PCET Concepts: HAT vs. EPT and Nonadiabaticity

Size: px
Start display at page:

Download "PCET Concepts: HAT vs. EPT and Nonadiabaticity"

Transcription

1 PCET Concts: HAT vs. EPT and Nonadiabaticity Sharon Hamms-Schiffr Rfrncs on HAT vs. EPT and nonadiabaticity: J. H. Skon, A.. Soudackov, and S. Hamms-Schiffr, Calculation of vibronic coulings for hnoxyl/hnol and bnzyl/tolun slf-xchang ractions: Imlications for roton-could lctron transfr mchanisms, J. Am. Chm. Soc. 128, (2006). A. Sirjoosingh and S. Hamms-Schiffr, Proton-could lctron transfr vrsus hydrogn atom transfr: Gnration of charg-localizd diabatic stats, J. Phys. Chm. A 115, (2011). A. Sirjoosingh and S. Hamms-Schiffr, Diabatization schms for gnrating charg-localizd lctron-roton vibronic stats in roton-could lctron transfr systms, J. Chm. Thory and Comut. 7, (2011). S. Hamms-Schiffr, Proton-could lctron transfr: Classification schm and guid to thortical mthods, Enrgy Environ. Sci. 5, (2012). A.. Soudackov and S. Hamms-Schiffr, Probing nonadiabaticity in th roton-could lctron transfr raction catalyzd by soyban lioxygnas, J. Phys. Chm. Ltt. 5, (2014). S. Hamms-Schiffr, Proton-could lctron transfr: Moving togthr and charging forward, J. Am. Chm. Soc. Prsctiv, 2015 PCET wb sit: htt://wbct.scs.uiuc.du/ Coyright 2015, Sharon Hamms-Schiffr, Univrsity of Illinois at Urbana-Chamaign

2 Dfinitions Rlvant to PCET SHS, Enrgy Environ. Sci. 2012; SHS, JACS Prsctiv 2015 PCET can occur by squntial or concrtd mchanism (not rigorously dfind but clarly squntial if a stabl intrmdiat can b isolatd and clarly concrtd if roducts of singl ET and PT ar much lss thrmodynamically favorabl than roduct of concrtd PCET) Concrtd PCET includs HAT (hydrogn atom transfr) and EPT (lctron-roton transfr) HAT: lctron and roton transfr from th sam donor and acctor* (not rigorous dfinition but usd in th fild); ngligibl amount of lctronic charg rdistribution as H transfrs; lctronically adiabatic ǂ EPT: lctron and roton transfr btwn diffrnt donors and acctors* (not rigorous); significant amount of lctronic charg rdistribution as H transfrs; lctronically nonadiabatic ǂ *donor/acctor can b molcular orbitals, chmical bonds, or atoms ǂ Distinguishing HAT and EPT by lctron-roton nonadiabaticity introducd in Skon, Soudackov, SHS, JACS 2006

3 Nonadiabaticity Skon, Soudackov, SHS, JACS 2006; SHS, Enrgy Environ. Sci Elctron-roton subsystm wrt othr nucli μν k T B PCET 2 k μν Elctron-roton nonadiabaticity: dtrmins form of vibronic couling nonadiabatic (na) l II, ˆ r H, I r r r adiabatic (ad) D/2 D quantum classical n nad vib nad : lctrons : roton(s) n: othr nucli

4 Elctron-Proton Nonadiabaticity Rlativ timscals of lctronic transition and roton tunnling - dtrmin timscals with smiclassical formulation - nonadiabatic whn roton tunnling fastr than lctronic transition Nonadiabatic couling with rsct to transfrring roton coordinat - dtrmin from lctronic wavfunctions - nonadiabatic whn charactr of lctronic wavfunction changs significantly with rsct to roton motion () l l 1 2 d 12 ( r ) dr Chang in lctronic charg distribution as roton transfrs - dtrmin from diol momnt, lctrostatic otntial, artial chargs - nonadiabatic whn significant chang - hydrogn atom transfr (HAT) vs lctron-roton transfr (EPT)

5 Rrsntativ Chmical Examls Mayr, Hrovat, Thomas, Bordn, JACS 2002; Skon, Soudackov, SHS, JACS 2006 bnzyl/tolun C---H---C hnoxyl/hnol O---H---O SOMO DOMO HAT sam donor/acctor lctronically adiabatic EPT diffrnt donors/acctors lctronically nonadiabatic HAT: hydrogn atom transfr EPT: concrtd PCET

6 Smiclassical Tratmnt: Timscals Gorgivskii and Stuchbrukhov, JCP 2000; Skon, Soudackov, SHS, JACS 2006 adiabaticity aramtr: l l D F v t Elctronically nonadiabatic PT: 1, l ( na) D A vibronic couling: v 2 E m : tunnling vlocity t c DF : diffrnc of slos of otntial nrgy curvs l at crossing oint : lctronic couling sc ( ad) ( ) Elctronically adiabatic PT: 1, ( ad) D D/2

7 Nonadiabaticity: Rlativ Timscals Skon, Soudackov, SHS, JACS 2006: CASSCF calculations Phnoxyl-hnol: O---H---O, lctronically nonadiabatic, EPT cm l 1 (na) l D A Bnzyl-tolun: C---H---C, lctronically adiabatic, HAT 0.25 l -1 (ad) 14,000cm D 2

