(n=1-6) Complexes The ab Initio Quantum Mechanical Investigation for the WeaklyBound H

전체 글

(1)Journal of the Korean Chemical Society 2001, Vol. 45, No. 5 Printed in the Republic of Korea. H (n=1-6) complex

(2) +. 2n+1. * (2001. 6. 7 ). The ab Initio Quantum Mechanical Investigation for the Weakly Bound H+2n+1(n=1-6) Complexes Eun-Jung In, Hyun-Il Seo, and Seung-Joon Kim* Department of Chemistry, HanNam University, Taejon 300-791, Korea Received June 7, 2001). . H (n=1~6) cluster

(3) (ab initio) , !" #$ (vibrational frequency), %&' (&

(4) )* + ,- ./. 0 H 1 *0 TZ2P+d CCSD(T)

(5) 2 %&' H H

(6) (20 TZ2P CCSD(T) 1* 3 ./. !" #$ 0 4 basis set

(7) 2 SCF 56 ,- .57, 8 9

(8) 2 3: ;< local minimum = >? ./. H 6@A H (&

(9) )*(D )0 BB 3:

(10) 2

(11) )* C6@A ,- .57, DE !"

(12) )*(ZPVE)F 'G , *H1* I JKL(D ) M N ./. +. 2n+1. +. 9. +. 11. +. 2n+1. +. 13. 2. e. 0. ABSTRACT. The geometrical parameters, vibrational frequencies, and dissociation energies for H2n+1+ (n= 1~6) clusters have been investigated using high level ab initio quantum mechanical techniques with large basis sets. The equilibrium geometries have been optimized at the self-consistent field (SCF), the single and double excitation configuration interaction (CISD), the coupled cluster with single and double excitation (CCSD), and the CCSD with connected triple excitations [CCSD(T)] levels of theory. The highest levels of theory employed in this study are TZ2P+d CCSD(T) up to H9+ and TZ2P CCSD(T) for H11+ and H13+. Harmonic vibrational frequencies are also determined at the SCF level of theory with various basis sets and confirm that all the optimized geometries are true minima. The dissociation energies, De, for H2n+1+(n=26) have been predicted using energy differences at each optimized geometry and zero-point vibrational energies(ZPVEs) have been considered to compare with experimental dissociation energies, D 0.. OBP ; H Q #R

(13) n-1 S H T U LV

(14) WXYZ [0 complex V\62

(15) 2 ]^ _`a bc

(16) de fg hi [0 V\/. U LV

(17) jklm no

(18) JK56 p q r

(19) 0 ZGs t/. %4u g# \v Twx H+2n+1 cluster. +. 3. 2. 1. @ C* ' [0 y Tz{ |

(20) 0 4 }~ V\ t WYZ [0 56 G [ 57, 1958 bo? Krasovskii0 m \v6. y clusters F k ./. T H 562 H 0 1912 ? J. J Thompson

(21) (2 36 pqY5u, g# |

(22) 2 H >? N 3

(23) M2 T ./. 1989

(24) Drossart + Jupiter r |

(25) 2 : H 2. +. 2n+1. +. 3. 3. +. 3. +. 3. 401.

(26) . 402. z p .57 1992

(27) 0 Miller +

(28) m SN 1987

(29) 2 JK56 p ./. a2 QeT 0e

(30) T1w 3 KM 0 bar

(31) T1w ! g# |

(32) [0 Tz {

(33) 2 H , H , H + cluster ¡¢ >£ fg /' ¤/. H (2 ≤ −n≤ − 6 ) complex

(34) 8¥? 90 1969

(35) R. ClampittM J. GowlandT 3 K QeM ~10 torr

(36) 2 v¦ z(mass spectrum)

(37) H (n=1~49) clusterF pq §a' ¨. [/. % JK L y cluster ©mYZ* 0 r

(38) 0 H Q T t uªu7, «P

(39) e¬ . n

(40) 0 H ®T T d uª¯ /. 62 «P

(41) 2 T kl H (n°2) cluster0 H ± 56 ²lY57 ³´ @? OB P ; H

(42) H T ²TY0 P6 y cluster d :/0 k ./. µ 1973

(43) 0 Deursen Reuss

(44) (2 ¶ v¦ H cluster e pqY*^ · v¦ y cluster ¸/ % ¹rT U 50ºle d uªu0 56 ¸'Y/. H 0 1962 Dawson Tickner

(45) JKJ

(46) 2 »¼56 pq: ½ 31* t I JK 9T ¾YZ ¿/. ÀÁ (&

(47) )*

(48) p 0 I JKL

(49) t ÂÃ j4¿/. 962 1969 PoshustaM % "Ä ab initio ,-56 Twx m(proton)

(50) Å S H T ²TYZ Æc F Pm¨ 56 Ç .',

(51) È LV

(52) )*T 10.8 kcal/mol le ¢ 56 É ./. %4u 1970 EasterfieldM Linnett0 Êe

(53) 962 OBP ; H

(54) H T Ë56 U LV Ì' [0 T T kl 7, (&

(55) )*0 9 kcal/mol6 Ç ./. µ 1971

(56) Arifov + JK

(57) H (&

(58) )*F 5.1 kcal/mol6 %&' /¼(? 1972

(59) 0 BennettM FieldT 9.7 kcal/mol6 BB É562 Â Í ÎY/. Z2 1974

(60) ElfordM Milloy 0 5.8±1.2 kcal/mol JKÏF %&' /¼(? 1975

(61) 0 HiraokaM Kebarle 9.6 kcal/mol Ð BB É ./. 4 ÂÍTwx 1976 Johnsen + 8.1±0.1 kcal/mol JKÏF k .57, § 1983 Yamaguchi, Jeffrey, Schaefer

(62) 9

(63) 20 4.0 kcal/mol Ð Ç ./. %4u % 4. IR. 5. +. +. +. 5. 7. 9. +. 2n+1. −10. +. 2n+1. 6. +. 15. +. 5. +. 2n+1. +. 5. +. 3. 2. +. 2n. 7. +. 5. 8. 9-25. 2. 9. +. 3. 2. 10. +. 5. 11,12. 13,14. 15. 16. Ñ ,- CISD 56 size-consistency o T [/. % § 1983

