Quimica de Materiales-1

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Equacion de Schrodinger

Hamiltoniano (Operador de energia total)

Funccion de ondaPrincipio de incertidumbre de Heisenberg

Fundamentos Basicos



3-dimensiones

Sistema de n particulas



sisi

Algebra de operadores



Operadores de dierentes !ariables



Operadores lineales

Operadores Hermitianos



"alores esperados







Principio de incertidumbre



Hamiltoniano de un sistema polielectronico en aproma#icion de Born$ Openheimer

Apro#imacion de Born % Openheimer



Particula en un po&o de Potencial



Particula en un po&o de Potencial (continuacion)







' (pm) heor% E#perimentc%anine * 3+, nm +3 nm

pinac%anol ,3 3 nm *. nm

dicarboc%anin

e

///+ ,. nm 0.* nm

Particula en un po&o de Potencial (aplicacion)



Principio de Pauli





Apro#imacion de Hartree-Foc1

Hamiltonian contains t2o terms that act

on one electron at a time the 1inetic

energ% and the electron-nucleus

attraction and a term that describes the

pair2ise repulsion o electrons4 he latterdepends on the coordinates o t2o

electrons at the same time

o a!oid this problem the

independent particle appro#imation is

introduced 5 the interaction o each

electron 2ith all the others is treated

in an a!erage 2a%4

hen the Schr6dinger equation 2hich initiall%

depended on the coordinates x (representing

spatial and spin coordinates) o all electrons

can be reduced to a set o equations

Spin orbital



He atom



7oopmans8 heorem

he Pauli principle states that the 2a!eunction must change sign

2hen t2o independent electronic coordinates are interchanged

For t2o electron s%stem

Slater determinant

P i i i i i l



Principio !ariacional



eoria de perturbacion independiente de tiempo

i d ti l d l d id d



eoria de unctionales de la densidad





Atomo de Hidrogeno % Atomos Polielectronicos

solucion

















Simetria de los orbitales







999



he Aubau Principal

: ;hen placing electrons into orbitals in theconstruction o pol%electronic atoms 2e use theAubau Principle4

: his principle states that in addition to adding protons and neutrons to the nucleus one simpl%adds electrons to the h%drogen-li1e atomic orbitals

: Pauli e#clusion principle5 <o t2o electrons ma%ha!e the same quantum numbers4 hereore onl%t2o electrons can reside in an orbital

(dierentiated b% ms)4



he Aubau Principal (cont4)

: Finall% orbitals are illed starting rom the lo2estenerg%4

:E#ample5 H%drogen

1s 2s 2p

: E#ample5 Helium (= > +)

1s 2s 2p

1s1

1s2




: 'ithium (= > 3)

1s 2s 2p

1s 2s 2p

: Berillium (= > )

: Boron (= > )

1s 2s 2p

1s22s1

1s22s2

1s22s22p1




: ?arbon (= > *)

1s 2s 2p

1s 2s 2p

: <itrogen (= > 0)

Hund’s Rule: Lowest energy configuration is

the one in which the maximum number of unpaired electrons

are distributed amongst a set of degenerate orbitals.

1s22s22p2

1s22s22p3




: O#%gen (= > ,)

1s 2s 2p

1s 2s 2p

: Fluorine (= > @)

1s22s22p4

1s22s22p5

1s 2s 2p

: <eon (= > /.)

1s22s22p6

full




: Sodium (= > //)

3s

1s22s22p63s1

3s 3p

: Argon (= > /,)

[Ne] 3s23p6

Ne [Ne]3s1

Ne




• We now have the orbital configurations for the first 18 elements.

• Elements in same column have the same # of valence electrons!




• Similar to Sodium, we begin the next row of the periodic table by adding electrons to the 4s orbital.

• Why not 3d before 4s?

• 3d is closer to the nucleus

• 4s allows for closer

approach; therefore, is energetically preferred.






