Pairwise Energy Model

전체 글

(1)Journal of the Korean Chemical Society 2003, Vol. 47, No. 3 Printed in the Republic of Korea.

(2) Cl+HD . Pairwise Energy Model. . . (2003. 2. 19

(3) ) Theoretical Study of the Isotope Effect for the Reaction Cl+HD at the High Energy Using Pairwise Energy Model Ju-Beom Song Department of Chemical Education, Kyungpook National University, Daegu 702-701, Korea (Received February 19, 2003). . Pairwise Energy Model(PEM) A+BC→AB+C( B C

(4) ) cross section A B pairwise energy E !". PEM #$%# O( P)+HD, Ar +(H , D , & HD)' ( ) * +,-. /012 345 6. 7 89 quasiclassical trajectory :;< 31 Cl+H Cl+HD < =>1? @ ABC# D D E * PEM< 31 F /0G

(5) HI. PEM< 31 Cl+H cross section J-.KL @ ABC# Cl+HD ) * "MN OPG

(6) HI. ( Q* /01 1 RST UKC# VW X P(E )* Y Z. RST UKC# VWX P(E ) "[ ABC# E Y\ ]^ _# "[ E J Y\ `X a,-. b. c d. PEM-. D < F /0` e

(7) H Q. Xf[ E+ @ ABC# ( A+BC g ,3h

(8) H< c. : ) , C# 3. S. +. 2. 2. 2. 2. int. int. S. ABSTRACT. The pairwise energy model (PEM) assumes that the cross section for the reaction cross section for the reaction A+BC→AB+C, where B and C are isotopes of hydrogen, depends on only the pairwise relative energy ES between A and B. Until now, the PEM has been used to interpret theoretically the isotope effect for the reactions such as O(3P)+HD and Ar++(H2, D2, and HD). In this paper we carry out extensive quasiclassical trajectory calculations for the three possible reactions Cl+H2 and HD and show that the PEM works very well at high energy. In particular we are able to accurately predict the intramolecular isotope effect at high energy for the reaction of Cl+HD using only the cross section data for Cl+H2. To understand that the PEM works so well at high energy, the internal energy distributions for the products are examined. The distributions for three reactions are different at a fixed relative collision energy E but are approximately same at a fixed pairwise energy ES. This suggests that the PEM works very well at high energy. We believe the conclusions reached here will apply to other A+BC systems. Keywords: Pairwise Energy, Isotope Effect. 191.

(9) . 192. ia Quasiclassical trajectory(QCT) :;< 31 @ ABC# jk lmno< `1 p qr`6. Ap p Vp BC @ ABC# RST< s 4!# t u .! H. 1-9. A + BC → A + BC. (1). → AB + C. (2). → AC + B. (3). →A + B+C. (4). (4)* collision-induced dissociation (CID)^1v ABC#! BC E\C# (g `wC#) x y z! {-| (4)! }[ .! [. @ ABC# ~" AB g AC RST< D | AB Y u1. CID! }[ . @ ABC# p g p A

(10) p HD VpU ) +, qr! 456. g X

(11) 456 , N Armentrout < Z. N @ ABC# O AH RST AD RST RS< + E . /0 jk1. ABC# E=600 kcal/mol Cl+HD < R` p. Cl. D , C# x 400 kcal/mol | Cl. H k# x 200 kcal/mol. . ClH ClD E\C# x 106 kcal/mol. p Vp R ST< S1 ` Vp UKC#! Vp E\C# . (. ClD* RS 1 ` H p x 300 kcal/mol { C#* !# 5 !1 | ClH* RS1 ` D p k# x 100 kcal/mol "X ! # 5 !| [. (. ClH cross section ¡¢ h c. ( jk 8w* £ ¤, ,31 ` 7 Pairwise Energy Model(PEM)* ¥ ¦ Z. A+BC→AB+C cross section A B pairwise energy c PEM . pairwise energy E 1,6-37. 38,39. 40. 7. S. 1 m Am B 2 Es ( AB ) = --- ------------------ vo 2 m A + mB. (5). , m m A B §¨v v AB©X. ABC# E A. B. o. 1 mB + m C 2 vo, E = --- m A -----------------M 2. (6). M = mA + m B + m C. . ª E (AB) E «=¬ S. Mm B E s (AB ) = ---------------------------------------------- E ( m A + mB ) ( m B + mC ). (7). . m » m and m E (AB) =[m /(m + m )]E . [. ® p HD g H D < W¯1 ° Vp F ,3h

(12) H±< ²³` 6. ( ® ´ ABC# < /012 p} µ< ¶. PEM 600 kcal/mol Cl+HD→ClH+D cross section 300 kcal/mol Cl+HD→ClD+H cross section (400 kcal/mol Cl+H →ClH+H cross section ) b OP. · y 5 ! p(H g D)! ,5X 100 kcal/mol C#* !# ¸ ~" ClH g ClD! RSh