(64) M2 Elford +

(65) 5.8±1.2 kcal/mol, %&' NÒ r

(66) Beuhler +

(67) 6.6±0.3 kcal/mol JKÏT ÉY57, 1987 Hiraoka + % Ó LF l 6.9±0.3 kcal/mol6 / É ./. µ 3 Ð(D )560 1987

(68) 0 Schaefer +

(69) full CI ,-56 5.45 kcal/mol k .', 1992 Farizon +

(70) TZP CISD

(71) 2 DeÐ56 7.84 kcal/ mol Ç .57, 1997 Chermette +

(72) 6-311G++ CCSD(T)

(73) 2 D Ð 5.26 kcal/mol É ./. µ H !" #$

(74) p JK90 1985

(75) Okumura +

(76) »¼56 ÉY57 (3532 cm , 3910 cm ), 1987

(77) Schaefer +

(78) ( 9T ¾YZ 3910 cm 0 H stretching mode 6 %&' 3532 cm 0 H symmetric stretching mode6 BB assign Y/. % § 1988 Okumura + H H W !" #$

(79) p JKL F É .57, 1991e

(80) 0 Bae

(81) H (& z JK

(82) 5400~10000 cm 1* D

(83) 2 ÔV Õ0 ÖV ×Ø(combination or overtone bands)F pq ' Ù ω ω F Ç ./. Õ 1993

(84) 0 SpirkoM KraemerT N m(anharmonicity)F 'G vibrational dynamics 9F Ú Û

(85) )* !" #$ F 9 ./. *H1* ÜÝ ÞM ß H

(86) p 90 fg à .5u H y cluster

(87) p 90 56 fg áU /' ¨ [/. H

(88) p J K960 1972 BennettM Field

(89) (2 LV â ãF 1.8 kcal/mol6 É .57, 1975 Hiraoka M Kebarle

(90) ( H @A H 1* M k lm 9 ./. %4u 1987

(91) JK LF äÖ H (&

(92) )*F 3.3 kcal/ mol6 É ./. Õ 1983 Elford + 3.1 kcal/ mol JKLF É ./. H cluster

(93) (20 1987 Hiraoka + 9T å±x H @A H 1* (&

(94) )*F BB 3.2, 1.72, 1.64, 1.54, 0.88, 0.80, 0.61 kcal/mol6 É ./. µ 960 1973 Harrison + Î56, 1978 Yamabe + H (n=1-5)

(95) , %&' 1980 HuberT H (n=3-6)

(96) SCF

(97) 2 BB 9 17. 18. 19. 0. 20. 21. 0. 22. +. 5. 23. −1. −1. −1. −1. 2. +. 3. 20. +. +. 7. 9. 24. +. 5. −1. 25. 1. 2. 1. +. 5. +. 7. +. 7. 12. +. +. 5. 11. 14. +. 7. 17. +. 9. 19. +. 9. +. 21. 26. +. 27. 2n+1. +. 2n+1. Journal of the Korean Chemical Society.

(98)

(99) H. + 2n+1.

(100) . Y57, 1983

(101) 0 Schaefer +

(102) H @ A H 1*

(103) CISD

(104) 2 56 9 Y/. Õ 1992 Farizon + TZP CISD

(105) 2 H H

(106) 9 .57, 1997 Chermette + H @A H 1*

(107) DFT CCSD(T)

(108) LF N Ù ./. % 4u CISD

(109) 2 90 size-consistency oT [Z l> Ð Ç r

(110) 0 @æ 7 1997 9

(111) 2e H

(112) ,- ©çYZ [Z 2 ¸/ c,? 9T èé /' ¤/. 3 1990

(113) M20 small cluster(H , n=1,2) ³´56 " JK 9 I pq Õ à d !¾Y' [/. %4u H , H , H , H

(114) p 90 _Ë fg i! 7 H M H

(115) p 9 Õ 9T èé /. a2 8 9

(116) 20 H (n=1-6)

(117) DZP, TZ2P, TZ2P+d basis set SCF, CISD, CCSD, CCSD(T) high level T Û

(118) )* F ê0 F ëì ', H -H (&

(119) ) *F ,- H cluster í klm ' q ./. Õ !" #$ F ,-562 3: T kl ?* î Ó ?*F ïì ', DE !"

(120) )*(ZPVE) ¸l Ú ¸/ l> (&

(121) )*F Ç ./. 28. +. 3. +. 9. 16. +. +. 11. 13. 21. +. +. 5. 403. (n=1-6) complex. 13. 22. +. 11. lù 56 úZû0 560 self-consistent field(SCF), configuration interation(CI), %&' coupled cluster(CC) + Y/. X

(122) rø: DZ, DZP, TZ2P, %&' TZ2P+d + basis set

(123) SCF level

(124) 2

(125)

(126) )* 1C i ,- T kl F Ç .57 2C i ,-562 üý(IR) z Ç . /. Õ H T H +H 6 (& Y0

(127) )*F , r X(20 BB 3:

(128) 2

(129) ) * C6@A ,- ./. 36,37. +. +. 5. 3. 2. +. 2n+1. 29-32. +. +. 7. 9. +. +. 11. 13. +. +. 3. 5. +. 2n+1. +. 2n+1. 2. +. 2n+1.

(130) 8 9

(131) 20 double zeta(DZ), double zeta plus polarization(DZP), triple zeta plus double polarization. %&' TZ2P plus d-funtion(TZ2P+d) + 4S basis set ./. DZ0 Huzinaga M Dunning É basis set62 y(H)

(132) (4s/2s) contracted gaussian function(CGF) 7, DZP polarization 60 p- orbital exponent, α (H)=0.75F ./. µ TZ2P

(133) 2 triple zeta0 HuginagaDunning (5s/3s) CGFF .57 Å ð ppolarization

(134) orbital-exponents0 α (H)= 1.5, 0.375F ./. TZ2P+d basis set TZ2P basis set

(135) u d- F ²T562 Óc

(136) ñ [0 Êe Ó òeF ¸/ ó ô X1* ,-

(137) Wõ l>eF ö÷/. *H1* rø basis set Schrödinger (TZ2P),. 33. 34. p. 35. p. 2001, Vol. 45, No. 5. De ( H 5 ) = E ( H5 ) – { E ( H 3 ) + E ( H2 ) } +. +. +. (1). r2 _½þ e0 3: «P

