Spin relaxation

Spin relaxation:

          Unlike the molecules which absorb in the UV/VIS region, the nuclei in the higher energy spin state cannot retru en to the lower energy spi state by the emission of radiation. A nucleus in the higher energy spin state returns to the lower energy spin state to reform the initial excess of nuclei in the lower energy spin state, , by losing the excess energy to some magnetic vector present in the surrounding .this is known as relaxation. There are two ways in which radiation less relaxation can occur spin lattice relaxation.

Spin lattice relaxation:

The term lattice refers to the framework of molecules which may belong to sample or solvent and which may be in the form of gas liquid or solid. All these molecules are normally undergoing translational, rotational and vibration motions and their nuclei which have motions and their nuclei which have magnetic properties are processing. Hence a variety of small magnetic fields is present in the lattice. A small magnetic field properly oriented in the lattice and precessing with a comparable frequency can induce transition in a nearby precessing nucleus from the higher energy spin state to the lower energy spin state. The energy from this transition is transferred to the components of the lattice as an additional translational rotational and vibrational energy. This spin lattice relaxation process causes an excess of nuclei in the lower energy spin state which is the necessary condition for the observation of the phenomenon of nuclear magnetic resonance the spin lattice relaxation time denoted by T₁ deoends on the nature and the environment of the nucleus being observed and therefore  can be very useful in the structure elucidation.

Spin spin relaxation.

Spin spin relaxation occurs by the mutual exchange of energy by two nuclei precessing in different spin states but at the same frequency in close proximity of each other. Even in the absence of an applied radio frequency individual nuclei convert from one spin state to another quite readily because they experience the magnetic field of other nearby nuclei although the mutual exchange of energy shortens the life time of individual nuclei in the higher energy spin state it does not contribute to the restoration of the required excess of nuclei in the lower energy spin state because while one nucleus loses energy another gains energy so that there is no net change in the population of the two spin states. The spi spin relaxation time is denoted by T_2.

Instrumentation:

          There are two types of spectrophotometers which are commonly used for the NMR study continuous wave (CW)NMR spectrophotometer and fourier transform (FT)NMR spectrophotometer. In the CW-NMR spectrophometer, the frequency of the electromagnetic radiation is kept constant and the strength of the applied magnetic field is gradually varied to sequentially bring the processional frequencies of all the nuclei in resonance with the frequency of the electromagnetic radiation. The spectrum is recorded directly as absorption verses frequency and it takes several minutes to complete in the FT-NMR spectrophotometer the strength of the applied magnetic field is kept constant and the radio frequency is applied as a single short duration power full pulse which effectively converse the whole frequency rage to studied. The signal detected in this case is recorded digized and stored in a computer as an array of number. Fourier transformation treatment performed by the computer of this data then provided as spectrum in exactly the same form as a CW spectrum. In the CW-NMR spectrophotometer, we measure the radiant energy which is absorbed whereas in the FT-NMR spectrophotometer it is the energy emitted by the relacing nuclei which is measured thus the VW-NMR experiments provides an absorption spectrum whereas the pulsed FT-NMR experiment provides as emission spectrum.

          The continuous wave mode was employed on the earl instruments but now except for some of the low resolution instruments it has been almost completely superceded by the pulsed fourier transform mode. However since it is easier to grasp the continuous wave mode of instrumentation it is going to be discussed first and the proton magnetic resonance spectroscopy will be disucussed in the light oof this mode o instrumentation.the plused fourier transform mode is being postponed until the discussion of the carbon 13 magnetic resonance spectroscopy.

          NMR spectrophotometers are available in wide ranging magnetic field strengths an NMR spectrophotometer is often is terms of the resonance frequency of a particular nucleus generally proton at a given magnetic field strength thus an instrument with a 23500 gauses magnet is termed as 100MHz NMR spectrophotometer because the resonance frequency of proton at this magnetic field strength  is 100 MHz similarly an instrument wih a 47000 gauss magnet is known as 200MHz NMR spectrophotometer a schematic diagram of a continuous wave NMR spectrophometer. Its main components include power ful magnet field sweep generator sample tube radio frequency transmitter radio frequency recover amplifier recorder and integrator.

