Bent Rule and Energetics

Bent Rule and Energetics of Hybridization From DRGP DREAM DOT Hybridisation is the concept of mixing atomic orbitals into ne hybrid orbitals ith different energies! shapes! etc" than the component atomic orbitals" #hen a set of hybrid orbital is constr$cted by a linear combination c ombination of atomic orbitals! the energy of the res$lting hybrids is a eight eighted ed a%erag a%eragee of the energi energies es of the partici participat pating ing atomic atomic orbital orbitals" s" Th This is energy energy of  hybridi&ation is of the order of magnit$de of bond energies and can th$s be important in determining the str$ct$re of molec$les" 'ent r$le encompasses the relationships beteen  bond polarity (ligand electronegati%ity) and central *atom geometry thro$gh their m$t$al connection to central*atom hybridi&ation"

Bent Rule and Energetics of Hybridization According to hybridisation atomic orbitals combine and redistrib$te their energies to form hybrid orbital" These are identical ith respect to energy! shape etc" +hapes of the hybrid orbital depends $pon contrib$tion of s! p orbitals and its affect the energy of hybridisation" 'ent,s r$le states that! -Atomic s character tends to concentrate in orbitals that are directed toard electropositi%e gro$ps and atomic p character tends to concentrate in orbitals that are directed toard electronegati%e gro$ps." /" s orbital orbitalss has lo lo energ energyy than than p orbi orbital tal"" 0" More s character character decrease decrease the the energy of bonding bonding orbitals orbitals and and hence they they ha%e shaped shaped more li1e a s orbital" More p character increase the energy of bonding orbitals and hence they ha%e shaped more li1e a p orbitals" 2" s orbitals orbitals are closer closer to the n$cle$s! n$cle$s! so it stabili&e stabili&e the the lone pair" pair" D$e to more more s character  character  less rep$lsion and less hybridisation energy and less bond angle" 3ice %ersa is tr$e for  more p character" 4" The The most most stable stable arran arrange geme ment nt o$ld o$ld be to $tili&e $tili&e p$re p$re p orbi orbita tals ls for bond bondin ingg and and letting the lone pair into the p$re s orbital" 5" s*Orbi s*Orbitals tals are more penetrati penetrating ng and electron electron density density is less a%ailabl a%ailablee for bondin bonding" g" Th$s! more electronegati%e atoms o$ld be able to ithdra more electron density from p orbitals than from s orbitals" e can also describe bent r$le as -More electronegati%e s$bstit$ents prefer hybrid orbitals ha%ing less s*character and more eletropositi%e s$bstit$ents prefer hybrid orbitals ha%ing more s*character".

Exaamples of Bent Rule and Energetics of Hybridization

6n sp2d Hybridisation one s! three p and one d*orbitals form 5 sp 2d hybridised orbital" All these fi%e hybrid orbitals are not of the same type so they can be di%ided into to non*e7$i%alent sets" The first set is 1non as e7$atorial set of  orbitals" 6t is formed from one s! one p x and one py orbitals" The second set is 1non as axial set" 6t is formed from one p & and one d orbitals" 6t is experimentally obser%ed that the more electronegati%e s$bstit$ent occ$pies the axial position (as it has less s character)that is f and less electronegati%e s$bstit$ents is e7$itorially sit$ated that is cl" 1. sp3d Hybridisation in PClxF!x "

6n the case of sp 2  hybrididsation! 8H 4  or 88l4  formed tetrahedral geometry ith bond angle /9:"5 o" '$t in the case of 8H 0F0! the F*8*F bond angle is less! this explained on the basis of 'ent,s r$le" F is more electronegati%e than H so F*8*F s* character is less than 05; hile in H*8*H it is more than 05;" D$e to less s*character bond angle is less in 8H 0F0" #. $ess bond angle in CH #F# "