• Elements Z=19 and Z= 20:

Z= 19, Potassium: 1s22s22p63s23p64s1 = [Ar]4s1

Z= 20, Calcuim: 1s22s22p63s23p64s2 = [Ar]4s2

• Elements Z=21to Z=30 have occupied d orbitals:

Z= 21, Scandium: 1s22s22p63s23p64s23d1 = [Ar] 4s23d1

Z= 30, Zinc: 1s22s22p63s23p64s23d10 = [Ar] 4s23d10

Z = 24, Chromium: [Ar] 4s13d5 exception




• This orbital filling scheme gives rise to the modern

periodic table.




• After Lanthanum ([Xe]6s25d1), we start filling 4f.




• After Actinium ([Rn]7s26d1), we start filling 5f.




• Heading on column given total number of valence

electrons.

h A b P i i l ( )










adio atomico



adio atomico

Potencial de ioni&acion



Potencial de ioni&acion

(g)

> (g)

C C e- ∆H > DP





Ai id d El t i



Ainidad Electronica

(g)

C e- > (g)

- ∆H > EA

Electronegati!it



%

ulli1en DPCAE+ Pauling

lli1 li



ulli1en !s Pauling

Electronegati!idad (cont)



Electronegati!idad (cont)

Atomos pequeGos

Son electronegati!os







Orbitales Hibridos



Etileno



Etileno

Acetileno





Elementos de teoria de grupos de simetria



Elementos de simetria molecular

























Character table for D3h point group



E 2C3 3C'2 σh 2S3 3σv

linear,

rotationsquadratic

A'1 / / / / / / #+C%+ &+

A'2 / / -/ / / -/ &

E' + -/ . + -/ . (# %) (#+-%+ #%)

A''1 / / / -/ -/ -/

A''2 / / -/ -/ -/ / &

E'' + -/ . -+ / . ( # %) (#&%&)



E C3 3C2 !S" !σd

linear,

rotationsquadratic

A1 / / / / / #+C%+C&+

A2 / / / -/ -/

E + -/ + . .(+&+-#+-%+

#+-%+)

#1 3 . -/ / -/ ( # % &)

#2 3 . -/ -/ / (# % &) (#% #& %&)

Character table for Td point

group

eoria de orbitales moleculares



























eoria de orbitales moleculares



Hermitian Operator

eoria de orbitales moleculares (cont)







S>.



S .



eoria de Huc1el



























HOO 'O







FE=AS D<EO'E?'AES

















FESAS D<EO'E?'AESMelting Points and Boiling Points of Similar Substances with Increasing Formula Weights

FW ( / l)

(°)

b (°)



Substance FW (g/mol) mp (°) bp (°)F

! "# $!!% $&##

l! '& $&%%# $"*+Br

! &+% $'! ,#'#I! !,* &&", &#*",

Melting Points and Boiling Points of Substances with Similar Formula Weights

Substance FW (g/mol) mp (°) bp (°)

F! "# $!!% $&##

-. "% $&+* $&,!

". "! $* +,

a *% #" &*#*

-aF *! " &+,





FE=AS D<EO'E?'AESdispersion

Iipolo-dipolo



po o d po o

Puentes de hidrogeno

Don-dipolo

u-momento dipolar

J-carga de ion

Iipolo-dipolo

inducido

FESAS D<EO'E?'AES





problemas











?alculate the 2a!elength and requenc% o the photon emitted i an

electron in a onedimensional

bo# o length /.00 nm (1.00×10−9 m) makes a transition from n 3 to

n 2

and the energ% dierence is entirel% con!erted into the energ% o the

photon

Pretend that electrons are bosons 2ith &ero spin4 Iescribe

ho2 the ground state o the helium atom 2ould dier rom

the actual ground state in the orbital appro#imation4



sp Hybrid Orbitals

F



Be

BeK



sp2 and sp3 Hybrid Orbitals$%3



?H



H+O



&%



"alence Shell Electron Pair epulsion ("SEP) odel











The bond angles decrease as

the number of nonbonding

electron pairs increases



Electrons in multiple bonds, like nonbonding electrons, exert a greater

repulsive force on adjacent electron pairs than do single bonds



(eo)etries of*olecules +ith

Epanded -alence

Shells



f there is a non!bonding pair of electrons "a #larger# electron cloud$,

it %ill go in the axial position to minimi&e electron repulsion

eoria de Enlaces de "alencia

H+



O de H+



eoria de esonancia

Many simple organic compounds, such as methane, ethene,

etc., can be adequately represented by a single Lewis



etc., can be adequately represented by a single Lewis

structure:

methane - CH4

ethene - H2C=CH

2

eoria de esonancia



Acidos % Bases



'r(nsted )cid!'ase Theory

BrLnsted argued that all acid-base reactions in!ol!e the transer o an HC ion or proton4 ;ater reacts2ith itsel or e#ample b% transerring an HC ion rom one molecule to another to orm an H

