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robert livingston
(MARICOPA, Ariz. – Sept. 22, 2016) – Harrah's Ak-Chin Casino has announced that Robert Livingston, the property's general manager is adding an additional title to his name. Livingston will now also serve as regional president, overseeing operations of both Harrah's Ak-Chin Casino in Maricopa and Harrah's Resort Southern California, just outside of San Diego.
Livingston has been with the Caesars family for 25 years, having begun his career with Caesars Entertainment in 1991 as a senior corporate accountant at the corporate headquarters in Memphis. He held several finance and operational roles throughout the Central Division of Caesars for the first half of his career before moving west in 2003. He served as vice president and assistant general manager at Harrah's Rincon (now Harrah's Resort Southern California) before being promoted to general manager and transferring to Harrah's Ak-Chin in 2011.
Livingston's appointment comes on the heels of the announcement that Janet Beronio, Harrah's longtime regional president and general manager for Harrah's Resort Southern California and Harrah's Ak-Chin, announced her retirement.
Livingston holds both bachelor's and master's degrees in accounting from the University of Mississippi.
Livingston is a resident of Ahwatukee.
About Harrah's Ak-Chin Casino:
Celebrating more than 20 years in Maricopa, Arizona, Harrah's Ak-Chin Casino is Arizona's first and only tribal casino to have an international management partner. Offering the largest selection of the latest reel and video slots in a range of denominations, Harrah's Ak-Chin features slot machines, video poker, video Keno as well as popular statewide progressives and live-action poker and Black Jack.
Harrah's Ak-Chin is the only casino in Arizona that allows guests, through its Total Rewards program, to unlock benefits and other prizes that can be used worldwide at the entire Caesars' family of casinos. Harrah's Ak-Chin also boasts the only Bingo hall in the Caesars organization, continuing the proud heritage of William F. Harrah, who opened his first Bingo hall in Reno in 1937.
Casino guests can also enjoy live entertainment in The Lounge and a variety of dining options including the Copper Cactus Grill, Agave's Restaurant, The Range Steakhouse, The Buffet and Dunkin Donuts®. Harrah's Ak-Chin Casino features 300 luxurious resort and tower guestrooms and an outdoor swimming pool with swim-up bar.
Harrah's Ak-Chin has been named a Most Admired Company by Arizona Business Magazine and BestCompaniesAZ, and Phoenix Business Journal has named the property one of the "Best Places to Work in the Valley" four consecutive years. Harrah's Ak-Chin was also awarded a Volunteer Service Award from the Arizona Governor's Commission on Service and Volunteerism.
For more information, please visit www.harrahsakchin.com.
Harrah's Ak-Chin Casino's Robert Livingston Named Regional President
(MARICOPA, Ariz. – Sept. 22, 2016) – Harrah's Ak-Chin Casino has announced that Robert Livingston, the property's general manager is adding an additional title to his […]


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19 Dark Tower Moments
Well, howdy, folks!
Or more appropriately, hile, folken!
In other words, life gets…
Well, lifey sometimes, I suppose.
And what's a nerd to do when life hands her its lifey-est?
Well, if you said grab the best fantasy series ever, written by The Master and delve back into for the whatever-eth time, you would be…
I'll take correct, for $19, Alex!
As if both er all of my readers need to be reminded as to what blog they are reading…
So yeah, you bet your fur (or should that be your billy-bumblers pelt) that when you need an escape, The Dark Tower series by Stephen King is just the ticket!
(Of course, hot chocolate sprinkled with nutmeg would make a great accompaniment, wink, wink…)
Now, I have already reviewed all of the books in the series when I did my literary keg stand a few years ago.
But, I love writing about this series so much!
And there is so much to unpack. I don't think anyone could ever write too much about The Dark Tower series.
EVAH.
So here I am,ready, at your disposal, ready to provide you with…
More written content about the series, ya perv!
Anyway, I have come up with a list of moments in the series.
Nineteen moments!
(Nineteen moments. See what I did there?)
*Casually pats self on the back for being able to make it approximately three blog minutes without bringing up the number 19*
So yes, another list! My INTJ attempts to inconspicuously wipe the drool from her face…mmmm, lists…
No particular order on this list, although don't hold me to that statement (it's still early, only 7 or so blog minutes.)
These moments are varied, and are pulled from all the books in the series.
Some are funny.
Some are head scratchers.
More than a few are tragic (we all know that reading almost anything written by The Master is a form of self-punishment. But oh so worth it.)
But all of these moments were selected because they stand out, for whatever reason.
So, let's quit beating on Sheemie's mule, and get to it.
Time to count down nineteen of the most memorable moments of The Dark Tower series!
Oh, and before I forget:
19. The Ending (The Dark Tower)
So, we are counting backwards.
And we begin with…
The ending?!
Clear as mud, right?
Well, actually this makes a certain amount of sense (well, about as much sense as anything written in this blog, whatever that is worth.)
I am going to assume…
(And request quiet from the Eddie Dean peanut gallery chattering about what happens when we ASS-U-ME.)
That you have probably read the series.
Including the ending…
Basically, it is the beginning of the end.
Throughout the seven books in the series (or 7.5, if we include The Wind Through the Keyhole), we journey with Roland.
We become invested in his quest. We root for him.
We grieve with him (see that part about how some of these entries are tragic.)
Finally, he makes it his Tower. He sacrificed countless people and creatures along the way, including a hawk. And a little boy. And his first love.
But, he makes it The Tower, so he gets closure, right? Something great waiting for him at the top of that Tower, right?
Lolz, says The Master. Aren't you cute?
Wouldn't it be funny if…
I just threw ole, long, tall and ugly right back to the Mohaine Desert, and have him re-start his quest?
And make you Constant Constant Readers (and long, tall and ugly, at least momentarily) come to the horrifying realization that Roland has done this before?
Many times before in fact. In fact, our friendly neighborhood gunslinger has been stuck in a loop.
*Cue "This Is The Song That Never Ends"*
I have to admit, that when I first read the ending, it threw me for a loop (okay, guess I gotta fess up and let you know that pun was fully intended.)
But, being the intrepid Constant Constant Reader that I am, I did the only thing I could think to do:
I re-read the book.
And came to an epiphany:
This is the only way the series could have ended.
After all, we all get caught in a loop, just like our friendly neighborhood gunslinger.
We repeat patterns, over and over.
We overlook some important, tiny detail, and we get stuck in that loop.
Until we pick up on something. Or something might be handed to us.
Like a certain horn…
And when we see that, this time, that we happen to be holding that horn, we come to a realization:
Hope. There is always hope for us.
There is hope even for the most hopeless of us.
And the hope is the only thing that can free us of that loop.
18. Oy (The Wastelands)
So, I want to focus on something pure.
And love stories are always pure, right?
They start out like so:
Boy gets hit by car.
Boy doesn't die, but gets drawn into a strange world that is alien to him, but strangely resembles his own.
Boy meets one of the grizzled inhabitants of this world by "chance" (emphasis on the air quotes around that word, haha.)
Boy bonds with grizzled inhabitant and joins him on his journey.
Grizzled inhabitant bonds with boy before casually letting him fall to his death off a cliff…
(Stay with me here, okay? The pure part is coming, I promise!)
Grizzled inhabitant later travels back to boy's world, and saves him from being hit by the car to begin with. Wasn't that nice?
Actually, it wasn't nice, because the grizzled inhabitant created a logical paradox.
Now both the boy and grizzled inhabitant have two sets of memories, and are slowly and surely going cuckoo for Cocoa Puffs…
(Really, give me a few blog minutes, I'm getting there, guys.)
Of course, the only thing to do at this point is to violently "birth" the boy into the world of the grizzled inhabitant, so that the logical paradox can cease to exist.
Isn't Mid-World logic something?
So boy makes it back into the world of the grizzled inhabitant, who is now accompanied by two other people who were fortunate enough to also be brought in this world, although their stories will be discussed on some later number on this list.
Boy is happy, but doesn't quite feel that he belongs in this strange new world of talking monorails and tribes who war against each other to the back beat of the tune "Velcro Fly."
Now the love part is coming…
He meets a creature that appears to be part raccoon, part dog, agile like a cat, able to mimic human speech like some kind of furry parrot, and all billy-bumbler!
Folken, I give you Oy!
Everyone's favorite billy-bumbler, aka Oy of Mid-World!
Like I said, he talks!
You can tell me Oy is just mimicking his humans, and you may be correct on that.
But I will never stop believing that Oy is just a little smarter than the average bear er bumbler.
And he can count. That is no accident!
And rescue his Jake from disgusting pedophiles dying of whatever nasty version of STD's that Mid-World boasts!
Good for snuggles too! Now I want my own billy-bumbler!
As stated before, Jake felt that he did not quite belong in Mid-World, until he happened to come across Oy (we can still laugh at the notion of chance here, I think.)
But that meeting solidified Jake's place in this strange, new world, giving him a sense of belonging, all due to the love and devotion of Oy, his best friend.
Ah, true love.
I'm not crying, you're crying…
17. Father Callahan (The Wolves of the Calla)
Now, who doesn't love a good vampire story?
Let me make one thing clear:
When I say vampire, I am talking about Un-Dead Creatures who will tear out your flesh, and drink your blood. Creatures with no redeeming qualities whatsoever, and not a drop of humanity.
In other words, none of this sparkly shit!
Of course, when I want to read about vampires who don't sparkle, one of my top choices is 'Salem's Lot.
It has everything a non-sparkly vampire lover could want:
Your Dracula (Barlow.)
Your Renfield (Mr. Richard Straker.)
Your protagonists who are the only ones in town without their heads up their asses who can see that the town is infested by vampires (Ben Mears and company.)
And an alcoholic priest who faith waivers, which happens to be a deadly mistake when he tries to confront the Dracula stand-in. Deadly, but unfortunately not fatal.
Of course, I am talking about Father Callahan, the world-hopping priest who formally headed the Catholic church in the damned (literally) town of Jerusalem's Lot, or 'Salem's Lot for short.
Who also happens to be an alcoholic.
At the conclusion of 'Salem's Lot, Father Callahan, after being forced to drink the blood of Barlow, flees the town of 'Salem's Lot.
The priest is unable to enter his church, as his faith wavered and he was forced to drink Barlow's blood.
So he flees, as he unable to face the horrors in his town.
I always thought that was a punk ending for the man.
Often, late at night, I would momentarily wonder what happened to Father Callahan. Then my thoughts would switch over to more important issues, such as the question of whether penguins have knees.
(Still haven't figured that one out, in case you were wondering. About penguins and knees, I mean.)
Well, thanks to The Master, one of those questions got answered.
We encounter Father Callahan in none other than the world of The Dark Tower series, in the book The Wolves of the Calla.
Makes perfect sense.
