Spin-spin splitting (n+1) Rule and Pascal's Triangle

Spin-Spin Splitting (n+1) Rule

When spins of two protons combine or couple then it is called spin-spin coupling. A minimum of two sets of protons is required for spin-spin coupling. Due to this coupling phenomenon between two protons that are close to each other splitting of signals observed is called spin-spin splitting. Spin-spin splitting happens due to the neighboring protons in a molecule. The spin state of a hydrogen atom in one solution is not the same as in the other solution. Spin state of atom change with solution types. The spin state or direction (+ 1/2 or – 1/2) of one proton is changed by the adjacent proton spin under the influence of a magnetic field. For example, we have a molecule in which two types of protons are present A and B type. The Spin of A proton influences the spin of B proton thus affecting the chemical shift, this is called coupling and here splitting occurs. As we know shielded and deshielded proton behaves differently in the magnetic field.

Spin-Spin Splitting

Criteria for Splitting

• Splitting occurs in those molecules that have a different chemical environment of their protons. For instance, CH3CH2Br, CH3CH2CH=CH, etc.
• Splitting does not occur in molecules that have symmetrical hydrogen atoms, their environment is identical. Singlet will be observed for example benzene and cyclobutane etc., molecules.
• Splitting also does not observe in a compound that has a set of identical protons but does not have another set of protons attached to nearby carbon. For example, in case of ^aCH3^bCH2CO^cCH3, butanone-2. The singlet peak will appear for proton c (-CH3) because there are no protons attached to carbonyl carbon in the molecule.
• In the case of methanol –OH functional group shows a singlet in the spectrum because no hydrogen atom is attached to carbon, here is a simple OH group present.

n+ 1 Rule

This rule tells that the number of protons present on the adjacent carbon. “n” is the number of protons on adjacent carbon and one is added to that number of protons. See the figure below,

n+1 Rule

Doublet means one proton is present on the adjacent carbon, triplet means two protons are present on the next carbon, and quartet means there are three protons present on the adjacent carbon so, doublet, triplet, quartet, etc. are not shown the number of protons attached to the carbon that gives signal but it shows the number of protons attached to the carbon that is near to that proton (adjacent) carbon.

 The (n+1) Rule, is an empirical rule utilized to find the multiplicity and, with the help of Pascal's triangle, peaks splitting pattern in spectra of proton NMR and 13C NMR.

In NMR spectrum peaks shows the types of protons in molecules. Peak area tells the number of protons and intensities of peaks predicted by Pascal’s triangle. Spin-spin splitting the number of protons adjacent to carbon.

Now we will discuss spin-spin splitting with the help of examples,

Example of Spin-spin splitting

Spin of a proton can arrange differently in the molecules. In the above example, you observe that signal for “a” and “c” type proton shows triplet means on the adjacent carbon there are 2 protons and the spin of these two protons can arrange in three different ways, spins can reinforce the applied magnetic field Bo or arrange parallel to it and also show middle position like one proton spin arrange parallel and other oppose the Bo. All other protons spin also shows this type of arrangement in a magnetic field and splitting of signal occurs that is either doublet or triplet and so on. In this way, spin multiplicity shows in the final NMR spectrum.

NMR and Spin-Spin Splitting 

Pascal's Triangle

You can draw this, first, you draw a single line then draw two lines below the above line far from it. Then join these lines with the first line above it in a dotted line and so on.

Peak intensity ratio is the sum of middle lines and writes 1 both on the left and right side of the number that is above the line.

    

 

Formation of Pascal`s Triangle

By using the n+1 rule we easily find the intensity ratio of the multiplet. In NMR spectrum peak arrangement occurs by following pascal`s triangle. It tells the height intensity of peaks in spectrum. As we observe that in pascal`s triangle 1 show a singlet as a signal and 1:2:1 shows as a triplet signal, this also tells that the height of the first and third peak is low as compared to the middle peak seen in the spectrum of NMR given above The same case is in other signals, in case of a quintet there are five lines in the spectrum and these lines' intensity is different from each other, the middle peak intensity is higher than the other four peaks. In case of a sextet, there is a ratio of 1:5:10: 10:5:1 sex peaks, which means the middle lines have equal and high intensity than the other two lines that have a ratio of 5 and 1 ratio line has a very small peak in the spectrum. See the figure given above.

Pascal`s Triangle

Chemical Shift and Coupling Constant (J value) , 1H-NMR

 

Chemical Shift

Chemical shift is the difference between the signal from the reference molecule and the resonance frequency of spinning protons. The chemical shift refers to the location on the plot where the nuclei absorb.

