Understanding Understanding weak interactionsweak interactions

““Symmetry E72 Symmetry E72 (Fish and Boats)”(Fish and Boats)”

by M.C. Escher - 1949by M.C. Escher - 1949

““Symmetry E70 Symmetry E70 (Butterflies)”(Butterflies)”by M.C. Escher - 1948by M.C. Escher - 1948

Understanding the origins and magnitudes of Understanding the origins and magnitudes of weak interactionsweak interactions

Molecular crystals being made up of molecules are affected Molecular crystals being made up of molecules are affected by intramolecular and intermolecular forces:by intramolecular and intermolecular forces:• Intramolecular forces affect the Intramolecular forces affect the physical propertiesphysical properties and and shapeshape

of molecules which are important in crystal packingof molecules which are important in crystal packing

• The intermolecular forces are generally much The intermolecular forces are generally much weakerweaker and and short-rangeshort-range in their effect in their effect

This combination of This combination of strong and weak introduces diversitystrong and weak introduces diversity in in the properties of molecular crystalsthe properties of molecular crystals

This is in contrast to simple ionic crystals which are This is in contrast to simple ionic crystals which are dominated by dominated by strong long-range columbic forcesstrong long-range columbic forces

Understanding the origins and magnitudes of Understanding the origins and magnitudes of weak interactions weak interactions contd.contd.

Understanding the Understanding the originsorigins and and magnitudesmagnitudes of intermolecular forces is of intermolecular forces is therefore necessary to understanding the properties of molecular therefore necessary to understanding the properties of molecular crystalscrystals

In particular it is necessary to understand their dependence on the In particular it is necessary to understand their dependence on the following:following:• molecular propertiesmolecular properties• intermolecular intermolecular separationseparation• intermolecular intermolecular orientationorientation

The understanding of intermolecular interactions in the context of The understanding of intermolecular interactions in the context of crystal packing and the utilization of such understanding in the design crystal packing and the utilization of such understanding in the design of new solids with desired physical and chemical properties is in fact of new solids with desired physical and chemical properties is in fact the focus of two closely related fields: the focus of two closely related fields: crystal engineering and crystal engineering and supramolecular chemistrysupramolecular chemistry

Crystal EngineeringCrystal Engineering The field of crystal engineering aims to The field of crystal engineering aims to predict and control predict and control

crystal assemblycrystal assembly, and hence , and hence structurestructure, solid state , solid state propertiesproperties and and reactivityreactivity..

Has a role to play in many fieldsHas a role to play in many fields: materials design, binding : materials design, binding of dyes onto clothing, the understanding of bone growth, of dyes onto clothing, the understanding of bone growth, the formation of clatharate hydrates which block pipes in the formation of clatharate hydrates which block pipes in the oil industry, melting point suppression, the oil industry, melting point suppression, etcetc..

Has found application in the Has found application in the field of “green” chemistryfield of “green” chemistry where reactions are carried out without the use of solvents, where reactions are carried out without the use of solvents, and where the reactions observed often do not have and where the reactions observed often do not have solution phase counterparts.solution phase counterparts.

Some examples of weak interactions in actionSome examples of weak interactions in action

Van Der Waals ForcesVan Der Waals Forces

Dipole-dipoleDipole-dipoleDipole-induced dipoleDipole-induced dipole

Dispersion/London forcesDispersion/London forces

IN

All interactions reflect a balance between attractive and repulsive forcesAll interactions reflect a balance between attractive and repulsive forces

Interaction between dipolar moleculesInteraction between dipolar molecules The electric field produced by a dipole The electric field produced by a dipole μμ along its own along its own

direction at a distance direction at a distance rr from its centre is from its centre is 22μμ//rr33

For two dipoles aligned head to tail at a distance For two dipoles aligned head to tail at a distance rr apart, the apart, the interaction energy interaction energy UU between them is given by: between them is given by:

UU = -2 = -2μμ11μμ22//rr33

Interaction between dipolar molecules Interaction between dipolar molecules contd.contd.

However, in crystals the dipoles will not be necessarily be However, in crystals the dipoles will not be necessarily be well aligned with each other. well aligned with each other.

