Interaction Potentials for Ch4 on Benzene - Copy

7/23/2019 Interaction Potentials for Ch4 on Benzene - Copy

1/51


2/51

Abstract

A+$ #-+% +/ #,%#-- # $ "-+, *!#-%* ,',!$'6 !/"!,+#-- +' $#' #$!#/ T*! /!

,-!#' !-/ $ !*+,-#$ #""-+,#%+'/ +/ %*/ /%$'.- !',$#.! N#%$#- .#/6 *+,* "$+$+-,'/+/%/ &!%*#'!6 +/ # #-#-! #-%!$'#%+! !- +%* $ ##'%#.!/ #/ ,&"#$! +%* .#/-+'!6

'#&!-: *.! $- $!/!$!/6 - ,/%6 ,-!#' $'+'. ,*#$#,%!$+/%+,/ (- !&+//+' -!!-/ #' -

.$!!'*/! +&"#,%) #' .$!#%!/% !'!$. "!$ '+% // #-- %*! %*!$ *$,#$'/ H!!$6 /+',!

/"!$,$+%+,#- +' STP ,'+%+'/6 &!%*#'! #-#/ *#/ # !$ - !'/+% S%$+'. %*! .$!#%!/%

#&'%/ &!%*#'! +' # .+!' -+&+%! -&! +/ %*/ # $!#- ,*#--!'.! $ +%/ #""-+,#%+' % %* .#/

%$#'/"$%#%+' #' .#/ "!$! !*+,-!/ A&'. %*! #$+/ /%$#.! &!%*/ /!6 #/$"%+' /+'.

#""$"$+#%! %!$+#-/ +/ # %!,*'-.+,#-- +&"$%#'% &!%* A/$! '#%$#- .#/ (ANG) *#/ %*!

"%!'%+#- % !,&! %*! &/% ,/%;!!,%+! &!%* ,&"#$! % %*!$ &!%*/ /,* #/ -+!+!

'#%$#- .#/ (LNG) #' ,&"$!//! '#%$#- .#/ (CNG)

I' %*! $!,!'% !#$/ %*!$! *#/ !!' # /%$'. +'%!$!/% +' !!-"+'. %!$+#-/ $ /%$#.!

'#%$#- .#/ (&!%*#'!) A *+-! #.6 %*! A%-#'%# G#/ L+.*% A/$!'% R!/!#$,* G$" /..!/%! %*!%#$.!% 150 -&!/ .#/ (&!#/$! +' STP ,'+%+'/) "!$ -&! /%$#.! !//!- (


3/51


4/51


5/51

%!&"!$#%$! H!!$6 +% +/ +&"$%#'% % ,'/+!$ %*#% *$.!' +/ ! ,#- .#/++,#%+'

$ #%!$ !-!,%$-/+/6 #' %*!/! "$,!//!/ .!'!$#%! #+$ "--%#'%/ +$!,%- $ +'+$!,%-

Natura# +as. N#%$#- .#/ (NG)6 *+,* "$+$+- ,'/+/%/ &!%*#'!6 +/ # #-#-!

#-%!$'#%+! !- +%* $ ##'%#.!/ #/ ,&"#$! +%* .#/-+'!6 '#&!-: *.! $-

$!/!$!/6 - ,/%6 ,-!#' $'+'. ,*#$#,%!$+/%+,/ (- !&+//+' -!!-/ #' - .$!!'*/!

+&"#,%) #' .$!#%!/% !'!$. "!$ '+% // #-- %*! %*!$ *$,#$'/ A '#%$#- .#/

!*+,-! (NG


6/51


7/51


8/51


9/51


10/51


11/51


12/51

Fi+ure 4: T*! C-& "%!'%+#- T*! %%& ,$! $!"$!/!'%/ %*! +'%!$#,%+' !%!!' %

"#$%+,-!/ ""/+%! ,*#$.! %*! %" ,$! $!"$!/!'%/ %*! +'%!$#,%+' "#$%+,-!/ !#- ,*#$.!

1)> Rotation !atrices

I' -+'!#$ #-.!$#6 # $%#%+' %$+ +/ # %$+%*#% +/ /! % "!$$& #$%#%+'+' E,-+!#' /"#,!