8 Nonadiabatic Couling Solid lins: hnoxyl/hnol, lctronically nonadiabatic, EPT Dottd lins: bnzyl/tolun, lctronically adiabatic, HAT Elctron-roton nonadiabatic couling from CASSCF stats () l l 1 2 d 12 ( r ) dr Nonadiabatic couling much gratr for EPT than for HAT EPT has gratr molcular charg rdistribution along r Sirjoosingh and SHS, JPC A 2011, JCTC 2011

9 Elctrostatic Potntial Mas hnoxyl/hnol: lctronically nonadiabatic, EPT bnzyl/tolun: lctronically adiabatic, HAT ractant transition stat roduct Rd: ngativ charg Blu: ositiv charg Sirjoosingh and SHS, JPC A 2011, JCTC 2011

10 Molcular Charg Rdistribution hnoxyl/hnol: PCET lctronically nonadiabatic bnzyl/tolun: HAT lctronically adiabatic Sirjoosingh and SHS, JPC A 2011, JCTC 2011

11 ibronic Coulings Phnoxyl-hnol: lctronically nonadiabatic, EPT cm l 1 (na) l D A ( ) ad ( ) sc ( ) ( ) full na coulings in cm -1 Bnzyl-tolun: lctronically adiabatic, HAT 0.25 l -1 (ad) 14,000cm D 2 ( ad) ( ) sc ( ) ( ) full na coulings in cm -1 μν k T B vibronically nonadiabatic Sirjoosingh and SHS, JPC A 2011, JCTC 2011

12 Nonadiabaticity in Lioxygnas Soudackov and Hamms-Schiffr, JPCL 2014 Modl systm CO distanc 2.7 Å Constraind DFT/ωB97X/6-31G** 85 l 4.6 kcal/mol (na) l D A D A kcal/mol Elctronically nonadiabatic PT and vibronically nonadiabatic PCET

13 Sin Dnsitis and Charg Distribution () l l 1 2 d 12 ( r ) dr Ractant Product Soudackov and Hamms-Schiffr, JPCL 2014

Title. Author(s)Koper, Marc T. M. CitationPhysical Chemistry Chemical Physics, 15(5): Issue Date Doc URL. Rights.

Title. Author(s)Koper, Marc T. M. CitationPhysical Chemistry Chemical Physics, 15(5): Issue Date Doc URL. Rights. Titl Thory of th transition from suntial to concrt Author(s)Kor, Marc T. M. CitationPhysical Chmistry Chmical Physics, 5(5): 99-4 Issu Dat --7 Doc URL htt://hdl.handl.nt/5/565 Rights Phys. Chm. Chm. Phys.,,5,

More information

Chapter 8: Electron Configurations and Periodicity

Chapter 8: Electron Configurations and Periodicity Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic

More information

Lecture 28 Title: Diatomic Molecule : Vibrational and Rotational spectra

Lecture 28 Title: Diatomic Molecule : Vibrational and Rotational spectra Lctur 8 Titl: Diatomic Molcul : Vibrational and otational spctra Pag- In this lctur w will undrstand th molcular vibrational and rotational spctra of diatomic molcul W will start with th Hamiltonian for

More information

Hydrogen Atom and One Electron Ions

Hydrogen Atom and One Electron Ions Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial

More information

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds.

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds. 1 Th diagram shows th lctronic configurations of six diffrnt atoms. A B C D E F (a) You may us th Priodic Tabl on pag 2 to hlp you answr this qustion. Answr ach part by writing on of th lttrs A, B, C,

More information

Coupled Pendulums. Two normal modes.

Coupled Pendulums. Two normal modes. Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron

More information

Constants and Conversions:

Constants and Conversions: EXAM INFORMATION Radial Distribution Function: P 2 ( r) RDF( r) Br R( r ) 2, B is th normalization constant. Ordr of Orbital Enrgis: Homonuclar Diatomic Molculs * * * * g1s u1s g 2s u 2s u 2 p g 2 p g

More information

Title: Vibrational structure of electronic transition

Title: Vibrational structure of electronic transition Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

Brief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008

Brief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008 Brif ots on th Frmi-Dirac and Bos-Einstin Distributions, Bos-Einstin Condnsats and Dgnrat Frmi Gass Last Updat: 8 th Dcmbr 8 (A)Basics of Statistical Thrmodynamics Th Gibbs Factor A systm is assumd to

More information

Elements of Statistical Thermodynamics

Elements of Statistical Thermodynamics 24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,

More information

Background: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals.