By considering:By considering:• the random orientation of the dipoles,the random orientation of the dipoles,• defining their relative orientations using polar coordinates,defining their relative orientations using polar coordinates,• and including attractive and repulsive interaction components, and including attractive and repulsive interaction components,

the following equation may be obtained: the following equation may be obtained:

UU = -( = -(μμ11μμ22//rr33){2cos ){2cos θθ11coscos θ θ 22 - sin - sin θ θ11sinsin θ θ22cos(φcos(φ1 - 1 - φφ22)})}

Attractive component Repulsive component

Interaction between dipolar molecules Interaction between dipolar molecules contd.contd.

UU = -( = -(μμ11μμ22//rr33){2cos ){2cos θθ11coscos θ θ 22 - sin - sin θ θ11sinsin θ θ22cos(φcos(φ1 - 1 - φφ22)})}

The above equation shows that the interaction energy The above equation shows that the interaction energy between two dipoles in a crystal will be inversely between two dipoles in a crystal will be inversely proportional to proportional to rr33

The equivalent equation for an interaction between two The equivalent equation for an interaction between two dipoles in solution has a dependence proportional to dipoles in solution has a dependence proportional to rr66

The dipole-dipole interaction in the solid-state therefore has The dipole-dipole interaction in the solid-state therefore has a longer effective rangea longer effective range

Lastly, and most importantly the above equation has Lastly, and most importantly the above equation has repulsiverepulsive and and attractiveattractive components so components so depending on the depending on the relative orientations of the dipoles this interaction can be relative orientations of the dipoles this interaction can be attractive or repulsiveattractive or repulsive

Dipole-induced dipole interactionsDipole-induced dipole interactions The electric field of one dipole can The electric field of one dipole can induceinduce a dipole on a a dipole on a

second second polarizablepolarizable molecule molecule

This interaction is dependent on the component This interaction is dependent on the component μμ11 of the of the electric field of the dipole along the line joining it and the electric field of the dipole along the line joining it and the molecule centered at distance molecule centered at distance rr

It is also dependent on the polarizability It is also dependent on the polarizability αα22 of the second of the second moleculemolecule

The interaction between the dipole and induced dipole is The interaction between the dipole and induced dipole is given by the following equation:given by the following equation:

UU = -4 = -4αα22μμ1122//rr66

Note the dependence proportional to Note the dependence proportional to rr66 indicating that this indicating that this is a very short range interactionis a very short range interaction

Dipole-induced dipole interactions Dipole-induced dipole interactions contd.contd.

In contrast to dipole-dipole interactions, this interaction is In contrast to dipole-dipole interactions, this interaction is always attractivealways attractive as only the magnitude of the interaction as only the magnitude of the interaction depends on the relative orientations of the two moleculesdepends on the relative orientations of the two molecules

Since polar molecules can also be polarized, this interaction Since polar molecules can also be polarized, this interaction also contributes to the total interaction energy between the also contributes to the total interaction energy between the two dipolar molecules, i.e.two dipolar molecules, i.e.

UUtotaltotal = = UUdipole-dipoledipole-dipole + Σ + ΣUUdipole-induced dipoledipole-induced dipole

Dispersion/London forcesDispersion/London forces

Non-polar molecules can interact with each other even Non-polar molecules can interact with each other even though they do not have permanent dipolesthough they do not have permanent dipoles

A dipole in one molecule can be created from small A dipole in one molecule can be created from small instantaneous and transientinstantaneous and transient changes in the positions of changes in the positions of electrons (charge displacements = electrons (charge displacements = rr11 = x = x11yy11zz11) in the ) in the molecule leading to a transient dipolemolecule leading to a transient dipole

This transient dipole can then This transient dipole can then induce a dipoleinduce a dipole in the second in the second molecule with the appropriate charge displacementsmolecule with the appropriate charge displacements

These These two dipoles attracttwo dipoles attract each other leading to a decrease in each other leading to a decrease in the potential energy of the systemthe potential energy of the system

The attraction between the molecules depends strongly on The attraction between the molecules depends strongly on their their polarizabilitypolarizability