$ !#&"-! %*! %$+

$%#%!/ "+'%/ +' %*!xy;C#$%!/+#' "-#'!,'%!$,-,+/! %*$.* #' #'.-! #% %*! $+.+'

%*!C#$%!/+#' ,$+'#%! //%!& T "!$$& %*! $%#%+' /+'. # $%#%+' %$+!6 %*! "/+%+'

!#,* "+'% &/% ! $!"$!/!'%! # ,-&' !,%$6 ,'%#+'+'. %*! ,$+'#%!/ %*! "+'% A

$%#%! !,%$ +/ %#+'! /+'. %*! %$+ &-%+"-+,#%+'! S+',! %$+ &-%+"-+,#%+' *#/ '

!!,% ' %*! ?!$ !,%$ (+!6 ' %*! ,$+'#%!/ %*! $+.+')6 $%#%+' %$+,!/ ,#' '- ! /! %

!/,$+! $%#%+'/ #% %*! $+.+' %*! ,$+'#%! //%!&

T*! --+'. %*$!! #/+, $%#%+' %$+,!/ $%#%! !,%$/ #% %*!x6y6 $"#+/6 +' %*$!!+&!'/+'/:

12
http://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Rotation_(mathematics)http://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Cartesian_coordinate_systemhttp://en.wikipedia.org/wiki/Cartesian_coordinate_systemhttp://en.wikipedia.org/wiki/Column_vectorhttp://en.wikipedia.org/wiki/Matrix_multiplicationhttp://en.wikipedia.org/wiki/Linear_algebrahttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Rotation_(mathematics)http://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Cartesian_coordinate_systemhttp://en.wikipedia.org/wiki/Cartesian_coordinate_systemhttp://en.wikipedia.org/wiki/Column_vectorhttp://en.wikipedia.org/wiki/Matrix_multiplication


13/51

T*!/! $%#%+' %$+,!/ *#/ !!' /! +' %*+/ /% $ ,*#'.+'. %*! $!-#%+! $+!'%#%+' 5;/+%!

&!%*#'! &-!,-! !$ !'?!'! ,!'%$!6 $%#%+'. %*! &!%*#'! &-!,-! #-'. 6 #' ?;#+/

/%#$%+'. $& %*! +'+%+#- $+!'%#%+'

13


14/51

) !ETHOD AND RESULT

)1 Introduction

I' %*+/ ,*#"%!$ +'%!$#,%+' "%!'%+#- ,$! #$! "-%%! $+%+'. /-- "$.$#&/ (/+'. C "$.$#&+'. ) $

%* '! /+%! #' +! /+%! &!- &!%*#'! #$+'. +/%#',! !%!!' %*! ,!'%$! &!%*#'! #' %*!

,!'%$! !'?!'! $+'. A-/ %*! +! /+%! &!- *#/ !!' .+!' #$+/ $+!'%#%+'/ !!"+'. %*! C;#%&

&!%*#'! + #! %*! !'?!'! $+'. ,!'%$! % +' %*! $+!'%#%+' +%* &+'+&& "//+-! !-- W! '!! %

+' %*! &+'+&& "//+-! !-- +' ,#/! &!%*#'! !'?!'! //%!& +' $!$ % ,*!, +%/ &/% /%#-!

$+!'%#%+'

) !ode#s o( !et"ane

Fi+ure >.M!%*#'! &!-/ /! +' %*! "$!/!'% ,#-,-#%+'/ T*! ' #'.-!/ #' ' -!'.%*/

/*' $ %*! +!;/+%! &!%*#'! &!- #$! /+&+-#$ $ #-- %*! '/ #' #'.-!/

T*!$! #$! % +!- /! ,-#//+,#- &!-/ $ &!%*#'!6 '#&!- %*! '!;/+%! #' K--' +!;/+%!

&!-/ T*! "#$#&!%!$/ $ %*! '!;/+%! &!- !$! !!-"! /+'. %*! #"$;-++ !+-+$+& #%#

*!$!#/ %*/! $ %*! K--' +!;/+%! &!- #/ #/! ' $!! !'!$. ,#-,-#%+'/ % "$!+,% /-#%+' #&!%*#'! &-!,-! +' - #%!$ B%* %*! &!-/ /,,!//-- $!"$,! %*! -+;"*#/! !*#+$

14


15/51

&!%*#'! T*! ,*#$.!/ #' %*! LJ "#$#&!%!$/ $ %*! % &!-/ #$! /*' +' %*! T#-! 3 I' %*! $+.+

K--' +!;/+%! &!- +'%!$&-!,-#$ /+%!;/+%! +'%!$#,%+'/ #$! %$!#%! /+'. %*! 12; L!''#$;J'!/

+'%!$#,%+' "%!'%+#- #' C-&+, +'%!$#,%+'/ #$! /! $ +'%!$#,%+'/ !%!!' ,*#$.!/ B%* %*! +!;/+%!

#' '!;/+%! &!-/ #$! !"+,%! +' %*! +.$! 5

Tab#e 4 : L!''#$;J'!/ "#$#&!%!$/ #' C-&+, ,*#$.!/ $ '!;/+%! #' +!;/+%!

&!%*#'! &!-/

One8site

*ode#

Fi,e8site *ode#

O (A) 373 C

H

34

25

(K) 148 C

H

55055

7901

(!) 00 CH ;0015

)$ !ode# o( 'en?ene

Fi+ure @.B!'?!'!&!-/ /! +' %*! "$!/!'% ,#-,-#%+'/ T*! ' #'.-!/ #' ' -!'.%*/

/*' $ %*! +!;/+%! &!%*#'! &!- #$! /+&+-#$ $ #-- %*! '/ #' #'.-!/

15


16/51


17/51

22

23

*!$!