          The magnet used in an NMR spectrophometer can be a permanent magnet electromagnet or superconducuing magnet. Permanent magnet is the cheapest and is convenient to use but it lacks flexibility in an electromagnet the flux density can be varied by varying the current that passes through the colis of the magnet electromagnet of relatively. Insensitive to temperature changes whereas the temperature of the other two types of magnet has to be controlled superconducting magnet is relatively compact and can be used to achieve a magnetic field that is much greater than that possible with the other types of magnets superconducting magnet can therefore provide high resolution all NMR spectrophotometers above 100MHZ are based on helium cooled (4⁰K) superconducting magnets are very stable and allow measurement to be made under homogeneous magnetic field over a long period.

          When a conductor metal is cooled in liquid helium to a temperature of 4⁰K (-269⁰C) its electrical resistance vanishes and the metal becomes superconductor the electromagnet of such can achieve enormous field strength the solenoid for a superconducting magnet is made from  the wire of a niobium alloy.

          The apllied magnetic field must be stable and homogenous i.e it must be constant over the period of time of the experiment and uniform over the area of the sample. If the applied magnetic field is not homogenous identical nuclei at different locations is the sampe will experience different magnetic fields, they will precess over a range of frequencies resulting in broadened signals.

          The applied magnetic field that is associated with the current flowinf through the sweep coils adds to the magnetic field applied from the poles of the magnet thus the strength of the magnetic field that passes through the sample can be varied by varying the current in the sweep coils.

          The sample tube usually 15cm long with 5mm diameter and made of borosilicate galss is mounted on a light turbine and placed between the pole faces of the magnet the sample tube is supn about its vertical axis at a rate of about 30Hz by an adjustable jet of air from a compressor in order to average out any field in homogeneities over that sample dimensions perpendicular to the vertical axis. In the electromagnet the sample tube placed in a probe spins at right angles to the z-axis which is horizontal whereas  in the superconducting magnet the sample tube fits in the solenoid and spins about the  z-axis which is vertical in this case. The instrument can also be provided with the facility of varying the temperature (-100⁰C to 200⁰C) of the sample to make its useful for the kinetics study.

          A radiation of controlled fluency from a radio-frequency transmitter is applied to the sample in a direction perpendicular to the magnetic field, through a coil wrapped around the sample tube radio-frequencies are generated by electronic multiplication of the natural frequency of a quartz crystal placed in a term stated block. Quartz crystals of dfferent sources are used for different frequency when the radiation from the transmitter is absorbed by the sample, it is detected by the radio frequency receiver (tuned to the frequency of the transmitter) connected to another coil also warpped around the sample tube. The transmitter coil and the reciver coil both are perpendicular to the nagnetic field and also perpendicular to each other. If the nuclei in the sample do not resonate with the applied frequency the detector will only record a weak signal coming directly from the transmitter coil to the receiver coil an enhanced absorption signal will be detected if nuclei in the sample resonate with the applied frequency since the signal in this case is transferred from the transmitter coil to be receiver coil through the nuclei which absorb the radiant energy.

          The signal from the radio frequency receiver is amplified and used to drive the y-axis of the recorder to produce an NMR spectrum the sweep generator is used to drive the x-axis of the recorder.

          Most NMR spectrophotometers are equipped with an automatic electronic integrator to measure the areas under the signals after the spectrum has been recorded in the normal manner the spectrophotometer is switched from the normal mode to the intergral mode and the spectrum is scanned once again the instrument continuously adds the mode and the spectrum is scanned once again area os all the signals trun by trun and superposes it as a series of steps on the original spectrum. The height of each step is proportional to the area under the corresponding signal and thus proportional to the number of nuclei responsible for that signal. It may not be possible to obtain an exact  integer but it is almost always possible to differentiate between the number of nuclei one two or three for a given area.

