This document provides an introduction to rotational spectra and microwave spectroscopy. It discusses the rotational spectra of rigid diatomic molecules, classification of molecules, selection rules, and moments of inertia. The key points are:
1) Rotational spectra are obtained from transitions between rotational energy levels within the same vibrational state, giving information about molecular parameters.
2) Molecules are classified based on their principal moments of inertia as linear, symmetric top, spherical top, or asymmetric top.
3) The rotational energy levels and spectra of rigid diatomic molecules can be described using a rigid rotor model based on the molecular moment of inertia.
4) The selection rule for rotational transitions in a rigid diatomic molecule is that
This document discusses ligand substitution reactions in octahedral complexes. It describes the main mechanisms of ligand substitution including dissociative (SN1), associative (SN2), and concerted (interchange) pathways. It also discusses hydrolysis reactions and anation reactions as types of ligand substitutions. Specific examples are provided of acid and base hydrolysis in octahedral cobalt complexes, and factors that influence the reaction mechanisms and rates are outlined.
This document discusses theories of unimolecular reaction kinetics, including the Lindemann-Christiansen theory, Hinshelwood theory, RRK theory, and RRKM theory. It notes limitations of earlier theories in explaining experimental data. The RRKM theory, developed by Marcus in 1951-1952, redefined the RRK treatment and addressed prior limitations. RRKM theory is now widely used to interpret thermal and photochemical reactions and allows calculating reaction rates from known vibrational frequencies of molecules.
The document discusses different types of electrophilic substitution reactions: SE1, SE2, and SEi. SE1 reactions follow first-order kinetics and involve two steps - rate-determining ionization and fast combination. SE2 reactions also follow first-order kinetics, but occur in a single step through a transition state. SE2 reactions can result in retention or inversion of configuration. SEi reactions are concerted mechanisms where the electrophile assists in removing the leaving group, leading to retention of configuration.
Acid Base Hydrolysis in Octahedral ComplexesSPCGC AJMER
This document discusses acid and base hydrolysis in octahedral complexes. It covers factors that affect the rate of acid hydrolysis, including the charge on the complex, steric hindrance effects, and the strength of the leaving group. A higher positive charge, more steric hindrance, or stronger metal-leaving group bond each decrease the rate of acid hydrolysis according to first-order kinetics through a dissociative SN1 mechanism. Base hydrolysis of octahedral complexes can proceed by either associative SN2 or dissociative SN1 pathways depending on conditions.
N-heterocyclic carbenes (NHCs) are stable species containing a carbene carbon atom adjacent to at least one nitrogen atom in a ring structure. NHCs were first synthesized in the 1960s but were not isolated until 1991. They are stable due to inductive, mesomeric, and aromatic effects. NHCs are stronger sigma donors than phosphines and provide greater stability and reactivity to transition metal complexes. They have widespread applications as ligands in catalysis due to their tunable activities and stability in air and moisture.
Selection rules for soectroscopic transitionsRukhsarLatif1
This document discusses selection rules and photochemistry concepts. It describes three main selection rules that govern transitions in complex metal ions: spin selection rules, orbital selection rules, and Laporte selection rules. Spin selection rules state that transitions can only occur between states of the same spin and multiplicity. Orbital selection rules indicate that d-d transitions are usually forbidden but can be partially allowed. Laporte selection rules are based on parity and state that transitions between states of the same parity are forbidden. The document also discusses the Franck-Condon principle and provides an abstract on photochemistry occurring on particulate matter and within liquid droplets.
Supramolecular host and guest design pptAfrina Jasy
This presentation summarizes concepts in supramolecular host-guest design, including:
- Host-guest chemistry involves noncovalent interactions between a host molecule and guest, such as electrostatic interactions or hydrogen bonding.
- Successful host-guest complexes rely on complementarity between the host's binding sites and the guest's structure, as well as preorganization of the host.
- Common noncovalent interactions that contribute to host-guest binding include ion-dipole interactions, hydrogen bonding, van der Waals forces, π-π interactions, and hydrophobic effects. The interplay of these interactions allows for selective and stable complex formation.
- Host design considerations include selectivity, complementarity between binding sites
This document discusses ligand substitution reactions in octahedral complexes. It describes the main mechanisms of ligand substitution including dissociative (SN1), associative (SN2), and concerted (interchange) pathways. It also discusses hydrolysis reactions and anation reactions as types of ligand substitutions. Specific examples are provided of acid and base hydrolysis in octahedral cobalt complexes, and factors that influence the reaction mechanisms and rates are outlined.
This document discusses theories of unimolecular reaction kinetics, including the Lindemann-Christiansen theory, Hinshelwood theory, RRK theory, and RRKM theory. It notes limitations of earlier theories in explaining experimental data. The RRKM theory, developed by Marcus in 1951-1952, redefined the RRK treatment and addressed prior limitations. RRKM theory is now widely used to interpret thermal and photochemical reactions and allows calculating reaction rates from known vibrational frequencies of molecules.
The document discusses different types of electrophilic substitution reactions: SE1, SE2, and SEi. SE1 reactions follow first-order kinetics and involve two steps - rate-determining ionization and fast combination. SE2 reactions also follow first-order kinetics, but occur in a single step through a transition state. SE2 reactions can result in retention or inversion of configuration. SEi reactions are concerted mechanisms where the electrophile assists in removing the leaving group, leading to retention of configuration.
Acid Base Hydrolysis in Octahedral ComplexesSPCGC AJMER
This document discusses acid and base hydrolysis in octahedral complexes. It covers factors that affect the rate of acid hydrolysis, including the charge on the complex, steric hindrance effects, and the strength of the leaving group. A higher positive charge, more steric hindrance, or stronger metal-leaving group bond each decrease the rate of acid hydrolysis according to first-order kinetics through a dissociative SN1 mechanism. Base hydrolysis of octahedral complexes can proceed by either associative SN2 or dissociative SN1 pathways depending on conditions.
N-heterocyclic carbenes (NHCs) are stable species containing a carbene carbon atom adjacent to at least one nitrogen atom in a ring structure. NHCs were first synthesized in the 1960s but were not isolated until 1991. They are stable due to inductive, mesomeric, and aromatic effects. NHCs are stronger sigma donors than phosphines and provide greater stability and reactivity to transition metal complexes. They have widespread applications as ligands in catalysis due to their tunable activities and stability in air and moisture.
Selection rules for soectroscopic transitionsRukhsarLatif1
This document discusses selection rules and photochemistry concepts. It describes three main selection rules that govern transitions in complex metal ions: spin selection rules, orbital selection rules, and Laporte selection rules. Spin selection rules state that transitions can only occur between states of the same spin and multiplicity. Orbital selection rules indicate that d-d transitions are usually forbidden but can be partially allowed. Laporte selection rules are based on parity and state that transitions between states of the same parity are forbidden. The document also discusses the Franck-Condon principle and provides an abstract on photochemistry occurring on particulate matter and within liquid droplets.
Supramolecular host and guest design pptAfrina Jasy
This presentation summarizes concepts in supramolecular host-guest design, including:
- Host-guest chemistry involves noncovalent interactions between a host molecule and guest, such as electrostatic interactions or hydrogen bonding.
- Successful host-guest complexes rely on complementarity between the host's binding sites and the guest's structure, as well as preorganization of the host.
- Common noncovalent interactions that contribute to host-guest binding include ion-dipole interactions, hydrogen bonding, van der Waals forces, π-π interactions, and hydrophobic effects. The interplay of these interactions allows for selective and stable complex formation.
- Host design considerations include selectivity, complementarity between binding sites
Reductive elimination is an elementary step where the metal's coordination number and oxidation state both decrease as a new covalent bond is formed. It is the reverse of oxidative addition. Reductive elimination is more common for metals in higher oxidation states. For reductive elimination to occur, the eliminating groups must be cis-oriented and there must be a high formal positive charge on the metal. Reductive elimination finds applications in important catalytic reactions like hydrogenation and hydroformylation.
Oxidative addition is a process where a metal complex increases its oxidation state and coordination number by addition of two ligands. It is the reverse of reductive elimination. It requires the metal to have available orbitals and be in a lower oxidation state. There are four mechanisms for oxidative addition: concerted, SN2, radical, and ionic. Oxidative addition and reductive elimination are important steps in many catalytic cycles in organometallic chemistry and homogeneous catalysis.
