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Electron configuration

and chemical periodicity.

1

Chapter 2

CM1502

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Need to now solve:

212121

,,, rrrrrr EH

Our wavefunction now depends on r1and r2,

i.e., (x1, y1, z1)and (x2, y2, z2)

Consider the He Atom

If a second electron is added to our atom (eg: H-or He), two newinteractions come into existence.

1. Attraction of the second electron to the nucleus, and

2.repulsion of the second electron by the first.

The Hamiltonian should include these interactions.

K.E. for e 1

12

2

2

2

1

2

0

21

22

4

1

r

e

r

e

r

eKKH

K.E. for e 2P.E. e 1 to nuc

P.E. e 2 to nuc

P.E. e-e rep

Adding a Second Electron

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No Exact Solution

!"#$# &' () #*+,- ')./-&)( -) -"&' #0/+-&)(1 !"# %!"

"&'&( )&2

3*+,- ')./-&)(' ,+( )(.4 #*&'- 5)$ '4'-#6' 7&-" )(#

#.#,-$)(1 &*+*1 81 8#91 :&;91 8;91 #-,2

!"&' &' + -"$##4 ?$)=.#61 @/'- .&A# -"# )$=&- )5 -"#

B/(

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Solving the Schrdinger Equation

G)$ '6+.. +-)6' +(> 6).#,/.#'1 7# ,+( >) -"&' ()7 5)$ +..?$+,-&,+. >#H$##' )5 ?$#,&'&)(1 /'&(H ,)6?/-#$'

I '&6?.# +??$)*&6+-&)(-) "#.? ').J# -"# B,"$K>&(H#$ 30/+-&)( &'-"# ') ,"#&-&"#&". -!(.,%/& 01#&/2

!"+- &'1 7# 7$&-#: (r1,r2 1(r1)2(r2).

8#$# 4L&' -"# +-)6&, )$=&-+. )5 #.#,-$)( L -"+- 6)J#' +' &51#.#,-$)( ; &' ()- ?$#'#(-2

B) 7"#( 4)/ 7$&-# L';5)$ -"# ,)(5&H/$+-&)( )5 8#1 7"+- 4)/ +$#+,-/+..4 7$&-&(H &'M (r1,r2 s(r1) s(r2)

4

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Atomic Orbital(AO) Energy and Total

Electronic Energy Solution to Schrdinger equation for systems with more than one electron

(using computers) results in two types of energies, 1. AO energies and

2. the total electronic energy.

For the H atom, the energy of an AO is equal to the total electronic energyof the H atom since it has only 1 electron.

Energy of a electron in a particular AO depends on several factors,the three relevant ones here are

The attraction felt by the electronbetween itself and thenucleus. i.e., the effective nuclear charge that the electron

experiences, Zeff. The repulsion of the electron with remaining electrons in theatom. e-e repulsion

Orbital Shape

This means the energy of an electron in 4s AO in one atom,is different to

the energy of an electron in the 4s AO of another atom. 5

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Zeffand Screening

Consider He

electron 1 blocks out some of the positivecharge of the nucleus so that electron 2does not get to see the full +2 charge(andvise versa).

Because of screening the effective nuclearcharge, Zeff, of He is 1.69 instead of 2.

It is illustrated in this movie(ILVE workbin-videos-Effective nuclear charge)

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7

355#,-&J# (/,.#+$ ,"+$H# >#?#(>' )(

L2 N/,.#+$ ,"+$H#

;2 B".>&(H =4 -"# #.#,-$)(' &( -"# '+6# #(#$H4 .#J#.

O2 B".>&(H =4 -"# #.#,-$)(' &( -"# &((#$ #(#$H4 .#J#.

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Zeffand Screening

For the H atom, the 2sand 2porbital have the same energy.

Screening occurs when there is more than 1 electron (cf. He).

The third electron in Li occupies 2s sublevel rather than 2p.Why?

Zeffis larger for the 2sthan 2p, but why?

We have to consider orbital shapes, that is radial probabilitydistributions.

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Orbital Penetration

2p orbital (orange curve) is slightly closer

to the nucleus than the maxima of the 2s

orbital (blue curve).

But small portion of 2s radial probabilitydistribution peaks with the 1s region.

Thus an electron in the 2s orbital spends

part of its time penetrating very close tothe nucleus.

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10

Penetration has two effects:

It increases the nuclear attraction for a 2s electron overthe 2p electron

It decreases the shielding of a 2s electron by the 1s

electron.

As a result an energy level splits into sublevels of differingenergy. The lower the /value of the sublevel, the

penetration is higher and hence greater the attraction

to the nucleus. Order of sublevel energies: s

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Electron spin quantum number This is the property of an electron and not the orbital.