(138) 2 (&

(139) )*Ð i/. µ SCF

(140) )* 0 Ópp,(electron correlation) ÿT 'GY* r no

(141) 56 Û ,- 7, F ¸ r X ,- ? CIM CC ./. CIM CC g single and double excitations term ^ 'G B B CISD %&' CCSD a' @7 ÀÁ CCSD g triple excitation ±@F 'G CCSD (T)/. a2 T basis function? TZ2P+d

(142) CCSD(T) 8 9

(143) 2 T . ,-/. ±56 CISD ¸/ CCSD T l> 56 G [57, CISD6 (&

(144) )*F ,- 0 g size consistency oT © /. µ CCSD Õ0 CCSD(T) " (perturbation theory)

(145) r ,-56 size consistency oT © * 0/. µ û@ É(internal coordinate, R)

(146)

(147) )* (E) 2C i (force constant, k)F ,-¨. [d 7 6@A !" #$ F ,-¨ [/. 8 9

(148) 20 *H1* rø: 9 H , H , H , H , H %&' H T kl , (&

(149) )*(D ), !"#$ + ,- . 57, ;< ,- workstation (IBM-RS6000)

(150) 2 PSI-2 6%

(151) 56 ¾ ./. 38. 39. +. +. +. +. +. +. 3. 5. 7. 9. 11. 13. e. 40. 0 H (n°2) cluster ´@5 6 ³´

(152) Ó F ê' [0 lOBP F T* Geometry H3+. +. 2n+1.

(153) . 404. d uªu0x, % å60 H T 3S

(154) 2S Ó(three-center two-electron bond)T N µ : P6 r no? 56 (Ù ¨ [¤/. µ LV B ;<

(155) 2 60 6 lOBP Ì ' [/. H T kl 0 C symmetryF ê' [57 H OB «Æ E

(156) 2 U 1.27 Z! &

(157) Ë56 H T U d LV: 6 ÇY/. 4

(158) 2 3: 0 Fig. 2

(159) uªû 57, Twx T TZ2P+d CCSD(T)

(160) 2 3: /. H Cluster

(161) 2 ³

(162) XÏ H 0 M Ë d LVYZ [0 H Dö56 l OBP Ì* ', R Ð 0.98656 R ? 0.811¸/ +R OBP ; T*' [57, ?B θ Õ 48.5 6 lOBP¸/ Î Ð uª û/. Õ H M H , R 0 1.27256 Ç Y57 R Ð 0.76856 ÇY/. r2 R R Ð Ópp,ÿ¸/ basis set

(163) Dö 56 t 0 56 uª¯0x d-. T W¢ g CCSD(T)

(164) 2 R Ð U 0.03 le Z*', R Ð 0.09le y 0 56 u ª¯/. 0 U LV ê' [0 z (weakly bound system)

(165) ,-

(166) 20 ¸ / ó D ÓWT 'G: basis function ( /' ¤/. *H1* ,-: T l> Ð? (4s2p) basis set

(167) 2 full CI ,-L +. 3. o. +. 5. 2v. +. 3. 2. +. 5. +. 3. 2. 1. Fig. 1. Predicted geometries of H3+ at various levels of theory. Bond lengths are in angstrom(Å) and bond angles are in degrees(o).. o. 1. +. 3. ' [57 3 : 0 Fig. 1

(168) uªû/.. y- y LV0 TZ2P+d basis set

(169) 2 CISD, CCSD, CCSD(T) +

(170) p ;Å ß Ð (0.875)56 ÇY0x 0 ÑÁ basis set

(171) 20 CISD

(172) 2 i Ópp, ÿT Á 'GY/0 i6 (Ù¨ [57 Dykstra +

(173) full CI L(0.873) M N(e ®d C T ¼ [/. Õ H2 JKÐ(0.742) N ¸Æ H R T 0.13 le 41. 42. +. 3. 2. 2. 3. 4. 1. 3. 1. 3. Fig. 2. Predicted geometries of H5+ at various levels of theory. Bond lengths are in angstrom(Å) and bond angles are in degrees(o). Journal of the Korean Chemical Society.

(174)

(175) H. + 2n+1.

(176) . 405. (n=1-6) complex. Fig. 3. Predicted geometries of H7+ at various levels of theory. Bond lengths are in angstrom(Å) and bond angles are in degrees(o).. M N( ¸Æ R Ð 0.999, R 0 0.810, R 0 1.247, R 0 0.771, %&' θ 47.8 6 R g 0.025 d ÇY57 % ü LV I Be 0 8 9LM ±Ï/' ¨ [/. µ T 3 Ð 1997 Chermette +

(177) 6311G++ basis set

(178) 2 CCSD(T) ,-LM N Æ R Ð 1.000, R 0 0.809, R 0 1.303, %&' R 0 0.77056 8 9L I full-CI LM N ±Ï *^ R g 0.031 le d ÇY/. H 0 H /È !*E

(179) H T u ²T: 56 C symmetryF 4

(180) 2 3 : F Fig. 3

(181) uªû/. ³´

(182) [0 H 0 Å S H T U d LVYZ +RO BP Ì7, ?B θ 65.4 6 lOBP ¸/ U "Z! F uªû/. r2 H M H &, R 0 1.57456 ÇY0x, 0 H 1.272¸/ ÑÁ(0.3 le) Z! 56 H T u ²T#

(183) a ³´ H M ? -: 5 6 Ç:/. µ TZ2P

(184) 20 H M H & R T TZ2P+d

(185) 2 ¸/ U 0.015le d ÇY Z H

(186) 2(0.03) ¸/0 d- Dö 5 6 d uª¯/. %4u R (0.872), R2(0.943), % &' R (0.755)

(187) (20 basis set u Óp p, ÿT 0.1 û6 %$d ®* 56 Ç 1. 2. 3. o. 4. 1. 3. 20. 1. 2. 3. 4. 22. 3. +. +. 7. 5. 2. 2v. +. 3. 2. o. 1. +. 2. 3. +. 3. 5. 2. +. 3. +. 3. +. 5. 1. 4. 2001, Vol. 45, No. 5. 2. 3. Y/. 1983 Schaefer group ,-LM N( ¸Æ DZP CISD(C )

