Atoms, ions, molecules y macromolecules

Master of Crystallography and Crystallization – 2013T02 – Mathematical, Physical and Chemical basis of

Crystallography

Elements, Atoms and IonsThe Chemical elements, their names and symbols,

are collected on the PERIODIC TABLE

Dmitri Mendeleev (1834 - 1907)

Atoms of Cooper on a surface of silicium.

• An Atom is the smallest particle of an element mantaining

all chemical properties of the element itself.

Distance = 1.8 nanometers (1.8 x 10-9 m)

COMPOSITIONOf the ATOM

The atom is mainly empty space

• Protons (p+)– electric charge +– mass = 1.672623 x 10-24 g– relative mass = 1.007 units of atomic mass (amu)

may be rounded to 1

• Electrons (e-)– electric charge -– relative mass = 0.0005 amu

may be rounded to 0

• Neutrons (no)– without electric charge – mass = 1.009 amu may be rounded to 1– Has a spin momentum of 1/2

Atomic Number, Z13

Al

26.981

Atomic Number

Atomic Symbol

AVERAGE Atomic Mass

Mass Number, A• # protons + # neutrons

• An atom of boron may have A = 5 p + 5 n = 10 amu

• The Atomic Mass is the AVERAGE of the atomic masses.

A

Z

10

5B

Isotopes

• An element (same Z) different mass number (A)

• Boron-10 (10B) has 5 p y 5 n

• Boron-11 (11B) has 5 p y 6 n 10B

11B

0.20 (10 amu) + 0.80 (11 amu) = 10.8 amu

IONS

• IONS are atoms or groups of atoms charged positive

o negatively.

– Removing an electron of one atom produces a CATION

with positive charge.

– adding an electron to an atom produces an ANION with

negative charge.

Mg --> Mg2+ + 2 e- F + e- --> F-

Depending on the type of atoms joining:

• Metal – Non metal: one gives and other accepts

electrons (cations and anions)

• Non metal – Non metal: both accept electrons,

share electrons

• Metal – Metal: both give electrons

Ionic Bond• The Ionic compound is formed by reacting one metal

with a non metal.

• The atomos of the metal lose electrons (producing a cation) whic are accepted by the non metal (producingan anion).

• The ions of different charge attract electricalyeachother, ordering itselves to form and ionic network.The Ionic compounds are not made of molecules.

• The bond results of the natural force of atraction stablished among ions with oposite charges.

• That forces of attraction keep them united, forming a compound of ionic type.

Ionic Bond between Cl and Na: formation of the ions Cl- and Na+

IonicNetworks

NaCl CsCl

The compounds joint by ionic bonds when are periodicaly ordered usually form crystals.

Metallic Bond

• The metalic substances are made of atomos of the same metallicelement (low electronegativity).

• The atoms of the metallic element may lose some electrons,producing one cation or “metallic rest”.

• Producing at the same time a Cloud or sea of electrons: set offree electrons, delocalized, which do not belong to any particularatoms.

• The cations repel each other, but are attacted by the sea ofelectrons existing among them. This is the way to form a metallicnetwork: metalic sustances neither are formed by discretemolecules.

The model of the cloud of electrons represents the metal as a set of cations occupaying the fixed positions of the network, being the free electrons moving easily, without being confinated/attached to any especific cation.

Fe

Covalent BondCovalent compounds originates by Sharing Electrons

among non metallic atoms.

Electrons highly localized.

This type of bonds is stablished among a group of special atoms, called the non metallic elements.

Their atoms have simmilar forces of electricalattraction, for that reason share valence electrons

when participate in one bond of such type.

Covalent Bond and Molecules

• Atoms bonded by covalent bonds form individualparticles maned molecules.

• So, a molecule is any stable set of two or moreatoms bonded covalently, but many may havehundreds or thousands of bonded atoms.

• Covalent bonding allowsthe formation of molecules of elements(H2, O2, N2), whencambinating atomos of the same element, and molecules of compounds (H2O, CH4, when combining atomsof diferent elements.

There Exist molecules, or are really giant structures?

• Covalent Networks

• Covalent Molecules (Small - Macromolecules)

Diamond: tetraedra of carbon atoms

Grafite: layers of carbon atoms

The union between atoms sharing

electrons is very strong, very dificult

to break. The shared electrons are highly

localized.