Background: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals. Chaptr 7 Th Hydrogn Atom Background: W hav discussd th PIB HO and th nrgy of th RR modl. In this chaptr th H-atom and atomic orbitals. * A singl particl moving undr a cntral forc adoptd from Scott Kirby

More information

Molecular Orbitals in Inorganic Chemistry

Molecular Orbitals in Inorganic Chemistry Outlin olcular Orbitals in Inorganic Chmistry Dr. P. Hunt p.hunt@imprial.ac.uk Rm 167 (Chmistry) http://www.ch.ic.ac.uk/hunt/ octahdral complxs forming th O diagram for Oh colour, slction ruls Δoct, spctrochmical

More information

Two-colour photoassociation spectroscopy of ultracold calcium to determine the ground-state scattering length

Two-colour photoassociation spectroscopy of ultracold calcium to determine the ground-state scattering length E. Pachomow, Vit Dahlk, F. Rihl, U. Strr (PTB) E. Timann (Libniz Univrsity Hannovr) Two-colour photoassociation spctroscopy of ultracold calcium to dtrmin th round-stat scattrin lnth E R RTG Workshop,

More information

CE 530 Molecular Simulation

CE 530 Molecular Simulation CE 53 Molcular Simulation Lctur 8 Fr-nrgy calculations David A. Kofk Dpartmnt of Chmical Enginring SUNY Buffalo kofk@ng.buffalo.du 2 Fr-Enrgy Calculations Uss of fr nrgy Phas quilibria Raction quilibria

More information

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot 5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg

More information

Supporting Information. Proton Quantization and Vibrational Relaxation in Nonadiabatic Dynamics. of Photoinduced Proton-Coupled Electron Transfer

Supporting Information. Proton Quantization and Vibrational Relaxation in Nonadiabatic Dynamics. of Photoinduced Proton-Coupled Electron Transfer Suorting Information Proton Quantization and Vibrational Relaxation in Nonadiabatic Dynamics of Photoinduced Proton-Couled Electron Transfer in a Solvated Phenol-Amine Comlex Puja Goyal, Christine A. Schwerdtfeger,

More information

Electrochemistry L E O

Electrochemistry L E O Rmmbr from CHM151 A rdox raction in on in which lctrons ar transfrrd lctrochmistry L O Rduction os lctrons xidation G R ain lctrons duction W can dtrmin which lmnt is oxidizd or rducd by assigning oxidation

More information

PRINCIPLES OF PLASMA PROCESSING Course Notes: Prof. J. P. Chang Part B3: ATOMIC COLLISIONS AND SPECTRA

PRINCIPLES OF PLASMA PROCESSING Course Notes: Prof. J. P. Chang Part B3: ATOMIC COLLISIONS AND SPECTRA Atomic Collisions and Spctra 125 PRINCIPLES OF PLASMA PROCESSING Cours Nots: Prof. J. P. Chang Part B3: ATOMIC COLLISIONS AND SPECTRA I. ATOMIC ENERGY LEVELS Atoms and molculs mit lctromagntic radiation

More information

Davisson Germer experiment

Davisson Germer experiment Announcmnts: Davisson Grmr xprimnt Homwork st 5 is today. Homwork st 6 will b postd latr today. Mad a good guss about th Nobl Priz for 2013 Clinton Davisson and Lstr Grmr. Davisson won Nobl Priz in 1937.

More information

University of Illinois at Chicago Department of Physics. Thermodynamics & Statistical Mechanics Qualifying Examination

University of Illinois at Chicago Department of Physics. Thermodynamics & Statistical Mechanics Qualifying Examination Univrsity of Illinois at Chicago Dpartmnt of hysics hrmodynamics & tatistical Mchanics Qualifying Eamination January 9, 009 9.00 am 1:00 pm Full crdit can b achivd from compltly corrct answrs to 4 qustions.

More information

PARTICLE MOTION IN UNIFORM GRAVITATIONAL and ELECTRIC FIELDS

PARTICLE MOTION IN UNIFORM GRAVITATIONAL and ELECTRIC FIELDS VISUAL PHYSICS ONLINE MODULE 6 ELECTROMAGNETISM PARTICLE MOTION IN UNIFORM GRAVITATIONAL and ELECTRIC FIELDS A fram of rfrnc Obsrvr Origin O(,, ) Cartsian coordinat as (X, Y, Z) Unit vctors iˆˆj k ˆ Scif

More information

26-Sep-16. Nuclear energy production. Nuclear energy production. Nuclear energy production. Nuclear energy production

26-Sep-16. Nuclear energy production. Nuclear energy production. Nuclear energy production. Nuclear energy production Aim: valuat nrgy-gnration rat pr unit mass. Sun: (chck L /M, human ) nrgy-gnration rat producd from fusion of two nucli a + A: nrgy rlasd pr raction raction rat pr unit volum (includs cross sction and

More information

September 23, Honors Chem Atomic structure.notebook. Atomic Structure

September 23, Honors Chem Atomic structure.notebook. Atomic Structure Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning

More information

PH300 Modern Physics SP11 Final Essay. Up Next: Periodic Table Molecular Bonding

PH300 Modern Physics SP11 Final Essay. Up Next: Periodic Table Molecular Bonding PH Modrn Physics SP11 Final Essay Thr will b an ssay portion on th xam, but you don t nd to answr thos qustions if you submit a final ssay by th day of th final: Sat. 5/7 It dosnʼt mattr how smart you

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

More information

Exam 2 Thursday (7:30-9pm) It will cover material through HW 7, but no material that was on the 1 st exam.

