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In what could be considered as Manna from Heaven, the Economic Confidential magazine gathered how a total sum of $1 billion was shared from Excess Crude Oil Savings Account among the tiers of government on the eve of New Year 2011.
The commissioners of finance from states and their accountants general were suddenly invited to attend an Emergency Meeting of the Federation Account Allocation Committee (FAAC) on December 31, 2010 were the allocation was shared in a foreign currency, US Dollar. The meeting came about two week after the December Allocation of over N500billions were shared and just about two week to the next meeting in January 2011 for another monthly disbursement.
There are no convincing reasons for the dollarized allocation when the country's legal tender is Naira. Apart from the constitutional implication of promoting a foreign currency against local legal tenders which could trigger off inflation and turn Naira notes to worthless tissues, the release of the amount few weeks to primaries of political parties in Nigeria called for concern.
At the meeting, it learnt that the governors mounted pressure on the President to release the money so they can "tackle the huge infrastructure deficit" in their states.
The Chairman of the FAAC who is also Finance Minister of State, Hajiya Yabawa Wabi, said the fund was disbursed for beneficiaries to execute capital projects.
The lowest recipients as revealed in the table below are Ebonyi $8mn, Gombe $8.3mn, Nasarawa $8.3mn, and Ekiti $8.4mn. The Economic Confidential can also confirm other disbursements from this special dollar allocation in December 2010: Federal Government $458mn, and FCT Councils $1.5mn.


text:
Iran arrests some people over airliner downing
TEHRAN: Iranian judiciary's spokesperson announced on Tuesday that authorities have arrests a few people in connection to the downing of a a Ukrainian passenger jet in Tehran last week.
"Extensive investigations have been carried out and some people have been arrested," judiciary spokesman Gholamhossein Esmaili told a televised news conference. The spokesperson did not specify how many people were arrested.
The arrests are the first to have been announced since the Ukraine International Airlines plane was brought down by a missile shortly after takeoff from Tehran before dawn on Wednesday.
After initially denying Western claims it was shot down, Iran came clean on Saturday and admitted the plane had been brought down by a missile.
The Revolutionary Guards' aerospace commander Brigadier General Amirali Hajizadeh accepted full responsibility, but said the missile operator who opened fire had been acting independently.
Also read: Punish those responsible for downing plane, pay compensation: Ukraine to Iran
"Numerous investigations have been conducted in this area and every night our judicial team has been seeking documents until midnight," said Esmaili.
"Suggestions have been made so far but we have to weigh all the dimensions to get to the truth," the judiciary spokesman added.
His statement came shortly after President Hassan Rouhani said everyone responsible for the tragedy must be punished for the incident that has sparked angry protests in Iranian cities.
The air disaster claimed the lives of all 176 passengers and crew on board, most of them Iranians and Canadians.
Photo: File

redpajama_set_name: RedPajamaCommonCrawl


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"Shorelines: Where We Live, Work, & Play." That's a charming little title for the recent "Friends" countywide mailer but I think there's something fishy about it. The evidence is clear that the "Friends" don't want people living, working, or playing, near the shoreline. They seek to control all human activity near the water while at the same time telling us how much they support it. What they say and what they do are very different.What do they say about local tourism?"Protecting our shorelines is good for our economy and our environment. Our visitors contributed over $158.5 million to our local economy last year," said Stephanie Buffum, Executive Director of "FRIENDS" of the San Juans.It sounds like they support tourism, right?
Not really. The "Friends" have recently taken up a fight to cripple island tourism by challenging permits at a Lopez Island resort for a modest expansion (see below). Like Rosario or Roche Harbor, small-scale island resorts benefit the local economy in many ways not the least of which is bringing customers that spend money and increase the tax base.
Do they really care about contributions to the local economy from tourism? Not according to what they do. They have undermined the whale watch industry by supporting the closure of the west side of San Juan to all boats (including kayaks). Does this sound like they support working and playing near the shore?
It makes no sense unless you understand the philosophy behind it. Here it is in a nutshell; they feel it is their duty to save the world from idiot hominids. If you believe humans are part of the natural world and you just want to live, work, or play here, they need to protect the islands from you. Of course the "Friends" are the enlightened hominids that obviously know the secrets of the natural universe. The enlightened ones must control all residential activity by the lesser hominids before the sea rises and the earth is destroyed.
At least they'll excuse us for living won't they? Not really. They'd rather we just go away.
The "Friends" goal seems to be restricting all human interaction with the environment. They support large "no-touch" buffers to keep people away from the shoreline and they're twisting the arms of legislators to impose them.
Each new regulation is another tool in the "no growth" toolbox that their attorneys can use to run up the cost and complexity of building a single family home. This is the strategy that they have used to stop growth. Jobs mean growth and growth is bad. The result of all this regulation is making the construction of a home only affordable to those few that can navigate the expensive, arbitrary, and unpredictable regulatory schemes.
The truth is that they don't want us idiot hominids to "live, work, and play" anywhere near the shoreline! Watch what they do not what they say.