Each electron behaves like a spinning charge and generates atiny magnetic field.

The two fields have opposing directions.

So half of the electrons are attracted by the large external

magnetic field while other half is repelled.

This gives rise to the spin quantum number mswith allowed

values of +1/2(spin up) or -1/2 (spin down)

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Paulis Exclusion Principle

N) -7) #.#,-$)(' &( + H&J#( +-)6 ,+( "+J# -"# #*+,-

'+6# '#- )5 0/+(-/6 (/6=#$'2

G)$ -"# 8# +-)61 -"# ,)(5&H/$+-&)( L';6#+(' -"+-

)(# #.#,-$)( "+' -"# 0/+(-/6 (/6=#$'"P L1 /P Q1 0/P Q1 02P 9R1+(> -"# )-"#$

"P L1 /P Q1 0/P Q1 02P ()- "+J# -"# ,)(5&H/$+-&)( L'O1 '&(,# -"#

-"&$> #.#,-$)( 7)/.> "+J# -) H#- -"# '+6# '#- )5

0/+(-/6 (/6=#$' +' )(# )5 -"# )-"#$ -7)2

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The Aufbau Principle

E' + $/.# 5)$ 5&(>&(H -"# .)7#'- #(#$H4#.#,-$)( ,)(5&H/$+-&)(5)$ +-)6'2

E- '-+-#' -"+- 4)/ 6/'- !## .3& &/&%.(1"241"& !. ! .,0&4 ,".1 .3& 1(),.!/2 .3!.

516/# 0!7& .3& !.10 012. 2.!)/&4 )6.1)&8,"+ .3& 9!6/, &:%/62,1" -(,"%,-/& !.

!// .,0&22

S4 T6)'- '-+=.#U 7# 6#+( .)7#'- J+./#

-) -)-+. #.#,-$)(&, #(#$H4132

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Stable Electronic Configurations

!"# )$>#$ )5 5&..&(H IV &' =#'-$#6#6=#$#> =4 ?&,-/$&(H -"#?#$&)>&, -+=.# &( 4)/$ 6&(>2

!"# -+=.# -) -"# $&H"- &../'-$+-#'-"&'2

1s2s 2p

3s 3p

4s 3d 4p

5s 4d 5p

6s 4f 5d 6p

7s 5f 6d 7p

Orbitals Filled

You should be able to give

ground state (most stable

state) electronic

configurations for any

element in the periodic tablegiven the Z only.

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Hunds Rule of Maximum Multiplicity

W+$- LM X#H#(#$+-# )$=&-+.' Y/Z Q[ +$# +.7+4' 5&..#> 7&-" '&(H.##.#,-$)(' =#5)$# +(4 )5 -"#6 +$# >)/=.4 ),,/?>2

D !"&' $#>/,#' #.#,-$)( -) -")'# ?+&$' 7"#$# -"#&$

'?&(' +$# )??)'&-#2D !"&' .#+>' -) #J#( .#'' #.#,-$)(

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Orbital Occupancy Diagram

The species with unpaired electrons

exhibits paramagnetism;it is attracted byan external magnetic field.

The species with all of its electrons

paired exhibits diamagnetism; it is not

attracted by an external magnetic field.

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Distribution of electrons

The electron configuration

nl#of electrons in the sublevel

as s,p, d, f

The orbital diagram (box or circle)

!"#$# +$# -7) ,)66)( 7+4' -) &(>&,+-# -"# >&'-$&=/-&)( )5 #.#,-$)('2

These configurations actually

represent electronic wave

functions i.e., approximatesolutions to the Schrdinger

equation.

The electronic configurations

and AO stability is responsible

for the periodic properties

observed in the elements.

The method of writing the electronic configuration

is illustrated in this movie(ILVE workbin-videos-Electronic configuration) 18

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A periodic table of partial, ground-state electron

configurations.

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Stability of AOs with different nand l

7"4 >)#' ] +(> ^+ ),,/?4 -"# _' IV =#5)$# -"# O>F

_' ?#(#-$+-#' =#--#$ &(-) -"# L';;';;?`O';O?`,)$# -"+( +(4 O> IV >)#'2

7"4 +$# #.#,-$)(' $#6)J#> 5$)6 -"# _' IV /?)( &)(&a+-&)( )5 + -$+('&-&)(6#-+.' &( -"# _-"?#$&)>1