Mid-World logic at work again…
Roland and his ka-tet learn of Pere Callahan's time in 'Salem's Lot, and his adventures afterwards.
Father Callahan is even "birthed" into Mid-World, in much the same way as Jake entered Mid-World.
Eventually, the priest becomes part of Roland's ka-tet, and his even able to redeem himself, by sacrificing himself to protect Jake from vampires.
Father Callahan dies on his terms, and is not tainted by the Un-Dead.
And a nerdy blogger finally got an important question answered, so she could ponder more important issues, such as the anatomy of certain, aquatic birds…
16. Odetta meets Detta (The Drawing of the Three)
Sometimes, the same person can actually be two different people.
Have you ever heard of that Bachman fella?
We also have Caitlyn Snow and Killer Frost.
It's your lucky day…
And then there is Odetta Susannah Holmes.
And Detta Susannah Walker.
Believe me, these two are nowhere near as much as the twins in that old gum commercial…
When Roland draws together his new ka-tet, after playing cards with an evil wizard and sleeping for a few years (man, Mid-World is fun sometimes), he told that one of the members will be The Lady of Shadows.
Roland believes that he will actually "draw" two women into his ka-tet.
And, in a way, he is correct.
Due to a traumatic brain injury, the woman known as Odetta Holmes (an intelligent civil rights protester living in 1964 New York City), manifests another personality. This other personality is Detta Walker.
Detta is not intelligent so much as she is cunning and crafty. And her methods are not peaceful.
Neither woman is aware of the other woman inhabiting her body.
Until Roland introduces the two to each other, by forcing them to look into the eyes of Jack Mort, the serial killer responsible for the two accidents which caused the traumatic brain injury and the splitting of the personality.
The two women realize that they share memories of Jack Mort, and a new personality emerges.
Ronda Rousey, move over…you now have competition for the title of "the baddest woman on planet!"
This union creates Susannah Dean.
Susannah is the best of both worlds:
She has Odetta's intelligence and sophistication. No one would have any problem bringing Susannah home to meet Mom.
But, Detta is not dead, as she is also a part of Susannah.
You may not bring Detta home to meet Mom (unless you are in that rebellious stage. Or you just hate Mom that much.)
But you would want to bring no one else with you when you face demons.
And I am talking about actual demons here, not just the ones in your head.
As in demons that appear to be a side effect of birthing someone into Mid-World (see above part about the love story.)
Bringing Odetta and Detta together is one merger that does not have disastrous consequences.
15. The gunfight with Enrico Balazar (The Drawing of the Three)
So, who doesn't love a good gunfight?
I am always up for one, in fact.
Things that make a good gunfight a great gunfight:
A dude with the nickname of Double Ugly gets pushed through a mysterious door into an alien world that is actually not that alien, as it has uncanny resemblances to our world, and said dude gets eaten by lobster monster creature thingies (lobstrosities for short.)
One of the participants is your friendly neighborhood gunslinger, who is an inhabitant of that alien world, and that participant REALLY knows his weaponry, especially guns.
And one the other participants puts up the fight of his life…
Naked?!
The battle between Roland, Eddie Dean and Enrico Balazar and his goons has always been on of my favorite parts of the series, and leaving it off this list would hurt me more than kicking a billy-bumbler er puppy.
The action sequence is amazing, and I don't think any onscreen treatment will ever match the movie that plays in my mind every time I read this part.
And not only is there action, we get our first in-depth look at Eddie Dean!
This is vintage Eddie Dean, before he becomes fully initiated into Roland's ka-tet, and before he earns the title of gunslinger.
We get to see Eddie the heroin addict. Eddie, who believes that his only purpose is to cater to the whims of his asshole big bro.
Eddie, who barely passed the clearing of the customs (sorry, I couldn't resist.)
And, like Roland, we get the surprise of our life, when we realize that there is steel hidden under that seemingly weak exterior.
After all, Eddie, who has never been in a gunfight in his life, is forced to fight in one, with no training. It's for realsies.
And did I mention he is also naked?
Oh, and one of Balazar's goons also beheads said asshole brother (although we could argue that was the biggest favor anyone had ever done for Eddie.)
But Eddie passes his on the spot test with flying colors.
As a recovering heroin addict, it will not be easy for Eddie in the coming days and weeks.
But that battle with Balazar reassures that Eddie is strong, and he has what it takes to break free of the prison that is addiction, and become the gunslinger that we (and Roland) know that he has been since birth.
14. The death of Susan Delgado (Wizard and Glass)
It's no secret that part of being a good writer is killing off characters.
Beloved characters, at that.
Often, a character is killed off, even if he/she did not "deserve" it.
(A moment of silence for Ned Stark. Just don't lose your head over this.)
A good writer will have us witness the death through our own eyes, and we feel we are there with that character living (and dying) in the moment with him or her.
However, a great writer will have us witness the death of a character through the eyes of another character, as the death takes place "off screen."
And somehow, the fact that the death takes place "off screen" does not make it any less agonizing. In fact, it may be even more agonizing.
In other words, I am talking about the death of Susan Delgado.
Many argue that the fourth book in The Dark Tower series is one that is unnecessary, as it largely tells the back story of Roland Deschain, and does not "advance" the plot of the series any further.
This argument is somewhat correct, as the story does not advance very much, since it tells us what happened to end Roland's childhood, and what happened to turn him into the man that we meet in The Gunslinger.
But skipping this book is a major disservice to the series.
This book gives insight into the character of Roland Deschain.
Apparently, people don't become cold-blooded killers, ready to sacrifice their friends for the sake of The Tower, overnight.
Roland, Cuthbert and Alain are sent to the town of Mejis because the adults in their lives believe that Meijis will provide safety again the evil that is taking root in Gilead.
However, ka says otherwise, as Meijis is actually the hotbed for that evil and corruption.
Meijis is also the home of Susan Delgado.
Roland never stood a chance against Susan. Almost immediately, Roland falls in love in Susan, even though she is "promised" to the mayor of Mejis (an old married man who seems to think he is entitled to a teenage body and whatever children that teenage body may bear. Ew.)
And Susan never did anything wrong, except maybe to fall in love with the wrong man.
But we cannot control who we fall in love with.
Wizard and Glass is a beautiful, bittersweet love story between two people who know, at some level, that they are on borrowed time.
But those two people still love each other. That love is intense, to say the least, perhaps because they are on borrowed time.
Susan Delgado is accused of treason, and burned at the stake.
Roland is not by her side, but is forced to watch through Maerlyn's Grapefruit, a magical artifact that gives its users the ability to see faraway events. Usually, these events are not pleasant ones.
As she dies, the last words uttered by Susan Delgado are:
Roland, I love thee!
We know that love is true when it is the last words we utter before our death.
Nothing is more pure. Or more tragic.
13. Tull (The Gunslinger)
So, let's get back to action, for a minute.
And death.
Since, you know, there is not enough death in these books (or any other King book, for that matter.)
Now, we've talked about characters dying, characters dying in a horrible manner, characters dying and being "born" into Mid-World, etc.
Well, now let's talk about the death of an entire village.
AN ENTIRE VILLAGE.
Let that sink in for a minute.
Now, I know that maybe part of a village can be bad, right?
Maybe a couple of guys, up to no good…
Making trouble in my…
(I don't really need to fill in the rest, right?)
But an entire village?
Men, women and…
Children?
Yes, even the children.
Even the kids living in Tull were not safe from our friendly, neighborhood gunslinger.
So, what gives?
Apparently, Sylvia Pittson.
Sylvia was one bad woman, and I don't mean the good kind of bad.
No, Sylvia was just bad.
Bad as in religious fanatic bad, which is really bad, both in the King universe and in real life.
Our friendly neighborhood gunslinger is hardened man, but he does operate by a code.
However, when a fanatical preacher turns an entire village against him and endangers his quest, along with his life, Roland's code gets thrown out the window.
Roland then proceeds to take care of business.
When Roland "takes care of business," things tend to turn deadly.
And the Battle of Tull is no different.
Roland is ruthless, dispatching each and everyone residing in that village, as they have been poisoned.
After all, if your limbs turn gangrenous, you need to amputate them, right?
And this is exactly what Roland does: he amputates the gangrenous village of Tull.
He even kills Allie, his lover, along with the rest of the village's inhabitants, both young and old, male and female.
We then realize that Roland means business.
If business is deadly, then it must be ka, right?
12. Eddie outwits Blaine the Mono (Wizard and Glass)
For a moment, I would like to have some light-hearted fun.
You know what's really fun?
I will take a riddling contest for $19, Alex!
Even better if that riddling contest puts my friends and I up against a sentient monorail who has gone cuckoo for Cocoa puffs and my punishment for losing is death, as the monorail commits suicide while my friends and I are still on it!
(In a slightly related note, I need to check the sarcasm font here, as I am not sure it is working properly at the moment, Stayed tuned for further technical updates!)
Well, lucky for me, my man is on board…
*Swoon*
Eddie Dean.
*Swoons yet again, falling with no one to catch her*
Eddie handsome.
And smart.
And a gunslinger.
And crafty.
And has the ability to beat sentient crazy monorails by using logic.
Actually, Eddie does not use logic.
Quick: Why did the dead baby cross the road?
Because it was stapled to the chicken…duh!
But "duh" was the downfall of Blaine.
Roland had forgotten more riddles than Eddie had ever heard in his life.
Jake had a book, but that didn't help much.
Susannah did her part, by calling on Detta when the pump was primed backwards.
Oy looked cute, because that's what Oy does.
So it fell to Eddie to best Blaine.
And Eddie did what Eddie does best:
Trip up on sentient monorails with dumb jokes that fry the circuits of sentient monorails.
Because of those dumb jokes, our favorite ka-tet lived to fight another day, and continue the march towards The Tower.
11. Meeting Stephen King (The Song of Susannah)
Okay, remember when I said some of these moments may be on the weird side?
Well, it doesn't get much weirder than this one, sai.
And you read the title of this moment correctly:
We meet in Stephen King.
He is a character in his own books.
I mean, you know a series of books is awesome when its creator feels the need to make himself a character in them, right?
(Fun fact: this is called metafiction. Really.)
It brings to meaning to the phrase "the writer of your own story."
And it's weird, but also kinda cool.
Art affects people.
We think of fiction affecting the reader, and it does.
But fiction, like any form of art, affects the creator.
When an artist creates a piece of art, he/she changes the world.
Something is now created that did not exist previously.
But the artist also changes.
It is no secret that The Dark Tower series has had a major effect on King, both personally and artistically.
All of his books are connected to The Dark Tower series.
From the book about a killer clown living in the sewers of a small town in Maine, to the trilogy telling the adventure of a retired detective and his friends, they are all interlinked.
