Enthalpy of vaporization
The enthalpy of vaporization known as the heat of vaporization or heat of evaporation, is the amount of energy that must be added to a liquid substance, to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure; the enthalpy of vaporization is quoted for the normal boiling temperature of the substance. The heat of vaporization is temperature-dependent, though a constant heat of vaporization can be assumed for small temperature ranges and for reduced temperature T r ≪ 1; the heat of vaporization diminishes with increasing temperature and it vanishes at a certain point called the critical temperature. Above the critical temperature, the liquid and vapor phases are indistinguishable, the substance is called a supercritical fluid. Values are quoted in J/mol or kJ/mol, although kJ/kg or J/g, older units like kcal/mol, cal/g and Btu/lb are sometimes still used, among others; the enthalpy of condensation is by definition equal to the enthalpy of vaporization with the opposite sign: enthalpy changes of vaporization are always positive, whereas enthalpy changes of condensation are always negative.
The enthalpy of vaporization can be written as Δ H v a p = Δ U v a p + p Δ V It is equal to the increased internal energy of the vapor phase compared with the liquid phase, plus the work done against ambient pressure. The increase in the internal energy can be viewed as the energy required to overcome the intermolecular interactions in the liquid. Hence helium has a low enthalpy of vaporization, 0.0845 kJ/mol, as the van der Waals forces between helium atoms are weak. On the other hand, the molecules in liquid water are held together by strong hydrogen bonds, its enthalpy of vaporization, 40.65 kJ/mol, is more than five times the energy required to heat the same quantity of water from 0 °C to 100 °C. Care must be taken, when using enthalpies of vaporization to measure the strength of intermolecular forces, as these forces may persist to an extent in the gas phase, so the calculated value of the bond strength will be too low; this is true of metals, which form covalently bonded molecules in the gas phase: in these cases, the enthalpy of atomization must be used to obtain a true value of the bond energy.
An alternative description is to view the enthalpy of condensation as the heat which must be released to the surroundings to compensate for the drop in entropy when a gas condenses to a liquid. As the liquid and gas are in equilibrium at the boiling point, ΔvG = 0, which leads to: Δ v S = S g a s − S l i q u i d = Δ v H / T b As neither entropy nor enthalpy vary with temperature, it is normal to use the tabulated standard values without any correction for the difference in temperature from 298 K. A correction must be made if the pressure is different from 100 kPa, as the entropy of a gas is proportional to its pressure: the entropies of liquids vary little with pressure, as the compressibility of a liquid is small; these two definitions are equivalent: the boiling point is the temperature at which the increased entropy of the gas phase overcomes the intermolecular forces. As a given quantity of matter always has a higher entropy in the gas phase than in a condensed phase, from Δ G = Δ H − T Δ S,the Gibbs free energy change falls with increasing temperature: gases are favored at higher temperatures, as is observed in practice.
Estimation of the enthalpy of vaporization of electrolyte solutions can be carried out using equations based on the chemical thermodynamic models, such as Pitzer model or TCPC model. The vaporization of metals is a key step in metal vapor synthesis, which exploits the increased reactivity of metal atoms or small particles relative to the bulk elements. Enthalpies of vaporization of common substances, measured at their respective standard boiling points: Enthalpy of fusion Enthalpy of sublimation Joback method CODATA Key Values for Thermodynamics Gmelin, Leopold. Gmelin-Handbuch der anorganischen Chemie / 08 a. Berlin: Springer. Pp. 116–117. ISBN 978-3-540-93516-2. NIST Chemistry WebBook Young, Francis W. Sears, Mark W. Zemansky, Hugh D.. University physics. Read
Ultraviolet–visible spectroscopy or ultraviolet–visible spectrophotometry refers to absorption spectroscopy or reflectance spectroscopy in part of the ultraviolet and the full, adjacent visible spectral regions. This means it uses light in the adjacent ranges; the absorption or reflectance in the visible range directly affects the perceived color of the chemicals involved. In this region of the electromagnetic spectrum and molecules undergo electronic transitions. Absorption spectroscopy is complementary to fluorescence spectroscopy, in that fluorescence deals with transitions from the excited state to the ground state, while absorption measures transitions from the ground state to the excited state. Molecules containing bonding and non-bonding electrons can absorb energy in the form of ultraviolet or visible light to excite these electrons to higher anti-bonding molecular orbitals; the more excited the electrons, the longer the wavelength of light it can absorb. There are four possible types of transitions, they can be ordered as follows: σ–σ* > n–σ* > π–π* > n–π*.