          Occasionally a strong absorption band is symmetrically flanked by two small side bands these side bands usually called spinning side bands result from inhomogenities in the magnetic field and in the spinning sample tube they are readily recognized because of their symmetrical appearance on both sides of the main band. Their symmetrical separation from the main band varies with the spinning rate of the sample tube.

The chemical shift:

Shielding of a proton if the resonance frequencies of all the protons in a molecule were the same the nuclear magnetic resonance spectroscopy would be of little use one would observe only one peak for all protons in a PMR spectrum regardless of the environment or number of protons present. The usefulness of the PMR spectroscopy is based on the fact that the resonance frequencies of various protons in a molecule to some extent depend on the molecular environment of the protons.

          A proton in a molecule is surrounded by a cloud of electronic charge. The applied magnetic field induces circulation of electrons around the proton in the plane perpendicular to applied magnetic field in accordance with the left hand rule which states the circulation of electrons would be in the direction in which the fingers point in a fist made from the left hand when  the extended thumb points in the direction of the applied magnetic field in much the same way as a change in magnetic flux induces a current in a closed loop of wire. The circulating electrons then induce their own magnetic field that in the region of the proton is in the direction opposed to the direction of the applied in the region of the proton is the direction opposed to the direction of the applied magnetic field in accordance with the right hand rule this is shown in.

The magnitude of the induced magnetic field is directly proportional to the strength of the applied magnetic field. Since the induced magnetic field is in the direction opposed to the applied magnetic field the effective applied magnetic field experienced by the proton is reduced by this small indeced magnetic field such that

H_eff=H₀----H_ind

Thus the electron cloud around a particular proton can partially shield the proton from the externally applied magnetic field the proton is then said to be shielded. The strength of the applied magnetic field has to be increased accordingly so that the processional frequency of the proton corresponds to the radio frequency to cause spin flipping . the extent of shieldinf depends on the density of the electron cloud around the proton and the density of the electron cloud around the proton depends on the elctronegativity of the atom of group to which the proton is attached. As the elctronegativity of the atom or group increases electrons are drawn away from the proton and the amount of shielding decreases the proton is then said to be shielded.

          Proton in different electronic environments are shielded to different extent. The absorption of electromagnetic radiation from the radio wave region to cause spin flipping of various protons will therefore occur at different value of the applied magnetic field or the radio frequency as the case may be. In the most common mode of operation of the NMR spectropyometer, we fix the radio frequency at say 100MHz and vary the applied magnetic field gradually. As the applied magnetic field at each kind of proton reaches the resonance condition of the proton, spin flipping accompanied by the absorption of radiation occurs. This absorption as measured by the spectrophotometer and recorded as a function of the applied magnetic field in the form of PMR spectrum. The normal presentation of a PMR spectrum has low field values on the left of the spectrum which is generally termed as downfield and the high field values on the right of the spectrum which is termed as downfield and up field. Although the PMR spectrum is normally recorded by the field sweep operation the positions of absorption are better given in frequency units because the difference in frequencies can be measured more precisely than the difference in magnetic field strengths.(for proton I gauss is equivalent to 4260Hz ).

Molecular structure and chemical shifts:

          What makes PMR spectroscopy such a powerful tool for structure elucidation is that protons in different environments experience different environments experience different digress of shielding and thus have different chemical shift values. The shielding of a proton in a molecule is determined by the structure of the molecule and is mainly influenced by two types of effects which in a dilute solution are predominantly intermolecular these are local diamagnetic effect and magnetic anisotropic effect. In fact the net shielding that a proton experiences is a combination of these two types of shielding effects.