King's books are diverse, but the lynch pin is The Dark Tower series.
King also suffered a near fatal vehicle accident in 1999.
In the books, this (literally) put the fate of the multiverse at enormous risk.
This accident also put King's world at risk, as he did not know if he would be able to finish the series that was the center of the universe.
But luckily, for Roland, his ka-tet, and his Constant Readers, King's love of this world and the characters he created won out, and the series was finished.
And King's world and characters continue to live on, because he gave them life, and we continue to give them life by reading these books.
10. Roland reunites with Sheemie (The Dark Tower)
Okay, time for the waterworks.
With The Dark Tower series, there are plenty of waterworks. As we go further down the list, we will continue to encounter them.
But, I want to start off with a waterworks moment that actually does not involve a death.
No, this one is sad, but more of a bittersweet kind of waterworks moment.
Roland's time in Meijis was a formative time in his youth, and it shaped him into the man we met at the beginning of The Gunslinger.
Not only did Roland fall in love for the first time (and tragically lose that love), he also met some interesting characters.
One of the people Roland encountered during his time in Mejis was a young man named Stanley (Sheemie) Ruiz.
Sheemie is a supposedly mentally handicapped young man, although it is observed that if Sheemie is indeed a half-wit, there more than a few others who may be quarter wits or less.
Roland and his friends rescue Sheemie from the hands of The Big Coffin Hunters, and make a friend for life afterwards.
Sheemie helps Roland and his friends defeat Eldred Jonas and The Big Coffin Hunters, although Sheemie is unable to rescue Susan Delgado from her tragic fate.
Roland mentions in Wizard and Glass that Sheemie was a sort of squire to him and his friends, and the subject is dropped.
Until the final book of the series.
Ka is at work, and Roland and the tet finally make it to Thunderclap, which houses the Breakers, who are people who possess psi abilities.
These people are being used by The Crimson King to destroy reality as we know it.
And one of these Breakers is none other than Sheemie Ruiz.
When Roland encounters Sheemie, Sheemie appears to be afraid, as opposed to being happy to be reunited with an old friend.
It turns out that Sheemie has been carrying guilt over his perceived role in Susan Delgado's death.
Sheemie breaks down.
But old, long, tall and ugly has nothing but love for Sheemie, and we see that love shine through, when he addresses Sheemie.
And apparently I need to stop cutting onions when I am writing blog entries…
9. Jake's death, Part 2 (The Gunslinger)
Okay, time to go there.
Time to start talking about that four letter word that has the nerve to contain an extra letter.
In other words, we are going to start talking about death.
Trust me, there is not a lack of death in this series. And plenty of the deaths are brutal, at that.
One of these deaths is the death of Jake Chambers.
More specifically, the first time Jake died after hooking up with Roland.
(Yes, the first time after hooking up with Roland. No words.)
At the beginning of The Gunslinger, some guy whose first name we are not even given is trudging across the Mohaine Desert on some quest, minding his own business like your typical, run of the mill cold-blooded killer.
But someone has other ideas for our friendly, neighborhood gunslinger.
Ideas in the form of a kid who gets hit by a car in another world, and is somehow transported into Mid-World.
At some level, both Roland and Jake know that no sacrifice is too great for Roland's quest.
This includes Jake's life.
However, Roland gets attached to Jake, per the plan of that particular someone.
Roland even tells Jake stories from his boyhood, including the tale of Hax, the traitor cook from some faraway place by the name of Gilead.
But Roland is then forced to make a choice.
And he proves his dedication to his quest by allowing Jake to fall.
We shouldn't be surprised, but it is no less heartbreaking to have to say goodbye to Jake.
We comfort ourselves with this thought:
Go, then. There are other worlds than these.
8. The Battle of Call Bryn Sturgis (The Wolves of the Calla)
Again, action sequences.
I can't help it, I am a total junkie for them
One of the reasons why I love The Wolves of the Calla is the action in the book.
First come smiles.
Then lies.
Last is gunfire.
And there is gunfire aplenty in this particular battle. The smiles and the lies covered the first half of the book or so, but I digress.
However, we can't have gunfire without a lot of careful planning on the part of Roland and the rest of the ka-tet.
Actually, there was plate-throwing as well, not just gunfire.
Anyway, Roland deduces that the creatures who invade Calla Bryn Sturgis every 23 years or so are not actually creatures, but robots of a particular kind. Actually, a nasty kind, as these robots kidnap children.
These robots kidnap children who happen to be one of a set. Twins, in other words.
The robots harvest something from the kids' brains for their own disgusting purposes, and the kids are returned to the village.
But when the kids are returned, they are not themselves. They are "roont," or human beings who can barely communicate and function as normal people. They also turn into giants, via a painful growth spurt that hits them when they are in their teens.
Roland and his friend decide to help the people of Calla Bryn Sturgis, for a variety of reasons.
A few weeks are spent preparing for the battle. As stated before, Roland realizes that the so-called wolves are actually robots. When you know your enemy, that enemy becomes a little easier to fight.
And the fight is glorious.
This may actually be the ka-tet's finest moment, which is saying something, given how many fine moments they have throughout the series.
Jake, in particular, stands out in this battle.
Yep, a 12 year old has my vote for G.O.AT.
Jake would deserve it, given his actions, and the fact that he lost a good friend in the battle. This battle forced poor Jake to grow up even more, as he experienced things not experienced by most twelve year old boys.
Poor Benny the Younger. Just one of the many sacrificial lambs in the story.
I also loved the Sisters of Oriza, aka the throwers of the plates.
The gunslingers were essential to the battle, but the Sisters of Oriza also played a huge part.
Plus, throwing plates is just bad ass, period.
When the battle ends, we know that the defeat of the wolves has had a direct effect on Roland's quest to save The Tower, as the wolves were kidnapping children in order to feed the Breakers, people with psi abilities who were recruited by The Crimson King to destroy The Tower and reality itself.
But, the most important part?
We get the satisfaction of knowing that the people of The Call Bryn Sturgis will never have to worry about their children being tortured and being forced to live out the rest of their lives in horrible pain.
That alone makes the death and bloodshed just a little bit easier to endure.
7. The Death of Randall Flagg (The Dark Tower)
Cry pardon, whatever is that sound?
Why, sai, it's the sound of me scratching my head yet again, as I prepare to talk about this particular entry.
As we all know, one of the great things about any King book are the villains.
Every hero (or a kinda sort anti-hero) needs a good villain.
And one of King's most notable villains is Randall Flagg.
And Walter o'Dim.
And Richard Fanin.
And Richard Farris.
Oh, there is some guy that loves to wear dark clothes and cause mischief who is a really cool villain…
Yes, we all know that I am talking about the same (and I use this word quite loosely) person.
Randall Flagg is perhaps the most iconic villain in the universe.
(I will be referring to him as Randall Flagg in this entry. Don't want to knock the initials RF, after all.)
One of the reasons why Flagg is such a great villain is that he takes genuine glee in causing not just mischief, but utter chaos.
Flagg can just drop in anywhere, it seems, work his awful magic, watch the ensuing chaos and then disappear, skipping along on his merry way to next kingdom or reality, where he will repeat the cycle, if he is lucky.
For a long time, I thought that if there was a nuclear war, the cockroaches would survive, and they would have Flagg as their leader, sowing death and destruction among the roaches dumb enough not to join up with Flagg and his new roach army.
Which is why you hear that noise, when we talk about Flagg's death.
Now, you would think that there would be a grand showdown against Roland and Flagg, as Flagg is Roland's true enemy, and the cause for every bad thing that has happened to Roland, including the death of his mother, father and all of his friends.
Lolz, says The Master.
Why would we have that showdown, when we could have a were-spider boy force Flagg to tear his body parts off so that said were-spider could dine on them, saving the eyes for dessert, popping them into his mouth like grapes?
King's villains are arrogant, but really?
Has anyone ever told Flagg, "I told you so?"
Scratch that, saying those four words to the uber villain of all uber villains would mean that you wouldn't live to have those kind of bragging rights.
But, still…
I just have to…
I told you so!
6. The death of Oy (The Dark Tower)
I admit, I have been procrastinating a bit.
I have tried to keep things somewhat light, because the dark moments are just…so dark.
But, I can't put it off any longer. We need to talk about this entry.
The death of Oy.
Now, there is A LOT of death in this series.
Both major and minor characters are killed off.
Not even iconic uber-villains are safe from being killed off.
But the death of Oy is one of the most heartbreaking deaths I have ever endured in any work of fiction.
Now, when Oy dies, we should not be surprised.
After all, in the book Wizard and Glass, there is a bit of foreshadowing when Roland peeks into Maerlyn's Grapefruit and is shown a vision of a billy-bumbler being impaled on a stick.
But, that vision can't be right, can it?
That can't be our Oy, can it?
Can it?
It is, and the vision was right. That particular grapefruit has never been known to show whoever it bewitches anything pleasant.
And poor Oy.
He lost most of his tet.
In particular, Jake. Oy was forced to watch Jake die on the side of a road.
Oy had also witnessed the death of Eddie.
Even though Susannah didn't die, she may as well have, as she crossed over into another world via the Unfound Door.
Oy probably knew that his end would not be a good one.
He was given an out when Susannah crossed over, but he chose to stay with "Olan."
Oy was a gunslinger in his own right. He was an essential part of Roland's quest to save The Tower.
Ka had plans for Oy.
And Oy did not try to dodge those plans, even though he must have been tempted.
Instead, Oy fulfilled his destiny.
He was impaled on a stick for his troubles, and died protecting Roland.
Oy's last word was his version of Roland's name, and he licked Roland's hand before he died.
I Ake.
5. Jake and Oy swap bodies (The Dark Tower)
Finally, an entry with a little bit of humor.
I mean, a tyranno-sorbet-wrecks is pretty funny, right?
Actually, someone swapping bodies with another person is never not funny.
Freaky Friday, anyone?
But a boy swapping bodies with his billy-bumbler so that they can escape the vampires and get back to Mid-World is hilarious, amirite?
Jake is human, obviously.
Oy is not, obviously. Oy is also from Mid-World, so most of anything having to do with our world is pretty confusing to him.
Somehow, Oy accesses a memory of an old movie that frightened Jake as a child.
Enter the tyranno-sorbets-wrecks.
Jake also has to learn to navigate on four legs, while Oy has to learn how to use only two legs.
So yeah, enter more hilarity and high jinks.
All the while, Jake and Oy are running from vampires.
Being caught by these vampires would actually be a fate worse than death.
But Jake is a gunslinger. And Oy is also a gunslinger. Having four legs never stopped anyone from being a gunslinger.
Because they are gunslingers, Oy and Jake escape the vampires, and are able to return to Mid-World.
The tyranno-sorbets-wrecks is left in the dust.
At least for now.
