Part I

Question 1

Definition of a covalent chemical bond

(Feynman, 1939)

Answer 1

“A chemical bond is the result of the net electrostatic attraction exerted on the nuclei of a pair of atoms by the electron densityaccumulated between the nuclei.”

(Two atoms are bonded to each other if there is an electron-density accumulation between the two positively charged nuclei that keeps them together.

Question 2

Which is a chemical bond?

Answer 2

The first one, because of the saddle-shaped path of electron density.

The second isn’t one because there is no electron-density accumulation.

The last one isn’t one because the path has a plateau.

Question 3

What is measured in a chemical bond?

Answer 3

Only the electron density (ρ).

Not the wavefunction (ψ) and also not the bond itself.

Question 4

What are the four types of bonds and which are directional?

Answer 4

Directional forces:

1. Covalent bond / atomic bond /electron pair bond

Nondirectional forces:

2. Ionic bond
3. Metallic bond
4. Intermolecular interaction, e.g. hydrogen bond, van-der-Waals bond

(Mostly mixed states between the first 3)

Question 5

What is the “Noble Gas Rule”?

Answer 5

In its compounds, every atom aims for the same number of electrons in its outermost shell as the noble gas of the same period.

This means that compounds are preferentially formed in a way
that all the involved atoms reach noble gas configuration, i.e.
a filled outer shell.

Question 6

Covalent bond

Answer 6

Reach Noble Gas configuration by sharing electrons.

Occours if non-metal atoms react with each other.

Rule of thumb: Electronegativity difference < 1,7

Question 7

Lewis notation / Lewis formulas

Answer 7

• Only valence electrons are drawn.
• A single electron is denoted as a dot.
• An electronpair is denoted as a line.
• Bonding electron pairs are in contact with two atomic cores, whereas free (or lone) electron pairs are in contact with only one atomic core.
• LEWIS formulas do NOT represent the correct geometry.

Question 8

Ionic bond

Answer 8

Reach Noble Gas configuration by completely transferring electrons.

Ionic compounds consist of electropositive elements from the far left of the periodic system (e.g. sodium) and electronegative elements from the far right of the periodic system (e.g. chlorine).

Rule of thumb: Electronegativity difference > 1,7

Positively charged ions are called cations.

Negatively charged ions are called anions.

Cations are held together by electrostatic attraction according to Coulomb’s Law.

Question 9

Mettallic bond

Answer 9

Free electron model

Reach Noble Gas configuration by the metal atoms detaching their valence electrones from the core completely. These electrons are then located in a delocalized manner between the positively charged atom cores and can move freely like particles in a gas.

Question 10

Intramolecular Interaction

Answer 10

Cannot be explained by atoms aiming for the noble gas configuration, but are based on secondary forces.

Weaker interactions between molecules.

Question 11

Van-der-Waals bonding

Answer 11

Attraction between dipoles

permanent <-> permanent: Keesom orientation effect

permanent <-> induced: Debye induction effect

fluctuating <-> induced: London dispersion effect

Question 12

Uncertainity principle

(Heisenberg 1927)

Answer 12

It is impossible to determine the momentum and the location of an electron simultaneously.

Δx Δ(mv) ≈ h

Question 13

Relationship between wavelength λ and momentum p.

(De Broglie 1924)

Answer 13

Moving particles must own properties of waves and vice versa.

λ = h / p = h / (m*v)

Question 14

Photoelectric effect

(Einstein, 1905)

Answer 14

An increase in the intensity of light of constant wavelength does not lead to an emission of electrons; only a change of wave length regardless of intensity. This can only be explained if light acts as a particle, a socalled wave packet.

E_kin = h*v + φ

φ = work function

Question 15

Wave-particle dualism

Answer 15

Light can be treated as a wave or as a particle, according to the experimental conditions.

Electrons can be treated as waves or as a particles, according to the experimental conditions.

Question 16

Schrödinger Equation (general)

Answer 16

There is a mathematical relationship between the function value of a matter wave and its energy.