&*+*G#;9"+' -"# ,)(5&H/$+-&)( bI$c_'QO#`F

!"# O> IV &' $+?&>.4 =#,)6&(H 6)$# '-+=.# 5)$ 5/$-"#$ #.#6#(-'2 d"4F

D S4 +>>&(H L #.#,-$)( -) -"# _' &( ]1 7# 5&(> -"+- -"&' "+$>.4 ',$##(' -"# O>YO> 6+*&6/6 ,.)'#$ -"+( -"# _' 6+&( 6+*&6/6[1 ') +(4 O> # 7)/.> H+&( +(+.6)'- 5/.. &(,$#+'# )5 9L 5)$ &-';#552

D G)$ -"# '+6# $#+')(1 +>>&(H + '#,)(> #.#,-$)( -) -"# _' &( ^+1 "+$>.4',$##(' +(4 #.#,-$)( -"+- 6&H"- =# 5)/(> &( -"# O>

D -"/' -"# O> )$=&-+. >$)?' '-&.. 5/$-"#$ &( #(#$H42

D G&(+..4 +- B,1 -"# O> IV )&%10&2 !"#$2.!)/& .3!"

-"# _' IV1 +(> $#6+&(' ') 5)$ -"# $#'- )5 -"##(-&$# ?#$&)>&, -+=.#2

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Why isnt the lowest energy electronic

configuration of Sc [Ar]4s03d3?

The answer to this question lies

in electron-electron repulsion.

The extent of an n= 3AO is

significantly less than n= 4 AO.

Electrons in the 3d AO repel

each other more than electrons

in a 4s AO.

erepulsion(3d,3d) > erepulsion(3d,4s) > erepulsion(4s,4s).

E

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Anomalous Configurations 1

8#$# #

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AnomalousConfigurations 2

^/ "+' -"# ,)(5&H/$+-&)( _'LO>LQ

!"# #(#$H4 H+? =#-7##( O> +(> _' &' .+$H# #()/H"-) )J#$,)6# -"# &(,$#+'# &( #(#$H4 >/# -) #2

D !"# $#+')( 5)$ +()6+.' 5)$ f/1 f"1 W> +(> IH+$# -"# '+6# +' 7#..1 #*,#?- 7# +$# -+.A&(H +=)/--"# _> +(> e' $+-"#$ -"+( -"# O> +(> _' IV'2

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The consistent changes in properties such as atomic size, Ionization

energies etc within a group or period are called periodic properties.

Periodic Properties of the Elements

An understanding of how Zeffand nvary in the periodic table as wellas the most stable electronic configurations, helps us to understandthe trends in the following properties:

Ionization Energy.

Electron Affinity.

Atomic Radius.

Electronegativity.

Oxidation states (which we will not discuss, but you may reviewfor your own interest in the movie(IVLE workbin-videos-Oxidations states)

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Moving across a period,

nis constant, and Zeffincreases.

Moving down a group

Zeffincreases somewhat, but nincreases by

one unit

Zeffand n

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Atomic Radii There are different types of atomic radii.

Covalent radii (also unfortunatelysometimes called Atomic radii)

!the distance between the nuclei of single bondedatoms, e.g., Cl2

Metallic radius is one-half the shortestdistance between nuclei of adjacent individual atoms in a

crystal of an element, e.g., Fe(S)

Ionic radii Obtained from solids that exhibit ionic bonding, e.g.,

NaCl.

van der Waals radii

The radius of the sphere surrounding the nucleus that

contains 98% of the electron density. 26

P i di it i At i R dii

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Periodicity in Atomic Radii

P i di it i At i R dii

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Varies in a systematic way along the group and the period.

Review the trend in the movie (IVLE-workbin-videos-atomicradii)

From the radial distribution for a hydrogenic atomwe have

rnln2/Zeff

,

where nand lrefer to the highest occupied AO (HOAO).

Moving across a period,nis constant, but Zeffincreases,so the radii decrease.

Moving down a groupZeffincreases somewhat, but n2

increases more, so the radii increase.

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Periodicity in Atomic Radii

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Ionic Radii

E- &' + 6#+'/$# )5 '&a# )5 +( &)(+(> &' )=-+&(#> 5$)6

-"# >&'-+(,# =#-7##( -"# (/,.#& )5 +>@+,#(- &)(' &( +,$4'-+..&(# &)(&, ,)6?)/(>2

^+-&)(' +$# '6+..#$-"+( ?+$#(- +-)6' +(> +(&)('

+$# .+$H#$-"+( -"#&$ ?+$#(- +-)6'2

^+-&)( '&a# >#,$#+'# 7&-" -"# ,"+$H#

#2HM G#O9&' '6+..#$ -"+( G#;9

X)7( -"# H$)/? &)(&, '&a# &(,$#+'#'2

I,$)'' -"# ?#$&)> -"# ?+--#$( &' ,)6?.#*2

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Ionic Vs Atomic radii

30

Notice the trend in

the sizes for anisoelectronicseries like N3-, O2-,F-, Na+, Mg2+, Al3+.