O++/ %*! L!''#$;J'!/ +#&!%!$ $ %*! +%* /"!,+!/6

++/ %*! !-- !"%* $ %*! +%* /"!,+!/

1) Interaction o( one8site *et"ane 6it" ben?ene.

T*! "%!'%+#- ,$! $ '!;/+%! &!%*#'! #' !'?!'! +/ %#+'! "-#,+'. %*! &!%*#'! &-!,-!

#% +!$!'% "/+%+'/ #-'. %*! #+/ "#//+'. %*$.* %*! ,!'%$! %*! !'?!'! $+'. I' %*+/ //%!&

'- L!''#$;J'!/ +'%!$#,%+' +/ %*!$! #/ %- !#$-+!$ %*! ,-&+, "#$% +/ ?!$ $ &!%*#'!;

!'?!'! //%!& P$.$#& 1 (+' #""!'+ B) +/ $+%%!' ( +' C -#'.#.!) % ,#-,-#%! %*! "%!'%+#-

!'!$. #% #$' 100 +!$!'% "/+%+'/ #-'. %*! #+/ "#//+'. %*$.* %*! ,!'%$! %*! !'?!'!

$+'. /+'. %*! !#%+' *!$! %*! L!''#$;J'!/ "#$#&!%!$/ $ '!;/+%! &!%*#'! +/ .+!' +' %#-! 4

#' $ !'?!'! +' %#-! 5 T*! ,$! %#+'! %*$.* %*+/ "$.$#& +/ /*' +' +.$! 7 T*!

&+'+&& "%!'%+#- !'!$. !-- %#+'! +' %*+/ ,#/! +/ #$' ;4 J=&- #% # /!"!$#%+' 398

#'./%$& *+,* %,*!/ +%* %*!


18/51

,-&+, "#$% +/ ?!$ $ &!%*#'!;!'?!'! //%!&6 % %*+/ //%!& .+!/ +!$!'% "%!'%+#- !'!$.

!-- $ +!$!'% $+!'%#%+' +%* $!/"!,% % !'?!'! $+'.6 '% -+! %*#% +' ,#/! '!;/+%! &!%*#'!

*+,* .+!/ '- # /+'.-! &+'+&& "%!'%+#- !-- S +' $!$ % +' %*! &+'+&& "%!'%+#- !--

$ +!;/+%! &!%*#'!;!'?!'! //%!&6 %*! &!%*#'! &-!,-! +/ "-#,! !$ %*! ,!'%$! !'?!'!

$+'. #' .+!' 1400 $#'& $%#%+'/ #% +%/ ,!'%$! // #' %*!' $ !!$ $%#%+' ( /%#$%+'.

$& %*! +'+%+#- $+!'%#%+' ) %*! "%!'%+#- !'!$. #% #$' 100 +!$!'% "/+%+'/ #-'. %*! #+/

"#//+'. %*$.* %*! ,!'%$! %*! !'?!'! $+'. +/ ,#-,-#%! /+'. %*! !#%+' *!$! %*! L!''#$;J'!/ "#$#&!%!$/ $ +!;/+%! &!%*#'! +/ .+!' +' %#-! 4 #' $ !'?!'! +' %#-! 5

M#' /-- "$.$#&/ #$! $+%%!' % "-% %*! "%!'%+#- !'!$. ,$!6 % +' %*! &+'+&&

!'!$. !-- #&'. #-- $+!'%#%+' "//+-! #' ,$$!/"'+'. /!"#$#%+' I /%#$%! ,#-,-#%+'. %*!

+'%!$#,%+' "%!'%+#- $& %*! +'+%+#- $+!'%#%+' &!%*#'! !'?!'! //%!& .+!' % &! /*' +'

+.$! 8 T*! ,$+'#%!/ +'+%+#- +!;/+%! &!%*#'! #' !'?!'! +/ .+!' +' ,$+'#%!;2 #'

,$+'#%!;1 (+' #""!'+ A) $!/"!,%+!-

Fi+ure B. I'+%+#- $+!'%#%+' &!%*#'! !'?!'! //%!&

I "$,!! %*$.* --+'. /%!"/ % +' %*! &+'+&& "%!'%+#- !-- $ +!;/+%! &!%*#'!;

!'?!'! //%!&

1 C#-,-#%+' %*! "%!'%+#- !'!$. #% #$' 100 +!$!'% "/+%+'/ #-'. %*! #+/ "#//+'.

%*$.* %*! ,!'%$! %*! !'?!'! $+'. $ %*! +'+%+#- $+!'%#%+' &!%*#'! &-!,-! ( CH ')!$ !'?!'! #/ /*' +' +.$! (/+'. "$.$#& 2)6/+'. %*! !#%+' *!$! %*! L!''#$;J'!/

"#$#&!%!$/ $ +!;/+%! &!%*#'! +/ .+!' +' %#-! 4 #' $ !'?!'! +' %#-! 5 T*! ,$! %#+'!