(188) 2, R 0.863, R 0 0.928 , R 1.586, %&' R 0 0.74956 N% 56 Û ,-5u 8 9LM0 N ±Ï 0 LF ¸ #/. 1997 LM N Æ R T U 1.5426 8 9L ¸/ 0.032 le d ÇY/. ,|(2 H !*E

(189) H T u LV H F Pm¨ [57 4

(190) 2 3: F Fig. 4

(191) rø ./. H 0 H ¹ !*E

(192) ;Å H T &Z [r no

(193) ³´ H 0 / lO BP F uªû*^, TZ2P+d CCSD(T)

(194) 2 R Ð 0.89056 ÇYZ H ^ [0 gM N( 2 U 0.015le Z*0 ' [/. 0 B !*E

(195) U d LVYZ [0 H Dö* ^ 56 %$d ®* R62 LV t U( [¼ i/. µ H M H & R 0 1.67756 H

(196) 2 ¸/ U 0.1 le (Z ) Ð56, U ! LV ¸ /. %&' H M *+T*6 d- Dö56 TZ2P+d

(197) 2 R Ð TZ2P

(198) 2 ¸/ U 0.08le y ./. %4 u 4 d-polarization ÿ0 H T u [ n( H ) 0.03, Å S [ n (H ) 0.15, % &' ¹ S [ n 0.0856 H T u, ²T¢. 2v. 1. 3. 2. 4. 16. 3. 22. +. 7. 2. +. 9. +. +. 9. 3. +. 2. 3. 1. +. 3. 2. +. 2. 3. +. 2. 7. +. 7. 2. 2. +. +. 5. 7. 2.

(199) . 406. Fig. 4. Predicted geometries of H9+ at various levels of theory. Bond lengths are in angstrom(Å) and bond angles are in degrees(o).. % BB le, y 0 56 uª¯/. µ R (0.890) R (0.753)0 basis set u Ópp , ÿT fg Î(0.003û) 56 ÇY/. 1983 ,-Ð -' Æ DZP CISD

(200) 2 R 0.878 R 0 1.700, %&' R 0 0.74656 Ç .57, 1997 CCSD(T) LM N Æ R Ð 1.64756 0.03le LF ¸#/. H 0 H OB«Æ X

(201) u H T .[0 C symmetryF ê0 62 ¹ ,- L 0 Fig. 5

(202) ¸./. r2 d-

(203) 'G0 ®r

(204) no

(205) ©ç T ,- TZ2P CCSD(T)7 0 *H1* ,-: T L/. /6 þTY0 H

(206) H R0 %& ®* 57 * H ö56 &Z [0 H M & R 0 1.69856 d Dö 'G/Æ TZ2P+d CCSD(T)

(207) 2 1.690le(H

(208) 2 d- ÿ6 0.008 _0) 6 Ç¨ [57, 0 H M N 0.013l e Z*0 RF uªû/. H M /6 ²T: H & R R 0 BB 1.064, 2.7317 O 1. 3. 1. 2. 3. 16. 2. 22. +. +. 11. 9. 2. s. 2. +. +. 9. 3. 2. 3. +. 9. +. 9. +. 9. 8. 9. 2. B«Æ X1ö56 ÑÁ 2& Z [0 F ¸ #Z fg U LV Tv 56 Ç:/. Õ 1 H «Æ!*E

(209) 9L: H /6 ²T: H Dö56 U Ta3 PF ¸./. 8 9

(210) 2 ,- *H1* ¸': ,- Twx T ,-57, 1978 Yamabe

(211) 431G+p HF ,- LM N( ¸Æ R , R T BB 1.9502, 1.950656 ,-Y', H M H & R R BB U 1.012, 2.97356 5 6 CF ¸' [/. µ 3 ,-LM N Æ R , R Ð CISD

(212) 2 1.673, 1.656 %&' B (H)

(213) 2 1.654, 1.63056 N ±Ï 0 L F ¸ #/. %4u % DFT ,-

(214) 20 ² TY0 H T OB«Æ

(215) Þ6 X(H «Æ /6 ²T: H BeT 91.7 )

(216) XÏ 0 56 Ç : Æ 8 9

(217) 20 1.064le Z! XÏ

(218) 2 X156 &Z [0 56 ÇY/. H 0 H OB«Æ _½156 /6w H T ² T: C symmetryF ê0 6 4

(219) 2 ,: LF Fig. 6

(220) uªû/.

(221) 2 À4? +. 3. 2. 2. 3. 4. +. 9. 8. 2. 9. 27. 3. 4. 3. 22. +. 2. 3. o. 2. +. +. 13. 11. 2. s. Journal of the Korean Chemical Society.

(222)

(223) H. + 2n+1.

(224) . 407. (n=1-6) complex. Fig. 5. Predicted geometries of H11+ at various levels of theory. Bond lengths are in angstrom(Å) and bond angles are in degrees(o).. ü5

(225) LV: Å S H 0 H Ó{

(226) Dö56 OB«Æ «¾ * ' U r6Z! PF ¸./. c56 H M H û@ LV I LVB H M ®d /* 0 56 uª¯5 u, H M H U LV

(227) LV0 R , R T BB 1.706, 1.68456 H ¸/ U 0.1le Z! 56 ÇY57, ²T: H 1* & R R 0 BB 1.739, 2.31156 ÇYZ «Æ

(228) 2 0 2& Z! &

(229) 2 %&' X, _½60 U _! LVF ¸ #/. *H1* å± Ð? 1997 Chermette +

(230) ,- L

(231) 20 R R Ð 1.670, 1.630562 H H

(232) 2M ß 8 9L ¸/ U LVF uªû/. µ ¸'2

(233) 0 R R

(234) ÜÝ uª u [* 7/. Frequencies. !" #$ 0 3: T true minimum?* Õ0 Ó (transition state)?*F > ? 0 x èé 7, Õ (&