UV/Vis spectroscopy is used in analytical chemistry for the quantitative determination of different analytes, such as transition metal ions conjugated organic compounds, biological macromolecules. Spectroscopic analysis is carried out in solutions but solids and gases may be studied. Solutions of transition metal ions can be colored because d electrons within the metal atoms can be excited from one electronic state to another; the colour of metal ion solutions is affected by the presence of other species, such as certain anions or ligands. For instance, the colour of a dilute solution of copper sulfate is a light blue. Organic compounds those with a high degree of conjugation absorb light in the UV or visible regions of the electromagnetic spectrum; the solvents for these determinations are water for water-soluble compounds, or ethanol for organic-soluble compounds. Solvent polarity and pH can affect the absorption spectrum of an organic compound. Tyrosine, for example, increases in absorption maxima and molar extinction coefficient when pH increases from 6 to 13 or when solvent polarity decreases.
While charge transfer complexes give rise to colours, the colours are too intense to be used for quantitative measurement. The Beer–Lambert law states that the absorbance of a solution is directly proportional to the concentration of the absorbing species in the solution and the path length. Thus, for a fixed path length, UV/Vis spectroscopy can be used to determine the concentration of the absorber in a solution, it is necessary to know how the absorbance changes with concentration. This can be taken from references, or more determined from a calibration curve. A UV/Vis spectrophotometer may be used as a detector for HPLC; the presence of an analyte gives. For accurate results, the instrument's response to the analyte in the unknown should be compared with the response to a standard; the response for a particular concentration is known as the response factor. The wavelengths of absorption peaks can be correlated with the types of bonds in a given molecule and are valuable in determining the functional groups within a molecule.
The Woodward–Fieser rules, for instance, are a set of empirical observations used to predict λmax, the wavelength of the most intense UV/Vis absorption, for conjugated organic compounds such as dienes and ketones. The spectrum alone is not, however, a specific test for any given sample; the nature of the solvent, the pH of the solution, high electrolyte concentrations, the presence of interfering substances can influence the absorption spectrum. Experimental variations such as the slit width of the spectrophotometer will alter the spectrum. To apply UV/Vis spectroscopy to analysis, these variables must be controlled or accounted for in order to identify the substances present; the method is most used in a quantitative way to determine concentrations of an absorbing species in solution, using the Beer–Lambert law: A = log 10 = ε c L,where A is the measured absorbance, I 0 is the intensity of the incident light at a given wavelength, I is the transmitted intensity, L the path length through the sample, c the concentration of the absorbing species.
For each species and wavelength, ε is a constant known as the molar absorptivity or extinction coefficient. This constant is a fundamental molecular property in a given solvent, at a particular temperature and pressure, has units of 1 / M ∗ c m; the absorbance and extinction ε are sometimes defined in terms of the natural logarithm instead of the base-10 logarithm. The Beer–Lambert Law is useful for characterizing many compounds but does not hold as a universal relationship for the concentration and absorption of all s
Nuclear magnetic resonance spectroscopy
Nuclear magnetic resonance spectroscopy, most known as NMR spectroscopy or magnetic resonance spectroscopy, is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic field and the NMR signal is produced by excitation of the nuclei sample with radio waves into nuclear magnetic resonance, detected with sensitive radio receivers; the intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. As the fields are unique or characteristic to individual compounds, in modern organic chemistry practice, NMR spectroscopy is the definitive method to identify monomolecular organic compounds. Biochemists use NMR to identify proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about the structure, reaction state, chemical environment of molecules; the most common types of NMR are proton and carbon-13 NMR spectroscopy, but it is applicable to any kind of sample that contains nuclei possessing spin.
NMR spectra are unique, well-resolved, analytically tractable and highly predictable for small molecules. Different functional groups are distinguishable, identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has replaced traditional wet chemistry tests such as color reagents or typical chromatography for identification. A disadvantage is that a large amount, 2–50 mg, of a purified substance is required, although it may be recovered through a workup. Preferably, the sample should be dissolved in a solvent, because NMR analysis of solids requires a dedicated magic angle spinning machine and may not give well-resolved spectra; the timescale of NMR is long, thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. Although large amounts of impurities do show on an NMR spectrum, better methods exist for detecting impurities, as NMR is inherently not sensitive - though at higher frequencies, sensitivity is higher.
