Hauptvermutung: Difference between revisions
en>DexDor →External links: rm Terminology cat (the title may be a term, but the article is not about language) |
en>MetaplecticGroup No edit summary |
||
| Line 1: | Line 1: | ||
{{Merge |Car-Parrinello_Molecular_Dynamics |date=June 2012}} | |||
The '''Car–Parrinello method''' is a type of [[ab initio]] (first principles) [[molecular dynamics]], usually employing periodic [[boundary conditions]], planewave [[basis set (chemistry)|basis set]]s, and [[density functional theory]], proposed by [[Roberto Car]] and [[Michele Parrinello]] in 1985, who were subsequently awarded the [[Dirac Prize|Dirac Medal]] by [[ICTP]] in 2009. | |||
In contrast to [[Born–Oppenheimer approximation|Born–Oppenheimer]] [[molecular dynamics]] wherein the nuclear (ions) degree of freedom are propagated using ionic forces which are calculated at each iteration by approximately solving the electronic problem with conventional matrix diagonalization methods, the Car–Parrinello method explicitly introduces the electronic degrees of freedom as (fictitious) dynamical variables, writing an extended [[Lagrangian]] for the system which leads to a system of coupled [[equations of motion]] for both ions and electrons. In this way an explicit electronic minimization at each time step, as done in Born-Oppenheimer MD, is not needed: after an initial standard electronic minimization, the fictitious dynamics of the electrons keeps them on the electronic [[Ground State|ground state]] corresponding to each new ionic configuration visited along the dynamics, thus yielding accurate ionic forces. In order to maintain this [[Adiabatic process (quantum mechanics)|adiabaticity condition]], it is necessary that the fictitious mass of the electrons is chosen small enough to avoid a significant energy transfer from the ionic to the electronic degrees of freedom. This small fictitious mass in turn requires that the equations of motion are integrated using a smaller time step than the one (1–10 fs) commonly used in Born–Oppenheimer molecular dynamics. | |||
==Fictitious dynamics== | |||
===Lagrangian=== | |||
:<math> | |||
\mathcal{L} = | |||
\frac{1}{2}\left(\sum_I^{\mathrm{nuclei}}\ M_I\dot{\mathbf{R}}_I^2 + \mu\sum_i^{\mathrm{orbitals}}\int d\mathbf r\ |\dot{\psi}_i(\mathbf r,t)|^2 \right) | |||
- E\left[\{\psi_i\},\{\mathbf R_I\}\right], | |||
</math> | |||
where ''E''[{''ψ<sub>i</sub>''},{'''R'''<sub>''I''</sub>}] is the Kohn–Sham energy density functional, which outputs energy values when given Kohn–Sham orbitals and nuclear positions. | |||
===Orthogonality constraint=== | |||
:<math> | |||
\int d\mathbf r\ \psi_i^*(\mathbf r,t) \psi_j(\mathbf r,t) = \delta_{ij}, | |||
</math> | |||
where ''δ<sub>ij</sub>'' is the [[Kronecker delta]]. | |||
===Equations of motion=== | |||
The equations of motion are obtained by finding the stationary point of the Lagrangian under variations of ''ψ<sub>i</sub>'' and '''R'''<sub>''I''</sub>, with the orthogonality constraint. | |||
:<math> | |||
M_I \ddot{\mathbf R}_I = - \nabla_I \, E\left[\{\psi_i\},\{\mathbf R_J\}\right] | |||
</math> | |||
:<math> | |||
\mu \ddot{\psi}_i(\mathbf r,t) = - \frac{\delta E}{\delta \psi_i^*(\mathbf r,t)} + \sum_j \Lambda_{ij} \psi_j(\mathbf r,t), | |||
</math> | |||
where Λ<sub>''ij''</sub> is a Lagrangian multiplier matrix to comply with the orthonormality constraint. | |||
===Born–Oppenheimer limit=== | |||
In the formal limit where ''μ'' → 0, the equations of motion approach Born–Oppenheimer molecular dynamics. | |||
==See also== | |||
*[[Computational chemistry]] | |||
