Electron orbitals and the periodic table

In the planetary model of the atom, electrons orbit the nucleus, but if this actually happened, they should lose energy in a dying scream of electromagnetic radiation and crash into the nucleus (the gravitational equivalent is what happened to the space station Mir). This is because the negatively charged electron is inherently attracted to the positively charged nucleus, and crashing into it represents a lower energy, and therefore more favourable state.

The planetary structure of the atom has the nucleus as the sun and electrons like planets.

The solution to this problem is the quantum model of the atom. In quantum theory, the energy of an electron is only allowed to be gained or lost in discrete chunks called quanta. No 'scream' of energy is allowed, only discrete jumps between energy states. This makes the the allowed energy levels in an atom like the discrete steps of a staircase, rather than a continuous gentle slope. Furthermore, transitions are only allowed to unoccupied energy states (this is called the Pauli exclusion principle). Hence, energies higher than the lowest energy state are stable, because there is nowhere unoccupied further down the staircase of energy for the electrons to fall to. However, this still leaves the 'ground state' (the lowest energy state). Why is this stable? To account for this, we invoke Heisenburg's uncertainty principle, an important maxim of quantum theory, which states that an electron's position and velocity cannot be simultaneously known with certainty. One way we can tell where an electron is in space is by hitting it with light waves. However, the more precisely we need to know the position of the electron, the smaller the wavelength of light we will need: a dinghy will leave an obvious, observable shadow behind short-wavelength water waves, but a long-wavelength tsunami will not even notice it's there.

λ = h ⁄ p , or equivalently, E = m c² = hν

(λ is wavelength, ν frequency, E energy, p momentum, h Planck's constant, m mass, c speed of light)

However, by de Broglie's and Planck's relationships (above), short wavelengths carry more energy: X-rays (short wavelength) are more energetic than radio waves (long wavelength). These energetic light waves will kick the electron sufficiently to change its movement, so although we know exactly where the electron is, we will have no idea in which direction it is now travelling. From this, we can see that if an electron tries to get nearer the nucleus, its position will become more certain. Hence its velocity must become less certain, and therefore higher on average. This means its energy of motion is higher, and therefore there is no net energy advantage in crashing into the nucleus, because the increase in kinetic energy would exceed any loss in potential energy. Hence the ground state is also stable.

Quantum physics states that all particles have wave-like properties (like wavelength) and that all waves have particle-like properties (like momentum). In fact, all subatomic particles can be thought of as a sort of hybrid between a wave and a particle. For example, electrons, previously considered as particles (i.e. tiny billiard balls), also have wave like properties. The wave we're talking about here is a wave of probability of finding an electron at a given point. This is like a crime wave: the probability of getting mugged is higher when a crime wave runs through your town, hence when an electron probability wave runs through your equipment, you stand a good chance of seeing an electron particle somewhere. In an atom, the electron probability waves form 'standing waves', much like those you get when you pluck a guitar string. In a similar way to a guitar string, the atom allows various modes of vibration of the standing wave:

Different modes of vibration on a guitar string.

Schrödinger's equation describes these modes of vibration, and the solutions are generally graphically displayed as orbitals, which are the space where there's a better than 99% chance of finding an electron.

There are many sorts of orbitals, as we shall see. The various orbitals available to an atom are described by four quantum numbers, which can take certain values to create differently sized and shaped orbital of various energies:

Principal (n).
Azimuthal (l).
Magnetic (m_l).
Spin (m_r).

Th principal quantum number (n) describes the:

Largest energy differences ('shells').
Size of orbital.
Numbered 1, 2, 3, 4, 5, etc (although the shells it describes are often lettered K, L, M, etc.).
Low numbers are closest to the nucleus, and have the lowest energies.
Higher values of n indicate larger orbitals

The azimuthal quantum number (l) describes the:

Small energy differences ('subshells') due to angular momentum of the electron
Shape of orbital (number of lobes).
Given letters s, p, d, f, g, h, i, etc.
The blocks of the periodic table are named after the azimuthal quantum number of the orbitals being filled (alkali metals are the s-block, the nonmetals are in the p-block, the transition metals are the d-block, the footnote is the f-block).
The values of l run from 0 to n − 1, where n is the principal quantum number of the shell in question. An s orbital is just shorthand for l = 0, a p orbital is shorthand for l = 1, a d orbital l = 2, an f orbital l = 3, etc.
This also means that (for example) the n = 3 shell can only contain subshells with l = 0, 1 or 2, i.e. only s, p and d orbitals.