GIMP (GNU Image Manipulation Program) is a free, downloadable image-editing tool that is perfect for creating a banner for your Etsy shop. GIMP is also great for performing essential image-editing tasks like resizing, editing, and cropping. You can even use it for more advanced purposes, such as adjusting levels and the like.
Click File and choose New.
The Create a New Image dialog box opens.
Type 760 in the Width field, 100 in the Height field, and choose Pixels in the drop-down list.
Whatever program you use, the key to creating a banner is ensuring that it's cropped correctly to fit properly on your Etsy shop page. All banners must be 760 pixels wide and 100 pixels high.
GIMP creates a new image in the dimensions you specified.
Using the program's various tools, create your banner.
For guidance using GIMP's various features, see the program's help information; just click Help at the top of the screen.
To save your banner, click File and choose Save As.
The Save Image dialog box opens.
In the Name field, type a descriptive name for your banner file.
If you want to save your banner file somewhere other than the folder shown, click the plus sign next to the Browse for Other Folders entry, and then locate and select the folder where you want to save the file.
Click the plus sign next to the Select File Type (By Extension) entry, and then locate and select the JPEG Image option.
If your image contains multiple layers or any transparency, GIMP prompts you to export your file.
GIMP prompts you to select a compression setting.
Drag the Quality slider all the way to the right, for maximum image quality; then click the Save button.
GIMP saves your banner file in the folder you chose.
If you're no Rembrandt, why not let the pros take over and invest in a professionally designed custom banner? Many talented designers offer this service from their own Etsy shops. Try searching Etsy for "Etsy shop banner" and see what comes up.