Correlation spectroscopy is a development of ordinary NMR. In two-dimensional NMR, the emission is centered around a single frequency, correlated resonances are observed; this allows identifying the neighboring substituents of the observed functional group, allowing unambiguous identification of the resonances. There are more complex 3D and 4D methods and a variety of methods designed to suppress or amplify particular types of resonances. In nuclear Overhauser effect spectroscopy, the relaxation of the resonances is observed; as NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows for construction of a three-dimensional model of the molecule. NMR spectrometers are expensive. Modern NMR spectrometers have a strong and expensive liquid helium-cooled superconducting magnet, because resolution directly depends on magnetic field strength. Less expensive machines using permanent magnets and lower resolution are available, which still give sufficient performance for certain application such as reaction monitoring and quick checking of samples.
There are benchtop nuclear magnetic resonance spectrometers. NMR can be observed than a millitesla. Low-resolution NMR produces broader peaks which can overlap one another causing issues in resolving complex structures; the use of higher strength magnetic fields result in clear resolution of the peaks and is the standard in industry. The Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared the 1952 Nobel Prize in Physics for their discoveries; when placed in a magnetic field, NMR active nuclei absorb electromagnetic radiation at a frequency characteristic of the isotope. The resonant frequency, energy of the radiation absorbed, the intensity of the signal are proportional to the strength of the magnetic field. For example, in a 21 Tesla magnetic field, hydrogen atoms resonate at 900 MHz, it is common to refer to a 21 T magnet as a 900 MHz magnet since hydrogen is the most common nucleus detected, however different nuclei will resonate at different frequencies at this field strength in proportion to their nuclear magnetic moments.
An NMR spectrometer consists of a spinning sample-holder inside a strong magnet, a radio-frequency emitter and a receiver with a probe that goes inside the magnet to surround the sample, optionally gradient coils for diffusion measurements, electronics to control the system. Spinning the sample is necessary to average out diffusional motion, however some experiments call for a stationary sample when solution movement is an important variable. For instance, measurements of diffusion constants are done using a stationary sample with spinning off, flow cells can be used for online analysis of process flows; the vast majority of molecules in a solution are solvent molecules, most regular solvents are hydrocarbons and so contain NMR-active protons. In order to avoid detecting only signals from solvent hydrogen atoms, deuterated solvents are used where 99+% of the protons are replaced with deuterium; the most used deuterated solvent is deuterochloroform, although other solvents may be used depending on the solubility of a sample.
Deuterium oxide and deuterated DMSO (DMSO-d
In molecular geometry, bond length or bond distance is the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types independent of the rest of the molecule. Bond length is related to bond order: when more electrons participate in bond formation the bond is shorter. Bond length is inversely related to bond strength and the bond dissociation energy: all other factors being equal, a stronger bond will be shorter. In a bond between two identical atoms, half the bond distance is equal to the covalent radius. Bond lengths are measured in the solid phase by means of X-ray diffraction, or approximated in the gas phase by microwave spectroscopy. A bond between a given pair of atoms may vary between different molecules. For example, the carbon to hydrogen bonds in methane are different from those in methyl chloride, it is however possible to make generalizations. A table with experimental single bonds for carbon to other elements is given below.
Bond lengths are given in picometers. By approximation the bond distance between two different atoms is the sum of the individual covalent radii; as a general trend, bond distances decrease across the row in the periodic table and increase down a group. This trend is identical to that of the atomic radius; the bond length between two atoms in a molecule depends not only on the atoms but on such factors as the orbital hybridization and the electronic and steric nature of the substituents. The carbon–carbon bond length in diamond is 154 pm, the largest bond length that exists for ordinary carbon covalent bonds. Since one atomic unit of length is 52.9177 pm, the C–C bond length is 2.91 atomic units, or three Bohr radii long. Unusually long bond lengths do exist. In one compound, tricyclobutabenzene, a bond length of 160 pm is reported; the current record holder is another cyclobutabenzene with length 174 pm based on X-ray crystallography. In this type of compound the cyclobutane ring would force 90° angles on the carbon atoms connected to the benzene ring where they ordinarily have angles of 120°.
