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Ludwigsburg Train Station
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Address: Pflugfelder Str. 17
71636 Ludwigsburg DE +49-8966060060
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SIXT Num. Ludwigsburg Train Station ZODC02 Pflugfelder Str. 17 71636 Ludwigsburg 48.892162, 9.183688 +49-8966060060
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Exit the train station towards Weststadt. The Sixt branch is located in the exit passage on the right-hand side.
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text:
Kitto's Popular Cyclopedia of Biblial Literature
Uriah the Hitite
Hawker's Poor Man's Dictionary
Uriah; Urijah
Scott, Uriah, D.D.
Chamberlain, Uriah Tracy
Levy, Uriah Phillips
Uriah, Urijah
ܐܽܘܪܺܝܳܐ
Οὐρίας
אורִּיָּה , אורִּיָּהוּ
Uri´ah (flame of Jehovah), a Hittite, and therefore a descendant of the ancient inhabitants of Palestine, whose name occurs in the list of the 'worthies' or champions of King David, in whose army he was an officer. He was the husband of Bathsheba; and while he was absent with the army before Rabbah, David conceived and gratified a criminal passion for his wife. The king then directed Joab to send him to Jerusalem, but failing to make his presence instrumental in securing Bathsheba from the legal consequences of her misconduct, he sent him back with a letter directing Joab to expose him to the enemy in such a manner as to ensure his destruction. This the unscrupulous Joab accomplished; and David then took the widow into his own harem (2 Samuel 11; ) [DAVID; BATHSHEBA].
Public Domain.
Kitto, John, ed. Entry for 'Uriah'. "Kitto's Popular Cyclopedia of Biblial Literature". https://www.studylight.org/encyclopedias/eng/kbe/u/uriah.html.
Urijah