The term "chemical shift" refers to the shifting in the locations of NMR absorptions (reference and sample) that results from the shielding or deshielding of protons by electrons. The two most popular standards are CDCl3 (deuterochloroform), which has a chemical shift of 77 for 13C NMR and 7.26 for 1H NMR, and TMS (tetramethylsilane, chemical formula (Si(CH3)4)), which has a chemical shift of zero. So, it is necessary to utilize a common reference point because this can have any value.

Chemical shift

Parts per million (ppm), which are independent of spectrometer frequency, are a standard way to express the scale. One of the most important characteristics that can be used to determine molecular structure is nuclear magnetic resonance chemical change.

Different resonance frequencies and energy levels are produced in a magnetic field by atomic nuclei that have magnetic moments (also called nuclear spin). Local magnetic fields produced by electron flow in the molecular orbitals are included in the overall magnetic field that a nucleus experiences. The local geometry (bond lengths, binding partners, and angles between bonds, etc.) and, consequently, the local magnetic field at each nucleus, typically affect the electron allocation of the same type of nucleus (e.g. 13C, 15N & 1H).

Chemical shift Scale

The values of chemical shift usually come out in delta scale (⸹), its value ranges from 0 to 10 ppm. Zero value given to TMS as a reference standard.

The other scale that is used is Tau scale (ᵼ), its value for TMS is 10 and ranges between 0 to 10.

The relationship between these two scales is given as

ᵼ = 10 - ⸹

Chemical shift Values

Chemical Shift Formula

⸹ = ν _sample – ν _reference / ν _reference

⸹ = shift in Hz / frequency of spectrometer in MHz

The chemical shift value is calculated by using the above formula, sigma symbol (⸹) shows the value of chemical shift and ν is the frequency. First, we find the difference between the frequency of sample and reference and then divide this obtained value by the frequency of reference. Usually, we take TMS as a reference substance for finding chemical shift value. As we also know the signal for TMS in NMR Spectrum always occurs at zero on the scale so, we can simply say that the sigma value is the value of our sample. Also, the frequency of reference is actually refers to the frequency of the spectrometer because TMS is used as a reference it has highly shielded protons. By using the second formula we easily find the value of chemical shift. A shift in hertz means how much a proto in our sample is shifted from the reference substance that is TMS.

The values in the numerator are taken in hertz and in denominator values are shown in megahertz. Thus the obtained value will be in ppm, which is normally shown in the graph. As an example, if the NMR signal appears at 400 Hz then the reference signal will be 400 MHz.

⸹ = 400 Hz / 400 MHz

= 1 Hz / 1 * 10 ⁶ Hz

= 1 * 10 ^-6

= 1 ppm

Coupling Constant or J Value

The coupling constant, represented by the letter J, is a measure of the strength of the splitting effect. It is the distance between the peaks in a certain multiplet. Simply speaking, if we have doublet signals it means that signals are shown by two protons having the same chemical environment, it also described this signal consists of two closely spaced peaks when these peaks are split then the distance between the center of these two peaks gives a coupling constant value. The coupling means the joining of two protons and their peaks difference gives a constant value, which is known as the coupling constant.  J numerical value is given in cycles per second or Hertz. See the figure below,

 

Coupling Constant or J Value

The value of J, in contrast to chemical shifts, is completely dependent on the molecule structure and is independent of externally applied magnetic field strength.

Method for calculating Coupling Constant

The coupling constant is caused by the splitting of one proton that has the same value as the coupling constant caused by the splitting of the second proton for a pair of protons that are mutually connected. In other words, protons that are mutually connected exhibit the same degree of signal splitting.

The size of the coupling constant is generally influenced by the quantity and type of chemical connections that are present between the protons as well as their spatial relationships. For instance, protons with gauche conformation have a J value near 2-4 Hz whereas protons with anti-conformation have a J value close to 5-12 Hz in the case of freely rotating groups.

(1) Based on the spatial placements and overall structure of the molecules, J varies from 2-18 Hz for protons connected to nearby carbon atoms (vicinal protons).

(2) Based on the bond angle and general structure of the molecule, the values of J for protons bound to the same carbon atom (also known as germinal protons) range from 0 to 20 Hz.

(3) For ordinary molecules coupling constant ranges from 0-18 Hz.

The coupling constant for a doublet is the difference between its two peaks in the simplest situation. J is measured in Hz, not ppm, which is where the problem lies. The peaks from ppm must first be converted to hertz.

ppm = Hz / MHz

Hz = ppm * MHz

 Let's say there are two peaks, one at 5.250 ppm and the other at 5.237 ppm. Simply multiply these values by the field strength in MHz (400 MHz) to obtain Hz. Our peaks would be at 2100 Hz and 2094.8 Hz if we were using a 400 MHz NMR machine, respectively. So, the difference is represented by the J value. 2100-2094.8 in this instance equals 5.2 Hz. If a proton is split by more than one other proton, especially if the protons are not the same, this may become more challenging.

