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| '''Koopmans' theorem''' states that in closed-shell [[Hartree-Fock]] theory, the first [[ionization energy]] of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital ([[HOMO]]). This theorem is named after [[Tjalling Koopmans]], who published this result in 1934.<ref>{{cite journal
| | <br><br>It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you cherished this article and also you would like to acquire more info relating to [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC] i implore you to visit our own page. |
| | last = Koopmans
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| | first = Tjalling
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| | title = Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms
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| | journal = Physica
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| | year = 1934
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| | volume = 1
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| | issue = 1–6
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| | pages = 104–113
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| | publisher = Elsevier
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| | doi = 10.1016/S0031-8914(34)90011-2
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| | bibcode=1934Phy.....1..104K}}
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| </ref>
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| Koopmans became a [[Nobel laureate]] in 1975, though neither in physics nor chemistry, but in [[Nobel Memorial Prize in Economic Sciences|economics]].
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| Koopmans' theorem is exact in the context of restricted [[Hartree–Fock method|Hartree–Fock theory]] if it is assumed that the orbitals of the ion are identical to those of the neutral molecule (the ''frozen orbital'' approximation). Ionization energies calculated this way are in qualitative agreement with experiment – the first ionization energy of small molecules is often calculated with an error of less than two [[electron volt]]s.<ref name="politzer">{{cite journal|last1=Politzer|first1=Peter|first2=Fakher |last2=Abu-Awwad|year=1998|title=A comparative analysis of Hartree–Fock and Kohn–Sham orbital energies|journal=Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta)|volume=99|issue=2|pages=83–87|doi=10.1007/s002140050307}}</ref><ref name="hamel">{{cite journal|last1=Hamel|first1=Sebastien|first2=Patrick|last2= Duffyc|first3=Mark E. |last3=Casidad |first4= Dennis R. |last4=Salahub|year=2002|title=Kohn–Sham orbitals and orbital energies: fictitious constructs but good approximations all the same |journal=Journal of Electron Spectroscopy and Related Phenomena|volume=123|issue=2–3|pages=345–363|doi=10.1016/S0368-2048(02)00032-4}}</ref><ref>See, for example, {{Cite book|first1=A. |last1=Szabo |first2= N. S.|last2= Ostlund|title=Modern Quantum Chemistry|chapter=Chapter 3|isbn=0-02-949710-8}}</ref> Therefore, the validity of Koopmans' theorem is intimately tied to the accuracy of the underlying [[Hartree-Fock]] wavefunction.{{Citation needed|reason=Correlating the wave function with the HOMO seems to need more explanation than simply therefore|date=April 2009}} The two main sources of error are:
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| * '''orbital relaxation''', which refers to the changes in the [[Fock operator]] and [[Hartree-Fock]] orbitals when changing the number of electrons in the system, and
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| * '''[[electron correlation]]''', referring to the validity of representing the entire many-body wavefunction using the [[Hartree-Fock]] wavefunction, i.e. a single [[Slater determinant]] composed of orbitals that are the eigenfunctions of the corresponding self-consistent [[Fock operator]].