Dispersion/London forces Dispersion/London forces contd.contd. The total potential energy is therefore made up from the The total potential energy is therefore made up from the

energy needed to produce the dipoles (I) and the energy of energy needed to produce the dipoles (I) and the energy of interaction between the two resulting dipoles (II)interaction between the two resulting dipoles (II)::

UU = = ee22rr11

22/2/2αα + + ee22rr2222/2/2αα + ( + (ee22//rr33)()(xx11xx22 + + yy11yy22 - 2 - 2zz11zz22))

Allowing for notation Term II is the same as the equation for Allowing for notation Term II is the same as the equation for a dipole-dipole interaction that was shown earliera dipole-dipole interaction that was shown earlier

UU = -( = -(μμ11μμ22//rr33){2cos ){2cos θθ11coscos θ θ 22 - sin - sin θ θ11sinsin θ θ22cos(φcos(φ1 - 1 - φφ22)})}

Note that the repulsion term is present. This is because Note that the repulsion term is present. This is because transient dipoles can also be repulsivetransient dipoles can also be repulsive. However, because . However, because of of inductioninduction the interaction is on the interaction is on average attractiveaverage attractive and not and not zero as one would expect. (See Atkins)zero as one would expect. (See Atkins)

I II

(1)

Dispersion/London forces Dispersion/London forces contd.contd. An alternative and more powerful form of equation (1) can An alternative and more powerful form of equation (1) can

be obtained by expressing the transient dipole as an be obtained by expressing the transient dipole as an oscillator:oscillator:

EE00 = 3 = 3hvhv00 - (3/4) - (3/4)hvhv00αα22rr-6-6 + ....... + .......

The The 33hvhv00 term is the z term is the zero point energy of the two isolated species (depends on the ionization energy of each species) while the second term is the attractive dispersion energy

v0 is the characteristicc frequency of one of the species (how frequency of one of the species (how often it “flickers”) often it “flickers”)

The attraction between the molecules depends strongly on The attraction between the molecules depends strongly on their their polarizabilitypolarizability

(2)

Dispersion/London forces Dispersion/London forces contd.contd. In practice, more complex charge displacements can occur In practice, more complex charge displacements can occur

between molecules leading to between molecules leading to quadrupoles and higher quadrupoles and higher multipolesmultipoles

The true dispersion force experienced by a molecule is The true dispersion force experienced by a molecule is therefore better described by the following equation:therefore better described by the following equation:

UUdispersiondispersion = = cc66rr-6-6 + + cc88rr-8-8 + + cc1010rr-10-10 + ........ + ........ where where cc66,, cc88

etc. are constants.etc. are constants.

Quadropoles and higher terms have often been neglected Quadropoles and higher terms have often been neglected but can be very important. In CObut can be very important. In CO22 the heat of sublimation at the heat of sublimation at 0 K (27 kJ/mol) has been found to be 0 K (27 kJ/mol) has been found to be 45% due to 45% due to quadropole-quadropole interactions and 55% due to simple quadropole-quadropole interactions and 55% due to simple dispersion interactionsdispersion interactions..

Final comments on VDW forcesFinal comments on VDW forces

Dipole-dipole, dipole-induced dipole and dispersion forces Dipole-dipole, dipole-induced dipole and dispersion forces are often collectively referred to as are often collectively referred to as van der Waals forcesvan der Waals forces

The above expressions show that VDW forces should be The above expressions show that VDW forces should be largest between polar or very polarizable moleculeslargest between polar or very polarizable molecules

In general polarizability is known to increase with In general polarizability is known to increase with increasedincreased molecular volumemolecular volume (larger molecules) and increased (larger molecules) and increased numbers of numbers of ππ bonds bonds

Interaction typeInteraction type Distance Distance dependencedependence

Typical energy/(kJ molTypical energy/(kJ mol-1-1))

Ion-ionIon-ion 1/r1/r 250250

Ion-dipoleIon-dipole 1/r1/r22 1515

Dipole-dipoleDipole-dipole 1/r1/r33 22

DispersionDispersion 1/r1/r66 22

H-bondH-bond NANA 2020

Comparison of interaction energies (Atkins – 8th edition)

