Green–Davies–Mingos rules

Nucleophilic attack is preferred on even-numbered polyenes (even hapticity).[1]

Nucleophiles preferentially add to acyclic polyenes rather than cyclic polyenes.[1]

Nucleophiles preferentially add to even-hapticity polyene ligands at a terminus.[1] Nucleophiles add to odd-hapticity acyclic polyene ligands at a terminal position if the metal is highly electrophilic, otherwise they add at an internal site.

Simplified: even before odd and open before closed

The following is a diagram showing the reactivity trends of even/odd hapticity and open/closed π-ligands.

The metal center is electron withdrawing. This effect is enhanced if the metal is also attached to a carbonyl. Electron poor metals do not back bond well to the carbonyl. The more electron withdrawing the metal is, the more triple bond character the CO ligand has. This gives the ligand a higher force constant. The resultant force constant found for a ligated carbonyl represents the same force constant for π ligands if they replaced the CO ligand in the same complex.

Nucleophilic addition does not occur if kCO* (the effective force constant for the CO ligand) is below a threshold value [2]

The following figure shows a ligated metal attached to a carbonyl group. This group has a partial positive charge and therefore is susceptible to nucleophilic attack. If the ligand represented by L_n were a π-ligand, it would be activated toward nucleophilic attack as well.

${\displaystyle {\ce {L_{\mathit {n}}-{}}}{\overset {\color {Red}\delta +}{\ce {M}}}{\ce {-C#}}{\overset {\color {Red}\delta +}{\ce {O}}}}$

Incoming nucleophilic attack happens at one of the termini of the π-system in the figure below:

In this example the ring system can be thought of as analogous to 1,3-butadiene. Following the Green–Davies–Mingos rules, since butadiene is an open π-ligand of even hapticity, nucleophilic attack will occur at one of the terminal positions of the π-system. This occurs because the LUMO of butadiene has larger lobes on the ends rather than the internal positions.

The following is an example of a complex containing three types of π-ligands, demonstrating the preferential attack of a nucleophile at one of the π-systems.

The above complex contains three types of π-ligands. The cyclooctane ring contains a butadiene fragment on the left and an allyl fragment on the right. A cyclopentadiene ligand on the cobalt center gives the third type.

Attack of the cyanide nucleophile occurs preferentially at a terminus of the butadiene fragment. (The drawing above shows the incorrect product)
Following the rules given above, the butadiene fragment is an open ligand of even hapticity, which has greater reactivity than the allyl fragment, an open ligand of odd hapticity, or the cyclopentadiene, a closed ligand of odd hapticity.

Attack occurs at the terminus which will result in the conjugated product shown.

Here the ligand that is already attached to the metal acts as the nucleophile and attacks the metal center internally.[3][4]

Nucleophilic attack at terminal position of allyl ligands when π accepting ligand is present.[5]

If sigma donating ligands are present they pump electrons into the ligand and attack occurs at the internal position.

When asymmetrical allyl ligands are present attack occurs at the more substituted position.[6]

In this case the attack will occur on the carbon with both R groups attached to it since that is the more substituted position.

When large π ligands [7] are present they can undergo different kinds of nucleophilic attacks. In the following figure the nucleophilic attack can occur from either the top or bottom and reduce the double bond and add the nucleophile.

This nucleophilic attack can occur at either the top or bottom also and add the nucleophile.

Nucleophilic addition to π ligands can be used in synthesis. One example of this is to make cyclic metal compounds.[8] Nucleophiles add to the center of the π ligand and produces a metallobutane.