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| Empirical comparisons with experimental values and higher-quality [[ab initio]] calculations suggest that in many cases, but not all, the energetic corrections due to relaxation effects nearly cancel the corrections due to electron correlation.<ref name=Michl>{{cite book|last1=Michl|first1=Josef|last2=Bonačić-Koutecký|first2=Vlasta|title=Electronic Aspects of Organic Photochemistry|publisher= Wiley|year= 1990|page=35|isbn=978-0-471-89626-5}}</ref><ref name=Hehre>{{cite book|last1=Hehre|first1=Warren J.|last2=Radom|first2=Leo|last3=Schleyer|first3=Paul v.R.|last4=Pople|first4=John A.|title=Ab initio molecular orbital theory|publisher= Wiley|year= 1986|page=24|isbn=0-471-81241-2}}</ref>
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| A similar theorem exists in [[density functional theory]] (DFT) for relating the exact first [[Ionization energy#Vertical and adiabatic ionization energy in molecules|vertical ionization energy]] and electron affinity to the [[HOMO/LUMO|HOMO and LUMO]] energies, although both the derivation and the precise statement differ from that of Koopmans' theorem. Ionization energies calculated from DFT orbital energies are usually poorer than those of Koopmans' theorem, with errors much larger than two electron volts possible depending on the exchange-correlation approximation employed.<ref name="politzer"/><ref name="hamel"/> The LUMO energy shows little correlation with the electron affinity with typical approximations.<ref>{{cite journal|last1=Zhang|first1=Gang|first2=Charles B. |last2=Musgrave|year=2007|title=Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations|journal=The Journal of Physical Chemistry A|volume=111|issue=8|pages=1554–1561|doi=10.1021/jp061633o|pmid=17279730}}</ref> The error in the DFT counterpart of Koopmans' theorem is a result of the approximation employed for the exchange correlation energy functional so that, unlike in HF theory, there is the possibility of improved results with the development of better approximations.
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| ==Generalizations of Koopmans' theorem==
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| While Koopmans' theorem was originally stated for calculating ionization energies from restricted (closed-shell) Hartree-Fock wavefunctions, the term has since taken on a more generalized meaning as a way of using orbital energies to calculate energy changes due to changes in the number of electrons in a system.
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| ===Ground-state and excited-state ions===
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| Koopmans’ theorem applies to the removal of an electron from any occupied molecular orbital to form a positive ion. Removal of the electron from different occupied molecular orbitals leads to the ion in different electronic states. The lowest of these states is the ground state and this often, but not always, arises from removal of the electron from the HOMO. The other states are excited electronic states.
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| For example the electronic configuration of the H<sub>2</sub>O molecule is (1a<sub>1</sub>)<sup>2</sup> (2a<sub>1</sub>)<sup>2</sup> (1b<sub>2</sub>)<sup>2</sup> (3a<sub>1</sub>)<sup>2</sup> (1b<sub>1</sub>)<sup>2</sup>,<ref name=Levine>{{cite book|last=Levine|first= I. N.|title=Quantum Chemistry|edition=4th |publisher= Prentice-Hall|year= 1991|page=475|isbn=0-7923-1421-2}}</ref> where the symbols a<sub>1</sub>, b<sub>2</sub> and b<sub>1</sub> are orbital labels based on [[molecular symmetry]]. From Koopmans’ theorem the energy of the 1b<sub>1</sub> HOMO corresponds to the ionization energy to form the H<sub>2</sub>O<sup>+</sup> ion in its ground state (1a<sub>1</sub>)<sup>2</sup> (2a<sub>1</sub>)<sup>2</sup> (1b<sub>2</sub>)<sup>2</sup> (3a<sub>1</sub>)<sup>2</sup> (1b<sub>1</sub>)<sup>1</sup>. The energy of the second-highest MO 3a<sub>1</sub> refers to the ion in the excited state (1a<sub>1</sub>)<sup>2</sup> (2a<sub>1</sub>)<sup>2</sup> (1b<sub>2</sub>)<sup>2</sup> (3a<sub>1</sub>)<sup>1</sup> (1b<sub>1</sub>)<sup>2</sup>, and so on. In this case the order of the ion electronic states corresponds to the order of the orbital energies. Excited-state ionization energies can be measured by [[Ultraviolet photoelectron spectroscopy|photoelectron spectroscopy]].
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| For H<sub>2</sub>O, the near-Hartree-Fock orbital energies (with sign changed) of these orbitals are 1a<sub>1</sub> 559.5, 2a<sub>1</sub> 36.7 1b<sub>2</sub> 19.5, 3a<sub>1</sub> 15.9 and 1b<sub>1</sub> 13.8 [[Electronvolt|eV]]. The corresponding ionization energies are 539.7, 32.2, 18.5, 14.7 and 12.6 eV.<ref name=Levine/> As explained above, the deviations are due to the effects of orbital relaxation as well as differences in electron correlation energy between the molecular and the various ionized states.
