Документ взят из кэша поисковой машины. Адрес оригинального документа : http://electr003.chem.msu.ru/rus/asp2/RR_lecture3_MSU_2015.pdf Дата изменения: Thu Apr 23 00:04:09 2015 Дата индексирования: Sun Apr 10 00:49:42 2016 Кодировка:

III (- ).

.. , , 17.04.2015



1. . 2. . 3. . . 4. . 5. .


Solvent coordinate vs Quantum effects
- decreasing of the activation barrier - tunneling
decreasing rate constant

increasing rate constant

U

U

q

q


Effect of solvent quantum modes
e*ff k exp 2
frequency factor
* e*ff Ea exp exp[ ] 2 k BT

(s* I ) 2 exp[ ] * 4s k BT

s* s
2 C
2s C

*


0


Im ( )

( )

2

d

1 1 C st
Pekar factor





Im ( ) h ( )
2 2

d

*

tunneling factor


F 1 .0 0 .8 0 .6 0 .4 0 .2

I n t e r p o la t io n c h . . . s h w , w b y p o ly n o m ia l o f d e g r e e 6 o n t h e in t e r v a l 0 , 3 w


*



0.5


0

100

200

300

400

500

w



THz

ch{ h / 2} ch{(1 2 ) h / 2} F ( , ) sh{ h / 2}
1 / k BT


Dielectric spectra of water (J.A. Saxton, 1953)

0.8


Another dielectric spectrum of water
R. Buchner and co-w orkers (2005)

S1 S2 (v ) 1 i 2 v 1 1 i 2 v 2
2 S3 S 4 v4 2 2 1 i 2 v 3 v4 v i 4 v 2 2 S5v5 S6 v6 2 2 2 2 v5 v i 5v v6 v i 6v 2 S7 v6 2 2 v7 v i 7 v

0.9


R. Buchner and co-w orkers (2008)

Dielectric spectra of some ionic liquids

0.7




(wi(f) >> kBT)

k exp(Ea / k BT )

~ i( 0 ) (qin ) (f 0 ) ( qin ) dqi

2 n

in exp h ef

f





weff

2 wi w

«»

f

wi wi






* eff





eff ( s )

s in in

s in

*



2 eff ( s )

2 C


0

Im ( )d 2 ( )
1



C



opt

1 st


( I ) 2 k e exp 4 k BT


.

( I ) 2 Ea 4 E a -



- .. ..

I -




(i) (ii)


, e



PA exp(2 e )
(i)

e 1 PA 1 exp(2 e )

(ii)

1 exp(2 e ) 1 PA e 1 (1 / 2) PA 1 (1 / 2) exp( 2 e )


e ,

Ee 2 e heff

2

(s in ) k BT

« »



:

e 1 e e 1 e 1

e ()

()


H2

+

Ee H if H ii S 2 2 1 Sif

if

^ H if i H f dV ^ H ii i H i dV Sif i f dV

Ee H if H ii S Sis 1, 2

if


( )

1 E q 2
.

U i q U
2

f

q



U q
f

Ui q



2

4H
2 if

U i q q

0.1 E(q)

U f q q 1

2

0.0
= 1 eV

Hif = 0.1 eV

I 0

-0.1

Hif = 0.2 eV Hif = 0.4 eV

-0.5

0.0

0.5 q

1.0

1.5

heter




I 0

U i ( q, ) q
2

U f (q, ) (q 1) I
2
3

1 , 2 ,



( F e0 ) Ea ( ) 4 k BT
-

2

ks



e





( ) f FD ( ) exp{Ea ( ) / k BT }d
-




«»

( F ) k BT
* e

e



( F )
* e

e

adiab






k exp{E / k BT }
* a


« »



j ( ) ( ) f FD ( ) g ( F )
0.4 <


6

< 1.1
3-

+

e

= > F e (C N )

46
MC


- ( )

MC


A non-successful trajectory


A successful trajectory


( - - )
1.0 0.8 0.6
PL-Z=0.999 PL-Z=0.1 PL-Z=0.01 PL-Z=0.001



e

0.4 0.2 0.0 0 10 20

30 N

40

50

60

70



. .
tip

eo I ( F ) H h



2 if




0

bias

d ads ( )





W

W 5dz2 W


Model STM contrast

Cysteine adsorption on Au(110) elecrode (in situ STM images)


Rate constant of electron transfer (statistical averaging)

r r r k e (r ) exp[Wi (r ) / k BT ] exp[Ea (r ) / kBT ]d 2
* eff

r r r ( (r ) W f (r ) Wi (r ) I ) r Ea (r ) r 4 (r )k BT
heterogeneous ET
* eff

2

% % % k e ( x) exp[Wi ( x) / k BT ] exp[Ea ( x) / k BT ]dx 2
%%% e Wi Ea are averaged over orientations