2p_x

3d_xy

4f_xyz

These orbitals differ in their azimuthal quantum numbers: s orbitals (top left) are spherical and have just one lobe. p orbitals (top right) have two lobes, and a 'node' between the lobes where the electrons do not spend much time. Consequently, 2p orbitals have higher energy than 2s orbitals, because the electron spends a little longer distant from the nucleus. d (bottom left) and f (bottom right) orbitals have increasing numbers of lobes. In fact, d and f orbitals can have even more bizarre shapes than this:

A 4f_z³ orbital.

The magnetic quantum number (m_l) describes:

No energy differences at all (the orbitals are degenerate).
Orientation of the orbitals in space.
Named after the directions they point in (sort of) x, y, z, etc.
Can also be given numbers ranging from 0, ±1, ±2, ±3 … ±l. Hence the three sorts of p orbitals, p_x, p_y and p_z have m_l of -1, 0 and +1 respectively.
Consequently, there's only one sort of s orbital (because l = 0), but:
- 3 sorts of p
- 5 sorts of d
- 7 sorts of f
- 9 sorts of g
- 11 sorts of h
- 13 sorts of i
- 15 sorts of j…

2p_x

2p_y

2p_z

The 2p_x, 2p_y and 2p_z orbitals all have the same energy, but different orientations in space.

Summary of Orbitals:

n=1 shell
- One s-orbital: 1s
n=2 shell
- One s-orbital: 2s
- Three p-orbitals: 2p_x 2p_y 2p_z
n=3 shell
- One s-orbital: 3s
- Three p-orbitals: 3p_x, 3p_y, 3p_z
- Five d-orbitals: 3d_xy, 3d_xz, 3d_yz, 3d_x²−y², 3d_z²
n=4 shell
- One s-orbital: 4s
- Three p-orbitals: 4p_x, 4p_y, 4p_z
- Five d-orbitals: 4d_xy, 4d_xz, 4d_yz, 4d_x²−y², 4d_z²
- Seven f-orbitals: 4f_z³, 4f_xz² 4f_z(x²−y²), 4f_xy², 4f_xyz, 4f_{x(x²−3y²)}, 4f_{y(3x²−y²)}

The final quantum number is the spin quantum number (m_r). Each orbital (e.g. a 2p_x) can hold two electrons. The Pauli exclusion principle states that no two electrons in a single atom can have the same quantum numbers, hence they must differ in their spin quantum number, which takes the values +½ or -½. Two electrons in the same orbital have paired (opposite) spins. The number of electrons a set of degenerate orbitals can contain is therefore just 2 for an s orbital, 6 for a set of p orbitals (3p_x 3p_y 3p_z can hold 2 electrons each), 10 for a set of five d orbitals, 14 for a set of f, etc.

The periodic table is a list of the elements by their atomic number (i.e. by the number of electrons a neutral atom of the element possesses). Hence, as we traverse the periodic table, we are filling up electron orbitals from lowest energy to highest energy. We can write electronic configurations for atoms based on the arrangement of their electrons. We just need to write the (non-degenerate) orbitals out in energy order, then fill them up, writing the number of electrons each set of orbitals contains as a superscript

Hydrogen (1 electron) has the electronic configuration 1s¹

Boron (5 electrons) has the electronic configuration 1s² 2s² 2p¹

Sodium (11 electrons) has the electronic configuration 1s² 2s² 2p⁶ 3s¹

How does this relate to the periodic table?

The periodic table.

