K L Slater Popular Books
K L Slater Biography & Facts
Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method. They are named after the physicist John C. Slater, who introduced them in 1930. They possess exponential decay at long range and Kato's cusp condition at short range (when combined as hydrogen-like atom functions, i.e. the analytical solutions of the stationary Schrödinger equation for one electron atoms). Unlike the hydrogen-like ("hydrogenic") Schrödinger orbitals, STOs have no radial nodes (neither do Gaussian-type orbitals). Definition STOs have the following radial part: R ( r ) = N r n − 1 e − ζ r {\displaystyle R(r)=Nr^{n-1}e^{-\zeta r}\,} where n is a natural number that plays the role of principal quantum number, n = 1,2,..., N is a normalizing constant, r is the distance of the electron from the atomic nucleus, and ζ {\displaystyle \zeta } is a constant related to the effective charge of the nucleus, the nuclear charge being partly shielded by electrons. Historically, the effective nuclear charge was estimated by Slater's rules. The normalization constant is computed from the integral ∫ 0 ∞ x n e − α x d x = n ! α n + 1 . {\displaystyle \int _{0}^{\infty }x^{n}e^{-\alpha x}\,\mathrm {d} x={\frac {n!}{~\alpha ^{n+1}\,}}~.} Hence N 2 ∫ 0 ∞ ( r n − 1 e − ζ r ) 2 r 2 d r = 1 ⟹ N = ( 2 ζ ) n 2 ζ ( 2 n ) ! . {\displaystyle N^{2}\int _{0}^{\infty }\left(r^{n-1}e^{-\zeta r}\right)^{2}r^{2}\,\mathrm {d} r=1\Longrightarrow N=(2\zeta )^{n}{\sqrt {\frac {2\zeta }{(2n)!}}}~.} It is common to use the spherical harmonics Y l m ( r ) {\displaystyle Y_{l}^{m}(\mathbf {r} )} depending on the polar coordinates of the position vector r {\displaystyle \mathbf {r} } as the angular part of the Slater orbital. Derivatives The first radial derivative of the radial part of a Slater-type orbital is ∂ R ( r ) ∂ r = [ ( n − 1 ) r − ζ ] R ( r ) {\displaystyle {\partial R(r) \over \partial r}=\left[{\frac {(n-1)}{r}}-\zeta \right]R(r)} The radial Laplace operator is split in two differential operators ∇ 2 = 1 r 2 ∂ ∂ r ( r 2 ∂ ∂ r ) {\displaystyle \nabla ^{2}={1 \over r^{2}}{\partial \over \partial r}\left(r^{2}{\partial \over \partial r}\right)} The first differential operator of the Laplace operator yields ( r 2 ∂ ∂ r ) R ( r ) = [ ( n − 1 ) r − ζ r 2 ] R ( r ) {\displaystyle \left(r^{2}{\partial \over \partial r}\right)R(r)=\left[(n-1)r-\zeta r^{2}\right]R(r)} The total Laplace operator yields after applying the second differential operator ∇ 2 R ( r ) = ( 1 r 2 ∂ .... Discover the K L Slater popular books. Find the top 100 most popular K L Slater books.
Best Seller K L Slater Books of 2024
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Summary of The Widow By K.L. Slater
Justin ReeseDISCLAIMERThis is NOT the original K.L. Slater's bookThis is a wellDetailed Summary of The Widow By K.L. SlaterThe Widow is a gripping psychological thriller from the author of Gon...
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In Her Place
Edel CoffeyFrom the #1 bestselling author of Breaking Point and winner of Crime Novel of the Year at the An Post Irish Book Awards.'Edel Coffey is like an Irish Jodi Picoult! In Her Place exa...
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Falling Suns
J. A. Corrigan'An outstanding first novel, dark, disturbing and unputdownable' 5 review'Absolutely compelling' 5 review'Completely engrossing and I couldn't wait to get back to read another page...
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What Goes Around
Julie CorbinA gripping psychological thriller for fans of Lisa Jewell and C.L Taylor.500 five star Goodreads ratingOnce you start reading, you won't want to stop. Two women, two secrets, one...
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The Accused
Jackie KablerYOUR FRIEND IS INNOCENT. BUT CAN YOU PROVE IT?The second book in the muchloved Cora Baxter Mysteries series, from the acclaimed broadcaster, USA Today bestseller and bestselling au...