(13) H. §¨ y z ¹ H D! ºb 100 kcal/mol C#* !# ¸# 0»1# ¼½#, 7 O( P)+HD O( P)+H RST UKC # VWX* V¾ E * ²³1?. ( ² ³ @ ABC# O( P)+HD ) * PEM< 31 +,-. `G

(14) H±< ¿. c PEM iÀ +, Á³ I Â PEM ÃÄ -pVp N +(H , D , & HD) Ar +(H , D , & HD) ) * +,-. /012 34I. g PEM< MÅ1 H+H j & (4) b . ° CID* qr12X 345 6. 7 89 @ ABC# Cl+HD VpU ) * PEM< 31 /01 p . * ` ± D< qrZ. A. 2. C. A. B. S. B. C. 2. 38-53. 2. 3. 3. 2. 7. 3. + 2. 2. 2. +. 2. 2. 54. 2. 8. 55. Cl+H2(ν=0,J=0) → ClH+H. (8). Journal of the Korean Chemical Society.

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(16) Cl+HD . 193. Pairwise Energy Model. Cl+HD(ν=0, J=0) → ClH+D. (9a). → ClD+H. (9b). ν ÆÇp

(17) J ÈÉÇp

(18) . QCT :;< 31 É ABC# ÊË ¥ Potential Energy Surface(PES) D =>< 1?. (8) (9) lÌno< £ F `1 ` Hard Sphere Models 3 :;< 31?. Hard Sphere Models A+BC A, B, & C pD< Hard Sphere. !"12 ª R !# 9 x A! Í ± B ABG ª AB+C. ÎÏÐ n| AC+B. ÎÏÐ. Hard Sphere Models RST AB+C| “direct” ^ 1 AC+B | “knockout” ^ ". QCT =>X A! Í± B AB1# n| C ÑÒ AB1 # ,ÓN " | < y !#. VÔG

(19) H5 lmno< `12 XÕ [. 7 89 3 PES Ö zÄ ! C# Å × iÒ p! Vp Ø-. aG ª C # Å× !Å @. ]^ ´ ABC# k# “direct” !Ù1. ( @ ABC # “knockout” tu .Ú< ¿ ÃÛ89 ¶. E+,-. “knockout” ABC#* RST C#. ÜÝ¦Þ 2 “direct” ) ,. (. C # ÜÝ< £ F `1 ` 7 89 < “direct” “knockout” y !# -. Vw1 ß. 2. 1-4,7. à qrp! áÃ VENUS â.ã< 31 QCT =>< 1? => " 7 ¿ ÃÛ 89 /045 H. trajectory À Y< Standard Monte Carlo Sampling Procedure* 31 E"1?. ä i AB Ü

(20) * 2.5Å-. 1 AB C# 20000á trajectory* =>Z. => Persky PES* 31?. 7 89 ¥¦1 R ST UKC# P(E ) VWX* V¾1 ` 31? UK Fourier Expansion Technique<. 56,57. 1-6. int. 59-62. 2003, Vol. 47, No. 3. . (8) (2. ï), (9a), & (9b)* QCT :;-. => cross section< ABC# E ¯

(21) . 1 ð 1 X¦1?. Fig. 1 k direct cross section<, !2 knockout cross section <, w 1k y cross section \< ¶ . ´ ABC# direct }. ¤5 40 kcal/mol knockout ¤5 ¦ . (9b), Cl+HD→ClD+H knockout threshold x 40 kcal/mol (8), Cl+H ClH+H c 60 kcal/mol, w (9a), Cl+HD→ClH+D c x 80 kcal/mol. ð !Å ys (Æ KV (9) ) . AB C#! 150 kcal/mol 1 ¤ ª direct knockout í ClD RST ClH ñò F RS [ c(direct ` threshold Ka ¥). ( ) 7 ¿ ÃÛ 89 ó+Z. ClD! F RS4 Q Cl HD a¯ ]^ ôõ Ãõ-. !ö H p! ÷¢ !©45 5 ! ª9. ø

(22) p H! Cl.KL ÈÉ1 ù5# Cl D p p} AB1 Cl D F E\1¢ [. ( 2. Hase. 58. C# VWX k |,-. "å 1?. ä AB < y !#. æ. 1 “direct” -. A! B ÑÒ AB1 AB! RS4 ° 1 “knockout” -. A! B Ñ Ò AB Z# RST AC . Hard Sphere Models ( VÔ! kµ1# QCT => A! B g C Í± AB ¿! çè # "` . 3 PES Ö z Ä éS C#! !Å ´. É ê X¸ Z< ª Ö saddle point R(Cl-H)= 1.398Å. 7 QCT => ä trajectory ~ A-B A-C w* Y1 x A-B ë ! R(Cl-H) A-C ÑÒ X¸1| A! ÑÒ B AB !"1v ì| A! C ÑÒ A B ". (A-B A-C ë í Ú= ë R(Cl-H) X¸1# î1| ¤5# ¼ trajectory ¥[.) ( "-. ä < “direct” “knockout” -. 0»N VÔG

(23) H.. 1,3,9.

