Bonds and interactions in crystals: Conformations and Chirality

Master of Crystallography and Crystallization – 2013

T01 – Mathematical, Physical and Chemical basis of Crystallography

Intermolecular Links

Are established between atoms electrically charged andbelonging to two different chemical species.

The chemical species are ions, or molecules. The electricalcharge comes from these species which are ions, or atomsinvolved in a permanent dipole or an induced dipole.

Play a crucial role in the Biocrystallography and Crystal

Engineering.

Intermolecular Forces or Van der Waals Forces

• Forces between permanent dipoles

• Hydrogen bond Forces

• Forces between induced dipoles (London Forces)

Van der Waals Intermolecular Forces

The basis of the forces of van der Waals is the existence of electric dipoles in molecules.

These dipoles may be permanent, short-lived o induced.

Permanent dipoles derive fromelectronic charge asymmetry.

+-

m

+ +

-

H H

O

The permanent dipolar moment is determined by spectroscopy (Stark effect) or by the dielectric constant.

In the water molecule, The O has 0.82 e- in excess and each H0.41 e- indefect.

Dipolar Moment (m)

m/D

CCl4 0

H2 0

H20 1.85

HCl 1.08

HI 0.42

D (Debye): 3.3 x 10-30 C/m(1 ecu/1A)

+ +

-

H H

O -+ + -

Interaction Ion-Dipole that helps the dissolution of ionic crystals in

water. Arrows indicate Ion-Dipole interactions.

Intermolecular Forces

Separation Distance (nm)

0 10 20 30 40 50

Inte

ract

ion

Fo

rce/

Rad

ius

(mN

/m)

-2

-1

0

1

2

3

4

5

6van der WaalsElectrostaticStericDepletionHydrophobicSolvation

Repulsive Forces (Above

X-axis)

Attractive Forces

(Below X-axis)

Intermolecular Forces:

The summation of all interaction energies of a molecule with all other molecules in

a spherical system with size L is:

3n

3n L1

3n

C4Energy

)(

This expression gives us the all important relation of n 3

= Molecular

diameter

L

n

2L

2 drr

r4Cdrr4rWEnergy )(

1L

Long distance contributions to Energy do not occur

ONLY when n 3Since

For n < 3, the size of the system is important (E.g. Gravity: Distant planets and stars

interact)

For n 3, intermolecular force potentials become important

It is also for this reason that:

- As we go to sub micron size distances, properties of material changes –

Intermolecular Forces Start Taking Over !

Intermolecular force potentials for n 3

It is for this reason that:

Bulk properties of material is size independent (unless in the domains of

intermolecular forces)

(Boiling point of water in a test tube = boiling point of water in a bucket)

van der Waals Forces

1873: To explain deviations from ideal gas behavior,

van der Waals proposed a modification to the gas law:

RTbVV

aP

2

Molecules have finite volume (accounted by “b”)

• Attractive forces between the molecules (accounted by “a”)

The relation predicted gas behavior across a larger pressure range

The attractive intermolecular forces between

gas molecules is now known as “ van der Waals forces ”

van der Waals Forces

The three components that constitute van der Waals Forces

The London component is the most dominant.

n = 6 indicates van der Waals forces are short range

Dipole – induced

dipole

Debye

Induced Dipole –

Induced Dipole

London

(Dispersion)

Dipole-dipole Keesom

EquationOrigin of

Interactions

Interaction

Component

6

21

21

2

o

2o1o

r

1

II

II

42

3rw

)()()(

62

ro

o

2

r

1

4

urw

)()(

6

B

2

ro

2

2

2

1

r

1

Tk43

uurw

)()(

- Dipole-dipole interactions are generally weak

- These weak dipole-dipole interactions becomes

significant when 2 interacting dipoles approach each other

closely. e.g. O–-H+, N–-H+, F–-H+

Keesom (dipole - dipole) component

ui (i = 1, 2): dipole moment, o : Permittivity of free space

r : Relative Permittivity, kB: Boltzmann’s constant,

r: distance between dipoles, T: Temperature

6

B

2

ro

2

2

2

1

r

1

Tk43

uurw

)()(

(These strong dipole-dipole interactions are the well known: Hydrogen Bond)

