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Fourier Transform (FT) NMR and Determination of Molecular Diffusion Coefficients by Pulse Field Gradient (PFG) Experiment for Unknown Samples

-Revised and PFG implemented by Yoshitaka Ishii & Dan McElheny 10/19/2012 -Revised by Igor Bolotin 12/19/2011

1. Outline of Basic NMR Principles

Nuclear magnetic resonance (NMR), as all spectroscopic methods, relies upon the interaction

of the sample being examined with electromagnetic radiation, here in a range of radio frequencies (1-

1000 MHz). To absorb a photon of electromagnetic radiation, the transition energy ΔEsample due to the

interaction of a nuclear spin in the sample with a magnetic field must match that of the absorbed

radiation at a frequency of as

ΔEsample = Ephoton = ħω = hν = hc/λ (1-1) The NMR experiments will provide a broad range of information on a sample; in particular how the

NMR frequency can be used to determine structural and dynamical data.

Angular Momentum and Spin

Classically, a rotating particle possesses angular momentum. The nucleus of an atom can be

visualized as “rotating” and, consequently, has a spin angular momentum I. This angular momentum

is intrinsic to the nucleus, rather than the angular momentum arising from the molecule’s spinning in

space. While employing an analogy of spin with a rotating particle may be instructive, ultimately it

must be treated quantum mechanically. The magnitude of the spin angular momentum is given in

quantum mechanics by:

ħ [I(I +1)]½ I = 0, 1/2, 1, 3/2, … (1-2)

where ħ is Planck’s constant h divided by 2π and I is the spin angular momentum quantum number or

the “spin” of the nucleus. I has a quantized z-component:

Iz = ħm m = −I, …, 0, …, I (1-3)

where m is the magnetic quantum number with 2I +1 values. (The z-component is important as the

direction of the static magnetic field is chosen as the z axis and the component of the magnetic

moment which will interact with this magnetic field generated by the NMR spectrometer lies along

this axis.) Note the parallel between the orbital angular momentum quantum number l and magnetic

quantum number ml for the electron in a hydrogen atom and the I and m quantum numbers here.

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Nuclei of all elements are composed of protons (p) and neutrons (n), both of which have spin

I = 1/2. Thus the total nuclear spin is the sum of the spins of all the nucleons. The quantum treatment

indicates that protons and neutrons pair up separately and that even numbers of either have zero spin

angular momentum. The model leads to the three cases summarized in Table I.

Table I. Distinct Ways to Combine Spin of the Nucleons in an Atom

Spin Nucleon Description Examples

I = 0 even numbers of both p and n 12C: 6p, 6n

16O: 8p, 8n

I = n (integer) odd numbers of both p and n 2H: 1p, 1n, I = 1

10B: 5p, 5n, I = 3

I = n/2 (half integer) even p (n) and odd n (p) 13C: 6p, 7n, I = 1/2

23Na: 11p, 12n, I = 3/2

Nuclear Magnetic Moment

Classically, if a rotating particle is charged, it generates a magnetic dipole which creates a

magnetic field. The dipole has a magnetic moment. Associated with nuclear spin angular momentum

is the nuclear magnetic moment μ which can interact with a magnetic field:

μ = γ I (1-4)

where γ is the magnetogyric ratio, a constant characteristic of each nuclide. The magnetic moment

also has a quantized z-component:

μz= γIz = γħm (1-5)

Table II. Properties of Selected Nuclides

Nuclide I γ × 107 rad (Ts)-1 % Natural Abundance

Resonance

Frequency1 [MHz] 1H 1/2 26.7519 99.985 100

2H 1 4.1066 0.015 15.351

13C 1/2 6.7283 1.108 25.144

23Na 3/2 7.0801 100 26.466

1relative to a proton frequency of 100 MHz

Protons and neutrons are not actually true elementary particles but consist of charged fundamental

particles known as quarks. As such, both protons and neutrons contribute to the spin and can also

contribute to the nuclear magnetic moment, μ. However I = 0 spins have no spin and, thus, no

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magnetic moment. Table II summarizes properties of the four nuclides which will be encountered in

the NMR laboratory experiments.

Nuclear Spin in an External Magnetic Field (Zeeman Effect)

There is no preferred orientation for a magnetic moment in the absence of external fields. In

the absence of B0, the magnetic moments of individual nuclei are randomly oriented and all have

essentially the same energy. Application of an external magnetic field removes the randomness,

forcing the nuclei to align with or against the direction of B0. This change from a random state to an

ordered state is known as polarization. Such polarization means there is a difference in the population

of the various spin states.

Classically, in the presence of an external magnetic field B0 the energy of a magnetic moment

μ depends on its orientation relative to the field:

E = − μ . B0 (1-6)

which is a minimum when the magnetic moment is aligned parallel to the magnetic field and a

maximum when it is anti-parallel. From the quantum mechanical prospective, when a nucleus is

introduced into a magnetic field its magnetic moment will align itself in 2I +1 orientations (number

of values of the m quantum number) about the z direction of B0 where the energy is given by:

Em = − μz B0 = − γħmB0 (1-7)

For an I = 1/2 nucleus, there are only two orientations for the magnetic moment μ: 1) a lower energy

orientation parallel to B0 with a magnetic quantum number m = 1/2 often referred to as the α spin

state and 2) a higher energy anti-parallel orientation with m = −1/2 referred to as the β spin state. For

an I = 1 nucleus there are three possible orientations for the magnetic moment, these states are

illustrated below.

Directional quantization of the angular momentum P in

the magnetic field for nuclei with I=½ and 1

Energy level schemes for a nucleus

spin quantum number ½

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Transition Frequencies

NMR spectroscopy induces transitions between adjacent nuclear spin energy states (the

selection rule is Δm = ±1). The energy change for a nucleus undergoing an NMR transition from the

spin state characterized by the magnetic quantum number m to the state with quantum number m − 1

is:

ΔE = Em−1 – Em = [−γħ(m −1)B0] – [−γħmB0] = γħB0 (1-8)

Equation (8) follows from the previous discussions. The difference between the z-component of the

angular momentum of adjacent m states is ħ [Eq. (2)]. This difference is multiplied by γ to obtain the

difference in the magnetic moment z-component [Eq. (5)]. This result is then multiplied by the

magnetic field strength to obtain the energy difference between adjacent m states in a magnetic field

[(Eq.7)].