(235) )*(D )Ð J +. 2. 9. +. 3. 2. +. 11. +. 2. 3. 3. +. 4. 11. 2. 8. 9. 3. 4. 8. +. +. 7. 9. 9. 22. e. 2001, Vol. 45, No. 5. K lÐ? D (Dissociation energy)M Ë N r X èé ZPVE ¸l X(2e è a ¤/. !" #$

(236) )*F û@ É(internal coordinate)

(237) 2C i ¨ [57, ; Å Ð T*Æ kl (minimum structure) F i/. H clusters0 N=2n+1S 6 : N ýP 86 3N-6S 9:? !" ù ê0/. Æ B !"ù S T . T 3S? H 3S, H 9S, H 15S7 H 21S' H 27S, H 32S/. mode ³

(238) ; T 1SÆ Ó7, 2S Æ J 6 * 0 (ghost state), JK56 >? ¨ 0 F </. 8 9

(239) 20 SCF

(240) 2 û @ É(internal coordinate)

(241)

(242) )* 2C i åe: ù56@A ,- .57, SCF !"# $ 0 !" #$ 62 N m(anharmonicity) + å6 JKÐ ¸/ ±56 U 10%le 56 G [/. Table 1

(243) H (n=1~6) !" 0. +. 2n+1. +. +. 3. 5. +. +. 11. 13. +. +. 7. 9. 37. 43. +. 2n+1.

(244) . 408. Fig. 6. Predicted geometries of H13+ at various levels of theory. Bond lengths are in angstrom(Å) and bond angles are in degrees(o).. #$ F.

(245) 2 ,- wave number (cm ) X6 uªû57, ;Å Ð T056 local minimum = [/. H

(246) !" #$ 0 stretching modeT 3511 cm , %&' bending mode0 2861 cm 6 ÇY5 7, scaling factor6 0.9F Æ, 3160 cm , 2575 cm 62 1987 Majewski stretching mode

(247) JKÐ 3175 cm , %&' 1983 Oka bending ±Ï mode

(248) JKÏ 2521 cm N ¸./. H

(249) !" #$

(250) 2 ω H

(251) U d LVYZ [0 H stretching mode6 (Ù:/.

(252) p 1988 Okumura JK Ð 3910 cm 5 6, 8 9 4387 cm

(253) scaling factor 0.9F Æ ±Ï [/. Õ ω ~ω 0 H ring

(254) stretching bending mode6 (Ù¨ [¤ 0x, ω 0 H 3511 cm 6@A 3605 cm 6 U =T .57, H >?(degenerate)YZ [@ bending mode0 2580 cm , 2461 cm 6 &T ±Zu7 U TZ2P+d SCF −1. +. 3. −1. −1. −1. −1. −1. 44. −1. 45. +. +. 5. 1. 3. 2. −1. −1. 24. +. 2. −1. +. 2. 3. +. 3. −1. −1. 4. 3. −1. yY0 ' [/. 0 H

(255) 2 H T H OB «Æ

(256) LV¢ n OBP R _*' Å R Z*0 RM ±Ï 0 L/(Fig. 1 - ). µ ω ~ω H

(257) U d LVYZ [0 H

(258) ( ©r0 /A S mode62 H M H 9L: @

(259) 2 B %&' NB stretching modeM H

(260) wagging, rocking %&' twisting mode 6 ( Ù¨ [¤/. H 0 H

(261) LV: ÅS H stretching 4447 cm , 4443 cm

(262) 2 uª¯57, H

(263) 2 B stretching I bending ω ~ω 1* 3446, 2712, 2564 cm le6 ÇY/. C56 ω @A 1000 cm Ð H M H wagging, rocking, %&' twisting mode +56 Dì¨ [¤/. 1988 Okumura JK Ð υ 3980 cm 56 N m (anharmonicity) + 'G scaling factor 0.9F Æ ±Ï 0 L/. H H

(264) H T 3S L VYZ [r no

(265) ω ~ω 1* Ð 4472, 4467, +. +. 6. 2. 3. +. 5. 9. 3. 2. +. 2. 3. 2. +. −1. +. 7. 3. 2. −1. + 3. 3. 5. −1. −1. 6. + 3. 2. −1. 2. 24. 1. +. +. 9. 3. 2. 3. Journal of the Korean Chemical Society.

(266)

(267) H. + 2n+1.

(268) . Table 1. Vibrational frequencies of H2n+1+ (n=1~6) at the TZ2P+d SCF level of theory H3+ ω10 ω20 ω30 ω40 ω50 ω60 ω70 ω80 ω90 ω10 ω11 ω12 ω13 ω14 ω15 ω16 ω17 ω18 ω19 ω20 ω21 ω22 ω23 ω24 ω25 ω26 ω27 ω28 ω29 ω30 ω31 ω32 ω33. H5+. 3511 2861 2861. 4387 3605 2580 2461 937 721 596 480 170. H7+. H9+. 4447 4443 3446 2712 2564 822 759 647 613 488 455 385 141 112 92. H11+. 4472 4467 4467 3400 2681 2681 753 753 696 631 596 596 402 402 365 160 103 103 91 91 69. H13+. 4551 4477 4472 4471 3421 2709 2690 734 726 691 619 577 557 416 384 372 356 196 164 156 116 113 111 101 86 73 38. 4548 4547 4492 4487 4471 3456 2759 2694 729 685 666 575 571 520 437 417 395 329 284 199 187 169 160 150 146 142 121 109 100 94 60 42 41. +7, H

(269) 2 B stretching I ω ~ω 1* 3400, 2681, 2681 cm 6 ÇY /. 1988 Okumura H υ ~υ

(270) JKÐ 4020 cm 56 scaling factor 0.9F Æ ±Ï 0 LF ¸ #/. % ü U LV 0 H M H !" #$ ω ~ω 62 1000 cm Ð 6 ,-Y/. H !" #$ 0 H

(271) H 4ST &Z [0x % Twx 3S0 H å d uª¯', /6 ²T : H

(272) ω 4551 cm Ð56 ÇY/. −1. +. 4467 cm. 3. bending. 4. −1. 6. + 9. 1. 3. −1. 24. + 3. 2. 7. −1. +. +. 11. 3. 2. + 9. 2. 1. 2001, Vol. 45, No. 5. −1. 409. (n=1-6) complex. 21. 0 å H !" #$ (4585 cm )

(273) Ð 56 H

(274) &Z [0 H

(275) N( EF U d LV YZ [¼ i/. ω ~ω H

(276) Ð 6 3421, 2709, 2690 cm /. H

(277) 2e H

(278) 3S H T binding YZ [' % !" #$ 4492, 4487, 4471 cm

(279) 2, %&' ü5

(280) X _½6 2S H T binding YZ [¼56 ?( 4548, 4547 cm

(281) Óc 5S H stretching

(282) (Ñ 0 ®(peak)T ' 3S H

(283) (Ñ 0 peak %&' 25S 1000 cm ® d :/. Dissociation Energies. Table 2

(284) B cluster D E !"

