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| [[File:12-6-Lennard-Jones-Potential.svg|thumb|320px|right|A graph of strength versus distance for the 12-6 Lennard-Jones potential.]]
| | Many persons have this habit of doing all of the stuff by themselves, regardless of how important or simple they are! These people won't allow others interfere inside their matters. While this stance can work in other regions of existence, it is actually really not how to answer whenever you want to fix the Windows registry. There are some jobs like removing spywares, virus in addition to obsolete registry entries, that are best left to expert softwares. In this particular article I will tell we why it is important to fix Windows registry NOW!<br><br>Before really purchasing the software it is best to check on the companies which create the software. If you will discover details found on the form of reputation every company has, perhaps the risk of malicious programs is reduced. Software from reputed businesses have assisted me, plus other consumers, to create my PC run quicker.. If the product description does not look superior to we, refuses to include details regarding the software, does not include the scan functions, you need to go for another 1 that ensures you're paying for what we wish.<br><br>So what must you look for when we compare registry cleaners. Many of the registry cleaners accessible today, have extremely similar qualities. The leading ones which we should be searching for are these.<br><br>Handling intermittent mistakes - when there is a content to the effect which "memory or hard disk is malfunctioning", we might put inside modern hardware to replace the defective piece till the actual issue is found out. There are h/w diagnostic programs to identify the faulty portions.<br><br>Besides, should you could receive a [http://bestregistrycleanerfix.com/system-mechanic system mechanic professional] which can do the job for we effectively plus quickly, then why not? There is one such system, RegCure that is great and complete. It has qualities which additional cleaners never have. It is the many recommended registry cleaner now.<br><br>The initially thing you should do is to reinstall any system that shows the error. It's typical for several computers to have certain programs that require this DLL to show the error whenever we try plus load it up. If you see a certain program show the error, we must initially uninstall that program, restart a PC plus then resinstall the system again. This must replace the damaged ac1st16.dll file plus cure the error.<br><br>Maybe you're asking how come these windows XP error messages appear. Well, for we to be able to recognize the fix, you must initially know where those mistakes come from. There is this software called registry. A registry is software that shops everything on a PC from a normal configuration, setting, information, plus logs of escapades from installing to UN-installing, saving to deleting, and a lot more alterations we do in the system pass by it plus gets 'tagged' and saved because a easy file for healing purposes. Imagine it because a big recorder, a registrar, of all the records in your PC.<br><br>A registry cleaner is a program which cleans the registry. The Windows registry usually gets flooded with junk data, info which has not been removed from uninstalled programs, erroneous file organization plus additional computer-misplaced entries. These clean small system software tools are quite usual today and we can find many good ones found on the Internet. The advantageous ones provide you option to keep, clean, update, backup, and scan the System Registry. When it finds supposedly unwanted ingredients in it, the registry cleaner lists them and recommends the user to delete or repair these orphaned entries and corrupt keys. |
| {{Computational physics}}
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| The '''Lennard-Jones potential''' (also referred to as the '''L-J potential''', '''6-12 potential''', or '''12-6 potential''') is a mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules. A form of the potential was first proposed in 1924 by [[John Lennard-Jones]].<ref>{{Citation |last=Lennard-Jones |first=J. E. |year=1924 |title=On the Determination of Molecular Fields |journal=Proc. R. Soc. Lond. A |volume=106 |issue=738 |pages=463–477 |doi=10.1098/rspa.1924.0082 |bibcode = 1924RSPSA.106..463J }}.</ref> The most common expressions of the L-J potential are
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| :
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| :<math>\begin{alignat}{3}
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| V_{LJ}& = 4 \varepsilon &\left[ \left( \frac {\sigma} {r} \right)^{12} - \left( \frac {\sigma} {r} \right)^6 \right]\\
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| & = \varepsilon &\left[\left( \frac {r_{m}} {r} \right)^{12} - 2 \left( \frac {r_{m}} {r} \right)^6 \right]
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| \end{alignat}</math>
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| where ''ε'' is the depth of the [[potential well]], ''σ'' is the finite distance at which the inter-particle potential is zero, ''r'' is the distance between the particles, and ''r''<sub>m</sub> is the distance at which the potential reaches its minimum. At ''r''<sub>m</sub>, the potential function has the value −ε. The distances are related as ''r''<sub>m</sub> = 2<sup>1/6</sup>σ. These parameters can be [[Regression analysis|fitted]] to reproduce experimental data or accurate [[quantum chemistry]] calculations. Due to its computational simplicity, the Lennard-Jones potential is used extensively in computer simulations even though more accurate potentials exist.