Isoelectronic the sameelectronicconfiguration

(s2p6).

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Ionization Energy (IE)

The first IE is defined as the energy needed to remove the most weakly

bound electroni.e., the electron from the Highest Occupied Atomic Orbital

(HOAO).

This process requires energy to overcome their electrostatic attraction.

Hence IE is always positive.

The second, third and continuing IE correspond to removing theeasiest electron from A+, A2+, etc.

For a given element there is an increase in IE1, IE2,IE3..etc

This is because each electron is pulled away from a species witha higher positive charge.

31

Review the trend seen in the 1st, 2nd, and 3rd IE via the movie

(IVLE workbin-videos-Ionization Energy)

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Periodicity in the first IE For a given period as wemove from left to right,the IE increases.

This is because Zeffincreases from left toright.

The IE falls slowly downa group.

nincreases as wemove down a group,Zeffalso increases, but

slowly.

The increase in ndominates over the

gradual increase in Zeff.

322

2

eff

n

ZkE

n

Orbital energies very roughly follow

the Bohr formula:

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Little glitches occur at Be-B and N-O.

For Be-B, With the 2p> 2sthe

IE is therefore lower in B cf. Be.

For N-O, N has half filledpsub-shell, so the 4thelectron to enter thepsub shell in O is forced topair with another electron and produces significante-e repulsion. This increases the orbital energy,and hence reduces the IE.

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Electron AffinityDefined as the energy required to remove the least tightly

bound electron from an singly charged anion, A-.

Forming an A-depends on the stability and availabilityof an AO to hold the extra electron.

EA are always smaller than IE because there is very

little attraction between an e and a neutral atom at longdistances compared with an e and a positively charged

atom.

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Periodicity in the first EA

Those elements that require energy to add an electron are assigned an EA of zero.

!"# -$#(>' +$#

()- $#H/.+$2

!"#$# &' +()J#$+.. &(,$#+'#

5$)6 .#5- -) $&H"-

+(> >#,$#+'#

>)7( -"# H$)/?2

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Trends in metallic behavior.

!"# -4?&,+. =#"+J&)$ )5 6#-+.' &' -).)'# #.#,-$)(' -) ()(#,$#+'#

&( '&a#1 +( &(,$#+'# &( E3 +(> +

6)$# 5+J)/$+=.# 3I

E- &(,$#+'#' >)7( -"# H$)/?&(

-"# ?#$&)>&, -+=.#

+ >#,$#+'# &( E32

36

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Redox and Acid base behavior

!"# #.#6#(-' 7&-" .)7 E3 +(> '6+..3I Y#HMH?L1;[ +$# '-$)(H $#>/,&(H+H#(-'2

!"# #.#6#(-' 7&-" "&H" E3 +(> .+$H#3I Y#HM H? L` +(> Lg[ +$# '-$)(H

)*&>&a&(H +H#(-'2

I' -"# #.#6#(-' =#,)6# 6)$#6#-+..&,>)7( -"# H$)/?1 -"#&$)*&>#' =#,)6# 6)$# =+'&,2

I' -"# #.#6#(-' =#,)6# .#''6#-+..&, +,$)'' + ?#$&)>1 -"#&$ )*&>#'=#,)6# 6)$# +,&>&,2

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Electronegativity ()

Several definitions exist, but all give very similar results.

is proportional to the average of the ionization energy and electron affinity.

has no units(review its overall trend in the movie (IVLE workbin-videos-electronegativity).

If an element can readily give up an electron (low IE), and is not interested inaccepting an electron (small EA), then it will have a low , e.g., Na.

If an element does not easily ionize (high IE), and is quite interested in acceptingan electron (large EA), then it will have a high , e.g., F.

Small values of favor electron donation, whereas large values favor acceptingelectrons.

Metals have small values of , whereas nonmetals have large values.

Chemical bonds between atoms with large differences in have strong ioniccharacter.

Chemical bonds between atoms with similar valuesare largely covalent.

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39

IE (eV), EA (eV) and EN(Pauling scale) of elements

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Summary Anomalous electronic configurations can be understood by considering the

overall stability of a particular electronic configuration.

An understanding of how Zeffand nvary in the periodic table as well as the most

stable electronic configurations is enough to understand the trends in the

following properties.

Ionization Energy

Roughly follows Zeff2/n2, with some differences seen in the transition metals.

Electron Affinity

Depends on the stability and availability of an AO in a neutral atom to hold

the extra electron.

Atomic Radius Roughly follows n2/Zeff.

Electronegativity.

Proportional to the average of IE and AE.

Provides much insight into the nature of chemical bonds (covalent, ionic, and

b l t d t th h th t i d ti !)40