Exam 2 Thursday (7:30-9pm) It will cover material through HW 7, but no material that was on the 1 st exam. Exam 2 Thursday (7:30-9pm) It will covr matrial through HW 7, but no matrial that was on th 1 st xam. What happns if w bash atoms with lctrons? In atomic discharg lamps, lots of lctrons ar givn kintic

More information

IYPT 2000 Problem No. 3 PLASMA

IYPT 2000 Problem No. 3 PLASMA IYPT 000 Problm No. 3 PLASMA Tam Austria Invstigat th lctrical conducivity of th flam of a candl. Examin th influnc of rlvant paramtrs, in particular, th shap and polarity of th lctrods. Th xprimnts should

More information

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds How dos light intract with mattr? And what dos (this say about) mattr? REGISTER!!! If Schrödingr s Cat walks into a forst, and no on is around to obsrv it, is h rally in th forst? sourc unknown Phys 1010

More information

λ = 2L n Electronic structure of metals = 3 = 2a Free electron model Many metals have an unpaired s-electron that is largely free

λ = 2L n Electronic structure of metals = 3 = 2a Free electron model Many metals have an unpaired s-electron that is largely free 5.6 4 Lctur #4-6 pag Elctronic structur of mtals r lctron modl Many mtals av an unpaird s-lctron tat is largly fr Simplst modl: Particl in a box! or a cubic box of lngt L, ψ ( xyz) 8 xπ ny L L L n x π

More information

Phys 402: Nonlinear Spectroscopy: SHG and Raman Scattering

Phys 402: Nonlinear Spectroscopy: SHG and Raman Scattering Rquirmnts: Polariation of Elctromagntic Wavs Phys : Nonlinar Spctroscopy: SHG and Scattring Gnral considration of polariation How Polarirs work Rprsntation of Polariation: Jons Formalism Polariation of

More information

What is Solid State Physics?

What is Solid State Physics? What is Solid Stat Physics? Branislav K. Nikolić Dpartmnt of Physics and Astronomy, Univrsity of Dlawar, U.S.A. http://www.physics.udl.du/~bnikolic/taching/phys624/phys624.html Quantum Hamiltonian of Solid

More information

Schrodinger Equation in 3-d

Schrodinger Equation in 3-d Schrodingr Equation in 3-d ψ( xyz,, ) ψ( xyz,, ) ψ( xyz,, ) + + + Vxyz (,, ) ψ( xyz,, ) = Eψ( xyz,, ) m x y z p p p x y + + z m m m + V = E p m + V = E E + k V = E Infinit Wll in 3-d V = x > L, y > L,

More information

The Use Of Kinetic Isotope Effects To Study Enzyme Mechanisms

The Use Of Kinetic Isotope Effects To Study Enzyme Mechanisms The Use Of Kinetic Isotope Effects To Study Enzyme Mechanisms Kinetic Isotope Effect (KIE): ratio of rate constants describing a reaction, with that associated with the reaction of the lighter isotope

More information

Electric (Rocket) Propulsion. EP Overview

Electric (Rocket) Propulsion. EP Overview Elctric (Rockt) Propulsion EP Ovrviw Elctric Propulsion-1 Basics Rockt Propulsion Elmnts Propllant Enrgy Sourc Storag Fd Systm sam in chmical rockts Storag Convrsion Acclrator Elctric Propulsion- 1 Elctric

More information

Structure of the Atom. Thomson s Atomic Model. Knowledge of atoms in Experiments of Geiger and Marsden 2. Experiments of Geiger and Marsden

Structure of the Atom. Thomson s Atomic Model. Knowledge of atoms in Experiments of Geiger and Marsden 2. Experiments of Geiger and Marsden CHAPTER 4 Structur of th Atom 4.1 Th Atomic Modls of Thomson and Ruthrford 4. Ruthrford Scattring 4.3 Th Classic Atomic Modl 4.4 Th Bohr Modl of th Hydrogn Atom 4.5 Succsss & Failurs of th Bohr Modl 4.6

More information

Lecture 19: Free Energies in Modern Computational Statistical Thermodynamics: WHAM and Related Methods

Lecture 19: Free Energies in Modern Computational Statistical Thermodynamics: WHAM and Related Methods Statistical Thrmodynamics Lctur 19: Fr Enrgis in Modrn Computational Statistical Thrmodynamics: WHAM and Rlatd Mthods Dr. Ronald M. Lvy ronlvy@tmpl.du Dfinitions Canonical nsmbl: A N, V,T = k B T ln Q

More information

Workshop on New Materials for Renewable Energy October Non-equilibrium dynamics of photoinduced proton-coupled electron transfer

Workshop on New Materials for Renewable Energy October Non-equilibrium dynamics of photoinduced proton-coupled electron transfer 2269-23 Workshop on New Materials for Renewable Energy 17-21 October 2011 Non-equilibrium dynamics of photoinduced proton-coupled electron transfer Alexander V. SOUDACKOV Dept. of Chemistry, Pennsylvania

More information

Statistical Thermodynamics: Sublimation of Solid Iodine

Statistical Thermodynamics: Sublimation of Solid Iodine c:374-7-ivap-statmch.docx mar7 Statistical Thrmodynamics: Sublimation of Solid Iodin Chm 374 For March 3, 7 Prof. Patrik Callis Purpos:. To rviw basic fundamntals idas of Statistical Mchanics as applid

More information

(most) due to long range e m forces i.e. via atomic collisions or due to short range nuclear collisions or through decay ( = weak interactions)

(most) due to long range e m forces i.e. via atomic collisions or due to short range nuclear collisions or through decay ( = weak interactions) Spring 01, P67, YK Monday January 30, 01 8 Obsrvabl particl dtction ffcts ar : (most) du to long rang m forcs i.. via atomic collisions or du to short rang nuclar collisions or through dcay ( = wak intractions)

More information

Ab Initio Calculation of 2 H and 4 He Binding Energies

Ab Initio Calculation of 2 H and 4 He Binding Energies Journal of Modrn hysics, 1,, 179-1715 htt://dxdoiorg/16/jm1111 ublishd Onlin Novmbr 1 (htt://wwwscirorg/journal/jm) Ab Initio Calculation of H and H Binding Enrgis B Schaffr 7, ru d l Ambroisi 751 aris,

More information

Model neurons!!the membrane equation!