Debye (dipole–induced dipole) component

62

ro

o

2

r

1

4

urw

)()(

O: polarizability,

r: Relative Permittivity

r: distance between dipole and

induced dipole

- Interaction of a polarizable molecule with a dipole

- Polarizablility: Electron cloud of molecule responds to an

electric field by a localized shift

- Debye interactions are independent of temperature

London (Dispersion) component

6

21

21

2

o

2o1o

r

1

II

II

42

3rw

)()()(

Ii (i = 1,2): Ionization Potential

- The most important component of van der Waals interaction

- Keesom and Debye interactions require the presence of at

least 1 permanent dipole, but London interactions do not.

- Hence, London interaction exist between all molecules

- The London interaction component was always known, but

evolved only after the development of quantum mechanics

- Provides molecular level reasoning that at room

temperature

Small molecules (Ar, He, CH4) are gases,

Bigger molecules (hexane, decane) are liquids,

Even bigger molecules (C35H71) are solids.

Intermolecular Van der Waals Forces

The van der Waals forces generate molecular interactionswithout perturbing the chemical reactivity of the involvedmolecules.

Recognized in XIX century as responsibles for thedesviations from the ideal behaviour of real gases ( P =[nRT/V - nb] - [n/V]2 ) and the cohesion of electricalyneutral (as Argon).

Electric charges interact among them and are responsablefor the cohesion of matter, especialy in liquid state andparticularly in biological systems.

• We call weak interactions (4-20 kJ/mol) in oposition to thecovalent unions (C-C: 350 kJ/mol y C-H: 410 kJ/mol) and theionic unions (Cl-/Na+: 785 kJ/mol).

INTERACTIONS• Ion-ion U(r) 1/r

• ion-dipole 1/r2

• dipole-dipole 1/r3

• London 1/r6

• H Bond

• 3/2kT (298K)

• 250 kJ mol-1

• 15 kJ mol-1

• 2 kJ mol-1

• 2 kJ mol-1

• 20 kJ mol-1

• 3.7 kJ mol-1

Intermolecular Van der Waals interactions at 30 °C

Interacction Type kJ/mol

Ion/dipole Na+ ... H2O 60

2 Permanent Dipoles H2O...H2O (structure of H2O) 20

2 Permanent Dipoles =CO...HN= (peptidic union ) 15

Dipoles: permanent and induced H2O...CH2= 10

2 Induced Dipoles =H2C...CH2= (London) 4

2 Induced Dipoles Ar...Ar (London) 4

2 Dipoles (in rotaction) Metane..Cl4C 2

Hydrogen Bond: When the hydrogen atom is

bonded to very electronegative atoms (F, O, N), becomespractically a proton. Being small, these “naked” hydrogenatom strongly attracts (short distance) zones of negative

charge of other molecules

HF

H2O

NH3

Crystals of

benzoic acid

contain pairs of

molecules

associated by

hydrogen

bonds. These

pairs are then

arranged at

levels that are

held together by

dispersion

forces.

Hydrogen Bonds in ADN

Stacking Bases

May 08, 2002 lecture 2/ MBB 222 02-2 4

Non-covalent Bonds

Much weaker than covalent bonds

- these bonds break and reform at

Room Temperature (RT)

‘Transient Bonds’

- however, cumulatively they are very

effective e.g. helix for proteins and

double helix for DNA

Enlaces de hidrógeno

Interiorhydrofobo

skeletondesoxiribose-Phosphate

Hydrogen bonds

Exterior hydrofilo

A: adeninaG: guaninaC: citosinaT: timina

Nitrogenated Bases

nitrogenadas

Electrostatic Repulsion

DNA structure: the double hélixWatson and Crick for DNA (1953)

What is an hydrogen bond?

“Under certain conditions an atom of hydrogen is attracted by rather strong

forces to two atoms instead of only one, so that it may be considered to be

acting as a bond between them” (Pauling, 1939).