The frequency ν of the electromagnetic radiation used to induce an NMR transition between

adjacent m levels in an external magnetic field B0 is found from Eq. (1)

ν = ΔE/h = γħB0/h = γB0/2π (1-9)

The units of frequency (ν) are cycles/second, hertz (Hz) in SI units. In NMR spectroscopy, it is often

more convenient to use angular frequency (ω) with units of radians/second. Since one cycle equals

2π radians:

ω ≡ 2πν (1-10)

Since cycles and radians are not SI units, both ν and ω have the same SI units (s-1). The angular

frequency of an NMR transition is more commonly written as:

ω0 = γB0 (1-11)

which is the Larmor equation. Note that the use of ω

eliminates the occurrence of 2π in the Larmor equation. The

Larmor frequency has two important physical

interpretations. It is the frequency of the electromagnetic

radiation that induces a transition between nuclear spin

quantum states in the magnetic field. It is also the

precessional (or rotation) frequency of the nuclear magnetic

moment about the magnetic field as represented here for a

spin-1/2 nucleus (i. e. a spin with I = ½).

Precession of nuclear dipoles 

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TkE

low

highe

N

N

Boltzmann Statistics

In the presence of an external magnetic field, different nuclear spin states (with different

values of m) have different energies. The energy difference is proportional to B0. At thermal

equilibrium, these states will also have different populations, their ratio given by the Boltzmann

equation:

(1-12)

with Nhigh and Nlow the respective populations of the

upper and lower spin states, ΔE =Ehigh − Elow the energy

difference between the two states, k the Boltzmann

constant, and T the absolute temperature. In currently

achievable magnetic fields, the difference between

nuclear spin energy levels ΔE is much smaller than kT,

implying that Nlow is only very slightly in excess of

Nhigh. For 1H in a 9.4 Tesla field (400 MHz) and 300 K one obtains a population ratio N(α)/N(β) of

1.000064, i.e., for one million spins in the upper β state there are one million and sixty-four in the

lower energy α state! It is the excess 64 spins that respond to the NMR experiment and create the net

magnetization M0. To summarize, the larger B0 is the greater the energy difference ΔE between the

levels and the larger the ΔE the more excess population exists in the lower energy state (waiting to be

excited to the higher level).

The Pulse NMR Experiment and Fourier Transform NMR

The excess of nuclear spins in the lower energy α spin state is illustrated below on the far left.

In the presence of the B0 magnetic

field the precessing spins are distributed

equally about the z-axis. Their precessional

frequency ω0 is given by the Lamor equation

[Eq. (11)]. The vector sum of the individual

μ vectors [Eq. (4)] yields a net equilibrium

magnetization Mo along the positive z-axis.

(Due to the precession about the z-axis, the

Distribution of the precessing nuclear dipoles (total number N (=N+N) around the double cone. As N>N there is a resultant macroscopic magnetization M0 

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x and y components of the individual μ vectors sum to zero, leaving only the z component μz [(Eq.

(5)]). Excitation of the nuclei from the lower energy α spin state to the higher energy β spin state is

achieved with an oscillating radio frequency magnetic field B1 applied with a transmitter coil as a

short duration pulse along the x-axis (RF pulse). The oscillating magnetic field can be viewed as a

rotating magnetic field. When the rotating frequency of B1 is equal to the precession frequency of the

nuclear moments (ω0), B1 excites nuclei in the α spin state to the β spin state. This causes the net

magnetization M0 to rotate about the x-axis tipping it from the z-axis into the yz-plane. (One can

completely transform the z magnetization into y magnetization if the duration of the pulse is the

length of a π pulse, a 90° pulse.) The component of the magnetization in the xy plane, initially along

the y-axis (My) precesses about the z-axis at the precession frequency ω0. The net magnetization

along the y-axis is detected with an antenna coil illustrated with an eye in the figure on the previous

page. 

We will be conducting the experiments in a pulsed Fourier Transform NMR spectrometer

equipped with a superconducting magnet; a diagram of the spectrometer is shown below along with a

schematic of its operation. In the

pulse method of acquiring an NMR

spectra, all the nuclei of one species

in the sample are quickly excited

simultaneously by a “hard” pulse of

energy for a very short (~s)

duration of time. The power of this pulse is on the order of several

Watts at a range of frequencies such that all the nuclei absorb the

energy. This pulse of energy is applied perpendicular to the z-direction

of the applied magnetic field. As a result, the net magnetization of the

sample (M0) is itself turned 90°, and is thus “tipped” into the xy plane

as shown here.

This type of pulse is often called a pulse (as = 90°). Now that the magnetization

vector has turned on its side into the xy plane, the magnetization begins to precess which is detected

by a coil of wire. The wire experiences an oscillating magnetic field, and like a power plant, begins

to generate current which is amplified and detected by the electronics of the NMR spectrometer. The

signal will oscillate and eventually decays as the nuclear spins begin to precess incoherently from

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eachother and relax to their ground state. The signal is called a FREE

INDUCTION DECAY (FID). Here is a typical example

With respect to the eye, y-axis magnetization rises and falls in a

sinusoidal manner as the vector precesses about the z-axis. The amplitude

of the signal decays with time as nuclei in the higher energy β spin state return back to the lower

energy α state in a process known as nuclear spin relaxation. If the molecule has only a single

chemical shift, the signal appears as a simple decaying sine wave and the chemical shift in hertz is

the frequency of the sine wave relative to a reference frequency. Most molecules have many nuclei

with many different chemical shifts and correspondingly many different precession frequencies. The

B1 field actually contains a broad band width of frequencies that excite all the nuclei in a molecule at

the same time, and the net magnetization along the y-axis is the sum of the magnetization of each set

of equivalent nuclei, all precessing at different frequencies. The resulting complex waveform is

called the free induction decay (FID) or the time domain spectrum. It is a measure of y-axis

magnetization My as a function of time after the B1 pulse.

