Skydive with us into the quantum world and find out how carbon dioxide molecules absorb thermal IR radiation.
“I call this Spirit, unknown hitherto, by the new name of Gas, which can neither be constrained by Vessels, nor reduced into a visible body, unless the feed being first extinguished.”
Jan Baptist van Helmont (1580–1644), Flemish philosopher and chemist who recognised the existence of discrete gases and identified carbon dioxide
The atmospheric gases (N2, O2, H2O, Ar, CO2, He etc.) are constantly bombarded by IR radiation, or photons, emitted from Earth’s surface in myriads, but only the greenhouse gases (H2O, CO2, CH4, N2O, O3, CFCs, HFCs) can absorb the IR photon energy. When a photon hits a greenhouse gas molecule, the photon’s energy is absorbed, causing it to vibrate. A molecule, however, cannot absorb any old photon; the photon must have certain wavelengths, or energies. Those with energies not within the narrow wavelengths correct for the molecule will just pass by and look for friendlier greenhouse gas molecules that are able to absorb their energies. If they do not meet any friendly molecule, then they disappear into space. CO2 is an important player in the global climate system and is under scrutiny in this part of our series. (View from Bjønnkjeften/Bear Mouth Mountain, Hamarøy, Norway. Photo: Eli Reisæter.)
Infrared (IR) Emission Spectrum of the Earth
In Part I of this series of articles on carbon dioxide (GEO ExPro Vol. 16, No. 2) we introduced you to electromagnetic radiation which can be described in terms of a stream of photons, being mass-less particles travelling in a wave-like pattern at the speed of light. The different types of radiation are defined by the amount of energy found in the photons. The energy E of a single photon is related to the frequency f and wavelength λ of the radiation by:
E = hf = hc/ λ [1]
where c is the speed of light and h is Planck’s constant. For the IR region, the wavenumber v = 1/λ is commonly used to measure energy. Since many wavelengths are stated in micrometres it is useful to know that hc = 1.24 eV · μm. The eV unit of energy means electron volt. Photon energy is larger at high frequencies or shorter wavelengths and lower at low frequencies or longer wavelengths.
Earth emits long-wave radiation with wavelengths 4–100 μm. Contributions with wavelengths larger than 40 μm are few, therefore often only wavelengths up to 50 μm are considered. The wavelength range 4–50 μm reads wavenumber range 2,500–200 cm-1.
This outgoing radiation is absorbed by various gases in the atmosphere. CO2 absorbs IR radiation in two narrow bands around wavelengths 4.26 and 15 μm (wavenumbers 2,349 and 667 cm-1) and in narrow bands around 2.7 and 2 μm.
A gas molecule absorbs radiation of a given wavelength only if the energy can be used to increase the internal energy level of the molecule. This internal energy level is quantised in a series of electronic, vibrational and rotational states. Electronic transitions, where the orbital states of the electrons change in the individual atom, generally require UV radiation (<0.4 μm). Vibrational transitions, where the individual atoms vibrate with respect to the combined molecular centre of mass, require near-IR radiation (0.7–20 μm), corresponding to the wavelength range of peak terrestrial radiation. Rotational transitions, where the molecule rotates around the centre of mass, require far-IR radiation (>20 μm). Little absorption takes place in the range of visible radiation (0.4–0.7 μm) which falls in the gap between electronic and vibrational transitions.
Photons act as individual quanta. A photon can interact with individual electrons, atoms, molecules and so on, depending on the energy the photon carries. From equation 1 it follows that the energies in the Earth’s thermal IR radiation are 0.0248–0.31 eV. When we compare those photon energies with the eV-energies required for allowed molecular transitions in the above table, it reveals that the photons of Earth’s IR radiation can mainly affect the vibrational energies of molecules in the atmosphere.
Infrared Spectroscopy of Gas Molecules
In the IR range there are plenty of photons. IR spectroscopy is the study of how molecules – groups of atoms that share electrons (chemical bonds) – absorb IR radiation and ultimately convert it to heat. Spectral lines are the result of interaction between a quantum system (in our case, molecules) and a single photon.
The helium hydride ion or helonium was first produced in the laboratory in 1925. Its occurrence in the interstellar medium has been conjectured since the 1970s and it was finally detected in April 2019 using the airborne SOFIA telescope. Helium hydride is believed to be the first molecule to have formed after the Big Bang, in which the only chemical elements created were hydrogen, helium and lithium, the three lightest atoms in the periodic table. Made of a combination of hydrogen and helium, astronomers think the molecule appeared more than 13 billion years ago and was the beginning step in the evolution of the universe. Carbon and oxygen resulted from the nuclear fusions taking place in the early massive, short-lived stars; when these died, they spread the elements of life, carbon and oxygen, throughout space. Carbon dioxide was recognised as a gas different from others early in the 17th century by van Helmont when he observed that the mass of charcoal declined in the process of burning. From that he concluded that the rest of the charcoal must have turned into an invisible substance that he called Gas (from the Greek word chaos) or ‘Spiritus Sylvestre’ (wild spirit). Source: NASA/ESA.