(24) . 194. úzû ) (9a) ClH* RS1 knockout threshold! ¥¤ @ (9b) !Å ´ Q* /0`¶( (8) í H). Cl p! D ÑÒ AB G#^X 3p tjü.KL

(25) p H! ¸ É Cl p! D p }* B H p G ý AVN þ_# î1. direct D threshold Ka · y cross section ÿ c threshold Ka p Vp Æ) úzû ) ! . 1 E. . . 7 ¿ ÃÛ 89 } ´ ABC# Cl Hp -. a G ª! D-. a G ª HD ÆC#* ) ,-. 3G

(26) H. Ð1| HD Vp! ÆG ª H p! D p ë¢ w þ 9. Fig. 2. Various reactive cross sections for Cl+H2 and Cl+HD calculated by the QCT procedure plotted against the pairwise energy ES defined in Eqs. (5) and (7). Further details are given in the caption for Fig. 1.. _¢ 1 ª9. @ ABC# ) ì-. 4v Q + /0Z. Fig. 1 · (8), (9a), & (9b) cross sectionD . N _. º b cross sectionD< ¬ (5) (7) " pairwise energy E ¯

(27) . X¦ c Fig. 2. d . /0Z direct D threshold C# p Vp ÆC#* C# Å×< 1 2 ) ,-. 31! . µ (9a), (8), w (9b). [. direct D cross sectionD 150 kcal/mol cross section

(28) -. 5# E =250 kcal/mol%# · Ö b J< . knockout D cross sectionD É C# } Q1. E =100 kcal/mol Ka xj ¹ úzû ) ª9 . · y knockout threshold C # E J-. x 25 kcal/mol cross sectionD E =500 kcal/mol Ka

(29) -. 5Æ. S. Fig. 1. Various reactive cross sections for Cl+H2 and Cl+HD calculated by the QCT procedure plotted against the relative collision energy E. The top panel gives the results for direct reactions, the middle panel shows knockout reactions, and the bottom panel shows the total reactive cross sections. The solid circles show the reaction cross sections for Cl+H2→ClH+H divided by two. The results for Cl+HD are shown as inverted triangles for the ClD product and as open circles for the ClH product.. S. S. S. S. Journal of the Korean Chemical Society.

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(31) Cl+HD . Pairwise Energy Model. knockout cross section \)< | · Ö @ C# } Q J< . threshold Ka ClH! ClD RS4 Q /0Z T Vp! Æ 1 ª9v tj C# ClD! ClH RS4 Q úzû ) ª9. · Ö y E =250 kcal/mol b @ C# cross section k# E < ôõN ##`¶. ø Pairwise Energy Model (8) (9)* `1 ,\ ®Ú< ² ³1 c. QCT =>-. 5Æ · cross section Ö D E ¯

(32) . X¦ h ª @ C# } ÿ cross section(direct. S. S. S. 195. 1 Q* `1 ` => 5Æ RS T UKC# VWX P(E )* Y1?. E=300 kcal/mol direct, knockout, cross section QCT :;-. E * Fig. 3 X¦ 1?. direct D ` · ÖD } _. Cl+HD.KL RS[ ClD Vp `w =%# 45 H xj @ ABC# RST . ^§ c. Y,-. Cl+HD.K L RS[ ClH Vp UKC# ,-. ´ Cl+H .KL RS[ ClH Vp UKC# VW y Ö . knockout ` · y UKC#! ñò ´¢ . c @ ABC# knockout }. ¤5 Q. knockout direct pj AB. ABC#* R ST C#. £ ) ,-. ÉÝ ¦

(33) H ª9. Éü ` y ClH Ö ÿ1 ClD RST ñò @ UKC# VW X* . c ClD RS .! E=300 kcal/ mol !Å cross section< Q(Fig. 1Y). Fig. 4 E =154 kcal/mol =>[ UKC# V WX P(E ). C# Cl+H ` E=300 kcal/mol `1 UK C# VWX Fig. 3 b. E =154 kcal/mol 1 Cl+HD→ClH+D EJ 438 kcal/mol Cl+HD→ClD+H EJ 225 kcal/mol. ð · UKC# VWX §,-. b. ]^ C# (E =154 kcal/mol) · cross section b c ^ ¤ n(Fig. 2Y). direct -. RS[ RST UKC# VWX @. RST .! E =250 kcal/mol # ¼ c< ÷¢ `G