This signal is not very useful in its present form; to change it into an actual NMR spectrum,

we have to take the Fourier Transform

of the signal which is accomplished by

the following mathematical

relationship:

Spectrum () =

tetsignal ti )(

(13)

What the Fourier Transform shows

is how much of what oscillating frequencies

can be added together to equal the original

signal. Here are some examples of FIDs and

their Fourier Transforms (F.T.) where you

can see how the two are related:

Note that the frequency of the oscillations

changes the position of the peak. If the oscillating signal decays more quickly, the peak becomes broader due to the

fact that the FFT has less “signal”. This causes the FFT procedure to be less “sure” of the true frequency which is

why the peak broadens. Further, if there are clearly two frequencies overlapping, which appear as “beats” in the

FID, the FFT will reveal which two (or more!) frequencies are present.

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Nuclear Spin Relaxation

How do the nuclei rid themselves of the energy that they have absorbed from the NMR

spectrometer? The precession of spins in the xy-plane does not last forever. It decays due to three

distinct effects:

1. Spin-Lattice (or Longitudinal) Relaxation, T1 (mechanism which involves a net transfer of

energy from spin system to surroundings to reestablish Boltzmann distribution). Application of an

RF pulse and the consequent rotation of the net magnetization Mo from the z-axis is a disruption of

the thermal equilibrium of the spins. After being disturbed by an RF pulse thermal relaxation occurs

to reestablish equilibrium. This process involves a net transfer of energy from the spin system to the

environment until the populations of the energy states reach equilibrium, the Boltzmann distribution

given in Eq. (12). It is attributable to electromagnetic interactions between the nuclei and the

surrounding particles causing transitions between the alpha and beta spin states (when I = ½). As it is

the coherent combination of these spin states that contribute to the magnetization rotating in the xy-

plane, the result is a gradual decay of these coherent combinations and a return to the state of thermal

equilibrium in which the magnetization is in the z-direction and therefore no longer capable of

inducing a signal in the antenna coil. How fast the spins regain equilibrium is a measure of the

coupling of the spins to their environment. The approach to equilibrium is exponential and

characterized by a time constant denoted by T1, called the spin-lattice or longitudinal relaxation time.

- refers to the return to equilibrium of the z-component of the net magnetization of the sample at a

rate of 1/T1 (a rate is generally expressed in units of inverse time, i.e. s-1)

- the rate of change of Mz is described by the first order kinetic relationship:

1

0

T

MM

dt

dM zz (1-14)

The solution is: 00

/ )0()( 1 MMtMetM zTt

z (1-15)

2. Spin-Spin (or Transverse) Relaxation, T2 (mechanism which causes spin vectors to become

evenly distributed in xy-plane without transfer of energy to the surroundings). With the passage of

time after an RF pulse tips the net magnetization Mo from the z-axis, the magnetic moments interact

with one another by magnetic dipole interactions. Nuclei in any given substance are generally located

in several different molecular environments, each with a slightly different Bo. In each of these

regions the precession frequency will be perturbed to a slightly different extent. The result is a

collection of regions rotating at slightly different frequencies producing a gradual loss of phase

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coherence (precessing as a group) and a decay of the resultant magnetization. This loss of transverse

magnetization is characterized by a time constant denoted by T2, called the spin-spin or transverse

relaxation time.

- With the total energy of the system remaining the same, the entropy-driven exhance of spins

between neighboring nuclei results in a loss of the xy component of the magnetization. The rate of

changes of Mx and My are described by the first order kinetic relationships:

2T

M

dt

dM xx  and 2T

M

dt

dM yy (1-16)

The solutions are:

2/)( Ttx etM  and 2/)( Tt

y etM (1-17)

3. The magnetic field is not perfectly uniform. Nuclei in different parts of the sample precess at

slightly different frequencies and get out of phase with one another, thereby gradually decreasing the

net magnetization of the sample.

Spin-Lattice Relaxation Mechanisms

In many cases, the same physical relaxation mechanisms determine T1 and T2 so that they are

then equal. In spectroscopies involving higher energy excitation such as in the ultraviolet or visible

region of the electromagnetic spectrum, the return to the ground state of an excited molecule is very

rapid. The situation is quite different in NMR where the small energy difference between nuclear

spin states means that spontaneous emission is very slow. (The lifetime of an unperturbed excited

nucleus is in the range of years!) Consequently the excited nucleus must be induced to flip its spin

and return to the ground state by some external means. From an analysis of the interaction of

electromagnetic radiation with matter one can conclude that a spin subjected to a fluctuating

magnetic field will be induced to undergo transitions between all available energy levels at a rate that

is proportional to the intensity of the field. The principal mechanisms for producing fluctuating

magnetic fields include:

chemical shift (or shielding) anisotropy

– local magnetic field acting on a nucleus changes the shielding at the nucleus due to tumbling.

dipole-dipole interactions with other nuclei

– interactions similar to that observed between two small bar magnets modulated by molecular

tumbling or by translational diffusion; this is most important for I = ½ nuclei.

interactions with unpaired electrons

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– This is similar to the dipolar mechanism except that one of the magnetic moments belongs to an

unpaired electron

spin-rotation interactions

– interruption of the coupling between angular momentum due to molecular rotation and nuclear

spin arising from molecular collisions

scalar interactions

– indirect coupling of nuclear spins through electrons; like dipolar mechanisms except that one of

the magnetic moments is that of an electron (and thus requires a quadrupolar nucleus)

quadrupolar interactions

– For nuclei with I > ½ where a nuclear electric quadropole moment exists that interacts with

electric fields

Attributes of 1H NMR Spectroscopy: NMR Chemical Shift

Chemical shift, ppm = 610

Hzin frequency er spectromet

reference offrequency -signal offrequency (1-18)

• The chemical shift is the position on the δ scale (in ppm) where the peak occurs.

• There are two major factors that influence chemical shifts:

1. deshielding due to reduced electron density (due electronegative atoms)

2. anisotropy due to magnetic fields generated by π bonds

Table III – Proton Chemical Shifts

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Shielding in NMR

Nuclei are shielded by valence electrons surrounding them which circulate in an applied

magnetic field producing a local diamagnetic current in the opposite direction. This diamagnetic

shielding will affect the frequency of radiation necessary to cause a nucleus to spin flip (the

resonance frequency). Therefore nuclei will absorb radiation of slightly different frequencies

depending upon their local magnetic environment, which is determined by the structure of the

compound. Since the magnetic field strength dictates the energy separation of the spin states, and

hence the radio frequency of the resonance, the structural factors mean that different types of nuclei

will occur at different chemical shifts. This is what makes NMR so useful for structure

determination, otherwise all nuclei would have the same chemical shift. Some important factors

include:

• inductive effects by electronegative groups

• magnetic anisotropy

Electronegativity

Electrons around the nucleus create a magnetic field that opposes the applied field. This

reduces the field experienced at the nucleus. Since the induced field opposes the applied field the

electrons are said to be diamagnetic and the effect on the nucleus is referred to as diamagnetic

shielding. Since the field experienced by the nucleus defines the energy difference between the

different spin states, the frequency (and hence the chemical shift δ) will change depending on the

electron density around the nucleus. Electronegative groups decrease the electron density around the

nucleus, and there is less shielding (i.e. deshielding) so the chemical shift increases.

