Colour in Transition Metal Complexes (HL) (HL IB Chemistry)

• Transition elements form coloured complexes when they bond with ligands
• Ligands are molecules, such as ammonia and water, or ions, such as ammonium or chloride ions that form a coordinate bond to a central metal ion
  • For more information, see our revision note on Coordination Bonds

Crystal Field Theory (CFT)

• The crystal field theory is a model based on electrostatic point charges and is used to explain colour in transition metal compounds
• In a transition metal atom, the five orbitals that make up the d-subshell all have the same energy
  • The term for this is degenerate
• However, when ligands are attached to a transition metal ion, the electric field formed by the lone pairs of electrons on the ligands repel the electrons in the d-subshell causing the d-orbitals to split in energy
• The dative bonding from the ligands causes the five d orbitals to split into two sets
• These two sets are not equal in energy and are described as being non-degenerate orbitals

The effect of ligands on the d-orbitals of a central transition metal ion

Upon bonding to ligands, the d orbitals of the transition element ion split into two non-degenerate sets of orbitals

• The central metal ion in a complex has five d-orbitals for the electrons

Diagram showing the shapes and orientation of the five d-orbitals

The names of the different d-orbitals are based on their position in the x, y and z planes. The shapes are shown here for reference only. You are not required to know the shapes of d-orbitals in the exam

Perception of colour

• Most transition metal compounds appear coloured
• This is because the difference in energy between the non-degenerate orbitals allows electrons in the lower energy orbitals to be promoted into the higher energy orbitals
  • A larger splitting of the d-orbitals means that more energy is required to promote an electron
• This happens when the complex absorbs light energy with a wavelength corresponding to the energy gap between the orbitals
  • With a larger splitting of d-orbitals, light of a shorter wavelength and higher frequency is absorbed
• The amount of energy absorbed relates to certain parts of the visible electromagnetic spectrum
• The colour that is seen is complementary to the colour that is absorbed, i.e. it is made up of the parts of the visible spectrum that aren’t absorbed
  • For example, a green compound will absorb all frequencies of the spectrum apart from green light, which is transmitted

The colour wheel

The colour wheel shows complementary colours in the visible light region of the electromagnetic spectrum

• Complementary colours are any two colours which are directly opposite each other in the colour wheel
  • For example, the complementary colour of red is green and the complementary colours of red-violet are yellow-green

Absorption of light

• When white light passes through a solution of aqueous nickel(II) sulfate, an electron in the lower energy d-orbitals is excited and jumps up into the higher energy d-orbitals
•  A photon of red light is absorbed and light of the complementary colour (green) is transmitted
• This is why nickel(II) sulfate solution appears green
• The energy of the separation is ΔE corresponding to a wavelength of about 647 - 700 nm

Illustration of the electron promotion process in Nickel(II)

During electron promotion of a Ni(II) complex, an electron jumps from a d_x orbital to a d_x²-y² orbital when light is shone on the solution

Wavelength, frequency and energy

• A greater splitting of the d-orbitals results in a larger energy gap, ΔE 
• This means that more energy is needed to promote an electron from a lower to a higher energy orbital
• Therefore, the light needs to have:
  • Shorter wavelength
  • Higher frequency
• The equations relating wavelength, frequency and energy are:

speed of light (3.00 x 108 m s-1)	=	frequency (s-1)	x	wavelength (m)
c		f		λ
energy (J)	=	Planck's constant (6.63 x 10-34 J s)	x	frequency (s-1)
E		h		f

• These are given in Section 1 of the Data Booklet, so there is no need to memorise them, although you do need to how to manipulate them and what the units are
• The constants are listed in Section 2 of the data Booklet