1. Biomolecules Spring 2017 Department of Micro- and Nanosciences
Lectures: Ilkka Tittonen, prof
Assistants/Course coordination:
Jorma Selin
Camilla Tossi

2. Molecules Bonds between atoms Hydrogen molecule-ion
Some introduction to basic molecular physics (this should already be mostly familiar from basic courses)
Bonds between atoms
Hydrogen molecule-ion
2-atomic molecules and the molecular orbitals
Electron configuration for some 2-atomic molecules
Many-atomic molecules
Organic chain molecules
Electronic transitions in molecules

3. Bonds between atoms
All bonds between atoms are due to the electrostatic interactions between nuclei and electons
The type and strength of bonding and are determined from the atomic electron configurations
In a stable bond the particular spatial configuration has a smaller total energy than any other configuration
The energy difference between the individual atoms and the bound configuration (solid state lattice) is called cohesion energy (in case of molecules it is called the dissociation energy)

4. Types of bonds
Bonds between atoms are named into classified based on the property of the bond:
1. Ionic bond
2. Covalent bond
3. Metallic bond
4. Van der Waals –bond
5. Hydrogen bond
Cohesion energy gets values from 0,1 eV/atom (weak van der Waalsin solids) to 7 eV /atom for covalent solids

5. Ionic bond
Is created as a result of a pulling interaction between positively and negatively charged ions (between metals and non-metals)
Ions are formed when electrons become transfered from one atom to another. This is favourable and happens because of a large difference in electronegativity (which describes the ability of an atom to bind an extra electron)
All ionic compounds are solid at room temperature
NaCl is a typical example of ionic bonds

6. NaCl-ionic bond
”Metallic” atom gives away one electron becoming itself a positively charged ion. The atom that is more electronegative (nonmetal) receives an extra electron to become a negatively charged ion.

7. NaCl-ionic bond
When sodium atom looses an electron, its size becomes smaller. Correspondingly, chlorine grows in size when it receices and extra electron
After this electron transfer reaction Na+ ja Cl- -ions stay together with the help of the electrostatic foce creating an ionic bond

8. NaCl-ion bond
If Na+ ja Cl- -ions are very close to each other, their electron orbitals (electron clouds) overlap and the electrons start repelling each other (Coulomb force)
In that case, the potential energy of the system increases rapidly, it the ions continue approaching each other
This rapid increase in energy prevents breaking of the Pauli exclusion principle

9. Forming of the ionic bond
I Filling up the electron shell
II Forming of the ionic bond
Ionisation energy
Ionisation of sodium
Electron affinity
Chlorine binds an extra electron
Ions brought from infinity to the equilibrium distance
Dissociation energy to neutral atoms
5.79 eV eV – 5.14 eV = 4.27 eV
In this treatment the repulsive contribution at the equilibrium distance has been omitted.

10. Properties of the ionic bond

11. Potential model for the ionic bond

12. Ionisation energies and electron affinities

13. Properties of ionic bonds
Property
Explanation
Melting and boiling point
The melting and boiling points of ionic compounds are high, since a lot of energy is needed to break the strong electrostatic interaction between ions
Electrical conductivity
Solid ionic compounds are not electrical conductors, since solids do not have free electrons
Hardness
Most ionic compounds are hard (you cannot scratch the surface easily), because ions are strongly bound to the lattice and do not easily change the location
Fragility
Most ionic compounds are fragile. By bending the crystal, the ions of the same charge state get closer to each other, which leads to a strong repulsive interaction. This leads to the breaking of the crystal.

14. Covalent bond
A covalent bond is formed when the electronegativity difference is small and atoms are in a periodic table close to each other (two non-metals)
Atoms share the outmost shell electrons (electrons belong to both atoms)
By sharing electrons, atoms reach the noble gas electron configuration
Both nuclei pull shared electrons close to it

15. Properties of a covalent bond
Property
Explanation
Melting and a boiling point
High melting points, because atoms have been connected with strong covalent bonds. Melting requires breaking of many bonds, which is possible with high thermal energy.
Electrical conductivity
Electrons are either bound to the nuclei or to the covalent bonds and cannot move in the lattice meaning that electrical conductivity is very low.
Hardness
Covalent bonds are hard, so also the corresponding compounds are hard.
Fragility
These compounds are anyway rather fragile, since the covalent bond goes broken but does not change shape in a flexible manner.

