Diatomic molecule

Last updated

A space-filling model of the diatomic molecule dinitrogen, N2 Dinitrogen-3D-vdW.png
A space-filling model of the diatomic molecule dinitrogen, N2

Diatomic molecules (from Greek di- 'two') are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen (H2) or oxygen (O2), then it is said to be homonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such as carbon monoxide (CO) or nitric oxide (NO), the molecule is said to be heteronuclear. The bond in a homonuclear diatomic molecule is non-polar.

Contents

A periodic table showing the elements that exist as homonuclear diatomic molecules under typical laboratory conditions. Diatomic molecules periodic table.svg
A periodic table showing the elements that exist as homonuclear diatomic molecules under typical laboratory conditions.

The only chemical elements that form stable homonuclear diatomic molecules at standard temperature and pressure (STP) (or typical laboratory conditions of 1 bar and 25 °C) are the gases hydrogen (H2), nitrogen (N2), oxygen (O2), fluorine (F2), and chlorine (Cl2). [1]

The noble gases (helium, neon, argon, krypton, xenon, and radon) are also gases at STP, but they are monatomic. The homonuclear diatomic gases and noble gases together are called "elemental gases" or "molecular gases", to distinguish them from other gases that are chemical compounds. [2]

At slightly elevated temperatures, the halogens bromine (Br2) and iodine (I2) also form diatomic gases. [3] All halogens have been observed as diatomic molecules, except for astatine and tennessine, which are uncertain.

Other elements form diatomic molecules when evaporated, but these diatomic species repolymerize when cooled. Heating ("cracking") elemental phosphorus gives diphosphorus (P2). Sulfur vapor is mostly disulfur (S2). Dilithium (Li2) and disodium (Na2) [4] are known in the gas phase. Ditungsten (W2) and dimolybdenum (Mo2) form with sextuple bonds in the gas phase. Dirubidium (Rb2) is diatomic.

Heteronuclear molecules

All other diatomic molecules are chemical compounds of two different elements. Many elements can combine to form heteronuclear diatomic molecules, depending on temperature and pressure.

Examples are gases carbon monoxide (CO), nitric oxide (NO), and hydrogen chloride (HCl).

Many 1:1 binary compounds are not normally considered diatomic because they are polymeric at room temperature, but they form diatomic molecules when evaporated, for example gaseous MgO, SiO, and many others.

Occurrence

Hundreds of diatomic molecules have been identified [5] in the environment of the Earth, in the laboratory, and in interstellar space. About 99% of the Earth's atmosphere is composed of two species of diatomic molecules: nitrogen (78%) and oxygen (21%). The natural abundance of hydrogen (H2) in the Earth's atmosphere is only of the order of parts per million, but H2 is the most abundant diatomic molecule in the universe. The interstellar medium is dominated by hydrogen atoms.

Molecular geometry

All diatomic molecules are linear and characterized by a single parameter which is the bond length or distance between the two atoms. Diatomic nitrogen has a triple bond, diatomic oxygen has a double bond, and diatomic hydrogen, fluorine, chlorine, iodine, and bromine all have single bonds. [6]

Historical significance

Diatomic elements played an important role in the elucidation of the concepts of element, atom, and molecule in the 19th century, because some of the most common elements, such as hydrogen, oxygen, and nitrogen, occur as diatomic molecules. John Dalton's original atomic hypothesis assumed that all elements were monatomic and that the atoms in compounds would normally have the simplest atomic ratios with respect to one another. For example, Dalton assumed water's formula to be HO, giving the atomic weight of oxygen as eight times that of hydrogen, [7] instead of the modern value of about 16. As a consequence, confusion existed regarding atomic weights and molecular formulas for about half a century.

As early as 1805, Gay-Lussac and von Humboldt showed that water is formed of two volumes of hydrogen and one volume of oxygen, and by 1811 Amedeo Avogadro had arrived at the correct interpretation of water's composition, based on what is now called Avogadro's law and the assumption of diatomic elemental molecules. However, these results were mostly ignored until 1860, partly due to the belief that atoms of one element would have no chemical affinity toward atoms of the same element, and also partly due to apparent exceptions to Avogadro's law that were not explained until later in terms of dissociating molecules.

At the 1860 Karlsruhe Congress on atomic weights, Cannizzaro resurrected Avogadro's ideas and used them to produce a consistent table of atomic weights, which mostly agree with modern values. These weights were an important prerequisite for the discovery of the periodic law by Dmitri Mendeleev and Lothar Meyer. [8]

Excited electronic states

Diatomic molecules are normally in their lowest or ground state, which conventionally is also known as the state. When a gas of diatomic molecules is bombarded by energetic electrons, some of the molecules may be excited to higher electronic states, as occurs, for example, in the natural aurora; high-altitude nuclear explosions; and rocket-borne electron gun experiments. [9] Such excitation can also occur when the gas absorbs light or other electromagnetic radiation. The excited states are unstable and naturally relax back to the ground state. Over various short time scales after the excitation (typically a fraction of a second, or sometimes longer than a second if the excited state is metastable), transitions occur from higher to lower electronic states and ultimately to the ground state, and in each transition results a photon is emitted. This emission is known as fluorescence. Successively higher electronic states are conventionally named , , , etc. (but this convention is not always followed, and sometimes lower case letters and alphabetically out-of-sequence letters are used, as in the example given below). The excitation energy must be greater than or equal to the energy of the electronic state in order for the excitation to occur.