Model neurons!!the membrane equation! Modl nurons!!th bran quation! Suggstd rading:! Chaptr 5.1-5.3 in Dayan, P. & Abbott, L., Thortical Nuroscinc, MIT Prss, 2001.! Modl nurons: Th bran quation! Contnts:!!!!!! Ion channls Nnst quation Goldan-Hodgkin-Katz

More information

Derivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian

Derivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian Drivation of Elctron-Elctron Intraction Trms in th Multi-Elctron Hamiltonian Erica Smith Octobr 1, 010 1 Introduction Th Hamiltonian for a multi-lctron atom with n lctrons is drivd by Itoh (1965) by accounting

More information

Today. Wave-Matter Duality. Quantum Non-Locality. What is waving for matter waves?

Today. Wave-Matter Duality. Quantum Non-Locality. What is waving for matter waves? Today Wav-Mattr Duality HW 7 and Exam 2 du Thurs. 8pm 0 min rcap from last lctur on QM Finish QM odds and nds from ch.4 Th Standard Modl 4 forcs of Natur Fundamntal particls of Natur Fynman diagrams EM

More information

Non-Born-Oppenheimer Effects Between Electrons and Protons

Non-Born-Oppenheimer Effects Between Electrons and Protons Non-Born-Oppenheimer Effects Between Electrons and Protons Sharon Hammes-Schiffer Department of Chemistry University of Illinois at Urbana-Champaign Blue Waters Professor Funding: Computer time: NSF, AFOSR

More information

Classical Magnetic Dipole

Classical Magnetic Dipole Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg

More information

Workshop on Nano-Opto-Electro-Mechanical Systems Approaching the Quantum Regime September 2010

Workshop on Nano-Opto-Electro-Mechanical Systems Approaching the Quantum Regime September 2010 164-9 Workshop on Nano-Opto-Elctro-Mchanical Systms Approaching th Quantum Rgim 6-1 Sptmbr 1 Nano-Elctro-Mchanics of Suprconducting Wak Links Robrt SHEKHTER Chalmrs Univ. of Tchnology & Univrsity of GothnburgDpt.

More information

Non-Born-Oppenheimer Effects Between Electrons and Protons

Non-Born-Oppenheimer Effects Between Electrons and Protons Non-Born-Oppenheimer Effects Between Electrons and Protons Kurt Brorsen Department of Chemistry University of Illinois at Urbana-Champaign PI: Sharon Hammes-Schiffer Funding: NSF, AFOSR Computer time:

More information

K

K Alicyclic Chmistry. Lctur 3 Th ovrall strain in cycloalkns can b masurd by th magnitud of th complxation constants with Ag +. Th gratr th angl strain th mor it is rlivd in th π-complx which rducs th π-charactr

More information

Transport in a field aligned magnetized. C.M. Cooper, W. Gekelman, P. Pribyl, J. Maggs, Z. Lucky

Transport in a field aligned magnetized. C.M. Cooper, W. Gekelman, P. Pribyl, J. Maggs, Z. Lucky Transort in a fild alignd magntizd lasma and nutral gas boundary: Th nd of th lasma C.M. Coor, W. Gklman, P. Pribyl, J. Maggs, Z. Lucky UnivrsityofCalifornia California, LosAngls Fbruary 15, 2013 Motivation

More information

3.2.3 Molecules and Covalent Bonds

3.2.3 Molecules and Covalent Bonds Sav My Exams! Th Hom of Rvision For mor awsom GSE and lvl rsourcs, visit us at www.savmyxams.co.uk/ 3.2.3 Molculs and ovalnt onds Qustion Papr Lvl IGSE Subjct hmistry (0620) Exam oard ambridg Intrnational

More information

CHAPTER 16 HW: CONJUGATED SYSTEMS

CHAPTER 16 HW: CONJUGATED SYSTEMS APTER 6 W: JUGATED SYSTEMS NAMING PLYENES. Giv th IUPA nam for ach compound, including cis/trans or E/Z dsignations whr ndd. ompound no E/Z trans or E 2 3 4 3 Nam trans-2-mthyl-2,4-hxadin 2-mthoxy-,3-cyclohptadin

More information

Molecules and Covalent Bond

Molecules and Covalent Bond Molculs and ovalnt ond Qustion Papr 1 Lvl IGSE Subjct hmistry (0620/0971) Exam oard ambridg Intrnational Examinations (IE) Topic toms, lmnts and compounds Sub-Topic Molculs and covalnt bonds ooklt Qustion

More information

A central nucleus. Protons have a positive charge Electrons have a negative charge

A central nucleus. Protons have a positive charge Electrons have a negative charge Atomic Structur Lss than ninty yars ago scintists blivd that atoms wr tiny solid sphrs lik minut snookr balls. Sinc thn it has bn discovrd that atoms ar not compltly solid but hav innr and outr parts.