4. Susannah steps through the Unfound Door (The Dark Tower)
Well, at least this one is not about a death, right?
Although the person we are talking about experienced the death of her husband.
And her spiritual son.
Really, Susannah did not die, but does that fact really make a difference when we discuss what happened to her?
In fact, I think that the death of Eddie and Jake was also the death of Susannah.
She was just not the same after those events.
But she remained by Roland's side, and continued on the path of The Tower with him.
And the pain did not stop, as she had to endure cancer.
Mid-World did not want her there, and let her know, by the way of a disgusting pimple that just would not go away.
So, when Susannah was finally able to make the Unfound Door appear, I felt happy for her.
When she stepped through that door and into another world, I felt nothing but relief.
At least we will have one less casualty on this quest.
And it was beautiful when Jake and Eddie Toren, the Twinners of Jake Chambers and Eddie Dean, finally appeared.
Finally, Susannah could have happiness once again.
Now if you will excuse me, I am craving hot cocoa sprinkled with nutmeg…
3. Jake's death, Part 3 (rThe Dark Tower)
Yeah, part 3.
It wasn't enough for Jake to die once.
No, he had to die three times.
(Although I am a little skeptical about the first time, as Jake ended up in Mid-World. And died there. Right.)
But, when Jake died the first time, it was for keeps.
No take backs.
And, oh, how that realization hurts.
Jake, Roland and Oy travel to the "real world," in order to save a certain writer from an ugly death.
They are successful in their quest, but a huge price is paid.
The van that was supposed to hit and kill Stephen King still hits King, but Jake absorbs the brunt of the impact, and dies shortly afterwards.
In other words, King's characters save him.
This is beautiful when you thing about it, as art often impacts our lives in a big way, but it does not make the death of Jake any less painful for the reader.
In fact, when I read this scene, I wish that I could absorb some of that pain for Jake.
The thought of how courageous Jake was in his actions, and how painful his death is…
Well, I just can't find the words.
Yeah, the words on the computer screen are just a little blurry right now.
The eulogy that Roland utters for poor Jake is pure poetry, especially this line:
May his life on this earth and the pain of his passing become as a dream to his waking soul, and let his eyes fall upon every lovely sight; let him find the friends that were lost to him, and let everyone whose name he calls call his in return.
I have said it before, and I will say it again:
2. The fight with Shardik (The Wastelands)
Well, we are getting close to the finish line.
So of course, I need to insert one more.
That's right, one more battle sequence!
Come for the tooter fish popkins, stay for the battle scenes, right?
Although this entry could be considered more of a skirmish, as opposed to a battle.
But I still consider the fight with Shardik to be one of the more important action sequences in the series.
First of all, there is Shardik himself.
A cyborg, built to be a Beam Guardian, but who has gone insane and has treed Eddie Dean?
Yep, sign me up!
Oh, and he/it is infested with worms.
Only in Mid-World, right?
But most importantly, this particular battle gives Susannah Dean the chance to test her newly minted guns.
Even after a disturbing conversation with her dinh, in which said dinh confesses that that he believes to be going insane and begs for someone to take away his guns, Susannah shows us what she is made of.
After realizing that Eddie is trapped in the tree, and that she is the only who has a chance of saving him, Susannah proves that she is worthy to bear (okay, maybe I accidentally intended that pun) the title of gunslinger.
Susannah shoots the metal "thinking cap" above Shardik's head, and saves Eddie.
The ka-tet lives another day, and proves why they are ka-tet.
And the Constant Reader smiles, as memories are made.
Well guys, I need to confess something.
I know, I know.
Go ahead and beat me with that wet noodle.
Or Sheemie's mule, if that do ya fine.
I stated a few blog hours ago that this list was in no particular order.
But this post had determined that was a lie!
There is one moment in particular that sticks out to me, no matter how many times I read this series.
I present to you…
The death of Eddie Dean (The Dark Tower)
When reading The Dark Tower series, it is easy to start to take things for granted.
After all, how many times does our ka-tet live to fight another day?
Gun fight with Balazar. Check.
Fight with Shardik and other weird, animal cyborg minions. Check.
Susannah is forced to give birth to a not human baby that has interesting dietary preferences. Check.
Jake is kidnapped by pedophile who wants to sacrifice him to The Tick Tock Man. Check.
Throughout the series, the ka-tet fights and overcomes sometimes insurmountable odds.
Then, there was the Battle of Algul Siento.
King even warns us, before the fighting commences.
They are no longer a ka-tet, just good friends fighting the good fight.
But, we read on anyway. How can we not?
And at first, the fight goes in favor of our ka-tet.
The Breakers are freed. The Tower is saved.
And then, our hearts broken.
Eddie Dean is shot by a barely alive Pimli Prentiss.
The battle is done at the this point. Pimli should not have enough breath to open his eyes, let alone shoot a gunslinger.
But he has, and he does.
Indeed, ka-tet breaks, right along with our spirits.
There are times when you cry. Like when you stub your toe on errant furniture, maybe.
And there are times when you CRY.
When you CRY, it is not pretty.
The snot runs down your face. Your face turns red, then purple.
You draw in your breath in hitching gasps. You may try to speak, but if you manage to utter any words, they are incomprehensible.
The death of Eddie in this series is a moment that makes you CRY.
You CRY for Susannah, who has lost her husband and the man whose love made her a whole person.
You CRY for Roland, who Eddie called his true father before he passed to the clearing at the end of the path.
You CRY for Jake, the only child who found a true brother in Eddie. In turn, Jake becomes a true brother to Eddie.
But most of all, you CRY for yourself.
You have lost a friend.
A friend who had a sense of humor. Some of the most quotable quotes in these books are Eddie Dean-isms.
A friend who was sharp and dangerous, behind all the wisecracks.
A friend who more than proved himself to be worthy of the title of gunslinger.
And the book is still not done. You realize that you still have to finish it, and without the presence of Eddie Dean.
You also realize that this is just the beginning. There will be more hurt to come.
The death of Eddie Dean drives home what sacrifices need to be made for Roland's quest, and that the only guarantee is more bloodshed.
But, it still hurts.
It always will, no matter how many trips you take with Roland.
Well, thanks for hanging in there, folken!
These are my 19 most memorable moments of The Dark Tower series.
I am sure that are at least 19 more that I missed, so I cry pardon!
I will be back, with more insight on this series and other works by King.
Until then, long days and pleasant nights!
Oh, and happy reading!
Posted on January 24, 2019 by Leah	• This entry was posted in books, Dark Tower, horror, Stephen King and tagged A Song of Ice and Fire, Carrie, DC, Dracula, End of Watch, Finders Keepers, Game of Thrones, Gwendy's Button Box, horror, Insomnia, It, Mr. Mercedes, Randall Flagg, Rhonda Rousey, Richard Bachman, Robin Furth, Roland Deschain, Ronda Rousey, Salem's Lot, Stephen King, The Dark Tower, The Drawing of the Three, The Eyes of the Dragon, The Flash, The Gunslinger, The Song of Susannah, The Stand, The Wastelands, The Wind Through the Keyhole, The Wolves of the Calla, Twilight, vampires. Bookmark the permalink.
2 thoughts on "19 Dark Tower Moments"
Hi Leah. I couldn't find your contact info. I need your insight about a character for an audition. Can you email me?
Yes. My email address is clubred1978@gmail.com.

redpajama_set_name: RedPajamaCommonCrawl


Assessment: The financial condition of an individual is gauged by formulating balance sheets and income statements. The personal balance sheet calculates the assets on the one hand and liabilities on the other. Assets include car, house, stocks, and bank account. Personal liabilities include credit card debt, bank loan, mortgage etc. Information regarding personal income and expenses is listed under the personal cash flow statement.
Goal setting: After having done a proper assessment of the financial situation, we help our individual client to set up long term as well as short term goals.
Constructing a plan: Once the goals are set, appropriate strategies are formulated in order to fulfil the goals. This is achieved by curtailing unnecessary expenditure or by expanding the income level by investing in stocks, real estate or other interest earning assets.
Monitoring and reassessment: The financial plan of an individual is monitored from time to time for re-evaluation.


Spiritual growth does not happen automatically. Part of spiritual growth happens in your personal life as you talk with God, read the Bible, and practice obeying what He says. Another part of your spiritual growth happens with the church. This is where we can help: we want to help you fulfill God's plans for your life.
Approximately 259 million people in the United States and Canada do not have a personal relationship with Jesus Christ. Life on Mission is a North American Mission Board initiative that equips believers to live a missional lifestyle. A life lived on mission isn't a supersized version of an extraordinary Spirit-filled life. It isn't reserved only for top-level Christian risk-takers who have mastered the art of obedience. Living a life on mission is the story of everyday, ordinary believers leveraging whatever levels of influence they have to bring unbelievers to faith in Christ. This Bible study will not make you into an evangelist. However, it will invite you to connect with God's mission and equip you with tools to live a life that matters.
Each session will be facilitated by our pastors.
Discover the redemptive side of Job's story of suffering. Joy is the constant companion of the woman who trusts in the Lord. And while you can find it in friends, family, and circumstances, unfailing and persistent joy will only ever overflow from your relationship with Jesus. Just ask Job, the man from Uz who clung to God's goodness while all of his worldly joy were stripped away. But how is it possible to hold onto such joy in times of sorrow? In this study by Lisa Harper, discover the redemtive side to Job's story of suffering. Learn to use pain to strengthen your faith, point others to the gospel, and remember that God's providence will never take you to a place where His grace will not sustain you.
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Wednesday, July 7, 2021 | Case Studies, Public Safety
Disaster and Humanitarian Response Aided by Weather Intelligence
Team Rubicon was founded by two Marine Corps veterans who went to Haiti to help with relief efforts after the devastating 2010 earthquake. More than a decade later, Team Rubicon continues to coordinate disaster relief efforts led by military veteran volunteers, both internationally and domestically. The organization focuses on underserved and vulnerable communities and has deployed to over 440 disasters globally and boasts 135,000 registered disaster response volunteers. Teams on the ground focus on getting people back into their homes by mucking out flooded homes, removing downed trees, tarping roofs, and more.
A Team Rubicon volunteer clears downed trees after Hurricane Laura in 2020
Coordinating Relief
When coordinating volunteer efforts, the Team Rubicon staff looks at three factors:
Where the weather has caused or will cause damage
The location of vulnerable population, which is largely based on socio-economic data
The location of unmet need, which is determined by the response of emergency managers and volunteers during past disasters
"Weather is the most dynamic piece in all of this, it's going to be shifting," said Lauren Vatier, Senior Associate of Operational Planning at Team Rubicon.
Access to reliable weather data is key for Team Rubicon's operations. It needs to identify areas impacted by severe weather quickly to get teams deployed to help communities in need as soon as possible. Monitoring ongoing weather conditions is also necessary to ensure the safety of volunteers on the ground.