Topological Characterization of Bonds

maxima, minima and saddle points critical points

x, y,z Electron density, : derivable function

r r

x, r

y, r

z

r c 0

Gradient zero: neccesary condition for maximum,

minimum or saddle point

H r

2

x2

2

x y

2

xz

2

y x

2

y2

2

yz

2

z x

2

z y

2

z 2

Range (): number of non zero eigenvalues

Signature (): N. positive - N. negative eigenvalues

mathematical nature

(, )

denomination

(Bader´s theory)

maximum (3, -3) tridimensional atractor

second order saddle point (3, -1) bond critical point

first order saddle point (3, 1) ring critical point

minimum (3, 3) cage critical point

Alows to derive the nature of the bond from the electron density

Type of interaction and bond multiplicity

From the density at the bond critical point, b

Bond Anisotropy

Bond Elipticity,

1

2

2

1

2

1

1

012

1

n

2

22.012

1

n

character of the threemembered rings

High elipticity

Nuclea + Bonds

Nuclear Positions

accesible theoretically and experimentally

ACCESIBLE FROM

X-RAY DIFFRACCION

Uncertainty Sources in the Fourier map

Uncertainty on the

Identification

Single Peaks

Uncertainty on the existence

of a chemical bond

Pairs of Peaks

Entropy associated to the

Atomic Nature S(A )

Entropy associated to the

connectivity S(C)

Total Entropy associated to a Fourier map

S ( F ) = S ( A ) + S ( C )

V & E d: R3 x R3 R

COMPOSITION CONSTITUTION

CONFIGURATION

AND

CONFORMATION

TOPOLOGICAL SPACE

(adimensional space)

TOPOLOGICAL

MOLECULAR STRUCTURE

or MOLECULAR GRAPH

EUCLIDEAN METRIC SPACE

(3-D Space)

GEOMETRICAL

MOLECULAR STRUCTURE

M = (V, E, d)

EMPIRICAL FORMULA

C16O3

O

O

OG = (V, E)

Algebraic

Representatio

n

Diagramatic

Representation

Topological

Interpretation of

Fourier Maps

Structural

Refinement

II

I

? ? ?

?

???

??

? ?

? ?

?

?

?

III

Access toMolecularProperties

Electron Density:

(r) = ... ({r,s})*({r,s})dVdS

Spatial coordinates Wavefunction of many electrons

Hohenberg&Kohn (1964):

1) The electron density defines univocally the electronic fundamental state of

atoms, molecules and crystals.

2) The electron density provides a minimum of the energy functional.

E[] = G[] + ENe [] + Eee[] + Exc []

kinetic energy electron- electron energy

electron-nuclear energy change and correlation energy

Five characteristics of the atomic and molecular

interactions :

(rb), 2 (rb), g (rb), v (rb), E (rb)

Ee(r) = g (r) + v (r)

Atomic and molecular interactions characterized in terms

of bond critical points(acording to Bader, Bianchi, Espinosa, Macchi, Tsirelson y otros)

covalent and covalent-polar bonds

Vb << 0

gb << Vb

Eb << 0

Dative bonds

Vb < 0

gb Vb

Eb < 0

Metallic bonds

Vb < 0

gb Vb

Eb < 0

Ionic bonds

Vb < 0

gb Vb

Eb 0

vdW and H-bonds

Vb < 0

gb Vb

Eb 0

‘Shared’ Interactions

ρb > 0.5 eÅ-3, 2 ρ<0

‘Closed-shell’ Interactions

ρb < 0.5 eÅ-3, 2 ρ>0

Increase of gb, Vb, Eb

Sources of Electron densities:

1) Experiments of X-ray diffraction:

2) Theoretical :Calculation

- Four Circles Diffractometers

- Diffractometers equipped with area detectors (imaging plate or

CCD)

-non-empiric Hartree-Fock and methods based on

theTheory of the Density Functional

Dynamic electron density analysis:

Space of Nuclear ConfigurationsEquivalence Relation, E

Same Characteristic set of CP

Molecular Structure

B = 0.2 Å2

B = 0.0 Å2

C C

Topological Peculiarities of the conventional Fourier maps

Shared Interactions

ρb > 0.5 eÅ-3, 2 ρ<0

Closed-shell Interactions

ρb < 0.5 eÅ-3, 2 ρ>0

Deensity at the bond Critical Point, b

- non-covalent: 0.3 e/Å3 b 0.6 e/Å3

- Ionic or hightly polar covalent: 0.6 e/Å3 b 0.9 e/Å3

- Covalent Bonds

0.9 e/Å3 b 3.0 e/Å3

- simple: b < 2.0 e/Å3

- double: b ~ 2.0 e/Å3

- triple : b ~ 2.5 e/Å3

Bond paths

electron density

ridges created by

the gradient lines,

which go through

the bond CP and

connect some

nuclei

NaCl: ρ(r) field with bond paths and bond CP

Bond CP

Electron Density Modeling

Atomic Coordinates

Thermal displacement parameters

Electron Density parameters

Fmodel(q) = F [ {x,y,x}n, {Uij, Cijk, Dijkl }n, { P, κ }n ]