The document introduces the Heck reaction, which is a coupling reaction where a metal catalyst aids in coupling two hydrocarbon fragments. Specifically, the Heck reaction involves converting a terminal alkene to an internal alkene. Richard Heck, Ei-ichi Negishi, and Akira Suzuki were jointly awarded the Nobel Prize in 2010 for their work developing palladium-catalyzed C-C cross coupling reactions, including the Heck reaction. The mechanism of the Heck reaction involves oxidative addition, insertion, β-H elimination, and reductive elimination steps.
the photo chemistry of ligand field is very important to have an idea for the intrinsic properties of different coordination compound, and the electronic properties such as, LMCT,LLCT, MLCH etc..........
Nucleophilic Aromatic Substitution of BenzyneAadil Ali Wani
The document discusses the elimination-addition mechanism of nucleophilic aromatic substitution involving benzyne. Aryl halides undergo substitution when treated with strong bases like KNH2 or NH3 at -33°C. The new substituent attaches to either the carbon that bore the leaving group or the adjacent carbon. The mechanism proceeds in three steps: 1) formation of the highly reactive intermediate benzyne, 2) relief of angle strain in benzyne, and 3) addition of the nucleophile to form the substitution product. Benzyne is a reactive dienophile that gives Diels-Alder adducts when generated in the presence of conjugated dienes. Other methods like treating 1-
This document summarizes key concepts in organometallic chemistry. It discusses the definition of organometallic compounds as those containing metal-carbon bonds. It outlines different types of ligands that can bind to metals, including carbonyl, carbene, and cyclic π systems. It also describes principles for understanding bonding interactions between ligands and metals, such as the 18-electron rule and molecular orbital theory. Spectroscopic techniques for analyzing organometallic compounds are also summarized.
Two-dimensional NMR (2D-NMR) techniques such as COSY and HETCOR provide additional structural information about molecules beyond what can be learned from one-dimensional NMR. COSY identifies protons that are spin-coupled to each other, while HETCOR connects carbon signals to the protons bonded to those carbons. These 2D NMR techniques simplify analysis of complex molecules like proteins by separating overlapping signals.
This chapter discusses carbocations, which are positively charged carbon-containing ions that are highly reactive intermediates in organic chemistry. Carbocations have six electrons in the outer shell of the central carbon atom. They are stabilized by electron-donating groups and destabilized by electron-withdrawing groups. Carbocations undergo various reactions including reactions with nucleophiles, elimination reactions, rearrangement reactions, and additions to unsaturated systems. Non-classical carbocations are also discussed.
The document summarizes the dienone-phenol rearrangement, which is the acid- or base-catalyzed migration of alkyl groups in cyclohexadienones, resulting in highly substituted phenols. It was first described in 1893 for the rearrangement of santonin to desmotroposantonin under acidic conditions, but was more fully characterized in 1930. The rearrangement requires only moderately strong acids and is exothermic. It proceeds by a [1,3] sigmatropic migration of C-C bonds, which actually occurs through two subsequent [1,2] alkyl shifts. Depending on the migrating group, other rearrangements such as [1,2], [1,3], [
The document discusses the Von Richter rearrangement and Smiles rearrangement.
The Von Richter rearrangement involves the displacement of a nitro group by cyanide ion on an aromatic compound, with the carboxyl group entering ortho to the displaced nitro group. Evidence supports a mechanism where one oxygen of the carboxyl group comes from the nitro group and one from solvent.
The Smiles rearrangement involves an intramolecular nucleophilic substitution where a leaving group is displaced by a nucleophile activated by an ortho nitro group. Examples are given of substrates that undergo Smiles rearrangement where the linking chain can be aromatic or aliphatic. Electron withdrawing groups para to the nucleophile retard the
This document discusses sigmatropic rearrangements, a type of pericyclic reaction involving intramolecular migration of an atom or group across a conjugated pi system. It defines sigmatropic rearrangements and explains that they can occur through thermal or photochemical processes. The document categorizes different types of sigmatropic rearrangements such as Cope, Claisen, and [2,3] rearrangements. It provides examples of these reactions and discusses factors that determine reaction stereochemistry such as suprafacial versus antrafacial migration. The document also references several organic chemistry textbooks for further information on sigmatropic rearrangement mechanisms and applications.
This presentation describes about the preparation, properties, bonding modes, classification and applications of metal Dioxygen Complexes. Also explains the MO diagram of molecular oxygen.
This document discusses the relationship between vibrational frequency and the force constant of a covalent bond. It states that for a diatomic molecule acting as a simple harmonic oscillator, the restoring force is proportional to displacement, as described by Hooke's Law. It then provides the equation relating vibrational frequency, force constant, and reduced mass. Several examples are given of calculating force constants from given vibrational frequencies and reduced masses. The document also notes that a higher force constant corresponds to a stronger covalent bond.
This document provides an overview of group theory concepts. A group is a collection of elements that is closed under a binary operation, contains an identity element, and has inverse elements. Groups can be represented by multiplication tables. Symmetry operations within a point group can be classified into conjugacy classes based on their similarity transforms. Matrix representations allow symmetry operations to be modeled as transformations on object coordinates.
Basic inorganic chemistry part 2 organometallic chemistryssuser50a397
The document provides an overview of organometallic chemistry including:
- Key concepts such as the 18 electron rule, metal carbonyls, and sandwich compounds.
- Important discoveries such as Zeise's salt (first transition metal organometallic compound) and ferrocene (first sandwich compound).
- Industrial applications of organometallic catalysts in homogeneous catalysis including hydroformylation and hydrocarbon conversions.
- Methods for counting electrons in organometallic complexes using the neutral atom and oxidation state methods.
This document provides an overview of quantum mechanics (QM) calculation methods. It discusses molecular mechanics, wavefunction methods, electron density methods, including correlation, Hartree-Fock theory, semi-empirical methods, density functional theory, and their relative speed and accuracy. Key aspects that can be calculated using these methods are also listed, such as molecular orbitals, electron density, geometry, energies, spectroscopic properties, and more. Basis sets and handling open-shell systems in calculations are also covered.
This document discusses ligand substitution reactions in coordination compounds. It begins by defining ligand substitution and classifying the mechanisms as dissociative, associative, or interchange. For octahedral complexes, dissociative mechanisms are seen at high concentrations of the entering ligand and associative at low concentrations. Evidence for dissociative mechanisms includes little effect of the entering ligand on rate. Ligand substitution can also occur in octahedral complexes without breaking the metal-ligand bond. The document also discusses substitution in square planar complexes, factors affecting rate, and the trans effect, providing theories to explain it such as electrostatic polarization and pi bonding. Applications of the trans effect in synthesis are also mentioned.
Sir Cyril Hinshelwood and Nikolaevich received the 1956 Nobel Prize in Chemistry for their research on chemical reaction mechanisms. Hinshelwood modified Lindemann's explanation for unimolecular reactions by proposing that energized molecules (A*) may store energy in various molecular bonds and vibrational degrees of freedom, rather than immediately reacting. This statistical distribution of energy among s degrees of freedom leads to a modified rate constant expression containing an additional term of 1/(s-1) that can account for much higher observed reaction rates. However, Hinshelwood's theory does not fully explain some experimental observations such as the temperature dependence of rate constants and nonlinear plots of 1/k1 versus concentration.
The document discusses 1,3-dipolar cycloaddition reactions, which involve a 1,3-dipole reacting with a dipolarophile to form a 5-membered heterocyclic ring. Key points include:
- 1,3-dipoles are classified into three types based on their electronic structure. Common examples are azides, nitrones, and carbonyl ylides.
- The reaction typically proceeds by a concerted pericyclic mechanism through a six-electron transition state, though some exceptions involve a stepwise mechanism.
- Frontier molecular orbital theory can be used to classify dipoles as HOMO-controlled, LUMO-controlled, or ambiphilic based
The document provides information on rotational spectroscopy and the rotational spectra of molecules. It discusses key topics like:
1) Classification of molecules as linear, symmetric top, spherical top, and asymmetric top based on their moments of inertia.
