Question

(a) Explain why the \(^{19} \mathrm{F}\) NMR spectrum of \(\left[\mathrm{PF}_{6}\right]\) appears as a doublet. (b) The \(^{31} \mathrm{P}\left\\{^{1} \mathrm{H}\right\\}\) NMR spectrum of trans\(=\left[\mathrm{PtI}_{2}\left(\mathrm{PEt}_{3}\right)_{2}\right]\) (3.10) shows a three-line pattern, the lines in which have relative integrals of \(\approx 1: 4: 1 .\) What is the origin of this pattern?

Short answer

(a) The \(^{19}\text{F}\) NMR of \([\text{PF}_6]^−\) is a doublet because of coupling with one \(^{31}\text{P}\) nucleus. (b) The \(^{31}\text{P}\) NMR in trans-[PtI2(PEt3)2] is a triplet (1:4:1) due to coupling with two \(^{195}\text{Pt}\) nuclei.

Step-by-step solution

Understand NMR Splitting

In NMR spectroscopy, splitting occurs due to the interaction between magnetic moments of neighboring nuclei. This interaction is known as scalar (or J) coupling. The splitting pattern can reveal the number of nearby nuclear spins that are causing the interaction.

Analyze the Species [PF6]−

In the molecule \([\text{PF}_6]^−\), phosphorus (P) has one \(^{19}\text{F}\) nucleus attached directly to it. \(^{19}\text{F}\) has a nuclear spin of 1/2. The \(^{19}\text{F}\) NMR spectrum appears as a doublet because the single \(^{31}\text{P}\) nucleus, which also has a nuclear spin of 1/2, couples with each \(^{19}\text{F}\) nucleus, splitting the peak into two.

Recognize Doublet Formation

The number of peaks in a split signal is given by \(n + 1\), where \(n\) is the number of equivalent neighboring nuclei. Here, the \(^{19}\text{F}\) nuclei experience coupling with one neighboring nucleus \(^{31}\text{P}\) with a spin of 1/2, thus creating a doublet (1 + 1 = 2).

Analyze the Species Trans-[PtI2(PEt3)2]

In the compound trans\(=[\text{PtI}_2(\text{PEt}_3)_2]\), the \(^{31}\text{P}\) nucleus is coupled to \(^{195}\text{Pt}\) which has a spin of 1/2. Generally, coupling of such a nucleus (n=2) with spin-1/2 causes splitting into \(n + 1\), forming a triplet.

Explain Triplet Formation

The \(1:4:1\) triplet pattern arises from coupling of the \(^{31}\text{P}\) nucleus with two equivalent nuclei. These \(^{195}\text{Pt}\) nuclei result in splitting patterns where the probability of spin alignment produces a pascal triangle distribution \(1:2:1\), consistent with the \(2I + 1\) rule for one \(I = 1/2\) nucleus, adjusted slightly by \(^{195}\text{Pt}\) interaction probabilities achieving \(1:4:1\).

Key concepts

Scalar Coupling

Scalar coupling, also known as J coupling, is an important concept in NMR spectroscopy. It refers to the interaction between magnetic moments of nuclei via the bonding electrons in a molecule. This interaction causes the splitting of NMR signals, revealing valuable structural information. For example, if you have two nuclei close to each other, they can influence each other's magnetic environment.
These interactions are often mediated through chemical bonds and depend highly on the distance and number of bonds between the coupled nuclei. In the case of the \(^{19}F\) NMR spectrum of \(\left[\text{PF}_{6}\right]^{-}\), scalar coupling occurs between the \(^{31}P\) and \(^{19}F\) nuclei. These nuclei each have a spin of \(1/2\), leading to a doublet in the spectrum.
Understanding scalar coupling can help identify the number and types of neighboring nuclei around a specific atom in a molecule. This makes it a powerful tool for deducing molecular structures and configurations:

Nuclear Spin

Nuclear spin is a fundamental property of nuclei, just like charge and mass. It originates from the intrinsic angular momentum possessed by a nucleus. In NMR spectroscopy, nuclear spin is denoted by a quantum number, often \(I\).
Nuclei with a non-zero spin can have different alignments in the magnetic field, causing changes in energy levels which are detected in NMR. For example, \(^{1}H\), \(^{19}F\), and \(^{31}P\) all have a spin of \(1/2\), which is common for many NMR-active nuclei.
Their spins result in two possible orientations: either aligned or opposed to the magnetic field, leading to the absorption of energy at characteristic frequencies. This property is key to the principles of NMR, as it allows us to probe nuclei through radiofrequency pulses. In the \(\left[\text{PF}_{6}\right]^{-}\) molecule, both phosphorus and fluorine couple due to their spins, resulting in the observable splitting pattern.

Splitting Pattern

The splitting pattern in NMR spectroscopy provides insight into the number of neighboring nuclear spins affecting the observed nucleus. Such patterns arise due to scalar coupling between nuclei, and they obey the \(n + 1\) rule, where \(n\) is the number of equivalent neighboring nuclei.
For instance, in \(\left[\text{PF}_{6}\right]^{-}\), the \(^{19}F\) nucleus experiences scalar coupling with a single \(^{31}P\) nucleus. Since \(n = 1\), this leads to a doublet in the \(^{19}F\) NMR spectrum (1 + 1 = 2 peaks).
In another example, the \(^{31}P\) spectrum of trans\(=\left[\text{PtI}_{2}\left(\text{PEt}_{3}\right)_{2}\right]\) shows a triplet pattern with intensities of \(1:4:1\). This results from coupling with two equivalent \(^{195}Pt\) nuclei (spin 1/2 each), forming a triplet (2 + 1 peaks) reflecting the complex's structure.

Chemical Shift

Chemical shift is a critical concept in understanding NMR spectra. It refers to the change in resonance frequency of a nucleus due to its magnetic environment. The chemical shift provides clues about the electronic environment surrounding a nucleus.
Different chemical shifts reflect variations in electron density around the nuclei, influenced by electronegative atoms or functional groups. For example, nuclei closer to electronegative atoms will experience a greater electron shielding effect, appearing at a higher shift (more deshielded).
In our examples, both the \(^{19}F\) and \(^{31}P\) nuclei exhibit signals at characteristic chemical shifts. The environment around these nuclei can help deduce not just their atomic surroundings but also nuances in bonding and molecular conformation.