Magnetic Anisotropy

Magnetic anisotropy means

that there is a non-uniform magnetic

field. Electrons in π systems (e.g.

aromatics, alkenes, alkynes, carbonyls,

etc.) interact with the applied field

which induces a magnetic field that

causes the anisotropy. As a result, the

nearby nuclei will experience three

fields: the applied field, the shielding

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field of the valence electrons, and the field due to the π system. Depending on the position of the

nucleus in this third field, it can be either shielded (smaller δ) or deshielded (larger δ), which implies

that the energy required for, and the frequency of the absorption will change. Here are some

examples:

low field high field down field up field deshielded shielded high frequency low frequency large δ (ppm) small δ (ppm)

COUPLING IN 1H NMR

Spectra generally have peaks that appear in clusters due to coupling (scalar, spinspin, J-

coupling) with neighboring protons The coupling constant J (usually in frequency units, Hz) is a

measure of the interaction between a pair of protons.

Before looking at the coupling, examine the peak assignments

• δ = 5.9 ppm, integration = 1H; deshielded: agrees with the −CHCl2 unit

• δ = 2.1 ppm, integration = 3H; agrees with −CH3 unit.

What about the coupling patterns? Coupling arises because the magnetic field of adjacent protons

influences the field that the proton experiences. To understand the implications of this first consider

the effect the −CH group has on the adjacent −CH3.

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The methine –CH can adopt two alignments with respect to the applied field. As a result, the

signal for the adjacent methyl −CH3 is split into a doublet, two lines of equal intensity. Now consider

the effect the −CH3 group has on the adjacent −CH. The methyl -CH3 protons have 8 possible

combinations with respect to the applied field, only four of which are magnetically distinct. The

resulting signal for the adjacent methane −CH is split into a quartet, 4 lines of intensity ratio 1:3:3:1.

n + 1 Rule

As protons on a carbon atom experience the magnetic field of protons on adjacent carbon

atoms the signal for a particular proton will be split by these protons into n + 1 peaks where n is

the number of adjacent protons.

Pascal’s Triangle

The relative intensitites of the lines in a coupling pattern is given by a binomial

expansion or more conveniently by Pascal's triangle. Individual resonances are split due to

coupling with n adjacent protons. The number of lines in a coupling pattern is given, in general,

by 2nI + 1 for coupling with n spin I nuclei.

Doublet on CH3 Quartet on CHCl

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INTERPRETING 1H NMR SPECTRA

What can be obtained from a 1H NMR spectrum:

• number of equivalent types of H - number of groups of signals in the NMR spectrum.

• types of H – chemical shift of each functional group’s protons found in chemically identical

environments are chemically (and usually also magnetically) equivalent; these chemically equivalent

protons will have the same chemical shift.

• number of H of each type - NMR spectrometer can integrate (or calculate the area under each peak) all

peaks to determine the relative numbers of protons responsible for all peaks.

• connectivity - spin-spin splitting (J coupling with the n + 1 rule) – the coupling pattern identifies the

adjacent functional group(s).

Chemical shift

• The chemical shift is the position on the δ scale (in ppm) where the peak occurs.

• There are two major factors that influence chemical shifts: 1) deshielding due to reduced electron

density (due electronegative atoms) and 2) anisotropy (due to magnetic fields generated by π bonds).

Integration

• The area of a peak is proportional to the number of H that the peak represents

• The integral measures the area of the peak

• The integral gives the relative ratio of the number of H for each peak

Coupling

• The proximity of other n H atoms on neighboring carbon atoms, causes the signals to be split into n +1

lines (to first order).

• This is also known as the multiplicity or splitting of each signal.

Table IV. Magnitude of Some

Typical Coupling Constants1

1Magnitude of the coupling

constant is independent of the

strength of the applied field.

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Attributes of 13C NMR SPECTROSCOPY

It is useful to compare and contrast 1H NMR and 13C NMR as there are certain similarities as

well as differences.

• 12C isotope does not exhibit NMR behavior (nuclear spin I = 0)

• 13C isotope has a natural abundance of 1.108% (of all C atoms)

• Magnetogyric ratio γ for 13C is approximately four times smaller than γ for 1H

• As a result, a 13C nucleus is about 400 times less sensitive than a 1H nucleus in NMR spectroscopy

• 13C-13C coupling is seldom observed due to the low natural abundance of 13C

• Chemical shifts measured with respect to tetramethylsilane, (CH3)4Si (i.e., TMS)

• Chemical shift range is normally 0 to 220 ppm

• Similar factors affect the chemical shifts in 13C as in 1H NMR

• 13C spectra are normally broadband proton decoupled, removing J coupling between 13C and 1H, so peaks

appear as single lines

• Number of peaks indicates the number of distinct types of C

• Long relaxation times (excited state to ground state) mean no meaningful peak area integrations

The general implications of these points are that 13C take longer to acquire, though they tend

to look simpler. Overlap of peaks is much less common than for 1H NMR which makes it easier to

determine how many distinct types of C are present.

Table V. 13C Chemical Shifts. Note the importance of hybridization in the shielding of 13C chemical shifts and

the magnitude of the J coupling with bonded protons, both in the order: sp2 < sp < sp3

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There are four alcohols with the molecular formula C4H10O

Which one produced the 13C NMR spectrum below?

Interpreting 13C NMR Spectra

The following information can be obtained from a typical broadband decoupled 13C

NMR spectrum (all coupling with 1H removed):

• number of types of C - indicated by number of signals (peaks) in the spectrum.

• types of C - indicated by the chemical shift of each signal.