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| ===Koopmans' theorem for electron affinities===
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| It is sometimes claimed<ref>See, for example, {{Cite book|first1=A. |last1=Szabo |first2= N. S.|last2= Ostlund|title=Modern Quantum Chemistry|page=127|isbn=0-02-949710-8}}</ref> that Koopmans' theorem also allows the calculation of [[electron affinity|electron affinities]] as the energy of the lowest unoccupied molecular orbitals ([[LUMO]]) of the respective systems. However, Koopmans' original paper makes no claim with regard to the significance of eigenvalues of the [[Fock matrix|Fock operator]] other than that corresponding to the [[HOMO]]. Nevertheless, it is straightforward to generalize the original statement of Koopmans' to calculate the [[electron affinity]] in this sense.
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| Calculations of electron affinities using this statement of Koopmans' theorem have been criticized<ref>{{cite book
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| | last1 = Jensen
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| | first1= Frank
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| | title= Introduction to Computational Chemistry
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| | year = 1990
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| | publisher = Wiley
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| | pages = 64–65
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| | isbn = 0-471-98425-6}}</ref> on the grounds that virtual (unoccupied) orbitals do not have well-founded physical interpretations, and that their orbital energies are very sensitive to the choice of basis set used in the calculation. As the basis set becomes
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| more complete; more and more "molecular" orbitals that are not really ''on'' the molecule of interest will appear, and care must be taken not to use
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| these orbitals for estimating electron affinities.
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| Comparisons with experiment and higher-quality calculations show that electron affinities predicted in this manner are generally quite poor.
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| ===Koopmans' theorem for open-shell systems===
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| Koopmans' theorem is also applicable to open-shell systems. It was previously believed that this was only in the case for removing the unpaired electron,<ref>{{cite book
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| | last1 = Fulde
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| | first1 = Peter
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| | title = Electron correlations in molecules and solids
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| | year = 1995
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| | publisher = Springer
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| | pages = 25–26
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| | isbn = 3-540-59364-0}}</ref> but
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| the validity of Koopmans’ theorem for ROHF in general has been proven provided that the correct orbital energies are used.<ref>
| |
| {{cite journal | doi = 10.1063/1.2393223 | title = Koopmans' theorem in the ROHF method: Canonical form for the Hartree-Fock Hamiltonian | year = 2006 | last1 = Plakhutin | first1 = B. N. | last2 = Gorelik | first2 = E. V. | last3 = Breslavskaya | first3 = N. N. | journal = The Journal of Chemical Physics | volume = 125 | pages = 204110 | pmid = 17144693 | issue = 20 | bibcode=2006JChPh.125t4110P}}
| |
| </ref><ref> | |
| {{cite journal | doi = 10.1063/1.3418615 | title = Koopmans's theorem in the restricted open-shell Hartree–Fock method. II. The second canonical set for orbitals and orbital energies | year = 2010 | last1 = Davidson | first1 = Ernest R. | last2 = Plakhutin | first2 = Boris N. | journal = The Journal of Chemical Physics | volume = 132 | issue = 18 | pages = 184110 | bibcode=2010JChPh.132r4110D}}
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| </ref><ref>
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| {{cite journal | doi = 10.1021/jp9002593 | title = Koopmans' Theorem in the Restricted Open-Shell Hartree−Fock Method. 1. A Variational Approach† | year = 2009 | last1 = Plakhutin | first1 = Boris N. | last2 = Davidson | first2 = Ernest R. | journal = The Journal of Physical Chemistry A | volume = 113 | pages = 12386–12395 | pmid = 19459641 | issue = 45 | bibcode=2009JPCA..11312386P}}
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| </ref><ref>
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| {{cite journal | last1 = Glaesemann | first1 = Kurt R. | last2 = Schmidt | first2 = Michael W. | title = On the Ordering of Orbital Energies in High-Spin ROHF† | journal = The Journal of Physical Chemistry A | volume = 114 | issue =33 | pages = 8772–8777 | year = 2010 | pmid = 20443582 | doi = 10.1021/jp101758y}}