16. Comparison between ionic bond and covalent bond
Sharing of
electron
Electron
transfer
Negative
ion
Positive ion
Covalent bond O2
Ionic bond NaCl

17. Metallic bond 1/2 The type of bonding that appears in metals
A bond is created by the pulling electrostatic interaction between positive nuclei and delocalized electrons
Electrons that are free from atoms make up a ”gas” between positive ions
In a free electron gas approximation the potential created by positive ions is assumed to be almost constant
On the edges of the lattice the potential of the ions vanishes and the potential energy of the electrons grows correspondingly. This that there is a potential threshold.

18. Metallic bond 2/2
Electrons on the outermost band (conduction band) form elecron gas, that can freely move between nuclei. These electrons keep positive nuclei bound together. Free electrons act like ”glue”.
Metallic bond is weaker than ionic and covalent bonds
good electrical conductivity
good thermal conductivity
Metallic bonds are independent of direction and material geometry:
Metals can be pulled and machined (hammered)
Bonds do not break when metals are deformed

19. Van der Waals -bond Weak bond, typically 0,2 eV/atom
Bond between neutral atoms and molecules
Weak bonds are created when the electron density is fluctuating causing small temporary dipoles.
These dipoles attract each other. The resulting forces are called Van der Waals –forces.
Van der Waals –forces are in magnitude 1 % of the strength of the covalent bonds.

20. Dipole-dipole interaction
Electric field of the dipole is
Which at large distances becomes

21. Hydrogen bond
If the bond having permanet dipoles contains a hydrogen atom, the bond is called a hydrogen bond. Many biological and organic substances contain many hydrogen bonds. Hydrogen can form an electrostatic bond with a highly electronegative (for example F and O) atom. Then rather strong dipoles become created.
The magnitude of the hydrogen bond is 0,1-0,5 eV/atom.
Hydrogen bond
Binds water molecules in ice
Is present in proteins and nucleic acids

22. Lattice structure of ice
Water molecules are located at the tips of a tetrahedron
There is a hydrogen bond between oxygen and hydrogen
Tetrahedron configuration determines shapes of snowflakes.

23. Summary of different types of bonds
Ionic bond
Van der Waals
bond
Metallic bond
Covalent
Hydrogen bond
High melting point
Hard but fragile
Solid materials
with no elecrical
Conductivity
NaCl, CsCl, ZnS
Low melting point
Soft and fragile
No electrical
Ne, Ar, Kr, Xe
Melting point varies
Strength varies
Electrical
conductors
Fe, Cu, Ag
Very high
Melting point
Very hard
Usually do not
conduct electricity
Diamond, graphite
Ice,
organic
solid materials

24. Total potential energy
Hydrogen molecule ion
Total potential energy
Potential energy between protons
Also kinetic energy of electrons and vibrational and rotational energies contribute to the system total energy.

25. Born and Oppenheimer approximation

26. Forming of hydrogen molecule
Spin orbital is approaching the ”naked” proton.
Orbital is shared between 2 host atoms.
Symmetric combination leads to high electron density between protons
Electron density of the non-symmetric LCAO state = 0 in the central point. Shading of the repulsive proton interaction is weak.
Even wavefunction (gerade)
Odd wavefunction (ungerade)

27. Charge density and parity of the state
In an odd state the repulsive potential energy of the nuclei dominates and no stable chemical bond can be formed.
In an even state the negative electron charge density works as a ”glue” between positively charged nuclei.
Even
Odd

28. Symmetric and nonsymmetric orbital energies
The energy of the repelling (antibonding) orbital is higher than the free electron state energy, whereas the bonding orbital energy is lower than that of the free atom. Both electrons will will occupy the bonding orbital.