2. Advanced NMR Experiments to Aid Spectral Interpretation for This Lab

Each dimension of an NMR experiment represents a different observable nucleus. Normal 1H

and 13C NMR look at a single type of nucleus at one time by plotting intensity versus frequency. It is

possible to examine multiple nuclei simultaneously by using the Fourier Transform (FT) technique

coupled with a computer capable of directing RF pulses on both nuclei during the same time period.

In such experiments, intensity is plotted as a function of two frequencies generally in the form of a

contour plot. This part of the NMR lab will examine a useful one-dimensional technique DEPT and

two different two-dimensional NMR experiments: HETCOR and COSY.

Molecular Diffusion Measurements by Pulse Field Gradient (PFG) experiments: In this

experiment, two magnetic field-gradient pulses are applied at the beginning and the end of the

molecular diffusion period for a series of different field gradient strengths (G). Due to the

molecular diffusion process during the period , the 1H NMR signals decay exponentially with

respect to G2 as s() = exp(-aDG2). The rate of the exponential decay for each 1H species is

proportional to the molecular diffusion coefficient D, which characterizes how quickly molecule

travels in a solution. Thus, this PFG experiment provides information on the molecular identity for

different 1H peaks for a mixture sample.

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DEPT (Distortionless Enhancement by Polarization Transfer): A 1D experiment used for

enhancing the sensitivity of the carbon signal and for editing of 13C spectra. The sensitivity gain

comes from starting the experiment with proton excitation and subsequently transferring the

magnetization onto carbon (via the process known as polarization transfer). This gain arises due to

the larger population differences associated with protons, which are four times bigger than those of

carbon (γ is four times larger). DEPT alters the amplitude and sign of the carbon resonances

according to the number of directly attached protons, allowing the identification of carbon

multiplicities.

45 decoupler pulse - carbon spectrum contains only carbons with protons attached (quaternary

carbons are not observed).

90 decoupler pulse - carbon spectrum contains only carbons with a single attached proton,

methine CH

135 decoupler pulse - carbon spectrum with methyl (CH3) and methine (CH) carbon peaks up,

methylene (CH2) carbon peaks down (negative)

HETCOR: A 2D experiment used to identify couplings between heteronuclear spins. Most

often employed to correlate carbons with their directly bonded protons by the presence of cross-

peaks in the 2D spectrum. HETCOR relies on scalar coupling (spin-spin or J coupling) between the

different nuclei. The HETCOR spectra in our experiments plot proton versus carbon with 1D spectra

displayed along the appropriate axis. The 2D peaks show which protons are coupled to which

carbons.

COSY: A 2D experiment used to identify nuclei that share a scalar (J) coupling. The

presence of off-diagonal peaks (cross-peaks) in the spectrum directly correlates the coupled partners.

Most often used to analyze coupling relationships between protons, but may be used to correlate any

high-abundance homonuclear spins. The COSY spectra in our experiments plot the proton spectrum

versus itself. The 2D peaks show which 1H are coupled over three bonds.

For the 7 experiments on your unknown, include:

1. 1H spectrum with integration and tabulated peak assignments with reasoning

2. 13C spectrum and tabulated peak assignments with reasoning

3. DEPT 45. 90. 135 with explanations

4. HETCOR – explain C-H correlations

5. COSY – explain H-H correlations

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As you are obtaining these spectra to aid in the identification of your unknown structure

you should explain how the 1H and 13C spectra along with the DEPT, HETCOR, and COSY data

allowed you to determine the structure. Be sure to draw the structure!

For the PFG Diffusion experiment (be sure to do the appropriate regression analysis). You

present the following data after the data analysis.

1. Stacked plots of the 1H NMR spectra for different fractional PFG strength (fn)

2. Table of peak intensities measured from the stacked plots versus fn for each peak

3. Plots of peak intensity measured from the stacked plots versus fn for each peak

4. Table of a normalized signal In = Sn/S1 vs fn2

5. Plot of In vs fn2 with a fitting curve

6. Determine the diffusion coefficients D for all of the peaks.

3. Guide on Pulse Field Gradient for Diffusion Measurements

Magnetic Field Gradient, NMR Spectroscopy, and Magnetic Resonance Imaging (MRI)

NMR experiment also allows one to examine molecular diffusion process in solution. For this purpose, a pulse field gradient is typically used. A field gradient is the linearly tapered magnetic field, which allows us to identify the location of a molecule. When a field gradient is applied, a static magnetic field B0(x, y, z) is dependent on the location of the molecule as

B0(x, y, z) = B0 + GX (x – x0) + Gy(y – y0) + GZ (z – z0), (3-1)

where Gx, GY, GZ denote the field gradient along the x, y, z axes, respectively. Now assume a field gradient pulse is applied along the Z axis, then we obtain

B0(x, y, z) = B0 + GZ (z – z0). (3-2)

The NMR frequency NMR under the magnetic field now depends on the position of the molecule z as

NMR(z) = - B0(x, y, z) = - B0 - GZ (z – z0) = 0 - GZ (z – z0), (3-3)

where 0 is the NMR frequency when there is no field gradient (Larmor frequency). For simplicity, assume that Z = -(z – z0) and G = Gz. Then, eq. (3-3) is rewritten as

NMR(Z) = 0 + G Z, (3-4)

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Namely, the location of the molecule Z can be detected by monitoring the shift in the NMR frequency under a field gradient. This position dependent NMR frequency is a basis of MRI imaging used in hospitals.

Figure 3-1. NMR frequency depends on the Z position of the molecule under a magnetic field gradient.

Figure 3-2. Pulse sequence for diffusion measurements using field gradient spin echo.

Principle of diffusion experiments by a pulse field gradient

Now, assume that we perform a spin echo experiment listed in Fig. 3-2 under two field gradient pulses (rectangles accompanied by G). The field gradient pulse provides a position

dependent shift of the NMR frequency given by GZ. During the first field gradient pulse having a

pulse width of , a spin magnetic moment is subject to a rotation by GZ x .