D—H……..A

Other definitions of hydrogen bond, X–H…A

“A hydrogen bond is said to exist when (1) there is evidence of a bond,

and (2) there is evidence that this bond sterically involves a hydrogen

atom already bonded to another atom”

“Any cohesive interaction where H carries a positive charge and A a

negative charge (partial or full) and the charge on H is more positive than

on X”

Pimentel and McClellan (1960)

Steiner and Saenger (1993)

D—H……..A Very Strong

D—H………..A Strong

D—H……….….A Weak

Different types of Hydrogen Bonds

Hydrogen bond

Any cohesive

interaction X–H•••A

where H supports a

positive charge and A

one negative charge

(partial or complete)

and the charge on X

is more negative than

on H

O–H···O(-) O–H···O N–H···O

O–H···π N–H···π C–H···O

Os–H···O C–H···Ni C–H···π

Very Strong Strong Weak

[F–H…F]– N–H…O=C C–H…O

Energy (kcal/mol) –15 to –40 – 4 to – 15 < – 4

IR, νs >25% 5-25% <5%

∆(X–H), Å 0.05 to 0.2 0.01 to 0.05 < 0.01

H…A, Å 1.2 to1.5 1.5 to 2.2 2.0 to 3.0

Shorter than

van der Waals 100% ~100% 30-80%

Effect on

packing Pronounced Distinctive Variable

A complex interaction

Hydrogen Bond D—H……..A

A compose interaction which extend to a wide range of

geometries and energies.

Large chemical choice among the groups donor D—H and

acceptor A

Nevertheless, all Hydrogen Bonds have many common

characteristics.

Mainly, their effect on both Structure and Crystal Packing.

Dispersion ForcesOccur between all molecules and are the result of the net attraction force arising between molecules and originates from imbalances in induced charges.

The magnitude of the dispersion forces is dependent on the ease of the electronic cloud distortion. As more voluminous is the molecule greatest are the Dispersion forces.

induced-dipoles (London Forces)

The alkanes boiling point increases with the carbon chain length. Long chain alkanes have more high dispersion forces due to the increase of polarizability of its more extensive electronic cloud.

Liquid Crystals

IntermolecularVan der Waals interactionsImportance in biologic systems

Hydrogen Bonds

Nucleic Acids

Proteins

In the cells of living organisms the weak intermolecular Van der Waals interactions define the physical state

(semi-solid/semi-liquid).

Hydrophobic Union

Lipids and proteinhydrophobic domains

Hydratation of Solutes

Organic Metabolites

Ions

Structure of the living organisms

Water is 75 % of the weight of the cells.

Hydrogen bridges confer on the water itsextraordinary properties (PF: 0 ° C; PE 100 ° C;heat of vaporization: 2.26 J/g).

Hydrogen bridges have a very short half-life (1 x10-9 seg) (“flickering clusters”)

In the liquid water, each molecule forms hydrogenbridges with other 3.4 molecules and ice with 4molecules

Structure of water in living organisms

Water electrostaticaly interacts with the chargedsolutes: amino (+) or carboxyl (-) groups and ions(ion/dipole interaction).

Water form hydrogen bonds with organic soluteswith polar groups: alcohol (-OH), carbonyls (= O),Phosphonyls (= P = O), imino (= NH).

Intracellular water has a high degree oforganization called "structure of water". Anestimated 30-40 % of "fixed water".

The denaturing or fusion of DNA

The process is reversible, adjustable by temperature.

PCR (Polymerase Chain Reaction) technique is based on the denaturationand DNA copy.

The denaturing or fusion of DNA

The fusion temperatureis different for differentDNA (red or blue). Thefusion (temperature ofthe average height ofthe curve) pointdepends on the ionicstrength, pH and thecomposition of DNAbases.

The Hydrophobic union

Long chain fatty acidshave hydrophobic alkylchains, which to beintroduced into thewater, surrounded byhighly ordered watermolecules.

When fatty acid molecules are grouped laterally decreases the number of “ordered" water molecules

Similarly to grouped into micelles, fatty acids expose a hydrophilic surface and minimize the ordering of water molecules system . The micelle stabilizes due to the entropic effect of increasing unordered water.

