Orbital Teori

7/17/2019 Orbital Teori

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Molecular Orbital Theory

or

when electrons dont like

sitting between atoms!


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In the molecular orbital model,orbitals on individual atoms interactto produce new orbitals, calledmolecular orbitals, which are nowidentifed with the whole molecule.

THROW OUT TH I!" O# $O%"$I&!

'O(!I()


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Why !o "toms #orm

Molecules*The Aufbau principle tells us to put electrons into the lowest energyconfiguration in atoms. Similarly, molecules form when thetotal energy ofthe electrons is lower in the molecule than in individual atoms.

Just as we did with quantum theory for electron in atoms, we will use the molecularquantum theory to obtain.

1. Molecular rbitals !hat are the shapesof the waves"!here are the lobes and nodes"!hat is the electron density distribution"

#. Allowed $nergies. %ow do the allowed energies change when bonds form"

!e will use the results of these calculations to ma&e some simple models ofbond formation, and relate these to pre'quantum descriptions of bonding.

These will build a (tool&it) for describing bonds, compounds and materials.


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Wave+unctions and neries-

*f we calculate the wavefunctions and allowed energies of a two proton,

two electron system as a function of separation between the nuclei +thebond length, then we see how two atoms are transformed into amolecule.

This calculation tells us

- !hether a bond forms' *s the energy of the molecule lower than thetwo atoms"- The equilibrium bond length' !hat distance between the nuclei

corresponds to the minimum in the energy"- The structure of the bond' !hat is the electron density +charge

distribution +#"- $lectronic properties of the molecules' ond strength, spectroscopic

transitions +colour/, dipole moment, polari0ability, magnetic character...


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!iatomic Molecular Orbital

Theory In the case of diatomic molecules, the interactions are easy to see and may be

thought of as arising from the constructive interference of the electron waves(orbitals) on two different atoms, producing a bonding molecular orbital, and thedestructive interference of the electron waves, producing an antibondingmolecular orbital

A Little Math is need to

understand

Only a Little I promise!

-This Approach is called LCAO-MO+Linear Combination of Atomic Orbitals toProduce Molecular Orbitals


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How to impress your +riends and +amily/

Making Molecular Orbitals

Antibonding

Bonding

*n this case, the energies of the A..s are identical


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The lowest energy state of two isolated hydrogen atoms is two 1s orbitals

each with one electron. As the nuclei approach each other, the lowestenergy state becomes a molecular orbitalcontaining two paired electrons.

Molecular Orbital o+ H

This lobe represents the orbital or wavefunction of the electrons delocalisedaround the two protons. This is a bond.


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0uantum 1tates in H 2as

computed3%#also has other electronic quantum states with corresponding allowedenergies. These molecular orbitalshave lobe structures and nodes 2ustli&e atomic orbitals.

1s

2s

R= (H)

This diagram showssome allowed energylevels for atomic H

+There are two ofthem and molecularH2.

+R3 denotes the twoatoms at (infinite

separation) ' no bond.

The orbitals are filledwith electrons startingwith the lowest energy,

2ust li&e atoms.

0"# $(H2)


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0uantum 1tates in H- "llowed

neries4irst lets ignore the wavefunctions +orbitals, and consider only the

allowed energies, 2ust as we did with atoms. !hat do we observe"

1s

2s

R= (H)

0"# $(H2)


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0uantum 1tates in H

!e call this molecular orbital a bondingorbitalfor this very reason.

The other orbitals have higher energies thanthe atomic orbitals of %.

$lectrons in these orbitals would notcontribute to the stability of the molecule.

%#contains the simplest &ind of bond, a pair

of electrons delocalised between two nuclei,symmetric to rotation about the interatomic a5is.

This is &nown as asigma + bond.

The energy of the %#molecule is lower thanthe energy of two isolated %

atoms. That is, the energy changeof forming the bond is negative.

1s

2s

R= (H)

0"# $(H2)


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Molecular Orbitals in HThe ne5t'lowest energy orbital is unoccupied. As it lies above the

highest atomic orbital, we refer to it as an anti-bonding orbital.

6oo& also at the shape of the lobes7The anti-bonding orbitalhas a nodebetweenthe two nuclei.

!here the bonding orbital has an electrondensity build'upbetween the nuclei, the anti'bonding orbital would have a reduced

electron density +#.

%&is or'ital is calle t&eLoest *noccupieMolecular Or'ital (L*MO)

%&is or'ital is calle t&eHi+&est Occupie Molecular

Or'ital (HOMO)

1s

2s

R= (H)

0"# $(H2)


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The solution to the !ave $quation for molecules leads to quantum

states with discrete energy levelsand well'defined shapes of electronwaves +molecular orbitals,just like atoms.

$ach orbital contains a ma5imum of two +spin'paired electrons,just like atoms.

onds form because the energy of the electrons is lower in the molecules than itis in isolated atoms. Stability is conferred by electron delocalisationin themolecule as they are boundby more than one nucleus +longer de rogliewavelength.

This gives us a convenient picture of a bond as a pair of shared +delocalised

electrons. *t also suggests some simple +and commonly'used ways ofrepresenting simple sigma bonds as7

1. A shared pair of electrons +dots % 7 %

#. A line between nuclei. %'%


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'ondin o+ Multi4lectron

"toms!hat &inds of orbitals and bonds form when an atom has more than

one electron to share"

!e will step up the comple5ity gradually, first considering other diatomicmolecules. These fall into two classes

1. Homonuclear Diatomics. These are formed when two identicalatomscombine to form a bond. $.g. %#, 4#, 8l#, #/

2. Heteronuclear Diatomics. These are formed when two differentatoms combine to form a bond. $.g. %4, 9, 8, 8lr

ond lengths in homonuclear diatomic molecules are usedto define the covalent radius of the atom :6ecture ;


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nery $evels in #This diagram shows the allowed

energy levels of

Two isolated 4 atoms +1s##s##p;

and, between them, the 4#

molecule.