Repulsive forcesRepulsive forces The closest distance molecules can reach each other is the The closest distance molecules can reach each other is the

point where point where attractiveattractive and and repulsive forcesrepulsive forces are exactly in are exactly in balancebalance

The repulsive forces start becoming significant when the The repulsive forces start becoming significant when the electron clouds of electron clouds of two molecules begin to overlaptwo molecules begin to overlap

There are two sources for this force:There are two sources for this force:• The Pauli exclusion principle – maximum of 2 electrons per The Pauli exclusion principle – maximum of 2 electrons per

orbital with opposite spinsorbital with opposite spins• Decreased electron density in areas where overlap has Decreased electron density in areas where overlap has

occurred hence occurred hence less effective shieldingless effective shielding and hence greater and hence greater coulombic repulsion between the nuclei on the two moleculescoulombic repulsion between the nuclei on the two molecules

Repulsive forces Repulsive forces contd.contd. Repulsive forces are very difficult to calculate since they Repulsive forces are very difficult to calculate since they

depend on the shapes and nature of the molecule of depend on the shapes and nature of the molecule of interestinterest

Instead, empirical potentials are used and these tend to Instead, empirical potentials are used and these tend to have the form have the form

arar--nn ( (nn equal to equal to 1212 usually) or usually) or bebe--crcr with with aa, , bb, , cc and and nn being empirically determined constants being empirically determined constants for individual atoms types for individual atoms types

Since repulsion forces are inversely dependent on Since repulsion forces are inversely dependent on rr1212, they , they are only important at very close rangeare only important at very close range

Also, the above equations assume isotropic repulsions Also, the above equations assume isotropic repulsions between atoms. In practice anisotropic versions of these between atoms. In practice anisotropic versions of these equations are used as these better describe the behavior of equations are used as these better describe the behavior of real crystal structures.real crystal structures.

Summing attractive and repulsive components together – Summing attractive and repulsive components together – atom-atom potentialsatom-atom potentials

UU = ( = (qqiiqqjj)/()/(DrDrijij) + ) + AA//rrijij1212 - - CC//rrijij

66

Where Where qqii and and qqjj are the fractional charges on the atoms,are the fractional charges on the atoms, DD is the effective dielectric constant, is the effective dielectric constant, AAklkl is the repulsive coefficient, is the repulsive coefficient, and and CCklkl the attractive coefficient. the attractive coefficient. If one removes the electrostatic If one removes the electrostatic

component (to make the above equation component (to make the above equation more general) then one gets left with the more general) then one gets left with the 6:n6:n or or Lennard-Jones’Lennard-Jones’ form: form:

UUklkl((rrijij) = ) = AAklkl//rrijij

1212 - - CCklkl//rrijij66

Some typical atom-atom potentials as implemented in a typical lattice energy program

What about H-bonding?What about H-bonding?

UU = ( = (qqiiqqjj)/()/(DrDrijij) + ) + AA//rrijij1212 - - CC//rrijij

66

1 kcal = 4.184 kJ

H-bonding H-bonding contd.contd.

H-bonding H-bonding contd.contd. Strong H-bondsStrong H-bonds ( (ionic hydrogen bondsionic hydrogen bonds) are formed by groups ) are formed by groups

containing an containing an electron density deficiencyelectron density deficiency on the donor on the donor group, i.e. OHgroup, i.e. OH++, NH, NH++, or an , or an excessexcess of electron density in the of electron density in the acceptor group, i.e., Facceptor group, i.e., F--, OH, OH--, C-O, C-O--, P-O, P-O-- etc. etc.

Moderate H-bondsModerate H-bonds are are generally formed by neutral donor generally formed by neutral donor and acceptor groupsand acceptor groups, i.e., OH, NH, and –O-, C=O, N, i.e., OH, NH, and –O-, C=O, NArAr in which in which donor atoms are electronegative to the H-atom and acceptor donor atoms are electronegative to the H-atom and acceptor atoms have unshared lone-pair electrons.atoms have unshared lone-pair electrons.

