Editing Excited state

{{Short description|Quantum states with more energy than the lowest possible amount}}
{{Use American English|date = February 2019}}
[[File:Energy levels.svg|thumb|right| After absorbing energy, an electron may jump from the ground state to a higher energy excited state.]]
[[File:CuO2-plane in high Tc superconductor.png|thumbnail|right|Excitations of copper 3d orbitals on the CuO<sub>2</sub> plane of a high-''T''<sub>c</sub> superconductor. The ground state (blue) is ''x''<sup>2</sup>–''y''<sup>2</sup> orbitals; the excited orbitals are in green; the arrows illustrate inelastic x-ray spectroscopy.]]

In [[quantum mechanics]], an '''excited state''' of a system (such as an [[atom]], [[molecule]] or [[Atomic nucleus|nucleus]]) is any [[quantum state]] of the system that has a higher [[energy]] than the [[ground state]] (that is, more energy than the absolute minimum). Excitation refers to an increase in [[energy level]] above a chosen starting point, usually the ground state, but sometimes an already excited state. The [[temperature]] of a group of particles is indicative of the level of excitation (with the notable exception of systems that exhibit [[negative temperature]]).{{Citation needed|date=November 2024}}

The lifetime of a system in an excited state is usually short: [[Spontaneous emission|spontaneous]] or [[stimulated emission|induced emission]] of a quantum of energy (such as a [[photon]] or a [[phonon]]) usually occurs shortly after the system is promoted to the excited state, returning the system to a state with lower energy (a less excited state or the ground state). This return to a lower energy level is known as de-excitation<ref>Sakho, Ibrahima. ''Nuclear Physics 1: Nuclear Deexcitations, Spontaneous Nuclear Reactions''. John Wiley & Sons, 2021.</ref> and is the inverse of excitation.

Long-lived excited states are often called [[Metastability|metastable]]. Long-lived [[nuclear isomer]]s and [[singlet oxygen]] are two examples of this.{{Citation needed|date=November 2024}}

== Atomic excitation ==
Atoms can be excited by heat, electricity, or light. The [[hydrogen atom]] provides a simple example of this concept.

The ground state of the hydrogen atom has the atom's single [[electron]] in the lowest possible [[atomic orbital|orbital]] (that is, the spherically symmetric "[[1s orbital|1s]]" [[wave function]], which, so far, has been demonstrated to have the lowest possible [[quantum number]]s). By giving the atom additional energy (for example, by absorption of a [[photon]] of an appropriate energy), the electron moves into an excited state (one with one or more quantum numbers greater than the minimum possible). When the electron finds itself between two states—a shift which happens very fast—it's in a [[Quantum superposition|superposition]] of both states.<ref>[https://quantuminstitute.yale.edu/publications/quantum-leaps-long-assumed-be-instantaneous-take-time Quantum Leaps, Long Assumed to Be Instantaneous, Take Time]</ref> If the photon has too much energy, the electron will cease to be [[bound state|bound]] to the atom, and the atom will become [[Photoionization|ionized]].

After excitation the atom may return to the ground state or a lower excited state, by emitting a photon with a characteristic energy. Emission of photons from atoms in various excited states leads to an [[electromagnetic spectrum]] showing a series of characteristic [[emission line]]s (including, in the case of the hydrogen atom, the [[Hydrogen spectral series|Lyman, Balmer, Paschen and Brackett series]]).

An atom in a high excited state is termed a [[Rydberg atom]]. A system of highly excited atoms can form a long-lived condensed excited state, [[Rydberg matter]].

== Perturbed gas excitation ==
A collection of molecules forming a gas can be considered in an excited state if one or more molecules are elevated to kinetic energy levels such that the resulting velocity distribution departs from the equilibrium [[Boltzmann distribution]]. This phenomenon has been studied in the case of a [[two-dimensional gas]] in some detail, analyzing the time taken to relax to equilibrium.