Local diamagnetic effect:

          Local diamagnetic shielding of proton is associated with the circulation of electrons caused by the applied magnetic field around the proton itself as illustrated. The magnitude of the induced magnetic field due to the circulation of electrons around the proton and hence of the local diamagnetic shielding depends on the electron density in the immediate vicinity of the proton which in turn depends on the elctronegativity of the atom to which the proton is attached. For example in the series of methyl halides the protons of methyl fluoride are the least shielded and hence have the highest chemical shift value while the protons of methyl iodide are the most shielded and have the lowest chemical shift value because fluorine is the most electronegative and iodine the least electronegative of the series. This is evident from the chemical shift of methyl halides given below; the chemical shift of CH₄ is 0.23ppm

                   CH₃F                             CH₃Cl                  CH₃Br                  CH₃I

(ppm)        4.3                        3.1                       2.7                      2.2

          Similarly in group of compounds in which the methyl group is attached to the elements of the same row in the periodic table the shielding of protons increases and hence their chemical shift value decreses as the electronegativity of the element decreases

                   CH₃F                             (CH₃)₂O               (CH₃)₂N               CH₃CH₃

(ppm)        .3                            3.2                                2.7                      0.9

         

The local diamagnetic effects are cumulative as indicated by the chemical shift values for the variously chlorinated derivatives of methane.

                   CHCl          ₃                           CH₂Cl₂                 CH₃Cl                          

(ppm)        7.3                                  5.3                       3.1                     

Magnetic anisotropic effect:

          If the local diamagnetic effects were the only shielding mechanism one would expect to find that the chemical shift values for ethane ethylene and acetylene would increase in the same order in a regular way which would be in line with the elctronegativity of the carbon atoms (sp>sp²>sp³) to which the protons are attached. In actual practice the   value for ethylenic proton is higher and that for acethyllenic proton is lower than that can be accounted for by the elctroenegativity effect alone.

                   CH      CH                     CH₂     CH₂                   CH₃       CH₃

(ppm)           1.8                                  5.3                         0.9     

          The relatively decrease shielding of ethylenic protons and increased shielding of acetylenic protons may be attributed to the directional property of the induced magnetic field of the π electrons which is based on the fact that a magnetic field closes on itself a proton may experience additional shielding or deshielding depending on its orientating relative to the induced magnetic field caused by the circulation of electrons originating from the other parts of the molecule. Such effects are called magnetic anisotropic effect. Whereas the local diamagnetic effects operate only along a chain of atoms, the magnetic anisotopic effects operate through space no matter whether the influenced group is directly attached to the anisotropic group or not.

          Let us first consider the case of acetylene. The acetylene is linear with the carbon-carbon triple bond being symmetrical about the molecular axis. When the acetylene molecule is oriented with its molecular axis aluigned along the applied magnetic field the π electrons of the triple bond can easily circulate within the cylindrical π molecular orbital in a plane perpendicular to the applied magnetic field and generated the induced magnetic field that acts t shield the actylenic protons against the applied magnetic field. This will make the PMR signal of the acetylene proton to appear further up field than would be predicated by electromagnetically.

If the acetylene molecule is oriented with its molecular axis perpendicular to the applied magnetic field, the electrons are not as free to circulate to cause deshielding of the protons. Although only a small number of the rapidly tumbling acetylene molecules are aliged along the applied magnetic field the overall chemical shift is affected by these aligned molecules the net effect averaged over all a possible orientations must here fore result in a shielding of the acetylenic protons, and only a single peak s observed at a position intermediate between the two extreme  values which is low for such acidic protons. Protons with low local diamagnetic shielding. It may be point out that if in a complex molecule a proton is situated above the centre of the triple bond as In I it will be deshielded by the same anisotropic effect. For example in 4-ethynlphenathrene (II) the chemical shift of H-5 proton is 1.71 ppm downfield from the chemical shift of the same proton in phenanthrene itself. The chemical shift observed  for a particular proton is result of the sum of the local diamagnetic and the magnetic anisotropic effects.