Σ w q [F experim (q) - F model (q)]2 minimum

Least Square fit

Properties which can be derived from electron density

Electrostatic potential

Electron diffraction

Quadrupole

electric moments

Optical measurements

Inner-crystal electric

field

Electric field gradient

NMR, NQR, Mössbauer

spectroscopy

Diamagnetic

susceptibility

Magnetic

measurements

Dipole electric atomic

and molecular

moments

Electrostatic atomic

and molecular

interaction energy

DFT

Kinetic electron

energy

Electron

density

Clasification of the Chemical Compounds

• They may be clasified into two large groups:

• 1.- Organic Compounds and

• 2.- Inorganic Compounds.

Inorganic Compounds

• Are those formed by any of elements differentof Carbon, including carbon in some specialcases (CO2 y el CO).

• Water (H2O), the table salt(NaCl), thesaltpeter/nitre (NaNO3) or the sodiumbicarbonate (NaHCO3) are some examples ofinorganic compounds.

Organic Compounds• Contain carbon as main element. • Besides contain elements as hydrogen, oxygen,

nitrogen and, less frecuently, phosphorus and sulphur.

• CHONPS• Except CO2 and CO

• Sucrose, is an example of Organic Molecule, acarbohydrate un this particular case.

• Other organic compounds important to life are, thefates, the vitamins and the nucleic acids, including DNAand RNA.

Macromolecules in nature

• Are large molecules and, besides, of highestructural complexity.

• Macromolecules may be clasified, atending to theirorigen, in Natural and Synthetic.

• Biomolecules, which are the molecules constituents of the living organisms, are mainly made of the following elements: carbon, hydrogen, oxygen, and nitrogen.

The main biomolecules are: Carbohydrates, Lipids, Proteins and Nucleic

Acids.

Chemical elements on the living organisms

H, C, O, y N constitute thr 96.5% weight of a living organism

Carbohydrates.

• Play energetic and estructural functions.

• Are made by the union of basic units calledmonosacarids.

• Acording to the number of basic units they contain, may be clasified as:

• Monosacarids: basic unit.

• Oligosacarids : between 2 and 10 monosacarids.

• Polisacarids : more than 10.

Lipids.

• Are organic macromolecules containing carbon, hydrogen and oxygen,

• Functions: energetics and estructurals.

• One of most particular characteristics of the lipidsis their insolubility in water.

• Examples:

• Colesterol,

• Saturated and insaturated fats and

• hormones as testosterone.

Proteins.• Are the most abundant macromolécules.

• Have various functions:

• Antibodies, participating in the defense of the organism;

• Enzimes which acelerate the speed of the chemicalreactions of the cells;

• Estructurals, by forming part of different tissues as the skin, nails and hears;

• Hormonal, regulation of growing, levels of sugar in blood, etc.

• It is important to point out that, normaly, proteins DO NOTact as a source of energy.

Nucleic Acids.• These macromolecules are especialy important to the living

organisms, because thay store and transport the geneticmessage.

• There exist two types of Nucleic Acids:

desoxirribonucleic acid (DNA) and the ribonucleic (RNA).

ADN is the most important nucleic acid. It contains allgenetic information to determine the color of your eyes,whether your hair is straight or curl, and even the pattern ofyour fingerprints.

• ARN, is formed from the DNA and transports the information toallow cells syntesize all their proteins.

• Both DNA and RNA are formed by basic units called nucleotids.

- Are the most abundant biologicmacromolecules.

- Are present in all cell and everywhere withinthe cell.

- There exist thousans of different types andsizes of proteins.

- Exhibit an amasing number and diversity offunctions.

Proteins.

Each organism may biuld proteins using a base of 20 defferent aminoacids

Enzimes poisons

Hormones colagen (skin, bones)

Antibodies receptors

Transporters hemoglobin

Proteins of milk

Queratine (horns, scales, hairs, wool, nails)

•an amino group (-NH2)

•a carboxilo group (-COOH)

•an atomo of H

•a characteristic group R (lateral chain)

Basic estructural Units of proteins

a- aminoacids

connected carbon aatom

POLAR

NON POLAR

The difference among then is based in size, electric charge, hydrofobicity

aliphatic

aromatic

chargedpositively

negatively

• Proteins of all living organisms are build by20 aminoacids covalentely bonded indifferent combinations and sequences.

