Physical Chemistry (II)contents.kocw.net/KOCW/document/2014/Pusan/LimManho/... · 2016-09-09 · Physical Chemistry (II) 2014 Fall, CH22604 (034) 2) 강의개요 (Course Description)

Physical Chemistry (II)2014 Fall, CH22604 (034)

교재: "Introduction to quantum mechanics in chemistry", by Ratner & Schatz (2001)

참고문헌: "Quantum chemistry and spectroscopy", by T Engel, 2nd ed. (2010)"Physical chemistry" by Atkins, 9th ed (2009)"Quantum mechanics in chemistry" by Schatz and Ratner (1993)"8. 원자보다작은세계를이해하다“, ‘세상을바꾼열가지

과학혁명’ 곽영직저, 한길사(2009), pp221-244.

담당교수: 임만호화학관 403호, 510-2243 (O), [email protected]

Café: http://cafe.naver.com/enjoychemOffice hours: 수, 목 16:30 – 18:00

2014 Fall Physical Chemistry (II) by M. Lim1

mailto:[email protected]


1) 교수목표 (Course objectives)

1. 분자의역학을지배하는패러다임2. 간단한양자역학적계의기술3. 수소원자의에너지준위와전자의공간분포함수4. 분광법으로부터분자의정보를얻는방법등을이해하게한다.



2) 강의개요(Course Description)

물리화학 I, II는 화학과 전공공부에 가장 기본이 되는 과목으로전공필수로 지정되어 있다. 물리화학 I에서 열역학과 화학평형에대해 거시적인 관점에서 공부하고 물리화학 II에서는 화학적현상을미시적으로이해하기위해분자의구조및성질을공부한다.이를 위해 원자의 특성을 기술하는 양자역학을 배우고 이로부터분자의특성을이해하는양자화학을공부한다.기본적인양자화학을다루는강의이다. 우선필요한수학적내용과양자역학의 발생에 필요한 고전역학적인 내용을 짚어본다 .양자역학의가설들을심도있게공부한다음, 간단한양자역학적인계를 풀어볼 것이다. 또한 원자구조, 화학결합, 분자구조, 분광학등에대해양자역학적인내용을기초로강의한다.



시험: 각 시험은 범위 내의 내용을 수업한 시간만큼 비중을 두어 배점한다.

출석: 1시간 결석에 –1점 감점. 감점은 –5점에서 끝나지 않고 계속된다.(예, 15시간 결석, –10점). 매 수업은 1.5시간 강의이다.지각 두 번은 1번 결석.6회 이상 결석은 F 처리

대리출석과 관련된 학생은 1학기 45시간 모두 결석 처리한다. (–40 점)

숙제: 수업 중 제시된 숙제는 지정된 시간까지 제출해야 함. 모든 숙제는학기초에 미리 준비한 “문제풀이노트”에 풀어 제출한다. 퀴즈는필요에 따라 수업 중에 공지하여 실시한다

3. 평가방법(Requirements & Grading)3회의시험: 75%

숙제및퀴즈: 20%출석: 5%


Physical Chemistry (II)

개개의 원자나 분자의 구조를 이해하기 위해서는 이들이지배하는 힘에 대하여 소립자(전자, 양성자)가 어떻게움직이는지알아야한다.

PC I: the properties of bulk

(열역학적관점)

Statistical mechanics (statistical thermodynamics:

Atkins chap 16-17)

PC II: Individual atoms and molecules

(양자역학적관점)


양자역학(QM)을사용하여분자의행동을이해하기위해서는 QM 자체를기본적으로알아야한다.

• Key concepts from Classical Physics (including particle and wave behavior)

Energy, angular momentum double slit experiment

• Brief summary of the early history of QM wave-particle duality the uncertainty principle wave mechanics

1. Introduction and background to Quantum Mechanics


Energy: the capacity to do work. ‘conserved’• Etotal = Ek + Ep (or V)

• Kinetics energy (as a result of a body’s motion)

• Potential energy (as a results of a body’s position): force can be derived from

Ex1, a coulomb potentialEx2, a gravitational potentialEx3, a harmonic potential

Key concepts from classical physics-1


212kE mυ=

( )

( )

( )

1 2

0

2

4

1 2

q qV rr

V h mgh

V x kx

πε⋅ =

⋅ =

⋅ =

, dVF F Vdx

= − = −∇



2

velocity:

speed: linear momentum:

the total energy:

definit

( ) 2

: (tr e (a ), (jector )y )

drdt

p mpE V xm

x t p t

υ

υυ

=

=

= +

( ) ( )

( )( )

( )( )

( )( )

0

22

2

0

1 1, 2 2

2

2

2

2 ( ( ))

x

x

dxE m V x E V x mdt

dx E V xdt m

dx E V xdt m

mdxdtm E V x

dxt t mm E V x

υ= + − =

= −

= −

=−

− =−∫

Classical Mechanics• Behavior of objects: Etotal is constant, F=ma• The trajectory in terms of the energy