A spin echo sequence changes the direction of NMR nutation caused by the field gradient. Now, assume that your molecule is positioned at Z1 and Z2 at the first and second field gradient

pulses, respectively. If a molecule does not move during the period (i.e. Z1 = Z2), the net rotation

observed during the echo period is given by [NMR(Z2) - NMR(Z1)] =[NMR(Z2) - NMR(Z2)] = 0, where δ denotes a pulse width of the field gradient. However, if molecular diffusion takes place

Z 

  20

during and if the locations before and after the pulse are different (i.e. Z2 Z1), the net rotation due to the nutation is given by

{NMR(Z1) - NMR(Z2)} = G(Z2 – Z1) , (3-5)

where we assumed that the gradient pulse is strong and the diffusion during δ is negligible. Thus, the

signal detected during the detection period is attenuated by a factor s(GZ, )

s(GZ, , ) = cos[{NMR(Z1) - NMR(Z2)}] = cos{G (Z2 – Z1)}. (3-6)

The probability that a molecule diffuses by a distance r = Z2 – Z1 along the z-axis during the period is defined by Einstein Stokes diffusion process and given by

P(r) = P0 exp(-r2/4D), (3-7)

where D is a diffusion constant of molecule and P0 = (1/4Dπ)1/2. Then, the average attenuation of the signal from eq. (6) is given by

<s(G, , )> = < cos[{0(Z1) - 0(Z2)}] >

= < cos{G (r)}P(r) > = a/4)exp(-q})G ( cos{) /4Dr exp(- P 20

20 Padrr

, (3-8)

Where q = (γGδ), a = 4D, and (a)1/2P0 = 1. In summary, the diffusion attenuation factor I(G, , ) is given by

I(G, , ) = <s(G, , )> = exp(- q2D). (3-9)

When the diffusion during is not negligible, we use a modified equation

I(G, , ) = exp[- q2D(-/3)]. (3-10)

The diffusion constant is related to the hydrophobic radius of the molecule Rmol by

D = kBT/6Rmol, (3-11)

where kB is the Boltzmann constant, T Is the temperature, is viscosity of the solvent. Assuming the molecules A and B have spherical shapes and the density of these molecules are the same, the ratio of the molar masses are estimated from the diffusion constants as

DA/DB = RB/RA ~ (MB/MA)1/3, (3-12)

where DA and DB should be measured in the same solvent and at a common temperature. Estimate the molar mass of your unknown from D with DH2O and MH2O.

  21

Data Analysis Protocol

A group receives a stacked plot of the spectra that were collected for a series of different gradients Gn (n =1, 2, .. N) for the unknown sample in a solvent (water), for which diffusion constant D is known (see Fig. 3). For a peak for the control sample (i.e. water), signal intensities for a varied gradient Gn are given as

Scon(n) = S0 con exp[-(γGn δ)2Dcon(-/3)], (3-13)

where Gn denotes a field gradient for the n-th data points and S0 con is a constant that represents the signal intensity when Gn = 0. Now, we define the strength of the field gradient Gn using a fractional strength fn as Gn = Gmaxfn, where Gmax is the maximum gradient of the instrument. For example fn is denoted as 10% or 0.1 with respect to Gmax (Typically, we change fn from 5% to 95%). Then eq. (13) is rewritten as

Scon (n) = S0 con exp[-(γGmax δ)2Dcon(-/3) fn2], (3-14)

Now we define p as p = (γ Gmaxδ)2(-/3). Here p is a constant that does not depend on the sample or the analyte molecule. Then, the equation is simplified as

Scon(n) = S0 con exp[-Kcon fn2], (3-15)

where Kcon =p x Dcon. Using the peak table, plot Scon(n) along the Y-axis with respect to fn2 along

the X-axis for each peak, and you find

Y = exp[-Kcon X], (3-16)

By using a curve fitting of the plot to the exponential curve using software (such as Excel), you find Kcon = p x Dcon as a rate of the exponential decay. Once you get Kcon, p can be easily found from the known Dcon (if H2O is used as a control, DH2O = 2.299 x 10-9 m2s-1 at 25 ̊C) by

p = Kcon/Dcon. (3-17)

For a signal A ( or B, C, …) of your unknown, similarly,

SA(n) = SA 0 exp[-KA X], (3-18)

where kA =p x DA. Again, find KA by plotting SA(n) with respect to X = fn2. Then, once you find

kA, obtain DA from

DA = Dcon x (KA/Kcon) (3-19)

Estimate the molar mass of the unknown from eq. [9] (DA/DB = RB/RA = (MB/MA)1/3) as

MA ~ Mcon x (Dcon/DA)3. (3-20)

Hint: If the peaks A and C come from the same molecule for example, determined DA and DC should be similar within the range of the error.

  22

Figure 3-3. Example data for pulse field gradient molecular diffusion experiment.

4. Guide on Other Advanced Experiments

DEPT: Distortionless Enhancement by Polarization Transfer

A 1D experiment that utilizes polarization transfer from a

nucleus with a relatively larger magnetogyric ratio γ to one with a

smaller γ to increase the signal from the latter nucleus, here from 1H to 13C. By changing the last proton pulse from 45° to 90° to

135° the multiplicity of the carbon nucleus

can be determined.

Observed 13C signals are modulated

by the 13C−1H coupling constant so that

when 1) θ = 45°, signals from all CH, CH2,

and CH3 carbons are observed (no

quaternary C or C attached to D, as in a

deuterated solvent), 2) θ = 90° signals seen from only CH

carbons, and 3) θ = 135° signals from all CH, CH2, and CH3

carbons but the CH2 signals are negative.

On the right are the proton decoupled 13C spectrum and

DEPT spectra at 45°, 90°, and 180° for the compound on the

  23

left. DEPT 45 only shows C with a directly bonded H, DEPT 90 CH, and DEPT 135 has

negative peaks for CH2 C atoms.

DEPT 90 and 135 spectra on the left are sufficient to identify which of

A-E is the structure of the compound. The uppermost spectrum is the 1H decoupled 13C spectrum.

HETCOR: HETeronuclear CORrelation (also called 13C−1H COSY)

A 2D heteronuclear

correlation experiment where cross

peaks yield information about the

connectivity of two different spin

coupled spin 1/2 nuclei, here

protons with 13C nuclei. The

experiment takes advantage of the

large one-bond heteronucler J

coupling for polarization transfer

between the 1H and 13C nuclei. The

experiment can be modified to give

coupling information over more

than one bond.

The HETCOR experiment involves 13C-1H correlation by polarization transfer. It encodes

the proton chemical shift information into the observed 13C signals and yields cross signals for

all 1H and 13C nuclei that are connected by 13C-1H coupling over one bond.