*[[Car–Parrinello Molecular Dynamics]] | |||
*[[List of quantum chemistry and solid state physics software]] | |||
==References== | |||
* {{Cite journal|doi=10.1103/PhysRevLett.55.2471|title=Unified Approach for Molecular Dynamics and Density-Functional Theory|year=1985|last1=Car|first1=R.|journal=Physical Review Letters|volume=55|issue=22|pages=2471–2474|pmid=10032153|last2=Parrinello|first2=M|bibcode = 1985PhRvL..55.2471C }} | |||
* {{Cite journal|doi=10.1103/PhysRevLett.98.066401|title=Efficient and Accurate Car-Parrinello-like Approach to Born-Oppenheimer Molecular Dynamics|year=2007|last1=Kühne|first1=Thomas|last2=Krack|first2=Matthias|last3=Mohamed|first3=Fawzi|last4=Parrinello|first4=Michele|journal=Physical Review Letters|volume=98|issue=6|arxiv = cond-mat/0610552 |bibcode = 2007PhRvL..98f6401K }} | |||
* {{Cite book|url=http://www.fz-juelich.de/nic-series/Volume3/marx.pdf|first1=Dominik|last1= Marx |first2= Jurg |last2=Hutter |year=2000 |chapter= Ab initio molecular dynamics: Theory and Implementation|title=Modern Methods and Algorithms of Quantum Chemistry |editor-first=J.|editor-last= Grotendorst |publisher= John von Neumann Institute for Computing|location= Julich|series= NIC Series|volume=1|isbn= 3-00-005618-1|pages=301–449}} | |||
{{DEFAULTSORT:Car-Parrinello method}} | |||
[[Category:Molecular dynamics]] | |||
[[Category:Density functional theory]] | |||
Revision as of 11:23, 11 May 2013
2011 Acura TSX Sport Wagon-There are just some of us all around who would never drive an suv or a minivan but need something practical for family duties. The Acura TSX is one in all my favorite cars in sedan form but I felt that the wagon deserved special mention for bringing luxury, style, class and driving fun into the family transportation segment.
When my hubby brought this finding to the eye of the Ft. Wayne Indiana Toyota dealer, i was told that they would look into the matter. After wasting 7 days before actually doing everything to change this lease, i was told exercises, diet tips too newer. The salesman never offered us this wonderful deal, and the sales manager told us their dealership gave us the best deal toyota tundra off road they would probably. In the same sentence the sales team leader told us we qualified for the cheaper offer. In all honesty they didn't give us the cheapest price they can have. They gave us the highest lease price we were willing with regard to. My credit score is excellent, but it wouldn't have designed a difference for this dealership. After we had shopped around precisely what you want our lease, we might have definitely got a new better deal.
Now, Certain understand why Toyota doesn't offer the SE with rear seat DVD entertainment since most parents discovered that to be an indispensible feature nowadays. Besides that toyota tundra tuning the 3.5 liter V6 emits a lion-like and throaty roar under heavy acceleration that your call don't expect from a clever minivan. Do note I did not have a chance to drive a car the 2011 Honda Odyssey yet when I had the outcome might happen to different. We'll see this year.
Brian Ickler will make his begin of 2011 in the Kyle Busch Motorsports #18 Dollar General Toyota Tundra at Texas Motor Speedway on Friday, June 10. The WinStar World Casino 400K is being run when partnered with the IZOD IndyCar Series Twin 275s on Saturday, June eleventh.
The level came when he was a college junior. He'd just won the co-angler division for this 1994 Bassmaster Top 100 on Lake Norman. Diet plans . only or even bass tournament he'd ever entered.