• Newton’s second law



( )

2

2

2

2

,

,

1 for

dpF ma Fdt

dV d d xF adx dt dt

d x dV x tdt m dx

υ

= =

= − = =

∴ = −

2

2

ˆˆ , ,

ˆˆ ˆthe gradient operator,

- particle in many particles, i i i i

d d rr xi yj zk a F Vdt dt

d d di j kdx dy dz

i th F V m a

υ −= + + = = = ∇

∇ = + +

= −∇ =

2

2

2

22

2

1for HO ( ), 2

1

0, where

( ) cos sin

dVV kx F kxdx

d x dV k xdt m dx m

d x kxdt m

x t A t B t

ω ω

ω ω

= = − = −

∴ = − = −

+ = =

∴ = +

• For 3D (for Cartesian coordinate)



2, ( : moment of inertia)

Torque (accelarate a rotation)

J r pJ I I mr I

dJ Tdt

ω

≡ ×

= =

=

2 2 2 2 2 2

,

Similarly, =2 2 2 2k k

dp F p Fdt

p F T JE Em m I I

τ

τ τ

= ∴ =

= = =

J

m

r

ω

• Rotational motion: described by angular momentum J

• When a constant F is applied to a system for a time τ

E of a particle can be increased to any value! (continuous E)

2

, ,

vJ rp rmv mr Ir

dl dl r vdt dt

ω

θθ ω

= = = =

= ≡ ≡



2

2

212

pH Vm

dH d m Vdt dt

υ

≡ +

= +

( )

( )

2

2

2

2

2

2 , for 0

0

d dv dV dx dV Vdt dt dt dt dx t

dH dx d x dx dVmdt dt dt dt dx

dH dx d x dV dxm ma Fdt dt dt dx dt

υυ ∂

= = =∂

= +

= + = − =

0Vt

∂=

∂

• The Classical Hamiltonian (total energy)

H = E is constant for systems with‘conservative system’

if 0, 0V dHt dt

∂∴ = =

∂



( )0

0 phase( , ) cos

: wave amplitude, :

(wavelength) (per2 2 iod)k

A x t AA kx t

kx t

π π

ω

ωλ

ω

τ

=

−

−

= =

Classical Wave TheoryOne way to describe the motion:

specify the perpendicular displacement, x from its x0 in f(x,t)

- The collective motion of water molecules: ocean waves- The collective motion of gas molecules: sound waves- Harmonic waves can be expressed as sin, cos functions

1.4.1 Wave amplitude Figure 1.1 (p9)


( )0

0

( , ) cos : wave amplitude phase

2

:

(period)

(wavelength) 2

kA x t AAkx t

x t

k

ω

ω

π

ω

πτ

λ

=

−

=

−=



phase velocity: (EM waves)p

kx t const

x t constk

kcω νλ

ωω

υ

− =

=

=

+

→=

A traveling wave• A position of constant phase (a position where A(x,t) is fixed)

1.4.2 Superposition and diffraction• If two wave trains collide → coherent superposition

One example is the diffraction of light nλ = d sin θsee figure 1.2 (p10)


( ) ( )( ) ( )

( , ) cos cos

b.c. 0, , 0

A x t a kx t b kx t

A t A L t

ω ω= − + +

= =

( ) ( )( ) ( )

( ) ( )( ) ( )

(0, ) cos cos

cos 0

( , ) cos cos 0

2 sin sin 0

A t a t b t

a b t a b

A L t a kL t b kL t

a t kL kL n

ω ω

ω

ω ω

ω π

= +

+ = → = −

= − + + =

= → =


1.4.3 Standing waveWaves where boundary conditions must be imposed, (ex, a violin string)To describe this, sum up traveling waves moving in opposite direction

( ) ( ), 2 sin sin 1, 2,3n xA x t a t nLπω =∴ =


( )2 2

22 2

1

p

A Ax tυ

∂ ∂=

∂ ∂

2

2

k

p

dAEdt

E A

∝

∝ ( )

( )

( )

( ) ( )

0

22

02

22

02

220

( , ) cos ,

cos

cos

cos

p

p

A x t A kx tk

A k A kx txA A kx t

t

k A kx t

ωω υ

ω

ω ω

υ ω

= − =

∂= − −

∂∂

= − −∂

= − −


1.4.4 Energy associated with wave amplitude- For an oscillating string, each small segment of the string undergoes

periodic oscillation- The energy in the string: expressed essentially the same way as a HO

1.4.5 Wave equation

원자보다 작은 세계 이해하기.Concepts in quantum mechanics

“1900년에서 1930년까지의 30년동안은뉴턴역학으로대표되는고전물리학이퇴장하고양자물리학으로대표되는현대물리학이등장한시기였다. 이시기에등장한중요한개념은– 에너지를비롯한물리량이연속된양이아니라불연속적인양이다.– 입자와파동은서로다른물리적대상물이가지는성질이아니라같은대상물이가지는두가지측면이다.