Team Rubicon does not have a meteorologist on staff. In the organization's early years, it relied on multiple weather sources to piece together forecasts when planning response efforts.
Baron has delivered a streamlined weather solution to Team Rubicon. High-quality, up-to-the-minute weather data is now visible throughout the entire organization, enabling more effective monitoring and forecasting of weather conditions. Utilizing Baron weather data, the staff can access in-depth data for severe events, including hurricanes and tornados.
Lauren who doesn't have a meteorologist background says Baron delivers actionable current and forecast data when they need it most.
"Before I would look at NOAA and NWS, read their assessments, and try to understand by Googling what they were saying," Vatier said. "Now I can go in and say 'Ok, I understand this.' I can see what it looks like and be in more control and make my own analysis."
Throughout Team Rubicon's time as a Baron customer, Baron has provided multiple training opportunities, including sending staff to the Team Rubicon Leadership Conference, to ensure the organization can capitalize on the features and functionality of Baron tools. Baron offers around-the-clock weather support from a staff of degreed meteorologists, a service Team Rubicon often takes advantage of before a major event. In 2018, Baron sent a meteorologist to Team Rubicon's National Operations Center to help analyze the weather and plan relief efforts as Hurricane Florence was bearing down on the Carolinas.
"Having that deeper analysis is really helpful because it can help give perspective and help us make decisions further in advance," said Vatier.
The staff at Team Rubicon will start tracking and monitoring when a storm is forming in the Atlantic. When they see it is a threat to land, they start ramping up volunteer efforts and doing daily briefings with Baron data as their forecasting guide. Lauren says they have a set of go-to Baron products. Lauren says they have a set of go-to products within Baron Threat Net to get a better understanding of the impact of a severe weather event that includes:
Tropical layers
Precipitation accumulation
Wind speeds
"In a hurricane, we want to pre-position our assets, so we need to determine where we think the disaster is going to strike," Vatier said. "If it's going to be a wind event, we're going to see more tree damage and use chainsaws to remove vegetative debris. We're going to use a different cache and specifically skilled volunteers. If it's a more water-based event, we're going to do more muck outs. Knowing what those threats are and where they're going to hit is going to drive a lot of our decision making."
A Hurricane Season Unlike any Other
2020 was the most active hurricane season on record with 30 named storms, including 13 hurricanes. Baron gave Team Rubicon an easily accessible tool to pinpoint impacted areas and proactively plan relief efforts throughout the year.
"Last year (2020) hurricane season started bright and early and it was just one after another. It felt like a never-ending series of hurricane monitoring," Vatier claimed.
Two of the Hurricanes, Laura and Delta made landfall just 13 miles apart in Louisiana.
Laura was a Category 4 storm when it reached land on August 27th. It brought wind speeds as high as 150mph, storm surges that reached 15 feet, and up to 10 inches of rain. The storm knocked out power to more than 900,000 homes, caused $19 billion of damage, and claimed 26 lives.
A display of Baron data shows Hurricane Laura as it makes landfall in Louisiana
As Laura moved closer to land, Baron data helped Team Rubicon realize they needed to shift their response from a flooding event to a wind event. They positioned a road clearance team in Lafayette, LA, located just outside the forecasted storm surge area and safe from dangerous winds.
A Team Rubicon volunteer works on a damaged home in Lousiana
Hurricane Laura made landfall overnight. The first team quickly deployed to the hard-hit city of Lake Charles where they cleared debris and downed trees to ensure road access to critical infrastructure. This was done in conjunction with local authorities. The road clearance team was followed by waves of volunteers who were able to help hundreds of homeowners with clearing trees and debris, tarping roofs, and some muck-outs.
In early October Hurricane Delta was moving through the Gulf and projected to follow a strikingly similar path as Hurricane Laura. There were still approximately 100 Team Rubicon volunteers on the ground helping homeowners. Monitoring weather conditions was now important for planning an effective response and for the safety of those already deployed.
"Our volunteers were now at risk of getting hit by this new hurricane," said Lauren. "We had to monitor not only for our volunteers but also for homeowners who were going to be affected again."
Team Rubicon volunteers prioritize tarping roofs before Hurricane Delta arrived then evacuated to the Houston area. When the most dangerous part had passed, they returned to the Lake Charles area.
The Hurricane Laura relief efforts were extended to help homeowners impacted by Hurricane Delta. Crews stayed on the ground until November 30th. In total, Team Rubicon volunteers helped worked on 599 homes, cleared 12 roads, and helped more than 1200 people in the wake of the two hurricanes.
During a hectic hurricane season or any weather-related disaster, Lauren says effectively planning large-scale relief efforts would be much more difficult without Baron data at her fingertips.
"I'd be more at the mercy of less reliable information, which puts a lot more guesswork into what I'm trying to predict or forecast. That is going to slow down our teams. If we position them a little bit off, it might take days to determine the best location to go."
Team Rubicon Summary
Challenges: Safely deploy teams of volunteers before and after devasting natural disasters by quickly locating the area of impact along with a safe location for staging.
Solution: Implementation of a web-based solution that provides high-quality Baron weather data. Baron delivers actionable weather intelligence including advanced forecasts, location-specific data and interpreted weather guidance.
Quickly pinpoint areas impacted or expected to be impacted by a severe weather event.
Weather visibility throughout the entire Team Rubicon organization via the web platform or the companion mobile app for use in the field.
Safe deployment of teams and supplies on the ground at target locations before, during and after the event.


Patrolman Benjamin Yost was shot and killed in retaliation for a previous arrest he had made.
Patrolman Yost was on foot patrol when two men approached and shot him. He died from the wounds.
It was later discovered that Patrolman Yost was killed because he had previously arrested a member of a notorious gang know as the Order of the Molly Maguires. This group of local miners had assigned two men to murder Patrolman Yost following the arrest of one of the gang's members.
Ten men were later arrested and charged in connection with two murders, including Patrolman Yost's . All ten men were later executed.
Patrolman Yost had served in the Civil war. He is buried in Odd Fellows Cemetery, Tamaqua, Pennsylvania.
God Bless you, Officer Yost. So many years later, far from forgotten. You are not memorialized on Ancestry, not even on their census! I will find you and make sure you are there. History sees you. We honor you.


text:
1.4: Atomic and Molecular Stability
[ "article:topic", "showtoc:no", "license:ccby", "authorname:frioux", "Positronium", "licenseversion:40", "source@https://faculty.csbsju.edu/frioux/workinprogress.html" ]
https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FPhysical_and_Theoretical_Chemistry_Textbook_Maps%2FQuantum_Tutorials_(Rioux)%2F01%253A_Quantum_Fundamentals%2F1.04%253A_Atomic_and_Molecular_Stability
The Chemical Bond According to Slater and Ruedenberg
Literature cited:
Addendum: The Bohr Model of Atomic and Molecular Stability
A deBroglie‐Bohr Model for the Hydrogen Atom
A deBroglie-Bohr Model for Positronium
Extracting Atomic and Molecular Parameters From the de Broglie‐Bohr Model of the Atom
I apologize for the considerable overlap in the following, but it does provide some additional interpretive graphics. It also contains references to the publications of Slater and Ruedenberg.
John Slater pioneered the use of the virial theorem in interpreting the chemical bond in a benchmark paper published in the inaugural volume of the Journal of Chemical Physics (1). This early study indicated that electron kinetic energy played an important role in bond formation. Thirty years later Klaus Ruedenberg and his collaborators published a series of papers (2,3,4) detailing the crucial role that kinetic energy plays in chemical bonding, thereby completing the project that Slater started. This Mathcad worksheet recapitulates Slater's use of the virial theorem in studying chemical bond formation and summarizes Ruedenberg final analysis.
Equation [1] gives the virial theorem for a diatomic molecule as a function of internuclear separation, while Equation \ref{2} is valid at the energy minimum.
\[1 \cdot T(R) + V(R) = -R \frac{d}{dR} E(R) \label{1} \]
\[E(R_{e}) = \frac{v(R_{e})}{2} = -T(R_{e}) \label{2} \]
At non-equilibrium values for the internuclear separation the virial equation can be used, with \(E = T + V\), to obtain equations for the kinetic and potential energy as a function of the inter-nuclear separation.
\[T(R) : = -E(R)-R \frac{d}{dR} E(R) \label{3} \]
\[V(R) : = 2 E(R) + R \frac{d}{dR} E(R) \label{4} \]
Thus, if \(E(R)\) is known one can calculate \(T(R)\) and \(V(R)\) and provide a detailed energy profile for the formation of a chemical bond. \(E(R)\) can be provided from spectroscopic data or from ab initio quantum mechanics. In this examination of the chemical bond we employ the empirical approach and use spectroscopic data for the hydrogen molecule to obtain the parameters (highlighted below) for a model of the chemical bond based on the Morse function (5). However, it should be noted that quantum mechanics tells the same story and yields an energy profile just like that shown in the following figure.
\(R \equiv 30, 30.2 \ldots 400 \quad D_{e} \equiv 0.761 \quad \beta = 0.0193 \quad R_{e} \equiv 74.1\)
\[E(R) \equiv [D_{e} (1- \exp [- \beta (R - R_{e})])^{2} - D_{e}] \nonumber \]
The dissociation energy, De, is given in atta (10-18) joules, the internuclear separation in picometers, and the constant \(\beta\) in inverse picometers.
This energy profile shows that as the internuclear separation decreases, the potential energy rises, falls, and then rises again. The kinetic energy first decreases and then increases at about the same internuclear distance that the potential energy begins to decrease.
As the molecular orbital is formed at large \(R\) constructive interference between the two overlaping atomic orbitals draws electron density away from the nuclear centers into the internuclear region. The potential energy rises as electron density is drawn away from the nuclei, but the total energy decreases because of a larger decrease in kinetic energy due to charge delocalization. Thus a decrease in kinetic energy funds the initial build up of charge between the nuclei that we normally associate with chemical bond formation.
Following this initial phase, at an internuclear separation of about 180 pm the potential energy begins to decrease and the kinetic energy increases, both sharply (eventually), while the total energy continues to decrease gradually. This is an atomic effect, not a molecular one as Ruedenberg so clearly showed. The initial transfer of charge away from the nuclei and into the bond region allows the atomic orbitals to contract significantly (\(\alpha\) increases) causing a large decrease in potential energy because the electron density has moved, on average, closer to the nuclei. The kinetic energy increases because the orbitals are smaller and kinetic energy increases inversely with the square of the orbital radius.