Properties of elements exhibit periodic behaviour as we traverse the table: elements in a vertical group, like the halogens (F, Cl, Br, I) and alkali metals (Li, Na, K, Rb) have similar properties. The reason for this is that their outermost orbitals have a similar electronic configuration: the alkali metals all have s¹ and the halogens all have s²p⁵ in their outermost shell. Elements with similar electronic configurations have similar properties.

As we move across the horizontal periods, we are filling up electron orbitals from the lowest energy (nearest to nucleus) to the highest (furthest out). Filling them up is unfortunately not quite as simple as it might seem. Although we might expect the orbitals to fill up in the order:

1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 5g …

There is actually overlap between different shells: for example, the 3d orbitals actually have higher energy than the 4s orbitals. The electrons actually fill in the order below:

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p 8s …

This is easy to remember from the following diagram:

The order for filling up orbitals goes 1s 2s 2p 3s 3p 4s 3d 4p 5s …

So, the only rules for filling up energy levels are that they fill from the lowest energy upwards, and that electrons only pair if there's no orbital of the same energy available (Hund's rule). Looking at the periodic table, and the filling order, we can easily see that the following orbitals are filled by the elements listed:

1s : H He.
2s : Li Be.
2p : B C N O F Ne.
3s : Na Mg.
3p : Al Si P S Cl Ar.
4s : K Ca.
3d : Sc - Zn.

And so on: f-orbitals are filled in the f-block lanthanides/actinides (the footnote at the bottom of most periodic tables).

Molecular bonding

The previous section described how electrons fill up atomic orbitals, and how this relates to periodicity. What happens when there is more than one nucleus present? In short, how do electrons arrange themselves in molecules, and how do they form chemical bonds?

The short answer is that it's extremely difficult to work out! However, many models have been proposed, each with their advantages and disadvantages. The simplest is the valence bond theory of the chemical bond. In this theory, we only consider the outermost s and p valency electrons as being responsible for most of the chemistry of an atom (or at least the ones biochemists are interested in). Having a completely full or empty octet of these outermost electrons is a favourable low-energy state. Noble gases already have this configuration, and are therefore unreactive, but other elements 'try' to completely fill or empty their outermost octet of electrons by losing, gaining or sharing them. In iodine chloride, we can see that both Cl and I are one electron short of an octet. Hence they can share electrons and form a covalent bond between the two molecules, allowing both to have 8 electrons in their outermost orbitals, I-Cl. Note that both I and Cl have three pairs each of electrons not involved in the bond itself. These are termed lone pairs, and contribute to the shape of the molecule as we will see. The two electrons that are shared form a single covalent bond. Other molecules may share more than one pair of electrons between two atoms: in oxygen molecules (O₂), a double bond is formed (O=O), sharing four electrons in total, and in nitrogen (N₂) six electrons are shared to form a triple bond N≡N).

Lewis structure for iodine chloride.

However, rather than sharing electrons, some atoms find it easier to lose or steal them. The metallic elements are termed electropositive. This means that they are more likely to lose electrons (and become positive cations) than gain them. For example, the alkali metals (Li, Na, K, Rb, Cs, FR) each have 1 electron in their outermost s orbital. They can lose them to form cations (K⁺, Na⁺). This leaves them with a full octet at the next shell down. Metallic character increases towards the bottom left of the periodic table i.e. francium is the most electropositive, and therefore most metallic, metal.

On the other hand, the electronegative nonmetals are more likely to gain electrons and become negatively charged anions. For example, the halogens (F, Cl, Br, I, At) have 7 electrons in their outermost s and p orbitals. They can gain one more to form anions (Cl⁻, I⁻). This gives them a full outer octet. Nonmetallic character increases towards the top right of the periodic table, i.e. the most nonmetallic nonmetal is fluorine.