6n chemistry! Bent%s rule describes and explains the relationship beteen the orbital hybridi&ation of central atoms in molec$les and the electronegati%ities of s$bstit$ents" ?Atomic s character concentrates in orbitals directed toard electropositi%e s$bstit$ents?"<0= The chemical str$ct$re of a molec$le is intimately related to its properties and reacti%ity" 3alence bond theory proposes that molec$lar str$ct$res are d$e to co%alent bonds beteen the atoms and that each bond consists of to o%erlapping and typically hybridised atomic orbitals" Traditionally! p*bloc1  elements in molec$les are ass$med to hybridise strictly as spn! here n is either /! 0! or 2" 6n addition! the hybrid orbitals are all ass$med to be e7$i%alent (i"e" the n@/ spn orbitals ha%e the same p character)" Res$lts from this approach are $s$ally good! b$t they can be impro%ed $pon by alloing iso%alent hybridi&ation! in hich the hybridised orbitals may ha%e noninteger and $ne7$al p character" 'ents r$le pro%ides a 7$alitati%e estimate as to ho these hybridised orbitals sho$ld be constr$cted" <2= 'ents r$le is that in a molec$le! a central atom bonded to m$ltiple gro$ps ill hybridise so that orbitals ith more s character are directed toards electropositi%e gro$ps! hile orbitals ith more p character ill be directed toards gro$ps that are more electronegati%e" 'y remo%ing the ass$mption that all hybrid orbitals are e7$i%alent sp n orbitals! better predictions and explanations of properties s$ch as molec$lar geometry and bond strength can be obtained" 'ents r$le can be generali&ed to d*bloc1  elements as ell" The hybridisation of a metal center is arranged so that orbitals ith more s character are directed toards ligands that form  bonds ith more co%alent character" E7$i%alently! orbitals ith more d character are directed toards gro$ps that form bonds of greater ionic character "
1 History

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2 Justifcation

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3 Examples

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3.1 Bond angles

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3.2 Bond lengths

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3.3  JCH Coupling constants

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3.4 Inductie e!ect

4 "ormal theory

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# $ee also

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% &e'erences

History

6n the early /:29s! shortly after m$ch of the initial de%elopment of 7$ant$m mechanics! those theories began to be applied toards molec$lar str$ct$re by Pa$ling!<4= +later !<5= 8o$lson!
$tructure o' (uoromethane. )he C*H and C*" +onds are polar and so the electron density ,ill +e shi'ted to,ards car+on in the C*H +onds and to,ards (uorine in the C*" +onds. -irecting or+itals ,ith more s character to,ards the hydrogens is sta+iliing/ ,hile directing or+itals o' less s character to,ards the (uorine is desta+iliing +ut to a lesser extent.

An informal $stification of 'ents r$le relies on s orbitals being loer in energy than p orbitals"<0= 'onds beteen elements of different electronegati%ities ill be polar  and the electron density in s$ch bonds ill be shifted toards the more electronegati%e element" Applying this to the molec$le fl$oromethane pro%ides a demonstration of 'ents r$le"

'eca$se carbon is more electronegati%e than hydrogen! the electron density in the 8*H bonds ill be closer to carbon" The energy of those electrons ill depend hea%ily on the hybrid orbitals that carbon contrib$tes to these bonds beca$se of the increased electron density near the carbon" 'y increasing the amo$nt of s character in those hybrid orbitals! the energy of those electrons can be red$ced beca$se s orbitals are loer in energy than p orbitals" 'y the same logic and the fact that fl$orine is more electronegati%e than carbon! the electron density in the 8*F bond ill be closer to fl$orine" The hybrid orbital that carbon contrib$tes to the 8*F bond ill ha%e relati%ely less electron density in it than in the 8*H case and so the energy of that bond ill be less dependent on the carbons hybridisation" 'y directing hybrid orbitals of more p character toards the fl$orine! the energy of that bond is not increased %ery m$ch" 6nstead of directing e7$i%alent sp 2 orbitals toards all fo$r s$bstit$ents! shifting s character toards the 8*H bonds ill stabili&e those bonds greatly beca$se of the increased electron density near the carbon! hile shifting s character aay from the 8*F bond ill increase its energy by a lesser amo$nt beca$se that bonds electron density is f$rther from the carbon" The atomic s character on the carbon atom has been directed toard the more electropositi%e hydrogen s$bstit$ents and aay from the electronegati%e fl$orine! hich is exactly hat 'ents r$le s$ggests" Altho$gh fl$oromethane is a special case! the abo%e arg$ment can be applied to any str$ct$re ith a central atom and 0 or more s$bstit$ents" The 1ey is that concentrating atomic s character in orbitals directed toards electropositi%e s$bstit$ents is more fa%orable than remo%ing s character from orbitals directed toards electronegati%e s$bstit$ents" Examples