2) The rigid rotor model and how it leads to quantized rotational energy levels expressed by the rotational constant B.
3) The selection rule for rotational transitions of ΔJ = ±1, which results in a series of equally spaced spectral lines.
4) Factors that determine the intensity of rotational lines, including Boltzmann distribution of molecular populations and degeneracy of energy levels.
This document provides an overview of molecular spectroscopy techniques, including rotational spectroscopy, vibrational spectroscopy, and absorption and emission spectroscopy. Rotational spectroscopy uses microwave spectroscopy to study the quantized rotational energy levels of molecules. Vibrational spectroscopy uses infrared spectroscopy to analyze the quantized vibrational energy levels of bonds as they stretch, bend, and vibrate. Absorption and emission spectroscopy examines how molecules absorb and emit photons during electronic transitions between energy levels.
Reductive elimination is an elementary step where the metal's coordination number and oxidation state both decrease as a new covalent bond is formed. It is the reverse of oxidative addition. Reductive elimination is more common for metals in higher oxidation states. For reductive elimination to occur, the eliminating groups must be cis-oriented and there must be a high formal positive charge on the metal. Reductive elimination finds applications in important catalytic reactions like hydrogenation and hydroformylation.
Oxidative addition is a process where a metal complex increases its oxidation state and coordination number by addition of two ligands. It is the reverse of reductive elimination. It requires the metal to have available orbitals and be in a lower oxidation state. There are four mechanisms for oxidative addition: concerted, SN2, radical, and ionic. Oxidative addition and reductive elimination are important steps in many catalytic cycles in organometallic chemistry and homogeneous catalysis.
The document introduces the Heck reaction, which is a coupling reaction where a metal catalyst aids in coupling two hydrocarbon fragments. Specifically, the Heck reaction involves converting a terminal alkene to an internal alkene. Richard Heck, Ei-ichi Negishi, and Akira Suzuki were jointly awarded the Nobel Prize in 2010 for their work developing palladium-catalyzed C-C cross coupling reactions, including the Heck reaction. The mechanism of the Heck reaction involves oxidative addition, insertion, β-H elimination, and reductive elimination steps.
the photo chemistry of ligand field is very important to have an idea for the intrinsic properties of different coordination compound, and the electronic properties such as, LMCT,LLCT, MLCH etc..........
Nucleophilic Aromatic Substitution of BenzyneAadil Ali Wani
The document discusses the elimination-addition mechanism of nucleophilic aromatic substitution involving benzyne. Aryl halides undergo substitution when treated with strong bases like KNH2 or NH3 at -33°C. The new substituent attaches to either the carbon that bore the leaving group or the adjacent carbon. The mechanism proceeds in three steps: 1) formation of the highly reactive intermediate benzyne, 2) relief of angle strain in benzyne, and 3) addition of the nucleophile to form the substitution product. Benzyne is a reactive dienophile that gives Diels-Alder adducts when generated in the presence of conjugated dienes. Other methods like treating 1-
This document summarizes key concepts in organometallic chemistry. It discusses the definition of organometallic compounds as those containing metal-carbon bonds. It outlines different types of ligands that can bind to metals, including carbonyl, carbene, and cyclic π systems. It also describes principles for understanding bonding interactions between ligands and metals, such as the 18-electron rule and molecular orbital theory. Spectroscopic techniques for analyzing organometallic compounds are also summarized.
Two-dimensional NMR (2D-NMR) techniques such as COSY and HETCOR provide additional structural information about molecules beyond what can be learned from one-dimensional NMR. COSY identifies protons that are spin-coupled to each other, while HETCOR connects carbon signals to the protons bonded to those carbons. These 2D NMR techniques simplify analysis of complex molecules like proteins by separating overlapping signals.
This chapter discusses carbocations, which are positively charged carbon-containing ions that are highly reactive intermediates in organic chemistry. Carbocations have six electrons in the outer shell of the central carbon atom. They are stabilized by electron-donating groups and destabilized by electron-withdrawing groups. Carbocations undergo various reactions including reactions with nucleophiles, elimination reactions, rearrangement reactions, and additions to unsaturated systems. Non-classical carbocations are also discussed.
The document summarizes the dienone-phenol rearrangement, which is the acid- or base-catalyzed migration of alkyl groups in cyclohexadienones, resulting in highly substituted phenols. It was first described in 1893 for the rearrangement of santonin to desmotroposantonin under acidic conditions, but was more fully characterized in 1930. The rearrangement requires only moderately strong acids and is exothermic. It proceeds by a [1,3] sigmatropic migration of C-C bonds, which actually occurs through two subsequent [1,2] alkyl shifts. Depending on the migrating group, other rearrangements such as [1,2], [1,3], [
The document discusses the Von Richter rearrangement and Smiles rearrangement.
The Von Richter rearrangement involves the displacement of a nitro group by cyanide ion on an aromatic compound, with the carboxyl group entering ortho to the displaced nitro group. Evidence supports a mechanism where one oxygen of the carboxyl group comes from the nitro group and one from solvent.
The Smiles rearrangement involves an intramolecular nucleophilic substitution where a leaving group is displaced by a nucleophile activated by an ortho nitro group. Examples are given of substrates that undergo Smiles rearrangement where the linking chain can be aromatic or aliphatic. Electron withdrawing groups para to the nucleophile retard the
This document discusses sigmatropic rearrangements, a type of pericyclic reaction involving intramolecular migration of an atom or group across a conjugated pi system. It defines sigmatropic rearrangements and explains that they can occur through thermal or photochemical processes. The document categorizes different types of sigmatropic rearrangements such as Cope, Claisen, and [2,3] rearrangements. It provides examples of these reactions and discusses factors that determine reaction stereochemistry such as suprafacial versus antrafacial migration. The document also references several organic chemistry textbooks for further information on sigmatropic rearrangement mechanisms and applications.
This presentation describes about the preparation, properties, bonding modes, classification and applications of metal Dioxygen Complexes. Also explains the MO diagram of molecular oxygen.
This document discusses the relationship between vibrational frequency and the force constant of a covalent bond. It states that for a diatomic molecule acting as a simple harmonic oscillator, the restoring force is proportional to displacement, as described by Hooke's Law. It then provides the equation relating vibrational frequency, force constant, and reduced mass. Several examples are given of calculating force constants from given vibrational frequencies and reduced masses. The document also notes that a higher force constant corresponds to a stronger covalent bond.
This document provides an overview of group theory concepts. A group is a collection of elements that is closed under a binary operation, contains an identity element, and has inverse elements. Groups can be represented by multiplication tables. Symmetry operations within a point group can be classified into conjugacy classes based on their similarity transforms. Matrix representations allow symmetry operations to be modeled as transformations on object coordinates.
Basic inorganic chemistry part 2 organometallic chemistryssuser50a397
The document provides an overview of organometallic chemistry including:
- Key concepts such as the 18 electron rule, metal carbonyls, and sandwich compounds.
- Important discoveries such as Zeise's salt (first transition metal organometallic compound) and ferrocene (first sandwich compound).
- Industrial applications of organometallic catalysts in homogeneous catalysis including hydroformylation and hydrocarbon conversions.
- Methods for counting electrons in organometallic complexes using the neutral atom and oxidation state methods.
This document provides an overview of quantum mechanics (QM) calculation methods. It discusses molecular mechanics, wavefunction methods, electron density methods, including correlation, Hartree-Fock theory, semi-empirical methods, density functional theory, and their relative speed and accuracy. Key aspects that can be calculated using these methods are also listed, such as molecular orbitals, electron density, geometry, energies, spectroscopic properties, and more. Basis sets and handling open-shell systems in calculations are also covered.
This document discusses ligand substitution reactions in coordination compounds. It begins by defining ligand substitution and classifying the mechanisms as dissociative, associative, or interchange. For octahedral complexes, dissociative mechanisms are seen at high concentrations of the entering ligand and associative at low concentrations. Evidence for dissociative mechanisms includes little effect of the entering ligand on rate. Ligand substitution can also occur in octahedral complexes without breaking the metal-ligand bond. The document also discusses substitution in square planar complexes, factors affecting rate, and the trans effect, providing theories to explain it such as electrostatic polarization and pi bonding. Applications of the trans effect in synthesis are also mentioned.
