$($a$)$ In solution, a nickel$($II$)$ porphyrin undergoes a light induced cis$-$trans

isomerisation as shown in Figure $1.$ The isomerism is associated with

changes in the ${?}^{1}H-$NMR spectrum $($Figure $2),$ the magnetic and optical

properties.

Figure $2.$

Figure $1.$: Cis$-$trans isomerisation of a Ni$($II$)$ porphyrin; Figure $2.$: Changes in the

${?}^1$ H$-$NMR spectrum.

$($i$)$ Draw and label the d$-$orbital splitting diagrams to explain the observed

electronic changes and rationalise the changes observed in the ${?}^{1}H-$

NMR spectra.$($ii$)$ Using the spin$-$only formula, calculate the expected room temperature

magnetic moment of the cis and trans isomers.

$($iii$)$ Provide a reason for a possible deviation from the expected magnetic

moment of the cis isomer.

$($iv$)$ Sketch the expected temperature$-$dependence of the magnetic

susceptibility for the cis isomer on $($a$)$ cooling the sample, and $($b$)$

warming the sample.