== Calculation of excited states ==
Excited states are often calculated using [[coupled cluster]], [[Møller–Plesset perturbation theory]], [[multi-configurational self-consistent field]], [[configuration interaction]],<ref>{{cite book | last = Hehre | first = Warren J. | title = A Guide to Molecular Mechanics and Quantum Chemical Calculations | publisher = Wavefunction, Inc. | year = 2003 | location = Irvine, California | isbn = 1-890661-06-6|url =http://www.wavefun.com/support/AGuidetoMM.pdf }}</ref> and [[time-dependent density functional theory]].<ref>{{ cite journal | doi = 10.1021/jp101761d
| pmid = 20540550 | year = 2010
| title = EOMCC, MRPT, and TDDFT Studies of Charge Transfer Processes in Mixed-Valence Compounds: Application to the Spiro Molecule | pages = 8764–8771
| journal = The Journal of Physical Chemistry A
| volume = 114
 | issue = 33
| first1= Kurt R. | last1 = Glaesemann | first2 = Niranjan | last2 = Govind | first3 = Sriram| last3 = Krishnamoorthy| first4= Karol | last4 = Kowalski | bibcode = 2010JPCA..114.8764G
}}</ref><ref>{{cite journal| last1 = Dreuw| first1 = Andreas| last2 = Head-Gordon| first2 = Martin| title = Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules| journal = Chemical Reviews| volume = 105| issue = 11| pages = 4009–37| year = 2005| pmid = 16277369| doi = 10.1021/cr0505627}}</ref><ref>{{cite journal| last1 = Knowles| first1 = Peter J.| last2 = Werner| first2 = Hans-Joachim| title = Internally contracted multiconfiguration-reference configuration interaction calculations for excited states| journal = Theoretica Chimica Acta| volume = 84| pages = 95–103| year = 1992| issue = 1–2| doi = 10.1007/BF01117405| s2cid = 96830841}}</ref><ref>{{cite journal| last1 =Foresman| first1 =James B.| last2 =Head-Gordon| first2 =Martin| last3 =Pople| first3 =John A.| last4 =Frisch| first4 =Michael J.| title =Toward a systematic molecular orbital theory for excited states| journal =The Journal of Physical Chemistry| volume =96| pages =135–149| year =1992| doi =10.1021/j100180a030}}</ref><ref>{{ cite journal | doi = 10.1039/a808518h | title = A study of FeCO+ with correlated wavefunctions | year = 1999 | last1 = Glaesemann | first1 = Kurt R. | last2 = Gordon | first2 = Mark S. | last3 = Nakano | first3 = Haruyuki | journal = Physical Chemistry Chemical Physics | volume = 1 | pages = 967–975 | issue=6|bibcode = 1999PCCP....1..967G }}</ref><ref>{{Cite thesis|last=Ariyarathna|first=Isuru|date=2021-03-01|title=First Principle Studies on Ground and Excited Electronic States: Chemical Bonding in Main-Group Molecules, Molecular Systems with Diffuse Electrons, and Water Activation using Transition Metal Monoxides|hdl=10415/7601|hdl-access=free|language=en}}</ref>

==Excited-state absorption==
The excitation of a system (an atom or molecule) from one excited state to a higher-energy excited state with the absorption of a photon is called ''excited-state absorption'' (ESA). Excited-state absorption is possible only when an electron has been already excited from the ground state to a lower excited state. The excited-state absorption is usually an undesired effect, but it can be useful in upconversion pumping.<ref>{{Cite web |url=https://www.rp-photonics.com/excited_state_absorption.html |title=Excited-state Absorption |first=Rüdiger |last=Paschotta |website=www.rp-photonics.com}}</ref> Excited-state absorption measurements are done using pump–probe techniques such as [[flash photolysis]]. However, it is not easy to measure them compared to ground-state absorption, and in some cases complete bleaching of the ground state is required to measure excited-state absorption.<ref>{{cite journal |last1 = Dolan |first1 = Giora |last2 = Goldschmidt |first2 = Chmouel R. |title = A new method for absolute absorption cross-section measurements: rhodamine-6G excited singlet-singlet absorption spectrum |journal = Chemical Physics Letters |volume = 39 |issue = 2 |pages = 320–322 |year = 1976 |doi = 10.1016/0009-2614(76)80085-1 |bibcode = 1976CPL....39..320D}}</ref>

==Reaction==
{{main|Photochemistry}}
A further consequence of excited-state formation may be reaction of the atom or molecule in its excited state, as in [[Organic photochemistry|photochemistry]].

== See also ==
* [[Rydberg formula]]
* [[Stationary state]]
* [[Repulsive state]]

== References ==
{{Reflist}}

== External links ==
* [https://web.archive.org/web/20000901235539/http://imagine.gsfc.nasa.gov/docs/teachers/lessons/xray_spectra/background-atoms.html NASA background information on ground and excited states]

{{Quantum mechanics topics}}
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[[Category:Quantum states]]