’re after ?

Theory to explain electronic excitations/transitions observed for metal complexes

Selection rules(determine intensities)

Laporte rule

g g forbidden (that is, d-d forbidden)

but g u allowed (that is, d-p allowed)

Spin rule

Transitions between states of different multiplicities forbidden

Transitions between states of same multiplicities allowed

These rules are relaxed by molecular vibrations, and spin-orbit coupling

Breakdown of selection rules

Group theory analysis of term splitting

Free ion term for d2

3F, 3P, 1G, 1D, 1S

Real complexes

Tanabe-Sugano diagrams

d2

• show correlation of spectroscopic transitions observed for ideal Oh complexes with electronic states

• energy axes are parameterized in terms of Δo and the Racah parameter (B) which measures repulsion between terms of the same multiplicity

d2 complex: Electronic transitions and spectra

only 2 of 3 predicted transitions observed

TS diagrams Other dn configurations

d1 d9

d3

d2 d8

d3

Other configurations

The limit betweenhigh spin and low spin

the spectra of dn hexaaqua complexes of 1st row TMs

The d5 case

All possible transitions forbiddenVery weak signals, faint color

symmetry labels

Charge transfer spectra

LMCT

MLCT

Ligand character

Metal character

Metal character

Ligand character

Much more intense bands

[Cr(NH3)6]3+

Determining o from spectra

d1d9

One transition allowed of energy o

Lowest energy transition = o

mixing

mixing

Determining o from spectra

Ground state mixing

E (T1gA2g) - E (T1gT2g) = o