+/ /*' +' +.$! 9 T*! &+'+&& "%!'%+#- !'!$. !-- %#+'! +' %*+/ ,#/! +/ #$' ;4385

J=&- #% # /!"#$#%+' 415 #'./%$&/

18


19/51


20/51

,$+'#%!;3 #' ,$+'#%!;1(#""!'+ A) L+! $ +'+%+#- $+!'%#%+' &!%*#'!6 $ %*+/

$+!'%#%+' #-/ %*! "%!'%+#- !'!$. +/ ,#-,-#%! #% #$' 100 +!$!'% "/+%+'/ #-'. %*! #+/

"#//+'. %*$.* %*! ,!'%$! %*! !'?!'! $+'. /+'. %*! !#%+' T*! ,$! %#+'! +/ /*' +'

+.$! 11 T*! &+'+&& "%!'%+#- !'!$. !-- %#+'! +' %*+/ ,#/! ,&!/ % % ! #$' ;043

J=&- #% # /!"#$#%+' 374 #'./%$&/ T*!/! #-!/ %,*!/ +%*


21/51

Fi+ure 1$. C&"#$+/' "%!'%+#- ,$!/ $ 5;/+%! &!%*#'! !$ !'?!'! +%* +%/ CH;" #'

CH;' $+!'%#%+'

I' #-- ,#/!/ ! /!$! %*#% %*! /+'.-! /+%! &!-/ $ &!%*#'! "$!+,% # -!$ +'+'.

!'!$. *!' ,&"#$! +%* %*! +!;/+%! &!- (+%* CH ") #/ /*' +' +.$!14

Fi+ure 14. C&"#$+/' "%!'%+#- ,$!/ $ 5;/+%! &!%*#'! +%* +%/ CH;" #'

CH;' $+!'%#%+' #' 1;/+%! &!%*#'! !$ !'?!'!

T*! &/% /%#-! $+!'%#%+' &!%*#'!;!'?!'! //%!& +/ /*' +' +.$! 106 +%*

&+'+&& !'!$. !-- ;03 J=&- #' ,$$!/"'+'. +'%!$#%&+, +/%#',! 374

#'./%$&/

21


22/51


23/51


24/51


25/51


26/51

V

%%interaction of C( of met'ane wit' t'at of ben"ene

$0+XF"(18917537"(398133903;&+'62)605)

0+XFZ4Z#Z("(=$0+X612);"(=$0+X6))

==interaction of )* of met'ane wit' C of ben"ene

$4+XF"(18917537"(2895814297;&+'62)605)

4+XFZ4Z,Z("(=$4+X612);"(=$4+X6))

==interaction of )+ of met'ane wit' C of ben"ene

F"(434318007;&+'62)

$11+XF"(594457539605)

$12+XF"(3721211605)

$13+XF"(497953977605)

$14+XF"(093487815605)

$15+XF"(224229038605)

$1+XF"(0231441154605)11+XF4Z,Z("(=$11+X612);"(=$11+X6))

12+XF4Z,Z("(=$12+X612);"(=$12+X6))

13+XF4Z,Z("(=$13+X612);"(=$13+X6))

14+XF4Z,Z("(=$14+X612);"(=$14+X6))

15+XF4Z,Z("(=$15+X612);"(=$15+X6))

1+XF4Z,Z("(=$1+X612);"(=$1+X6))

1+XF3Z(11+X12+X13+X14+X15+X1+X)

==total &otential enegy

+XF"Z(0+X1+X4+X)

$+XF398133903;&+'

,%Y['YYD+/%#',! (+' #&./%$') : Y$+X

,%Y[%YYE'!$. (+' J=&-):Y+X

F&+';+',

&+'F

\

&+'!-!F0X ==finding t'e minimum energy well and corres&onding distance

&+'+/F$0X

$(+'% F0F99)

V

+(X&+'!-!)

V

&+'!-!FX

&+'+/F$X

\

26


27/51


28/51

-#% $11100X6$12100X6$13100X6$14100X6$15100X6$1100X611100X612100X613100X614100X6

15100X61100X6$21100X6$22100X6$23100X6$24100X6$25100X6$2100X621100X622100X623100X6

24100X625100X62100X6$31100X6$32100X6$33100X6$34100X6$35100X6$3100X631100X632100X6

33100X634100X635100X63100X6$41100X6$42100X6$43100X6$44100X6$45100X6$4100X641100X6

42100X643100X644100X645100X64100X

-#% *13X1X6*23X1X6*33X1X6*43X1X63X3X6'!13X1X6'!23X1X6'!33X1X6'!43X1X

-#% &+'!-!&!'%1400X6&+'+/%#',!1400X6&+'!-!6&+'+/6&&+'!-!&!'%6&&+'+/%#',!6$+!'%#%+'1400X6

$+!'%#%+'