redpajama_set_name: RedPajamaCommonCrawl


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Business News by Sector
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Soham inquiry chief praises Wrexham record check firm for helping save lives
Lisa Baker, Editor, North Wales Business
A former top civil servant who conducted the Soham inquiry following the horrific murders of two young schoolgirls says a North Wales criminal record checks company is helping to save lives.
The comment from Lord Michael Bichard came during a visit to Wrexham-based Disclosure Services which owes its existence to the recommendations in his landmark report.
In 2004 he was appointed by the then Home Secretary, David Blunkett, to chair an inquiry into the murders of Holly Wells and Jessica Chapman, both aged 10.
They were killed by Ian Huntley, who was a caretaker at the local secondary school, Soham Village College, in Cambridgeshire.
The main recommendation in his report was that there should be a system where anyone working with children or vulnerable people should be vetted before being allowed to work with them.
The crossbench peer was invited to Disclosure Services by one of the directors, Mario Kreft MBE, who is also the proprietor of the Pendine Park Care Organisation which has eight care homes in Wrexham and Caernarfon.
They got to know each other when they were both members of the Social Care Institute for Excellence which was chaired by Lord Bichard.
Disclosure Services was originally established 16 years ago by husband and wife team, John and Caroline Clark, when it became a legal requirement for organisations that employed people with vulnerable adults or children to undertake criminal record checks following the Soham Inquiry.
The company began carrying out disclosure and barring checks for Pendine Park who are major shareholders.
It then started providing a similar service for other care organisations and has since grown to become the seventh largest company of its kind in the UK.
Last year the firm moved from Gobowen, near Oswestry, and invested £1.5 million in its new state-of-the-art headquarters on Wrexham Technology Park where Lord Bichard also met chief executive Paul Barlow.
Lord Bichard said:
"I'm pleased my recommendations are coming to fruition. Seeing people who are clearly committed to what they are doing and being efficient in providing an effective service is really important for the safety of kids and older people so I'm delighted to see it.
"I do feel that the existence of Disclosure Services and other companies like them is saving lives
"If you get access to some of the police intelligence, you realise we are dealing with some really nasty people and they have got to be kept away from children and vulnerable old people and this is what we are doing here.
"I still think there is too much bureaucracy and that we need to adjust the system.
"For example, you can work with a young person or a child and if you can show if you are supervised you do not need an enhanced check.
"My view is in a digital world, if you work with young children, and are supervised you can still groom the kids and make approaches at weekends.
"I think everyone who works with young kids or vulnerable adults should now be subject to an enhanced check.
"Although the system is imperfect, it's a massive improvement on what it was before I chaired the Soham inquiry."
Paul Barlow said:
"We were delighted to welcome Lord Bichard because his recommendations were pretty much the birth of safeguarding as we know it today.
"Obviously what sparked all of this was a terrible tragedy when those poor little girls were murdered in such an awful way but something really important has come out of that and we are a lot better as a society because of it.
"There were some big lessons to be learned in terms of making sure that we protect vulnerable individuals and that's what Lord Bichard's recommendations have achieved.
Mr Kreft added:
"It's appropriate in a number of ways that Lord Bichard came to visit because Disclosure Services is helping to make his vision a reality.
"We're now one of the largest providers of disclosure and barring services in the UK, providing a service for leading UK businesses and charities.
"We have now launched a new service for individuals who need to have checks done and we are seeing a significant growth in the market of people who are not in regulated settings who are not dealing with vulnerable people.
"They just want to be sure that as part of a robust and thorough recruitment process that they are doing what a lot of intelligent and forward-thinking employers are now doing and that is just checking on the background of the people, particularly the criminal background, of any people who are coming into their organisation."
Previous Award-winning trainee soldier from Holyhead is the Queen's new neighbour
Next Wrexham finance firm boss scales Montenegro mountain charity challenge
Pupils and staff must isolate after confirmed Covid-19 case at Rhyl School
Denbighshire County Council
North Wales Council receives funding for Waste Reduction and Re-Use Projects
Denbighshire residents thanked for lockdown efforts
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text:
BattlePenguin
copy_reddit
eyePodify
Gentoo Update
lnSponge
oggfolder2mp3
Ruby E-Mail Script
Breaking the Multi-Colored Box
Graph Mapper
isszy
MPlayerBuddy
RearViewMirror
RSS: The Original Federated Social Network Protocol
I Want to Believe in RSS T-Shirt by Richard Stevens
In 2013, Google discontinued their Reader web application. It had become a dominant application for RSS feeds, in a time when many felt RSS was dying. After Google discontinued their terrible product, people seeking alternatives found other web applications and quickly discovered tools that weren't pieces of garbage. Readers like Feedly, Newsblur, and others, would report bad feeds and errors. Google Reader would instead silently fail, often leading people to believe their favorite bloggers had simply stopped publishing. Today, few people use RSS Readers, relying instead on liking Facebook pages, subscribing to YouTube channels or following people on Twitter. However, all of these methods are totally inadequate in relaying all potential updates between content providers and their audience. The best way to keep track of the people and content you care about is to subscribe to their RSS feeds using a good reader app, many of which work both on the web and on mobile.
Replacing Okta Verify with Open Source Software
I have owned way too many cellphones. I'd like to break free of Android without switching to iOS, but one of the applications I'm required to have for work is Okta Verify. Moving from Okta Verify to an open source solution was easier than I expected, but the path to discovering how to do so was not a simple one. The following explains how to get the secret used for Okta's multi-factor auth codes, and use it in open source alternatives to Okta Verify, as well as in Python scripts.
Every Cellphone I've Ever Owned
My Nokia 6800
I'm old enough to remember the era before cellphones. Back in high school, a group of us once planned a caving trip. We all met at the parking lot beside the tennis courts at 8am. "Where is Nick?" someone asked; Nick being the person we were waiting on. Someone took 35 cents, walked over to a payphone, and came back to us saying, "His mom said he left 30 minutes ago." Today, we don't have to blindly wait on our friends. We can send them a text, or organize outings using group chat software. Phones have drastically changed the way we plan gatherings and interact with one another, for better or for worse. Here is my personal history of cellphones, from my first black and white prepaid device, all the way up to the modern era of the Google/Apple spy devices we all carry around in our pockets.
Microservices and Biological Systems
In 2010, several researchers at Yale attempted to look at biological systems versus computer software design. As would be expected, biological systems, which evolved over millions of years, are much more complex, have a considerable amount of redundancy and lack a direct top-down control architecture as found in software like the Linux kernel. While these comparisons aren't entirely fair, considering the complexity of biology, they are a fun thought experiment. Microservices are a new-emergent phenomenon in the software engineering world, and in many ways, microservice architectures evolve in environments that are much closer to a biological model than that of carefully architected, top-down approaches to monolithic software.
Facebook and the Silent Bob Effect
In high school, I had a band director who would rarely say anything to his students which wasn't related to music, marching or directing us. When he did talk to us, typically before a big competition, all two-hundred students in our marching band would be silent and attentive. He retired my sophomore year and was replaced by another band director who loved giving us pep talks all the time, so much so that most people constantly tuned him out and ignored what he had to say.
The filmmaker Kevin Smith plays a reoccurring character, named Silent Bob, in many of his movies. Silent Bob rarely ever talks. When he does, his lines are intended to be profound or at least memorable, even if they're very simple. I rarely post on social media, unless it's to direct friends to content on my website, which I host independently. In normal social interactions, when a person doesn't talk much, more weight is often given to their words when they do. However, social networks, like Facebook and Twitter, use custom algorithms for sorting posts. Although these systems are closely guarded secrets, they seem to reward people who interact with their platforms more. People like myself, who rarely post content, often get less exposure than those who frequently interact with other users.
A History of Personal and Professional Websites
I started creating websites in the late 90s, while I was in high school. In the early 2000s, while in college, I kept a professional website with my coding and web design work, as well as a personal journal. Some time after college, I also created separate political and philosophical websites, maintaining all of them using a WordPress installation. While backpacking around the world in 2015, I migrated all my WordPress sites to Jekyll and combined their look and feel. In September of 2019, I finally unified all these independent microsites back into BattlePenguin.com, with full redirects from the former websites. The following is a history of some of these websites, and the technologies they used.
Voat: What Went Wrong?
Tenderness by Ricardo Gomez Angel
Voat is a link aggregation platform, where users can submit text or links to content, comment on existing submissions and vote both links and comments up or down. It's essentially a Reddit clone, but, due to several bad design decisions, it has become known on the rest of the Internet as a community that promotes intolerance and hate speech. Voat didn't start this way, and many of its early users were similar to those in the communities on other social networks. But due to a series of design decisions, including its contributor point systems, Voat was constructed in such a way as to converge on narrow view points and become the platform that it is today.
The Death of the Mom and Pop e-Store
Back before I first left the United States in 2012, I'd often use price comparison websites when trying to find parts for computers and system builds. These sites tracked prices from hundreds of small vendors, some of which had brick and mortar stores, others were storage warehouses, and others were simply drop shippers. Upon returning to the country, I found that most of the old comparisons sites I used were void of those smaller individual stores, replaced by less than a dozen of the big retailers. While I was away, the era of the mom-and-pop e-commerce website had ended, with most retailers now using marketplaces provided by the large players like Amazon, eBay, Newegg and others.
Rooting a Razer Phone Requires a USB 2.0 Link
I'm not one of those people that can buy a phone and start using it. I usually root my device and flash a custom ROM not long after I first turn it on. Where normal people can start using a new device immediately, it usually takes me a day or two before I can do the same, dealing with some weird edge case of missing documentation, just to get basic administration rights on my mobile device. Although Razer has official instructions for unlocking their devices, and there are many third party guides, I attempted to avoid a critical step mentioned in their documentation. Even when I followed it, I still ran into problems, and found it fascinating that Razer devices can only be flashed via a USB 2.0 link. I've documented some of my error messages here, in case anyone is confounded by similar issues.
Louqe Ghost S1 Build and Review
I had been working off of my laptop for several months, but some performance issues and thermal throttling led me to revert back to building a desktop. I had sold my previous build before traveling across the US, so for this particular build I wanted something in an ultra small, easily transportable form factor. I decided to jump in on a crowdfunding effort for the Louqe Ghost S1 ITX case. This review covers installing my system into this very compact ITX case, my first experience with water cooling and what to expect for others when considering the Ghost case.
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Copyright © 2021 Sumit Khanna


A yummy, healthy smoothie for breakfast can kick start your day positively. This is one such smoothie with loaded yumminess of mango and pistachios.
Add required water to get the consistency you desire.
You can increase or decrease the number of pistachios as per your taste.
Thank you Pia?… Welcome to my space… Keep coming ?
Thank you so much Payal?…ya..it tastes really good?
Ooohhh girl, now my mouth is watering! Yum!
I love mango smoothies, usually have mango, spinach and pineapple with chia seeds. I'm definitely adding pistachios, love those, too! Thanks for suggesting!
Thank you so much?… glad you love it… thanks for suggesting your version too??… let me know when you try it?
I am so glad to know this?… Thank you?
Thank you priya?.. glad you like it??