Most polyatomic molecules have vibrational transitions in an energy range corresponding to IR radiation in the wavelength region between 2.5–25 μm. At lower-atmospheric temperatures, the vibrational excitation is most often from the ground state to the first excited level. When ‘broad-band’ IR radiation passes through the atmospheric gas containing an infrared-active molecule, then the energy of wavelengths corresponding to the transitions will be absorbed and lost from the path of radiation. Thus, when the photon has the right amount of energy to allow a change in the energy state of the molecule, the photon is absorbed. Gases that absorb in the wavelength range 4–50 μm, where most terrestrial radiation is emitted, are called greenhouse gases.
Absorption spectra of various gases in the atmosphere and of the atmosphere as a whole. 98% of the radiative power from the Sun is emitted in the 0.25–4 μm range; 98% of the radiative power from Earth is emitted in the 5–80 μm range. Greenhouse warming is related to the fraction ‘x’ of radiation emitted by Earth’s surface that is prevented from escaping to space by the greenhouse gases. H2O is the main greenhouse gas responsible for blocking Earth’s IR radiation. CO2 is also seen to contribute with additional blocking around the 15 μm spectral range; it alone blocks around 20–21% of Earth’s radiation. The ‘blocked’ radiation must ultimately return to the surface. Observe that the absorption bands of H2O and CO2 overlap in part.
A selection rule from quantum mechanics is that vibrational transitions are allowed only if the change in vibrational state changes the dipole moment p of the molecule. Vibrational states represent different degrees of stretching or flexing of the molecule, and a photon incident on a molecule can modify this flexing or stretching only if the electric field has different effects on different ends of the molecule, that is if p ≠ 0. Most of the gases in the atmosphere, including the major gases N2 and O2 are homonuclear, symmetric molecules, and can therefore not absorb (or emit) IR radiation at all. All diatomic heteronuclear molecules (with just one vibration) are active in IR. Likewise, most polyatomic molecules in some of their vibrations are IR active.
Simplified vibrational energy levels for the electronic ground state of the CO2 molecule. A manifold of finely spaced rotational energy levels (not shown) is associated with each vibrational level. The excitation of the CO2 molecule is commonly characterised by a triplet of vibrational quantum numbers (νS, νB, νA) for symmetric stretching, bending and asymmetric stretching. The vibrational excitation energy for the bending mode, (νS, νB, νA)=(000) → (010), is 0.082eV, and correspondingly, for the asymmetric stretch mode (000) → (001), is 0.291eV.
In the following discussion we focus on CO2 as this gas plays a dominant role in global-warming research.
The CO2 Molecule’s Absorption Lines
In this section we describe how CO2 has absorption lines in the near-IR. The CO2 molecule has three atoms. It is a linear molecule with four vibrational modes, where the vibrations consist of coordinated motions of atoms in such a way as to keep the centre of mass stationary and non-rotating. These modes are called normal modes, where each can be described by a wavelength or wavenumber. The vibrational state is defined by a combination of the normal mode and by a quantised energy level within each mode. The modes are shown in the figure below.
The villain: CO2 has three vibrational modes, but the molecule can absorb radiation to access only two of them. Vibrations occur only where the dipole moment can change. This is a general selection rule from quantum mechanics: a change in molecular dipole moment must occur in the vibration for the transition to the vibrational level to be allowed. CO2 does not have a molecular dipole moment in its ground state. The symmetric stretch mode has no dipole moment and does not couple to IR radiation. Note that the bending mode of CO2 is doubly degenerate.
In the ‘symmetric stretch’ mode vibrations represent stretching of the chemical bonds in a symmetric fashion, in which both C=O bonds lengthen and contract together, in-phase. Since the distribution of charges is perfectly symmetric this mode has no dipole moment; transition to a higher energy level of that mode is forbidden. The symmetric stretch is not infrared active, and so this vibration is not observed in the IR spectrum of CO2. In the ‘asymmetric stretch’ mode the stretching of the chemical bonds differs, as one bond shortens while the other lengthens. The asymmetric stretch is infrared active because there is a change in the molecular dipole moment during this vibration. IR radiation at 2,349 cm-1 (4.26 μm) excites this particular vibration. The two bending mode vibrations in CO2 are degenerate (have equal energy); one mode is in the plane of the paper, and one is out of the plane (not shown). IR radiation at 667 cm-1 (15 μm) excites these vibrations.