The existence of a long C–C bond length of up to 290 pm is claimed in a dimer of two tetracyanoethylene dianions, although this concerns a 2-electron-4-center bond. This type of bonding has been observed in neutral phenalenyl dimers; the bond lengths of these so-called "pancake bonds" are up to 305 pm. Shorter than average C–C bond distances are possible: alkenes and alkynes have bond lengths of 133 and 120 pm due to increased s-character of the sigma bond. In benzene all bonds have the same length: 139 pm. Carbon–carbon single bonds increased s-character is notable in the central bond of diacetylene and that of a certain tetrahedrane dimer. In propionitrile the cyano group withdraws electrons resulting in a reduced bond length. Squeezing a C–C bond is possible by application of strain. An unusual organic compound exists called In-methylcyclophane with a short bond distance of 147 pm for the methyl group being squeezed between a triptycene and a phenyl group. In an in silico experiment a bond distance of 136 pm was estimated for neopentane locked up in fullerene.
The smallest theoretical C–C single bond obtained in this study is 131 pm for a hypothetical tetrahedrane derivative. The same study estimated that stretching or squeezing the C–C bond in an ethane molecule by 5 pm required 2.8 or 3.5 kJ/mol, respectively. Stretching or squeezing the same bond by 15 pm required an estimated 21.9 or 37.7 kJ/mol. Bond length tutorial
Mass spectrometry is an analytical technique that ionizes chemical species and sorts the ions based on their mass-to-charge ratio. In simpler terms, a mass spectrum measures the masses within a sample. Mass spectrometry is used in many different fields and is applied to pure samples as well as complex mixtures. A mass spectrum is a plot of the ion signal as a function of the mass-to-charge ratio; these spectra are used to determine the elemental or isotopic signature of a sample, the masses of particles and of molecules, to elucidate the chemical structures of molecules and other chemical compounds. In a typical MS procedure, a sample, which may be solid, liquid, or gas, is ionized, for example by bombarding it with electrons; this may cause some of the sample's molecules to break into charged fragments. These ions are separated according to their mass-to-charge ratio by accelerating them and subjecting them to an electric or magnetic field: ions of the same mass-to-charge ratio will undergo the same amount of deflection.
The ions are detected by a mechanism capable of detecting charged particles, such as an electron multiplier. Results are displayed as spectra of the relative abundance of detected ions as a function of the mass-to-charge ratio; the atoms or molecules in the sample can be identified by correlating known masses to the identified masses or through a characteristic fragmentation pattern. In 1886, Eugen Goldstein observed rays in gas discharges under low pressure that traveled away from the anode and through channels in a perforated cathode, opposite to the direction of negatively charged cathode rays. Goldstein called these positively charged anode rays "Kanalstrahlen". Wilhelm Wien found that strong electric or magnetic fields deflected the canal rays and, in 1899, constructed a device with perpendicular electric and magnetic fields that separated the positive rays according to their charge-to-mass ratio. Wien found. English scientist J. J. Thomson improved on the work of Wien by reducing the pressure to create the mass spectrograph.
The word spectrograph had become part of the international scientific vocabulary by 1884. Early spectrometry devices that measured the mass-to-charge ratio of ions were called mass spectrographs which consisted of instruments that recorded a spectrum of mass values on a photographic plate. A mass spectroscope is similar to a mass spectrograph except that the beam of ions is directed onto a phosphor screen. A mass spectroscope configuration was used in early instruments when it was desired that the effects of adjustments be observed. Once the instrument was properly adjusted, a photographic plate was exposed; the term mass spectroscope continued to be used though the direct illumination of a phosphor screen was replaced by indirect measurements with an oscilloscope. The use of the term mass spectroscopy is now discouraged due to the possibility of confusion with light spectroscopy. Mass spectrometry is abbreviated as mass-spec or as MS. Modern techniques of mass spectrometry were devised by Arthur Jeffrey Dempster and F.
W. Aston in 1918 and 1919 respectively. Sector mass spectrometers known as calutrons were developed by Ernest O. Lawrence and used for separating the isotopes of uranium during the Manhattan Project. Calutron mass spectrometers were used for uranium enrichment at the Oak Ridge, Tennessee Y-12 plant established during World War II. In 1989, half of the Nobel Prize in Physics was awarded to Hans Dehmelt and Wolfgang Paul for the development of the ion trap technique in the 1950s and 1960s. In 2002, the Nobel Prize in Chemistry was awarded to John Bennett Fenn for the development of electrospray ionization and Koichi Tanaka for the development of soft laser desorption and their application to the ionization of biological macromolecules proteins. A mass spectrometer consists of three components: an ion source, a mass analyzer, a detector; the ionizer converts a portion of the sample into ions. There is a wide variety of ionization techniques, depending on the phase of the sample and the efficiency of various ionization mechanisms for the unknown species.