Welcome to the Computing Department. We have a great team of specialist teachers.
The Computing Department has dedicated computer rooms with great facilities. All computer rooms come with printers, interactive whiteboards and access to further printing using the "follow me" set up.
AQA Computer Science has been successfully introduced at GCSE level and there are two classes who are enjoying themselves. The focus of this course is programming and understanding how computers work. The alternative provision is is OCR Creative iMedia, which is a very hands on course where students can sue their creative talents to make such things as websites.
At the Foundation Stage, Year 7 and 8 have one lesson per week. The topics that we study in Year 7 are Cyber Security, Computational Thinking, Small Basic and a Website Project. In Year 8 students study Computer Systems, Networks, Python programming and Graphics.
All students complete one assessment at the end of a unit of work/complete a project to demonstrate their skills in a topic. These pieces will have a DIRT activity linked to improving their work. Homework is set once every half term, or as part of a long-term project assigned at the beginning of a term.
Homework is set weekly. Computer Science homework swaps between theory and practical programming work. Students compete using the website codecademy.com to do independent learning in Python. We encourage students to read around the topic studied, and suggest YouTube videos or news articles to support. Students are also participating in the "Scorch Trials".
Students will have a theory assessment at the end of each unit. They will have a programming assessment every 3-4 weeks.
Google Classroom is our primary vehicle for distributing homework and assessment tasks.
In Creative iMedia, homework is set weekly where students wilbe completing written and practical work. In between, students will be assigned to do research on the web and read around the topic being covered. Students will sit for a written assessment in Year 9 and a pre-public written examination (PPE) in Year 10 and/or 11. All students will be entered for the external written examination in June of Year 10 and if necessary, may retake the examination in Year 11. The remaining assessment will be coursework based where students complete three controlled assessments moderated by the exam board. Students who successfully complete all units will be awarded a Level 2 qualification overall. Grades awarded are Pass, Merit, Distinction or Distinction *.
Students are supported in Computer Science through drop-in sessions after school. They can also access the codecademy.com website for support with Python.
Creative iMedia/ICT support sessions run every Monday after school in L5 but students can speak to their teachers to arrange an agreed suitable time if they need support on other days.


Hotel Aroma, Nainital is the perfect spot for travelers who would like to enjoy outstanding natural beauty of this city. It was established in the year 1967 and situated at the tranquil woods of Ayarpata Nainital.
Hotel Aroma, Nainital is surrounded by immense Oak and Deodar tress and its distance from Naini Lake is just 300 mtrs. The hotel is listed among the best 3 start deluxe hotel in Nainital.
1. Free pick and drop facility from bus stop.
4. Car parking in hotel premises, Lawns for outdoor games and bonfire, Courtesy car.
There are total 39 rooms available in Hotel Aroma, Nainital. Rooms are categorized into Luxury base rooms, Super deluxe rooms, Suite rooms and Luxury premium rooms. Basic amenities such as color tv, mini-refrigerator, direct-dial telephone facilities are available with every room.
Numerous tourist spots are situated at very least distance from Hotel Aroma, Nainital. We are listing here few name which are Naini Lake, Pangot and Kilbury Bird Sanctuary, Goddess Naina Devi, Eco Cave Gardens, Corbett Museum, Bara Bazaar, Raj Bhawan, Tiffin Top, Jim Corbett National Park, Guano Hills, snow view points etc.


text:
\section{Introduction}
The calculation of excitation energies in density-functional theory
(DFT) is nowadays mostly done by means of linear response theory in
the time-dependent framework. Linear-response time-dependent
DFT (TDDFT)~\cite{Casida1995} exhibits an
excellent price--performance ratio and is, within the usual adiabatic
semi-local approximations, very successful at describing
excitations to low-lying valence states. However, these approximations
introduce several limitations, especially
for the treatment of static correlation~\cite{Gritsenko2000}, Rydberg
and charge-transfer excitations~\cite{Casida1998, Dreuw2003}, and
double or multiple excitations~\cite{Maitra2004}.

Time-dependent theory is, however, not mandatory for calculating
excitation energies, as stated by the Hohenberg--Kohn
theorem~\cite{Hohenberg1964}. Indeed, several time-independent DFT
approaches for calculating excitation energies exist and are currently
being developed.  These include ensemble DFT~\cite{Theophilou1979,
  Gross1988a, Pastorczak2013, Franck2013, Yang2014,
  Pribram-Jones2014}, $\Delta$SCF~\cite{Gunnarsson1976, Ziegler1977,
  Barth1979, Kowalczyk2011, Seidu2014} and related
methods~\cite{Ferre2002, Gilbert2008, Krykunov2013, Evangelista2013},
or perturbation theory~\cite{GorLev-PRB-93, Gorling1995, Gorling1996,
  Filippi1997} along the standard adiabatic connection using the
non-interacting Kohn--Sham (KS) Hamiltonian as the zero-order
Hamiltonian.

Range-separated DFT constitutes an alternative to standard KS
DFT~\cite{Hohenberg1964, Kohn1965} where the physical electronic
Hamiltonian is replaced not by an effective non-interacting
Hamiltonian but by a partially interacting Hamiltonian that
incorporates the long-range part only of the electron--electron
interaction~\cite{Savin1996, Yang1998, Pollet2003, Savin2003,
  Toulouse2004}. This partially interacting Hamiltonian corresponds to
an intermediate point along a range-separated adiabatic connection,
which links the KS Hamiltonian to the physical Hamiltonian by
progressively switching on the long-range part of the two-electron
interaction, whilst simultaneously modifying the one-electron
potential so as to maintain a constant ground-state density.

In range-separated time-dependent DFT, the excitation energies of the
long-range interacting Hamiltonian act as starting approximations to
the excitation energies of the physical system and are corrected using
a short-range density-functional kernel, in the same manner as the KS
excitation energies act as starting approximations in linear-response
TDDFT.  Several such range-separated linear-response schemes have been
developed, in which the short-range part is described by an
approximate adiabatic semi-local density-functional kernel and the
long-range linear-response part is treated at the
Hartree--Fock~\cite{Rebolini2013, Toulouse2013a, FroKneJen-JCP-13,
  Hedegard2013}, multi-configuration self-consistent field
(MCSCF)~\cite{FroKneJen-JCP-13, Hedegard2013}, second-order
polarization-propagator approximation
(SOPPA)~\cite{Hedegard2013}, or density-matrix functional
theory (DMFT)~\cite{Per-JCP-12} level.

Within the time-independent framework, a standard method for improving
upon the excitation energies of the partially interacting Hamiltonian
would be to use perturbation theory. However, given that perturbation
theory in its standard Rayleigh--Schr\"odinger based formulation does
not keep the ground-state density constant at each order in the
perturbation, it has not led to a systematic
improvement~\cite{Rebolini2015}.

In this work, we propose a time-independent alternative method for
correcting the excitation energies of the partially-interacting
system, based on extrapolation along the range-separated adiabatic
connection. Given that the long-range part of the interaction is
included in the partially interacting system, its excitation energies
constitute better approximations to the energies of the physical
system than do the excitation energies of the KS system.  The analysis
of the Taylor expansion of the energies in the range-separation
parameter $\mu$ about the physical system ($\mu \to +\infty$)
presented in Ref.~\onlinecite{Rebolini2014} shows that the energies of
the partially interacting system converge towards their physical
limits as $\mu^{-2}$. Using this information, it is possible to
develop a scheme for extrapolating the energies of the physical system
from the energies of the partially interacting system by following the
ideas of Refs.~\onlinecite{Savin2011, Savin2014}. This extrapolation
scheme involves low-order derivatives of the energies with respect
to $\mu$ and constitutes an alternative to perturbation theory and to
range-separated TDDFT~\cite{Tawada2004, Fromager2013, Rebolini2013}.