9otice that the +filled 1s energy levelsare at much lower energythan the #sand #p orbitals. Their energy isvirtually unchanged when the bond

forms.

Such electrons, below the outermostelectron shell +n are commonlyreferred to as core electrons, and are

ignoredin simple models of bonds.

1s

2s

2p

,, ,2

2s


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=alence Ms

1s

2s

2p

,, ,2

nery $evels in #

This diagram shows the outer,unfilled, valenceenergy levels of

%o , atoms an ,2

4 has > electrons, hence ? outer shellelectrons in the configuration shown.i.e. ne unpaired electron each.

The electronic configuration of the 1@valence electrons of 4#is shown in

blue.

$ach molecular orbital contains two,spin'paired electrons.The total energy of the electrons islower in the molecule than in the

atoms.

5 l M l l O bit l i


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5alence Molecular Orbitals in#

The two lowest'energy molecular

orbitals are similar to the orbitals of %#.

The lowest is a sigma bonding orbital, with apair of delocalised electrons between thenuclei.

The second'lowest is a sigma-star !"anti-bonding orbital.

*n 4#, the bondingand anti'bonding

orbitals both contain apair of electrons.

The sum of these isno nett bond.

+!ell see where the bond comes from later.

2s

2p

=alence Ms


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'ondin o+ Multi4lectron

"tomsefore considering the other molecular orbitals of 4#, we will loo& at a

simple heteronucleardiatomic molecule, %4.

%ere the atomic energy levels are different, so this will give us an ideaabout what constitutes a bond between unli&e atoms.

%owever, %4 is in some ways simpler to deal with as it has fewerelectrons ' both valence electrons and total electrons.


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=alence Ms

1s

,H H,

2s

2p

nery $evels in H#This diagram shows the allowed

energy levels of

*solated % +1s1 and 4 +1s##s##p;atomsand, between them, the %4molecule.

9ote71. 4 1s is at much lower energy than %1s +because of the higher nuclearcharge

#. 4 1s#electrons are core electrons.Their energy does not change when %4is formed.

B. % 1s and 4 #p valence electrons gointo molecular orbitals with new

energies.


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'ondin in H#

This diagram shows the outer,valenceenergy levels of %, 4 and%4.

The electronic configuration of the Cvalence electrons of %4 is shown inblue.

There are four orbitals, each containinga pair of electrons.

%ow do we represent these"

=alence Ms

1s

,H H,

2s

2p


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1s

,H H,

2s

2p

Molecular Orbitals in H#

This core orbitalisalmost unchanged fromthe 4 1s orbital. Theelectrons are boundtightly to the 4 nucleus.

This non-bondingmolecularorbital +n has an almostspherical lobe showing onlyslight delocalisationbetween the two nuclei.9on'bonding orbitals loo&only slightly different toatomic orbitals, and havealmost the same energy.

H ,

n

n


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Molecular Orbitals in H#

%&ese to e+enerate (ille) HOMO.s arecentre on t&e , atom/ lie 2pan 2py

or'itals

%&is MO/ &ic& is is lie a2por'ital/ is loer in ener+y

in t&e molecule (a 'onin+or'ital)/ an one lo'e is

elocalise aroun t&e Hatom

%&is (empty) L*MO is ananti'onin+ or'ital it& anoeon t&e interatomicais 'eteen H an ,

$lectrons in these two orbitals are not shared+much by the fluorine nucleus. They behave li&ethe #p orbitals and are alsonon-bonding n".

1s

,H H,

2p

n

n

n n


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What do we ta6e +rom all this*

Three simple &inds of molecular orbitals

1. Sigma +bonding orbitals +.

#. 9on'bonding orbitals +n

B. Sigma star +anti'bonding orbitals +

$lectrons delocalised along the a5is between two nuclei.These may be represented as shared electrons, e.g. %7%or %74D %'% or %'4

rbitals that are essentially unchanged from atomic orbitals, and remainlocalisedon a single atom +unshared.These may be represented as a pair of electrons on one atom.

rbitals with a node or nodes along the a5is betweentwo nuclei. These do not contribute to bonding, they(undo) bonding.


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1ummary

Eou should now be able to

- $5plain the reason for bond formation being due to energy lowering ofdelocalised electrons in molecular orbitals.- Fescribe a molecular orbital.- Gecognise +some sigma bonding, sigma star antibonding and non'

bonding orbitals.- e able to assign the +ground electron configuration of a diatomic

molecule.- Fefine %M and 6HM, and homonuclear and heteronuclear

diatomic molecules.


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Molecular Or'ital %&eoryFiatomic molecules7 The bonding in %e#

%e also has only 1s A, so the M diagram for the molecule %e#can be formed in

an identical way, e5cept that there are two electrons in the 1s A on %e.

%e

$nergy

%e%e#

1s 1s

g

u

Molecular rbital theory is powerful because it allows us to predict whethermolecules should e5ist or not and it gives us a clear picture of the of theelectronic structure of any hypothetical molecule that we can imagine.

The bond order in %e#is +#'#I# 3 , sothe molecule ill not eist.

%owever the cation :%e# 1.#@ 1.1 1.#1 1.@# nIa

ond $nergy +&JImol 1; nIa #C> Q> >@1 @>@ 1;; nIa

*n this diagram,the labels arefor the valenceshell only ' theyignore the 1sshell. Theyshould reallystart at #gand#u.

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