The document discusses the Walsh diagram, introduced by Arthur Donald Walsh, which helps predict the geometries of triatomic molecules by calculating the energies of molecular orbitals. It explains how the shapes of molecules like H2O, BeH2, and BH2 are determined through graphs relating energy and distortion parameters. This method provides insights into the most stable geometries and extends to various polyatomic species.

1. WALSH DIAGRAM
2015
BASUDEV BARAL
REGD NO - 1311106007
MASTER INSCIENCE( APPLIED CHEMISTRY)
COLLEGE OF ENGINEERINGAND TECHNOLOGY( CET ) | BHUBANESWAR

2. 1
WALSH DIAGRAM
CONTENTS
 INTRODUCTION
 CONCEPTS OF WALSH DIAGRAM
 APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur DonaldWalsh FRS The introducer of walsh diagram (8 August1916-23 April1977) was
a British chemist, professor of chemistry atthe University of Dundee . He was elected FRS in
1964. Hewas educated at Loughborough Grammar School.
Walsh diagrams werefirstintroduced in a series of ten papers in one issueof
the Journalof the Chemical Society . Here, he aimed to rationalizethe shapes adopted by
polyatomic molecules in the ground stateas well as in excited states, by applying theoretical
contributions made by Mulliken .
CONCEPTS
Normally we explain the experimentally observed
geometries of molecules by certain devised rules and concepts
such as VSEPR theory , hybridisation , etc . But Walsh actually
Calculated the energies of molecular orbitals of a reference
Geometry and its several distortion for simple tri atomic molecules .
he correctly predicted the actual geometries of a number of simple tri atomic molecules like
H⁺3 , H₂O , BeH₂etc by plotting a graph between the calculated energies of molecular orbitals
of reference geometry and those of the distorted geometries of a molecule vs the distortion
parameter i.e, bond angle.
The position of the minimum energy of filled molecular orbitals in the graph indicates the most
stable geometry of the molecule . Such graphs are known as “WALSH DIAGRAM”

3. 2
 Here there are three tri atomic molecules we take in example BeH2,BH2,H2O , the
number of H atoms presentis 2 , let them Ha , Hb . thus the outer shell of these atoms
are 1sHa , 1sHb .
 In caseof Be , B , O the outer mostshell are2s , 2p .
 Here ,
2s has one orbital
2p has three orbital ( px, py , pz) .
 So total of 6 numbers of outer most orbitals are presenthere namely
1sHa , 1sHb , 2s , 2px, 2py , 2pz .
 6 atomic orbitals combines to form6 molecular orbitals out of which ,
two BMOs = 2
g
,1
u
two ABMOs = 1
u
two areNBMOs = 3
g ,
2
u
 The electrons are filling in the orbitals on account of the lowestenergy of the orbitals .
 So the orbitals with lowestenergy filled first.
 Atomic orbitals represents with a wavefunction related to Hamiltonian operator ,
Ψ = C1 1sHa+ C2 1sHb+ C3 2sH + C4 2pxA + C5 2pyA +C6 2pzA
FOR BeH2MOLECULE
For linear structureAngle HAH = 180⁰

4. 3
Electronic configuration is (2
g
)² (1
u
)²
So in diagramit corresponds to minimumenergy ,so it is the perfect structure .
For bent structure,angle HAH = 90⁰ or 90⁰-180⁰
electronic configuration are,
(2a₁)² (3a₁)² | (2a₁)² (1b₂)²
Itcorresponds to Emaxso unstable not perfectone .
FOR BH2 MOLECULE
for linear structure angle HAH =180° where configuration is ,
(2
g
)² (1
u
)² (1
u
)¹
here energy is maximum , so unstable not preferred one
for bent structure,angle is 90⁰ or 90⁰-180
electronic configuration is ,
(2a₁)² (3a₁)² (1b₂)¹ | (2a₁)²(1b₂)² (3a₁)¹
Stabilisation & destabilisation of energy(Emin)
the electronic configuration is preferred one .
The angle is HAH= in between 90⁰-180⁰i.e, 131
FOR H2O MOLECULE
FOR linear structure angle HAH = 180⁰
electronic configuration is , (2
g
)² (2
u
)² (1
u
)⁴
This structure correspondsto maximum energy so destabilize and not perfect one
Now for bent structureangleis 90 degree or 90-180 degree.
electronic configuration is ,
(2a₁)² (3a₁)² (1b₂)² (1b₁)² | (2a₁)²(1b₂)² (3a₁)²(1b₁)²
stabilisation& destabilisation constant(Emin.)
The second electronic configuration is preferred ,
angle is HAH = 90⁰-180⁰, very closeto 90⁰ (104⁰.28˝).

5. 4
This same concept can be applied to other species including non-hydride AB
2
and BAC
molecules, HAB and HAAH molecules, tetra atomic hydride molecules (AH
3
), tetra atomic non
hydride molecules (AB), H
2
AB molecules, acetaldehyde, penta atomic molecules (CH3I), hexa
atomic molecules (ethylene), and benzene.
☺ ☺ ☺ ☺ ☺ ☺

6. 5