The extrapolation scheme is also applied to the linear adiabatic
connection, where the interaction is scaled by a parameter $\lambda$
going from 0 to 1, and where the analysis of the excitation energies
around $\lambda=1$ provides the required information to improve the
estimation of the energies of the physical system from an intermediate
point of the connection.

The expression for the energies of the partially interacting system and for
their extrapolations are given in Section~\ref{sec:extrapolation}
for the range-separated and linear adiabatic connections. The extrapolation is
subsequently applied to the range-separated energies
of the helium and beryllium atoms and
of the hydrogen molecule at its equilibrium and stretched geometries;
for helium, we also use the linear adiabatic connection. The
computational details are given in Section~\ref{sec:compdet} and the
results are discussed in Section~\ref{sec:chap5results}.

\section{Energy extrapolation along the range-separated and linear
  adiabatic connections}
\label{sec:extrapolation}
\subsection{Range-separated adiabatic connection}
Range-separated DFT uses a partially interacting system, where the
long-range part of the Coulomb interaction is included instead of the
more traditional non-interacting KS system---see, for example,
Ref.~\onlinecite{Toulouse2004}.  In terms of the long-range (lr)
electron--electron interaction operator
\begin{eqnarray}
  \hat{W}_\text{ee}^{\ensuremath{\text{lr}},\mu} \!=\! \frac{1}{2} \iint
  w_\text{ee}^{\ensuremath{\text{lr}},\mu}(r_{12}) \hat{n}_2(\b{r}_1,\b{r}_2) \mathrm
  d\b{r}_1 \mathrm d\b{r}_2,
\end{eqnarray}
where $\hat{n}_2(\b{r}_1,\b{r}_2)$ is the pair-density operator and
$w_\text{ee}^{\ensuremath{\text{lr}},\mu}(r_{12})$ is the error-function interaction
\begin{equation}
  w_\text{ee}^{\ensuremath{\text{lr}},\mu}(r_{12}) = \frac{\erf(\mu r_{12})}{r_{12}},
\end{equation}
the Hamiltonian of the partially interacting system is given by
\begin{equation}
  \hat{H}^{\ensuremath{\text{lr}},\mu} = \hat{T} + \hat{V}_\text{ne} +
  \hat{W}^{\ensuremath{\text{lr}},\mu}_\text{ee} + \hat{\bar{V}}_{\H
    \text{xc}}^{\ensuremath{\text{sr}},\mu}.
\label{Hmu}
\end{equation}
The parameter $\mu$ controls the range of the separation, with $1/\mu$
acting as a smooth cut-off radius.  This Hamiltonian also contains the
short-range Hartree--exchange--correlation potential operator
$\hat{\bar{V}}_{\H \text{xc}}^{\ensuremath{\text{sr}},\mu}$, whose role is to  ensure that the
ground-state density of the partially-interacting system
\begin{equation}
n_0(\b{r}) = \bra{\Psi_0^{\mu}} \hat{n}(\b{r}) \ket{\Psi_0^{\mu}},
\end{equation}
is equal to the
ground-state density of the physical system for all $\mu$. Here
$\Psi_0^{\mu}$ is the ground-state wave function of the partially
interacting Hamiltonian and $\hat{n}(\b{r})$ is the density operator.
The remaining terms in the Hamiltonian of Eq.~\eqref{Hmu} are the usual
kinetic-energy operator $\hat{T}$ and nuclear--electron interaction
operator $\hat{V}_\text{ne} = \int v_\text{ne}(\b{r}) \hat{n}(\b{r})
\mathrm d\b{r}$.

The eigenvectors and eigenvalues of $\hat{H}^{\ensuremath{\text{lr}},\mu}$ are the
ground- and excited-state wave functions $ | \Psi_k^{\mu} \rangle$ and
energies ${\cal E}_k^{\mu}$ of the partially interacting system
\begin{equation}
  \hat{H}^{\ensuremath{\text{lr}},\mu} | \Psi_k^{\mu} \rangle = {\cal E}_k^{\mu} |
  \Psi_k^{\mu} \rangle.
\label{HlrmuPsi}
\end{equation}
These excited-state wave functions and energies provide natural first
approximations to the excited-state wave functions and energies of the
physical system. For $\mu=0$, they reduce to the single-determinant
eigenstates and associated energies of the non-interacting KS
Hamiltonian,
\begin{equation}
  \hat{H}^{\ensuremath{\text{KS}}} | \Phi_k^{\ensuremath{\text{KS}}} \rangle = {\cal E}_k^{\ensuremath{\text{KS}}} |
  \Phi_k^{\ensuremath{\text{KS}}} \rangle,
\end{equation}
while, for $\mu \to \infty$, they reduce to the excited-state wave
functions and energies of the physical Hamiltonian
\begin{equation}
\hat{H} | \Psi_k \rangle = E_k | \Psi_k \rangle.
\end{equation}

In Ref.~\onlinecite{Rebolini2014}, it was shown that the asymptotic
expansion of the total energy of state $k$ around the physical
system is
\begin{equation}
  {\cal E}_k^{\mu}= E_k + \dfrac{1}{\mu^2} E_k^{(-2)} +
  \dfrac{1}{\mu^3} E_k^{(-3)} + \mathcal{O}\left(\dfrac{1}{\mu^4}
  \right),
  \label{eq:E0infty}
\end{equation}
where $E_k^{(-2)}$ and $E_k^{(-3)}$ are the corrections entering at
the second and third powers of $1/\mu$, respectively.  Following the
scheme proposed in Refs.\;\onlinecite{Savin2011,Savin2014}, it is possible
to estimate the energy of the physical system $E_k$ from the energy of
the partially interacting system ${\cal E}_k$ and its first- and
second-order derivatives with respect to $\mu$.

>From the Taylor expansion of the energies when $\mu \to \infty$,
the first-order derivatives of the energies with respect to $\mu$
behave as
\begin{equation}
  \dfrac{\partial {\cal E}_k^{\mu}}{\partial \mu} =
  -\dfrac{2}{\mu^3}E_k^{(-2)} + \mathcal{O} \left( \dfrac{1}{\mu^4}
  \right),
\end{equation}
around the real system.  Inserting this into Eq.~\eqref{eq:E0infty},
the exact energies $E_k$ can be written as a function of the energies
along the adiabatic connection and of their first-order derivative as
\begin{equation}
  E_k = {\cal E}_k^{\mu} + \dfrac{\mu}{2}
  \dfrac{\partial  {\cal E}_k^{\mu}}{\partial \mu}
  + \mathcal{O}\left(\dfrac{1}{\mu^3}\right).
\end{equation}
This scheme gives extrapolated energies
\begin{equation}
  E^{\text{EE},\mu}_k={\cal E}_k^{\mu} + \dfrac{\mu}{2} \dfrac{\partial
    {\cal E}_k^{\mu}}{\partial \mu},
\label{eq:extrapolation}
\end{equation}
that are correct up to and including the second power of $1/\mu$
relative to the energies of the physical system.  The correction given
by the extrapolation scheme vanishes at $\mu=0$ by construction, but
should improve the description of the energies as soon as the
interaction is switched on. One should note that the absence of
a correction at $\mu=0$ is only due to the choice of $1/\mu^k$ as the basis
for the expansion. Other basis functions such as $\mu^2/(a + \mu^5)$
would lead to a correction at $\mu=0$ but are not considered in this
work.