More information

Herre van der Zant. Molecular Electronics and Devices group

Herre van der Zant. Molecular Electronics and Devices group transport through (magntic) nanoscal objcts Hrr van dr Zant Molcular Elctronics and Dvics group transport mchanisms: Ohms law lctrons ar viwd as particls in a pinball machin, bouncing around rsistanc rsults

More information

Contemporary, atomic, nuclear, and particle physics

Contemporary, atomic, nuclear, and particle physics Contmporary, atomic, nuclar, and particl physics 1 Blackbody radiation as a thrmal quilibrium condition (in vacuum this is th only hat loss) Exampl-1 black plan surfac at a constant high tmpratur T h is

More information

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator. Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r

More information

Dynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA *

Dynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA * 17 nd Intrnational Confrnc on Mchanical Control and Automation (ICMCA 17) ISBN: 978-1-6595-46-8 Dynamic Modlling of Hoisting Stl Wir Rop Da-zhi CAO, Wn-zhng DU, Bao-zhu MA * and Su-bing LIU Xi an High

More information

Dynamics of Barrier Crossings for the Generalized Anderson Holstein Model: Beyond Electronic Friction and Conventional Surface Hopping

Dynamics of Barrier Crossings for the Generalized Anderson Holstein Model: Beyond Electronic Friction and Conventional Surface Hopping Articl pubs.acs.org/jctc Dynamics of arrir Crossings for th Gnralizd Andrson Holstin Modl: yond Elctronic Friction and Convntional Surfac Hopping Wnjun Ouyang, Wnji Dou, Ambr Jain, and Josph E. Subotni*

More information

Photosynthesis: Life from Light and Air

Photosynthesis: Life from Light and Air Photosynthsis: Lif from Light and Air SUN CO 2 12/7/2016 1 12/7/2016 2 Enrgy nds of lif All lif nds a constant input of nrgy Htrotrophs (Animals) gt thir nrgy from ating othrs at food = othr organisms

More information

AP Biology. AP Biology Photosynthesis: Life from Light and Air

AP Biology. AP Biology Photosynthesis: Life from Light and Air 2007-2008 Photosynthsis: Lif from Light and Air 2007-2008 1 Enrgy nds of lif All lif nds a constant input of nrgy Htrotrophs (Animals) consumrs producrs gt thir nrgy from ating othrs at food = othr organisms

More information

NARAYANA I I T / P M T A C A D E M Y. C o m m o n P r a c t i c e T e s t 1 6 XII STD BATCHES [CF] Date: PHYSIS HEMISTRY MTHEMTIS

NARAYANA I I T / P M T A C A D E M Y. C o m m o n P r a c t i c e T e s t 1 6 XII STD BATCHES [CF] Date: PHYSIS HEMISTRY MTHEMTIS . (D). (A). (D). (D) 5. (B) 6. (A) 7. (A) 8. (A) 9. (B). (A). (D). (B). (B). (C) 5. (D) NARAYANA I I T / P M T A C A D E M Y C o m m o n P r a c t i c T s t 6 XII STD BATCHES [CF] Dat: 8.8.6 ANSWER PHYSIS

More information

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012 Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor

More information

Division Ave. High School AP Biology

Division Ave. High School AP Biology 2007-2008 Photosynthsis: Lif from Light and Air 2007-2008 Enrgy nds of lif All lif nds a constant input of nrgy u Htrotrophs (Animals) gt thir nrgy from ating othrs consumrs w at food = othr organisms

More information

Precise Masses of particles

Precise Masses of particles /1/15 Physics 1 April 1, 15 Ovrviw of topic Th constitunts and structur of nucli Radioactivity Half-lif and Radioactiv dating Nuclar Binding Enrgy Nuclar Fission Nuclar Fusion Practical Applications of

More information

Collisions between electrons and ions

Collisions between electrons and ions DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision

More information

Self-interaction mass formula that relates all leptons and quarks to the electron

Self-interaction mass formula that relates all leptons and quarks to the electron Slf-intraction mass formula that rlats all lptons and quarks to th lctron GERALD ROSEN (a) Dpartmnt of Physics, Drxl Univrsity Philadlphia, PA 19104, USA PACS. 12.15. Ff Quark and lpton modls spcific thoris

More information

Analysis of the Monochloroacetic Acid Crystallization Process by Entropic Modeling

Analysis of the Monochloroacetic Acid Crystallization Process by Entropic Modeling A ublication of 2071 VOL 32, 2013 CHEMICAL ENGINEERING TRANSACTIONS Chif Editors: Sauro Pirucci, Jiří J Klmš Coyright 2013, AIDIC Srvizi Srl, ISBN 978-88-95608-23-5; ISSN 1974-9791 Th Italian Association

More information

ECE507 - Plasma Physics and Applications

ECE507 - Plasma Physics and Applications ECE507 - Plasma Physics and Applications Lctur 7 Prof. Jorg Rocca and Dr. Frnando Tomasl Dpartmnt of Elctrical and Computr Enginring Collisional and radiativ procsss All particls in a plasma intract with