'ent,s r$le can be $sed to explain trends in both molec$lar str$ct$re and reacti%ity" After determining ho the hybridisation of the central atom sho$ld affect a partic$lar property! the electronegati%ity of s$bstit$ents can be examined to see if 'ent,s r$le holds" Bond angles

noing the angles beteen bonds is a cr$cial component in determining a molec$lar str$ct$re" 6n %alence bond theory! co%alent bonds are ass$med to consist of to electrons lying in o%erlapping! $s$ally hybridised! atomic orbitals from bonding atoms" Orbital hybridisation explains hy methane is tetrahedral and ethylene is planar for instance" Hoe%er! there are de%iations from the ideal geometries of sp n hybridisation s$ch as in ater  and ammonia" The bond angles in those molec$les are /94"5 and /9C respecti%ely! hich are belo the expected tetrahedral angle of /9:"5" The traditional approach to explain those differences is 3+EPR theory" 6n that frameor1! %alence electrons are ass$med to lie in locali&ed regions and lone pairs are ass$med to repel each other to a greater extent than  bonding pairs"

'ent,s r$le pro%ides an alternati%e explanation as to hy some bond angles differ from the ideal geometry" First! a trend beteen central atom hybridisation and bond angle can be determined by $sing the model compo$nds methane! ethylene! and acetylene" 6n order! the carbon atoms are directing sp 2! sp0! and sp orbitals toards the hydrogen s$bstit$ents" The  bond angles beteen s$bstit$ents are /9:"5! /09! and /9" This simple system demonstrates that hybridised atomic orbitals ith higher p character ill ha%e a smaller angle  beteen them" This res$lt can be made rigoro$s and 7$antitati%e as 8o$lsons theorem (see Formal theory section belo)"

 Io that the connection beteen hybridisation and bond angles has been made! 'ent,s r$le can be applied to specific examples" The folloing ere $sed in 'ent,s original paper! hich considers the gro$p electronegati%ity of the methyl gro$p to be less than that of the hydrogen atom beca$se methyl s$bstit$tion red$ces the acid dissociation constants of formic acid and of acetic acid"<0= Molecule

Bond angle between substituents

1110 -imethyl ether

1*10 ethanol

14.#0 5ater

13.70 6xygen di(uoride

As one mo%es don the table! the s$bstit$ents become more electronegati%e and the bond angle beteen them decreases" According to 'ents r$le! as the s$bstit$ent electronegati%ies increase! orbitals of greater p character ill be directed toards those gro$ps" 'y the abo%e disc$ssion! this ill decrease the bond angle" This agrees ith the experimental res$lts" 8omparing this explanation ith 3+EPR theory! 3+EPR cannot explain hy the angle in dimethyl ether  is greater than /9:"5 6n predicting the bond angle of ater! 'ent,s r$le s$ggests that hybrid orbitals ith more s character sho$ld be directed toards the %ery electropositi%e lone pairs! hile that lea%es orbitals ith more p character directed toards the hydrogens" This increased p character in those orbitals decreases the bond angle beteen them to less than the tetrahedral /9:"5" The same logic can be applied to ammonia! the other canonical example of this phenomenon" Bond lengths

+imilarly to bond angles! the hybridisation of an atom can be related to the lengths of the  bonds it forms"<0= As bonding orbitals increase in s character! the J bond length decreases" Molecule

Average carbon–carbon bond length

1.#4 8

1.# 8

1.4% 8

'y adding electronegati%e s$bstit$ents and changing the hybridisation of the central atoms!  bond lengths can be manip$lated" 6f a molec$le contains a str$ct$re K*A**L! replacement of the s$bstit$ent K by a more electronegati%e atom changes the hybridi&ation of central atom A and shortens the adacent A**L bond" Molecule

Average carbon–fuorine bond length

1.377 8 "luoromethane

1.3#7 8 -i(uoromethane

1.32 8  )ri(uoromethane

1.323 8  )etra(uoromethane

'eca$se fl$orine is so m$ch more electronegati%e than hydrogen! in fl$oromethane the carbon ill direct hybrid orbitals higher in s character toards the three hydrogens than toards the fl$orine" 6n difl$oromethane! there are only to hydrogens so less s character in total is directed toards them and more is directed toards the to fl$orines! hich shortens the 8F bond lengths relati%e to fl$oromethane" This trend holds all the ay to tetrafl$oromethane hose 8*F bonds ha%e the highest s character (05;) and the shortest  bond lengths in the series" The same trend also holds for the chlorinated analogs of methane! altho$gh the effect is less dramatic beca$se chlorine is less electronegati%e than fl$orine" <0= Molecule