An extraction system removes ions from the sample, which are targeted through the mass analyzer and into the detector. The differences in masses of the fragments allows the mass analyzer to sort the ions by their mass-to-charge ratio; the detector measures the value of an indicator quantity and thus provides data for calculating the abundances of each ion present. Some detectors give spatial information, e.g. a multichannel plate. The following example describes the operation of a spectrometer mass analyzer, of the sector type. Consider a sample of sodium chloride. In the ion source, the sample is ionized into sodium and chloride ions. Sodium atoms and ions are monoisotopic, with a mass of about 23 u. Chloride atoms and ions come in two isotopes with masses of 35 u and 37 u; the analyzer part of the spectrometer contains electric and magnetic fields, which exert forces on ions traveling through these fields. The speed of a charged particle may be increased or decreased while passing through the electric field, its direction may be altered by the magnetic field.
The magnitude of the deflection of the moving ion's trajectory depends on its mass-to-charge ratio. L
Infrared radiation, sometimes called infrared light, is electromagnetic radiation with longer wavelengths than those of visible light, is therefore invisible to the human eye, although IR at wavelengths up to 1050 nanometers s from specially pulsed lasers can be seen by humans under certain conditions. IR wavelengths extend from the nominal red edge of the visible spectrum at 700 nanometers, to 1 millimeter. Most of the thermal radiation emitted by objects near room temperature is infrared; as with all EMR, IR carries radiant energy and behaves both like a wave and like its quantum particle, the photon. Infrared radiation was discovered in 1800 by astronomer Sir William Herschel, who discovered a type of invisible radiation in the spectrum lower in energy than red light, by means of its effect on a thermometer. More than half of the total energy from the Sun was found to arrive on Earth in the form of infrared; the balance between absorbed and emitted infrared radiation has a critical effect on Earth's climate.
Infrared radiation is emitted or absorbed by molecules when they change their rotational-vibrational movements. It excites vibrational modes in a molecule through a change in the dipole moment, making it a useful frequency range for study of these energy states for molecules of the proper symmetry. Infrared spectroscopy examines transmission of photons in the infrared range. Infrared radiation is used in industrial, military, law enforcement, medical applications. Night-vision devices using active near-infrared illumination allow people or animals to be observed without the observer being detected. Infrared astronomy uses sensor-equipped telescopes to penetrate dusty regions of space such as molecular clouds, detect objects such as planets, to view red-shifted objects from the early days of the universe. Infrared thermal-imaging cameras are used to detect heat loss in insulated systems, to observe changing blood flow in the skin, to detect overheating of electrical apparatus. Extensive uses for military and civilian applications include target acquisition, night vision and tracking.
Humans at normal body temperature radiate chiefly at wavelengths around 10 μm. Non-military uses include thermal efficiency analysis, environmental monitoring, industrial facility inspections, detection of grow-ops, remote temperature sensing, short-range wireless communication and weather forecasting. Infrared radiation extends from the nominal red edge of the visible spectrum at 700 nanometers to 1 millimeter; this range of wavelengths corresponds to a frequency range of 430 THz down to 300 GHz. Below infrared is the microwave portion of the electromagnetic spectrum. Sunlight, at an effective temperature of 5,780 kelvins, is composed of near-thermal-spectrum radiation, more than half infrared. At zenith, sunlight provides an irradiance of just over 1 kilowatt per square meter at sea level. Of this energy, 527 watts is infrared radiation, 445 watts is visible light, 32 watts is ultraviolet radiation. Nearly all the infrared radiation in sunlight is shorter than 4 micrometers. On the surface of Earth, at far lower temperatures than the surface of the Sun, some thermal radiation consists of infrared in the mid-infrared region, much longer than in sunlight.
However, black body or thermal radiation is continuous: it gives off radiation at all wavelengths. Of these natural thermal radiation processes, only lightning and natural fires are hot enough to produce much visible energy, fires produce far more infrared than visible-light energy. In general, objects emit infrared radiation across a spectrum of wavelengths, but sometimes only a limited region of the spectrum is of interest because sensors collect radiation only within a specific bandwidth. Thermal infrared radiation has a maximum emission wavelength, inversely proportional to the absolute temperature of object, in accordance with Wien's displacement law. Therefore, the infrared band is subdivided into smaller sections. A used sub-division scheme is: NIR and SWIR is sometimes called "reflected infrared", whereas MWIR and LWIR is sometimes referred to as "thermal infrared". Due to the nature of the blackbody radiation curves, typical "hot" objects, such as exhaust pipes appear brighter in the MW compared to the same object viewed in the LW.