More information

Electrochemical Energy Systems Spring 2014 MIT, M. Z. Bazant. Midterm Exam

Electrochemical Energy Systems Spring 2014 MIT, M. Z. Bazant. Midterm Exam 10.66 Elctrochmical Enrgy Systms Spring 014 MIT, M. Z. Bazant Midtrm Exam Instructions. This is a tak-hom, opn-book xam du in Lctur. Lat xams will not b accptd. You may consult any books, handouts, or

More information

fiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics

fiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics Atoic and olcular Physics JEST Q. Th binding nrgy of th hydrogn ato (lctron bound to proton) is.6 V. Th binding nrgy of positroniu (lctron bound to positron) is (a).6 / V (b).6 / 8 V (c).6 8 V (d).6 V.6

More information

Graduate Students Seminar Paul-Scherrer-Institut. Search for Excited Quarks

Graduate Students Seminar Paul-Scherrer-Institut. Search for Excited Quarks Graduat Studnts Sminar 01.10.2003 Paul-Schrrr-Institut Sarch for Excitd Quarks Jan Bckr Univrsity of Zurich Sarch for Excitd Quarks Framwork Excitd frmions and comositnss Phnomnological framwork Production

More information

Pion condensation with neutrinos

Pion condensation with neutrinos Pion condnsation with nutrinos Or how dos QCD bhav undr high dnsitis of lctron/muon nutrinos Harmn Warringa, Goth Univrsität, Frankfurt Basd on work don with Hiroaki Abuki and Tomas Braunr arxiv:0901.2477

More information

Phosphonate-Functionalized Polystyrene Microspheres with Controlled Zeta Potential for Efficient Uranium Sorption

Phosphonate-Functionalized Polystyrene Microspheres with Controlled Zeta Potential for Efficient Uranium Sorption Elctronic Supplmntary Matrial (ESI) for RSC Advancs. This journal is Th Royal Socity of Chmistry 2016 Supporting Information Phosphonat-Functionalizd Polystyrn Microsphrs with Controlld Zta Potntial for

More information

Electromagnetic Schrödinger Equation of the Deuteron 2 H (Heavy Hydrogen)

Electromagnetic Schrödinger Equation of the Deuteron 2 H (Heavy Hydrogen) World Journal of Nuclar Scinc and Tchnology, 14, 4, 8-6 Publishd Onlin Octobr 14 in SciRs. htt://www.scir.org/journal/wjnst htt://dx.doi.org/1.46/wjnst.14.449 Elctromagntic Schrödingr Equation of th Dutron

More information

On the Hamiltonian of a Multi-Electron Atom

On the Hamiltonian of a Multi-Electron Atom On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making

More information

The Angular Momenta Dipole Moments and Gyromagnetic Ratios of the Electron and the Proton

The Angular Momenta Dipole Moments and Gyromagnetic Ratios of the Electron and the Proton Journl of Modrn hysics, 014, 5, 154-157 ublishd Onlin August 014 in SciRs. htt://www.scir.org/journl/jm htt://dx.doi.org/.436/jm.014.51415 Th Angulr Momnt Diol Momnts nd Gyromgntic Rtios of th Elctron

More information

AS 5850 Finite Element Analysis

AS 5850 Finite Element Analysis AS 5850 Finit Elmnt Analysis Two-Dimnsional Linar Elasticity Instructor Prof. IIT Madras Equations of Plan Elasticity - 1 displacmnt fild strain- displacmnt rlations (infinitsimal strain) in matrix form

More information

Sara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case

Sara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case wwwnvisol-canadaca Sara Godoy dl Olmo Calculation of contaminatd soil volums : Gostatistics applid to a hydrocarbons spill Lac Mgantic Cas Gostatistics: study of a PH contamination CONTEXT OF THE STUDY

More information

What are molecular simulations? Introduction. Numerical Tools : Fluid Mechanics

What are molecular simulations? Introduction. Numerical Tools : Fluid Mechanics What ar molcular simulations? Introduction MSE 60 Computational Matrials Scinc / CME 599-001 Molcular Simulations S.E. Rankin Dpartmnt of Chmical and Matrials Enginring Univrsity of Kntucky, Lxington KY

More information

Definition1: The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.

Definition1: The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. Dirctivity or Dirctiv Gain. 1 Dfinition1: Dirctivity Th ratio of th radiation intnsity in a givn dirction from th antnna to th radiation intnsity avragd ovr all dirctions. Dfinition2: Th avg U is obtaind

More information

Quantum transport in 2D

Quantum transport in 2D Quantum transport in D Quantum transport : wat is conductanc? mtallic ring atomic contact nanotub Landaur-üttikr formalism of quantum transport D gas grapn wir ntwork GRAPHENE & CO, Cargès April -3, 08

More information

Chemical Engineering 412

Chemical Engineering 412 Chical Enginring 4 Introductory Nuclar Enginring Lctur 6 Nuclar Radiation Typs Ky oints Typs of cay Na roprtis athatical scriptions Cavats cay Charts (KNOW HOW TO USE!) Nuclar Equation for cay -Valus for

More information

Lecture #15. Bipolar Junction Transistors (BJTs)

Lecture #15. Bipolar Junction Transistors (BJTs) ctur #5 OUTN Th iolar Junction Transistor Fundamntals dal Transistor Analysis Rading: hatr 0,. 30 ctur 5, Slid iolar Junction Transistors (JTs Ovr th ast 3 ads, th highr layout dnsity and low-owr advantag