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Whispers of a Scandal
Julie CorbinWho knows your darkest secret?After every parents' evening, friends Nina, Bel and Rachel look forward to their regular debrief at the pub. But there will be no clinking Prosecco to...
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The Locksmith
Linda CalveyWith a foreword from Martina Cole, the Queen of CrimeMost authors write what they know. Linda Calvey writes what she lived. They grew up with nothing. Just a regular family scrapin...
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Go Seek
Michelle Teahan'Tense, pacy and full of surprises, Go Seek is like nothing I've ever read before . . . Actionpacked, suspenseful and a nail biting joy' ANDREA MARA'A twisty and gripping debut!' C...
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Cold Grave
Craig Robertson'Robertson is doing for Glasgow what Rankin did for Edinburgh' Mirror1993. Scotland is in the grip of an icecold winter and the Lake of Menteith is frozen over. A young man and wom...
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Stay
Jane Bailey'There was so much suspense I could feel my heart pound in my chest... This is the first book I've read by this author and it certainly will not be the last. Loved it!' Twilight Re...
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All My Lies
Sophie Flynn'Perfectly paced, suspenseful and gripping a real pageturner' SOPHIE HANNAH, author of Haven't They Grown 'A rollercoaster ride with a cast of flawed characters an exce...
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The Stranger Next Door
Adam SouthwardSHE WAS THE PERFECT NEIGHBOUR. UNTIL SHE WASN'T.'A brilliant, twisty, read, that kept me reading late into the night' SUE WATSON'All the very best ingredients for a perfect thrille...
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The Housemate
C. L. PattisonYOU SHOULD NEVER HAVE LET HER IN.A gripping and twisting psychological thriller with an ending you'll never forget, THE HOUSEMATE is perfect for fans of Louise Jensen, Jane Corry, ...
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The Girls Inside
NJ MackayA gripping, compelling psychological thriller about a cult, a fire, and the dark secrets that four young girls have carried with them but can no longer keep buried...Blue grew up i...
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What We Did
Natalie ChandlerONE SMALL SCRATCH AND THE SECRETS WILL COME POURING OUT . . . Jenna has spent the last twentyfive years trying to forget what happened to her as a teenager. Trying to forget what t...
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Keep Her Quiet
Emma Curtis'Will keep you reading long into the night. I absolutely loved it.' Lesley Kara, author of The Rumour'Absolutely outstanding.' Lauren North, author of The Perfect BetrayalJenny has...
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The Fallen
Jackie KablerCould the truth be hiding in plain sight?The first 'sharp and totally gripping' book in the muchloved Cora Baxter Mysteries series, from the acclaimed broadcaster, USA Today bestse...
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Believe Me Not
Natalie Chandler'This was a FANTASTIC book, I will not forget this one for a loooooooooong time and if ever . . . a MUST READ!' Real Reader ⭐ ⭐ ⭐ ⭐ ⭐'I SWALLOWED THIS BOOK WHOLE. Devoured it. Coul...
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Until I Find You
Anna Smith'Gritty, violent and very dark, it is a real page turner. I loved the character of Billie Carlson' Patricia GibneyThis nailbiting Glasgowset crime thriller introduces Billie Carlso...
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The Buried
Sharon BoltonAN OLD ENEMY IS LAID TO REST . . . AND A NEW CRIME IS DISCOVEREDFlorence Lovelady, the most senior serving policewoman in Britain, visits convicted serial killer Larry Glassbrook i...
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When She Came Back
C J Parsons'I forgot to breathe in parts!' 5 review'I haven't been able to put down' 5 review'Worth far more than five stars' 5 reviewWhen her fiveyearold daughter disappears from the park, C...
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Between the Lines
S. J. Butler'An excellent debut novel, I couldn't put this down! A definite must read' 5 reader reviewThe closer you are, the less you see . . .When Kev's girlfriend is killed in a hitandrun, ...
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Watch Him Die
Craig RobertsonNOMINATED FOR THE McILVANNEY PRIZE 2020 FOR SCOTTISH CRIME BOOK OF THE YEAR 'Truly difficult to put down’ Daily Mail 'Highconcept plot keeps the 'tecs and the ...
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The Silenced
Jackie KablerHow far would you go to prove the truth?The third book in the muchloved Cora Baxter Mysteries series, from the acclaimed broadcaster, USA Today bestseller and bestselling author of...