User Guide

Changing the Plot View

In the simulation plot frame, the following mouse actions by default will adjust the plot:

  • Left mouse click and drag: moves the plot.
  • Right mouse click and drag: compresses/stretches the plot (left/right horizontally, up/down vertically).
  • Middle scroll wheel: zoom in/out.
  • after an adjustment has been made, clicking the “A” symbol in the lower left corner resets the view.

In addition to these actions, a single right mouse button-click will open a context menu (this feature is built into the pyqtgraph widget used to create the plots). Many of these options aren’t useful for NMR plots, but here are some options that are useful:

  • X Axis and Y Axis let you select the x- and y- range for the plot. In addition to this, selecting the “Auto” radio button under Y Axis ensures that the largest peak uses the entire vertical range. This is very useful for DNMR simulations, because as line widths broaden towards coalescence their intensity is greatly reduced. Selecting this option allows the signal to fill the window, and scale the y-axis labels as needed.
  • Mouse Mode ▶ 1 button changes the default mouse behavior, so that clicking and dragging a rectangular region of the spectrum zooms to that region.
  • Export… allows you to save the plot in a variety of formats, including PNG, TIF, JPG and SVG. You can also export the plot data as a CSV file.

Calculation Type Selection

The Calc Type menu lets you choose from three submenus of models:

  • Multiplet: Simulation of first-order multiplets (“1stOrd”), plus common second-order patterns such as AB, ABX and AA’XX’ that have algebraic solutions (i.e. quantum mechanical solutions are not required).
  • ABC…: Second-order (quantum-mechanical) simulation of up to 8 coupled nuclei. (‘ABC…’ refers to the Pople nomenclature convention of using a different upper-case letter for each set of chemical shift-nonequivalent nuclei, e.g. AB; AB2)
  • DNMR: Dynamic NMR lineshape simulations.

The Multiplet Menu: non-QM Solutions

These models have alebraic solutions that don’t require a quantum-mechanical approach: [1]

  • 1stOrd: a first-order multiplet
  • AB: an AB quartet.
  • AB2: an AB2 system.
  • ABX: an ABX system.
  • ABX3: an ABX3 system.
  • AAXX: an AA’XX’ system.
  • AABB: an AA’BB’ system.

Conventions Used

Vcentr: The central frequency that a signal is distributed about. For 1stOrd, this is the centre of the multiplet. For other models, it is the average frequency (in the absence of coupling) between the two signals that are the focus of the simulation (A and B for AB, ABX and ABX3; A/A’ and B/B’ or X/X’ for AA’BB’/AA’XX’). i.e.

\[V_{centr} = \frac{|\nu_A - \nu_B|}{2}\]

Vab: The difference in frequency between nuclei A and B (in the absence of coupling), i.e. \(\Delta\nu_{AB}\)

Jmn corresponds the the Jmn coupling between M and N nuclei. “Jax” and “Jax_prime” refer to the JAX and JAX′ couplings, respectively.

First-Order Multiplet

This model will simulate a first-order multiplet. The simulation is limited to a maximum of 4 different J values (JAX/JBX/JCX/JDX) but can have multiple couplings of each size.

AB and AB2

These simulations take parameters for Jab, Vab and Vcentr. Keep in mind that, if you are trying to match an experimental AB pattern, that Vab is not the midpoint of the individual “doublet” for A and B. As the degree of second-order behavior increases (as Vab decreases), \(\nu_A\) and \(\nu_B\) will be closer to the larger, inner peaks than the smaller, outer peaks:

TODO: add graphic

ABX

This ABX model is an analytic solution for the case where the frequency of HX is far from Vcentr. This simplifies the math, but the appearance of the HX does not change as \(\nu_X\) changes. If accuracy is required, the “ABC…” Calc Type should be used to model the exact second-order behavior.

ABX3

This simulation makes two simplifying assumptions:

  • the frequency of HX is far from Vcentr
  • \(J_{AX} \approx J_{BX}\) (which is usually the case)

This is effectively an AB quartet where each of the 4 lines is further split into a first-order quartet. The simulation only displays the AB part of the signal.

AA’XX’

This simulates one half (e.g. the A part) of an AA’XX’ spin system. The simulation assumes a very large frequency difference between HA and HX.

AA’BB’

This is a complete second-order (quantum-mechanical) simulation for an AA’BB’ spin system. No simplifying assumptions are made.

[1]See: Pople, J.A.; Schneider, W.G.; Bernstein, H.J. High-Resolution Nuclear Magnetic Resonance. New York: McGraw-Hill, 1959.

The ABC… Menu: QM Simulation of Second-Order Spin Systems

uw-dnmr can simulate a second-order spin system for up to 8 spin-1/2 nuclei. [2] Frequencies for each nucleus 1-n can be entered using the V1 … Vn entry widgets along the top of the application window. Clicking the Enter Js button to the right of these entries pops up a window with a grid of entries for the J coupling constants. The frequencies of the nuclei can be adjusted in the pop-up window as well as the main window.

[2]This is the same limit as in WINDNMR. However, the nmrsim library behind the QM calculations can simulate systems of up to 11 nuclei, so this could be increased at some point in the future.

The DNMR Menu: Simulated Lineshapes for Exchanging Nuclei

Currently uw-dnmr can sumulate DNMR lineshapes for:

  • two uncoupled nuclei undergoing exchange
  • two coupled nuclei undergoing exchange

More models from WINDNMR will be added over time, as they are added to the nmrsim library.

2-spin

This lineshape is calculated by the method reported by Sandström. [3] The parameters are:

  • Va/Vb: the frequencies of nuclei A and B (as seen at the slow-exchange limit)
  • ka: the rate constant for the transition of a nucleus from state A to state B.
  • Wa/Wb: the line widths at half height, at the slow-exchange limit
  • %a: the percent population of state A (vs. state B).

One difference between uw-dnmr and WINDNMR is that the latter used ka + kb. So, a uw-dnmr simulation using ka = 100 should produce an identical result to a WINDNMR simulation using ka + kb = 200.

AB Coupled

This lineshape is calculated using the method reported by J.A. Weil et al. [4] The parameters are:

  • Va/Vb: the frequencies of nuclei A and B (as seen at the slow-exchange limit and in the absence of coupling)
  • J: the JAB coupling constant
  • kAB: the rate of exchange between the nuclei in state A and state B
  • W: the line width at half height, at the slow-exchange limit
[3]Sandström, J. Dynamic NMR Spectroscopy; Academic Press: New York, 1982.
[4]

Brown, K.C.; Tyson, R.L.; Weil, J.A. J. Chem. Educ. 1998, 75, 1632. Note: an important math correction to the previous reference. Equation (2b) should read:

\[\begin{split}b_\pm &= 4\pi(\nu_o-\nu\pm J/2)(\tau^{-1}+\tau_2^{-1})\mp 2\pi J\tau^{-1}\\\end{split}\]

In the original paper, the final term erroneously used \("\pm"\) instead of \("\mp"\).