In quantum theory, an electronic state of a diatomic molecule is represented by the molecular term symbol

where is the total electronic spin quantum number, is the total electronic angular momentum quantum number along the internuclear axis, and is the vibrational quantum number. takes on values 0, 1, 2, ..., which are represented by the electronic state symbols , , ,.... For example, the following table lists the common electronic states (without vibrational quantum numbers) along with the energy of the lowest vibrational level () of diatomic nitrogen (N2), the most abundant gas in the Earth's atmosphere. [10]

The subscripts and superscripts after give additional quantum mechanical details about the electronic state. The superscript or determines whether reflection in a plane containing the internuclear axis introduces a sign change in the wavefunction. The sub-script or applies to molecules of identical atoms, and when reflecting the state along a plane perpendicualr to the molecular axis, states that does not change are labelled (gerade), and states that change sign are labelled (ungerade).

StateEnergy [lower-alpha 1] (, cm−1)
0.0
49754.8
59306.8
59380.2
65851.3
67739.3
68951.2
71698.4
  1. The "energy" units here are actually the reciprocal of the wavelength of a photon emitted in a transition to the lowest energy state. The actual energy can be found by multiplying the given statistic by the product of c (the speed of light) and h (Planck's constant); i.e., about 1.99 × 10−25 Joule-metres, and then multiplying by a further factor of 100 to convert from cm−1 to m−1.

The aforementioned fluorescence occurs in distinct regions of the electromagnetic spectrum, called "emission bands": each band corresponds to a particular transition from a higher electronic state and vibrational level to a lower electronic state and vibrational level (typically, many vibrational levels are involved in an excited gas of diatomic molecules). For example, N2- emission bands (a.k.a. Vegard-Kaplan bands) are present in the spectral range from 0.14 to 1.45 μm (micrometres). [9] A given band can be spread out over several nanometers in electromagnetic wavelength space, owing to the various transitions that occur in the molecule's rotational quantum number, . These are classified into distinct sub-band branches, depending on the change in . [11] The branch corresponds to , the branch to , and the branch to . Bands are spread out even further by the limited spectral resolution of the spectrometer that is used to measure the spectrum. The spectral resolution depends on the instrument's point spread function.

Energy levels

The molecular term symbol is a shorthand expression of the angular momenta that characterize the electronic quantum states of a diatomic molecule, which are also eigenstates of the electronic molecular Hamiltonian. It is also convenient, and common, to represent a diatomic molecule as two-point masses connected by a massless spring. The energies involved in the various motions of the molecule can then be broken down into three categories: the translational, rotational, and vibrational energies.

Concerning history, the first treatment of diatomic molecules with quantum mechanics was made by Lucy Mensing in 1926. [12]

Translational energies

The translational energy of the molecule is given by the kinetic energy expression:

where is the mass of the molecule and is its velocity.

Rotational energies

Classically, the kinetic energy of rotation is

where
is the angular momentum
is the moment of inertia of the molecule

For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by

where is a non-negative integer and is the reduced Planck constant.

Also, for a diatomic molecule the moment of inertia is

where
is the reduced mass of the molecule and
is the average distance between the centers of the two atoms in the molecule.

So, substituting the angular momentum and moment of inertia into Erot, the rotational energy levels of a diatomic molecule are given by:

Vibrational energies

Another type of motion of a diatomic molecule is for each atom to oscillate—or vibrate—along the line connecting the two atoms. The vibrational energy is approximately that of a quantum harmonic oscillator:

where
is an integer
is the reduced Planck constant and
is the angular frequency of the vibration.

Comparison between rotational and vibrational energy spacings

The spacing, and the energy of a typical spectroscopic transition, between vibrational energy levels is about 100 times greater than that of a typical transition between rotational energy levels.

Hund's cases

The good quantum numbers for a diatomic molecule, as well as good approximations of rotational energy levels, can be obtained by modeling the molecule using Hund's cases.

Mnemonics

The mnemonics BrINClHOF, pronounced "Brinklehof", [13] HONClBrIF, pronounced "Honkelbrif", [14] and HOFBrINCl, pronounced "Hofbrinkle", have been coined to aid recall of the list of diatomic elements. Another method, for English-speakers, is the sentence: "Never Have Fear of Ice Cold Beer" as a representation of Nitrogen, Hydrogen, Fluorine, Oxygen, Iodine, Chlorine, Bromine.