(285) )*(ZPVE)F uí .57, ∆(ZPVE)0 / ¼ ß ,- kcal/mol6 uªû/. −1. 2. + 9. 2. +. 5. −1. 7. 3. +. +. 13. 3. 2. −1. −1. 2. 2. + 3. −1. ∆( ZPVE ) = ZPVE ( H2n + 1 ) – { ZPVE ( H2n – 1 ) + ZPVE ( H2 ) } +. +. 0 ,-: (&

(286) )*(D )F JKÏ(D )M N r X 'GY0x, 8 9

(287) 20 SCF

(288) 2 !"

(289) )*F ,- § 0.9 scaling factor F N m(anharmonicity) + ¸ ∆(ZPVE)*6 uªû/. µ H (2≤ −6) complex −n≤

(290) (&

(291) )*(D )0 BB 3:

(292) 2

(293) )* C6@A ,- ./. , H T H M H 6 (& Y0 g D (H )=E(H )-{E(H )+E(H )}6 ¨ [/. g CISD Ópp, ÿ 0 'GY*^, size consistency oT [Z2 l¦ ? l>m Z!/. %4u coupled cluster(CC) 56 size consistency oT © * 586 T l> a' ¨ [¤/. a2 T ,- H 1*0 TZ2P+d CCSD(T) 7 H M H

(294) (20 TZ2P CCSD(T) /. 4

(295) 2 ,-: (&

(296) )* Ð(D ) ZPVE l W D Ð G Table 3

(297) uªû 57, *H1* I JKLM N ./. H (&

(298) )*0 1970@A 31* I JKÐ U 5~10 kcal/mol

(299) 2 t ÂÃ j4 ¿/. N 3 JKLF HI¸Æ 1983

(300) Elford +

(301) 5.8±1.2 kcal/mol, %&' NÒ r

(302) Beuhler +

(303) 6.6±0.3 kcal/mol, %&' 1987 Hiraoka +

(304) 6.9±0.3 kcal/mol6 É Y/. µ J¨^ Ð560 1987

(305) 0 Schaefer +

(306) full CI ,-56 5.45 kcal/mol ZPVE. e. 0. +. 2n+1. e. +. +. 5. 2. e. +. +. +. 5. 5. 3. 3. 2. + 9. +. +. 11. 13. e. 0. + 5. 9-22. 17. 18. 19.

(307) . 410. Table 2. Zero-point vibrational energies(ZPVEs) in kcal/mol for the hydrogen clusters, H2n+1+ (n=1~6) at the DZP, TZ2P, TZ2P+d SCF levels of theory DZP SCF ZPVE 6.64 13.30 23.05 31.96 40.34 48.12 55.75. H2 H3+ H5+ H7+ H9+ H11+ H13+. ∆(ZPVE). TZ2P SCF ∆(ZPVE)*. ZPVE. 2.77 2.03 1.55 1.02 0.89. 6.56 13.26 22.88 31.73 40.09 47.79 55.43. 3.12 2.28 1.74 1.15 1.00. ∆(ZPVE). TZ2P+d SCF ∆(ZPVE)*. ZPVE. ∆(ZPVE). ∆(ZPVE)*. 2.75 2.06 1.62 1.02 0.97. 16.56 13.20 22.78 31.63 40.00 47.72 55.45. 3.03 2.29 1.81 1.16 1.17. 2.75 2.09 1.65 1.06 1.07. 3.05 2.29 1.80 1.14 1.08. ∆(ZPVE) : obtained from ZPVE (H +2n + 1) – { ZPVE (H +2n – 1) + ZPVE(H 2 )}. ∆(ZPVE)*: applied scaling factor of 0.90. Table 3. Dissociation energies (in kcal/mol) De and D0 of H2n+1+(n=1~6) at various levels of theory H5+. H7+. H9+. H11+. H13+. De. (D0). De. (D0). De. (D0). De. (D0). De. (D0). DZP SCF TZ2P SCF TZ2P+d SCF. 5.56 5.61 5.67. (2.75) (2.83) (2.95). 3.65 3.85 3.87. (1.60) (1.77) (1.81). 3.11 3.26 3.30. (1.54) (1.64) (1.67). 0.96 1.14 1.18. (-0.08) (0.11) (0.13). 0.91 1.07 1.13. (0.01) (0.11) (0.07). DZP CCSD TZ2P CCSD TZ2P+d CCSD. 7.76 7.64 8.09. (4.96) (4.90) (5.37). 4.07 4.72 4.70. (2.02) (2.66) (2.64). 3.55 4.06 4.16. (1.99) (2.54) (2.53). 1.15 1.62. (0.12) (0.60). 1.10 1.58. (0.20) (0.61). DZP CCSD(T) TZ2P CCSD(T) TZ2P+d CCSD(T). 8.03 7.91 8.44. (5.23) (5.17) (5.71). 4.11 4.82 4.79. (2.06) (2.76) (2.72). 3.60 4.16 4.27. (2.04) (2.54) (2.64). 1.18 1.69. (0.15) (0.67). 1.12 1.65. (0.22) (0.68). Previous Theories. 7.94a (5.26)a 8.34b (5.45)b 6.9±0.3c 6.6±0.3d 5.8±1.2e. 3.72a. (0.13)a. 3.37a. (1.53)a. Experiments. 3.3±0.2c 3.1±0.1d. 3.2±0.2c. De(H11+)+De(H13+)=2.08a* 1.72±0.1c. 1.64±0.1c. a: reference 22: 6-311G++ CCSD(T), * H13+ H9+ + 2H2 b: reference 20: Estimated (6s3p) full CI c: reference 19 d: reference 18 e: reference 17. k .', 1997 Chermette +

