Hausdorff moment problem

2013-07-16T13:43:53Z

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{{dablink|This article is about molecular photodissociation. The term "photodissociation" may also refer to nuclear photodissociation.}}

'''Photodissociation''', '''photolysis''', or '''photodecomposition''' is a [[chemical reaction]] in which a [[chemical compound]] is broken down by [[photon]]s. It is defined as the interaction of one or more photons with one target molecule.

Photodissociation is not limited to [[visible light]]. Any photon with sufficient [[energy]] can affect the chemical bonds of a chemical compound. Since a photon's energy is inversely proportional to its wavelength, [[electromagnetic wave]]s with the energy of visible light or higher, such as [[ultraviolet light]], [[x-ray]]s and [[gamma ray]]s are usually involved in such reactions.

==Photolysis in photosynthesis==
Photolysis is part of the [[light-dependent reaction]]s of [[photosynthesis]]. The general reaction of photosynthetic photolysis can be given as

H2A + 2 photons (light) → 2 e- + 2 H+ + A

The chemical nature of "A" depends on the type of organism. In [[purple sulfur bacteria]], [[hydrogen sulfide]] (H2S) is oxidized to sulfur (S). In oxygenic photosynthesis, water (H2O) serves as a substrate for photolysis resulting in the generation of [[dioxygen|diatomic oxygen]] (O2). This is the process which returns oxygen to earth's atmosphere. Photolysis of water occurs in the [[thylakoid]]s of [[cyanobacterium|cyanobacteria]] and the [[chloroplast]]s of [[green algae]] and [[plant]]s.

=== Energy transfer models ===
The conventional, [[First quantization|semi-classical]], model describes the photosynthetic energy transfer process as one in which excitation energy hops from light-capturing pigment molecules to reaction center molecules step-by-step down the molecular energy ladder.

The effectiveness of photons of different wavelengths depends on the absorption spectra of the [[photosynthetic pigment]]s in the organism. [[Chlorophyll]]s absorb light in the violet-blue and red parts of the spectrum, while [[accessory pigment]]s capture other wavelengths as well. The [[phycobilin]]s of red algae absorb blue-green light which penetrates deeper into water than red light, enabling them to photosynthesize in deep waters. Each absorbed photon causes the formation of an [[exciton]] (an electron excited to a higher energy state) in the pigment molecule. The energy of the exciton is transferred to a [[chlorophyll]] molecule ([[P680]], where P stands for pigment and 680 for its absorption maximum at 680 nm) in the reaction center of [[photosystem II]] via [[resonance energy transfer]]. P680 can also directly absorb a photon at a suitable wavelength.

Photolysis during photosynthesis occurs in a series of light-driven [[Redox|oxidation]] events. The energized electron (exciton) of P680 is captured by a primary electron acceptor of the photosynthetic [[electron transfer chain]] and thus exits photosystem II. In order to repeat the reaction, the electron in the reaction center needs to be replenished. This occurs by oxidation of water in the case of oxygenic photosynthesis. The electron-deficient reaction center of photosystem II (P680*) is the strongest biological oxidizing agent yet discovered, which allows it to break apart molecules as stable as water.<ref name="Campbell">{{cite book | last = [[Neil Campbell (scientist)|Campbell]]| first = Neil A. | coauthors = Reece, Jane B. | title = Biology, 7th Edition | publisher = Pearson - Benjamin Cummings | year = 2005 | location = San Francisco | pages = 186–191 | isbn = 0-8053-7171-0}}</ref>

The water-splitting reaction is catalyzed by the [[oxygen evolving complex]] of photosystem II. This protein-bound inorganic complex contains four manganese ions, plus calcium and chloride ions as cofactors. Two water molecules are complexed by the manganese cluster, which then undergoes a series of four electron removals (oxidations) to replenish the reaction center of photosystem II. At the end of this cycle, free oxygen (O2) is generated and the hydrogen of the water molecules has been converted to four protons released into the thylakoid lumen.