Sir Cyril Hinshelwood and Nikolaevich received the 1956 Nobel Prize in Chemistry for their research on chemical reaction mechanisms. Hinshelwood modified Lindemann's explanation for unimolecular reactions by proposing that energized molecules (A*) may store energy in various molecular bonds and vibrational degrees of freedom, rather than immediately reacting. This statistical distribution of energy among s degrees of freedom leads to a modified rate constant expression containing an additional term of 1/(s-1) that can account for much higher observed reaction rates. However, Hinshelwood's theory does not fully explain some experimental observations such as the temperature dependence of rate constants and nonlinear plots of 1/k1 versus concentration.
The document discusses 1,3-dipolar cycloaddition reactions, which involve a 1,3-dipole reacting with a dipolarophile to form a 5-membered heterocyclic ring. Key points include:
- 1,3-dipoles are classified into three types based on their electronic structure. Common examples are azides, nitrones, and carbonyl ylides.
- The reaction typically proceeds by a concerted pericyclic mechanism through a six-electron transition state, though some exceptions involve a stepwise mechanism.
- Frontier molecular orbital theory can be used to classify dipoles as HOMO-controlled, LUMO-controlled, or ambiphilic based
The document provides information on rotational spectroscopy and the rotational spectra of molecules. It discusses key topics like:
1) Classification of molecules as linear, symmetric top, spherical top, and asymmetric top based on their moments of inertia.
2) The rigid rotor model and how it leads to quantized rotational energy levels expressed by the rotational constant B.
3) The selection rule for rotational transitions of ΔJ = ±1, which results in a series of equally spaced spectral lines.
4) Factors that determine the intensity of rotational lines, including Boltzmann distribution of molecular populations and degeneracy of energy levels.
This document provides an overview of molecular spectroscopy techniques, including rotational spectroscopy, vibrational spectroscopy, and absorption and emission spectroscopy. Rotational spectroscopy uses microwave spectroscopy to study the quantized rotational energy levels of molecules. Vibrational spectroscopy uses infrared spectroscopy to analyze the quantized vibrational energy levels of bonds as they stretch, bend, and vibrate. Absorption and emission spectroscopy examines how molecules absorb and emit photons during electronic transitions between energy levels.
This document provides an introduction to molecular spectroscopy and rotational spectroscopy. It discusses how electromagnetic radiation interacts with molecules to produce absorption or emission spectra. Rotational spectroscopy specifically analyzes the microwave spectra produced when molecules absorb microwave radiation, undergoing rotational transitions between energy levels. The frequency differences between lines in the rotational spectra are directly related to the rotational constant of the molecule.
1) The document discusses rotational (microwave) spectroscopy and the conditions for molecules to be microwave active. Only polar molecules with a permanent dipole moment can absorb microwave radiation.
2) It presents the expression for the moment of inertia of a diatomic rigid rotator molecule. The moment of inertia depends on the reduced mass and bond length.
3) The energy levels of a diatomic rigid rotator are quantized. The rotational energy increases with the rotational quantum number J and is proportional to the rotational constant B, which is specific to each molecule.
Rotational spectroscopy deals with the rotational energy transitions of molecules using microwave or far infrared radiation. When radiation of the proper frequency interacts with a rotating molecule, it can cause transitions between different rotational energy levels within the same vibrational state. This produces a pure rotational spectrum. The spectrum provides information about molecular parameters like the rotational constant. Only molecules with a dipole moment can interact with electromagnetic radiation and be observed spectroscopically. Replacement of one atom with its isotope changes the molecular moment of inertia slightly, resulting in a small measurable shift in the rotational transition frequencies.
Rotational spectroscopy measures the energies of rotational states of molecules. It can observe the rotation of polar molecules using microwave or infrared spectroscopy, and of non-polar molecules using Raman spectroscopy. Molecules can be modeled as rigid or non-rigid rotors. Diatomic and linear molecules can be modeled as rigid rotors, while distortions are accounted for in non-rigid rotor models. Vibrational states are modeled as harmonic oscillators, though anharmonicity is considered. Rotational and vibrational states are quantized, and selection rules apply to rotational-vibrational transitions.
This document discusses rotational spectra and molecular spectroscopy. It begins by explaining that molecular spectra appear as broad bands due to transitions between different molecular energy states caused by absorption, emission, or scattering of photons. It then discusses the differences between atomic and molecular spectroscopy, noting that molecular spectroscopy provides information about molecular structure, properties, and degrees of freedom. The main focus is on rotational spectroscopy, which occurs in the microwave or far-infrared region and arises from transitions between rotational energy states. This is observed in heteronuclear diatomic polar molecules with a permanent electric dipole moment. The energy levels of rotating diatomic molecules are also explained.
The document discusses Raman spectroscopy, which analyzes the scattering of light by molecules rather than light absorption. When a sample is irradiated with monochromatic light, most light is Rayleigh scattered at the same frequency, but a small amount is Raman scattered at lower (Stokes) or higher (anti-Stokes) frequencies. The frequency shift between incident and scattered light is independent of the incident light frequency and depends on molecular structure. Raman scattering occurs due to changes in molecular polarizability during vibrations or rotations. Spectra provide information about molecular vibrational and rotational energy levels.
Phonon frequency spectrum through lattice dynamics and normal coordinate anal...Alexander Decker
The document discusses the lattice dynamics and normal coordinate analysis of the high-temperature superconductor Tl2Ca3Ba2Cu4O12. It presents the following key points:
1. Lattice dynamics calculations using the three-body force shell model reproduce observed Raman and infrared phonon frequencies reasonably well.
2. Normal coordinate analysis using Wilson's F-G matrix method yields vibrational frequencies in good agreement with experimental values and lattice dynamics calculations.
3. Potential energy distribution calculations confirm that the chosen vibrational frequencies make the maximum contribution to the potential energy of the material's normal coordinate frequencies.
This document discusses crystal structures, including periodic arrays of atoms, fundamental lattice types, crystal planes indexed using Miller indices, and imaging atomic structures. It covers common lattice types like simple cubic, body-centered cubic, and face-centered cubic. Simple crystal structures presented include sodium chloride, cesium chloride, diamond, and zinc sulfide. Non-ideal crystal structures can involve random stacking or polytypism with long repeat units along stacking axes.
This document discusses crystal structures, including periodic arrays of atoms, fundamental lattice types, crystal planes indexed using Miller indices, and imaging atomic structures. It covers common lattice types like simple cubic, body-centered cubic, and face-centered cubic. Simple crystal structures presented include sodium chloride, cesium chloride, diamond, and zinc sulfide. Non-ideal crystal structures can involve random stacking or polytypism with long repeat units along stacking axes.
1. The document discusses the basic principles of Nuclear Magnetic Resonance (NMR) spectroscopy. It explains how certain nuclei can have spin and magnetic moments, and how these nuclei absorb electromagnetic radiation in the radiofrequency region when in a strong magnetic field.
2. The key parameters that determine whether a nucleus can be observed by NMR are discussed, including spin quantum number, magnetic moment, natural abundance, and quadrupole moment. Common nuclei observed by NMR like 1H, 13C, 19F, and 31P are described.
3. The basic NMR equation is presented, showing the relationship between resonance frequency, magnetic field strength, and the gyromagnetic ratio. Important NMR parameters like chemical shift, integration, and
IR spectroscopy . P.K.Mani, BCKV, West Bengal, IndiaP.K. Mani
This document provides an introduction to infrared (IR) spectroscopy, including:
1. IR spectra originate from the vibrational and rotational motions of molecules, which can absorb IR radiation if there is a change in dipole moment.
2. Molecules absorb specific frequencies that correspond to their natural vibrational frequencies. Stretching and bending vibrations within different functional groups absorb in characteristic regions of the IR spectrum.
3. IR spectroscopy can be used to identify molecules based on their absorption fingerprints between 400-1300 cm-1, which are influenced by the whole molecular structure.