See also

Related Research Articles

<span class="mw-page-title-main">Bohr model</span> Atomic model introduced by Niels Bohr in 1913

In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity. It came after the solar system Joseph Larmor model (1897), the cubical model (1902), the Hantaro Nagaoka Saturnian model (1904), the plum pudding model (1904), the quantum Arthur Haas model (1910), the Rutherford model (1911), and the nuclear quantum John William Nicholson model (1912). The improvement over the 1911 Rutherford model mainly concerned the new quantum physical interpretation introduced by Haas and Nicholson, but forsaking any attempt to align with classical physics radiation.

<span class="mw-page-title-main">Covalent bond</span> Chemical bond that involves the sharing of electron pairs between atoms

A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than ionic bonding.

<span class="mw-page-title-main">Molecule</span> Electrically neutral group of two or more atoms

A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and molecule is often used when referring to polyatomic ions.

<span class="mw-page-title-main">Molecular orbital</span> Wave-like behavior of an electron in a molecule

In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.

<span class="mw-page-title-main">Energy level</span> Different states of quantum systems

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.

Chemisorption is a kind of adsorption which involves a chemical reaction between the surface and the adsorbate. New chemical bonds are generated at the adsorbent surface. Examples include macroscopic phenomena that can be very obvious, like corrosion, and subtler effects associated with heterogeneous catalysis, where the catalyst and reactants are in different phases. The strong interaction between the adsorbate and the substrate surface creates new types of electronic bonds.

Rotational–vibrational spectroscopy is a branch of molecular spectroscopy concerned with infrared and Raman spectra of molecules in the gas phase. Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational transitions. When such transitions emit or absorb photons, the frequency is proportional to the difference in energy levels and can be detected by certain kinds of spectroscopy. Since changes in rotational energy levels are typically much smaller than changes in vibrational energy levels, changes in rotational state are said to give fine structure to the vibrational spectrum. For a given vibrational transition, the same theoretical treatment as for pure rotational spectroscopy gives the rotational quantum numbers, energy levels, and selection rules. In linear and spherical top molecules, rotational lines are found as simple progressions at both higher and lower frequencies relative to the pure vibration frequency. In symmetric top molecules the transitions are classified as parallel when the dipole moment change is parallel to the principal axis of rotation, and perpendicular when the change is perpendicular to that axis. The ro-vibrational spectrum of the asymmetric rotor water is important because of the presence of water vapor in the atmosphere.

<span class="mw-page-title-main">Hyperfine structure</span> Small shifts and splittings in the energy levels of atoms, molecules and ions

In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucleus and electron clouds.

<span class="mw-page-title-main">Rotational spectroscopy</span> Spectroscopy of quantized rotational states of gases

Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The spectra of polar molecules can be measured in absorption or emission by microwave spectroscopy or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy. Rotational spectroscopy is sometimes referred to as pure rotational spectroscopy to distinguish it from rotational-vibrational spectroscopy where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy where rotational, vibrational and electronic energy changes occur simultaneously.

In quantum mechanics, a rotational transition is an abrupt change in angular momentum. Like all other properties of a quantum particle, angular momentum is quantized, meaning it can only equal certain discrete values, which correspond to different rotational energy states. When a particle loses angular momentum, it is said to have transitioned to a lower rotational energy state. Likewise, when a particle gains angular momentum, a positive rotational transition is said to have occurred.

In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in atomic nuclei, and so on. The selection rules may differ according to the technique used to observe the transition. The selection rule also plays a role in chemical reactions, where some are formally spin-forbidden reactions, that is, reactions where the spin state changes at least once from reactants to products.

The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of a sample of the substance divided by the amount of substance of the sample; or also the specific heat capacity of the substance times its molar mass. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1.

In molecular physics, the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule, i.e. its electronic quantum state which is an eigenstate of the electronic molecular Hamiltonian. It is the equivalent of the term symbol for the atomic case. However, the following presentation is restricted to the case of homonuclear diatomic molecules, or other symmetric molecules with an inversion centre. For heteronuclear diatomic molecules, the u/g symbol does not correspond to any exact symmetry of the electronic molecular Hamiltonian. In the case of less symmetric molecules the molecular term symbol contains the symbol of the group representation to which the molecular electronic state belongs.

In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation play a central role in computational chemistry and physics for computing properties of molecules and aggregates of molecules, such as thermal conductivity, specific heat, electrical conductivity, optical, and magnetic properties, and reactivity.

A molecular orbital diagram, or MO diagram, is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular. A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.

A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 1013 Hz to approximately 1014 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm−1 and wavelengths of approximately 30 to 3 µm.