(308) 6-311G++ CCSD(T)

(309) 2 5.26 kcal/mol É ./. 8 9

(310) 2 TZ2P+d CCSD(T)

(311) 2 5.71 kcal/mol6 ÇY0x 0 Elford +

(312) JKÐ fg ±Ï 0 LF ¸ #/. H M H 0 H OB«Æ _ [0 !*E

(313) H T u, U d LVY0 F ê' [57 5 6 H ¸/ klm Z!/' ¤/. H M H (&

(314) )*(D )0 TZ2P+d CCSD(T)

(315) 2 BB 2.72 20. 22. +. +. +. 7. 9. 3. 2. +. +. +. 5. 7. 9. 0. 2.64 kcal/mol6 NÒ klm T* 7 H M N le6 y 0 ö uªû/. H

(316) 3 9 L620 1997 Chermette +

(317) D Ð 3.72 kcal/mol (15.55 kJ/mol) %&' D Ð 0.13 kcal/mol(0.54 kJ/ mol)6 ÉY5u, 0 ZPVE ¸l Y u ZK J T [@ 56 ¸?/. Õ *H1* JKÐ560 1983 Elford +

(318) 3.1±0.1 kcal/mol, %&' 1987 Hiraoka +

(319) 3.3±0.2 kcal/mol kcal/mol + 5. + 7. e. 0. 22. 17. 19. Journal of the Korean Chemical Society.

(320)

(321) H. + 2n+1.

(322) . 6 8 9LM N ±Ï/' ¤/. H

(323) (20 1997 Chermette + ,-56 1.53 kcal/mol6 ÇY57, JKÐ560 1987 Hiraoka +

(324) 3.2±0.2 kcal/mol å± d ÉY/. 8 9L0 H M H klm56 ' n JK Ð fg å L I ö uªû/. 56 9 T H H 0 _Ë J¨ ^ LT ÉY* 7 8 9 T T ,-562 TZ2P CCSD(T).

(325) 2 D 0 1.69, 1.65 kcal/mol %&' D 0 0.67, 0.68 kcal/mol6 NÒ klm ê0 56 Ç Y/. *H 1* É: ,-560 1992 Farizon +

(326) TZP CISD

(327) 2 D Ð 0.96, 0.89 kcal./mol6 É .5u size consistency o n o

(328) JeT Z*7, 1997 Chermette +

(329) , 6-311G++ CCSD(T)

(330) 2 ,- .5u H

(331) ,- ©çYZ H M H (&

(332) )*(D ) V56 2.08 kcal/mol É ./. µ å± JKL62 1987 Hiraoka + H

(333) 1.72±0.1 kcal/mol, %&' H

(334) (20 1.64±0.1 kcal/mol É ./. 8 9L0 JK Ð

(335) N D Ð U 1 kcal/mol le ®d ÇY 0x 0 d- ÿ I basis set superposition error (BSSE) 'G +56 Sý¢ [ 56 Ä:/. + 9. 22. 19. +. +. 7. 9. +. +. 11. 13. e. 0. e. 21. +. +. +. 11. 11. 13. 22. e. +. 11. +. 13. 19. 0.

(336)

(337) 2 !" #$ , %&' (&

(338) )* + ,- ./. 0 H 1*0 TZ2P+d CCSD(T)

(339) 2 % &' H H

(340) (20 TZ2P CCSD(T) 1 * 3 ./. *H1* I JK

(341) ¸ 'M ß H 1*0 H OB !*E

(342) H T Ë 56 LVYZ [57, H H

(343) 20 H T OB« Æ X, _½

(344) ¸/ U d LVYZ [0 F ¸ #/. %4u Okumura + u, Paul + Ç 6 OB«Æ Þ6 X, _½

(345) H T LVYZ [ 0 _`a, OBP R 1

(346) 2 U 1.064( H ), 1.739(H ) le Z! XÏ

(347) 2 X, _½6 U 2.3~ 2.7 . [0 6 ÇY/. \ LV fg U r no

(348) Q

(349) 2 H T åLd MÓw" ¨ 56 ©BY7, a2 JK56 H2n+1+ series(n=1~6) ,. + 9. +. +. 11. 13. +. +. 9. 3. 2. +. +. 11. 13. 2. 24. 46. 2. +. 11. +. 13. 2. 2001, Vol. 45, No. 5. 411. (n=1-6) complex. XÏF l>Á pq 0 N* 56 Ç:/. µ !" #$ 0 4 basis set

(350) 2 SCF 56 ,- .57, 8 9

(351) 2 3: ;< local minimum = >? ./. Õ JK

(352) pq: fundamental frequencyM N ±Ï 0 Ð O57, Ð

(353) scaling factor 0.9F ZPVEF 'G (&

(354) )*(D ) F ,- ./. H (n=1~6)

(355) (&

(356) )*(D ) 0 Ó56 *H1* I JKÐ ±Ï 0 LF O/. H M H 0 26 NÒ kl m T*', (&

(357) )*(D )0 H M N U le6 y 0 ö uªû/. H M H Õ 26 NÒ klm T*7, % (&

(358) )*T H M H N y 0 ö uªû /. 0 H

(359) ²T6 LVY0 H U LV leF uªû0 56

(360) 2 Ç: % öm ±ÏY0 LF ¸/. o. +. 2n+1. o. +. +. 7. 9. +. 0. 5. +. +. 11. 13. + 7. + 9. + 9. 2. 8 90 2000e û ø9N *