Average carbon–chlorine bond length

1.73 8 Chloromethane

1.2 8 -ichloromethane

1.% 8  )richloromethane

1.%% 8  )etrachloromethane

The abo%e cases seem to demonstrate that the si&e of the chlorine is less important than its electronegati%ity" A prediction based on sterics alone o$ld lead to the opposite trend! as the large chlorine s$bstit$ents o$ld be more fa%orable far apart" As the steric explanation contradicts the experimental res$lt! 'ent,s r$le is li1ely playing a primary role in str$ct$re determination"  JCH Coupling constants

Perhaps the most direct meas$rement of s character in a bonding orbital beteen hydrogen and carbon is %ia the / HN /28 co$pling constants determined from IMR spectra" Theory  predicts that J 8H %al$es ill be m$ch higher in bonds ith more s character" <=<:= Molecule

JCH (o the methyl protons)

12# H

ethane

12 H 9cetaldehyde

134 H 1/1/1:)richloroethane

141 H ethanol

14 H "luoromethane

As the electronegati%ity of the s$bstit$ent increases! the amo$nt of p character directed toards the s$bstit$ent increases as ell" This lea%es more s character in the bonds to the methyl protons! hich leads to increased J 8H co$pling constants" nductive e!ect

The ind$cti%e effect can be explained ith 'ent,s r$le"
"ubstituent

#olar substituent constant (larger values imply greater electron$withdrawing ability)

*.3 t:Butyl

. ethyl

1.# Chloromethyl

1.4 -ichloromethyl

2.%#  )richloromethyl "ormal theory

'ents r$le pro%ides an additional le%el of acc$racy to %alence bond theory" 3alence bond theory proposes that co%alent bonds consist of to electrons lying in o%erlapping! $s$ally hybridised! atomic orbitals from to bonding atoms" The ass$mption that a co%alent bond is a linear combination of atomic orbitals of $st the to bonding atoms is an approximation (see molec$lar orbital theory)! b$t %alence bond theory is acc$rate eno$gh that it has had and contin$es to ha%e a maor impact on ho bonding is $nderstood"
orbital to bonds" <4= 6f atoms co$ld only contrib$te hydrogen*li1e orbitals! then the experimentally confirmed tetrahedral str$ct$re of methane o$ld not be possible as the 0s and 0p orbitals of carbon do not ha%e that geometry" That and other contradictions led to the  proposing of orbital hybridisation" 6n that frameor1! atomic orbitals are alloed to mix to  prod$ce an e7$i%alent n$mber of orbitals of differing shapes and energies" 6n the aforementioned case of methane! the 0s and three 0p orbitals of carbon are hybridi&ed to yield fo$r e7$i%alent sp2 orbitals! hich resol%es the str$ct$re discrepancy" Orbital hybridisation alloed %alence bond theory to s$ccessf$lly explain the geometry and properties of a %ast n$mber of molec$les" 6n traditional hybridisation theory! the hybrid orbitals are all e7$i%alent"
is bonded to to gro$ps K and L and L is more electronegati%e than K! then A ill hybridise so that λK  λL" More sophisticated theoretical and comp$tation techni7$es beyond 'ent,s r$le are needed to acc$rately predict molec$lar geometries from first principles! b$t 'ent,s r$le  pro%ides an excellent he$ristic in explaining molec$lar str$ct$res"

$imitation of CF& /" The 8FT ignores the attracti%e forces beteen the d* electrons of the metal ion and n$clear charge on the ligand atom" Therefore all properties are dependent $pon the ligand orbital and their interactions ith metal orbitals are not explained" 0" 6n 8FT model partial co%alencey of metal*ligand bonds are not ta1en into consideration" According to 8FT metal S ligands bonding is p$rely electrostatic" #hich is not so tr$e" 2" 6n 8FT only d* electrons of the metal ion are considerd the other orbitals s$ch as s! p x!  py! p& are not ta1en into consideration" 4" 6n 8FT  orbitals of ligand are not considerd" 5" 8FT mainly affected by spectra chemical series ! hich is as belo> 6 S  'r  S  8l S  F S  OH S  H0O  IH2  8O etc" /" As a ligand are ass$med to be point charges! it is expected that the ionic ligand sho$ld ha%e greater splitting effect" Hoe%er act$ally they fo$nd to be at loer end of the spectrochemical series" 0" Tho$gh OH S in the spectrochemical series lies belo H0O  and  IH2  ! yet it  prod$ces greater splitting effect" 2" 8FT is $nable to explain the relati%e strength of ligands" B" 8FT ga%e no information abo$t  bond formation in ligand" C" 8FT don,t explain the effect of  bond on U9"