Weak H-bondsWeak H-bonds are formed when the H-atom is are formed when the H-atom is covalently covalently bonded to a slightly more electronegative atombonded to a slightly more electronegative atom, as in C-H, , as in C-H, Si-H, or when the acceptor has Si-H, or when the acceptor has no lone pairsno lone pairs but has but has ππ electrons.electrons.

H

H

H

O O

O O

H

H

H O

H

OH

H

CH3

O

O

O

O

O

O

a) b) c)

H-bonding H-bonding contd.contd.

H-bonding H-bonding contd.contd. H-bonds have group-pair properties,H-bonds have group-pair properties, e.g., P-OH, H-O-H and e.g., P-OH, H-O-H and

C-OH have different donor and acceptor abilities resulting in C-OH have different donor and acceptor abilities resulting in different H-bonds with different D…A distances and angles. different H-bonds with different D…A distances and angles.

Covalent interactions on the other hand are more Covalent interactions on the other hand are more atom-atom-atom pair in natureatom pair in nature. This means that C-C, C=C, C-N etc . This means that C-C, C=C, C-N etc bonds can be more easily classified into typical bond bonds can be more easily classified into typical bond lengths and angles, VDW and covalent radii etc…lengths and angles, VDW and covalent radii etc…

TypeType Functional group involvedFunctional group involved

Reliable donorReliable donor -OH, -NH-OH, -NH22, -NHR, -CONH, -NHR, -CONH22, -CONHR, -COOH, -CONHR, -COOH

Occasional donorOccasional donor -COH, -XH, -SH, -CH-COH, -XH, -SH, -CH

Reliable Reliable acceptoracceptor

-COOH, -CONHCO-, -NHCONH-, -CON<, >P=O, -COOH, -CONHCO-, -NHCONH-, -CON<, >P=O, >S=O, -OH>S=O, -OH

Occasional Occasional acceptoracceptor

>O, -NO>O, -NO22, -CN, -CO, -COOR, -N<, -Cl, -CN, -CO, -COOR, -N<, -Cl

Three- and four-centre H-bondingThree- and four-centre H-bonding One of the consequences of H-bonding being mostly One of the consequences of H-bonding being mostly

electrostatic in nature is its ability to form electrostatic in nature is its ability to form bifurcated (3 bifurcated (3 centre) and trifurcated (4 centre) bondscentre) and trifurcated (4 centre) bonds, i.e., it is possible , i.e., it is possible for an H-atom to interact with more than one acceptor. for an H-atom to interact with more than one acceptor.

These commonly occur when the These commonly occur when the number of acceptors number of acceptors exceed the numbers of donorsexceed the numbers of donors in a crystal, e.g. in in a crystal, e.g. in carbohydrates, nucleosides and nucleotides where a lot of carbohydrates, nucleosides and nucleotides where a lot of ether (R-O-R) or carbonyl groups are present.ether (R-O-R) or carbonyl groups are present.

A

A

D H

A

AA N+

HH

H

A

AA N+

HH

H

A

A A

A

AA

N+

HH

H

2- and 3-centre H-bonds typically found in amino acid structures

Three- and four-centre H-bonding Three- and four-centre H-bonding contd.contd.What are the criteria for picking out trifurcated H-bonds?What are the criteria for picking out trifurcated H-bonds?

1.1. Since the interaction is an attractive one the H atom should lie with Since the interaction is an attractive one the H atom should lie with 0.2 Å0.2 Å from the plane defined by the donor and two acceptor atoms. from the plane defined by the donor and two acceptor atoms.

2.2. Alternatively, the 3 angles around the H atom, Alternatively, the 3 angles around the H atom, a + b + a + b + c ≈ 360°c ≈ 360°..

A

A

D H

a

bc

Resonance assisted hydrogen bonding (RAHB)Resonance assisted hydrogen bonding (RAHB) H-bonding can often be H-bonding can often be assisted by the presence of assisted by the presence of

conjugated conjugated ππ bonds bonds. In effect the . In effect the ππ bonds act to bonds act to cooperatively assistcooperatively assist the H-bond making the interaction the H-bond making the interaction more covalent in character and as a consequence stronger.more covalent in character and as a consequence stronger.