A more elaborate scheme can be developed by using also the correction
$E_k^{(-3)}$ and the second-order derivative.  In this case, the
first- and second-order derivatives are given by
\begin{align}
  \dfrac{\partial {\cal E}_k^{\mu}}{\partial \mu} &=
  -\dfrac{2}{\mu^3}E_k^{(-2)} -\dfrac{3}{\mu^4}E_k^{(-3)}
+  \mathcal{O} \left( \dfrac{1}{\mu^5} \right)
, \\
  \dfrac{\partial^2 {\cal E}_k^{\mu}}{\partial \mu^2} &=
  \dfrac{6}{\mu^4}E_k^{(-2)} + \dfrac{12}{\mu^5}E_k^{(-3)}
 +  \mathcal{O} \left( \dfrac{1}{\mu^6} \right)
,
\end{align}
and, after eliminating $E_k^{(-2)}$ and $E_k^{(-3)}$, the extrapolated
energies become
\begin{equation}
  E^{\text{EE} 2,\mu}_k={\cal E}_k^{\mu} + \mu \dfrac{\partial {\cal
      E}_k^{\mu}}{\partial \mu} + \dfrac{\mu^2}{6} \dfrac{\partial^2
    {\cal E}_k^{\mu}}{\partial \mu^2}.
\label{eq:extrapolation2}
\end{equation}
Higher-order derivatives should further reduce errors.  Additionally,
several points along the adiabatic connection could be used to perform
the extrapolation to increase the accuracy of the extrapolated
energies. However, only first- and second-order corrections at a
single point of the adiabatic connection are considered hereinafter.

\subsection{Linear adiabatic connection}
If the linear adiabatic connection is performed, then the partially
interacting Hamiltonian is defined as $\hat{H}^{\lambda} = \hat{T} +
\lambda \hat{W}_{\text{ee}} + \hat{V}^{\lambda}$ where $\hat{V}^{\lambda}$
is adjusted to keep the ground-state density constant.  This potential
can be expressed in terms of the connecting parameter $\lambda$ as
\begin{equation}
  \hat{V}^{\lambda} = \hat{V}_\text{ne} + (1-\lambda)\hat{V}_{\H \text{x}} +
  \hat{V}_\text{c} - \hat{V}_\text{c}^\lambda,
\end{equation}
where $\hat{V}_\text{c}^\lambda$ enters at second order in $\lambda$ and is
equal to $\hat{V}_\text{c}$ at $\lambda=1$.  The energies of the
partially interacting system can then be expanded around the physical
system as
\begin{equation}
  {\cal E}^{\lambda}_k = E_k + (\lambda-1)E_k^{(1)} +
  (\lambda-1)^2E_k^{(2)} + \mathcal{O}(\lambda-1)^3,
\end{equation}
where $E_k^{(1)}$ and $E_k^{(2)}$ are the contributions entering at
the first and second power of $(\lambda-1)$, respectively.
As in the range-separated case, by differentiation with respect to
$\lambda$, it is then possible to extrapolate the energies of the
physical system at first order by considering only the correction
$E_k^{(1)}$ as
\begin{equation}
  E_k^{\text{EE},\lambda} = {\cal E}^{\lambda}_k+ (1-\lambda)\dfrac{\partial {\cal
      E}_k^{\lambda}}{\partial \lambda}.
  \label{eq:extrapolation lambda}
\end{equation}
When $\lambda=0$, this extrapolation is equivalent to
the first-order correction of G\"orling--Levy perturbation
theory~\cite{Gorling1995,Filippi1997}.

A second-order correction can be obtained by using also the correction
$E_k^{(2)}$. The first- and second-order derivatives are
\begin{align}
  \dfrac{\partial {\cal E}_k^{\lambda}}{\partial \lambda} &=
  E_k^{(1)} + 2 (\lambda_1) E_k^{(2)} + \mathcal{O}(\lambda-1)^2, \\
  \dfrac{\partial^2 {\cal E}_k^{\lambda}}{\partial
    \lambda^2} &= 2 E_k^{(2)} + \mathcal{O}(\lambda -1),
\end{align}
 and the extrapolated energies become
\begin{equation}
  E^{\text{EE} 2,\lambda}_k={\cal E}_k^{\lambda} + (1- \lambda)
  \dfrac{\partial {\cal E}_k^{\lambda}}{\partial \lambda} +
  \dfrac{1}{2} (1-\lambda)^2 \dfrac{\partial^2 {\cal
      E}_k^{\lambda}}{\partial \lambda^2}.
\label{eq:extrapolation lambda2}
\end{equation}

\section{Computational Details}
\label{sec:compdet}
Calculations were performed for the He and Be atoms and the H$_2$
molecule with a development version of the DALTON
program~\cite{Dal-PROG-11}, see
Refs.~\onlinecite{TeaCorHel-JCP-09,TeaCorHel-JCP-10,TeaCorHel-JCP-10b}.
Following the procedure of Ref.~\onlinecite{Rebolini2014}, a
full CI (FCI) calculation was first carried out to get the exact
ground-state density within the basis set considered:
uncontracted t-aug-cc-pV5Z for He,
uncontracted d-aug-cc-pVDZ for Be, and uncontracted d-aug-cc-pVTZ for H$_2$.
A Lieb optimization of the short-range potential $v^{\ensuremath{\text{sr}},\mu}(\b{r})$ was then
performed to reproduce the FCI density with the long-range
electron--electron interaction $w_{\text{ee}}^{\ensuremath{\text{lr}},\mu}(r_{12})$. Finally, an FCI
calculation was carried out with the partially-interacting Hamiltonian
constructed from $w_{\text{ee}}^{\ensuremath{\text{lr}},\mu}(r_{12})$ and $v^{\ensuremath{\text{sr}},\mu}(\b{r})$ to
obtain the zeroth-order energies and wave functions.

Starting from the analytical form of the fit given in the
supplementary material of Ref.~\onlinecite{Rebolini2014}, it is then
straightforward to calculate the analytical derivatives of the
energies with respect to $\mu$. In the linear case, a cubic fit of the
energies was performed.  The extrapolated energies were calculated
using
Eqs.~\eqref{eq:extrapolation},~\eqref{eq:extrapolation2},~\eqref{eq:extrapolation
  lambda}, and~\eqref{eq:extrapolation lambda2}.

All the unextrapolated curves shown hereinafter correspond to the
curves of Ref.~\onlinecite{Rebolini2014}.