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| ==Explanation==
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| The ''r''<sup>−12</sup> term, which is the repulsive term, describes [[Pauli repulsion]] at short ranges due to overlapping [[Atomic orbital|electron orbitals]] and the ''r''<sup>−6</sup> term, which is the attractive long-range term, describes attraction at long ranges ([[van der Waals force]], or [[London dispersion force|dispersion force]]). Whereas the functional form of the attractive term has a clear physical justification, the repulsive term has no theoretical justification. It is used because it approximates the Pauli repulsion well, and is more convenient due to the relative computational efficiency of calculating ''r''<sup>12</sup> as the square of ''r''<sup>6</sup>.
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| The Lennard-Jones (12,6) potential can be further approximated by the [[Buckingham potential|(exp-6) potential]] later proposed by R. A. Buckingham, in which the repulsive part is [[exponential function|exponential]]:<ref>[[Peter Atkins]] and Julio de Paula, "Atkins' Physical Chemistry" (8th edn, W. H. Freeman), p.637</ref>
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| :<math>V_B = \gamma \left[ e^{-r/r_0} - \left( \frac{r_0}{r} \right)^6 \right].</math>
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| The L-J potential is a relatively good approximation and due to its simplicity is often used to describe the properties of gases, and to model dispersion and overlap interactions in molecular models. It is particularly accurate for [[noble gas]] atoms and is a good approximation at long and short distances for neutral atoms and molecules.
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| The lowest energy arrangement of an infinite number of atoms described by a Lennard-Jones potential is a hexagonal [[close-packing]].
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| On raising temperature, the lowest [[Thermodynamic free energy|free energy]] arrangement becomes cubic [[close packing]] and then liquid. Under pressure the lowest energy structure switches between cubic and hexagonal close packing.<ref>{{Citation |last=Barron |first=T. H. K. |last2=Domb |first2=C. |title=On the Cubic and Hexagonal Close-Packed Lattices |journal=Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences |year=1955 |volume=227 |issue=1171 |pages=447–465 |doi=10.1098/rspa.1955.0023 |bibcode = 1955RSPSA.227..447B }}.</ref> Real materials include BCC structures as well.<ref>Calculation of the Lennard-Jones n–m potential energy parameters for metals. Shu Zhen,G. J. Davies. physica status solidi (a)Volume 78, Issue 2, pages 595–605, 16 August 1983</ref>
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| Other more recent methods, such as the [[Stockmayer potential]], describe the interaction of molecules more accurately. [[Quantum chemistry]] methods, [[Møller–Plesset perturbation theory]], [[coupled cluster]] method or [[full configuration interaction]] can give extremely accurate results, but require large [[Algorithmic efficiency|computational cost]].