This phenomenon is referred to as Resonance-Assisted This phenomenon is referred to as Resonance-Assisted Hydrogen bonding (Hydrogen bonding (RAHBRAHB).).

HO O

HO O

d1

d2

d3

d4

HOO

HOO

d1

d2

d3

d4

Resonance assisted hydrogen bonding (RAHB) Resonance assisted hydrogen bonding (RAHB) contd.contd.

The effect of RAHB on H-bonding has been illustrated by The effect of RAHB on H-bonding has been illustrated by examining molecules of the following type, in which the examining molecules of the following type, in which the degree of delocalization/conjugation (Q) was determined degree of delocalization/conjugation (Q) was determined from the molecular bond lengthsfrom the molecular bond lengths, and plotted against the H-, and plotted against the H-bond O…O distance. Increased delocalization (lower Q bond O…O distance. Increased delocalization (lower Q values) leads to shorter O…O lengths.values) leads to shorter O…O lengths.

Q = d1 – d4 + d3 – d2

HO O

HO O

d1

d2

d3

d4

HOO

HOO

d1

d2

d3

d4

Principles of Crystal PackingPrinciples of Crystal Packing

Trends Followed by Molecules when Trends Followed by Molecules when Forming a CrystalForming a Crystal

Rule 1Rule 1 Maximize density and minimize free volumeMaximize density and minimize free volume

This is the This is the primaryprimary packing rule in all kinds of crystals and packing rule in all kinds of crystals and is referred to as Kitaigorodsky’s principle of close packingis referred to as Kitaigorodsky’s principle of close packing

It is especially important in polymorphic systems for It is especially important in polymorphic systems for crystals that are stable at T = 0 K where no energy is crystals that are stable at T = 0 K where no energy is available to support more open structures available to support more open structures

At higher temperatures, entropy (At higher temperatures, entropy (TSTS) plays a large role in ) plays a large role in allowing polymorphs with more molecular freedom to occur allowing polymorphs with more molecular freedom to occur

Rule 2Rule 2 Satisfy hydrogen bond donors and Satisfy hydrogen bond donors and

acceptors and any other special kind of acceptors and any other special kind of

intermolecular interactionsintermolecular interactions

H-bonds are very strong in comparison with VDW forces. As H-bonds are very strong in comparison with VDW forces. As a consequence their presence is a consequence their presence is structure determiningstructure determining in in molecular crystals.molecular crystals.

Also, in a structure, the Also, in a structure, the strongeststrongest hydrogen bond hydrogen bond donorsdonors always connect to the strongest hydrogen always connect to the strongest hydrogen acceptorsacceptors

Rule 3Rule 3 Minimize electrostatic energyMinimize electrostatic energy

Like - like repulsive interactions must be minimized in favor Like - like repulsive interactions must be minimized in favor of like - unlike attractive interactions of like - unlike attractive interactions

Lets look now at the observed space Lets look now at the observed space group frequenciesgroup frequencies

Though there are 230 space groups more than Though there are 230 space groups more than 75%75% of all of all organic molecules crystallize in only organic molecules crystallize in only 1010 of these – of these – probably 99% of all molecules crystallize in just 30 space probably 99% of all molecules crystallize in just 30 space groupsgroups

The top ten are: The top ten are: PP2211//cc, , PP-1-1, , PP221122112211, , PP2211, , CC2/2/cc, , PbcaPbca, , PnmaPnma, , PnaPna2211, , PbcnPbcn and and PP11

Now that we have some understanding of the nature of Now that we have some understanding of the nature of weak interactions can we rationalize why these space weak interactions can we rationalize why these space groups are so popular?groups are so popular?• Are some symmetries more favorable than others?Are some symmetries more favorable than others?

Principles of Crystal PackingPrinciples of Crystal Packing

Classification of Symmetries into Classification of Symmetries into Favorable and UnfavorableFavorable and Unfavorable

Inversion centers are favorableInversion centers are favorable In centrosymmetric space groups molecules are related to In centrosymmetric space groups molecules are related to

each across a centre of symmetryeach across a centre of symmetry

Inversion centers are especially favorable for crystal Inversion centers are especially favorable for crystal packing since they packing since they diminish like-like interactionsdiminish like-like interactions and and are compatible with translation.are compatible with translation.