The dihydrogen cation or hydrogen molecular ion is a cation with formula H+
2
. It consists of two hydrogen nuclei (protons) sharing a single electron. It is the simplest molecular ion.

Triatomic hydrogen or H3 is an unstable triatomic molecule containing only hydrogen. Since this molecule contains only three atoms of hydrogen it is the simplest triatomic molecule and it is relatively simple to numerically solve the quantum mechanics description of the particles. Being unstable the molecule breaks up in under a millionth of a second. Its fleeting lifetime makes it rare, but it is quite commonly formed and destroyed in the universe thanks to the commonness of the trihydrogen cation. The infrared spectrum of H3 due to vibration and rotation is very similar to that of the ion, H+
3
. In the early universe this ability to emit infrared light allowed the primordial hydrogen and helium gas to cool down so as to form stars.

In physics and chemistry, "monatomic" is a combination of the words "mono" and "atomic", and means "single atom". It is usually applied to gases: a monatomic gas is a gas in which atoms are not bound to each other. Examples at standard conditions of temperature and pressure include all the noble gases, though all chemical elements will be monatomic in the gas phase at sufficiently high temperature. The thermodynamic behavior of a monatomic gas is much simpler when compared to polyatomic gases because it is free of any rotational or vibrational energy.

Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in the application of Quantum Mechanics in physics and chemistry, for example it can be used to predict or explain many of a molecule's properties, such as its dipole moment and its allowed spectroscopic transitions, without doing the exact rigorous calculations. To do this it is necessary to classify the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule. Among all the molecular symmetries, diatomic molecules show some distinct features and they are relatively easier to analyze.

References

  1. Hammond, C.R. (2012). "Section 4: Properties of the Elements and Inorganic Compounds" (PDF). Handbook of Chemistry and Physics.[ permanent dead link ]
  2. Emsley, J. (1989). The Elements. Oxford: Clarendon Press. pp. 22–23.
  3. Whitten, Kenneth W.; Davis, Raymond E.; Peck, M. Larry; Stanley, George G. (2010). Chemistry (9th ed.). Brooks/Cole, Cengage Learning. pp. 337–338. ISBN   9780495391630.
  4. Lu, Z.W.; Wang, Q.; He, W.M.; Ma, Z.G. (July 1996). "New parametric emissions in diatomic sodium molecules". Applied Physics B. 63 (1): 43–46. Bibcode:1996ApPhB..63...43L. doi:10.1007/BF01112836. S2CID   120378643.
  5. Huber, K. P.; Herzberg, G. (1979). Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules. New York: Van Nostrand: Reinhold. ISBN   978-0-442-23394-5.
  6. Brown, Catrin; Ford, Mike (2014). Standard Level Chemistry (2nd ed.). Prentice Hall. pp. 123–125. ISBN   9781447959069.
  7. Langford, Cooper Harold; Beebe, Ralph Alonzo (1 January 1995). The Development of Chemical Principles. Courier Corporation. ISBN   9780486683591.
  8. Ihde, Aaron J. (1961). "The Karlsruhe Congress: A centennial retrospective". Journal of Chemical Education. 38 (2): 83–86. Bibcode:1961JChEd..38...83I. doi:10.1021/ed038p83. Archived from the original on 28 September 2007. Retrieved 24 August 2007.
  9. 1 2 Gilmore, Forrest R.; Laher, Russ R.; Espy, Patrick J. (1992). "Franck-Condon Factors, r-Centroids, Electronic Transition Moments, and Einstein Coefficients for Many Nitrogen and Oxygen Band Systems". Journal of Physical and Chemical Reference Data . 21 (5): 1005–1107. Bibcode:1992JPCRD..21.1005G. doi:10.1063/1.555910. Archived from the original on 9 July 2017.
  10. Laher, Russ R.; Gilmore, Forrest R. (1991). "Improved Fits for the Vibrational and Rotational Constants of Many States of Nitrogen and Oxygen". Journal of Physical and Chemical Reference Data . 20 (4): 685–712. Bibcode:1991JPCRD..20..685L. doi:10.1063/1.555892. Archived from the original on 2 June 2018.
  11. Levine, Ira N. (1975), Molecular Spectroscopy, John Wiley & Sons, pp. 508–9, ISBN   0-471-53128-6
  12. Mensing, Lucy (1 November 1926). "Die Rotations-Schwingungsbanden nach der Quantenmechanik". Zeitschrift für Physik (in German). 36 (11): 814–823. Bibcode:1926ZPhy...36..814M. doi:10.1007/BF01400216. ISSN   0044-3328. S2CID   123240532.
  13. "Mnemonic BrINClHOF (pronounced Brinklehoff) in Chemistry" . Retrieved 1 June 2019.
  14. Sherman, Alan (1992). Chemistry and Our Changing World. Prentice Hall. p. 82. ISBN   9780131315419.

Further reading