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P.E.I.'s deep-water well moratorium should include all uses: standing committee
Stu Neatby ([email protected])
A farmer in Queens county irrigates his field. - File
Recommendations from a legislative standing committee tasked with examining water extraction on P.E.I. make no direct mention of a proposed research project that would examine the impacts of the wells on streams.
A report from the standing committee on natural resources and environmental sustainability, tabled in the legislature, contained seven recommendations to government, five of which concerned high-capacity wells.
Notably absent were any recommendations about whether government should permit a research project aimed at providing hard data on the environmental impact of high-capacity wells.
The project was proposed by UPEI researcher Michael van den Heuvel, who spoke before the standing committee in September. The four-year project would involve the construction of four high capacity wells in order to study their impacts on stream flows.
If allowed, researchers would need to obtain an exemption from an existing moratorium on new high-capacity agricultural wells.
Committee chairman Cory Deagle said committee members need more information about the proposed research. The project would be partly funded by industry groups, including Cavendish Farms and the P.E.I. Federation of Agriculture.
P.E.I. MLA Cory Deagle stands in the legislature in this file photo. - File
"That's the elephant in the room is this research project," Deagle told The Guardian in an interview. "I think we would like to see the terms of reference for any research project before it goes forward."
After an exceptionally dry growing season over the summer, some farming organizations have called for a lifting of the moratorium on agricultural high-capacity wells.
The P.E.I. Federation of Agriculture (PEIFA) has urged government to allow the research project to go ahead.
In a presentation before the committee in September, PEIFA executive director Ron Maynard spoke highly of van den Heuvel's past research.
"His team is impeccable; his research will be the same. Allow him to provide proof or disprove the current science. Give him the green light as soon as possible," Maynard told the committee.
Almost two months later, one recommendation from the committee's report was for the government to refer "all future research proposals on the impacts of high-capacity wells" to the standing committee, including detailed terms of reference.
"At the end of the day we would like to listen to science and let that dictate to us what we should do," Deagle said.
The report recommended government immediately proclaim the Water Act, a bill passed almost three years ago, which would regulate the construction of high and medium-capacity wells.
The committee also recommended maintaining the moratorium on high-capacity wells for agricultural use but recommended including new wells built for non-agricultural purposes under the moratorium. Wells built for residential or municipal use would be exempted.
This recommendation was in response to claims from agricultural groups that the moratorium was discriminatory, as other businesses, such as golf courses or car washes, can build new high-capacity wells.
"We wanted to make sure that if there's a moratorium on agriculture, it should be a moratorium for all sectors, not just agriculture," Deagle said.
The committee also recommended shortening the period of time allowed for bringing an out-of-compliance well to compliance from five years to two and recommended regulations that differentiated between wells requiring freshwater with those that draw saltwater.
Another recommendation called for the Department of Agriculture work with the province's climate change secretariat to research ways that farmers could be compensated for carbon that is sequestered in soil.
A final recommendation urged government to implement a training session for all MLAs on the Lands Protection Act.
Stu Neatby is the political reporter for The Guardian.
Twitter.com/stu_neatby
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Alex Cross must confront a criminal from his past before his master plan to frame him succeeds, in the latest instalment to the bestselling series by James PattersonCould a ghost from his past take everything away from Alex Cross?Mere hours after witnessing the execution of a killer he helped put behind bars, Alex Cross is called to the scene of a copycat murder. A note signed 'M' rests on the corpse: 'You messed up big time, Dr. Cross.'Was an innocent man just put to death? As the executed convict's family launch a vicious campaign against Cross, his abilities as a detective are called into question.The enigmatic 'M' lures Cross out of Washington, DC to the sites of multiple homicides, all marked with distressingly familiar details that conjure up decades-old cases and Cross family secrets.Details that make it clear M is after a prize so dear that – were the killer to attain it – Cross's life would be destroyed.
James Patterson is one of the best-known and biggest-selling writers of all time. His books have sold in excess of 385 million copies worldwide. He is the author of some of the most popular series of the past two decades – the Alex Cross, Women's Murder Club, Detective Michael Bennett and Private novels – and he has written many other number one bestsellers including romance novels and stand-alone thrillers.James is passionate about encouraging children to read. Inspired by his own son who was a reluctant reader, he also writes a range of books for young readers including the Middle School, I Funny, Treasure Hunters, Dog Diaries and Max Einstein series. James has donated millions in grants to independent bookshops and has been the most borrowed author of adult fiction in UK libraries for the past eleven years in a row. He lives in Florida with his wife and son.
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Business Mentors
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The company was a second generation family business. The son purchased the company and immediately brought in Business Mentors to help add infrastructure and growth.
The company was primarily known for construction. They had just purchased a cleaning company, but did not have a steady flow of cleaning or water damage business.
The owner was engaged in the company but looking for direction and leadership skill development. The company was not making money and had cash flow challenges. Very little marketing activity was occurring and the company did not have an identifiable brand in the market.
Many of the decisions and much of the strategy was very reactive and little strategic planning was occurring.
The company re-branded and developed a significant water damage and cleaning department. Total revenue has more than tripled and a 8,000 SF addition was added to the facility. Gross margins and net margins have significantly improved. A new satellite office was added. The company re-branded from the marketing promotional material to the logo and even the company name was adjusted to reflect the new emphasis on cleaning and water damage. A general manager was appointed and the owner started working on big picture activities. In addition to the revenue growth, the company achieved very strong profitability. This company became the strongest performer in a competitive environment with work coming from many different sources. The company implemented many new systems and procedures. They now are a very proactive company that performs annual strategic planning meetings in order to guide daily decisions and adjust the plan as needed. Strong financial reporting and quantifiable measurements are used to manage performance and communicate expectations.
When you work with Business Mentors you will have the confidence that you know where you're going and can move forward with conviction.
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Bee keeping among the Boni who live in Lamu County has totally collapsed following a prolonged government ban from accessing the Boni forest for security reasons.
The Boni, who are the major honey producers in the county, are now languishing in poverty after their main source of livelihood was affected by the ongoing multi-agency security Operation Linda Boni which has been denying them access to their ancestral forest.
The operation was launched in September 2015 with the aim of flushing out Al-Shabaab militants believed to be hiding inside the dense forest.
Following the operation, the Boni, who are traditionally hunters and gatherers, have not been allowed to proceed with their activities, a move which they say has directly affected their lives.
They can no longer harvest honey, wild fruits gathering or even go hunting.
Speaking to the Nation in Basuba, Milimani, Mangai, Mararani and Kiangwe villages, all of which are within Boni Forest, the residents said they are unable to do bee keeping in their villages due to the many restriction that have been imposed since the security operation started four years ago.
Musa Tete, a bee keeper from Milimani, said apart from the restriction from accessing Boni Forest, most of them had to quit the trade due to lack of market for their honey.
Mr Tete said the frequent Al-Shabaab attacks that have been witnessed in the region between 2014 and 2018 forced many of their customers who used to drive from various parts of the country to buy honey in bulk from them no longer do so.
"It's in the forest where we place our beehives. We still use the traditional methods of beekeeping. It's unfortunate that the government has denied us access to the forest and many of us were discouraged and quit the trade. Terrorism has also robbed us of our major customers who used to travel from far to buy honey in bulk from us. That no longer happens. Beekeeping is now a thing of the past among the Boni," said Mr Tete.
In 2016, the Boni complained that thousands of litres of honey were getting spoilt daily in their villages since they had no ready market for it.
Mr Suleiman Abdi said such frustrations also contributed the Boni to leave the venture and engage in modern farming.
Mr Abdi called on the national government to consider allowing the Boni to access the forest.
"Immediately after the introduction of the Linda Boni operation, our forest was declared a no-go zone by the Kenya Defence Forces (KDF). Four years have now passed and we are told normalcy has been restored. We are therefore urging the government to allow us to venture into the forest. We want to revive bee keeping in our villages but that can only happen if we are allowed to access the forest," said Mr Abdi.
Mr Doza Diza, a Boni elder, said the insecurity in Basuba Ward resulted to some well-wishers who used to sponsor beekeeping ventures to stop.
In 2015 for example, the Wild Wide Fund for Nature (WWF) purchased 90 modern beehives to facilitate modern honey farming for the Boni.
Mr Doza says they no longer receive such aid as almost all well-wishers have shied away from the region.
"Insecurity has dealt us a blow. We used to receive assistance from various non-governmental organisations but since insecurity incidents started in this region, many of the well-wishers have kept off," said Mr Doza.