The valency of an atom can be determined by the number of electrons it has in its outermost orbitals. As a general rule, for elements in the s and p blocks, those with 1 or 7 electrons in the outermost shell have valency one (i.e. can form just one bond), since they are only one electron away from a completely full or empty outer octet. Those with 2 or 6 electrons have valency 2, those with 3 or 5 have valency 3, and those with 4 have valency 4. The noble gases (Ne, Ar, Kr, Xe, Rn) have valency 0, since they already have full outer octets. There are numerous exceptions though, the most important being hydrogen. Hydrogen has valency one because the n = 1 shell can contain only two electrons: there is no 'octet' of s and p orbitals to fill, only a doublet of a single s orbital. The transition metals (the d block) can generally have more than one valency, since there are various energetically favourable arrangements using their partially filled s, p and d orbitals for bonding.

Different types of bond form depending on the character of the elements involved. Ionic bonds are formed between elements of very different electronegativities. For example, fluorine desperately 'wants' an electron, and caesium is 'desparate' to lose an electron, and therefore they will readily react to form ions:

F₂ + 2Cs → 2F⁻ + 2Cs⁺

The bond between the F⁻ and Cs⁺ ions is called an ionic bond, and is typical in compounds formed between a metal and a nonmetal.

Metallic bonds are formed between two metals, and indeed, between atoms of a single metallic element. They are somewhat like covalent bonds (as in iodine fluoride), in that the electrons are shared between the metal atoms, but rather than a 1:1 sharing, all the valency electrons are shared between all the atoms, forming a sort of 'electron gas' between the metal atoms, and accounting for the electrical conductivity of metals. These sorts of bond are not very important in biochemistry, as most organisms are not made of metal ☺

Covalent bonds are formed when electrons are shared between two atoms, as in the iodine fluoride above. If two nonmetals react to form a compound, they usually form a covalent bond, because nonmetals have similar electronegativities. However, a 'perfect' covalent bond is only formed between the atoms of the same element, e.g. in Cl₂. All other covalent bonds have a slight ionic character, called polarity, and such bonds are called polar covalent. In ICl, the chlorine (Cl) is rather more electronegative than the iodine (I), and hence the electrons will spend slightly longer around the chlorine than the iodine. This gives the chlorine a slight negative charge (δ-), and the iodine a slight positive charge (δ+). Various weak bonds can be formed between such polar molecules. The most important in biochemistry is the hydrogen bond, which will be covered later.

An important consequence of polarity is the concept of oxidation number. The oxidation number of an atom in a molecule is basically the charge that the atom would have if the molecule were broken up into the ions that the atoms might 'like' to be. For example, the O-H bond in water is very polar: H is slightly positive (and valency 1), and O slightly negative (and valency 2). Hence, the oxidation numbers are -2 for the oxygen, and +1 for the hydrogens, because if we could break H₂O into the ions it might 'like' to be, we'd get H⁺ O²⁻ H⁺ . In fact, in almost all biochemical compounds, H has an oxidation number of +1, and O an oxidation number of -2. Other elements have more variable oxidation numbers, but a few simple rules will get you by in most cases:

The sum of the oxidation numbers in the molecule must add to the charge on the molecule or ion (zero if it is uncharged).
The electronegativity series for the common biochemical elements goes (most negative) F > O > Cl > N > S > C > H > P > Fe > Mg > Ca > Na > K > Fr (least negative).
An element in combination with itself has oxidation number 0, hence Cl in Cl₂ has oxidation number 0, as there's no polarity in the Cl-Cl bond.
Oxygen almost always has oxidation number −2, except in e.g. OF₂ (where it's +2, because F is more electronegative), and in peroxides H₂O₂ (where it's −1, because the oxygen is half in combination with itself).
Hydrogen almost always has oxidation number +1, except in e.g. H₂ (0) and NaH (−1).
Transition element compounds are usually named by their oxidation numbers in Roman numerals. Iron (III) chloride is FeCl₃, iron (II) oxide is FeO.