 

Shielded and Deshielded Proton (1H-NMR)

  Shielded and Deshielded Proton (¹H-NMR)

Shielded and deshielded protons are used to determine the environment of molecules in NMR spectroscopy. Shielded simply means protective covering around atoms and deshielded without protective field/covering around a proton.

As far as we are aware, the fundamental idea behind NMR is to apply an external magnetic field termed B0 and detect the frequency at which a nucleus reaches resonance. A weak magnetic field produced by electrons in the nucleus opposes the B0. In this instance, we can argue that the electrons are protecting the nucleus from B0.

Shielded Protons

As we know NMR spectrum is formed on the basis of applied radio frequency against absorption. The position of signals in the spectrum tells the chemical shift value. This chemical shift or position of signals is affected by the nature of protons. Proton shielding and deshielding occur due to the electronegative atoms around the specific proton.

An opposing magnetic field to the applied field is produced by the proton's electrons. Because this minimizes the field experienced at the nucleus, the electrons are considered to protect the proton. As shown below,

Electronegative atoms attract electrons towards themselves more strongly than other simple atoms, we also know that electronegativity is the ability of an atom to attract the shared pair of electrons towards its own nuclei.

So, shielding is the ability of an atom to resist the external field around it.

In the case of the NMR spectrum, shielded protons are those protons that have electrons around themselves and these electrons work as a protective cover.

The effective nuclear charge of the nucleus exerts a strong attractive pull on each of its electrons. There is very little shielding between the nucleus and the electrons since all of the electron levels are drawn extremely close to it. The stronger the shielding, the higher the opposing magnetic fields to B0. from the electrons are relative to the nucleus' electron density. The chemical shift shifts up a field (lower ppm) because the proton receives a lower external magnetic field and hence requires a lower frequency to reach resonance.

 

Shielded Proton Behavior in NMR

Shielded protons have spin slight opposite to applied magnetic field, so they require low energy to bring them into resonance, upfield signal appear. when the applied magnetic field and proton magnetic field becomes equal in direction, signals appear (this is called resonance).

Deshielded protons

Deshielded protons don’t have electrons around them.

 

The density of electrons is low so, when a magnetic field is applied these protons feel more externally applied magnetic field. Their signals appear downfield in the spectrum.

The term "deshielded" refers to a nucleus that is more sensitive to the external magnetic field B0 as the electron density around it falls and the opposing magnetic field shrinks. The chemical shift shifts downfield (higher ppm) because the proton experiences a greater external magnetic field and hence requires a higher frequency to establish resonance.

Example:

The hydrogen nucleus will become unshielded as a result of the electronegative atom fluorine pulling the electron density towards it (electron withdrawing). This will cause an increase in the resonance frequency and a shift to higher ppm. In the case of CH4, the hydrogen nucleus is protected, hence the peak is on the lower ppm side.

 

Deshielded Proton Behavior in NMR 

A downfield signal or high value of sigma means these protons are deshielded and their spins are opposite to applied magnetic field, so they require high amount of energy for resonance.

Major differences between Shielded and Deshielded Protons

Shielded Proton	Deshielded Proton
Require less energy for flipping	Take more energy for flipping
Peak appear upfield	Peak formed downfield
Less β effective (applied magnetic field effect)	High β effective (applied magnetic field effect)
Signals nearer to TMS	Signals far from TMS
Low chemical shift value	High chemical shift value

 

The conclusion is that shielded protons absorb radiation at higher frequencies, whereas deshielded protons absorb at lower frequencies.

Position of signal in NMR

Types of Electronic Transition in UV-Visible Spectroscopy

 Types of Electronic Transition in UV-Visible Spectroscopy

Types of Electronic Transition in UV-Visible Spectroscopy

“UV-Visible absorption spectroscopy is the measurement of the attenuation or weakening of the strength of a light beam when it passes through the sample or after reflection from a sample surface.”

Types of Transitions in UV-Visible Spectroscopy

UV-light and visible light cause the same transitions in molecules so they are commonly combined and called as UV-Visible, when they interact with the matter then it becomes UV-Visible spectroscopy. This kind of spectroscopy is also called electronic spectroscopy because electronic transition occurs in molecules when they absorb UV-Visible light promotion of electrons from low to high energy level occurs, and only outermost shell electron transitions occurs in compounds.

By using UV-Visible spectroscopy or from the types of transitions we can determine the number of double bonds conjugated molecules, aromatic conjugated, simple conjugated, or non-conjugated molecules.