– 원자보다작은세계에서일어나는현상을제대로기술하기위해서는입자와파동의두가지측면을모두고려해야한다.” by 곽영직


불연속적인물리량을다룰수있는새로운물리학이필요: 행렬역학, 파동역학

Early history of quantum mechanics

• 1.6 Particle nature of light• 1.6.1 Blackbody radiation (M Planck, 1900)

Planck postulated that E seen in the blackbody spectrum comes in discrete qunata of magnitude, hν

• 1.6.2 Photoelectric effect (A Einstein, 1905)KE = hν – hν0

• 1.7 Wave nature of particles• 1.7.1 Atomic spectra and the Bohr model

The electron orbits around he proton in circular orbits with

• 1.7.2 de Broglie waves and electron diffraction

• 1.8 Uncertainty principle


Several key experiments that were in conflict with the predictions of CM1) Light could not be described exclusively using wave theory2) Particle possesses wave-like properties

2xx p∆ ∆ ≥

hp

λ =

(orbital angular momentum)l n=

1.6 Particle nature of light• 1.6.1 Blackbody radiation

The distribution of frequencies of light emitted by a heated solid


( )5

Planck distribution:8

1hc

kT

hc

e λ

πρλ

=−

Quantization of energy: E = nhν+ classical statistical mechanics

( ) B

hk TP E eν

−

=

max 3000T m Kλ µ≈ ⋅

1.6 Particle nature of light• 1.6.2 Photoelectric effectEmission of electrons from the surface of a metal irradiated with light


0

034

: work function

6.626 10 sec

KE h h

hh J

ν ν

ν−

= −

= ×

Each electrons absorbs on quantum of energy equal to hν

1.7 Wave nature of particles• 1.7.1 Atomic spectra and the Bohr model

consists of discrete lines in regular patterns


E hν∆ =

Bohr (1911): orbital angular momentum l = nh/2π

• Works well for one-e atom• fails for atoms where two e’s interact strongly• Approximation to the correct formulation of QM

1.7 Wave nature of particles• 1.7.2 de Broglie waves and electron diffraction

In 1923 de Broglie postulates e’ s and other particles have waves

In 1927, Davison and Germer observed the diffraction of e’sIn 1932, Stern observed the diffraction of He and H2


hp

λ =


1.8 Uncertainty principleIn 1925 by Heisenberg

It is impossible to measure the p and x of a particle simultaneously to arbitrary precision

2xx p∆ ∆ ≥

1.9 Discovery of quantum mechanics• 1.9.1 Schrodinger wave mechanics and Heisenberg

matrix mechanics– In 1925, Schrodinger solved wave equation for the H atom– The physical meaning of wave function ΨBorn and Copenhagen interpretation: ІΨІ2 is the probability density for

finding the particle at a particular location

• 1.9.2 Relativistic QM– In 1929, Dirac introduced spin to the wavefunction to deal with

relativistic contribution: Dirac equation– The application of the Dirac equation to the motions of electrons,

subject only to Coulomb interactions between them, correctly describes all the properties of electrons that we are aware of. The corresponding description of protons, neutrons, and other heavy particles requires the introduction of nuclear forces.


1.10 Concepts in quantum mechanics– Particle is described as waves with an associated wavefunction Ψ– Ψ behaves like classical waves:

exhibiting diffraction and satisfying b.c. that leads to discrete energy levels– Some important distinctions between quantum waves and classical waves


( ) ( )

( )

cos in CM in QM

~ exp

i kx tkx t ehp k

E h

i px Et

pk

E

ωω

λ

ν ω ω

−

=

=

−

Ψ −

→

= = ∴

= =

∴

∴

2 2 2 2 2

2 2 2

2

2 2

2

1

1 2 2

since for a free particle,2

2

iE E it t

p px m m x

pEm

it m x

∂Ψ − Ψ ∂Ψ= → =

∂ ∂ Ψ∂ Ψ Ψ ∂ Ψ

= − → = −∂ ∂ Ψ

=

∂Ψ ∂ Ψ= −

∂ ∂

2 2 2 2

2 2 2 2

1 , in CM 2 p

A Ai cft m x x tυ

∂Ψ ∂ Ψ ∂ ∂= − = ∂ ∂ ∂ ∂

Schrodinger eqn for a free particle:

(properties of particles)

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Physical Chemistry (II)contents.kocw.net/KOCW/document/2014/Pusan/LimManho/... · 2016-09-09 · Physical Chemistry (II) 2014 Fall, CH22604 (034) 2) 강의개요 (Course Description)