From these rules, you can work out that the oxidation number of N in NH₃ is −3, that of S in SO₄⁻² is +6, N in NO₃⁻ is +5, Fe in Fe⁺² is +2, etc. I hope ☺

The valence bond theory of covalent bonds is somewhat simplistic, and more quantum mechanical treatments of molecular bonding try to apply the same sort of reasoning to molecular bonds as to atomic orbitals. In the most refined treatment, molecular orbital theory, the valence electrons (in fact, all the electrons) are shared in molecular orbitals. However, somewhere between valence bond theory and full blown molecular orbital theory, we come across the concept of hybridisation, which is used to account for the shapes of covalent molecules. The valence orbitals (outermost s and p orbitals) are hybridised (mathematically mixed) before bonding, converting some of the dissimilar s and p orbitals into identical hybrid spⁿ orbitals.

sp³ hybrid orbital

sp² hybrid orbital

sp hybrid orbital

sp³ hybrids are formed by mixing the outermost s and all three outermost p orbitals to form four sp³ hybrids. The furthest these four [negatively charged, and therefore repulsive] orbitals can get from each other is the corners of a tetrahedron (109°).

sp3 hybrid orbitals are directed to the corners of a tetrahedron.

Any hybrid orbitals containing one electron can overlap with orbitals on other atoms to form bonds. For example, hydrogen has an s orbitals containing just one electron. An sp³ hybridised carbon atom has four sp³ hybrids each containing a single electron:

Hydrogen 1s¹: one electron available for bonding
Carbon (unhybridised) 1s² 2s² 2p_x¹ 2p_y¹ 2p_z⁰: only two unpaired electrons available for bonding.
Carbon (hybridised) 1s¹ (2sp³)₁¹ (2sp³)₂¹ (2sp³)₃¹ (2sp³)₄¹: four unpaired electrons available

The overlap and pairing of the s orbitals of four hydrogen atoms with the sp³ hybrids on a carbon forms four covalent bonds in the methane molecule CH₄.

The overlap of hydrides with other orbitals forms σ bonds.
Overlap four s orbitals from four hydrogens (blue) with four sp3 hybrids on carbon leads to formation of bonds, each containing one electron from the carbon and one from the hydrogen: these are represented by up and down pointing arrows, showing the pairing of the electron spins.

The hybridisation also accounts for the shape of molecules like methane (tetrahedral), ammonia (trigonal pyramid), water (V-shaped), and hydrogen fluoride (linear). Note that the orbitals not involved in bonding to hydrogen are still hybridised, but end up as lone pairs of electrons (symbolised by the two dots in the diagram below).

The shape of the hybrid orbitals of hydrides of C, N, O and F are the same, but in methane, none are lone pairs, in ammonia one is a lone pair, so ammonia is a sort of pyramid shape, water is a V shape because two orbitals are lone pairs, and HF is linear with three lone pairs.

sp² hybrids are formed when only one s and two p orbitals are involved. This leaves one remaining p orbital, which may be involved in forming a double bond. The furthest these orbitals can get from one another is a trigonal bipyramid, with the sp² hybrids arranged at 120° to each other in a plane. This is characteristic of molecules with double bonds.

sp2 hybrids.
Three sp² hybrids in lilac, with two lobes of the remaining p orbital in orange.

Finally, sp hybrids are formed using just one s and one p orbital. Two sp hybrids are formed from them, and the two p-orbitals remaining may contribute to a triple bond. These arrange themselves at the corners of an octahedron, with the two sp hybrids diametrically opposite one another. sp hybridisation is characteristic of the triple bond.

sp hybrids.
Two sp hybrids in pale-blue, with four lobes of the two remaining p orbitals in orange.

The formation of bonds involves the overlap of hybrid orbitals with the orbitals of other atoms, as we saw with methane. However, two sorts of bond can result from different sorts of overlap. When s and/or hybrid orbitals overlap 'end-on', sigma bonds (σ) are formed: these have a single area of electron density between the nuclei of the two atoms whose orbitals are overlapping. In the diagrams below, σ bonds are shown as simple lines. However, p orbitals can overlap sideways too: when this happens (as in ethene and ethyne below), two lobes of electron density are formed between the atoms. This is termed a pi bond (π). From the diagram, you can see that the double bond in ethene is composed of one σ plus one π bond, and the triple bond in ethyne is one σ pus two π. (There are also δ and φ bonds that describe the various ways d and f orbitals can overlap, but we don't want to go there!).