CO2 Absorbtion in the Atmosphere
The figure on the right shows Earth’s blackbody spectrum for outgoing radiation flux and number of emitted photons as function of wavenumber for surface temperature 288K (15°C). The CO2 667 cm-1 centred absorption band (bluish, 540–800 cm-1) is positioned near the peak radiation wavelength for Earth’s temperature and is therefore very important for terrestrial radiative transfer in the atmosphere. It renders the atmosphere fully opaque around the centre wavenumbers while partly absorbing towards either side of these wavenumbers. The CO2 2,349 cm-1 centred absorption band (red, 2,100–2,400 cm-1) is located out on the edge of the thermal radiation band. The area under the top curve is proportional to the total outgoing flux. The effect of CO2 absorption is to take a bite out of Earth’s blackbody spectrum, thereby decreasing the outgoing energy flux to space.
Earth’s blackbody spectrum (white curve) for outgoing radiation flux (top) and number of emitted photons (bottom) as function of wavenumber for surface temperature 288K (15°C).
The number of emitted photons from Earth per second per square metre is computed by using Watt equals Joule per second, where 1J = 6.24 · 1018 eV. The number of photons per wavenumber is the flux energy divided by the photon energy (given by equation 1). In the lower figure the red area is around 0.5% of the bluish area; therefore, the 2,349 cm-1 centred band is only of moderate importance for CO2 photon absorption.
Can CO2 Molecules Ever Relax?
For CO2 we have seen that the bending mode vibration at 667 cm-1 dominantly absorbs Earth’s IR radiation as this band is positioned near the peak radiation wavelength for Earth’s temperature. Further, we have seen that IR radiation interacts with an IR-active molecule by a photon transferring its energy to the molecule. The photon is removed from the radiation field while the photon energy raises the molecule to a higher vibrational state. But excited states are energetically unfavourable; the molecule wants to return to the ground state by giving up energy. Keep reading GEO ExPro to learn about the life events that disrupt the usual activities of CO2 molecules, causing substantial changes and readjustments in their lives.
Acknowledgement
The authors have enjoyed many helpful discussions with Tore Karlsson.
Further Reading in the ‘Recent Advances in Climate Change Research’ Series
Recent Advances in Climate Change Research: Part I – Blackbody Radiation and Milankovic Cycles
Martin Landrø and Lasse Amundsen, NTNU / Bivrost Geo
Geoscience will probably play an important role in mitigating carbon dioxide emissions. In part one of this series, we discuss some history and physics behind the topic of climate change including the concepts behind blackbody radiation and Millankovic Cycles.
This article appeared in Vol. 16, No. 2 – 2019
Recent Advances in Climate Change Research: Part II – Arrhenius and Blackbody Radiation
Martin Landrø and Lasse Amundsen, NTNU / Bivrost Geo
In Part II we look at Arrhenius’ seminal 1896 paper and see how it relates to blackbody radiation and absorption of infrared radiation by the atmosphere, taking a closer look at his model of the greenhouse effect.
This article appeared in Vol. 16, No. 3 – 2019
Recent Advances in Climate Change Research: Part III – A Simple Greenhouse Model
Martin Landrø and Lasse Amundsen, NTNU/Bivrost Geo
What would the temperature of Earth be without the atmosphere? By using simple physical models for solar irradiation and the Stefan-Boltzmans law for blackbody radiation, we can estimate average temperatures with and without atmosphere.
This article appeared in Vol. 16, No. 4 – 2019
Recent Advances in Climate Change Research: Part IV – Challenges and Practical Issues of Carbon Capture & Storage
Martin Landrø, Lasse Amundsen and Philip Ringrose
The basic idea behind CCS (Carbon Capture and Storage) is simple, but what are the main challenges and practical issues preventing a more global adoption of this method?
This article appeared in Vol. 16, No. 5 – 2019
Recent Advances in Climate Change Research: Part V – Underground Storage of Carbon Dioxide
Eva K. Halland, Norwegian Petroleum Directorate. Series Editors: Martin Landrø and Lasse Amundsen, NTU/Bivrost Geo
By building on knowledge from the petroleum industry and experience of over 23 years of storing CO₂ in deep geological formations, we can make a new value chain and a business model for carbon capture and storage (CCS) in the North Sea Basin.
This article appeared in Vol. 16, No. 6 – 2019
Recent Advances in Climate Change Research: Part VI – More on the Simple Greenhouse Model
Lasse Amundsen and Martin Landrø, NTNU/Bivrost Geo
We continue the discussion of the simple greenhouse model introduced in Part III.
This article appeared in Vol. 17, No. 1 – 2020
Recent Advances in Climate Change Research: Part VII – Arrhenius’ Greenhouse Rule for Carbon Dioxide
Lasse Amundsen and Martin Landrø, NTNU/Bivrost Geo
Here, we investigate the relationship between radiative forcing (heat warming) of carbon dioxide and its concentration in the atmosphere to better understand climate feedback and sensitivity.
This article appeared in Vol. 17, No. 2 – 2020