\section{Results and discussion}
\label{sec:chap5results}

\subsection{Range-separated adiabatic connection of the helium atom}
\begin{figure}
  \centering
  \includegraphics[scale=1]{fig1a.eps}
  \includegraphics[scale=1]{fig1b.eps}
  \includegraphics[scale=1]{fig1c.eps}
  \caption{(Color online) Helium ground-state energy (top) ${\cal E}_0^{\mu}$, and
    first $\S$ (middle) and $\P$ (bottom) excitation energies $\Delta
    {\cal E}_k^{\mu} = {\cal E}_k^{\mu} - {\cal E}_0^{\mu}$ calculated
    without extrapolation (full lines), with first-order extrapolation
    (dashed) and second-order extrapolation (dot--dashed) as a
    function of $\mu$. The dotted horizontal lines are the physical
    energies. The colored regions represent errors of $\pm 10$ and
    $\pm 1$~mhartree for the ground-state and excitation energies,
    respectively.
    \label{fig:he_tacpv5z_svd07_0_fit}
  }
\end{figure}

\subsubsection{Ground-state energy}
The results of the first- and second-order extrapolation schemes on
the ground-state total energy of the helium atom are shown in
Figure\;\ref{fig:he_tacpv5z_svd07_0_fit} (top). By construction, the
extrapolation has no effect at $\mu=0$ and the ground-state energy of
the KS system is, therefore, unaffected by the extrapolation. However,
for $\mu > 0$, the extrapolated energies show a systematic improvement
with respect to the unextrapolated ground-state energy, that is, the
ground-state energy of the partially interacting Hamiltonian without
any correction.

Without extrapolation, a range-separation parameter of about
6\;bohr$^{-1}$ is needed to give an error smaller than
10\;mhartree relative to the energy of the physical system.  With
the first- and second-order corrections added, the same accuracy is
achieved with a range-separation parameter of only 2.8 and
1.5 bohr$^{-1}$, respectively.

\subsubsection{Rydberg excitation energies}
Figure\;\ref{fig:he_tacpv5z_svd07_0_fit} also shows the effects of
extrapolation on the lowest Rydberg S (middle) and P (bottom)
excitation energies of helium.  The convergence of the excitation
energies towards their physical limit is overall improved by the
first- and second-order corrections with respect to the unextrapolated
curves. In fact, the range-separation parameter required to achieve an
accuracy of 1~mhartree is divided by approximately a factor 2 or a
factor 3 by the first- and second-order schemes, respectively.
For the excitation energies considered here, a range-separation value
of 2 and 1\;bohr$^{-1}$ suffices to reduce the error to less than
1\;mhartree with the first- and second-order schemes,
respectively.

The $^1\S$ and $^3\S$ excitation energies change monotonically with
increasing $\mu$. Accordingly, extrapolation provides a systematic
improvement, the sign of the derivative pulling the excitation
energies towards their physical limits at both first- and second-order
levels.

The $^3\P$ excitation energy also changes monotonically with $\mu$ and
the first-order extrapolation provides therefore a systematic
improvement. However, the first-order extrapolated energy does not
converge monotonically towards its physical limit (not visible),
leading to a slight degradation of the excitation energies around
$\mu=1.5$ bohr$^{-1}$ at second order.

Finally, the $^1\P$ excitation energy shows a non-monotonic behavior
even before extrapolation, exhibiting a ``bump'' for small $\mu$ that
is probably a basis-set effect~\cite{Rebolini2014}.  In fact, for such
small $\mu$, only the very long-range part of the interaction is
modified, which is poorly described by Gaussian basis functions. The
higher a given state is in energy, the more sensitive it becomes to
this basis-set defect.

As a consequence, the $^1\P$ excitation energy approaches its physical
limit from above, its first-order derivative changing sign around
0.7\;bohr$^{-1}$.  In this region, the extrapolated energies become
less accurate than the unextrapolated energy.  However, this behavior
is observed only in a small region.  As soon as the excitation energy
recovers a monotonic convergence towards its physical limit (for $\mu$
larger than 0.7\;bohr$^{-1}$), the energy is improved by the
extrapolation and converges faster to its physical limit.

\subsection[Range-separated adiabatic connection for the valence of Be]
           {Range-separated adiabatic connection for the valence
             excitation of the beryllium atom}

\begin{figure}
  \centering
  \includegraphics[scale=1]{fig2a.eps}
  \includegraphics[scale=1]{fig2b.eps}
  \caption{(Color online) Ground-state energy ${\cal E}_0^{\mu}$ (top) and excitation
    energies $\Delta {\cal E}_k^{\mu} = {\cal E}_k^{\mu} - {\cal
      E}_0^{\mu}$ (bottom) of beryllium as a function of $\mu$.  The
    unextrapolated energies are shown as full lines, the first-order
    extrapolated energies are plotted in dashed lines and the
    second-order ones in dot-dashed lines. The energies of the
    physical system are given as horizontal dotted lines. An error of
    $\pm 50$ mhartree is colored around the physical ground-state
    energy and an error of $\pm 2$ mhartree is colored around the
    physical excitation energies.
    \label{fig:be_dacpvdz_0_fit}
  }
\end{figure}

The ground-state energy of the beryllium atom is shown in
Figure~\ref{fig:be_dacpvdz_0_fit} (top).  Since beryllium has a core
orbital, the convergence of its total energies is slower than for
helium as the density is more contracted and a larger range-separation
parameter is needed to describe correctly the core region.  However,
this affects all valence states in a similar fashion (not shown here).

Extrapolation systematically improves the convergence of the
ground-state energy along the adiabatic connection.  First-order
extrapolation reduces the error to less than 50\;mhartree with
$\mu \approx 5$\;bohr$^{-1}$, an order of magnitude smaller than the
error without the extrapolation correction but still
large. Second-order extrapolation gives the same error reduction
already with $\mu \approx 3$\;bohr$^{-1}$.

The effect of the extrapolation on the valence excitation energies of
beryllium is shown in Figure\;\ref{fig:be_dacpvdz_0_fit} (bottom).  As
the errors associated with the core largely cancel in the excitation
energies, the unextrapolated excitation energies already converge
faster than do the total energies.  With first-order extrapolation, an
error smaller than 2\;mhartree is reached with $\mu \approx
0.5$\;bohr$^{-1}$, to be compared with a much larger error of
4\;hartree in the total energies with the same $\mu$ value.  The
second-order extrapolation allows one to reach the same accuracy with
a range-separation parameter as small as 0.3\;bohr$^{-1}$. However,
once again, some bumps are observed in the extrapolated energies probably due
to the limited size of the basis set. This fast convergence of the
excitation energies with respect to the range-separation parameter is
due to the fact that in beryllium, static correlation is important and
the multi-configurational character of the wave function is quickly
established when the interaction is switched on; see
Ref.~\onlinecite{Fromager2007}.