(361) ¾Y57

(362) F Ø:`/.. 1. Spirko, V.; Kraemer, W. P. J. Mol. Spectrosc. 1993, 159, 521. 2. Krasovskii, V. I. Sov. Astron. 1958, 2, 775. 3. Thompson, J. J. Philos. Mag. 1912, 24, 209. 4. Drossart, P. et al, Nature. 1989, 340, 539. 5. Miller, S.; Tennyson, J.; Lepp, S.; Dalgarno, A. Nature. 1992, 355, 420. 6. Clampitt, R.; Towland, L. Nature (London) 1969, 223, 815. 7. Van Deursen, A.; Reuss, J. Int. J. Mass. Spectrom. Ion Phys. 1973, 11, 483. 8. Dawson, P. H.; Tickner, A. W. J. Chem. Phys. 1962, 37, 672. 9. Poshusta, R. D.; Haugen, J. A.; Zetik, D. F. J. Chem. Phys. 1969, 51, 3343. 10. Easterfield, J.; Linnett, J. W. Chem. Commum. 1970, 64. 11. Arifov, U. A.; Pozharov, S. L.; Chernov, I. G. and Mukhamediev, Z. A. High Energy Chem. (USSR) 1971, 5, 69. 12. Bennett, S. L.; Field, F. H. J. Am. Chem. Soc. 1972, 94, 8669. 13. Elford, M. T.; Milloy, H. B. Aust. J. Phys. 1975, 62, 2267. 14. Hiraoka, K.; Kebarle, P. J. Chem. Phys. 1975, 27, 795..

(363) 412. . 15. Johnsen, R.; Huang, C.; Biondi, M. A. J. Chem. Phys. 1976, 65, 1539. 16. Yamaguchi; Gaw, J. F.; Schaefer, H. F. J. Chem. Phys. 1983, 78(6), 15. 17. Elford, M. T. J. Chem. Phys. 1983, 79, 5951. 18. Beuhler, R. J.; Ehrenson, S.; Friedman, L. J. Chem. Phys. 1983, 79, 5982; Beuhler, R. J.; Friedman, L. Ber. Bunsenges. Phys. Chem. 1984, 88, 265. 19. Hiraoka, K. J. Chem. Phys. 1987, 87, 4048. 20. Yamaguchi, Y.; Gaw, J. F.; Remington, R. B.; Schaefer, H. F. J. Chem. Phys. 1987, 86, 5072. 21. Farizon, M.; Chermette, H.; Farizon-Mazuy, B. J. Chem. Phys. 1992, 96, 1325. 22. Chermette, H.; Razafinjanahary, H.; Carrion, L. J. Chem. Phys. 1997, 107, 10643. 23. Okumura, M.; Yeh, L. I.; Lee, Y. T. J. Chem. Phys. 1985, 83(7), 3705. 24. Okumura, M.; Yeh, L. I.; Lee, Y. T. J. Chem. Phys. 1988, 88(1). 25. Bae, Young K. Chem. Phys. Lett. 1991, 180. 26. Harrison, S. W.; Massa, L. J.; Solomon, P. Nature (London) Phys. Sci. 1973, 245, 31. 27. Yamabe, S.; Hirao, K.; Kitaura, K. Chem. Phys. Lett. 1978, 56, 546. 28. Huber, H, Chem. Phys. Lett. 1980, 70, 353. 29. Boothroyd, Arnold I.; Keogh, William J.; Matin,Peter G.; Peterson, Michael R.; J. Chem. Phys. 1991, 95(6). 30. Larsson, M.; Danared, H.; Mowat, J. R.; Sigray, P.; Sundström, G.; Broström, L.; Filevich, A.; Këllberg, A.; Mannervik, S.; Rensfelt, K. G. and Datz, S. J. Am. Phys. Soc. 1993, 70, 430. 31. Jiao, Haijun.; Schleyer, Paul Ragué; N, Mikhail; Glukhovtsev, J. Phys. Chem. 1996, 100, 12299. 32. Aguado, Alfredo; Tablero, César and Paniagua, Miguel J. Chem. Phys. 1999, 110(16), 7789-7795.. 33. Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. 34. Dunning, T. H. J. Chem. Phys. 1970, 53, 2823. 35. Dunning, T. H. J. Chem. Phys. 1971, 55, 716. 36. Pulay, P, In Modern Theoretical Chemistry, Schaefer, H. F., Ed.; Plenum: New York, U. S. A., 1977; Vol. 4, p 153.: Goddard, J. D.; Handy, N. C.; Schaefer, H. F. J. Chem. Phys. 1979, 71, 1525. 37. Saxe, P.; Yamaguchi, Y.; Schaefer, H. F. J. Chem. Phys. 1987, 77, 5647. 38. Brooks, B. R.; State, W. D.; Goddard, P.; Yamaguchi, Y.; Schaefer, H. F. J. Chem. Phys. 1980, 72, 4652. 39. Scheiner, A. C.; Scuseria, G. E.; Rice, J. E.; Lee, T. J.; Schaefer, H. F. J. Chem. Phys. 1987, 87, 5361. 40. Janssen, C. L.; Seidl, E. T.; Scuseria, G. E.; Hamilton, T. P.; Yamaguchi, Y.; Remington, R. B.; Xie, Y.; Vacek, G.; Sherrill, C. D.; Crawford, T. D.; Fermann, J. T.; Allen, W. D.; Brocks, B. R.; Fitzgerald, G. B.; Fox, D. J.; Gaw, J. F.; Handy, N. C.; Laidig, W. D.; Lee, T. J.; Pitzer, R. M.; Rice, J. E.; Saxe, P.; Scheiner, A. C. and Schaefer, H. F. PSI 2.0.8; PSITECH Inc.; Watkinssvills, GA. U.S.A., 1994. 41. Dykstra, C. E.; Gaylord, A. S.; Gwinn, W. D.; Swope, W. C. and Schaefer, H. F. J. Chem. Phys. 1978, 68, 3951. 42. Kolos, W.; Wolniewicz, L. J. Chem. Phys. 1968, 49, 404.; J. Mol. Spectrosc. 1975, 54, 303. 43. Yamaguchi, Y; Scherfer, H. F. J. Chem. Phys. 1980, 73, 2310. 44. Majewski, W. A.; Marshall, m. D.; Mckellar, A. R. W.; Johns, J. W. C. and Watson, J. K. G. J. Mol. Spectrosc. 1987, 122, 341. 45. Oka, T. In Molecular Ions: Spectroscopy, Structure, and Chemistry.; Miller, T. A.; Boudeybey, V. E.; NorthHolland: Amsterdam, 1983. 46. Paul, W.; Schlemmer, S.; Lücke, B.; Gerlich, D. Chem. Phys. 1996, 209, 265.. Journal of the Korean Chemical Society.

(364)