(34) H. Y,-. knockout UKC# V WX E 0.2D (E RST UKC# D ClH `wC#) * ¥1 1. Q! Fig. 2

(35) H @ ABC #X knockout ` =© ~" RST D5§

(36) H Q* /0`¶. A! H g HD 1 AH(g AD)* RS 1 cross section A H(g A D) pairwise energy E k# ¯< Pairwise Energy int. 2. S. int. 2. S. S. S. Fig. 3. Product internal energy distributions plotted against Eint/De, where Eint is the internal energy of the product ClH and De is the dissociation energy of the product ClH, computed at fixed relative collision energies E=300 kcal/mol using the QCT procedure. The area under each curve is one. The top panel shows the results for direct reactions, the middle panel for knockout reactions, and the bottom panel shows the results for all reactions. The solid curve gives the results for Cl+H2→ClH+H, data for Cl+HD are shown as a dashed curve for the ClD product and a dotted curve for the ClH product. 2003, Vol. 47, No. 3. int. e. 2. S. int. e.

(37) . 196. Fig. 5. The intramolecular isotope effect QR(ClD)/QR(ClH) plotted against the relative collision energy E. The solid circles show the exact results computed for the Cl+HD reaction using the QCT procdure. The uncertainty in each isotope effect is approximately twice the size of the symbol. The open circles show the isotope effect calculated from the cross sections from Cl+H2 using the pairwise energy model as described in the text. Fig. 4. Product internal energy distributions plotted against Eint/De, where Eint is the internal energy of the product ClH and De is the dissociation energy of the product ClH, computed at fixed relative collision energies ES=154 kcal/mol using the QCT procedure. The area under each curve is one. Further details are given in the caption for Fig. 3.. Model.

(38) H. c g A+H cross section < 31 A HD! 1 VpU ). * OP1 c< !Ù1X . O. E=300 kcal/mol Cl+HD < R` p. C# ClD RST ` E =205 kcal/mol ClH RST ` E =106 kcal/mol `. E =205 kcal/ mol(106 kcal/mol) Cl+H ` ABC# E=399 kcal/mol (206 kcal/mol) b. ]^ E=300 kcal/mol Cl+HD→ClH+D(ClD+H) cross section E=399 kcal/mol(206 kcal/mol) Cl+H cross section, Q b OPG

(39) H. ¢ 1 Cl+H cross section J-. Cl+HD cross section JD< OPG

(40) H , c< !# ) X OPG

(41) H. Cl+H cross section J-.KL OP ) Cl+HD < QCT :;-. =>1 2. S. S. S. 2. 2. R. 2. 2. ) * ÿ1 E=150 kcal/mol X¦ E. ! Fig. 5. E=250 kcal/mol 1 í ¹! H. c /0 cb p Vp (H ) úzû ) ! tu1# ¼ # p Vp (HD) tu1 ª 9. úzû ) Cl p! p Vp a 1 ©X! @<

(42) #. @ ABC# ç¦ h

(43) H. ]^ ABC#! Ì§

(44) PEM-. OP ) ¥. => J a 1¢ [. ð 5 E=450 kcal/mol PEM-. OP ) QCT : ;-. => E ! ¤¯<

(45) H. D< /012 PEM Q3 Q çè¤%? /0 c b @ ABC# ~"p Vp* RS15. A+BC→AB+C < R` p( Vp BC AB É "#` H !".) pD 31 É A B , C# ¬ (5) (7) "[ E (AB) . }5# p C lab frame g É! ÕØ# ¼. x ¤5 C! ØX Õ Ø# ¼-| c< Spectator Stripping Model^ 2. S. 14,63-65. Journal of the Korean Chemical Society.

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(47) Cl+HD . Pairwise Energy Model. 1v ª E (AB)≈E (AB). ( QCT => ¥ " AB Vp p C Ãõ 31 , j Ãõ-. RST UK C# VWX P(E )! #1¢ [. Fig. 4 · y UKC# VWX P(E )! a, -. b "X. #1¢ VW. c A+BC } ¤, @ ABC# ° A+BC ` PEM F ,3h

(48) H< c^ . ux1|, QCT :;< 31 Cl+H Cl+HD < =>1?. @ ABC# D D E. * PEM< 31 F /0G

(49) HI. PEM 31 Cl+H cross section J-.KL @ A BC# Cl+HD ) * "MN OPG

(50) HI. ( Q* /01 1 R ST UKC# VWX P(E )* Y Z. RST p Vp 5! p Ã õ 3-. UKC# VWX P(E ) #1¢ 4 ( # "X "[ E J (Fig. 4Y) ä Y\ ` a,-. b. c d. cross section PEM ¯< ¿. Xf[ E+ ( A+BC g ,3h

(51) H< c int. S. int. int. 2. 2. int. int. S.

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Pairwise Energy Model  

Pairwise Energy Model