The shape and number of π and σ bonds in ethane, ethene and ethyne.
Ethane (top) has only sigma bonds, ethene (middle) and ethyne (bottom) have pi bonds too.

Rotation is possible about a σ bond, but not (at room temperatures) about a π bond, which causes geometric isomery.

2s σ bond

2p π bond

Full blown molecular orbital theory is even more complex than this, and we will only look at a few simple examples, for example the formation of a bond between two oxygen atoms. To consider the bond formation in this molecule, we mathematically add and subtract orbitals of similar energy and orientation to form molecular orbitals. Oxygen has the electronic configuration 1s² 2s² 2p⁴. When two oxygen atoms are brought together, orbitals of similar energy and orientation can be combined to form molecular orbitals, as shown in the diagram below. On the left and right, we can see the atomic orbitals of two oxygen atoms, replete with their electrons, When we bring them close enough together to form a bond, they combine to form the molecular orbitals shown in the middle, which are then filled with electrons as usual (lowest energy first, only pair if we must). So how do we predict the shape and number of the molecular orbitals?

Molecular orbitals for dioxygen.

It's actually much easier than you might think. s orbitals can only overlap 'end-on'. If we mathematically add these orbitals together, we get a sigma bonding orbital (bottom), if we subtract them, we get a sigma antibonding orbital (top). Hence, in out molecule of dioxygen, we have one σ_1s and one σ_1s^* orbital from the overlap of the 1s orbitals, and likewise, a σ_2s σ^*_2s from the overlap of the 2s orbitals.

s σ orbitals.

p orbitals can overlap in two ways: if we bring two oxygen atoms together, you can see that one orientation of p orbitals (say p_x for the sake of argument) will meet 'end on', whereas the other two pairs, p_y p_z will meet 'sideways on'. The first direction will form a sigma bond/antibond pair and the sideways overlap will form a pi bond, as we saw with the hybridisation theory earlier, and a pi antibonding orbital too:

p σ orbitals.
p_x orbitals overlap end-on, forming a σ_2px orbital and a σ_2px^* antibonding orbital.

p π orbitals.
p_y orbitals overlap sideways on forming a π_2py orbital and a π_2py^* antibonding orbital. The same applies to the 2p_z orbitals.

The exact order of molecular orbital energies in the dioxygen molecule is somewhat difficult to discern, as hybridisation of the s and p orbitals (as we saw earlier) has some influence over this. However, the diagram earlier shows the actual order, and it is a simple (!) matter to determine that the electronic structure of dioxygen is:

(σ_1s)²(σ_1s^*)²(σ _2s)²(σ_2s^*)²(σ _2px) ²(π_2py)⁴ (π_2py^*)²(σ_2px^*) ⁰

The bond-order of dioxygen (or any molecule) is the number of electrons in bonding (unstarred) orbitals minus those in antibonding (starred) orbitals divided by two. It's easy to see that for dioxygen, this is ( 10 − 6 ) ⁄ 2 = 2 (a double bond). If the bond order is greater than zero, the bond will form, showing that dioxygen is a real molecule. On the other hand, the equivalent for dihelium would be:

(σ_1s)²(σ_1s^*)²

Here the bond order is zero, and that's why He₂ doesn't exist. And that's enough of that!

Intermolecular bonds

Before we finish off on bonding, we'll quickly mention the various sorts of intermolecular bond. Intramolecular bonds, such as we have been describing up until now, form within molecules. Intermolecular bonds are those formed between different molecules or atoms. They come in two main sorts: the hydrogen bond, very important in biology's favourite solvent, water, and Van Der Waals' forces.

Water is slightly warped from a perfect tetrahedron because the lone pairs repel a little more than the sigma bonds.