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| ==Alternative expressions==
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| There are many different ways of formulating the Lennard-Jones potential The following are some common forms. | |
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| ===AB form===
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| This form is a simplified formulation that is used by some simulation software packages:
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| :<math> V_{LJ}(r) = \frac{A}{r^{12}} - \frac{B}{r^6}, </math>
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| where, <math>A = 4\varepsilon \sigma^{12}</math> and <math>B = 4\varepsilon \sigma^6</math>. Conversely, <math>\sigma = \sqrt[6]{\frac{A}{B}}</math> and <math>\varepsilon = \frac{B^2}{4A}</math>. This is the form in which Lennard-Jones wrote the 12-6 potential.<ref name=LennardJones1931>{{Cite doi|10.1088/0959-5309/43/5/301}}</ref>
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| ===Truncated Lennard-Jones potential===
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| To save computational time, the Lennard-Jones potential is often truncated at a cut-off distance of ''r''<sub>c</sub> = 2.5''σ'', where
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| :{| style="width:100%" border="0"
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| |-
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| | style="width:95%" |
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| <math>
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| \displaystyle
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| V_{LJ} ( r_c )
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| =
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| V_{LJ} ( 2.5 \sigma )
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| =
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| 4 \varepsilon
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| \left[
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| \left(
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| \frac
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| {\sigma}
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| {2.5 \sigma}
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| \right)^{12}
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| -
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| \left(
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| \frac
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| {\sigma}
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| {2.5 \sigma}
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| \right)^6
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| \right]
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| \approx
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| -0.0163 \varepsilon
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| </math>
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| | style= | (1)
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| |}
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| i.e., at ''r''<sub>c</sub> = 2.5''σ'', the Lennard-Jones potential, ''V<sub>LJ</sub>'', is about 1/60th of its minimum value, ''ε'' (the depth of the potential well).
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| Beyond
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| <math>\displaystyle r_c</math>, the truncated potential
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| is set to zero.
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| To avoid a jump discontinuity at <math>\displaystyle r_c</math>, the LJ potential must be shifted upward a little
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| so that the truncated potential would be zero exactly at the cut-off distance, <math>\displaystyle r_c</math>.
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| For clarity, let <math>\displaystyle V_{LJ}</math> denote the LJ potential as defined above, i.e.,
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| :{| style="width:100%" border="0"
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| |-
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| | style="width:95%" |
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| <math>
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| \displaystyle
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| V_{LJ}
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| (r)
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| =
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| 4 \varepsilon
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| \left[
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| \left(
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| \frac
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| {\sigma}
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| {r}
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| \right)^{12}
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| -
| |
| \left(
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| \frac
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| {\sigma}
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| {r}
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| \right)^6
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| \right].
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| </math>
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| | style= | (2)
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| |}
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| Then the truncated Lennard-Jones potential
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| <math>\displaystyle V_{{LJ}_{trunc}}</math>
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| is defined as follows<ref>
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| [http://matdl.org/matdlwiki/index.php/softmatter:Lennard-Jones_Potential softmatter:Lennard-Jones Potential],
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| [http://matdl.org/matdlwiki/index.php/softmatter:Main_Page Soft matter],
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| [http://matdl.org/matdlwiki/index.php/softmatter:Main_Page Materials Digital Library Pathway]
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| </ref>
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| :{| style="width:100%" border="0"
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| |-
| |
| | style="width:95%" |
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| <math>
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| \displaystyle
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| V_{{LJ}_{trunc}}
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| (r)
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| :=
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| \begin{cases}
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| V_{LJ} (r)
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| -
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| V_{LJ} (r_c)
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| &
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| \text{for } r \le r_c
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| \\
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| 0
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| &
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| \text{for } r > r_c.
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| \end{cases}
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| </math>
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| | style= | (3)
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| |}
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| It can be easily verified that ''V''<sub>LJ<sub>trunc</sub></sub>(''r''<sub>c</sub>) = 0,
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| thus eliminating the jump discontinuity at ''r'' = ''r''<sub>c</sub>. Although the value of the (unshifted) Lennard Jones potential at ''r'' = ''r''<sub>c</sub> = 2.5''σ'' is rather small, the effect of the truncation can be significant, for instance on the gas–liquid critical point.<ref>{{Citation |last=Smit |first=B. |title=Phase diagrams of Lennard-Jones fluids |journal=[[Journal of Chemical Physics]] |volume=96 |issue=11 |pages=8639 |year=1992 |doi=10.1063/1.462271 |bibcode = 1992JChPh..96.8639S }}.</ref> Fortunately, the potential energy can be corrected for this effect in a mean field manner by adding
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| so-called tail corrections.<ref>{{Citation |last=Frenkel |first=D. |lastauthoramp=yes |last2=Smit |first2=B. |title=Understanding Molecular Simulation |edition=Second |publisher=Academic Press |location=San Diego |year=2002 |isbn=0-12-267351-4 }}.</ref>
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| ===Limitations of the Lennard-Jones Potential===
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|
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| * The L-J Potential has only two parameters (A and B) and so can be fit to a maximum of two physical quantities. It may be necessary to match three different properties (for example, a length scale, an energy scale and elasticity). It is impossible to match all three properties together with the Lennard-Jones potential.