In Russia's isolated and remote region of Siberia, an underground economic boom is taking shape. Radio Free Europe photographer Amos Chapple, back in 2016, went inside the dark world of the Russian men illegally mining for tusks and remains of the long-extinct woolly mammoth, in hopes of cashing in on black market trade. The images he captured show a compelling cycle of toil, desperation, and environmental consequence.
Woolly mammoths, lost arctic relatives of the modern elephant, are thought to have lived in Siberia about 400,000 years ago. The area now experiences year-round permafrost, a thick layer of ice beneath the ground, which has helped to preserve submerged mammoth skeletons for millennia. In order to reach the buried treasures of this hostile land, the men seeking it have to blast the thick, icy mud with water pumped from nearby rivers, which can take months on end. It's a dangerous, illegal, and taxing job, but with mammoth tusks selling at around $35k a piece to eager Chinese buyers, it's a worthwhile risk to men coming from cities where the average monthly wage is under $500.
It's not all diamonds and glory, however. The men setting out on tusk hunts leave their families behind to brave rugged terrain, hoards of mosquitoes, and constant fear of detection by police, which could result in fines or jail sentences. They guzzle quarts of vodka and cheap beer to cope with the ordeal, leading to frequent fights among miners. Perhaps worst of all is the toll their work takes on the environment; the run-off water from the frozen earth they douse returns to the surrounding rivers, polluting water streams and raising silt levels dramatically.
Take in the entire series below, accompanied by Chapple's own commentary as written in his RFE article, and witness the plight of men craving to get rich, and willing to die trying.


text:
Q: how to split a string in javascript
Possible Duplicate:
How do I split this string with JavaScript?

how to split a string in javascript?
example str = "this is part 1 one wall this is part 2 "
now I want to split the str in 2 parts separated by word wall
so I want output to be:
st1 ="this is part 1 "
st2 ="this is part 2 "

A: Just for the sake of completeness, I'll add a regular expressions answer:
var splits = str.split(/wall /);
alert("'"+splits[0]+"'"); //'this is part 1 '
alert("'"+splits[1]+"'"); //'this is part 2 '

A: var str1 = "When I say wall I want to split";
var chunks = str1.split("wall");

alert(chunks[0]); /* When I say */
alert(chunks[1]); /* I want to split */

A: var parts = str.split('wall ');

var st1 = parts[0];
var st2 = parts[1];

A: String.split

A: var s = str.split("wall");
var st1 = s[0];
var st2 = s[1];

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}

The $4d-5d$ transition metal (TM) compounds attract considerable attention in recent years. For example, a new Mott state described by the effective total angular momentum J$_{eff}$=$1/2$  and induced by relativistic spin-orbit coupling was found in  $5d$ transition metal oxide Sr$_2$IrO$_4$ \cite{2008prl}. Another interesting effect thoroughly studied nowadays is a possible realization of the so-called Kitaev model \cite{kitaev} on hexagonal lattices, where nearest neighbor exchange Hamiltonian has a form $J\sum_{ij} \vec S^{\alpha}_i \vec S^{\alpha}_j$, where along each of metal-metal bonds only one spin projection $\alpha=x,y,z$ enters \cite{2009prl}.

