NMR Calculation¶

A Nuclear Magnetic Resonance (NMR) calculation predicts how the nuclei in a molecule respond to an external magnetic field — specifically, the extent to which the surrounding electron density shields each nucleus from that field. This shielding is what determines the chemical shift observed in an experimental NMR spectrum, so a computed NMR calculation gives a direct, first-principles route to predicting and assigning NMR spectra before (or instead of) running the experiment.

Unlike a Geometry Optimization or Frequency calculation, an NMR calculation is a property calculation on a single, fixed geometry — it does not move the atoms. It answers a different question entirely: not "what shape is lowest in energy?" but "how does the electron distribution around each nucleus respond to a magnetic field, at this geometry?"

What Is Nuclear Magnetic Shielding?¶

When a molecule is placed in an external magnetic field, the surrounding electrons circulate in response to it, generating a small local magnetic field that partially opposes the external one at each nucleus. The nucleus therefore experiences a slightly weaker effective field than the one actually applied — it is shielded, and the degree of shielding depends on the local electronic environment.

This gives each chemically distinct nucleus in a molecule

an isotropic shielding constant, the orientation-averaged value most directly connected to the observed chemical shift,
and a full shielding tensor, since the shielding is not the same in every direction — describing how it varies with the orientation of the molecule relative to the field.

Why Perform an NMR Calculation?¶

Computing NMR shielding provides information that is often difficult to obtain from experiment alone.

A successful NMR calculation allows the determination of

isotropic shielding constants for every nucleus in the molecule,
the full anisotropic shielding tensor at each nucleus,
chemical shifts, once referenced against a standard compound (e.g. TMS),
which nuclei are chemically equivalent by symmetry,
support for assigning or reinterpreting an experimental spectrum.

How Does Gaussian Calculate NMR Shielding?¶

Gaussian computes nuclear shielding using Gauge-Including Atomic Orbitals (GIAO), requested with the NMR=GIAO keyword. This avoids a well-known mathematical difficulty (the choice of gauge origin) that would otherwise make the computed shielding depend on an arbitrary coordinate choice — see Gauge-Including Atomic Orbitals (GIAO) for the underlying theory.

The general workflow is

Optimized Ground-State Geometry
        │
        ▼
NMR=GIAO Single-Point Calculation
        │
        ▼
Coupled-Perturbed Hartree-Fock/DFT Equations
        │
        ▼
Shielding Tensor at Each Nucleus
        │
        ▼
Isotropic Shielding + Anisotropy
        │
        ▼
Chemical Shift (relative to a reference compound)

Because this is a property calculation on a fixed geometry, the input geometry should already be a converged energy minimum — see Geometry Optimization if that step hasn't been done yet.

Characteristics of a Valid NMR Calculation¶

A correctly run NMR calculation should satisfy the following:

The job reaches normal termination.
The geometry used is a genuine, converged stationary point (ideally confirmed with a prior frequency calculation showing zero imaginary frequencies).
Chemically equivalent nuclei (by molecular symmetry) show matching isotropic shielding values, as a built-in sanity check on the calculation.
The method and basis set are consistent with whatever reference compound will be used to convert shielding into chemical shift.

Typical Applications¶

NMR calculations are commonly performed to study

Structure elucidation and verification.
Assignment of experimental ¹H, ¹³C, and other nuclei spectra.
Distinguishing between candidate structures or conformers.
Hydrogen-bonding and solvation effects on chemical shift.
Reaction intermediates too unstable to isolate experimentally.

Prerequisites¶

An NMR calculation is normally run on a geometry that has already been optimized (and ideally frequency-verified) at a consistent level of theory — see Geometry Optimization and Optimization + Frequency if these haven't been covered yet.

What You Will Learn¶

This section demonstrates how to perform an NMR calculation using Gaussian, on the formic acid dimer. The following topics are covered:

Preparing the Gaussian input file for an NMR=GIAO calculation.
Understanding the NMR-specific keywords.
Interpreting the Gaussian shielding tensor output.
Reading isotropic shielding and anisotropy values.
The GIAO method and why it is needed.
Converting computed shielding into a chemical shift.

Download Input

Complete Gaussian input used in this tutorial.

NMR Input
Download Output

Complete output file discussed below.

NMR Output