          Similar arguments can be put forward to explain the unexpectedly high chemical shift value for the thalamic proton. When the thylene molecule is so oriented that he plane of the double bond is perpendicular to the applied magnetic field circulation of the π electrons generates as induced magnetic field which augments the applied magnetic field in the region of the ethylenic protons. This causes deshielding of the ethylenic protons and hence resylt in their higher calue.

          The same argument can be used to account for the rather large amount of deshielding of aldehydic proton, resulting in its value.

          In the molecule of benzene (and other aromatic compounds) he pi molecular orbital provides a favorable path by which electrons can circulate. If the benzene molecule is oriented such that plane of the ring is perpendicular to the applied magnetic field the π electrons are relatively free to move and circulate above and below the plane of the ring as shown.

          The circular motion of the π electrons produces a substantial electric current called the ring current. The ring current induces a circular magnetic field around the edges of the benzene ring such that in the plane of the ring out opposes the applied magnetic field inside the ring and reinforeces it outside the ring. This effect called the ring-current effect accounts for the large deshielding (High value) of the ring protons (or any group oriented such that it is contained in the plane of the benzene ring will). Theprotons held in the region of space immedictely above or below the benzene ring will be shielded due to the same effect. An interesting example of the mainfesation of the ring current effect is provided by [180]-annulene, where the protons inside the ring arestrongly shielded ( =-2.88ppm, i.e future upfield from TMS), whereas the protons outside the ring are strongly deshielded (9.25ppm).

          If the benzene ring is so oriented that the plane of the ring of is parallel to the applied magnetic field, little circulation of the π electrons is possible and therefore no anisotropic increase or decreases in the shielding of the ring protons is experienced onlu local diamagnetic chielding is observed.

          The ring current in aromatic compound (cyclically delocalized π electrons) has greater deshielding effect as compared to the conhugated alkene groups (having no cyclic delocalization) as is evident from the fact that in the molecule of toluene, the cycle protons resonate at 2.34ppm whereas a methyl group attached to an acyclic conjugated akene such as in 4-nethyl-1,3,5-heptariene, appears at 1.95ppm. this criterion can be used to determine the aromatic character of an organic molecule.

          In the case of acetophene all the ring protons are found downfiled because of the ring current effect, but the ortho protons are shifted slightly future downfield (₀=7.85ppm, _m,p=7.40ppm) because of the additional anisotropic deshielding effects of the carbonyl group, due to the copanarity of the carbonyl double bond and the benzene ring as show below.

          Both ortho protons are equally deshielded by the carbonyl group since another equally populated structure can be written I which the carbonyl; group is directed toward the other ortho proton.

Effect of hydrogen-bonding:

          The proton attached to ahighly electronegative atom, Such as oxygen nitrogen or sylfur  shows a compels behaviors because such proton is generally involved in hydrogen bonding. The position of its absorption beside the nature of the compound and its purity often largely depends on the nature of the solvent used the concentration of the sample sokution and the temperature.

          Hydrogen-bonding causes transfer of electron-cloud from the hydrogen atom to a neighboring electronegative atoms (O, N or S) resulting in deshielding of the hydrogen atoms (proton). The greater the extent of hydrogen-bonding hydroxyl proto absorbs at 5.53ppm. At the commonly used concentration (5-20%) in no polar solvent such as carbon tetrachloride where the ethanol molecules earnestly present as dimmers or trimmers the resonance frequency of the hydroxyl proton shifts upfield to absorb at 2-4ppm. In a very dulute solution or in the vapour phase, where practically no hydrogen-bonding is involved the proton resonance occurs at 0.5ppm. Furthermore since the extent of hydrogen-bonded proton moves upfield at higher temperature.

                    However the position of absorption of a proton involved in tramolecular hydrogen-bonding in salicylates is not effected on dilution. Its PMR spectrum virtually remains unchanged on varying the concentration or temperature.