Going from the $3d$ to $4d$ and $5d$ transition metal compounds, we not only start to deal with more heavy elements, which implies stronger spin-orbit coupling, but also gradually decrease the on-site Coulomb repulsion (characterized by $U$ parameter) and simultaneously increase spacial extension of $d-$wavefunctions \cite{Khomskii2014}. This drives $4d$ and $5d$ systems to a regime where hopping parameters $t_{ij}$ are comparable with the on-site Hubbard repulsion $U$. Such a growth of $t_{ij}$ is especially pronounced in dimerized systems, where this effect may result in an orbital-selective behavior, when only a part of the $d-$electrons bear magnetic moments, while others form molecular-orbitals \cite{Streltsov2014}. This effect, decreasing the total magnetic moment of a system and suppressing the double exchange mechanism, was found in such systems as Y$_5$Mo$_2$O$_{12}$ \cite{Streltsov2015MISM} and Ba$_5$AlIr$_2$O$_{11}$ \cite{Streltsov2016,Terzic2015}.

In the present paper we discuss a very similar effect of the orbital-selective behavior and partial suppression of the magnetic moment in a recently synthesized niobium oxyfluoride Nb$_2$O$_2$F$_3$ \cite{Tran2015}. This compound presents a special interest, since here the orbital-selective behavior is observed together with a charge disproportionation. We argue that the mechanism of charge ordering in this system is of a novel type and is connected not with the gain of interaction energy, as in the conventional mechanisms of charge ordering,  but is rather due to the gain in kinetic (bonding) energy due to formation of tightly bound dimers.

Nb$_2$O$_2$F$_3$ crystallizes in a monoclinic structure (space group: I2/a) and undergoes a structural transition at $\sim$90K to a triclinic structure (space group: P-1) in the lower temperatures \cite{Tran2015}. The phase transition at 90K is accompanied by a strong suppression of magnetic susceptibility, which is ascribed to formation of the spin gap. Effective magnetic moment in the Curie-Weiss theory $\mu_{eff}=2.24\mu_B$ (per dimer) in the high temperature (HT) phase is much smaller than expected for Nb having nominal valence $3.5+$.  The transport measurement have been performed for $T>90$K, where Nb$_2$O$_2$F$_3$ was found to be insulating.

The Nb ions are in octahedral surrounding, and these octahedra share their edges forming Nb-Nb dimers (see Fig.~\ref{cryst.str}). There is one type of such dimers in the HT phase with crystallographically equivalent Nb ions and each Nb having $3.5+$ charge state (electronic configurations $4d^{1.5}$). The transition at $\sim$90K results in a strong modification of the crystal structure. There appears two inequivalent types of Nb and each of them form its own type of dimers: ``short'' Nb1-Nb1 (2.50\AA) and ``long'' Nb2-Nb2 (2.66\AA) dimers. The difference in Nb-Nb bond distances was proposed to be a signature of charge disproportionated state with Nb1 being in the $3+$ (electronic configurations $4d^{2}$) and Nb2 in the $4+$ (configurations $4d^1$) charge states. The origin of the phase transition at 90K is unclear and demands thorough investigation, which we carry out in this paper using ab-initio band structure calculations.
\begin{figure}[!b]
\begin{center}
\includegraphics[angle=0,width=0.5\columnwidth]{Nb2O2F3-str}
\end{center}
\caption{\label{cryst.str} Crystal structure of Nb$_2$O$_2$F$_3$ (generated by the Vesta software \cite{vst}). Niobium ions are in the octahedra formed by oxygen (red balls) and fluorine (grey balls).}
\end{figure}

\section{Calculation details}
For the band-structure calculations the pseudopotential PWscf code \cite{pwscf} was mainly used. We utilized the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof version of the exchange-correlation potential \cite{pbe} and ultrasoft scalar-relativistic pseudopotentials with nonlinear core correction. The charge density and kinetic energy cutoffs were taken as 40 Ry and 180 Ry, respectively. The mesh of 6x6x6 $k$-points in a full Brillouin zone was used in the calculation.

In order to estimate the crystal field splitting parameters, the Wannier function projection method \cite{Streltsov2005} was used as realized in the linearized muffin-tin orbitals (LMTO) method \cite{lmto}.