These protons, as well as additional protons pumped across the thylakoid membrane coupled with the electron transfer chain, form a [[proton gradient]] across the membrane that drives [[photophosphorylation]] and thus the generation of chemical energy in the form of [[adenosine triphosphate]] (ATP). The electrons reach the [[P700]] reaction center of [[photosystem I]] where they are energized again by light. They are passed down another electron transfer chain and finally combine with the [[coenzyme]] NADP+ and protons outside the thylakoids to [[NADPH]]. Thus, the net oxidation reaction of water photolysis can be written as:

2 H2O + 2 NADP+ + 8 photons (light) → 2 NADPH + 2 H+ + O2

The free energy change (ΔG) for this reaction is 102 kilocalories per mole. Since the energy of light at 700 nm is about 40 kilocalories per mole of photons, approximately 320 kilocalories of light energy are available for the reaction. Therefore, approximately one-third of the available light energy is captured as NADPH during photolysis and electron transfer. An equal amount of ATP is generated by the resulting proton gradient. Oxygen as a byproduct is of no further use to the reaction and thus released into the atmosphere.<ref name="Raven">{{cite book | last = Raven | first = Peter H. | coauthors = Ray F. Evert, Susan E. Eichhorn | title = Biology of Plants, 7th Edition | publisher = W.H. Freeman and Company Publishers | year = 2005 | location = New York | pages = 115–127 | isbn = 0-7167-1007-2}}</ref>

==== Quantum models ====

In 2007 a quantum model was proposed by [[Graham Fleming]] and his co-workers which includes the possibility that photosynthetic energy transfer might involve quantum oscillations, explaining its unusually high [[Photosynthetic efficiency|efficiency]].<ref name="QB">Gregory S. Engel, Tessa R. Calhoun, Elizabeth L. Read, Tae-Kyu Ahn, Tomáš Mančal, Yuan-Chung Cheng, Robert E. Blankenship and Graham R. Fleming, "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems", in [[Nature (journal)|Nature]] '''446''', 782-786 (12 April 2007)</ref>

According to Fleming<ref name="QBC">http://www.physorg.com/news95605211.html Quantum secrets of photosynthesis revealed</ref> there is direct evidence that remarkably long-lived wavelike electronic quantum coherence plays an important part in energy transfer processes during photosynthesis, which can explain the extreme efficiency of the energy transfer because it enables the system to sample all the potential energy pathways, with low loss, and choose the most efficient one.

This approach has been further investigated by Gregory Scholes and his team at the [[University of Toronto]], which in early 2010 published research results that indicate that some marine algae make use of [[quantum coherence|quantum-coherent]] electronic [[energy transfer]] (EET) to enhance the efficiency of their energy harnessing.<ref>[http://www.chem.utoronto.ca/staff/SCHOLES/scholes_home.html Scholes Group Research]</ref><ref>{{citation
|author = Gregory D. Scholes
|title = Quantum-coherent electronic energy transfer: Did Nature think of it first?
|journal = [[Journal of Physical Chemistry Letters]]
|volume = 1
|number = 1
|pages = 2–8
|date = 7 January 2010
|doi = 10.1021/jz900062f
}}</ref><ref>{{citation
|author1 = Elisabetta Collini
|author2 = Cathy Y. Wong
|author3 = Krystyna E. Wilk
|author4 = Paul M. G. Curmi
|author5 = Paul Brumer
|author6 = Gregory D. Scholes
|title = Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature
|journal = [[Nature (journal)|Nature]]
|volume = 463
|date = 4 February 2010
|doi = 10.1038/nature08811
|pmid=20130647
|bibcode = 2010Natur.463..644C
|issue=7281}}</ref>

==Photolysis in the atmosphere==
Photolysis also occurs in the atmosphere as part of a series of reactions by which primary [[pollutants]] such as [[hydrocarbons]] and [[nitrogen oxides]] react to form secondary pollutants such as [[peroxyacyl nitrates]]. See [[photochemical smog]].

The two most important photodissociaton reactions in the [[troposphere]] are firstly:

:O3 + hν → O2 + O(1D) λ < 320 nm

which generates an excited oxygen atom which can react with water to give the [[hydroxyl radical]]:

:O(1D) + H2O → 2 •OH

The hydroxyl radical is central to [[atmospheric chemistry]] as it initiates the [[oxidation]] of hydrocarbons in the atmosphere and so acts as a detergent.

Secondly the reaction:

:NO2 + hν → NO + O

is a key reaction in the formation of [[tropospheric ozone]].

The formation of the [[ozone layer]] is also caused by photodissociation. Ozone in the Earth's [[stratosphere]] is created by ultraviolet light striking oxygen molecules containing two oxygen [[atom]]s (O2), splitting them into individual oxygen atoms (atomic oxygen). The atomic oxygen then combines with unbroken O2 to create [[ozone]], O3. In addition, photolysis is the process by which [[Chlorofluorocarbon|CFC]]s are broken down in the upper atmosphere to form ozone-destroying chlorine [[free radicals]].