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| * With the L-J potential, the number of atoms bonded to an atom does not affect the bond strength. The bond energy per atom therefore increases linearly with the number of bonds per atom. Experiments show instead that the bond energy per atom increases quadratically with the number of bonds {{cn|date=November 2012}}.
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| * Bonding has no directionality: the potential is spherically symmetric. Directional bonding is important for many systems.
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| * The sixth-power term models dipole-dipole interactions due to electron dispersion in noble gasses ([[London dispersion forces]]), but it does not represent other kinds of bonding well. The twelfth-power term appearing in the potential is chosen for its ease of calculation for simulations (by squaring the sixth-power term) and is not physically based.
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| * The potential diverges when two atoms approach one another. This may create instabilities that require special treatment in molecular dynamics simulations.
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| ==See also==
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| * [[Morse/Long-range_potential | Morse/Long-range Potential]]
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| * [[Molecular mechanics]]
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| * [[Embedded atom model]]
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| * [[Morse potential]]
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| * [[Force field (chemistry)]]
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| * [[Force field implementation]]
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| * [http://www.sklogwiki.org/SklogWiki/index.php/Lennard-Jones_model Lennard-Jones model] on [http://www.sklogwiki.org SklogWiki].
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| ==References==
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| {{Reflist}}
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| {{DEFAULTSORT:Lennard-Jones Potential}}
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| [[Category:Thermodynamics]]
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| [[Category:Chemical bonding]]
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| [[Category:Intermolecular forces]]
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| [[Category:Computational chemistry]]
| |
| [[Category:Theoretical chemistry]]
| |
| [[Category:Potentials]]
| |
Many persons have this habit of doing all of the stuff by themselves, regardless of how important or simple they are! These people won't allow others interfere inside their matters. While this stance can work in other regions of existence, it is actually really not how to answer whenever you want to fix the Windows registry. There are some jobs like removing spywares, virus in addition to obsolete registry entries, that are best left to expert softwares. In this particular article I will tell we why it is important to fix Windows registry NOW!
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The initially thing you should do is to reinstall any system that shows the error. It's typical for several computers to have certain programs that require this DLL to show the error whenever we try plus load it up. If you see a certain program show the error, we must initially uninstall that program, restart a PC plus then resinstall the system again. This must replace the damaged ac1st16.dll file plus cure the error.
Maybe you're asking how come these windows XP error messages appear. Well, for we to be able to recognize the fix, you must initially know where those mistakes come from. There is this software called registry. A registry is software that shops everything on a PC from a normal configuration, setting, information, plus logs of escapades from installing to UN-installing, saving to deleting, and a lot more alterations we do in the system pass by it plus gets 'tagged' and saved because a easy file for healing purposes. Imagine it because a big recorder, a registrar, of all the records in your PC.
A registry cleaner is a program which cleans the registry. The Windows registry usually gets flooded with junk data, info which has not been removed from uninstalled programs, erroneous file organization plus additional computer-misplaced entries. These clean small system software tools are quite usual today and we can find many good ones found on the Internet. The advantageous ones provide you option to keep, clean, update, backup, and scan the System Registry. When it finds supposedly unwanted ingredients in it, the registry cleaner lists them and recommends the user to delete or repair these orphaned entries and corrupt keys.