B.tech. ii engineering chemistry Unit 1 atoms and moleculesRai University
1) The document describes the potential energy diagram and mathematical expression for a particle confined in a 1D box between 0 and L.
2) It shows that the Schrodinger equation inside the box is similar to the free particle equation, and the solutions are sine waves with allowed energies of En = n^2*h^2/8mL^2.
3) This particle in a box model is used to understand the quantization of energy levels for electrons in an atom.
Molecular mechanics uses classical mechanics to model molecular systems by calculating the potential energy. It can study small molecules as well as large biological systems with many thousands to millions of atoms. Molecular mechanics represents atoms as spheres and bonds as springs, with interactions described by classical potentials. It has been used to calculate properties like binding constants, protein folding kinetics, and to design binding sites.
The document discusses electrons in atoms and is divided into three sections. Section 5.1 covers light and quantized energy, explaining that light has both wave and particle properties and matter emits and absorbs energy in quanta. Section 5.2 discusses quantum theory and the atom, comparing Bohr's model to the quantum mechanical model which assumes electrons have wave properties. Section 5.3 is about electron configuration, explaining that the arrangement of electrons in an atom follows rules such as the aufbau principle and can be represented with orbital diagrams and electron configuration notation.
This document presents a framework for determining the rotational-vibrational spectra and stability of diatomic molecules using quantum mechanics. It summarizes:
1) The framework models the diatomic molecule using a Hamiltonian that accounts for the kinetic energy of the nuclei and electrons, as well as the potential energies between nuclei, electrons, and nuclei-electron interactions.
2) It approximates the molecule as rigid to simplify the problem, treating nuclear motion as a perturbation. This allows separating the wavefunction into electronic and nuclear components.
3) It then solves for rotational states using a rigid rotor model that describes nuclear rotation, yielding energy levels dependent on the angular momentum quantum number. This provides insights into diatomic molecular stability and
This document discusses infrared (IR) spectroscopy and how it can be used to analyze molecular vibrations. It explains that IR spectroscopy measures the absorption of IR radiation by materials as their atoms vibrate in different ways. Molecules absorb IR radiation at frequencies related to their unique compositions, structures, and bond types. The number and types of vibrational modes a molecule can undergo depends on the number of atoms and whether the molecule is linear or nonlinear. For a vibration to be IR active, it must involve a change in the molecule's dipole moment as it vibrates. Examples are provided of analyzing the vibrational modes and IR activity of molecules like water.
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1. UNIT-1
ROTATIONAL SPECTRA
(Microwave Spectroscopy)
Lesson Structure
1.0 Objective
1.1 Introduction
1.2 Classification of molecules
1.3 Rotational spectra of regid diatomic molecules
1.4 Selection rules
1.5 Non-rigid rotator
1.6 Spectrum of a non-rigid rotator
1.7 Linear polyatomic molecules
1.8 Non-linear polyatomic molecules
1.9 Asymmetric top molecles
1.10. Starck effect
Solved Problems
Model Questions
References
1.0 OBJECIVES
After studyng this unit, you should be able to
• Define the monent of inertia
• Discuss the rotational spectra of rigid linear diatomic molecule
• Spectrum of non-rigid rotator
• Moment of inertia of linear polyatomic molecules
2. 2
Rotational Spectra (Microwave Spectroscopy)
• Explain the effect of isotopic substitution and non-rigidity on the rotational spectra
of a molecule.
• Classify various molecules according to thier values of moment of inertia
• Know the selection rule for a rigid diatomic molecule.
1.0 INTRODUCTION
Spectroscopy in the microwave region is concerned with the study of pure
rotational motion of molecules. The condition for a molecule to be microwave active is that
the molecule must possess a permanent dipole moment, for example, HCl, CO etc. The
rotating dipole then generates an electric field which may interact with the electrical
component of the microwave radiation. Rotational spectra are obtained when the energy
absorbed by the molecule is so low that it can cause transition only from one rotational level
to another within the same vibrational level. Microwave spectroscopy is a useful technique
and gives the values of molecular parameters such as bond lengths, dipole moments and
nuclear spins etc.
1.1 OBJECTIVES
Transitions between different rotational levels within same vibrational level give rise
to pure rotational spectra in the microwave or far infrared region. The study of such
transitions provides a direct method for the evaluation of molecular parameters.
Main objectives :
• To explain the effect of isotopic substitution and non rigidity on the rotational
spectra of a molecule.
• To discuss the rotational spectra of rigid diatomic molecule.
• To give applications of study of rotational spectra.
1.2 CLASSIFICATION OF MOLECULES
The rotation of a three dimensional body may be quite complex and it is convenient to
resolve it into rotational components about three mutually perpendicular direction through
the centre of gravity - the principal axes of rotation. Thus a body has three principal moments
of inertia, one about each axis, usually disignated IA, IB and IC.
C
A
B
IC
IA
IB
3. 3
Rotational Spectra (Microwave Spectroscopy)
IA = Moment of inertia about A
IC = Moment of inertia in plane of paper
IB = Moment of inertia r
to the plane of paper
Molecules may be classified into groups according to the relative values of their three
principal moments of inertia IA, IB and IC. In general A, B, C axes are selected in such a way
that IA < IB < IC. The molecules are usually classified into four groups based on the relative
values of principal moments of inertia.
1. Linear molecules
As the name suggests, in this case, all the atoms of the molecules are
arranged in a straight line. Some of the molecules of this category are HCl, CO2, OCS, HCN,
C2H2 etc. The three directions of rotation may be taken as
(a) about the bond axes
(b) end-over-end roation in the plane of the paper and
(c) end-over-end rotation at right angles to the plane. As the nuclei of the atoms
which give the main contribution to the mass are situated in the axis A, the moment of
inertia about this axis is approximately zero. i.e. IA= 0. The moments of inertia IB and IC
correspond to the end- over-end rotation of the molecule and therefore they are equal.
Thus, for a linear molecule IA= 0 and IB = IC.
2. Symmetric tops
In a symmetric top, two of the principal moments of inertia are equal and all the three
are non zero. Examples CH4, CH3Cl etc in which the carbon has a tetrahedral coordination.
The C–Cl bond axis (in CH3Cl) having a three fold axis of symmetry in the A-axis and on
this the centre of gravity of the molecules lies. The two mutually perpendicular B and C axis
lie in a plane perpendicular to the A-axis. It is obvious IB=IC. A molecule of this type spinning
about the A-axis resembles a spinning top and hence the name symmetric top. The molecule
in this class are further subdivided into the groups prolate symmetric top and the oblate
symmetric top. In prolate IB = IC > IA (e.g. CH3Cl, CH3F, CH3CN, NH3 etc.) and in oblate IB
= IC < IA (e.g. BF3, BCl3 etc.)
3. Spherical tops
When all the three principal moments of inertia of a molecule are equal, it is called a
spherical top (e.g. CH4, OsO4, SF6, CCl4 etc.) i.e. IA = IB = IC.
4. Asymmetric tops
These molecules, to which the majority of substance belong, have all three moments
of inertia different is IA IB IC. Some of the example are
H2O, CH3OH, CH2 = CHCl etc.
4. 4
Rotational Spectra (Microwave Spectroscopy)
Linear
molecule
H-Cl
O-C-S
O-C-O
Symmetric top
(It has axes of symmetry)
Spherical
Top
Assymmetric tops
F
C
H H
H
Prolate Oblate
(I is not negligible)
A
H
C
H H
H
O
H H
C =C
H
H H
H
Vinyl Chloride
Most of the molecules
fall in this catogory
F
C
H H
H
B —Cl
Cl
Cl
(I is negligible and =0)
A
Types of molecules
B C A
I I I
= =
B C A
I I I
= =
B C A
I I I
= <
A B C
I I I
= =
(No interest)
B C A
I I I
= =
1.3 ROTATIONAL SPECTRA OF RIGID DIATOMIC MOLECULE (RIGID
ROTATOR MODEL)
A rigid diatomic molecule means that the distance between the atoms (bond length)
does not change during rotation. No vibrational movement is taking place during rotation.
Let us consider a diatomic molecule A—B in which the atoms A and B having masses
m1 and m2 are joined together by a rigid bond of length r0 = r1 + r2 (figure 1). The molecule
A—B rotates about a point C, the centre of gravity: this is defined by the moment, or
balancing, equation.