We only deal with the time-indipendent Schrödinger equation for stationary systems in the ground state.

It is a differential equation of second order. It can only be solved for a single electron with coordinates x, y, z, this means only for the hydrogen atom.

Question 17

Schrödinger Equation solution for the hydrogen atom

Answer 17

Yields orbitals that are characterized by the three quantum numbers n, l, m_l. A fourth quantum number is obtained via a side condition.

The wavefuntions of the hydrogen atom are called orbitals. There are as many orbitals as there are combinations of the quantum numbers.

Question 18

Electron density

Answer 18

|Ψ(x, y, z)|² is the probability of finding a particle at the coordinates x, y, z. It is called probability density.

If the particle is an electron, |Ψ(x, y, z)|² is the electron density.

Question 19

Principal quantum number n

Answer 19

Determines the possible energy levels of the electron in the hydrogen atom.

The mathematical solution for the energy of the H atom depending on the principal quantum number n is identical between the Schrödinger equation and the Bohr model.

The energy levels determined by n are referred to as shells in analogy to the Bohr model.

If an electron is in the K-shell (ground state), the energy of the hydrogen atom is -13.6 eV.

The energies of orbitals with the same principal quantum number are degenerate in the hydrogen atom.

Question 20

Ionization Energy

Answer 20

The energy needed to detach an electron and bring it into infinite distance from the core is called ionization energy.

H –> H⁺ + e^- E_I = + 13.6 eV

Question 21

Azimuthal quantum number l

Answer 21

Determines the shape of the orbital

l =< n -1

Question 22

Symbol of the atomic orbitals

Answer 22

Given by principal and azimuthal quantum numbers.

Question 23

Magnetic quantum number m_l

Answer 23

Determines the orientation of the orbital in three-dimensional space.

-l =< m_l =< +l

Question 24

s-orbitals

Answer 24

Question 25

p-orbitals

Answer 25

Question 26

d-orbitals

Answer 26

Question 27

f-orbitals

Answer 27

Question 28

Spin quantum number m_s

Answer 28

Describes the angular momentum of an electron spinning around it’s own centre of gravity: the spin angular momentum.

The spin quantum number m_s describes the orientation of the electron spin in a magnetic field.

Possible values are:

Question 29

Orbitals for more-electron atoms

Answer 29

Can only be solved for the hydrogen atom. For all other atoms, approximations must be used.

Nevertheless, the shapes of orbitals in more-electron atoms are similar to the shapes in the hydrogen atom.

The energies of the orbitals only depend on the principal quantum number n for the hydrogen atom.

In more-electron atoms, the energy also depends on the second (azimuthal) quantum number l.

Question 30

Aufbau Principle

Answer 30

The electrons will first occupy the energetically lowest-lying levels.

Question 31

Pauli Principle

Answer 31

An atom never bears two electrons that are identical concerning all four quantum numbers.

==> Each spatial orbital can be filled with a maximum of two electrons.

==> The maximum number of electrons per principal quantum number n is 2n².

Question 32

Hund’s Rule

Answer 32

The orbitals of a sub-shell are filled in a way that the number of electrons with the same spin is maximized.

==> Principle of highest multiplicity

Question 33

Valency

Answer 33

The principle of valency explaines how many covalent bonds a particular non-metal atom can form according to its electron configuration.

Question 34

Promotion into excited states

Answer 34

Example of carbon:

For carbon to form four equivalent bonds, an electron in the 2s-orbital needs to be promoted into the 2p-orbital.

This process requires energy.

Question 35

Octet Rule

Answer 35

Atoms strive for a filled outer shell of eight electrons (noble gas rule).

Atoms of elements of the second period can form a maximum of four bonds with eight electronst (an electron octet) because only four spatial orbitals are available.

If an element of a higher period only uses s- & p-orbitals for bonding, the octet rule holds.

Elements of the third and higher periods form many molecules that formally exceed the octet rule for the central atom.

The coordination number is often higher than four and the central atoms have high oxidation states. The highest oxidation states are only reached with the most electronegative bonding partners, mainly oxygen and fluorine.