\subsection[Range-separated adiabatic connection for H$_2$]
           {Range-separated adiabatic connection for the hydrogen
             molecule}
\begin{figure}
  \centering
  \includegraphics[scale=1]{fig3a.eps}
  \includegraphics[scale=1]{fig3b.eps}
  \caption{(Color online) Unextrapolated (full lines), first-order extrapolated
    (dashed lines) and second-order extrapolated (dot-dashed lines)
    excitation energies $\Delta {\cal E}_k^{\mu} = {\cal E}_k^{\mu} -
    {\cal E}_0^{\mu}$ of the H$_2$ molecule at the equilibrium
    internuclear distance $R_{\text{eq}}$ (top) and three times the equilibrium
    distance (bottom) as a function of $\mu$.  The excitation energies
    of the physical system $\Delta E_k = \Delta {\cal
      E}_k^{\mu\to\infty}$ are plotted as horizontal dotted lines. An
    error of $\pm 1$ mhartree is colored around the physical
    excitation energies at equilibrium and an error of $\pm 5$
    mhartree at stretched geometry.
    \label{fig:h2_dacpvtz_exc_0_fit}
  }
\end{figure}
Finally, we consider extrapolation of the lowest excitation energies
of the hydrogen molecule along the range-separated adiabatic
connection, at the equilibrium geometry and at a stretched geometry.
The results of the first- and second-order extrapolations on the
singlet and triplet $\Sigma_\text{g}^+ \to \Sigma_\text{u}^+$
excitation energies at the equilibrium geometry are shown in
Figure~\ref{fig:h2_dacpvtz_exc_0_fit} (top).  First- and
second-order extrapolations provide a systematic improvement in the
excitation energies, $\mu \approx 2$\;bohr$^{-1}$ for first order
and $\mu \approx 1$\;bohr$^{-1}$ for second order being sufficient
to reproduce the physical energies to within 1\;mhartree.

Having stretched the hydrogen molecule to three times the equilibrium
distance, we apply extrapolation to the singlet and triplet
excitations to the $1\Sigma_\text{u}^+$ state and to the double
excitation to the $2\Sigma_\text{g}^+$ state---see the bottom part of
Figure~\ref{fig:h2_dacpvtz_exc_0_fit}.  Again, the improvement is
systematic. The triplet extrapolated energy shows a monotonic behavior
with respect to $\mu$, whereas the singlet energy shows a slight bump
at 0.8\;bohr$^{-1}$.  However, all extrapolated excitation energies
converge faster than their unextrapolated counterparts.  Extrapolation
works remarkably well, reducing errors to less than 5\;mhartree
with $\mu \approx 0.6$\;bohr$^{-1}$, compared with 2\;bohr$^{-1}$
without extrapolation. In particular, extrapolation allows us to
describe double and single excitation energies equally well.  In this
case, one should note that the second-order scheme does not improve
significantly the convergence of the $1 ^1\Sigma_\text{g}^+ \to 2
^3\Sigma_\text{g}^+ (\sigma_\text{u}^+)^2 $ and $1 ^1\Sigma_\text{g}^+
\to 1 ^1\Sigma_\text{u}^+ $ excitation energies because of their
nonmonotonicity probably due to the limited basis set.

\begin{figure}
  \centering
  \includegraphics[scale=1]{fig4a.eps}
  \includegraphics[scale=1]{fig4b.eps}
  \includegraphics[scale=1]{fig4c.eps}
  \caption{ (Color online) Helium ground- and excited-state energy
    (top), $\S$ excitation energies (middle), and $\P$ excitation
    energies (bottom) calculated without extrapolation (full lines),
    with first-order extrapolation (dashed), and second-order
    extrapolation (dot--dashed) along the linear connection. The
    dotted horizontal lines are the physical energies. The colored
    regions represent errors of $\pm 1$~mhartree for the
    excitation energies.
    \label{fig:he_tacpv5z_svd07_0_lambda}
  }
\end{figure}
\subsection{Linear adiabatic connection for the helium atom}
\ignore{In order to apply the extrapolation scheme on the linear
  adiabatic connection, the zero-order total and excitation energies
  of the helium atom along this connection are calculated following
  the procedure described in Chapter~\ref{chap:zeroth AC} and are
  shown in Figure~\ref{fig:he_tacpv5z_svd07_0_lambda}.}

\subsubsection{Total energies}

The total energies of the helium atom along the linear adiabatic
connection are plotted in Figure~\ref{fig:he_tacpv5z_svd07_0_lambda}
(top).  When $\lambda=0$, no interaction is included, so the KS
energies are recovered as for $\mu=0$. When $\lambda =1$, the full
interaction is present and the energies of the physical system are
recovered, which corresponds to the limit $\mu \to\infty$.  The two
limiting cases are, therefore, identical for the two adiabatic
connections but the way they are connected differs.

The evolution of the total energies with respect to $\lambda$ is
almost linear. Although this behavior is easier to predict and should
provide an efficient framework for extrapolations, the value of
$\lambda$ required to have an error of 10 mhartree is very close
to 1; in the range-separation case, an intermediate value of $\mu$ is
sufficient. In general, we note that, in the linear case, the
calculation of the wave function is by and large equally expensive at
all points along the connection since the electron-electron cusp must
always be described (except at $\lambda =0$); in the range-separated
case, by contrast, the calculation becomes less expensive with
decreasing $\mu$ since the description of the cusp is then avoided.

\subsubsection{Excitation energies and comparison with the range-separated case}
The lowest (Rydberg) excitation energies of helium along the linear
adiabatic connection are also plotted in
Figure~\ref{fig:he_tacpv5z_svd07_0_lambda} (middle and bottom). As for
the total energies, the end points are the same as in the
range-separated case but the behavior of the energies along the
connection is more linear. As in the range-separated case, the $^1\P$
excitation energy does not evolve monotonically with $\lambda$,
probably because of basis-set limitations.

When the first- and second-order extrapolation corrections are added,
a systematic improvement is observed for the triplet excitation
energies. With the second-order correction, the physical energies are
already reproduced to 1\;mhartree at
$\lambda=0$.  The singlet excitation energies are less affected by the
correction but are still overall improved, the amount of interaction
required to reproduce the physical limit within an accuracy of
1\;mhartree dropping to 50\%. Moreover, unlike in the range-separated
case, the KS excitation energy also benefits from this correction,
which no longer vanishes in this limit. Indeed, at $\lambda=0$, the
extrapolated excitation energy matches the results obtained in
Ref.~\onlinecite{Filippi1997}, using first-order G\"orling--Levy
perturbation theory.