29. Simple H2+ LCAO-model 1/4

30. Simple H2+ LCAO-malli 2/4

31. Simple H2+ LCAO-model 3/4

32. H2+ LCAO-model
The symmetric state in LCAO leads to the bond length of 1,3 Å which is close to the accurate numerical value 1,06Å.
Dissociation energies are for LCAO 1,76 eV and for an accurate numerical solution 2,8 eV.
Compatibility is rather good taking into account the simplicity of the method.

33. Total energy of the hydrogen molecule ion

34. Excited states of hydrogen molecules
Also at excited states there can be local energy minima
H2+-ion is rather weak molecule, so it does not have many strongly bound excited states.
Energy minima are observed at higher proton distances from each other.

35. Repulsion between electrons
Hydrogen molecule
Repulsion between electrons

36. Binding energy in hydrogen atom
In a hydrogen molecule, both electrons occupy the binding 𝝈g1s orbital, one spin down, another one spin up.
The binding energy of the molecule is double that of 𝐻 2 +

37. Marking of molecular orbitals
Molecule
Separate atoms

38. s-symmetric molecular orbitals
ns atom orbitals; symmetric and antisymmetric linear combination, compare to 𝐻 2 + .
For ns orbitals ml = 0 so only sigma states are possible.

39. Molecular orbitals: p-symmetry
Sigma orbitals (having |ml| = 0 ), are formed from directed pz orbitals which have ml = 0.
Pi orbitals (having |ml| = 1 are formed from directed px,y orbitals which have ml = +1 or -1.
The picture shows formation of LCAO molecular orbitals as even and odd linear combinations of directed p orbitals. Z axis is chosen to be the symmetry axis of the molecule.

40. Molecular orbitals in some diatomic systems

41. Diatomic electronic states with similar nuclei

42. Directional orbitals
Directional orbitals can be presented as linear combinations of spherical harmonics.
Directional orbitals are so called unitary linear combnations, so they have been normalized in a same way as sperical harmonics and the square of the absolute value integrated over all angles gives = 1.

43. Forming of hybride orbitals
This picture shows the forming of methane sp3 hybride orbitales in a given coordinate system.
One hydrogen atom is marked with angles that define a hybride orbital.
The picture also shows the angles in a laboratory coordinate system defing px, py and pz orbitals.
The chosen hydrogen atom is part of the hybride orbital given by y1= 0.25 s + cos (ϴx)px + cos (ϴy)py + cos (ϴz)pz .
What is still needed is to find the normalization so that the integral of the square becomes = 1.

44. Sp2 hybridisation in water molecules
Hybridisation means reordering of atomic orbitals to correspond to the symmetry of the molecule.
The chemical bond is energetically favourable, if changing of the symmetry of the atomic orbitals does dot require a lot of energy.
With a bit of energy one can form from carbon 2s ja 2p orbitales different so called directed orbitals as a linear combination of the original ones.
In water molecule the directed px and py orbitales are approximately pointed towards hydrogen atoms. The bonding angle is 104,50 instead of the original 900 sijaan due to the electron-electron repulsion

45. Sp3 hybridisation in methane
The hybridisation describes the spatial reconstruction of electron orbitals of free atoms in such a way which produces a high electron density between those atoms that belong to a methane molecule and thus makes a stable bond between the carbon atom and the surrounding hydrogen atoms.
The carbon 2s ja 2p orbitales form as a linear combination four (4) LCAO-orbitales of which probability densities are directed towards the corners of the tetrahedron where the hydrogen atoms are located.

46. Sp hybridisation

47. Transitions between electronic states
In this molecule there is a stable excited electronic state.
Notice that in the excited state the sum of nuclear repulsion and electronic energy corresponds to the longer bond length than in the ground state.
Rotational state does not usually change in an electronic transition.
Excited electronic state
Vibrational states
Lowest (ground) state
Rotational states
of the second
vibrational state
Rotational states of the
lowest vibrational state
Total energy of electron and nuclei

48. Combined electron vibration-rotation
Emission spectrum of N2 molecule, J. A. Marquisee