More information

2. Background Material

2. Background Material S. Blair Sptmbr 3, 003 4. Background Matrial Th rst of this cours dals with th gnration, modulation, propagation, and ction of optical radiation. As such, bic background in lctromagntics and optics nds

More information

Chapter 7b Electron Spin and Spin- Orbit Coupling

Chapter 7b Electron Spin and Spin- Orbit Coupling Wintr 3 Chm 356: Introductory Quantum Mchanics Chaptr 7b Elctron Spin and Spin- Orbit Coupling... 96 H- atom in a Magntic Fild: Elctron Spin... 96 Total Angular Momntum... 3 Chaptr 7b Elctron Spin and

More information

Advanced Radiation Calculations of Hypersonic Reentry Flows Using Efficient Databasing Schemes

Advanced Radiation Calculations of Hypersonic Reentry Flows Using Efficient Databasing Schemes JURAL F THERMPHYSICS AD HEAT TRASFER Vol. 4, o. 3, July Sptmbr Advancd Radiation Calculations of Hyprsonic Rntry Flows Using Efficint Databasing Schms I. Sohn, A. Bansal, and D. A. Lvin Pnnsylvania Stat

More information

Performance Evaluation and Parametric Optimum Criteria of an Irreversible Molten Carbonate Fuel Cell-Heat Engine Hybrid System

Performance Evaluation and Parametric Optimum Criteria of an Irreversible Molten Carbonate Fuel Cell-Heat Engine Hybrid System Int. J. Elctrochm. Sci., 6 () 474-479 Intrnational Journal of ELECTROCHEMICAL SCIENCE www.lctrochmsci.org Prformanc Evaluation Paramtric Optimum Critria of an Irrvrsibl Moltn Carbonat Ful Cll-Hat Engin

More information

Brief Introduction to Statistical Mechanics

Brief Introduction to Statistical Mechanics Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.

More information

the electrons. Expanding the exponential and neglecting the constant term Ze 2 λ, we have

the electrons. Expanding the exponential and neglecting the constant term Ze 2 λ, we have LECTURE.8 Prof.R.Parthasarathy Atomic Structur - Elmntary Tratmnt Th ground stat of hydrogn atom has bn solvd xactly in th nonrlativistic tratmnt. Th ground stat of hlium atom has bn handld in variational

More information

Linear regression correction to first principle theoretical calculations Improved descriptors and enlarged training set

Linear regression correction to first principle theoretical calculations Improved descriptors and enlarged training set Chmical Physics Lttrs 49 (25) 315 321 www.lsvir.com/locat/cpltt Linar rgrssion corrction to first principl thortical calculations Improvd dscriptors and nlargd training st Xu-Mi Duan a, Zhn-Hua Li a,b,

More information

Dual Nature of Matter and Radiation

Dual Nature of Matter and Radiation Higr Ordr Tinking Skill Qustions Dual Natur of Mattr and Radiation 1. Two bas on of rd ligt and otr of blu ligt of t sa intnsity ar incidnt on a tallic surfac to it otolctrons wic on of t two bas its lctrons

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

The following information relates to Questions 1 to 4:

The following information relates to Questions 1 to 4: Th following information rlats to Qustions 1 to 4: QUESTIN 1 Th lctrolyt usd in this ful cll is D watr carbonat ions hydrogn ions hydroxid ions QUESTIN 2 Th product formd in th ful cll is D hydrogn gas

More information

Application and Evaluation of Data in Population Models for

Application and Evaluation of Data in Population Models for Max-Planck-Institut für Plasmaphysik EURATOM Association Application and Evaluation of Data in Population Modls for E [V] 14 1 10 8 6 4 0 and Singlt systm Triplt systm 16 5 s 1 Σ n= g p 1 Π d 1 u Π g s

More information

by g-factor Measurements

by g-factor Measurements Intrnational Bound-Stat Acclrator Quantum Facility Elctrodynamics for Bams in Strong of Ions and Filds Antiprotons Byond at Darmstadt th Furry Pictur by g-factor Masurmnts Wolfgang Quint GSI Darmstadt

More information

Nonlinear electron dynamics in metallic nanostructures

Nonlinear electron dynamics in metallic nanostructures Nonlinar lctron dynamics in mtallic nanostructurs Giovanni MANFREDI Institut d Physiqu t Chimi ds Matériaux d Strasbourg Strasbourg - Franc Giovanni.Manfrdi@ipcms.u-strasbg.fr Mastr Lctur 1 1 Plan of th

More information

Deepak Rajput

Deepak Rajput Q Prov: (a than an infinit point lattic is only capabl of showing,, 4, or 6-fold typ rotational symmtry; (b th Wiss zon law, i.. if [uvw] is a zon axis and (hkl is a fac in th zon, thn hu + kv + lw ; (c

More information

Short Course on Density Functional Theory and Applications IV. Problems and Insights

Short Course on Density Functional Theory and Applications IV. Problems and Insights Short Cours on Dnsity Functional Thory and Applications IV. Problms and Insights Samul B. Tricky Spt. 2008 Quantum Thory Projct Dpt. of Physics and Dpt. of Chmistry tricky@qtp.ufl.du KS Eignvalus Spctroscopy

More information