,%YE'%!$ %*! &+' #' +/%#',! ,$+'#%! !'?!'! $& &!%*#'! ( + ,#$' &!%*#'! +/ #%

,$+'#%! ?F398 #' +/ #! !'?!'!): Y

,+'&+'+

+',F(#'.-!;&+'#'.-!)=1440

+',F(&+'+;)=100

,'F(138Z022)=1000 ==conversion of unit of energy from # to k$%mol

==rotation of met'ane along x-axis about its c-atom

$(+'% F0F1400)

V

&+'F&+'+

$(+'% +F0+F99+)

V

%%interaction of C( of met'ane wit' t'at of ben"ene

$0+XF"(18917537"(398133903;&+'62)605)

0+XFZ4Z#Z("(=$0+X612);"(=$0+X6))

==,$+'#%!/ H4 +%* $+.+' #% ,!'%$! C;#%& &!%*#'!

*4F0

*4F0

?*4F;1085524733

*1F;099995285

*1F;02502515

?*1F031841577

*2F0718721927*2F;0732812593

?*2F031841577

*3F0275273359

*3F0988837743

?*3F031841577

*40X0XF*4 *41X0XF*4 *42X0XF?*4

*10X0XF*1 *11X0XF*1 *12X0XF?*1

*20X0XF*2 *21X0XF*2 *22X0XF?*2*30X0XF*3 *31X0XF*3 *32X0XF?*3

28


29/51


30/51


31/51

,%Y[%YY!'!$. (+' J=&-):Y+X

F&+';+',

&+'F

\

%%storing minimum energy for a &articular rotaion in an array

&+'!-!F0X

&+'+/F$0X

$(+'% F0F99)

V

+(X&+'!-!)

V

&+'!-!FX

&+'+/F$X

\

\

&+'!-!&!'%XF&+'!-!

&+'+/%#',!XF&+'+/

$+!'%#%+'XF&+'#'.-!

#'.-!F&+'#'.-!+',

&+'#'.-!F#'.-!

\

%%calculating minimum energy after all &ossible rotaion along x-axis

&&+'!-!&!'%F&+'!-!&!'%0X

&&+'+/%#',!F&+'+/%#',!0X

$+!'%#%+'F$+!'%#%+'0X

$(+'% +F0+F1400+)

V

+(&+'!-!&!'%+X&&+'!-!&!'%)

V

&&+'!-!&!'%F&+'!-!&!'%+X&&+'+/%#',!F&+'+/%#',!+X

$+!'%#%+'F$+!'%#%+'+X

\

\

%%finding t'e coordinates of .-site met'ane wit' minimum orientation &osition

10X0XF1 11X0XF0 12X0XF0 10X1XF0 11X1XF,/($+!'%#%+') 12X1XF;/+'($+!'%#%+')

10X2XF0 11X2XF/+'($+!'%#%+') 12X2XF,/($+!'%#%+')

%%coordinate of )+,),) and )*

31


32/51


33/51


34/51


35/51


36/51


37/51


38/51

$+!'%#%+'F$+!'%#%+'+X

\

\

==finding t'e coordinates of .-site met'ane wit' minimum orientation &osition

10X0XF,/(&+'#'.-!) 11X0XF0 2X0XF/+'(&+'#'.-!) 10X1XF0 11X1XF1 12X1XF0

10X2XF;/+'(&+'#'.-!) 11X2XF0 12X2XF,/(&+'#'.-!)

==coordinate of )+,),) and )*

$(+'% F03)

V

$(+'% F01)

V

'!1XXF0

'!2XXF0

'!3XXF0

'!4XXF0$(+'% -F0-3-)

V

'!1XXF'!1XX(1X-XZ*1-XX)




\

\

\

'!*1F'!10X0X

'!*1F'!10X1X

'!?*1F'!10X2X3981339030

'!*2F'!20X0X

'!*2F'!20X1X

'!?*2F'!20X2X3981339030

'!*3F'!30X0X

'!*3F'!30X1X

'!?*3F'!30X2X3981339030

'!*4F0

'!*4F0

'!?*4F'!40X2X3981339030

,%Y['YY['YY['YYM+'+&& !'!$. !-- #%!$ #-- "//+-! $%#%+' #-'. ;#+/ F

Y&&+'!-!&!'%Y J=&-Y

,%Y['YY#% # +/%#',! F Y&&+'+/%#',!Y #&./%$&Y

,%Y['YY$ #' $+!'%#%+' F Y$+!'%#%+'Z(180=314159254)Y !.$!!Y

,%Y['YY['YY#' %*! ,$+'#%!/ 5;/+%! &!%*#'! +%* &+'+&& $+!'%#%+' "/+%+' +/ : YY['Y

,%Y['YY,0YY[%Y0Y[%YY[%Y0Y[%YY[%Y3981339

,%Y['YYH1YY[%Y'!*1Y[%Y'!*1Y[%YY[%Y'!?*1

,%Y['YYH2YY[%Y'!*2Y[%Y'!*2Y[%Y'!?*2

38


39/51

,%Y['YYH3YY[%Y'!*3Y[%Y'!*3Y[%Y'!?*3

,%Y['YYH4YY[%Y'!*4Y[%YY[%Y'!*4Y[%YY[%Y'!?*4

==storing t'e values of coordinates of met'ane wit' minimum energy

/%$!#& "