The International Commission on Illumination recommended the division of infrared radiation into the following three bands: ISO 20473 specifies the following scheme: Astronomers divide the infrared spectrum as follows: These divisions are not precise and can vary depending on the publication. The three regions are used for observation of different temperature ranges, hence different environments in space; the most common photometric system used in astronomy allocates capital letters to different spectral regions according to filters used. These letters are understood in reference to atmospheric windows and appear, for instance, in the titles of many papers. A third scheme divides up the band based on the response of various detectors: Near-infrared: from 0.7 to 1.0 µm. Short-wave infrared: 1.0 to 3 µm. InGaAs covers to about 1.8 µm. Mid-wave infrared: 3 to 5 µm (defined by the atmospheric window and covered by indium antimonide and mercury cadmium telluride and by lead
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determine the position of each atom. Molecular geometry influences several properties of a substance including its reactivity, phase of matter, color and biological activity; the angles between bonds that an atom forms depend only weakly on the rest of molecule, i.e. they can be understood as local and hence transferable properties. The molecular geometry can be determined by diffraction methods. IR, microwave and Raman spectroscopy can give information about the molecule geometry from the details of the vibrational and rotational absorbance detected by these techniques. X-ray crystallography, neutron diffraction and electron diffraction can give molecular structure for crystalline solids based on the distance between nuclei and concentration of electron density.
Gas electron diffraction can be used for small molecules in the gas phase. NMR and FRET methods can be used to determine complementary information including relative distances, dihedral angles and connectivity. Molecular geometries are best determined at low temperature because at higher temperatures the molecular structure is averaged over more accessible geometries. Larger molecules exist in multiple stable geometries that are close in energy on the potential energy surface. Geometries can be computed by ab initio quantum chemistry methods to high accuracy; the molecular geometry can be different as a solid, in solution, as a gas. The position of each atom is determined by the nature of the chemical bonds by which it is connected to its neighboring atoms; the molecular geometry can be described by the positions of these atoms in space, evoking bond lengths of two joined atoms, bond angles of three connected atoms, torsion angles of three consecutive bonds. Since the motions of the atoms in a molecule are determined by quantum mechanics, one must define "motion" in a quantum mechanical way.
The overall quantum mechanical motions translation and rotation hardly change the geometry of the molecule. In addition to translation and rotation, a third type of motion is molecular vibration, which corresponds to internal motions of the atoms such as bond stretching and bond angle variation; the molecular vibrations are harmonic, the atoms oscillate about their equilibrium positions at the absolute zero of temperature. At absolute zero all atoms are in their vibrational ground state and show zero point quantum mechanical motion, so that the wavefunction of a single vibrational mode is not a sharp peak, but an exponential of finite width. At higher temperatures the vibrational modes may be thermally excited, but they oscillate still around the recognizable geometry of the molecule. To get a feeling for the probability that the vibration of molecule may be thermally excited, we inspect the Boltzmann factor β ≡ exp , where Δ E is the excitation energy of the vibrational mode, k the Boltzmann constant and T the absolute temperature.
At 298 K, typical values for the Boltzmann factor β are: β = 0.089 for ΔE = 500 cm−1. When an excitation energy is 500 cm−1 about 8.9 percent of the molecules are thermally excited at room temperature. To put this in perspective: the lowest excitation vibrational energy in water is the bending mode. Thus, at room temperature less than 0.07 percent of all the molecules of a given amount of water will vibrate faster than at absolute zero. As stated above, rotation hardly influences the molecular geometry. But, as a quantum mechanical motion, it is thermally excited at low temperatures. From a classical point of view it can be stated that at higher temperatures more molecules will rotate faster, which implies that they have higher angular velocity and angular momentum. In quantum mechanical language: more eigenstates of higher angular momentum become thermally populated with rising temperatures. Typical rotational excitation energies are on the order of a few cm−1; the results of many spectroscopic experiments are broadened because they involve an averaging over rotational states.
It is difficult to extract geometries from spectra at high temperatures, because the number of rotational states probed in the experimental averaging increases with increasing temperature. Thus, many spectroscopic observations can only be expected to yield reliable molecular geometries at temperatures close to absolute zero, because at higher temperatures too many higher rotational states are thermally populated. Molecules, by definition, are most held together with covalent bonds involving single, and/or triple bonds, where a "bond