An energy minimum is reached while the potential energy is still in a significant decline (6), indicating that kinetic energy is the immediate cause of a stable bond and the molecular ground state in H2. The final increase in potential energy which is due mainly to nuclear-nuclear repulsion, and not electron-electron repulsion, doesn't begin until the internuclear separation is less than 50 pm, while the equilibrium bond length is 74 pm . Thus the common explanation that an energy minimum is reached because of nuclear-nuclear repulsion does not have merit.
The H2 ground state, E = -0.761 aJ, is reached at an internuclear separation of 74 pm (1.384 a0). In light of the previous arguments it is instructive to partition the total H2 electron density into atomic and molecular contributions. Each electron is in a molecular orbital which is a linear combination of hydrogenic 1s orbitals, as is shown below.
\[\Psi_{mo} = \frac{\Psi_{1sa} + \Psi_{1sb}}{\sqrt{2 + 2S_{ab}}} \quad where \quad \Psi_{1sa} = \sqrt{\frac{\alpha^{3}}{\pi}} \exp (- \alpha r_{a}) \quad \Psi_{1sb} = \sqrt{\frac{\alpha^{3}}{\pi}} \exp (- \alpha r_{b}) \nonumber \]
The total electron density is therefore 2\(\Psi_{MO}^{2}\). The atomic, or non-bonding, electron density is given by the following equation, which represents the electron density associated with two non-interacting atomic orbitals.
\[\rho_{n} = 2 \left( \Bigg| \dfrac{\Psi_{1sa} + i \Psi_{1sb}}{\sqrt{2}} \Bigg| \right)^{2} = \Psi_{1sa}^{2} + \Psi_{1sb}^{2} \nonumber \]
Clearly, the bonding electron density must be the difference between the total electron density and the non-bonding, or atomic, electron density.
\[\rho_{b} = \Psi_{MO}^{2} - \rho_{n} = \rho_{t} - \rho_{n} \nonumber \]
These three terms are plotted along the bond axis in the figure below. Alpha is the optimum orbital scale factor, Sab is the overlap integral, and R is the equilibrium internuclear distance in atomic units.
\(\alpha : = 1.197 \quad S_{ab} : = 0.681 \quad R : = 1.384 \quad y : = 0 \quad z : = 0 \quad x : = -3, -2.99 \ldots 5\)
\[\rho_{t} (\alpha, x, y, z) : = \frac{\frac{\alpha^{3}}{\pi} \bigg[ \exp (- \alpha \sqrt{x^{2} + y^{2} + z^{2}}) + \exp (- \alpha \sqrt{(x - R)^{2} + y^{2} + z^{2}}) \bigg]^{2}}{1 + S_{ab}} \nonumber \]
\[\rho_{n} (\alpha, x, y, z) : = \frac{\alpha^{3}}{\pi} \bigg[ \exp (-2 \alpha \sqrt{x^{2} + y^{2} + z^{2}}) + \exp (-2 \alpha \sqrt{(x-R)^{2} + y^{2} + z^{2}}) \bigg] \nonumber \]
\[\rho_{b} (\alpha, x, y, z) : = \rho_{t} (\alpha, x, y, z) - \rho_{n} (\alpha, x, y, z) \nonumber \]
The bonding electron density illustrates that constructive interference accompanying atomic orbital overlap transfers charge from the nuclei into the internuclear region, while the non-bonding density clearly shows the subsequent atomic orbital contraction which draws some electron density back toward the nuclei.
Slater, J. C. J. Chem. Phys. 1933, 1, 687-691.
Ruedenberg, K. Rev. Mod. Phys. 1962, 34, 326-352.
Feinberg, M. J.; Ruedenberg, K. J. Chem. Phys. 1971, 54, 1495-1511; 1971, 55, 5804-5818.
Feinberg, M. J.; Ruedenberg, K.; Mehler, E. L. Adv. Quantum Chem. 1970, 5, 27-98.
McQuarrie, D. A.; Simon, J. D. Physical Chemistry: A Molecular Approach, University Science Books, Sausalito, CA, 1997, p. 165.
Slater, J. C. Quantum Theory of Matter, Krieger Publishing, Huntington, N.Y., 1977, pp. 405-408.
Rioux, F. The Chemical Educator, 1997, 2, No. 6.
I close with a rather mystical description of the chemical bond by Charles A. Coulson, the author of Valence, an influential monograph on the chemical bond published in 1952.
Sometimes it seems to me that a bond between two atoms has become so real, so tangible, so friendly, that I can almost see it. Then I awake with a little shock, for a chemical bond is not a real thing. It does not exist. No one has ever seen one. No one ever will. It is a figment of our own imagination.... Here is a strange situation. The tangible, the real, the solid, is explained by the intangible, the unreal, the purely mental.
The purpose of this study was to outline the success of quantum mechanics in explaining the stability and structure of matter. But quantum mechanics didn't emerge out of a vacuum; it had a precursor – the Bohr model. So I thought it appropriate to take a brief look at that precursor and present its explanation of atomic and molecular stability.
My starting point (for the development of the Bohr model) was not at all the idea that an atom is a small-scale planetary system and as such governed by the laws of astronomy. I never took things as literally as that. My starting point was rather the stability of matter, a pure miracle when considered from the standpoint of classical physics. -Niels Bohr
All matter consists of elements that are made up of electrons, protons and neutrons. Given that the electron and the proton have opposite charges and therefore are attracted to one another provides the problem that classical physics has in explaining the stability of matter. What keeps these oppositely charged building blocks apart? There is no more fundamental question in science and Bohr was the first to attempt an explanation of atomic stability by creating, by fiat, the necessary rudimentary quantum mechanical concepts.
We begin with the Bohr model for the simplest element, the hydrogen atom. In the following tutorial the Bohr model is enriched with de Broglie's hypothesis of wave properties for the electron. This allows the reinterpretation of some of the apparently arbitrary features of Bohr's initial atomic model.
The 1913 Bohr model of the hydrogen atom was replaced by Schrödingerʹs wave mechanical model in 1926. However, Bohrʹs model is still profitably taught today because of its conceptual and mathematical simplicity, and because it introduced a number of key quantum mechanical ideas such as the quantum number, quantization of observable properties, quantum jump and stationary state.
Bohr calculated the manifold of allowed electron energies by balancing the mechanical forces (centripetal and electron‐nucleus) on an electron executing a circular orbit of radius R about the nucleus, and then arbitarily quantizing its angular momentum. Finally by fiat he declared that the electron was in a non‐radiating stationary state because an orbiting (accelerating) charge radiates energy and will collapse into the oppositely charge nucleus. In 1924 de Broglie postulated wave‐particle duality for the electron and other massive particles, thereby providing the opportunity to remove some of the arbitariness from Bohrʹs model. For example, an electron possessing wave properties is subject to constructive and destructive interference. As will be shown this leads naturally to quantization of electron momentum and kinetic energy, and consequently a manifold of allowed energy states for the electron relative to the nucleus.
The de Broglie‐Bohr model of the hydrogen atom presented here treats the electron as a particle on a ring with wave‐like properties.
$$\lambda = \frac{h}{m_{e} \nu}$$ de Broglieʹs hypothesis that matter has wave‐like properties
$$n \lambda = 2 \pi r$$ The consequence of de Broglieʹs hypothesis; an integral number of wavelengths must fit within the circumference of the orbit. This introduces the quantum number which can have values 1,2,3,... The n = 4 electron state is shown below.
$$m_{e} \nu = \frac{n \cdot h}{2 \pi r}$$ Substitution of the first equation into the second equation reveals that momentum is quantized.
$$T = \frac{1}{2} m_{e} \nu^{2} = \frac{n^{2} h^{2}}{8 \pi^{2} m_{e} r^{2}}$$ If momentum is quantized, so is kinetic energy.
$$E = T + V = \frac{n^{2} h^{2}}{8 \pi^{2} m_{e} r^{2}} - \frac{e^{2}}{4 \pi \epsilon_{0} r}$$ Which means that total energy is quantized. The second term is the electron‐proton electrostatic potential energy.
The quantum mechanical interpretation of these ʺBohr orbitsʺ is that they are stationary states. In spite of the fact that we use the expression kinetic energy, which implies electron motion, there is no motion. The electron occupies the orbit as a particle‐wave, it is not orbiting the nucleus. If it was orbiting in a classical sense it would radiate energy and quickly collapse into the nucleus. Clearly the stability of matter requires the quantum mechanical version of kinetic energy.
The ground state energy and orbit radius of the electron in the hydrogen atom is found by plotting the energy as a function of the orbital radius. The ground state is the minimum in the total energy curve. Naturally calculus can be used to obtain the same information by minimizing the energy with respect to the orbit radius. However, the graphical method has the virtue of illuminating the issue of atomic stability.
Fundamental constants: electron charge, electron mass, Planckʹs constant, vacuum permitivity. \(e : = 1.6021777 \times 10^{-19}\; coul\) \(m_{e} : = 9.10939 \times 10^{-31}\; kg\)
\(h : = 6.62608 \times 10^{-34}\; joule \cdot sec\) \(\epsilon_{0} : = 8.85419 \times 10^{-12}\; \frac{coul^{2}}{joule \cdot m}\)
Quantum number and conversion factor between meters and picometers and joules and attojoules. \(n : = 1 \qquad pm : = 10^{-12}\; m \qquad ajoule : = 10^{-18}\; joule\)
\[r : = 20, 20.5 \ldots 500\; pm \quad T(r) : = \frac{n^{2} h^{2}}{8 \pi^{2} m_{e} r^{2}} \quad V(r) : = \frac{e^{2}}{4 \pi \epsilon_{0} r} \quad E(r) : = T(r) + V(r) \nonumber \]
This figure shows that atomic stability involves a balance between potential and kinetic energy. The electron is drawn toward the nucleus by the attractive potential energy interaction (~ ‐1/R), but is prevented from collapsing into the nucleus by the extremely large kinetic energy (~1/R2) associated with small orbits.
As shown below, the graphical approach can also be used to find the electronic excited states.
\[n : = 2 \quad T(r) : = \frac{n^{2} h^{2}}{8 \pi^{2} m_{e} r^{2}} \quad V(r) : = - \frac{e^{2}}{4 \pi \epsilon_{0} r} \quad E(r) : = T(r) + V(r) \nonumber \]
As mentioned earlier the manifold of allowed electron energies can also be obtained by minimizing the energy with respect to the orbit radius. This procedure yields,
\[E_{n} = - \frac{m_{e} e^{4}}{2(4 \pi \epsilon_{0})^{2} \hbar^{2}} \frac{1}{n^{2}} \quad and \quad r_{n} = \frac{4 \pi \epsilon_{0} \hbar^{2}}{m_{e} e^{2}} n^{2} \nonumber \]
The Bohr model gives correct results for any one-electron atomic atom or ion. The following tutorial shows that it is also accurate when applied to the rather esoteric and short-lived hydrogen atom analog positronium, in which the proton is replaced the positron, the electron's antiparticle.