==Astrophysics==
In [[astrophysics]], photodissociation is one of the major processes through which molecules are broken down (but new molecules are being formed). Because of the [[vacuum]] of the [[interstellar medium]], molecules and [[free radical]]s can exist for a long time. Photodissociation is the main path by which molecules are broken down. Photodissociation rates are important in the study of the composition of [[interstellar clouds]] in which [[star]]s are formed.

Examples of photodissociation in the interstellar medium are (<math>h\nu</math> is the energy of a single [[photon]] of frequency <math>\nu</math>):

:<math>H_2O + h\nu \rightarrow H + OH</math>

:<math>CH_4 +h\nu \rightarrow CH_3 + H</math>

== Atmospheric Gamma Ray Bursts ==
Currently orbiting satellites detect an average of about one gamma-ray burst per day. Because gamma-ray bursts are visible to distances encompassing most of the [[observable universe]], a volume encompassing many billions of galaxies, this suggests that gamma-ray bursts must be exceedingly rare events per galaxy.

Measuring the exact rate of Gamma Ray bursts is difficult, but for a galaxy of approximately the same size as the [[Milky Way]], the expected rate (for long GRBs) is about one burst every 100,000 to 1,000,000 years.<ref name="rates">[[#Podsiadlowski|Podsiadlowski 2004]]</ref> Only a few percent of these would be beamed towards Earth. Estimates of rates of short GRBs are even more uncertain because of the unknown beaming fraction, but are probably comparable.<ref>[[#Guetta|Guetta 2006]]</ref>

A gamma-ray burst in the Milky Way, if close enough to Earth and beamed towards it, could have significant effects on the [[biosphere]]. The absorption of radiation in the atmosphere would cause photodissociation of [[nitrogen]], generating [[nitric oxide]] that would act as a catalyst to destroy [[ozone]].<ref>[[#Thorsett|Thorsett 1995]]</ref>

The atmospheric photodissociation
* N2 -> 2N
* O2 -> 2O
* CO2 -> C + 2O
* H2O -> 2H + O
* 2NH3 -> 3H2 + N2

would yield
* NO2 (consumes up to 400 [[Ozone]] molecules)
* CH2 (nominal)
* CH4 (nominal)
* CO2

(incomplete)

According to a 2004 study, a GRB at a distance of about a [[parsec|kiloparsec]] could destroy up to half of Earth's [[ozone layer]]; the direct UV irradiation from the burst combined with additional solar UV radiation passing through the diminished ozone layer could then have potentially significant impacts on the [[food chain]] and potentially trigger a mass extinction.<ref name="Melott2004">[[#Melott|Melott 2004]]</ref><ref name="ancient">[[#Wanjek|Wanjek 2005]]</ref> The authors estimate that one such burst is expected per billion years, and hypothesize that the [[Ordovician-Silurian extinction event]] could have been the result of such a burst.

There are strong indications that long gamma-ray bursts preferentially or exclusively occur in regions of low metallicity. Because the Milky Way has been metal-rich since before the Earth formed, this effect may diminish or even eliminate the possibility that a long gamma-ray burst has occurred within the Milky Way within the past billion years.<ref name="Stanek">[[#Stanek|Stanek 2006]]</ref> No such metallicity biases are known for short gamma-ray bursts. Thus, depending on their local rate and beaming properties, the possibility for a nearby event to have had a large impact on Earth at some point in geological time may still be significant.<ref>[[#Ejzak|Ejzak 2007]]</ref>

==Multiple photon dissociation==
Single photons in the [[infrared]] spectral range usually are not energetic enough for direct photodissociation of molecules. However, after absorption of multiple infrared photons a molecule may gain internal energy to overcome its barrier for dissociation. Multiple photon dissociation (MPD, [[Infrared multiphoton dissociation|IRMPD]] with infrared radiation) can be achieved by applying high power lasers, e.g. a [[carbon dioxide laser]], or a [[free electron laser]], or by long interaction times of the molecule with the radiation field without the possibility for rapid cooling, e.g. by collisions. The latter method allows even for MPD induced by [[black body radiation]], a technique called [[Blackbody infrared radiative dissociation]] (BIRD).

==See also==
*[[Flash photolysis]]
*[[Photocatalysis]]
*[[Photohydrogen]]
*[[Photochemistry]]

==References==
{{reflist}}

[[Category:Chemical reactions]]
[[Category:Astrophysics]]
[[Category:Photosynthesis]]

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Hausdorff moment problem