16-year-old Erik Jones brought home his second top finish because many races in the absolutely no. 51 SUV for Kyle Busch Motorsports, finishing ninth in Sunday's NC Education Lottery 200 at Rockingham Speedway. Jones started at the tail-end belonging to the field in 36th, dropping a lap early along. The "lucky dog" award put him back with the lead lap, and Jones climbed in the top 10 in morrison a pardon stages belonging to the 200-lap race, which was won by Kyle Larson.
Another disadvantage in the Platinum package continually that it adds more chrome trim with regard to an exterior overburdened with it and forces Toyota to stoop a new low no Japanese truck maker has ever gotten to. Yes, the Tundra Platinum comes standard with chrome wheels. They are as tacky just like the optional Red Rock Leather (that really looks orange) and the cheesy half wood/half leather steering interior.
Then either the CrewMax Limited Platinum Package which pulls out all of the stops with vented and heated seats, wood grain style trim and a sunroof. Three cab sizes can be had - regular, double and CrewMax. The Tundra also has three wheelbase and bed lengths. Quite a few options? Not what this means you can build ultimate truck, get style, performance and practicality and always be able to cover it.
The Car–Parrinello method is a type of ab initio (first principles) molecular dynamics, usually employing periodic boundary conditions, planewave basis sets, and density functional theory, proposed by Roberto Car and Michele Parrinello in 1985, who were subsequently awarded the Dirac Medal by ICTP in 2009.
In contrast to Born–Oppenheimer molecular dynamics wherein the nuclear (ions) degree of freedom are propagated using ionic forces which are calculated at each iteration by approximately solving the electronic problem with conventional matrix diagonalization methods, the Car–Parrinello method explicitly introduces the electronic degrees of freedom as (fictitious) dynamical variables, writing an extended Lagrangian for the system which leads to a system of coupled equations of motion for both ions and electrons. In this way an explicit electronic minimization at each time step, as done in Born-Oppenheimer MD, is not needed: after an initial standard electronic minimization, the fictitious dynamics of the electrons keeps them on the electronic ground state corresponding to each new ionic configuration visited along the dynamics, thus yielding accurate ionic forces. In order to maintain this adiabaticity condition, it is necessary that the fictitious mass of the electrons is chosen small enough to avoid a significant energy transfer from the ionic to the electronic degrees of freedom. This small fictitious mass in turn requires that the equations of motion are integrated using a smaller time step than the one (1–10 fs) commonly used in Born–Oppenheimer molecular dynamics.
Fictitious dynamics
Lagrangian
![{\displaystyle {\mathcal {L}}={\frac {1}{2}}\left(\sum _{I}^{\mathrm {nuclei} }\ M_{I}{\dot {\mathbf {R} }}_{I}^{2}+\mu \sum _{i}^{\mathrm {orbitals} }\int d\mathbf {r} \ |{\dot {\psi }}_{i}(\mathbf {r} ,t)|^{2}\right)-E\left[\{\psi _{i}\},\{\mathbf {R} _{I}\}\right],}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32f5f677a70b944112a892d1c917600387172f32)
where E[{ψi},{RI}] is the Kohn–Sham energy density functional, which outputs energy values when given Kohn–Sham orbitals and nuclear positions.
Orthogonality constraint
where δij is the Kronecker delta.
Equations of motion
The equations of motion are obtained by finding the stationary point of the Lagrangian under variations of ψi and RI, with the orthogonality constraint.
![{\displaystyle M_{I}{\ddot {\mathbf {R} }}_{I}=-\nabla _{I}\,E\left[\{\psi _{i}\},\{\mathbf {R} _{J}\}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93b6b4c232308a6ba65a718f8f80b12f046942df)
where Λij is a Lagrangian multiplier matrix to comply with the orthonormality constraint.
Born–Oppenheimer limit
In the formal limit where μ → 0, the equations of motion approach Born–Oppenheimer molecular dynamics.
See also
- Computational chemistry
- Car–Parrinello Molecular Dynamics
- List of quantum chemistry and solid state physics software
References
- One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534