  24

1D 1H NMR plotted vs. 1D 13C NMR; cross peaks observed

at intersection of the x and y values denoting the CH

interactions. Peak A shows that the H at ~ 4 is bonded to the

C at ~ 60 ppm. Peak B shows that H at ~ 1.8 ppm is bonded

to C at ~18 ppm. The quaternary C is identifiable as no cross

peak appears (*). HETCOR pulse sequence

                                                        

COSY: COrrelation SpectroscopY

A 2D homonuclear correlation experiment where cross peaks yield information on the

protons which are spin-spin coupled to each other. The experiment uses polarization transfer

between the coupled spins. The technique can be modified to yield COSY spectra for four-, five-,

and occasionally six-bond couplings.

P

COSY pulse sequence

COSY experiment involves 1H-1H correlation by polarization

transfer. It encodes the proton

coupling information into the

observed 1H signals and yields

cross signals for all 1H that are

coupled over three bonds.

1D 1H NMR plotted vs. 1D 1H NMR generating a 2D xy plot. If a signal on the x-axis has an

interaction with a signal on the y, a cross peak is observed at the intersection of the x and y

values, denoting the interaction. The peaks on the diagonal represent the 1H spectrum and the

COSY is symmetric with respect to the diagonal. Peak A indicates that the peak at ~ 6.9 ppm is

  25

proton coupled to the peak at ~ 1.8. Peak B indicates that the peak at ~ 4.2 ppm is coupled to the 1H at ~1.3.

5. Laboratory Report Requirements

The following information is required in your laboratory report for this experiment.

Please note that both students of each group are required to have all copies of all spectra,

printouts, and any other data, notes, etc., recorded during the laboratory meetings.

5. Laboratory Report Requirements

The following information is required in your laboratory report for this experiment. Please

note that both students of each group are required to have all copies of all spectra, printouts, and any

other data, notes, etc., recorded during the laboratory meetings.

I. Abstract (1 page)

II. Introduction (3-4 pages)

• Introduce what is NMR (How is NMR used in chemistry and other fields?

• Briefly summarize the principles of NMR spectroscopy (What is detected in NMR? How is the

NMR signal observed? What are 13C NMR and 1H NMR?)

• Briefly discuss how DEPT and 2D 1H/13C correlation NMR can be used.

• Briefly discuss the pulse field gradient experiments for characterizing molecular diffusion.

III. Spectra

• 13C spectrum of your unknown, with 13C chemical shift assignments made and your prediction of

the sample name and chemical structure of the compound (carbons should be labeled for assignments

as CA, CB, CC, …). Indicate the numbers in the spectrum for assignments.

• 1H spectrum of your unknown, with 1H chemical shift assignments and chemical structure of the

compound (protons should be numbered for assignments as HA, HB, HC). Indicate the numbers in

the spectrum for assignments.

• 13C DEPT 45, 90, 135 spectra of the unknown with assignments made.

• A contour plot of 2D spectrum (COSY, HETCOR) of your unknown sample and assignments of

13C and 1H.

• A stack plot of 1H NMR spectra for varied pulse field gradient strengths.

  26

IV. Data sheet and calculations

For the PFG Diffusion experiment

(1) Table of peak intensities measured from the stacked plots versus fn for each peak

(2) Plots of peak intensity measured from the stacked plots versus fn for each peak

(3-1) Table of a normalized signal In = Sn/S1 vs fn

(4-2) Table of a normalized signal In vs fn2

(5) Plot of Y = In vs X = fn2

(6) Use Excel or other program to obtain the best fit curve for Y = Aexp(-BX) for (6). If f12~ 0, you

can assume that A = 1. If the curve does not fit to the exponential curve well, check the calculation

in (5-1) and (5-2) again.

(7) Determine the diffusion coefficients D for all of the 1H peaks using the B value. Show sample

calculations.

V. Results

Peak table and summary of assignments and the calculated diffusion coefficients D.

(1) Peak table for your 13C spectrum. List ppm positions and your assignments

Indicate the chemical structure and numbering clearly.

Example.

Signal assignments for 13C NMR spectrum Peak position

(ppm)

182 125 55 40 32 25

Peak # a b c d e F Assignments CA CP CB CC CD CQ

Molecules Mol A Mol B Mol A Mol A Mol A Mol B  

 

CPH3-CQHCl2

Mol A (Name) Mol B (Name)

  27

(2) Peak table for your 1H spectrum. List ppm positions and your assignments with D values

(obtain from the analysis in Sec .3). Indicate the chemical structure and numbering clearly.

Signal assignments for 1H NMR Peak position

(ppm)

1.3 2.1 3.5 4.6 6.2 7.5

Peak # a b c H2O d E Assignments HB HC HD H2O HP HQ D (10-9 m2/s) 3.2 1.3 2.3 0.5 5.2 6.3

Molecule Mol A Mol A Mol A H2O Mol B Mol B As for the structure follow the above example & Label 1H clearly.

VI. Discussion (5-8 pages)

Questions to be answered in Discussion

(i) Discuss your reasoning for your 13C NMR assignments of the unknown sample based on your 1D 13C NMR, 1D 13C DEPT, and 2D 13C/1H HMQC NMR spectra. What is the sample?

(ii) Is the sample a mixture or a pure substance? What is the basis of the estimation?

(iii) Discuss your reasoning for your 1H NMR assignments of the unknown sample based on your 1D 1H NMR and 2D 13C/1H HMQC NMR spectra, and your 13C NMR assignment.

(iv) Discuss how the 2D NMR enhances resolution and aids your signal assignments.

(v) Analyze the obtained diffusion coefficients to estimate the molar mass and hydrophobic radius

for the samples.

(vi) Do the diffusion coefficient measurements assist in making signal assignments?

VII. References

Hint: Your sample is unknown, thus, the first task is to identify your sample out of several

possibilities. You can consider the following factors: (1) the number of non-equivalent 13C, (2) the

existence of phenyl groups or carboxyl/carbonyl groups (their 13C shifts are distinctive from those of

aliphatic groups), (3) the number of non-equivalent protonated 13C.  

