Use the delta scale and TMS reference

On a 400 MHz instrument a signal 400 Hz from TMS has δ = 1.00 ppm.

GCE A-Level H3 Chemistry 9813-2027

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Learning objectives

Use the delta scale and TMS reference

Anchor shifts to TMS

On a 400 MHz instrument a signal 400 Hz from TMS has δ = 1.00 ppm.

The same environment at 600 MHz is 600 Hz from TMS but remains δ = 1.00 ppm.

TMS provides one sharp reference signal because all twelve of its protons are equivalent. Its signal is assigned δ = 0 ppm, allowing sample positions to be reported relative to a common standard.

Define the reference and scale

Tetramethylsilane, Si(CH₃)₄, defines δ = 0 ppm and gives one sharp line from twelve equivalent protons.

Use δ=(νsample−νTMS)/ν0 × 10⁶, with both frequencies in the same units.

Chemical shift is the frequency difference from TMS divided by the instrument operating frequency, multiplied by 10⁶. The ratio removes the instrument-frequency dependence and produces the ppm scale.

Why ppm transfers

Absolute Hz separation grows with operating frequency, while division by ν0 removes that field dependence.

TMS is chemically unreactive in typical samples, volatile, and normally appears away from organic proton signals.

TMS is highly shielded, so most ordinary organic proton signals appear at positive δ values downfield from it. It is also volatile and chemically unreactive under normal measurement conditions, making removal and non-interference practical.

Calculate a shift

A 500 MHz spectrum places a signal 750 Hz from TMS: 750/(500 × 10⁶)×10⁶ = 1.50 ppm.

The MHz-to-Hz conversion must be made before cancellation.

A 300 Hz separation on a 300 MHz instrument gives δ = (300/300,000,000) × 10⁶ = 1.00 ppm. State the ratio before cancelling powers of ten.

Try this

Find δ for 750 Hz at 500 MHz.

Check your answer

A strong answer should include 1.50 ppm and correct frequency ratio.

Convert ppm to hertz

Supplied data: a signal at δ = 2.00 ppm on a 300 MHz spectrometer.

Use offset (Hz) = δ (ppm) × operating frequency (MHz); the 10⁻⁶ in ppm cancels the 10⁶ in MHz.

If both the frequency separation and operating frequency double for the same chemical environment, δ remains unchanged. This is the key reason spectra from different field strengths can be compared.

Try this

Find the offset for δ = 2.00 at 300 MHz.

Check your answer

2.00 × 300 = 600 Hz from TMS. Dividing instead (300 ÷ 2.00 = 150 Hz) is the common slip.

Compare instruments

Supplied data: a signal at δ = 4.20 is recorded on a 400 MHz and a 600 MHz spectrometer.

Apply the same conversion at each frequency, then say whether δ changes.

When reading a conventional spectrum, remember that δ increases to the left even though a mathematical number line normally increases to the right. Use the printed axis rather than guessing.

Try this

Calculate both offsets.

Check your answer

4.20 × 400 = 1680 Hz and 4.20 × 600 = 2520 Hz from TMS. The separation in hertz scales with the operating frequency, so δ stays 4.20 on both instruments.

Common mistake: an absolute-scale claim

TMS is assigned zero by convention; it does not have zero resonance frequency.

Every nucleus resonates near the instrument frequency, while δ reports only a relative displacement.

TMS does not make every sample proton resonate at zero. It defines the reference from which each sample displacement is measured.

Try this

Better reasoning: ‘TMS absorbs at 0 Hz.’

Check your answer

State δ = 0 ppm rather than zero absolute frequency.

Apply the portable scale

After the check questions, complete the 500 MHz calculation without notes. Return later for a different 600 MHz question.

Next: explain inductive deshielding.

For a calculation, show frequency difference, operating frequency, the 10⁶ factor and the unit ppm. For an interpretation, state upfield/downfield relative to TMS explicitly.

Try this

Annotate νsample, νTMS, ν0 and δ on the fixed table.

Check your answer

A strong answer should include units, sign convention and field-independent ppm.