Regions in UV-Visible Spectra

UV-Visible absorption region ranges between 10 nm to 800 nm where 10 to 400 nm is Ultra Violet region and 400 to 800 nm is a visible region. The region between 200 to 800 nm is the most prevalent region for the electronic transition so this region is named as excitation region. The region below 200 nm is called as vacuum region. Because oxygen and nitrogen that are present in the atmosphere show absorption in spectra, so vacuum instruments are required for this region's studies. The region between 200 to 400 nm is known as the ordinary or quartz region.

Absorption laws

Beer’s Law

“This law states that when a beam of monochromatic light passes through a homogenous absorbing medium. The rate of decrease of intensity of radiation with a thickness of absorbing medium is proportional to the intensity of the incident light as well as concentration.”

Mathematically,

-dI/ dx = K`IC

Lambert Law

“This law states that when a beam of monochromatic light passes through a homogenous absorbing medium. The rate of decrease of intensity of radiation with a thickness of absorbing medium is proportional to the intensity of the incident light.”

Mathematically,

-dI/ dx = K`I

Beer`s Lambert law

“Beer-Lambert law states that the concentration of the sample and path length is directly proportional to the absorbance of the light.”

A = ε Lc

Here,

A = Amount of light absorbed for a particular wavelength by the sample

ε = Molar absorptivity coefficient

L = Distance covered by the light through the solution

c = Concentration of the absorbing species

Beer`s Lambert law

Molar absorptivity

ε = A/ Lc

The sample's molar absorptivity, also called the extinction coefficient, is represented by the symbol. The ability of the sample to absorb light at a specific wavelength is related to a special physical constant of the sample's chemistry.

By dividing both the concentration and the length of the solution that the light travels through, molar absorptivity is found.

Following are cases where Beer's law is destroyed:

• when many molecular kinds are in balance with one another.
• Solute and solvent combine to generate an association complex.
• when using fluorescent chemicals.

As the ratio of light entering a solution to light leaving it determines how much light travels through it, absorbance has no units. Absorbance is sometimes expressed in "absorbance units," which is abbreviated as AU and has no dimension.

It is necessary to use a diluted solution, avoid light beam scattering, and employ monochromatic electromagnetic radiation.

Beer-Lambert law at high concentrations

The Beer-Lambert law fails at larger concentrations because its linearity is restricted to chemical and instrumental parameters. The molecules' closeness gets so close as the solution's concentration rises that the absorptivity changes. Moreover, the refractive index varies when the concentration is high. when the excited state and the ground state have reached thermal equilibrium.

Beer-Lambert law at high concentrations

 

Now we discuss different types of transitions that are as follows,

ϭ to ϭ⃰ transitions

These type of transitions occurs in saturated hydrocarbons that contain sigma bonds.

Absorption occurs near 150 nm that is of high energy for saturated hydrocarbons because the sigma bond is a strong bond and those organic compounds in which all the valence electrons are involved in the formation of a sigma bond do not show absorption in normal UV-Visible region that is in the range of 180-400nm. Electrons excite from one sigma orbital to another.

ϭ to ϭ⃰ transitions

n to ϭ⃰ transitions

For these types of transitions, the wavelength range is between 150 to 250nm. These transitions occur when non-bonding electrons are promoted to anti-bonding sigma orbitals. Most commonly these transitions occur in saturated compounds that contain one heteroatom along with unshared pair of electrons. For example, ethers, alcohols, aldehydes, ketones, etc. These transitions require less amount of energy as compared to the first one. Water and methyl chloride absorbs at 167nm and 169nm in the UV-Visible region respectively.

n to ϭ⃰ transitions

ᴫ to ᴫ⃰ transitions

The wavelength range for these types of transition is between 170nm to 190/200 nm. These occur when electrons move from one pi bon to another pi bond. Compounds like alkenes, alkynes, carbonyl, cyanides, and azo show these types of transitions. Normally if we increase one alkyl group in olefins the wavelength increase by 3 to 5 nm. Carbonyl compounds show absorbance at 180nm.

ᴫ to ᴫ⃰ transitions

n to ᴫ⃰ transitions

These electronic transitions occur when electrons of an unshared pair of heteroatom get promoted to anti-bonding orbitals. The wavelength range is high from all above and energy is lower (as we know energy and wavelength have an inverse relationship with each other) as compared to the above three. The Wavelength range is between 200 to 700 nm.

           

These are of total six types of electronic transitions, the transitions that are discussed above are allowed transitions and their energy order is as follows,

ϭ to ϭ⃰ transitions > n to ϭ⃰ transitions > ᴫ to ᴫ⃰ transitions > n to ᴫ⃰ transitions

The other two types of transition are forbidden transitions that are ϭ to ᴫ⃰ transitions and ᴫ to ϭ⃰ transitions.

Electronic Transitions