All parameters in the paper for both LT (low temperature) and HT (high temperature) phases were calculated with using of experimentally obtained structures \cite{Tran2015}.

\section{Magnetic properties}
We start with the analysis of the nonmagnetic GGA calculation results for the HT monoclinic phase. Since this approximation does not take into account strong on-site Hubbard repulsion \cite{gga+u}, Nb$_2$O$_2$F$_3$ is metallic in this type of calculations with the Nb $t_{2g}$ states forming both valence and conduction bands. The absence of a band gap is a standard drawback of the GGA method, which can be corrected by such methods as LDA/GGA+U \cite{gga+u} or LDA+DMFT \cite{Anisimov97}. In spite of this fact, GGA/LDA is known to be accurate for the
estimation of the on-site energies and hopping parameters, which are of most interest for us here.

We calculated these parameters (hopping integrals and crystal-field splitting) using so-called Wannier function projection procedure. In the edge-sharing geometry there are $xy-$orbitals pointing exactly to each other in the Nb-Nb dimer (we use notations of local coordinate system, where $x$ and $y$ axis are directed to common ligands in a dimer). This results in a strong bonding-antibonding splitting, $\sim 3.3$ eV, see Fig.~\ref{hoppings}. The energy difference between the bonding $xy$ and next (higher in energy) orbitals is $\Delta =$1.1 eV. Using ionic approximation and neglecting on-site Coulomb repulsion one may expect that for a Nb-Nb dimer with 1.5 electrons per site the state with maximal spin $S_{tot}=3/2$ will be stabilized, if $\Delta < J_H/2$, where $J_H$ is the intra-atomic Hund's exchange, but smaller net spin would exist in the opposite case \cite{Streltsov2014,Streltsov2016}.
\begin{figure}[t]
\begin{center}
\includegraphics[angle=0,width=0.9\columnwidth]{1}
\end{center}
\caption{\label{hoppings} Formation of the molecular orbitals: (a) in the high temperature and (b) in the low temperature phases, as obtained in of the Wannier function projection method in frames of the LMTO method.}
\end{figure}

We estimated $J_H$ in Nb$_2$O$_2$F$_3$ using the so-called constrained supercell method \cite{Anisimov1991} in the LMTO calculations and found that $J_H = 0.7$ eV. Since the bonding-antibonding splitting is much larger than $J_H/2$, the state with minimal total spin $S_{tot}=1/2$ per dimer is realized in the HT phase of Nb$_2$O$_2$F$_3$, see the level scheme in Fig.~\ref{hoppings}. This state is orbital-selective, since $xy$ orbitals behave here as nonmagnetic molecular-orbital like, while $xz/yz$ orbitals provide local magnetic moment.

The ferromagnetic GGA calculations, results of which are presented in Fig.~\ref{DOS}a, show that total magnetic moment is $\mu = 1 \mu_B$ per formula unit (f.u.). This state corresponds to $\mu_{eff} = \sqrt{3} \mu_B$ (per dimer), which is of the order of value observed experimentally \cite{Tran2015}. The bonding and antibonding $xy$ bands are at $\sim -1$ eV and $\sim 3.5$ eV, while remaining peaks in vicinity of the Fermi energy correspond to the $xz$ and $yz$ orbitals.
\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=0.48\columnwidth]{DOS_PWSCF_mn_FM}
\includegraphics[angle=-90,width=0.48\columnwidth]{DOS_PWSCF_tr_NM}
\end{center}
\caption{\label{DOS} Total and partial densities of states (DOS) for the  high-temperature (HT) monoclinic phase (a) and low-temperature (LT) triclinic phase (b) obtained in the GGA calculation. Only nonmagnetic solution survives in the LT phase, while for the HT phase the results for the ferromagnetic order are presented. Positive and negative values of DOS in lower panel of (a) correspond to different spin projections. The Fermi level is set zero.}
\end{figure}

The electronic structure in the low temperature (LT) phase is more complex. It was proposed that there can be charge disproportionation in this phase \cite{Tran2015}. Analysis of the hopping parameters shows that the bonding-antibonding splittings in Nb1-Nb1 dimers are even larger than in the HT phase, which is due to smaller bond distance. This is true for both $xy$ and $xz/yz$ orbitals. One may see from the partial density of states (DOS), shown in Fig.~\ref{DOS}b, that both bonding $xy$ and one of the low-lying $xz/yz$ orbitals are occupied in the Nb1-Nb1 dimer. Therefore, one may conclude that there has to be four electrons in the Nb1-Nb1 dimer and only two electrons in the Nb2-Nb2 dimer.
However, difference in L\"owdin charges (total number of $d$ electrons) \cite{Lowdin1950} for two types of Nb is minimal, $\delta n = n_{Nb1} - n_{Nb2} \sim  0.1e$. It is rather typical that the degree of charge disproportionation in a band-structure calculation turns out to be much smaller than what one would expect from formal valencies. The difference in total atomic charges or in corresponding magnetic moments in the GGA or GGA+U calculations is often an order magnitude smaller than it should formally be \cite{Streltsov2014d,Leonov2004,Pickett2014}.