1 1 2 2
m r m r ...(1.1)
A B
m2
m1
0
1 2
r
r r
Fig. (1.1) : A rigid diatomic molecule A-B having atomic masses,
m1 and m2, joined together by a rigid bond of length r0 =r1 + r2 and
rotates about a point C.
The moment of inertia about C is defined by
5. 5
Rotational Spectra (Microwave Spectroscopy)
2 2
1 1 2 2
I m r m r
1 1 2 2
m r m r
2 2 1 1 1 2
m r r m r r
2 1 1 2
r r m m ....(1.2)
from eqn (1)
1 1 2 2 2 0 1
–
m r m r m r r
1 1 2 0 2 1
–
m r m r m r
or
1 1 2 1 2 0
m r m r m r
or
1 1 2 2 0
r m m m r
2 0
1
1 2
m r
r
m m Similarly
1 0
2
1 2
m r
r
m m ...(1.3)
Putting the value of 1 2
&
r r from (3) in (2)
2 0 1 0
1 2
1 2 1 2
m r m r
I m m
m m m m =
2
2
1 2 0
0
1 2
m m r
r
m m
...(1.4)
where is the reduced mass of the system i.e.
1 2
1 2
m m
m m ...(1.5)
Equation (1.4) defines the moment of inertia conveniently in terms of the atomic masses
and the bond length.
By the use of the Schrödinger equation it may be shown that the rotational energy
levels allowed to the rigid diatomic molecule are given by the expression
2
2
1
8
J
h
E J J
I
Joules when J = 0, 1, 2 ...... ...(1.6)
In this expression h is Planck’s constant, are I is the moment of inertia,
either IB or IC, since both are equal. The quantity J, which can take integral values from zero
upwards, is called the rotational quantum number and each level is
(2J + 1) fold degenerate.
Often it is convenient to analyse the rotational energy spectrum in wave number units.
Therefore we may write.
6. 6
Rotational Spectra (Microwave Spectroscopy)
1
2
1
8
J
J
E h
J J cm
hc Ic
1
E
hc
1
1
BJ J cm J = 0, 1, 2.... ...(1.7)
where B is the rotational constant and is given by
2
1
2 2
8 8
h h
B cm Joule
Ic I
Denoting the lower state by J´´ and the upper state by J´
–
J J J
1 1
BJ J BJ J
1 1
B J J J J
use of the selection rule
1
J
or
1
J J gives the frequency of the absorption
line as
1 2 1
J J
v B J J J J
1 2
B J ...(1.8)
1
J J
1 1 2
J B J J
1
J B J J
1 2
B J J J
1
2 1 0,1, 2....
B J cm where J
The rotational constant B is assumed to be the same in both lower and
upper rotational states and double prime is dropped from equn (8)
The allowed energy levels of a rigid diatomic rotor are illustrated in
Fig. 1.2(a). Thus a step-wise raising of the rotational transitions result in an absorption
spectrum consisting of spectral lines with a separation of 2 B, that is at 2B, 4B, 6B, .... (Fig.
1.2(b)). The lowering of stepwise energy results in identical emission spectrum.
7. 7
Rotational Spectra (Microwave Spectroscopy)
Fig. (a) allowed energy levels of a rigid diatomic rotor showing electric dipole allowed
transitions and (b) the resulting absorption spectrum.
42 B
30 B
20 B
12 B
6 B
2 B
0
6
5
4
3
2
1
0
12B
10 B
8 B
6 B
4 B
2 B
2 B 4 B 6 B 8 B 10 B 12 B
0 1 2 3 4 5 J
Absorption
intensity
ms
J
Fig. 1.2 (a) Fig. 1.2(b)
Fig. 1.2(a) allowed energy levels of a right diatomic rotor showing electric dipole
allowed transitions and 1.2(b) the resulting absorption spectrum.
1.4 THE SELECTION RULES
The selection rule for a transition between any two rotational states is
quantum chemically given by
ij i jd
where i and j are the wave functions for the rotational states i and j and is the
permanent dipole moment of the molecule. The dipole moment being a vector quantity can
be expressed by its three components along the Cartesian coordinates axes,
x y z
and
2 2 2 2
x y z . The transition moment integral can be split in terms of the components
of the dipole moment,
x
ij i j
x d
y
ij i j
y d
z
ij i j
z d
If atleast any one of the integrals is non zero, then the transition is allowed and forbidden
otherwise. The intensity of an allowed rotational transition depends on the square of the
8. 8
Rotational Spectra (Microwave Spectroscopy)
transition dipole moment. Consequently, the intensity of the rotational line depends on the
square of the permanent dipole moment of the molecule.
Schrödinger equation shows that for a diatomic rigid rotor (in the absence of an external
electric or magnetic field) only transitions in which J changes by one unit, that is, 1
J
are allowed and all other transactions are forbidden. Thus the selection rule for rotational
spectra is 1
J ( plus sign for absorption and minus sign for emission) and second, the
molecule must have a permanent dipole moment (only hetronucelar diatomic molecules
will exhibit the rotational spectrum since homonuclear diatomic molecules do not possess
permanent dipole moment)
1.5 NON RIGID ROTOR
It is observed that in the pure rotational spectra of a diatomic molecule when the bond
in it is considered as a rigid, the spacing between successive lines is same, i.e. 2 B cm–1.
However, the assumption that the bond is rigid is only an approximation. Actual bond is
not a rigid bond and the bond length is not constant. It increases with rotations and is
elastic. In a rapidly rotating molecule, there is always a tendency of the bond to stretch due
to centrifugal effects. Hence, the moment of inertia increases with the rotational energy.
This causes rotational levels to be same what closer as the J value increases.
For example, consider the spectrum of hydrogen fluoride
1
0 1 20.56 0.0929
1 2 20.48 0.0931
2 3 20.43 0.0932
4 5 20.31 0.0935
. . .
. . .
. . .
. . .
10 11 18.91 0.0969
B cm r nm
J J
J J
J J
J J
J J
It is evident that the separation between successive lines (and hence the apparent B
value) decreases steadily with increasing J.
The reason for this decrease may be seen if we calculate internuclear distance from the
B values. In simple harmonic motion a molecular bond is compressed and extended an
equal amount on each side of the equilibrium distance and the average value of the distance
is therefore unchanged, the average value for a bond of equilibrium length 0.1 nm vibrating
between the limits 0.09 and 0.11 nm, we have
9. 9
Rotational Spectra (Microwave Spectroscopy)
0.11 nm
0.09 nm
r = 0.1 nm
Compression
Stretching
e
0.09 0.11
0.1
2 e
av
r nm r
But we know
2 2 2
8 8
h h
B
Ic c r
2
1
B
r
[since all other quantities are independent of vibration
2 2
2
2
1 1
0.09 0.11
1
103.05 ( )
2
av
nm
r
1
0.0985
103.5
av
r nm
The value differ from re. The difference, through small, is not negligible compared
with the precision with which B can be measured spectroscopically. In fact the real situation
is more different. For chemical bonds we know stretching is easier than compression, so the
result av
r being greater than eq
r . Thus the more vibration (i.e. higher J value), the difference
is more due to high rotation.
1.6 SPECTRUM OF A NON-RIGID ROTATOR
From Schrödinger equation for a non-rigid rotator in simple harmonic force field.