PH₅ and SH₆ do not exist, but PF₆ and SF₆ do exist.

Within the same group, formulas of analogous compounds are identical:

Question 36

Hypervalent compounds

Answer 36

Atoms that own more than four valence electron pairs in their compounds, thus breaking the octet rule, are referred to as hypervalent.

A possible explanation for this behaviour involves the participation of d-orbitals in the bonding.

For elements of the third period, participation of d-orbitals in bonding is not a valid explanation for hypercoordination. It has been used in the past, but has been proven to be incorrect.

Question 37

Hypovalent compounds

Answer 37

Electron-deficient compounds

Do not reach the octet.

Question 38

Formal charge

Answer 38

Important auxiliary tools for the construction of Lewis formulas.

Formal charges in a Lewis structure are encircled to distinguish them from real ionic charges or partial atomic charges.

The charge of the molecule or ion must correspond to the sum of all formal charges.

To determine the formal charge, binding electron pairs are shared between the two bonding partners to equal amounts. Subsequently, the resulting number of electrons of the particular atom is compared to the electron number of the neutral element.

The formal charge does not correspond to a real atomic charge of the respective atom. The calculation of formal charges is purely a tool for the chemist to write simplified Lewis structures that relate two-center-two-electron bonds to the valency of the atom.

Question 39

Rules for the construction of Lewis formulas

Answer 39

1. Count the total number of valence electrons.
2. Distribute the electrons according to the octet rule for elements of periods 1 and 2.
3. For elements of periods 3 and above, the octet rule may be broken.
4. Calculate formal charges.
5. The geometry is not part of the Lewis formalism. This means that always the simplest geometry is to be chosen. (Example: Water is linear in the Lewis picture.)

Question 40

Resonance

Answer 40

Sometimes Mesomerism is used.

There is a large number of molecules that connot be described by a single Lewis structure sufficiently.

Multiple resonance forms are needed to describe atoms. This does not mean that there is a mixture of three different ions, but that the real electronic form is a superposition of the resonance forms.

<–> The double-arrow is the symbol for resonance.

Resonance forms must only be different in their electron distributions, not in the arrangement of the atomic nuclei.

Aromaticity in benzene is the result of perfect delocalization between two identical resonance forms.

If two resonance forms are not identical, they have different percentage contributions to the real electron distribution.

Question 41

Resonance Energy

Answer 41

Resonance leads to energetic stabilization of a molecule, so called resonance energy.

Due to the delocalization of electrons that come into the vicinity of more than one positive atomic nucleus that attracts them simultaneously.

The more similar in energy two resonance forms are the more pronounced is the delocalization. In turn, the resonance energy becomes bigger the more similar the resonance forms are.

Question 42

Rules for the determination of the weights of different Lewis resonance forms

Answer 42

– For all elements of the first three periods, the resonance forms that obey the octet rule are more likely. For periods 1 and 2, forms exceeding the octet rule are forbidden. For period 3, forms exceeding the octet rule are highly unlikely.
– Resonance forms with a smaller amount of formal charges are more likely.
– Resonance forms where the distribution of formal charges agrees with the distribution of electronegativities are more likely.
– Neighboring atoms should not have the same sign of their formal charge.

Question 43

VSEPR Model

Answer 43

Valence-shell electron pair repulsion

1. Electrons repel each other. The molecular geometry is a consequence of mutual electron-pair repulsion.
2. In molecules of the type AB_n, electron pairs are arranged in such a way that they minimize their distance from each other.
3. All electrons of the valence shell of the central atom are accounted for – the bonding and the non - bonding (free) electron pairs.
4. The free electron pairs E in a molecule AB_nE_m require more room than the bonding electron pairs. Hence, they reduce the room available for bonding electron pairs.
5. Electronegative substituents attract electron pairs more strongly and hence diminish their sterical demands.
6. Multiple bonds have higher sterical demands than single bonds and therefore compress angles between single bonds.