The Hidrophobic union

Top view generation of a hydrophobic Union each hydrocarbon chain (of 9 C) issurrounded by 4 columns 6 water molecules each of the “solvent cell”

G = H – T S H = H2 –H1 y S = S2 – S1

H calculation (for the described molecular complex):

Break of 12 unions H2O/CH2= + 120 kJFormation of 9 unions =H2C/H2C= - 36 kJFormation of 6 unions H2O/H2O - 120 kJ

H = - 36 kJ

S calculation: Asumming the change water (s) => water (l)

S = 22 J/K . mol of water and 12 moles of water(22 J/K x 12 x 300 K) = 79.2 kJ TS = - 79 kJ

Domains (spaces) hydrophobic shared between molecules, which exclude water molecules are referred to as hydrophobic union.

In reality, there is not a hydrophobic union, but a number of attractions van der Waals type and London type together with the hydrogen bridges of the solvent (water). Hydrophobic unions are responsible for the formation of micelles, biological membranes,

lipid monolayers and bilayers and protein folds.

G = H – T SG = - 36 kJ – 79 kJ

G = - 115 kJEspontaneous Process

Biologic MembranesFormed by a double layer of phospholipids and internal

and peripheral proteins (Singer y Nicholson, 1961)

“It seems to me that experimental study of the scattered radiation, in particular from light atoms, should get more attention, since along this way it should be possible to determine the arrangement of the electrons in the atoms”

P. Debye, Ann. Phys, 1915, 48, 809.

Electron density by x-ray diffraction studies

“Any attempt to determine the state of ionization of atoms in a crystal is likely to fail, since scattering factor curves will differ appreciably only

at angles for which no spectra exist”

R.W. James, The optical principles of X-ray diffaction, 1948

“It would be desirable to base X-ray structure refinements on a more appropriate model, taking proper account of the asymmetry of the several atomic charge clouds and of the modification of the free atom densities due to chemical bonding”

F. L. Hirshfeld, Israel J. Chem. , 1964, 2, 87.

Spherical and non Spherical Atomic ModelsSpheric Diffusion

Same diffusion at the same q Different diffusion at the same q

Spherical atomic modeladopted as routine to solve and refine

Crystal Structures

Non spherical atomic modelNon conventional approximation to the refinement of crystal structures and to

study the chemical bonds.

MODELING

Non Spheric Diffusion

Spherical

Harmonics

Original from the

Atomic Orbitals

May be contracted

or expanded

Non Spherical Atomic Model(multipolar)

Orbital Function

< | >

Orbital Density

+

=

Properties of the Spherical Harmonic functions

problem: density “multi-centric”??

Approximate in terms of linear combination of multicentric base functions

Orbitals vs. multipoles

New properties from the studies of electron density

Atomic, Charges/Moleculars, multipolar moments

Interaction Energies between “building blocks” in crystals

(→ Lattice Energies and lattice properties)

Investigation of the chemical bond:Analysis of deformation densities.Topological Analysis.

Electrostatic Potential

Empirical Analysis of theOrbital populations

ρ (r)

New properties from the studies of electron density

• Analysis of static electron density and electrostatic potential; • Analysis of interatomic interactions; • “atoms in crystals” topology;• Interaction Energies in crystals; • Distributions of energy density;

LiAl(SiO3)2 : Electrostatic Potential Map and evaluation of the electric potential on the atomic positions.

Applications

Electrostatic Interactions

Crystal Energies

Volkov, A.; King, H. F.; Coppens, P.; Macchi, P.

EP

aMM

mMM

Total bond Energy in the Crystal :

-------------------------------------------------

Exchange-Repulsion = 433.18131 kJ/mol

Dispersion = -205.60893 kJ/mol

-------------------------------------------------

Exch.-Rep. + Disp. = 227.57239 kJ/mol

Electrostatic = -334.77971 kJ/mol

-------------------------------------------------

Total de Interaction Energy = -107.20732 kJ/mol

-------------------------------------------------

Molecular multipoles

Exact potential

Distributed atomic multipoles

ICE VIII

Bond length

Conformational Parameters – Form Descriptors

Conformation: The structure or outline of an item or entity, determined by the

arrangement of its parts.

Bond (valence) angle

Dihedral (torsional) angle

The C-O-H plane is rotated counterclockwise about the C-O bond from

the H-C-O plane.