| |
| </ref>
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| The spin up (alpha) and spin down (beta) orbital energies do not necessarily have to be the same.<ref>
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| {{cite journal|last1=Tsuchimochi|first1=Takashi|last2=Scuseria|first2=Gustavo E.|title=Communication: ROHF theory made simple|journal=The Journal of Chemical Physics|volume=133|issue=14|pages=141102|year=2010|pmid=20949979|doi=10.1063/1.3503173|bibcode = 2010JChPh.133n1102T |arxiv = 1008.1607|volume=3|issue=2 }}
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| </ref>
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| ==Counterpart in density functional theory==
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| Kohn-Sham (KS) [[density functional theory]] (KS-DFT) admits its own version of Koopmans' theorem (sometimes called the '''DFT-Koopmans' theorem''') very similar in spirit to that of Hartree Fock theory. The theorem equates the first (vertical) ionization energy <math> I </math> of a system of <math> N</math> electrons to the negative of the corresponding KS HOMO energy <math>\epsilon_H </math>. More generally, this relation is true even when the KS systems describes a zero-temperature ensemble with non-integer number of electrons <math> N - \delta N</math> for integer <math>N</math> and <math>\delta N \rightarrow 0</math>. When considering <math>N + \delta N</math> electrons the infinitesimal excess charge enters the KS LUMO of the ''N'' electron system but then the exact KS potential jumps by a constant known as the "derivative discontinuity".<ref name="perdew82">{{cite journal
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| |last1=Perdew
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| |first1=John P.
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| |first2=Robert G. |last2=Parr|first3=Mel |last3=Levy|first4=Jose L.|last4= Balduz, Jr.
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| |year=1982
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| |title=Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy
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| |journal=Physical Review Letters
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| |volume=49
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| |issue=23
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| |pages=1691–1694
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| |doi=10.1103/PhysRevLett.49.1691 |bibcode=1982PhRvL..49.1691P}}</ref> It can be shown that the vertical electron affinity is equal exactly to the negative of the sum of the LUMO energy and the derivative discontinuity.<ref name="perdew82" /><ref>{{cite journal
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| |last1=Perdew
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| |first1=John P.
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| |first2=Mel|last2= Levy
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| |year=1997
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| |title=Comment on "Significance of the highest occupied Kohn–Sham eigenvalue"
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| |journal=Physical Review B
| |
| |volume=56
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| |issue=24
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| |pages=16021–16028
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| |doi=10.1103/PhysRevB.56.16021|bibcode = 1997PhRvB..5616021P }}</ref>
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| Unlike the approximate status of Koopmans' theorem in Hartree Fock theory (because of the neglect of orbital relaxation), in the exact KS mapping the theorem is exact, including the effect of orbital relaxation. A sketchy proof of this exact relation goes in three stages. First, for any finite system <math>I</math> determines the <math>|\bold{r}|\rightarrow\infty</math> asymptotic form of the density, which decays as <math>n(\bold{r})\rightarrow e^{-2\sqrt{\frac{2 m_e}{\hbar} I}|\bold{r}|}</math>.<ref name="perdew82" />
| |
| <ref name="almblad85">{{cite journal
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| |last1=Almbladh|first1=C. -O.|first2=U. |last2=von Barth
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| |year=1985
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| |title=Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues
| |
| |journal=Physical Review B
| |
| |volume=31
| |
| |issue=6
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| |pages=3231
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| |doi=10.1103/PhysRevB.31.3231|bibcode = 1985PhRvB..31.3231A }}</ref> Next, as a corollary (since the physically interacting system has the same density as the KS system), both must have the same ionization energy. Finally, since the KS potential is zero at infinity, the ionization energy of the KS system is, by definition, the negative of its HOMO energy and thus finally: <math>\epsilon_H = -I </math>, QED.