 

Web References 1. Jim Clark http://www.chemguide.co.uk/analysis/nmrmenu.html#top 2. Joseph P. Hornak, Rochester Institute of Technology

  28

http://www.cis.rit.edu/htbooks/nmr/bnmr.htm 3. Ian Hunt, University of Calgary http://www.chem.ucalgary.ca/courses/351/Carey5th/Ch13/ch13-2dnmr-1.html#cosy On-Line Learning Center for "Organic Chemistry" (Francis A. Carey), University of Calgary, http://www.chem.ucalgary.ca/courses/351/Carey/Ch13/ch13-nmr-1.html 4. Tad Koch, University of Colorado http://orgchem.colorado.edu/hndbksupport/nmrtheory/main.html 5. Brent P. Krueger, Hope College http://www.chem.hope.edu/~krieg/Chem348_2002/NMR/Principles_of_NMR_Spectrosc opy.html 6. Arvin Moser, Advanced Chemistry Development, Inc (ACD Labs) http://acdlabs.typepad.com/elucidation/hsqchmqc 7. Tom Newton, University of Southern Maine http://www.usm.maine.edu/~newton/Chy251_253/Lectures/DEPT/DEPT.html 8. William Reusch, Michigan State University: http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm#

Chem 343 NMR LabUIC Chemistry RRC Building

Logging into the computer and starting the NMR software TOPSPIN 1.3 on Linux CentOS

1. In the login window login: chem343 password: train343

BOLD lettering is typed on topspin command line or are keys pressed on board to right.

Additional information regarding topspin is on the Desktop in folder 'TOP_processing_a4.pdf' or 'Topspin1p3_users_guide.pdf'. Focus mainly on the processing, such as integration and phasing, if you get stuck.

Changing the samples and shimming- have the TA help you with these steps- it is critical not to drop a sample into the magnet without hearing the air, as the sample will free fall down and break in the probe. On the bsms board to right: a) Spin-Off b) Lock-Off c) Lift-On.

Sample should be swapped out, CLEANED with kim wipe, and set to probe depth using the sample gauger.

-make sure you hear the air is on before placing the sample into the magnet.

Insert sample: a) Lift-Off b) Spin-On.

rsh shims.bbo This will read in standard shim files. lock D2O and the spectrometer will lock onto the solvent (wait until finished). lockdisp Maximize lock (Shim) on bsms board below:

Shim Z1 and use wheel to maximize lock signal. Then Z2 and do the same. Repeat 2 times. STDBY key to put the bsmsboard into standby mode.

Proton NMR data acquisitionedc - Add the name as you like eg) sample_1. This creates folder of your experiment.rpar h1.bbo all – reads in 1D 1H experiment.ii - this is used to initiate the interface or reset communications to the nmr. rga - sets the receiver gain automatically and takes several seconds to do so. zg - starts experiment and overwrites current data). In pop up cl. OK to overwrite.Processing:efp (when experiment finishes we fourier transform and process the data). apk (autophase the spectrum, all peaks should be pointing up now). Or try manual phasing :Adjust scaling etc with:

Phasing

Integration/peak picking:abs – baseline correctionint – auto integrate; use auto-find regionsin the integration mode (above), right click over integral region to calibrate the number of protons.pps – autopick peaksexport – save as whatevername.jpg and so on. Ok to create directory if you like.

*Chapter 11.2 of 'Topspin1p3_users_guide.pdf ' has much more detail regarding processing if needed.

Acquisition of 13C NMR spectrum

Create 2nd exptl data set: edc and edit EXPNO entry to 2.

Note it is common practice to use the experiment # entry as:1: 1D 1H 2: 1D 13C3: Dept135 and so on. just be sure to keep track in your notes.

* you can also change quickly between these expts once created by: re 1 or re 2 etc...

edc – create expt 2rpar c13.bbo all

We use very similar steps as in the 1H expt. iizg (experiment takes 5 minutes).

*If signal to noise is still too low you can increase the number of scans ns (eg 2X-4X's more) and type go to continue signal averaging onto the previous FID.

efp - process the dataapk - autophase. Now adjust peaks intensities so they fit to screen. use the *2 or /2 buttons. Or phase manually again as well.setti -include appropriate titlepps – autopick peaksexport – save as whatevername.jpg and so on. Ok to create directory if you like.

Additional experiments can be collected in a very similar fashion (please see the end of this document). All experiments are easily setup using the 'rpar' command.

Acquisition of DEPT-135 13C NMR spectrum (CH3/CH up; CH2 Down)edc – create expt 3rpar dept135.bbo alliizg (experiment takes 5 minutes).

Manually phase from above. Note some peaks are supposed to point down if present.setti -include appropriate titlepps – autopick peaksexport – save as whatevername.jpg and so on. Ok to create directory if you like.

Acquisition of DEPT-90 13C NMR spectrum (CH only up)edc – create expt 4rpar dept90.bbo alliizg (experiment takes 5 minutes).

Manually phase from above. setti -include appropriate titlepps – autopick peaksexport – save as whatevername.jpg and so on. Ok to create directory if you like.

Acquisition of DEPT-45 13C NMR spectrum (CH3/CH2/CH all up)edc – create expt 5rpar dept45.bbo alliizg

Manually phase from above. All peaks point up.setti -include appropriate titlepps – autopick peaks

export – save as whatevername.jpg and so on. Ok to create directory if you like.Export your data..

2D HMQC (1H/13C)_Correlation via 1 Bond (direct attachment)edc – create expt 6rpar cosy.bbo alliizg

2D processing (for cosy and hmqc above)xfb – does 2d fourier transform and phase correction.

*scaling of intensities/contours down just like with the 1Ds.*use LMB and box in area of zoom if you like.export – save as whatevername.jpg

2D HMQC (1H/1H)_Correlation edc – create expt 7rpar hmqc.bbo allii1 td 128zg

2D processing (for cosy and hmqc above)xfb – does 2d fourier transform and phase correction.

*scaling of intensities/contours down just like with the 1Ds.*use LMB and box in area of zoom if you like.export – save as whatevername.jpg

When finished email yourself the data

*data .jpgs are stored on desktop 'chem343's Home' ..

Finishing up with XWINNMR and logging off the computer

36. Remove your sample and replace it with the CDCl3 standard following steps 3, 4 and 5 above again.

37. Type exit to leave the NMR program. 38. logout icon (> type arrow) is on top bar.