Previously – Dual nature of electrons

(1)

Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**

Consortium leader

PÁZMÁNY PÉTER CATHOLIC UNIVERSITY

Consortium members

SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER

The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***

**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben

***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.

CATHOLIC UNIVERSITY UNIVERSITY

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WORLD OF MOLECULES

PROPERTIES OF CHEMICAL BONDS, SPECTROSCOPY

(Molekulák világa)

(A kémiai kötések tulajdonságai, spektroszkópia)

KRISTÓF IVÁN

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1. Dual nature of light

2. Particle nature of electron

3. Wave nature of electrons (de Broglie) 4. Particle-wave duality of electrons

5. Schrödinger equation

6. The wave functions of the electron in 1D

7. The wave functions of the electron in a harmonic oscillator 8. The wave functions of the electron in 3D

9. The wave functions of the electron in the Hydrogen atom 10. Short introduction to complex numbers

semmelweis-egyetem.hu

Previously – Dual nature of electrons

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photon

electron

Previously - Double-slit experiment

http://en.wikipedia.org/wiki/File:Single_slit_and_double_slit2.jpg | http://upload.wikimedia.org/wikipedia/commons/7/7e/Double-slit_experiment_results_Tanamura_2.jpg

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• Erwin Schrödinger found the mathematical model which satisfies the Bohr postulates and results in the de Broglie wave theory.

1. The wave equation has to satisfy the Planck and de Broglie postulates

2. The energy of a particle is made up of its kinetic and potential energy

3. The wave equation has to be linear (superposition principle) to return the interference results correctly

Previously - The Schrödinger model (1926)

, h

h W

p =

= ν

λ

pot 2

2 W

m W = p +

( )

^{x t}^,

( ) ( )

^x ^t

ψ = Ψ ⋅ Ψ

1D, time dependent

(6)

from the potential field the Hamiltonian can be expressed, and the

„one electron problem” can be solved:

e.g. electron in a 1D well e.g. electron in a 3D box

Previously - Wave functions of any potential field

( )^r ^H _pot( )^r

pot W

W ⇒ = − m Δ + 2

=2

→

=Wψ ψ

H

( )

^; ^,

( )

^; ^... ^,

( )

^;^...

, ₁ ₂ ₂

1 ψ r W ψ r W_n ψ_n r

W ^ψ_n

( )

^r^,^t ⁼^ψ_n

( )

^r ^e⁻^j^W⁼ⁿ^t^; ⁿ ⁼¹^,²^,...

⇒

∂ =

∂ ψ

t

ψ H

= j

2 2 2

8 n

ma h Wn =

( ) ⁿ ^t

W a

x n t a

n x j =

e 2 sin

,

= π −

ψ

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ + +

= ² ¹₂² ²₂² ³₂² 8

h 3 2

1 c

n b

n a

n n m

n Wn

( ) ^t

n n Wn c

n z b

n y a

n x t abc

z y n x n

n =

3 2 j 1

e sin

sin 8 sin

; , , 3 2

1 ¹ ² ³

⋅ −

⋅

= π π π

ψ

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1. Spectroscopy

2. Absorption spectroscopy 3. Emission spectroscopy

4. Chemical properties of atoms 5. Types of chemical bondings

6. Basic properties of chemical bonds 7. Covalent, ionic and metallic bonds 8. Hydrogen bonds

9. van der Waals forces

Spectroscopy

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• Atomic absorption spectroscopy

• elements with absorption between 185 – 900 nm can be measured, ppm sensitivity, the radiation excites electrons to higher energies

• UV and visible light (UV/Vis) spectroscopy

• excitation between 200 – 800 nm, useful for colorful or small

molecules (organic molecules, or transition metal ions), the radiation excites electrons to higher energies in the molecule or metal ion

• Infrared (IR) spectroscopy

• excitation between 800 – 30 000 nm, useful for the identification of specific groups within a molecule (molecular structure determination), the radiation excites vibration modes of bonds and atom groups

• ...