• Due to that each of these aminoacids havediferent lateral chains, with different chemicalproperties, this group of 20 molecules may beconsidered as the ALFABET to WRITE thelanguage of the proteins.

• Thanks to this variety the cells may produceproteins with Physical and functionalpropierties fully different

Aminoacids with aliphatic lateral chains

Glicina(Gly, G)

Alanina(Ala, A)

Valina(Val, V)

Leucina(Leu, L)

Isoleucina(Ile, I)

Prolina(Pro, P)

Glicina(Gly, G)

Alanina(Ala, A)

Valina(Val, V)

Leucina(Leu, L)

Isoleucina(Ile, I)

Prolina(Pro, P)

Fenilalanina(Phe, F)

Tirosina(Tyr, Y)

Triptofano(Trp, W)

Aminoacids whith aromatic lateral chains

Sulphur containing lateral chains

Cisteína(Cys, C)

Metionina(Met, M)

SH

Aminoacids with positively charged (+) lateral chains

Lisina(Lys, K)

Arginina(Arg, R)

Histidina(His, H)

pKa=10.8 pKa=12.5 pKa=6.0

Aminoacids with negatively charged (-) latetral chains

Glutamato(Glu, E)

Aspartato(Asp, D)

Such subunits linked by AMIDE BOND orPEPTIDIC BOND provide the structure ofproteins

The skeleton of the whole protein is made by repetition of the N-Ca-C.This unit propagates bonded by peptidic bonds

Bonded to the polipeptidic skeleton we find, hydrogens of the aminogroup, oxygens of the carbonil group and hydrogens and the lateralchains of the alpha carbons.

Proteins are macromolecules which maycontain from 400 to 25,000 residues

MW between5,000 y 700,000

Ser Gly

Tyr

Ala

Leu

The aminoacid sequence of a protein are geneticallydetermined :

The nucleotids sequence of DNA codifies a

Complementary sequence of nucleotids on the RNA

Which determines the aminoacids sequence of the protein

Espacial structure function

mutationsgenetic alterations

Electric dipole Trans position

CHARACTERISTICS OF THE PEPTIDIC BOND

Double bond character

These 6 atoms are on the same plane

Sheets

a Helix

a Helix (left)

Gráfico de Ramachandran

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

* La Naturaleza del Enlace Químico. L. Pauling, (1939) ¡A clasic!

* Atomo. I. Asimov, (1992). Ed. Plaza-Janés ¡On the way to become a clasic!

* Física Cuántica: Atomos, Moléculas, Sólidos, Núcleos y Partículas.

R. Eisberg, (1992, 16ª re-impresión 2002). Ed. Limusa

* Construyendo con Átomos y Moléculas. Indigo, (2006). Ed. Eudeba

* Enlaces Químicos. A.L. Companion, (2008). Ed. Reverté.

* Electrones, Neutrinos y Quarks. F.J. Indurain, (2001). Ed. Crítica (Collection Drakontos)

* Partículas Elementales. G.T. Hooft, (2008). Ed. Crítica (Collection Drakontos)

* An Introduction to the Electronic Structure of Atoms and Molecules. R.F.W. Bader, (1970).

* Atoms in Molecules. A Quantum Theory.

R.F.W. Bader, (1994). Ed. Oxford University Press.

* Density-Functional Theory of Atoms and Molecules.

R.G. Parr & Y. Weitao, (1994). Ed. Oxford University Press

* Bonding and Structure of Molecules and Solids.

D.G. Pettifor, (1995). Ed. Oxford University Press

* Physics of Atoms and Molecules.

B.H. Bransden & C.J. Joachain, (2003, 2ª edición) Ed. Prentice Hall.

* The Chemist's Guide to Valence Bond Theory.

S.S. Shaik & P.C. Hiberty, (2007). Ed. Wiley-Interscience

* The Quantum Theory of Atoms in Molecules.

C.F. Matta & R.J. Boyd, (2007). Ed. Wiley-

VCH

* The Chemical Bond: A Fundamental Quantum-Mechanical Picture.

T. Shida, (2008, 2ª edition corrected). Ed. Springer

On the Chemical Bond (antecedents-history):

http://platea.pntic.mec.es/~jrodri5/web_enlaces_quimicos/antecedentes.htm

On molecular structures. Links to various “books” electronics and pages on several aspects of chemical bond(formulas, characteristics, figures, geometries, etc..)http://www.uhu.es/quimiorg/estructuraweb.html

Atoms, ions, molecules y macromolecules

Master of Crystallography and Crystallization – 2013T01 – Mathematical, Physical and Chemical basis of

Crystallography

END