It is clear that, having formally two electrons, Nb2-Nb2 dimer stays nonmagnetic since they occupy bonding $xy$ molecular orbitals. The situation with Nb1-Nb1 dimer with four electrons per dimer is more tricky. In principle one may have three different ``molecular spin-states'' in this case (4 electrons per dimer) with total spin per dimer $S_{tot}=2$, $S_{tot}=1$, and $S_{tot}=0$, and one could even expect magnetic transitions between these states as it occurs in MoCl$_4$ \cite{Korotin2016}. The final electronic configuration is determined by competition between Hund's rule coupling, given by $J_H$, and splitting between molecular orbitals of the $xz$ and $yz$ symmetry. Simple estimates in an ionic model show that these are the states with $S_{tot}=1$ and $S_{tot}=0$, which can be stabilized in the LT phase. If the splitting between bonding $xz/yz$ orbitals $\Delta_{xz/yz} > J_H/2$ (for definition see Fig.\ref{hoppings}) then $S_{tot}=0$ is realized. The Wannier function analysis shows that $\Delta_{xz/yz}=0.7$ eV, which is much larger than $J_H/2 = 0.35$ eV, i.e. for Nb1-Nb1 dimers a nonmagnetic $S_{tot}=0$ state is realized.
This is consistent both with the results of our GGA calculations, where magnetic solution does not survive in the LT phase, and with the experimental results showing nonmagnetic behavior for $T<90$K \cite{Tran2015}.

\section{Charge ordering}
We saw that the band structure calculations indeed show some degree of the charge disproportionation in the low-temperature phase of Nb$_2$O$_2$F$_3$. Generally speaking there can be many different origins of the charge ordering. The simplest one is the gain in long-range Coulomb (Madelung) energy, like in Wigner crystals \cite{Wigner1983,Hubbard1978}.  In real transition metal compounds the electron-lattice coupling (usually to the  breathing mode of MeL$_6$ octahedra, where L is a ligand ion) often plays even more important role. Sometimes orbital degrees or spin degrees of freedom may help to stabilize the charge order \cite{Khomskii2014,Solovyev1999,Streltsov2014d}.
In all these mechanisms actually the onset of the charge ordered state is related with the tendency to gain an interaction energy.
Using simple arguments we propose that the mechanism of the charge disproportionation in Nb$_2$O$_2$F$_3$ is of very different nature and is connected with the formation of the molecular orbitals in this compound, i.e. it has a two-site nature.

The bonding-antibonding splitting for the molecular orbitals in Nb$_2$O$_2$F$_3$ is defined by corresponding hopping integrals, or overlap between atomic $d-$orbitals. These hoppings are strongly nonlinear $t \sim 1 /r^5$ \cite{Harrison1999}, where $r$ is the distance in a dimer. Therefore making short and long dimers instead of two Nb-Nb dimers having the same bond length we win a lot of kinetic energy. Similar idea was used before to explain isotope effect in manganites \cite{Babushkina1998} and cobaltates\cite{Babushkina2014eng}.
Moreover, it turns out that one gains a kinetic energy not only due to the $xy-$orbitals having direct overlap in the common edge geometry. Other Nb $4d-$orbitals also contribute to lowering of the charge ordered state. One can construct molecular orbitals of the $xz/yz$ symmetry. By making a linear combination $xz+yz$ we maximize direct hopping keeping overlap via ligand $p_z$ orbital nearly the same \cite{Kimber2014}.