2 4
2
2
2 4 2 2
1 – 1
8 32
J
h h
E J J J J Joules
I I r K
K = force constant
2 4
2
2 1
2 4 2 2
1 1
8 32
J
J
E h h
J J J J cm
hc Ihc I r Khc
10. 10
Rotational Spectra (Microwave Spectroscopy)
2
2 1
1 – 1
BJ J DJ J cm
... (1.9)
when B is the rotational constant and D is the centrifugal distortion constant which is
a positive quantity
2 3
1
2 4 2 2
;
8 32
h h
B D cm
Ihc J r Kc
Relationship between B and D
2
2 2
8 8
h h
B
Ihc Ic
2 2 2
4
K c w
4 3 3 2
4 2 2 4 2 2 6 3 3 2
16
32 32 8 2 4 8
h h h Ic
D
I r Khc I r Kc I c Kr
2 2 2
3
3
6 3 3
2 2 2 2
[
1
2
4 ]
[ B ]
8 8 8
[ I r ; k 4 c ]
frequency
w
w
c
frequency
wave number
k
c
k mc
h
I c
2 2 2 2 2 3 3
3 3
2 2 2 2 2 2 3
16 16 4 4
4
Ic r c B B
B B
Kr w c r w w
3
2
4B
D
w
If B = 10 cm–1 & w = 103 cm–1
3
1
3
3 1
2 6
3
10 10
10
10
10
cm
D cm
So D << B
i.e. D is much smaller than B. For small values of J, the correction term is equation
(1.9) is negligibly small. For higher values of J, say 10 or more the value of D may be
appreciable. The selection rule 1
J
is of course still valid. The spectral line given by the
equation
2
2 1
1 1
BJ J DJ J cm
2
2 1
1 1
J J
B J DJ J cm
11. 11
Rotational Spectra (Microwave Spectroscopy)
If D is neglected, the spectral lines occur at interval of 2B.
0
1
2
3
4
5
6
7
Rigid rotator Non-rigid-rotator
8
J
Fig. 1.3 (a)
0 2B 4B 6B 8B 10B 12B 14B 16B
Rigid rotor
Non-rigid rotor
0 2B´ 4B´ 6B´ 8B´ 10B´ 12B´ 14B´ 16B´
Fig. 1.3(b)
Fig. 1.3 (a) rotational energy levels and 1.3 (b) allowed spectral lines for rigid and
non-rigid rotors.
For the an harmonic oscillator the expression (1.9) should be modified as
2 3 4
2 3 4 1
1 1 1 1
J BJ J DJ J HJ J KJ J cm
...(1.10)
where the constants H, K etc, are dependent on the molecule. These
constants H, K etc. are very small compared to D and hence can be neglected.
The value of D is also given by
3 2 2 3
2
16 4
B c B
D
K w
12. 12
Rotational Spectra (Microwave Spectroscopy)
The spectral line J
v is given by the equation
3 1
1 2 1 4 1
J J J
E E v B J D J cm
...(1.11)
If D is neglected, the spectral lines occur at intervals of 2B. The rotational spectrum of
a diatomic molecule such as HF, CO etc. can be fitted to the equation (1.11).
Information from D
1. Determination of J value
2. Determination of vibrational frequency
3
2
2
2
4
4
B
D
w
B
w
D
In HF B = 41.122 cm–1
3 1
8.52 10
D cm
3
3 2
2 1 6 1
3 1
4 41.122
16.33 10
8.52 10
w cm cm
cm
3 1 1
4.050 10 4050
w cm cm
The accurate value is 4138.3 cm–1. The 2% inaccuracy in the present calculation is due
partly to the assumption of simple harmonic motion and partly to the very small and hence
relatively inaccurate, value of D.
The force constant follow directly
2 2 2 1
4 960
K c w Nm
which indicates, as expected, the H-F is a relatively strong bond.
1.7 LINEAR POLYATOMIC MOLECULES
Linear polyatomic molecules can be treated like diatomic molecules. The rotational
energy, J
E in this case is given by
1
J
E Bhc J J
The transition from one rotational state to other in rotational spectra is governed by
1. Bohr quantum condition, E hv or hcv
13. 13
Rotational Spectra (Microwave Spectroscopy)
2. Molecule must have a permanent dipole moment
3. 1
J
Thus, the rotational spectra of a linear polyatomic molecule will consist of a set of
nearly equally spaced lines from which the rotational constant, B is determined. This value
of B can be used to determine I and r in the molecule for a molecule. For a molecule with n
atom, there are (n – 1) unknown inter nuclear distance to be determines. Thus for a triatomic
molecule (OCS, HC CCl etc.) there are two bond distance to be determined. But only
one moment of inertia for the end-over-end rotation can be obtained from the spectrum. It
is impossible to obtain two unknown from one equation. This difficulty is overcome by
obtaining the rotational spectra from (n – 1) different isotopic species for n- atom molecule
to derive (n –1) different moments of inertia. The internuclear distance for the isotopic
molecules are assumed to be the same. Consider linear unsymmetrical triatomic molecule
such as OCS and HCN.
Example OCS
Let us consider the rotation of OCS molecule r0, rc and rs represent the atoms from the
centre of gravity
0
–
co c
s cs c
r r r
r r r
consideration of moments gives
0 0 c c s s
m r m r m r
0
0 0
0 0
0 0
0
co c c c s cs c
co c c c s cs s c
c c c s c s cs co
c s c s cs co
c s cs co
m r r m r m r r
m r m r m r m r m r
m r m r m r m r m r
m m m r m c m r
Mr m r m r
14. 14
Rotational Spectra (Microwave Spectroscopy)
where M is the total mass of the molecule
0 c s
M m m m
0
s cs co
c
m r m r
r
M
...(1.12)
The moment of inertia of the molecule about an axis passing through centre of mass
will be given by
2 2 2
0 0 c c s s
I m r m r m r
2 2
2
0 co c c c s cs c
m r r m r m r r
2 2 2 2 2
0 0 0
2 2
co c co c c c s cs s c s cs c
m r m r m r r m r m r m r m r r
2 2 2
0 0 0
2
c s c co s cs c co s cs
m m m r m r m r r m r m r
2 2 2
0 0
2
c co s cs c co s cs
Mr m r m r r m r m r
2
2 2 0
0 0
2 s cs co
co s cs c co s cs
m r m r
m r m r r m r m r M
M
[from (1.12)]
2
0 0
2 2
0 0
2 s cs co s cs co
co s cs co s cs
m r m r m r m r
m r m r m r m r
M M
0
2 2
0 0 0
2
s cs co
co s cs co s cs s cs co
m r m r
m r m r m r m r m r m r
M
2 2 0
0 0
s cs co
co s cs co s cs
m r m r
m r m r m r m r
M
2 2
0
o co s cs
co s cs o co s cs
m r m r
m r m r m r m r
M
2
2 2
0
o co s cs
co s cs
m r m r
m r m r
M
...(1.13)
In order to obtain another equation of the type (1.13), use of isotopes is
made and an assumption that the internuclear bond distance do not change in
isotopic substitution is also required.
15. 15
Rotational Spectra (Microwave Spectroscopy)
2
0
2 2
0
´ co s cs
co s cs
m r m r
I m r m r
M
[Note : we don’t write 1
co
r since we assume that the bond length is unaltered by isotopic
substance]
From isotopic substitution, two moments of inertia are obtained. These two moments
of inertia are used to calculate two bond lengths.
Question : State bond lengths for difference pairs of OCS.
Solution :Pairs are (i) 16 12 32 16 12 34
O C S and O C S
(ii) 16 12 32 16 13 32
O C S and O C S
(iii) 16 12 34 16 13 34
O C S and O C S
(iv) 16 12 34 18 12 32
O C S and O C S
Value of bond length are
(i) C — O 1.1647, C—S 1.5576 Å
(ii) C — O 1.1629, C—S 1.5591 Å
(iii) C — O 1.1625, C—S 1.5594 Å
(iv) C — O 1.1552, C—S 1.5653 Å
The discrepancies between various bond determinations are chiefly due to the neglect
of zero point vibration.
1.8 NON-LINEAR POLYATOMIC MOLECULES
Symmetric top molecules
The rotational spectra of symmetric top molecules are simple. This is
because the rotation of a symmetric top rotor about its unique principle axis has no effect
on its rotation about an axis perpendicular to this an vice-versa. So it is
possible to separate the rotation about the principal axis from the other rotations for a
symmetric top. Consider a prolate symmetric top (CH 3Cl) where B c A
I I I
& 0
A
I . The
C—Cl bond is its molecular symmetry axis. Consequently we need two quantum numbers
to describe he degree of rotation one for IA and the other for IB or IC.
For the rigid prolate symmetric top, the solution of Schrödinger equation give the
energy levels.