""!'(Y%%Y)

"Y['YY,0YY[%Y0Y[%YY[%Y0Y[%YY[%Y3981339

"Y['YYH1YY[%Y'!*1Y[%Y'!*1Y[%YY[%Y'!?*1

"Y['YYH2YY[%Y'!*2Y[%Y'!*2Y[%Y'!?*2

"Y['YYH3YY[%Y'!*3Y[%Y'!*3Y[%Y'!?*3

"Y['YYH4YY[%Y'!*4Y[%YY[%Y'!*4Y[%YY[%Y'!?*4

",-/!()

$!%$'(0)

\

%ro+ra* > . CALCULATING THE !INI!U! ENERG ELL IN INTERACTION OF >8SITE

39


40/51

!ETHANE 31B= de+ree i)e0 CH u% ITH 'EN5ENE

+',-!+/%$!#&

+',-!+'+"

+',-!,/%+

+',-!,%*

+',-!/%$!#&

+',-!/%-+*

+',-!%+&!*

+',-!-+&+%/

/+'. '#&!/"#,! /%

/+'. /%::'&!$+,-+&+%/

+'% +'()

V

-#% #F590851756F35756,F2237896F326&+'6B,'6&+'#'.-!F3141592546+',

-#% *16*16?*16'!*16'!*16'!?*16*26*26?*26'!*26'!*26'!?*26*36*36?*36'!*36

'!*36'!?*36*46*46?*46'!*46'!*46'!?*4

-#% $100X6$0100X60100X61100X62100X63100X64100X6100X

-#% $11100X6$12100X6$13100X6$14100X6$15100X6$1100X611100X612100X613100X614100X6

15100X61100X6$21100X6$22100X6$23100X6$24100X6$25100X6$2100X621100X622100X623100X6

24100X625100X62100X6$31100X6$32100X6$33100X6$34100X6$35100X6$3100X631100X632100X6

33100X634100X635100X63100X6$41100X6$42100X6$43100X6$44100X6$45100X6$4100X641100X6

42100X643100X644100X645100X64100X

-#% *13X1X6*23X1X6*33X1X6*43X1X63X3X6'!13X1X6'!23X1X6'!33X1X6'!43X1X

-#% &+'!-!6&+'+/

,%Y!'%!$ %*! &+' #' +/%#',! !'?!'! $& &!%*#'! ( + ,#$' &!%*#'! +/ #% ,$+'#%!

?F398 #' +/ #! !'?!'!: Y

,+'&+'

+',F(&+';)=100

,'F(138Z022)=1000 ==conversion of unit of energy from # to k$%mol

%% +/( deg !01A1203 04 M51)A35 A037 8-A829

$(+'% +F0+F99+)

V

==interaction of c( wit' ben"ene

$0+XF"(18917537"(398133903;&+'62)605)

0+XFZ4Z#Z("(=$0+X612);"(=$0+X6))

==coordinates of )* wit' origin at centre of C-atom of met'ane

*1F;099995285

*1F;02502515

?*1F031841577

40


41/51


42/51

4+XF41+X42+X43+X44+X45+X4+X

%%interaction of )+ wit' ben"ene

'!*1F'!10X0X

'!*1F'!10X1X

'!?*1F'!10X2X3981339030

$11+XF"("('!*1;13751793362)"('!*1002533910262)"('!?*1;&+'62)605)

$12+XF"("('!*1;05441062)"('!*112030771062)"('!?*1;&+'62)605)

$13+XF"("('!*1;070953277362)"('!*1;1178280762)"('!?*1;&+'62)605)

$14+XF"("('!*1070953277362)"('!*11178280762)"('!?*1;&+'62)605)

$15+XF"("('!*105441062)"('!*1;12030771062)"('!?*1;&+'62)605)

$1+XF"("('!*113751793362)"('!*1;002533910262)"('!?*1;&+'62)605)

11+XF4Z,Z("(=$11+X612);"(=$11+X6))

12+XF4Z,Z("(=$12+X612);"(=$12+X6))

13+XF4Z,Z("(=$13+X612);"(=$13+X6))

14+XF4Z,Z("(=$14+X612);"(=$14+X6))

15+XF4Z,Z("(=$15+X612);"(=$15+X6))

1+XF4Z,Z("(=$1+X612);"(=$1+X6))