They are unique in that they change the direction but not They are unique in that they change the direction but not the orientation of intermolecular vectors, i.e. the orientation of intermolecular vectors, i.e. minimize the minimize the repulsive component of dipole-dipole interactionsrepulsive component of dipole-dipole interactions

Molecules related by inversion centers are Molecules related by inversion centers are often connected often connected to each other by hydrogen bondingto each other by hydrogen bonding which is an energy which is an energy lowering interactionlowering interaction

H

H

H

O O

O O

H

H

H O

H

OH

H

CH3

O

O

O

O

O

O

a) b) c)

Inversion centers are favorable Inversion centers are favorable contd.contd.

Mirror planes are always occupied, Mirror planes are always occupied, usually by mirror-symmetric moleculesusually by mirror-symmetric molecules

Unoccupied mirror planesUnoccupied mirror planes are especially are especially unfavorableunfavorable because they require like-like interactions between because they require like-like interactions between adjacent molecules adjacent molecules

This symmetry This symmetry maximizes the repulsive componentmaximizes the repulsive component of of the dipole-dipole interactionthe dipole-dipole interaction

If If unoccupiedunoccupied, they , they produce a sheet of empty spaceproduce a sheet of empty space in in the crystal which has serious consequences in terms of the crystal which has serious consequences in terms of packing density. packing density.

Mirror planes are always occupied, Mirror planes are always occupied, usually by mirror-symmetric molecules usually by mirror-symmetric molecules

contd.contd.

Mirror symmetric molecules Note relatively empty space

Groups with 3-, 4- and 6-fold rotation axes do not Groups with 3-, 4- and 6-fold rotation axes do not usually occur unless the axes are located within usually occur unless the axes are located within

molecules of appropriate symmetrymolecules of appropriate symmetry

The reason for this is that it is The reason for this is that it is difficult to fill the space difficult to fill the space around these rotation axesaround these rotation axes unless the molecules have unless the molecules have the shape of the symmetry. The problem is especially acute the shape of the symmetry. The problem is especially acute for 4- and 6-fold axes. How many organic molecules for 4- and 6-fold axes. How many organic molecules containing a 4-fold axis do you know?containing a 4-fold axis do you know?

If If unoccupiedunoccupied, they create an , they create an infinite rod of empty infinite rod of empty space with a diameter of 3-3.5 Åspace with a diameter of 3-3.5 Å in the crystal, hence in the crystal, hence lowering the packing density of the structurelowering the packing density of the structure

To compensate for this, areas where these occur are To compensate for this, areas where these occur are usually filled with disordered solvent leading to the usually filled with disordered solvent leading to the formation of a solvateformation of a solvate

Groups with 3-, 4- and 6-fold rotation axes Groups with 3-, 4- and 6-fold rotation axes contd.contd.

Benzene

Twofold axes are sometimes occupied Twofold axes are sometimes occupied and sometimes notand sometimes not

There seems to be There seems to be no energy gain or loss associated with no energy gain or loss associated with the use of this symmetrythe use of this symmetry

As mentioned for rotation axes above, if they are As mentioned for rotation axes above, if they are unoccupied they unoccupied they can lead to lower packing densitiescan lead to lower packing densities

FinallyFinally 2211 screw axes are more favorable than glide planes screw axes are more favorable than glide planes, which are , which are

comparable to pure translations. comparable to pure translations.

Translations are however still very favorable otherwise crystals Translations are however still very favorable otherwise crystals would not exist. would not exist.

Translations tend to occur together with other symmetry elements, Translations tend to occur together with other symmetry elements, i.e. i.e. PP1 is not that popular1 is not that popular

Having gone through the last few slides have a look at the Having gone through the last few slides have a look at the top 10 space groups again:top 10 space groups again: • PP2211//cc, , PP-1, -1, PP221122112211, , PP2211, , CC2/2/cc, , PbcaPbca, , PnmaPnma, , PnaPna2211, , PbcnPbcn and and PP11

Supplementary – examples of weak interactionsSupplementary – examples of weak interactions