Improper dihedral (torsional) angle

Bond length calculation

jizzyyxxd ijijijij 222

xi yi

zi

xj

zj

xj

jkji

jkij

jkjijkjijkji

ijk

jk

jk

ji

ji

jkji

jkji

dd

zzzzyyyyxxxx

uu ˆˆ

cos

ijk

i

j

k

Bond angle calculation

i

j

k

l

bijkl

a

b

ba

Dihedral angle calculation

jklijkkljkij

ijkl

jklijk

jklijk

klij

ijkl

ddd

jkklji

dd

klji

b

b

sinsinsin

sinsin

coscos

cos

ba

ba

Conformation of the proteins

All proteins have a NATIVE state, a characteristic tridimensionalform known as CONFORMATION.

The conformation can be described interms of different structural levels

1ry, 2ry, 3ry and 4ry structures

Tridimensional Ordering

Concerns the ordering of the covalentskeleton of the polypeptidic chain,

GIVEN BY THE SEQUENCE OF aminoacids

1ry Structure

Will be determining the tridimensional ordering to be adopted by the protein

Different forces participate in the estabilization of the peptidic skeleton in order to reach the

tridimensional conformation

Hydrogen bonds

Hidrofobic interactions

Electroestatic atraction

NON COVALENT

COVALENT S-S Bidges

2ry, 3ry and 4ry Structures

• - helix (like a cylinder)

• b - sheet (fold)

• Turns (, b, )

• Random coil (desordered)

Different spacial dispositions or 2ry

structures

Conformation -helix

link C=O of rn

with N-H of rn+4

ALL RESIDUES GET BONDED by H-bond in thesame polipeptidic chain

Conformation b

- Sheet fold

Antiparallel

Parallel

b - Sheet fully extended !

H bond between the NH and CO groups of different polipeptidicchains

Turns

1/3 of the aminoacids are found on turns orloops where the CHAINS INVERT the their

direction

b turns

The C=O group of one residue n bonded by H bondwith the NH groupof residue (n+3)

3ry Structure

Concerns the way in which the polipeptidicchain folds or curvs itself to

produce the folded o compact structureof the soluble proteins

Forces participating in the estabilization of theterciary structure

Cisteine, with sulphur containing lateral chains (S), may oxidateand form S-S BRIDGES

4ry Structure

Only present in proteins with more thanone polipeptidic chain

May participatecovalent and non covalent bonds

CONFORMATION OF PROTEINS

hierarchic structure

Sequence of aminoacids of thepeptidic skeletonand S-S

Array / distribution / ordering of the skeletonand lateral chains of the

protein in space

Describes the tridimensional order of the

protein

Stereochemistry

• The properties of many drugs depends on their stereochemistry:

CH3

HN

CH3

O

Cl

NH

O

Cl

NH

(S)-ketamine

CH3

HN

CH3

O

Cl

NH

O

Cl

NH

(R)-ketamine

anesthetic hallucinogen

La Coupe du Roi

Types of Stereoisomers

• Two types of stereoisomers:

– enantiomers

• two compounds that are nonsuperimposable mirror images of each other

– diastereomers

• Two stereoisomers that are not mirror images of each other

• Geometric isomers (cis-trans isomers) are one type of diastereomer.

(R) And (S) Nomenclature

• Stereoisomers are different compounds and often have different properties.

• Each stereoisomer must have a unique name.

• The Cahn-Ingold-Prelog convention is used to identify the configuration of each asymmetric carbon atom present in a stereoisomer.

– (R) and (S) configuration

(R) and (S) Nomenclature

• The two enantiomers of alanine are:

Natural alanine Unnatural alanine(S)-alanine (R)-alanine

CO2H

C

H2NH CH3

CO2H

C

H3C NH2

H

C

H

H3C

OCH2CH

3

Cl

(R) and (S) Nomenclature

1

23

4

Example priorities:

I > Br > Cl > S > F > O > N > 13C > 12C > 3H > 2H > 1H

C

CH3

NH2

FH

12

3

4

R,S Rules

A) Absolute Configuration

1) +/- tell us the interaction of light, not the exact structure of enantiomers

2) X-Ray Crystallography gives us Absolute Configuration

a) Crystals are regularly arranged solid forms

b) They Diffract X-rays regularly, so we can tell what atom is where

c) X-Ray and Polarimetry lets us match +/- with a specific structure

d) Similar molecules usually have same +/- correlation

B) R/S Labels

1) Cahn-Ingold-Prelog System assigns name to each enantiomer

2) Arrange substituents with lowest priority in back

a) Clockwise arrangement high-to-low = R (rectus = right)

b) Counterclockwise = S (sinister = left)

A

B

D

C

A

B

D

C

R enantiomer S enantiomer

Louis Pasteur 1822-1895

The scientific contributions of Pasteur were among the most valuable in the history of science,and he is claimed equally by chemistry and microbiology. Best known to chemists for his work on the tartaric acids, he recognized the structural relationships (now called chirality)responsible for optical isomerism, and that microorganisms can distinguish between enantiomers. Pasteur also showed that micro-organisms cause fermentation andvarious diseases, and he developed methods for "pasteurization" and for vaccination against anthrax and rabies. His work saved the wine,beer, and silkworm industriesfor France.

C

COO

H

HOCH3

CCH3

HHO

COO

C

H3N

H

H3C

C

H3N

H

H3C

C

COO H3NCH3

H

HOCH3

CCH3

HHO

COO H3NCH3

C

COOH

H

HOCH3

CCH3

COOH

HHO

+

(R) salt

(S) salt

CH3NH2

(R)

(S)

MirrorEnan-tiomer

C

COOH

H

HOCH3

CCH3

COOH

HHO

+

(R)

(S)

C

NH2

HH3C

(R)-1-PhenylamineAn R,R-salt

An S,R-salt

Resolution of racemic lactic acid

Dia-stereomer

X-ray crystallography can be used to determine the absolute

configuration of Chiral molecules when they crystallize in non

centrosymetric space groups. To understand how it is possible,

we must consider the effect of the "anomalous Dispersion" in

structure factors.

The "normal" elastic scattering.

The "Anómalous" dispersion refers to elastic effects

that are delayed due to absorption by atoms.

While this effect is not observable

in centrosymmetric crystals (where

Fhkl is real), it is observable in the

acentric crystals.

Annomalous Dispersion & Absolute Configuration

While this effect is not observable in a Centro-symmetric Crystal (where

Fhkl is real), it has an effect, however in the acentric crystals: Friedel law

is not valid in this second case. Given that the anomalous diffusion is a

delay, we can consider that the phase difference associated with this

delay (shown with red vectors) will be in the same "direction" (the angle

between the vector of dissemination and the vector of anomalous

diffusion is the same).

Modern detectors can

measure differences in

intensities between

reflections that would be

equivalent in accordance

with the law of Friedel. It

should be noted that in the

past, the anomalous

dispersion required the

presence of heavy atoms.

This requirement is not

necessary for the majority of

molecules using current

technology.

If there is no appreciable

Anomalous Dispersion resulting

structure factors are equivalent.

The values of the resulting

structure factors are altered when

there is Anomalous Dispersion.

Since the law of Friedel does not verify strictly structures in

non-centrosymmetric, there will be differences in intensities

of the reflections which should be equal. These reflections

are known as Bijvoet pairs.

For space groups not centrosimetricos we can then compare F (hkl) and F(-h-

k-l) to determine the absolute configuration.

This can be carried out by calculating F(hkl) and F(-h-k-l) to the structural

model and the same inverted model and comparing the figures calculated

from the experimental data.

F(obs) xyz model-F(calc) -x-y-z-model-

F(calc)

F(hkl) 200 160 190

F(-h-k-l) 180 150 170

The calculation is repeated for several hundred reflections confirm the

absolute configuration of the molecule.

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J.N. Israelachvili, (2008). Ed. Elsevier Publishing Company

* Crystallography and the World of Symmetry. S.K. Chatterjee, (2008). Ed. Springer

* The Nature of the Hydrogen Bond: Outline of a Comprehensive Hydrogen Bond Theory.

G. Gilli & P. Gilli (2009). Ed. Oxford University Press

Bonds and interactions in crystals: Conformations and Chirality

Master of Crystallography and Crystallization – 2013

T01 – Mathematical, Physical and Chemical basis of Crystallography

END