1+XF11+X12+X13+X14+X15+X1+X

==interaction of ) wit' ben"ene

'!*2F'!20X0X

'!*2F'!20X1X

'!?*2F'!20X2X3981339030

$21+XF"("('!*2;13751793362)"('!*2002533910262)"('!?*2;&+'62)605)

$22+XF"("('!*2;05441062)"('!*212030771062)"('!?*2;&+'62)605)

$23+XF"("('!*2;070953277362)"('!*2;1178280762)"('!?*2;&+'62)605)

$24+XF"("('!*2070953277362)"('!*21178280762)"('!?*2;&+'62)605)$25+XF"("('!*205441062)"('!*2;12030771062)"('!?*2;&+'62)605)

$2+XF"("('!*213751793362)"('!*2;002533910262)"('!?*2;&+'62)605)

21+XF4Z,Z("(=$21+X612);"(=$21+X6))

22+XF4Z,Z("(=$22+X612);"(=$22+X6))

23+XF4Z,Z("(=$23+X612);"(=$23+X6))

24+XF4Z,Z("(=$24+X612);"(=$24+X6))

25+XF4Z,Z("(=$25+X612);"(=$25+X6))

2+XF4Z,Z("(=$2+X612);"(=$2+X6))

2+XF21+X22+X23+X24+X25+X2+X

=%interaction of ) wit' ben"ene

'!*3F'!30X0X

'!*3F'!30X1X

'!?*3F'!30X2X3981339030

$31+XF"("('!*3;13751793362)"('!*3002533910262)"('!?*3;&+'62)605)

$32+XF"("('!*3;05441062)"('!*312030771062)"('!?*3;&+'62)605)

$33+XF"("('!*3;070953277362)"('!*3;1178280762)"('!?*3;&+'62)605)

$34+XF"("('!*3070953277362)"('!*31178280762)"('!?*3;&+'62)605)

$35+XF"("('!*305441062)"('!*3;12030771062)"('!?*3;&+'62)605)

$3+XF"("('!*313751793362)"('!*3;002533910262)"('!?*3;&+'62)605)

31+XF4Z,Z("(=$31+X612);"(=$31+X6))

42


43/51


44/51


45/51

&+'F&+'+

$(+'% +F0+F99+)

V

%%interaction of c( wit' ben"ene

$0+XF"(18917537"(398133903;&+'62)605)

0+XFZ4Z#Z("(=$0+X612);"(=$0+X6))

%%coordinates of )* wit' origin at centre of C-atom of met'ane

*4F0

*4F0

?*4F1085524733

*1F;099995285

*1F02502515

?*1F;031841577

*2F0718721927

*2F0732812593

?*2F;031841577

*3F0275273359

*3F;0988837743

?*3F;031841577

*10X0XF*1 *11X0XF*1 *12X0XF?*1

*20X0XF*2 *21X0XF*2 *22X0XF?*2

*30X0XF*3 *31X0XF*3 *32X0XF?*3

*40X0XF*4 *41X0XF*4 *42X0XF?*4

0X0XF,/(&+'#'.-!) 1X0XF;/+'(&+'#'.-!) 2X0XF0 0X1XF/+'(&+'#'.-!)

1X1XF,/(&+'#'.-!) 2X1XF0 0X2XF0 1X2XF0 2X2XF1

$(+'% F03)

V

$(+'% F01)

V

'!1XXF0

'!2XXF0

'!3XXF0

'!4XXF0

$(+'% -F0-3-)V

'!1XXF'!1XX(X-XZ*1-XX)




\

\

\

%%interaction of )* wit' ben"ene

'!*4F'!40X0X

'!*4F'!40X1X

45


46/51

'!?*4F'!40X2X3981339030

$41+XF"("('!*4;13751793362)"('!*4002533910262)"('!?*4;&+'62)605)

$42+XF"("('!*4;05441062)"('!*412030771062)"('!?*4;&+'62)605)

$43+XF"("('!*4;070953277362)"('!*4;1178280762)"('!?*4;&+'62)605)

$44+XF"("('!*4070953277362)"('!*41178280762)"('!?*4;&+'62)605)

$45+XF"("('!*405441062)"('!*4;12030771062)"('!?*4;&+'62)605)

$4+XF"("('!*413751793362)"('!*4;002533910262)"('!?*4;&+'62)605)

41+XF4Z,Z("(=$41+X612);"(=$41+X6))

42+XF4Z,Z("(=$42+X612);"(=$42+X6))

43+XF4Z,Z("(=$43+X612);"(=$43+X6))

44+XF4Z,Z("(=$44+X612);"(=$44+X6))

45+XF4Z,Z("(=$45+X612);"(=$45+X6))

4+XF4Z,Z("(=$4+X612);"(=$4+X6))

4+XF41+X42+X43+X44+X45+X4+X

%%interaction of )+ wit' ben"ene

'!*1F'!10X0X'!*1F'!10X1X

'!?*1F'!10X2X3981339030

$11+XF"("('!*1;13751793362)"('!*1002533910262)"('!?*1;&+'62)605)