Absorption spectroscopy

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Absorption spectrum from the Sun

http://en.wikipedia.org/wiki/File:Fraunhofer_lines.svg

The visible range of radiation from the sun is lacking certain lines due to the absorption of those wavelengths by the respective elements

on the surface of the Sun and in our atmosphere (e.g. Oxygen)

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• Nuclear magnetic resonance (NMR) spectroscopy

• the method exploits the

magnetic behaviour of certain nuclei (in organic chemistry it is ¹H and the ¹³C), useful for the identification of functional groups, or even molecular

structure, provides more information than IR.

the radiation is absorbed by the nuclei which are resonant at the given frequency

Absorption spectroscopy

http://upload.wikimedia.org/wikipedia/commons/9/93/Pr%C3%A4zession2.png

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• Fluorescence spectroscopy

• used for analyzing organic molecules, usually UV light excites the sample and as part of the relaxation from the excited state the sample emits visible light, and the amount of light emitted is proportional to the amount of molecules present, the radiation excites electrons to a higher energy level

• X-ray fluorescence spectroscopy

• useful for electron structural studies, elemental or chemical analysis of metals, glass, and ceramics, the high energy radiation (X-rays or

gamma-rays) excites electrons from the inner orbitals of the atoms and the sample emits X-ray photons in the range of 50 nm – 50 pm

wavelength.

Emission spectroscopy

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Emission spectrum of Fe

http://en.wikipedia.org/wiki/File:Emission_spectrum-Fe.png

Emission spectrum of iron (Fe) in the visible light range

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Emission in gas discharge tubes

http://commons.wikimedia.org/wiki/File:Gase-in-Entladungsroehren.jpg

Visible emission of different gases in discharge tubes

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• Electronegativity (EN)

• first defined by Linus Pauling in 1932

• the ability of an atom to attract electrons towards itself in a molecule

• helps calculate the polarity of a chemical bond between heteroatoms

• dimensionless quantity (Pauling scale) running from

0.7 to 3.98 (3.98 being the most electron attracting atom)

• other scales:

• Mulliken EN (from first ionization energy, and electron affinity)

• Allen EN (average energy of the valence electrons in a free atom)

The chemical properties of atoms

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Electronegativity using the Pauling scale

http://en.wikipedia.org/wiki/Electronegativity

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• Atomic radius

• the size of the typical radius of the atom from the nucleus to the boundary of its electron cloud

• „boundary” is not well defined, different sizes may exist

• Ionic radius

• the radius of the atom’s ion in a crystal lattice

• First ionization energy

• the energy required to remove (to infinity) one electron (the outermost) from the neutral atom, usually measured in

eV (electronvolts) or kJ/mol

• Second ionization energy, ...

The chemical properties of atoms

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Atomic radius in picometers (pm)

http://en.wikipedia.org/wiki/Atomic_radius

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Comparison of atomic and ionic radii

http://it.wikipedia.org/wiki/File:Cationi-anioni.png

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First ionization energy in kJ/mol

http://es.wikipedia.org/wiki/Energ%C3%ADa_de_ionizaci%C3%B3n

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Successive ionization energies in kJ/mol

http://en.wikipedia.org/wiki/Ionization_energy

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• Chemical bonds

• covalent bonds

• polar covalent bond

• non-polar covalent bond

• ionic bonds

• metallic bonding

• Intermolecular forces

• Hydrogen bond

• Van der Waals forces

• dipole –dipole, induced dipole – induced dipole, ...

Types of chemical bondings

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Polar and non-polar covalent bonds

http://it.wikipedia.org/wiki/File:Legame_chimico_covalente_polare.PNG | http://it.wikipedia.org/wiki/File:Legame_chimico_covalente_puro.PNG

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• electrostatic attraction between a metal and a non-metal ion

• e.g.:

• extremely polar covalent bond

• the ionic character is dependent on the electronegativity difference of the participating atoms

• purely ionic bond does not exist

• a covalent character is always present

• the solution or melt of such compounds conducts electricity

• (since charge (as ions) can migrate through it)