3OC ion

and an OH- ion4

)cid!*issociation E+uilibrium onstant

Acids are oten di!ided into categories such as MstrongM and M2ea14M One measure o the strength o an

acid is the acid.dissociation equilibriu) constant K a or that acid4



;hen K a is relati!el% large 2e ha!e a strong acid4

H?l5 K a > / # /.3

;hen it is small 2e ha!e a 2ea1 acid4

?H3

?O+

H5 K a

> /4, # /.-

Dn /@.@ S P ' SLrenson suggested that the enormous range o concentrations o the



Dn /@.@ S4 P4 '4 SLrenson suggested that the enormous range o concentrations o the

H3OC and OH- ions in aqueous solutions could be compressed into a more manageable

set o data b% ta1ing ad!antage o logarithmic mathematics and calculating the pH or pOH o the solution4

pH > - log NH3OC

pOH > - log NOH-

he MpM in pH and pOH is an operator that indicates that the negati!e o the logarithm

should be calculated or an% quantit% to 2hich it is attached4 hus p7 a is the negati!e

o the logarithm o the acid-dissociation equilibrium constant4

p7 a

> - log K a

he onl% disad!antage o using p7 a as a measure o the relati!e strengths o acids isthe act that large numbers no2 describe 2ea1 acids and small (negati!e) numbers

describe strong acids4

H?l5 p7 a > -3

?H3?O

+H5 p7

a > 40

H+O5 p7

a > /40



K a K

b > K

2 > / # /.-/

Compound K a pK a Conjugate Base K pK

HD 3 # /.@ -@4 D- 3 # /.-+ +34

H?l / # /.* -* ?l- / # /.-+. +.



H+SO

/ # /.3 -3 HSO

- / # /.-/0 /0

H3OC -/40 H

+O /4, # /.-/* /40

H<O3 +, -/4 <O

3- 34* # /.-/* /4

H3PO

04/ # /.-3 +4/ H

+PO

- /4 # /.-/+ //4@

?H3?O

+H /4, # /.- 40 ?H

3?O

+- 4* # /.-/. @43

H+S /4. # /.-0 04. HS- / # /.-0 04.

H+O /4, # /.-/* /40 OH- -/40

?H3OH / # /.-/, /, ?H

3O- / # /. -

H? ?H / # /.-+ + H? ?- / # /.// -//

<H3 / # /.-33

33 <H+-

/ # /./@

-/@

H+ / # /.-3 3 H- / # /.+/ -+/

?H+>?H

+ / # /.- ?H

+>?H- / # /.3. -3.

?H / # /.-@ @ ?H

3- / # /.3 -3

/e+is acid5 An electron-pair acceptor such as the HC ion

he pair o electrons that 2ent into the ne2 co!alent bond 2ere donated b% the OH- ion4 'e2is thereore

argued that an% substance that can act as an electron-pair donor is a /e+is base4

/e+is base5 An electron pair donor such as the OH- ion



/e+is base5 An electron-pair donor such as the OH ion





+H+O> H3OCCOH-

+<H3> <HC<H+-

+HF> H+F

C

CF

-

+SO+> SO+CCSO3+-

<aOHCNH3O?l> <a?lC+H+O

<a<H+C<H?l> <a?lC+<H3

<aFCNH+F?l> <a?lC+HF

<aFCNH+F?l> <a?lC+HF

<a+SO3CSO?l+> +<a?lC+SO+

eaciones de neutrali&acion

aromaticidad













Estado Solido























































Solidos uno % bidimencionales

#rans.poliacetileno



Cis.poliacetileno

calentar

a b

a0b

a-b>

banda de conducion

banda de !alencia

Solidos uno % bidimencionales





































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