$12+XF"("('!*1;05441062)"('!*112030771062)"('!?*1;&+'62)605)

$13+XF"("('!*1;070953277362)"('!*1;1178280762)"('!?*1;&+'62)605)

$14+XF"("('!*1070953277362)"('!*11178280762)"('!?*1;&+'62)605)

$15+XF"("('!*105441062)"('!*1;12030771062)"('!?*1;&+'62)605)

$1+XF"("('!*113751793362)"('!*1;002533910262)"('!?*1;&+'62)605)

11+XF4Z,Z("(=$11+X612);"(=$11+X6))

12+XF4Z,Z("(=$12+X612);"(=$12+X6))

13+XF4Z,Z("(=$13+X612);"(=$13+X6))14+XF4Z,Z("(=$14+X612);"(=$14+X6))

15+XF4Z,Z("(=$15+X612);"(=$15+X6))

1+XF4Z,Z("(=$1+X612);"(=$1+X6))

1+XF11+X12+X13+X14+X15+X1+X

%%interaction of ) wit' ben"ene

'!*2F'!20X0X

'!*2F'!20X1X

'!?*2F'!20X2X3981339030

$21+XF"("('!*2;13751793362)"('!*2002533910262)"('!?*2;&+'62)605)

$22+XF"("('!*2;05441062)"('!*212030771062)"('!?*2;&+'62)605)

$23+XF"("('!*2;070953277362)"('!*2;1178280762)"('!?*2;&+'62)605)

$24+XF"("('!*2070953277362)"('!*21178280762)"('!?*2;&+'62)605)

$25+XF"("('!*205441062)"('!*2;12030771062)"('!?*2;&+'62)605)

$2+XF"("('!*213751793362)"('!*2;002533910262)"('!?*2;&+'62)605)

21+XF4Z,Z("(=$21+X612);"(=$21+X6))

22+XF4Z,Z("(=$22+X612);"(=$22+X6))

23+XF4Z,Z("(=$23+X612);"(=$23+X6))

24+XF4Z,Z("(=$24+X612);"(=$24+X6))

25+XF4Z,Z("(=$25+X612);"(=$25+X6))

2+XF4Z,Z("(=$2+X612);"(=$2+X6))

46


47/51


48/51

"$+!'%#%+'%XZ(180=314159254)Y[%Y&+'!-!&!'%%XY['Y

\

",-/!()

#'.-!F&+'#'.-!+',

&+'#'.-!F#'.-!

\

&&+'!-!&!'%F&+'!-!&!'%0X

&&+'+/%#',!F&+'+/%#',!0X

$+!'%#%+'F$+!'%#%+'0X

!F&+'!-!&!'%0X

F&+'+/%#',!0X

F$+!'%#%+'0X

%%minimum energy after all &ossible rotaion along "-axis

$(+'% +F0+F72+)

V+(&+'!-!&!'%+X&&+'!-!&!'%)

V

&&+'!-!&!'%F&+'!-!&!'%+X

&&+'+/%#',!F&+'+/%#',!+X

$+!'%#%+'F$+!'%#%+'+X

\

\

,%Y['YY['YY['YYM+'+&& !'!$. !-- #%!$ #-- "//+-! $%#%+' #-'. ?;#+/ F

Y&&+'!-!&!'%Y J=&-Y

,%Y['YY#% # +/%#',! F Y&&+'+/%#',!Y #&./%$&Y

,%Y['YY$ #' $+!'%#%+' F Y$+!'%#%+'Z(180=314159254)Y !.$!!Y

%%maximum energy well among all i&ossible rotaion along "-axis

$(+'% F0F72)

V

+(&+'!-!&!'%X!)

V

!F&+'!-!&!'%X

F&+'+/%#',!X

F$+!'%#%+'X

\

\

,%Y['YY['YY['YYM#+&& !'!$. !-- #%!$ #-- "//+-! $%#%+' #-'. ?;#+/ F Y!Y

J=&-Y

,%Y['YY#% # +/%#',! F YY #&./%$&Y

,%Y['YY$ #' $+!'%#%+' F YZ(180=314159254)Y !.$!!Y

,%Y['YY['YYT*! + +' #' &+' !'!$. !-- #%!$ $%#%+' #-'. ?;#+/ F Y!;

&&+'!-!&!'%Y J=&-Y

=%finding t'e coordinates of .-site met'ane wit' minimum orientation &osition

10X0XF,/($+!'%#%+') 11X0XF;/+'($+!'%#%+') 12X0XF0 10X1XF/+'($+!'%#%+')

11X1XF,/($+!'%#%+') 12X1XF0 10X2XF0 11X2XF0 12X2XF1

48


49/51


50/51

$!%$'(0)

\

Re(erences


51/51

Interaction Potentials for Ch4 on Benzene - Copy

Documents

Transcript of Interaction Potentials for Ch4 on Benzene - Copy