16. 16
Rotational Spectra (Microwave Spectroscopy)
1
2 2 2
2
2 2 2
1
8 8 8
J k
B A B
h h h
E J J K Joule
I I I
, 2 1
1
J K
J
E
BJ J A B k cm
hc
...(1.14)
For oblate
2
1 ,
J BJ J C B k k J
...(1.15)
So that (C—B) is positive
The rotational constant, A, B and C in cm–1 are
2 2 2
, ,
8 8 8
A B c
h h h
A B c
I c I c I C
...(1.16)
J = 0, 1, 2, 3 ......
k = 0, ±1, ±2, ±3 ... ± J
The quantum number J represents the total angular momentum of the molecule and
K represents the projection of the total angular momentum upon the molecular symmetry
axis. Note that the energy depends on K2, so that it is immaterial whether the top spins
clockwise or anticlockwise, the energy is the same for a given angular momentum. For all k
>0, therefore, the rotational energy levels are doubly degenerate. Selection rules (in the
absence of external fields) for the rotational spectra of symmetric top molecules are
(i) The molecule must have a permanent dipole moment directed. Symmetry top
molecules have their dipole moment directions among unique axis
(ii) The transition should obey 0, 1
J
and
0 0
K K
, 1
J
i.e. transitions
with 0
J
do not occur. Thus transitions between different k levels are not allowed. k
characteristics rotation about the unique axis. For a symmetric top, rotation about the
unique axis does not change dipole moment and hence cannot interact with radiation.
Transition are identical to diatomic molecules and the spacing is also 2B
1
J J
(from (1.14)
2 1
1
2 1
1
1 2
1
2 1 ....(4)
J
J
B J J A B k cm
BJ J A B k cm
E B J cm
.....1.17
17. 17
Rotational Spectra (Microwave Spectroscopy)
equation (1.17) shows that the spectrum is just the same as for a linear molecule and
that only one moment of inertia- that for a end-over-end end roation- can be measured.
Planar symmetrical molecules such as BCl3, SO3, C6H6 do not exhibit rotational spectra. In
symmetric top molecules bond lengths and bond angles can be determined using isotopic
substitution method.
1.9 ASYMMETRIC TOP MOLECULES
Since spherical tops show no microwave spectrum, the only other class of molecule of
interest here is the asymmetric top. These molecules, having three different moment of
inertia, also have much more complicated rotational energy levels and specta. No simple
general expression for J
and J
can be derived for them, and they are usually treated by
approximative methods much computation being required before agreement between
observed and calculated spectra is achieved. However, such methods have been very
successful for small molecules and much accurate bond length and bond angle data have
been derived.
1.10 STARK EFFECT
The splitting of molecular rotational energy levels in presence of external electric field
(E) is known as the stark effect. Stark effect was first observed in atomic spectra. The rotational
lines may be shifted as well as splitted. Consider a rotating linear molecule with angular
momentum perpendicular to the electric field, the field tends to twist the dipole and gives
a faster rotation when the dipole is oriented in the direction of the field and slower rotation
when it is opposite to the field. This minor difference between the dipoles pointing in two
directions causes the splitting of energy levels. If the dipole moment has a component along
the angular moment J, a first order stark effect is observed and if the dipole moment is
perpendicular to the angular momentum, a second order stark effect is seen. A first order
stark effect applies when the splitting of rotional level is directly proportional to the electric
field. Symmetric top molecule, which have the component of dipole moment along the
direction of the total rotational angular momentum, exhibit first order stark effect. In second
order stark effect the splitting of rotational level by an electric field E is proportional to E2
and there is no component of in the direction of J. This type of behaviour is exhibited by
linear molecule (CO, OCS, HCN etc.) where dipole moment ( ) is perpendicular to the
total angular momentum of the molecular rotation. The shift of rotional frequency v
, for
a linear gaseous molecule is given by,
2
,
v E
18. 18
Rotational Spectra (Microwave Spectroscopy)
1
0
2
J MJ
0
±1
±2
0
± 1
0
Splitting of rotational level of
molecule by Stark effect
J
E
M
By knowing E and measuring v
, the electric dipole moment ( ) can be calculated.
Since the magnitude of splitting is dependent on the molecular dipole moment, so stark
effect permits a direct method for its accurate determination. The dipole moment of the
molecule in a particular vibrational state could be measured rather than the average moment
of all the states. The splitting under an electric field also depend on the rotational quantum
number of the transition involved and it can be utilized to identify transitions. Stark effect
splits the degeneracy of the J level into (2 J + 1) levels and hence multiplet structure has
been observed for all the lines with J > 0 since the mesurements can be made on gas samples
at 10–3 torr, the measured dipole moment is accurate and not affected by molecular
interactions and solvents effect.
Some Solved Problems
Q.1. Calculate the principal moments of inertia, Ia, Ib, Ic for
(a) BF3 (b) C2H4 and (c) CH3Cl
Ans. (a) 10BF3 : B —F 1.295 Å FBF 120º each Ia = Ib = 47.790, IC = 95.580 amu
(Å)2
(b) C2H4 : C—H 1.09 Å, C = C 1.34 Å HCC, HCH each 120º
Ia = 3.591, Ib = 16.725, IC = 20.318 amu (Å)2
(c) CH3
3J Cl : C—H 1.093 Å, C—Cl 1.77Å, Bond angle all tetrahedral
Ia = 3.2105, Ib = IC = 37.633 amu (Å)2
19. 19
Rotational Spectra (Microwave Spectroscopy)
Q.2. Calculate rotational constant of (a) H2 and (b) HCl. The H—H and H—Cl bond length
is 136 pm.
Ans. (a) For H2 molecule, the moment of inertial I = r2
27 2
12
1.67 10
74.12 10
2
I m
= 48 2
4.587 10 kg m
Thus
34
2 2 48 2 10 1
6.626 10
8 8 4.587 10 3 10
h Js
B
Jc kg m cms
= 61cm–2
For HCl, I =r2 =
2
27 12 47 2
1 35.5
1.67 10 136 10 3.004 10
35.5 1
kg kg m
Hence =
34
2 47 2 10 1
6.626 10
8 3 10 3 10
Js
B
kg m cms
= 9.33 cm–1
Q.3. Calculate the moment of inertia for chloroacetylene HCCCl and also rotational
constant B, assuming r(C—H) = 1.10 Å, r (C C) = 1.20 Å and r (C—Cl) =1.60 Å.
Ans. Ia =0, Ib = Ic = 86.916 amu (Å)2
34
2 47 8
6.626 10 7 7
8 22 86.916 1.66034 10 3 10
Js
B
1 1
19.366 0.19366
B m cm
Model Questions
1. Distinguish between symmetric top (prolate and oblate), spherical top and asymmetic
top molecules.
2. To which symmetric top, the benzene (C6H6) molecule belongs.
3. Diatomic molecules such as CO, HF will show a rotational spectrum where as N2, O2,
H2 .... do not. Why! will the molecule 17O—16O show a rotational spectrum
4. Out line the effect of isotopic substitution on the rotational spectra of molecules.
5. What is stark effect! Out line the importance of stark effect studies in microwave
spectroscopy !
6. use 2 1 2 2
m r m r
derive
1
2
1 2
m r
r
m m
20. 20
Rotational Spectra (Microwave Spectroscopy)
7. Calculate the energy in term of v of the energy level corresponding to J = 7 [Hint BJ
(J + 1) = B × 7 (7 + 1) = 56 B]
8. What is the selection rule for a rigid diatomic molecule to show rotational spectrum?
9. Which of the following molecule will show rotational spectra?
O = C = O, HF, N2 [Hint HF]
10. If the rotational constant for H35Cl is 10.59 cm–1. What is the value of rotational constant
for 2D35Cl?
use mass of 35Cl = 58.06 × 10–27 kg
mass of 2D = 3.344 × 10–27 kg
mass of 1H = 1.673 × 10–27 kg [Ans : 5.446 cm–1]
References :
1. R.P. straughen, and S. Walker, spectroscopy Vol 1, II, and III, Chapman and Hall,
Londan 1976.
2. Michael Hollas, Modern spectroscopy, 3rd ed., John Wiley, New York, 1987.
3. M.D. Harmony, introduction to Molecular Energies and Spectra, Holt, Rinehart and
Winston, Inc, 1972.