To compare the range-separated and linear cases, the effects of
first-order extrapolation on the lowest excitation energy of helium
are shown in Figure\;\ref{fig:he_comp_mulambda_fit} in both cases.
Without extrapolation, the scaling parameter $\lambda$ must be greater
than 0.95 to reproduce energies within 1\;mhartree. By contrast, a
small change in $\mu$ near zero gives a large change in the energies;
thus, a range-separation parameter of 2\;bohr$^{-1}$ is sufficient to
ensure the same accuracy. Clearly, the range-separated connection
includes the most significant region of the interaction first, whereas
the linear connection treats all ranges equally, independently of
their importance for the excitation energies.

\begin{figure}
  \centering
  \includegraphics[scale=1]{fig5.eps}
  \caption[Comparison of the range-separated and linear adiabatic
    connections]{Error in the $^3\S$ excitation energy along the
    range-separated and linear adiabatic connections for the helium
    atom as functions of $\mu$ and $\lambda$. The unextrapolated
    energies are given in full lines and the extrapolated ones in
    dashed lines.  An error smaller than 1\;mhartree around the
    physical limit is given by the colored
    region.\label{fig:he_comp_mulambda_fit}}
\end{figure}

For the KS system, it is obviously better to use the correction
obtained from the linear connection as the corresponding
range-separated correction vanishes.  For a partially interacting
system, the comparison is more difficult.

\section{Conclusion}

In this work, we have exploited the asymptotic behavior of the
energies of a partially interacting system along the range-separated
adiabatic connection to design an energy correction that allows us to
extrapolate to the physical energies of the system from its partially
interacting energies.  The simplest possible extrapolations were
obtained by using either only the first-order derivative of the
energies with respect to the range-separation parameter at a given
point or by using the first- and second-order derivatives.

This extrapolation scheme was tested at the FCI level of theory on the
helium and beryllium atoms and on the hydrogen molecule (at equilibrium
and at stretched geometry), where it significantly improves the
convergence of energies and excitation energies towards their physical
limits.  Moreover, the improvements are systematic, except at $\mu=0$
(where the correction is zero by construction) and in a few cases where
the partially interacting energies present a bump for small $\mu$.
In all cases, with respect to the unextrapolated case, the
extrapolation schemes reduce the smallest value of the range-separation
parameter required to reproduce the physical energies of the system
with a given accuracy by approximately a factor of 2 with the
first-order scheme and by a factor of 3 with the second-order scheme.
This is of particular relevance for truncated wave
functions, as the smaller the range-separation parameter is, the fewer
Slater determinants are needed to describe the wave functions with an
equivalent accuracy.

Finally, the extrapolation scheme was applied along the linear
adiabatic connection, where it also improves significantly the
description of the excitation energies along the connection.

All results discussed here were obtained without the use of
approximate functionals. The proposed extrapolation scheme should now
be tested in a more pragmatic case, where the potential is not
obtained by Lieb optimization but from different approximations such
as the (semi)local approximations or more interestingly approximations
where the long-range behavior of the potential is correct, such as the
optimized-effective potential (OEP)~\cite{Sharp1953,Talman1976}. The
effects of the inclusion of higher-order derivatives and of multiple
points on this extrapolation should also be explored.

\section{Acknowledgments}
 This work was supported by the Norwegian Research Council through the
 CoE Centre for Theoretical and Computational Chemistry (CTCC) Grants
 No.\ 179568/V30 and No.\ 171185/V30 and through the
 European Research Council under the European Union Seventh Framework
 Program through the Advanced Grant ABACUS, ERC Grant Agreement
 No.\ 267683. A. M. T. is grateful for support from the Royal Society
 University Research Fellowship scheme.

redpajama_set_name: RedPajamaArXiv


text:
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1.1 Sports
1973: EOKA B' abduct Christos Vakis, Minister of Justice of the Republic of Cyprus.
1976: Greek Cypriot, Stavros Sykopetritis, attempts to assassinate Bulent Ecevit in New York City. Ecevit was the Turkish PM who ordered the invasion of Cyprus two years earlier.
1993: The Greek government expresses regret over Ukraine's decision to recognise FYROM.
1996: Leonidas Kokkas wins silver in weightlifting in the Atlanta Olympic Games.
2007: The Greek Under-19 football team play in the final of the European Cup in Linz, Austria, where they lose 1-0 to Spain.
1903: Michail Stasinopoulos, politician, President of Greece
1948: Pavlos Sidiropoulos, rock musician
1962: Theodoros Voutyritsas, footballer
1992: Jenny Karezi, actress
2022: Giorgos Andreou, footballer
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text:
Irbie History, Family Crest & Coats of Arms
Irbie is a name that was carried to England in the great wave of migration from Normandy following the Norman Conquest of 1066. The Irbie family lived in Lincolnshire, at Irby, from where they took their name.
Early Origins of the Irbie family
The surname Irbie was first found in Lincolnshire at Irby by the Marsh, a village and civil parish in the East Lindsey district which dates back to c. 1115 when it was listed as Irebi. Irby upon Humber or Irby-on-Humber is a small village and civil parish in North East Lincolnshire. This local dates back further to the Domesday Book of 1086 when it was listed as Iribi. [1] Other locals include: Irby, a village on the Wirral Peninsula; Ireby, a village in Cumbria; and Ireby, a small hamlet and civil parish bordering on Lancashire and North Yorkshire. The place name is believed to literally mean "farmstead or village of the Irishmen," having derived from the Old Scandinavian name "Irar" + "by." [2]
Important Dates for the Irbie family
This web page shows only a small excerpt of our Irbie research. Another 150 words (11 lines of text) covering the years 1068, 1114, 1547, 1625, 1589, 1622, 1577, 1610, 1605, 1681, 1676, 1718, 1702, 1707, 1707 and 1708 are included under the topic Early Irbie History in all our PDF Extended History products and printed products wherever possible.
Irbie Spelling Variations
Before English spelling was standardized a few hundred years ago, spelling variations of names were a common occurrence. Elements of Latin, Norman French and other languages became incorporated into English throughout the Middle Ages, and name spellings changed even among the literate. The variations of the surname Irbie include Irby, Irbey, Irbie, Irbye and others.
Early Notables of the Irbie family (pre 1700)
Outstanding amongst the family at this time was Anthony Irby (1547-1625), English Master of Chancery, Recorder and Member of Parliament for Boston between 1589 and 1622; Sir Anthony Irby (1577-1610), English Member of Parliament...
Another 33 words (2 lines of text) are included under the topic Early Irbie Notables in all our PDF Extended History products and printed products wherever possible.
Migration of the Irbie family
In England at this time, the uncertainty of the political and religious environment of the time caused many families to board ships for distant British colonies in the hopes of finding land and opportunity, and escaping persecution. The voyages were expensive, crowded, and difficult, though, and many arrived in North America sick, starved, and destitute. Those who did make it, however, were greeted with greater opportunities and freedoms that they could have experienced at home. Many of those families went on to make important contributions to the young nations in which they settled. Early immigration records have shown some of the first Irbies to arrive on North American shores: Walter Irby, who came to Virginia in 1652; William Irby, who was on record in Virginia in 1714; and Robert Irby, also on record in Virginia in 1715.
Irbie (English)


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