One may estimate the total energies of the charge ordered and homogeneous states in a simple ionic approximation using Kanamori parametrization for the Coulomb interaction \cite{Kanamori1963} and calculated with the LMTO hopping parameters. Since the Nb-Nb distance in the HT phase is nearly exactly the arithmetic mean of short and long Nb-Nb bonds in the LT phase, one may use these data to calculate the difference in hopping parameters for homogeneous (H) and charge ordered (CO) states $\delta t_{xy}$ and $\delta t_{xz+yz}$ for the $xy$ and $xz+yz$ orbitals, correspondingly. Then the total energy difference between these two states in the ionic approximation can be estimated as
\begin{eqnarray}
\delta E = E_{H} - E_{CO} = \delta t_{xy} + \delta t_{xz+yz} - U/2.
\end{eqnarray}

The direct calculation based on the results of the Wannier function analysis shows that  $\delta t_{xy}=0.8$ eV and $\delta t_{xz+yz}=1$ eV. One may expect that $U$ for Nb is smaller than 3 eV (typical value for, e.g., Ru$^{4+}$ having much larger number of electrons \cite{Lee2006}). Thus, we see that at zero temperature indeed a gain in the kinetic energy due to formation of molecular orbitals exceeds a loss in the Coulomb energy because of the charge ordering, which in its turn is even overestimated in the simple Hubbard-like treatment used above: when we take into account  $p-d$ covalency, the actual charge transfer in transition metal system with charge ordering is never complete, as was assumed in the crude estimate above,  but is   much smaller, typically near $ \pm0.2e$ \cite{Khomskii2014}. At finite temperature $T$ instead of the total energies, $E$, one has to compare free energies $F=E-TS$ and increasing temperature the entropy term will dominate, which stabilizes homogeneous state and finally leads to the transition to this state.

However, one has to note that there are two important ingredients, which we did not take into account in aforementioned model. First of all, Coulomb interaction not simply adds a penalty due to inhomogeneous charge distribution, but also modifies the wavefunctions of the corresponding states increasing contributions from the ionic terms (i.e. changing them from molecular-orbital like to Heitler-London like). This will decrease energy gain due to the formation of the molecular orbitals \cite{Streltsov2016}.

Second, there is a very important contribution due to the elastic energy, which normally stabilizes homogeneously states. This correction is not easy to estimate on a model level for such a complicated structure as in Nb$_2$O$_2$F$_3$. However, there is an extra feature of the Nb$_2$O$_2$F$_3$ crystal structure, which has to be mentioned and which helps the observed charge ordering. Dimerization of one class of Nb drives another one to change its charge state. Indeed, if, e.g., we decrease Nb1-Nb1 bond distance and want to keep Nb1 valence as it is (i.e. keep the same average Nb1-O and Nb1-F bond lengths), then oxygen ions linking Nb1-Nb1 and Nb2-Nb2 dimers should move towards Nb2 as it is shown in Fig.~\ref{Distortions}. This should lead to decrease of corresponding Nb2-O bond distance and hence to the increase of the valence of Nb2 as a result. It is interesting to note that the low temperature crystal structure of Nb$_2$O$_2$F$_3$ indeed shows this effect with shortest Nb-O bond (1.89~\AA, while other Nb2-O bond lengths are 2.03~\AA~and Nb2-F are $\sim$2.07-3.0~\AA) linking two dimers together. Thus, we see that in this sense dimerization goes hand in hand with the charge disproportionation in Nb$_2$O$_2$F$_3$. This situation actually strongly resembles that in M$_1$ and M$_2$ phases of VO$_2$ \cite{Ghedira1977,Whittaker2011,Khomskii2014}.
\begin{figure}[t]
\begin{center}
\includegraphics[angle=0,width=0.6\columnwidth]{dist}
\end{center}
\caption{\label{Distortions}  Illustration of cooperative distortions, which support formation of the charge ordered state.}
\end{figure}

\section{Summary}

To sum up, we show in the present paper that magnetic response in Nb$_2$O$_2$F$_3$ at  the high-temperatures ($T>$90 K) is related to the orbital selective regime, when part of the electrons form molecular orbitals while other electrons have local magnetic moments. The charge disproportionation, which occurs at $T\sim$90 K is seen in the GGA calculations, but its degree ($\delta n \sim 0.1$ electron) is far from what one would expect from naive expectations based on the formal ionic valences. The mechanism of the charge ordering is argued to be related with a sizable kinetic energy gain due to formation of two molecular orbitals in short Nb$^{3+}$-Nb$^{3+}$ dimers caused by a strong nonlinearity of the distance dependence on electron hopping. We think that this mechanism of charge ordering, stabilized not by decrease of  interaction energy, but rather by the gain  in kinetic energy, may be operative in many other systems, especially consisting of structural dimers.

\section*{Acknowlegments}
We are grateful to B. Lorenz for informing us of their results on Nb$_2$O$_2$F$_3$. This work was supported by Russian Science Foundation via project 14-22-00004.

\section*{References}

redpajama_set_name: RedPajamaArXiv


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