Chemically, water is hydrogen oxide, H₂O. The oxygen atom is sp³ hybridised, forming two sigma bonds to two hydrogen atoms, and leaving two orbitals containing just lone pairs of electrons. Oxygen is highly electronegative, hence the water molecule is very polar, with δ− on the oxygen and δ+ on the hydrogens. The negative charge is partially localised in the lone pairs, which repel each other just enough to squash the H-O-H bond angle to slightly less than the 109.5° you get in a symmetrical molecule like methane. The slight positive charge on the hydrogen atoms is attracted to the slight negative charge on the oxygen atoms in other water molecules, hence there is a great deal of intermolecular attraction between water molecules, somewhat akin to the forces you would have if you threw hundreds of bar-magnets into a cardboard box. The attraction is called a hydrogen bond and is extremely important for stabilising the structure of many biological macromolecules (e.g. DNA, RNA, proteins, cellulose).

Water forms intermolecular hydrogen bonds.

In water, the hydrogen-bond donor is the H bonded to the electronegative O and the acceptor is the lone pair of another O. Note that the hydrogen bond is about twice as long (0.18 nm) as the covalent O-H bond (0.1 nm). However, other acceptors and donors exist:

Other donors : H bonded to N, F, Cl.
Other acceptors : lone pairs on N, F, Cl.

So NH₃ (ammonia) is also H-bonded in the liquid state, but more weakly than water (the reason it is a gas at STP), because nitrogen is less electronegative than oxygen, and hence the polarity of the N-H bond is less pronounced. Hydrogen bonds also form in ice, and since this holds the ice in a more open structure than in liquid water, it is actually less dense than water, and it floats.

There is another sort of weak intermolecular force besides the H-bond (and also beside the strong bonds of covalent, ionic and metallic bonds). This is the Van Der Waals' force, which comes in three varieties:

Dipole dipole interactions: between other partial charges on polar molecules.
Dipole induced dipole interactions: between a polar molecule and a non-polar molecule which has developed a dipole in response (like a piece of non-magnetic iron is attracted to a magnet).
London dispersion forces: between non-polar molecules which by chance occasionally have an imbalance of charge, and are fleetingly polar.

The strength of weak intermolecular forces varies from strong (hydrogen bonds) to very weak (London forces).

The Van Der Waals' radius of an atom is the 'size' of an atom. There is a weak attractive force between any two atoms, up to a point. If you squash atoms/molecules more closely than this they will begin to repel each other. The VDW radius is the size of the molecule just on the cusp between attraction and repulsion.

Hydrophobic forces (the way that fats seem to attract one another and hence form a layer on top of water) are often described as being due to Van der Waals' force between lipids. This is rubbish. The forces are far too weak. In fact, lipids force water to be more ordered around them, and ordered states, like high energy states, are unfavourable, hence the association of lipids is favoured because less water is forced to be ordered, not because of the very weak attraction between alkyl chains.

Test yourself

Why does fluorine form anions readily, but potassium forms only cations?
Write the electronic configuration for iron.
What is the oxidation number of chlorine in KClO₃?

Fill in this table to show the number of sigma and pi bonds present between the two atoms indicated in bold. Ethanenitrile is the correct name for acetonitrile (methyl cyanide), which is used in chromatography.

Name	Formula	Type of bond	Number of σ	Number of π
Ethane	H₃C-CH₃	Single	1	0
Propyne	H₃C-C≡CH
But-1-ene	H₃C-CH₂-HC=CH₂
Propan-1-ol	H₃C-H₂C-CH₂OH
Ethanenitrile	H₃C-C≡N

What is the bond order for Ne₂? Its molecular orbitals follow the same energy level pattern as oxygen.
Why is hydrogen-bonding important in biological systems?

Answers

This page has been peer reviewed by 4 people. Thanks to Avnish Patel, Heather Drew and Frank Miskevich for their corrections.

Science

Reference

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Contents

Electron orbitals and the periodic table

Molecular bonding

Intermolecular bonds

Test yourself