• when crystallized it forms ionic crystal lattices

Ionic bonds

− +

+

→ Na Cl

NaCl

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Ionic bonds

http://it.wikipedia.org/wiki/File:Legame_chimico_ionico.PNG

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• forms in solid state when positively charged metal ions are in a lattice and

• their valence electrons are delocalized over the whole structure

• the valence electrons are not bound to only one or two atoms/ions

• more exactly, the bonding orbitals of the lattice are almost identical for the electrons and these orbitals are spread on whole lattice

• this specific bonding accounts for most of the unique properties metals have (strength, thermal and electrical conductivity)

Metallic bonding

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Metallic bonding

http://de.wikipedia.org/w/index.php?title=Datei:Nuvola_di_elettroni.svg

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Hydrogen bond

• attractive force between a hydrogen atom in a bond, and an highly electronegative atom

• weaker bond than covalent bonds but magnitudes stronger than dipole or induced dipole attractive forces

• can occur both between molecules (e.g. water, ammonia) and within bigger molecules (e.g. proteins, DNA)

• has vital importance in biology, since the structure of proteins, DNA and RNA both rely on Hydrogen bonds.

Intermolecular forces

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Hydrogen bonds in hexagonal ice crystals

http://en.wikipedia.org/wiki/File:Hex_ice.GIF

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Hydrogen bonds in a protein (with β-sheet arrangement)

http://commons.wikimedia.org/wiki/File:1gwe_antipar_betaSheet_both.png

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Hydrogen bonds in a DNA fragment

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van der Waals forces

• weak electrostatic attractive force between dipoles and induced dipoles

• two orders of magnitude weaker than ionic bonds

• a molecule is a dipole if its electron cloud is not homogenously arranged over the whole molecule

• dipole – dipole

• dipole – induced dipole

• induced dipole – induced dipole

Importance: properties of organic compounds, protein structure, proteins and cell membrane interaction

Intermolecular forces

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van der Waals forces

http://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:%E8%AA%AC%E6%98%8E%E5%9B%B3_%E3%83%95%

E3%82%A1%E3%83%B3%E3%83%87%E3%83%AB%E3%83%AF%E3%83%BC%E3%83%AB%E3%82%B9%E5%8A%9B1.png

Previously – Dual nature of electrons

WORLD OF MOLECULES

Previously – Dual nature of electrons

photon

electron

Previously - Double-slit experiment

• Erwin Schrödinger found the mathematical model which satisfies the Bohr postulates and results in the de Broglie wave theory.

Previously - The Schrödinger model (1926)

( )

( ) ( )

Previously - Wave functions of any potential field

( )

( )

( )

( )

( )

1. Spectroscopy

2. Absorption spectroscopy 3. Emission spectroscopy

4. Chemical properties of atoms 5. Types of chemical bondings

6. Basic properties of chemical bonds 7. Covalent, ionic and metallic bonds 8. Hydrogen bonds

9. van der Waals forces

Table of Contents

Spectroscopy

Absorption spectroscopy

Absorption spectrum from the Sun

Absorption spectroscopy

Emission spectroscopy

Emission spectrum of Fe

Emission in gas discharge tubes

• Electronegativity (EN)

The chemical properties of atoms

Electronegativity using the Pauling scale

The chemical properties of atoms

Atomic radius in picometers (pm)

Comparison of atomic and ionic radii

First ionization energy in kJ/mol

Successive ionization energies in kJ/mol

• Chemical bonds

• Intermolecular forces

Types of chemical bondings

Polar and non-polar covalent bonds

Ionic bonds

+

→ Na Cl

NaCl

Ionic bonds

Metallic bonding

Metallic bonding

Hydrogen bond

Intermolecular forces

Hydrogen bonds in hexagonal ice crystals

Hydrogen bonds in a protein (with β-sheet arrangement)

Hydrogen bonds in a DNA fragment

van der Waals forces

Intermolecular forces

van der Waals forces

1. Modeling of the molecular and electron structure 2. Different methods

3. MM

4. Hartree-Fock 5. Semi-empirical 6. DFT

7. Møller Plesset 8. Approximations

9. Display options and methods

Next – Modeling of electron and molecular structure