Positronium is a metastable bound state consisting of an electron and its positron antiparticle. In other words it might be thought of as a hydrogen atom in which the proton is replaced by a positron. Naturally it decays quickly after formation due to electron-positron annihilation. However, it exists long enough for its ground state energy, -0.25 Eh, to be determined. The purpose of this tutorial is to calculate this value using the Bohr model for positronium shown below.
The electron occupies a circular orbit of radius R which has a positron at its center. Likewise the positron occupies a circular orbit of radius R which has an electron at its center. Occupies has been emphasized to stress that there is no motion, no orbiting. Both particles are behaving as waves (this is the meaning of wave-particle duality) occupying the orbit. As waves they are subject to interference, and to avoid destructive interference the wavelength for the ground state is one orbit circumference.
\[\lambda = 2 \pi R \nonumber \]
Introducing the de Broglie relationship between wavelength and momentum, \(\lambda = \frac{h}{p}\), yields the following expression for momentum in atomic units (h = 2\(\pi\)).
\[p = \frac{h}{2 \pi R} = \frac{1}{R} \nonumber \]
In atomic units me = mp = 1. Therefore, the kinetic energy of each particle is,
\[T = \frac{p^{2}}{2m} = \frac{1}{2R^{2}} \nonumber \]
The total energy of positronium is the sum of electron and positron kinetic energies and their coulombic potential energy.
\[E = T_{e} + T_{p} + V_{ep} = \frac{1}{2R^{2}} + \frac{1}{2R^{2}} - \frac{1}{R} = \frac{1}{R^{2}} - \frac{1}{R} \nonumber \]
Energy minimization with respect to the electron-positron distance R yields the following result.
\[\frac{d}{dR} \left(\dfrac{1}{R^{2}} - \dfrac{1}{R}\right) = 0 \quad \text{solve,}\; R \rightarrow 2 \nonumber \]
The optimum R value yields a ground state energy of -0.25 Eh, in agreement with experiment.
\[E = \frac{1}{R^{2}} - \frac{1}{R} \quad \text{substitute,}\; R = 2 \rightarrow E = - \frac{1}{4} \nonumber \]
Including the symbols for mass in the kinetic energy contributions facilitates the introduction of the concept of effective mass of the composite system.
\[T = \frac{1}{2 m_{e} R^{2}} + \frac{1}{2m_{p} R^{2}} = \frac{1}{2R^{2}} \left(\dfrac{1}{m_{e}} + \dfrac{1}{m_{p}}\right) = \frac{1}{2R^{2}} \left(\dfrac{m_{e} + m_{p}}{m_{e} \cdot m_{p}} \right) = \frac{1}{2 \mu_{ep} R^{2}} \nonumber \]
\[\mu_{ep} = \frac{m_{e} \cdot m_{p}}{m_{e} + m_{p}} = \frac{1 \cdot 1}{1 + 1} = \frac{1}{2} \nonumber \]
The positronium energy minimum can also be located graphically.
Plotting kinetic and potential energy along with total energy reveals that a ground state is achieved because beginning at R = 2, the kinetic energy is approaching positive infinity more quickly than the potential energy is approaching negative infinity.
After reviewing the Bohr model for the hydrogen atom, the following tutorial outlines Bohr's model for the hydrogen molecule. It shows that it yields plausible values for bond energy and bond length.
The 1913 Bohr model of the hydrogen atom was replaced by Schrödingerʹs wave mechanical model in 1926. However, Bohrʹs model is still profitably taught today because of its conceptual and mathematical simplicity, and because it introduced a number of key quantum mechanical ideas such as the quantum number, quantization of observable properties, quantum jump and stationary state. In addition it provided realistic values for such parameters as atomic and molecular size, electron ionization energy, and molecular bond energy.
In his ʺplanetaryʺ model of the hydrogen atom Bohr began with a Newtonian analysis of the electron executing a circular orbit of radius R about a stationary nucleus, and then arbitrarily quantized the electronʹs angular momentum. Finally, by fiat he declared that the electron was in a non‐radiating stationary state because an orbiting (accelerating) charge radiates energy and will collapse into the oppositely charge nucleus.
In 1924 de Broglie postulated wave‐particle duality for the electron and other massive particles, thereby providing the opportunity to remove some of the arbitrariness from Bohrʹs model. For example, an electron possessing wave properties is subject to constructive and destructive interference. As will be shown this leads naturally to quantization of electron momentum and kinetic energy, and consequently to a stable ground state for the hydrogen atom.
The de Broglie‐Bohr model of the hydrogen atom presented here treats the electron as a particle on a ring with wave‐like properties. The key equation is wave‐particle duality as expressed by the de Broglie equation. The particle concept momentum and the wave concept \(\lambda\) are joined in a reciprocal relationship mediated by the ubiquitous Planckʹs constant.
\[p = \frac{h}{\lambda} \nonumber \]
This equation will be used with the Bohr model of the hydrogen atom to explain atomic stability and to generate estimates of atomic size and electron binding energy in the atom.
In the de Broglie version of the Bohr hydrogen atom we say that the electron occupies a ring of radius R. It is not orbiting the nucleus, it is behaving as a stationary wave. In order to avoid self‐interference the following wavelength restriction must be obeyed for the ground state of the hydrogen atom.
When combined with the de Broglie equation it reveals the following restriction on the electronʹs particle property, linear momentum.
\[p = \frac{h}{2 \pi R} \nonumber \]
This means there is also a restriction on the electronʹs kinetic energy. Use of this equation in the classical expression for kinetic energy yields the quantum mechanical kinetic energy or more accurately electron confinement energy
\[T = \frac{p^{2}}{2m} = \frac{h^{2}}{8 \pi^{2} mR^{2}} = \frac{1}{2R^{2}} \nonumber \]
In this equation we have moved from the classical definition of kinetic energy to the quantum mechanical version expressed on the right in atomic units.
\[\frac{h}{2 \pi} = m = e = 4 \pi \epsilon_{0} = 1 \nonumber \]
The electrostatic potential energy retains its classical definition in quantum mechanics.
\[V = \frac{-e^{2}}{4 \pi \epsilon_{0} R} = \frac{-1}{R} \nonumber \]
The total electron energy, EH(R) = T(R) + V(R), is now minimized with respect to the ring or orbit radius, the only variational parameter in the model. The total energy, and kinetic and potential energy are also displayed as a function of ring radius.
\[R : = 0.5 \quad E_{H} (R) : = \frac{1}{2R^{2}} - \frac{1}{R} \quad R : = \text{Minimize} (E_{H}, R) \quad R = 1.000 \quad E_{H}(R) = -0.500 \nonumber \]
From this simple model we learn that it is the wave nature of the electron that explains atomic stability. The electronʹs ring does not collapse into the nucleus because kinetic (confinement) energy goes to positive infinity (~R‐2) faster than potential energy goes to negative infinity (~‐R‐1). This is seen very clearly in the graph. The ground state is due to the sharp increase in kinetic energy as the ring radius decreases. This is a quantum effect, a consequence of de Broglieʹs hypothesis that electrons have wave‐like properties. As Klaus Ruedenberg has written, ʺThere are no ground states in classical mechanics.ʺ
The minimization process above the figure provides the ground state ring radius and electron energy in atomic units, a0 and Eh, respectively. R = 1 a0 = 52.9 pm gives us the benchmark for atomic size. Tables of atomic and ionic radii carry entries ranging from approximately half this value to roughly five or six times it. The ground state (binding) energy, E = ‐0.5 Eh = ‐13.6 eV = ‐1312 kJ/mol, is the negative of the ionization energy. This value serves as a benchmark for how tightly electrons are held in atoms and molecules.
A more comprehensive treatment of the Bohr atom utilizing the restriction that an integral number of wavelengths must fit within the ring, n\(\lambda\) = 2\(\pi\)R , where n = 1, 2, 3, ... reveals a manifold of allowed energy states (‐0.5 Eh/n2) and the basis for Bohrʹs concept of the quantum jump which ʺexplainedʺ the hydrogen atom emission spectrum. Here for example is the n = 4 Bohr atom excited state.
Rudimentary estimates of some molecular parameters, the most important being bond energy and bond length, can be obtained using the following Bohr model for H2. The distance between the protons is D, the electron ring radius is R, and the bond axis is perpendicular to the plane of the ring
There are eight contributions to the total molecular energy based on this model: electron kinetic energy (2), electron‐proton potential energy (4), proton‐proton potential energy (1) and electron‐electron potential energy (1).
\[E_{H2} (R,D) : = \frac{1}{R^{2}} - \frac{4}{\sqrt{R^{2} + (\frac{D}{2})^{2}}} + \frac{1}{D} + \frac{1}{2R} \nonumber \]
Minimization of the energy with respect to ring radius and proton‐proton distance yields the following results.
\[D : = 2 \quad \begin{pmatrix} R \\ D \end{pmatrix} : = \text{Minimize} (E_{H2}, R,D) \quad \begin{pmatrix} R \\ D \end{pmatrix} = \begin{pmatrix} 0.953 \\ 1.101 \end{pmatrix} \quad E_{H2} (R,D) = -1.100 \nonumber \]
The H‐H bond energy is the key parameter provided by this analysis. We see that it predicts a stable molecule and that the energy released on the formation of H2 is 0.1 Eh or 263 kJ/mol, compared with the experimental value of 458 kJ/mol. The model predicts a H‐H bond length of 58 pm (D.52.9 pm), compared to the literature value of 74 pm. These results are acceptable given the primitive character of the model.
\[H + H = H_{2} \nonumber \]
\[\Delta E_{bond} : = E_{H2} (R,D) = -2 E_{H}(1) \quad \Delta E_{bond} = -0.100 \nonumber \]
In addition to these estimates of molecular parameters, the model clearly shows that molecular stability depends on a balancing act between electron‐proton attraction and the ʺrepulsiveʺ character of electron kinetic energy. Just as in the atomic case, it is the 1/R2 dependence of kinetic (confinement) energy on ring radius that prevents molecular collapse under electron‐proton attraction. As the energy profile provided in the Appendix shows, the immediate cause of the molecular ground state is a rise in kinetic energy. Potential energy is still declining at this point and does not begin to rise until 0.55 a0, well after the ground state is reached at 1.10 a0.
Although the model is a relic from the early days of quantum theory it still has pedagogical value. Its mathematical simplicity clearly reveals the importance of the wave nature of matter, the foundational concept of quantum theory.
Two relatively recent appraisals of Bohrʹs models of atomic and molecular structure have been appeared in Physics Today:
ʺNiels Bohr between physics and chemistry,ʺ by Helge Kragh, May 2013, 36‐41.