| |
| | |
| While these are exact statements in the formalism of DFT, the use of approximate exchange-correlation potentials makes the calculated energies approximate and often the orbital energies are very different from the corresponding ionization energies (even by several eVs!).<ref name="spring">{{cite journal | title = Koopmans' springs to life | journal = The Journal of Chemical Physics | volume = 131 | issue = 23
| |
| | year = 2009 | pages = 231101–4 | doi = 10.1063/1.3269030 | first1 = U. |last1 = Salzner | first2 = R. |last2 = Baer |bibcode = 2009JChPh.131w1101S }}</ref>
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| | |
| A tuning procedure is able to "impose" Koopmans' theorem on DFT approximations thereby improving many of its related predictions in actual applications.
| |
| <ref name="spring" /><ref>{{cite journal | title = "Tuned" Range-separated hybrids in density functional theory | journal = Annual Review of Physical Chemistry | volume = 61 | year = 2010 | pages = 85–109 | doi = 10.1146/annurev.physchem.012809.103321 | first1 = R. |last1 = Baer | first2 = E. |last2 = Livshits | first3 = U. |last3 = Salzner | pmid = 20055678 }}{{cite journal | title = Fundamental gaps of finite systems from the eigenvalues of a generalized Kohn-Sham method | journal = Physical Review Letters | volume = 105 | year = 2010 | pages = 266802 | doi = 10.1103/PhysRevLett.105.266802 | first1 = T. |last1 = Stein | first2 = H. |last2 = Eisenberg | first3 = L. |last3 = Kronik | first4 = R. |last4 = Baer | issue = 26 | pmid = 21231698 |arxiv = 1006.5420 |bibcode = 2010PhRvL.105z6802S }} {{cite journal
| |
| |last1=Kornik
| |
| |first1=L.
| |
| |first2=T. |last2=Stein|first3=S. |last3=Refaely-Abramson|first4=R.|last4= Baer
| |
| |year=2012
| |
| |title=Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals
| |
| |journal=Journal of Chemical Theory and Computation
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| |volume=8
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| |issue=5
| |
| |pages=1515
| |
| |doi=10.1021/ct2009363}}</ref>
| |
| | |
| In approximate DFTs one can estimate to high degree of accuracy the deviance from Koopmans' theorem using the concept of energy curvature.<ref>{{Cite journal|doi=10.1021/jz3015937 |arxiv=1208.1496|title=Curvature and frontier orbital energies in density functional theory|year=2012|journal=The Journal of Physical Chemistry Letters|pages=3740|last1=Stein|first1=Tamar|last2=Autschbach|first2=Jochen|last3=Govind|first3=Niranjan|last4=Kronik|first4=Leeor|last5=Baer|first5=Roi}}</ref>
| |
| | |
| ==References==
| |
| {{reflist|30em}}
| |
| | |
| ==External links==
| |
| *{{cite web|url=http://www.chemistry.emory.edu/faculty/bowman/old_classes/chem531/lectures/koopman's_theorem.pdf|title=Lecture on Koopmans' Theorem Chem 531|first=Joel|last= Bowman}}
| |
| *{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/1975/koopmans-autobio.html | title=Koopmans' autobiography|publisher=The Nobel Foundation|year= 1975}}
| |
| | |
| {{DEFAULTSORT:Koopmans' Theorem}}
| |
| [[Category:Quantum chemistry]]
| |
| [[Category:Computational chemistry]]
| |
| [[Category:Theoretical chemistry]]
| |
It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.
Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.
At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.
Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.
Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.
Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.
Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.
Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.
In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.
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