ʺBohrʹs molecular model, a century later,ʺ by Anatoly Svidzinsky, Marlan Scully, and Dudley Herschbach, January 2014, 33‐39.
\[R : = 0.1 \quad \text{Energy} : = -1 \quad Given\; \text{Energy} = E_{H2} (R,D) \quad \frac{d}{dR} E_{H2} (R,D) = 0 \quad \text{Energy(D) : = Find(R, Energy)} \nonumber \]
\[D : = 0.15, 0.16 \ldots 4 \quad T(D) : = \frac{1}{[Energy(D)_{0}]^{2}} \quad V(D) : = - \frac{4}{\sqrt{[Energy(D)_{0}]^{2} + (\frac{D}{2})^{2}}} + \frac{1}{D} + \frac{1}{2 \cdot \text{Energy}(D)_{0}} \nonumber \]
The examples presented in this addendum are based on classical pictures of the hydrogen atom, positronium, and the hydrogen molecule that have been moved in the quantum direction with de Broglie's hypothesis of wave-particle duality for matter. Bohr and de Broglie are the early quantum theorists who cut a path for those who created modern quantum theory.
This page titled 1.4: Atomic and Molecular Stability is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Frank Rioux via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
1.5: Quantum Computation - A Short Course
Positronium


text:
Moncada headlines top prospect performers Wednesday
By David Adler
Yoan Moncada showed off what made him the centerpiece of the Chris Sale trade on Wednesday.The No. 2 prospect in baseball, the top second baseman prospect and the top prospect in the White Sox organization hit his first two home runs of Spring Training in a monster game against the
Yoan Moncada showed off what made him the centerpiece of the Chris Sale trade on Wednesday.
The No. 2 prospect in baseball, the top second baseman prospect and the top prospect in the White Sox organization hit his first two home runs of Spring Training in a monster game against the Royals.
"You have to keep working hard," Moncada said through an interpreter. "I'm very happy with the process, and I know that the results are going to be there when I need it."
The 21-year-old Cuba native, who made his MLB debut in September just 18 months after turning pro, was the jewel of Chicago's deal with the Red Sox in December. He had been off to somewhat of a slow start this spring, but he broke out in a big way with Wednesday's Cactus League performance.
Moncada's two homers in the White Sox's 7-3 win came against quality competition. The first, a two-run homer in the fifth inning, was off veteran right-hander Jason Hammel. The second was a leadoff shot off All-Star closer Kelvin Herrera in the seventh.
More notable performances from top prospects:
• Bradley Zimmer -- the Indians' No. 1 prospect, the No. 22 overall prospect and the No. 7 outfield prospect -- went 2-for-5 with a double and an RBI groundout in Cleveland's 11-10 loss to the Rangers on Wednesday. Zimmer continues to rake in Spring Training -- the 24-year-old, a non-roster invitee, is hitting .359 with two homers.
• Outfielder Hunter Renfroe (Padres No. 3, MLB No. 42) hit his first home run of Spring Training on Wednesday, a two-run shot in the first inning against the Reds. The 25-year-old is batting .278 this spring.
• Brewers No. 1 prospectLewis Brinson, also the No. 18 overall prospect in baseball and the No. 5 outfield prospect, continued a strong showing this spring. Brinson doubled in his only at-bat Wednesday as a late-game replacement. The 22-year-old is now batting .313 this Spring Training with a pair of home runs.
• The Dodgers had a pair of prospects perform well on Wednesday. Top prospectCody Bellinger (No. 1 first baseman, No. 12 overall) went 1-for-3 and drove in three runs, on a two-run single and a sacrifice fly, in the Dodgers' 12-7 win over the Mariners.
In addition, Alvin Toles (Dodgers No. 9), who baseball fans know from his strong performance in last year's playoffs, went 3-for-4 with a triple, an RBI and three runs scored. Toles' big day brought the 24-year-old's batting average up to .280 this spring.
• Casey Gillaspie (Rays No. 5, No. 5 first baseman) continued his recent power surge with a go-ahead two-run homer on Wednesday against the Red Sox. The 24-year-old hit a pair of home runs on Sunday.
• In the same game as Gillaspie, Red Sox first baseman Sam Travis -- the team's No. 4 prospect and the 10th-ranked first base prospect -- went 2-for-3 with a home run of his own, his third of Spring Training. The 23-year-old is hitting an impressive .321 with an 1.174 OPS this spring.
• Moncada wasn't the only prospect to impress in the White Sox-Royals tilt on Wednesday. Royals No. 12 prospectJorge Bonifacio homered in his only at-bat after coming into the game. The 23-year-old outfielder is making the most of his spring at-bats, hitting .462 with a 1.404 OPS.
• Twins left-hander Adalberto Mejia, Minnesota's No. 8 prospect, made his first start of Spring Training against the Cardinals and was thoroughly dominant. The 23-year-old shut out a lineup that included several of the St. Louis regulars, like Aledmys Diaz and Stephen Piscotty, for 3 2/3 innings, scattering four hits to pick up the win. Most impressive, he racked up eight strikeouts -- more than two per inning -- and didn't walk a batter.
• For the Rockies, No. 6 prospectKyle Freeland was impressive on the mound. The 23-year-old left-hander tossed four scoreless innings against the Brewers, allowing five hits and no walks and striking out five. Freeland has a 2.45 ERA this spring.
David Adler is a reporter for MLB.com based in New York. Follow him on Twitter at @_dadler.


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The Washington Post vs. "Fake News": Pot, Meet Kettle
by Thomas L. Knapp…….
"Freedom of expression is a bedrock of American democracy," the Washington Post's editorial board writes in a November 18 jeremiad, "but its irresponsible exercise can distort and destabilize our politics."
The Post's editors, mining the bottomless pit of mainstream media excuses for not predicting Donald Trump's victory in November's presidential election, think they've hit the mother lode with their newfound focus on "fake news" stories going viral in social media.
The Post coming out against "fake news?" That's rich, especially given the last few months, during which the Post's reporters went all in for Hillary Clinton even to the extent of manufacturing "news" that Trump, and Julian Assange of Wikileaks, were in bed with Vladimir Putin and the Russian government.
Neither the Post nor its sources have publicly revealed so much as a crumb of actual evidence for the assertion. The case for the claim consists entirely of rumor and innuendo. But since doing so seemed to benefit Clinton's campaign, the Post unreservedly ran with that rumor and innuendo, helpfully packaged for it by the Obama administration and the Democratic National Committee.
A one-time lapse? An artifact of Jeff Bezos's takeover of the newspaper? No. The Post has been a vector for "fake news" for decades.
In the run-up to George W. Bush's invasion of Iraq, the Post led American media's cheering section, cheerfully publishing one bald-faced administration lie after another concerning Saddam's "weapons of mass destruction" — then in the aftermath assisting the administration in taking revenge on Joseph Wilson (who had exposed one of the lies) by exposing his wife, Valerie Plame, as a CIA agent.
Woodward and Bernstein's glorious expose of the Watergate affair is long past and may have been an exception to the rule even back then. These days, at any rate, "fake news" is the Washington Post's stock in trade. Half their "reportage" comes down to nothing more complex than re-wording government press releases. The other half requires the extra work of slanting alleged "news" in favor of the paper's favored causes and against their political opponents.
The Post's editors pathetically close their diatribe with a veiled threat, channeling their masters' voice: Social media needs to crack down on other people doing what the Post does to "avoid giving tyrants any impetus to crack down on dissent and free expression."
This, from the paper which used Edward Snowden's whistle-blowing work to grab a Pulitzer … then publicly advocated prosecuting their source!
The Post's editors have no problem with tyrants cracking down — they work for the tyrants. Their problem is purveyors of "fake news" — other than the variety pushed by the Post — gobbling up revenue in a niche the Post considers its own.
~~~~~~~~~~~~~~
Thomas L. Knapp (Twitter: @thomaslknapp) is director and senior news analyst at the William Lloyd Garrison Center for Libertarian Advocacy Journalism (thegarrisoncenter.org). He lives and works in north central Florida.
November 25, 2016 Posted by Thomas L. Knapp at 1:00 am Issue #194, Thomas L. Knapp	Add comments
One Response to "The Washington Post vs. "Fake News": Pot, Meet Kettle"
margiebargie says:
You accuse the Washington Post of "manufacturing "news" that Trump, and Julian Assange of Wikileaks, were in bed with Vladimir Putin and the Russian government." But that issue is mentioned nowhere in the link you provided.
Fox News also reported on the Russian hacking story, which was based on a joint statement released by the Office of the Director of National Intelligence and the Department of Homeland Security.
Here's a link: http://www.foxnews.com/politics/2016/10/07/us-accuses-russia-hacking-political-sites.html
So is Fox also "manufacturing news"?
Every publication is going to have it's own personality and point-of-view. That will be partially reflected by the particular stories they choose to publish. For example, you're more likely to hear about problems with Obamacare on Fox News then you will on MSNBC. But MSNBC will report on the people that Obamacare has helped. It's every citizens responsibility to get information from a variety of sources so they are well-informed and can make sound decisions.
That said, fake news is a whole other category. Those are sites that simply make stuff up out of thin air. Sometimes its for the purposes of trolling. Sometimes it's just to make money.
Sheriff's Crime Report Numbers of Key Deer Deaths Stabilizing


A remarkable total of 84 ratified World records have been set in the city of Berlin, with an impressive total of 26 having been recorded in the 1936 Olympic stadium, the traditional home of ISTAF meeting.
However, due to renovation work being carried out on the Olympic stadium, when Germany's premier meeting takes place this Friday 6 September it will have a temporary new home in the Friedrich Ludwig Jahn Sportpark, on the eastern side of the capital city.
Thanks to Berlin's impressive athletics history, the relocation merely means that one illustrious venue has been replaced by another, as the Friedrich Ludwig Jahn Sportpark has been the site of 25 records.
In fact ISTAF's new home holds a particularly special place in athletics history. On the 20 July 1984, the figures 104.80 resounded round the world of javelin throwing. At the XXII Olympic Day meet in the then East Germany, Uwe Hohn with his second throw of the competition obliterated the 13 month old World record of America's Tom Petranoff (99.72), to become the first man over 100m.
A new throwing era had dawned and with it came the realization that with such distances the javelin was potentially a threat, even to members of the crowd. By 1986 a new specification implement was introduced, which by moving the centre of gravity forwards by 4cm, both reduced the distances that could be thrown and enabled the javelin always to stick in the ground for easier measurement.
As well as a new venue in 2002, ISTAF is also under the control of new meeting organisers who will no doubt hope that just as Hohn's gigantic throw was a watershed in the history of javelin throwing, so a change of venue and new management will also mark the renaissance of a meeting which has been a German sporting icon since 1921.


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