supp_b_1.doc 708KB Jun 05 2011 09:30:50 PM
Dr. H. Baumann
Tel: (01) 632 2901
FAX: (01) 632 1280
e-mail: [email protected]
Supplementary Material
Semiempirical Computation of Large Organic Structures and their UV/vis Spectra:
Program Discription and Application to Poly(triacetylene) Hexamer and Taxotere
by Harold Baumann*, Rainer E. Martin and François Diederich
Laboratorium für Organische Chemie der Eidgenössischen Technischen Hochschule,
Universitätstr. 16, CH-8092 Zürich
(9. 12. 1997)
Procedure sido.c 1
Interactions between the doubly and singly excited configurations and between the
doubly excited and the ground configuration.
1 = (hl | hl)
1 llhhl | H|
0
1
1
lm
hh | H| 0 =
(1)
2 (hl | hm)
(2)
2 (hm | km)
(3)
1
1 mm
hk | H| 0
1
1 lm
hk | H| 0 (hm | kl) + (hl | km)
(4)
1
1 lm
hk | H| 0 3 (hm | kl) (hl | km)
(5)
1 s 0
1 llhh | H|
r
(6)
1 l
1 llhh | H|
r
(7)
2 (hl | hr)
1 s 2 (hl | ls)
1 llhh | H|
h
1 l =
1 llhh | H|
h
(8)
n
2 H hl + 2
2(ii | hl)
(ih | il) +
i
(9)
2 (ll | hl) (hh | hl)
1
1 s
lm
kk | H| r 0
(10)
1 l
1 lm
kk | H| r (km | rk)
(11)
1 m
1 lm
kk | H| r (kl | rk)
(12)
1 s
1 lm
kk | H| k (kl | ms) + (km | ls)
(13)
1 m
1 lm
kk | H| k Flk + (mk | lm ) (kl | kk) + (kl | mm)
(14)
1 l
1 lm
kk | H| k Fmk + (lk | lm ) (km | kk) + (km | ll)
1 s
1 mm
hk | H| r 0
(15)
(16)
1 m
1 mm
hk | H| r (km | hr) + (mh | kr)
(17)
1 s
1 mm
hk | H| k (mh | ms)
(18)
1 s
1 mm
hk | H| h (mk | ms)
(19)
1 m
1 mm
hk | H| k Fmh + (mk | hk ) + (mh | kk) (mh | mm)
(20)
1 m
1 mm
hk | H| h Fmk + (mh | hk) + (mk | hh) (mk | mm)
(21)
1 s
1 lm
hk | H| r 0
(22)
1 m
1
1 lm
hk | H| r
2
(kr | hl) + (hr | kl)
(23)
2
1 l
1
1 lm
hk | H| r
2
1 s
1 lm
hk | H| h
1
1 s
1 lm
hk | H| h
1
(kr | hm) + (hr | km)
(24)
2
(mk | ls ) + (lk | ms)
(25)
2
(mh | ls) + (lh | ms)
(26)
1 m
1
1 lm
hk | H| k
2
Flh (mh | ml) + (lh | kk) (lh | mm) + (lk | hk)
1 l
1
1 lm
hk | H| k
2
[ Fmh ( lh | ml) + (mh | kk)
(27)
(28)
(mh | ll) + ( mk | hk)]
1 m
1
1 lm
hk | H| h
[ Flk ( mk | ml) + (lk | hh )
2
(29)
(lk | mm ) + (lh | hk)]
1 l
1
1 lm
hk | H| h
2
[ Fmk ( lk | ml) + (mk | hh)
( mk | ll) + (mh | hk)]
1 s
1 lm
hk | H| r 0
1 m
1 lm
hk | H| r
3
1 s
1 lm
hk | H| h
3
1 s
1 lm
hk | H| k
1 m
1 lm
hk | H| k
(31)
(lh | kr)
(hr | lk)
(32)
2
(mh | kr)
(hr | mk)
(33)
2
(ms| kl)
(sl | mk)
(34)
(ms| hl) (sl | mh)
(35)
3
1 l
1 lm
hk | H| r
(30)
2
3
2
3
2
[ Flh + (kk | lh) (mm | lh) + (ml | hm)
(36)
(kl | hk)]
1 l
1 lm
hk | H| k
3
2
[ Fmh + (kk | mh) (ll | mh) + (ml | hl )
(37)
(km | hk)]
1 m
1 lm
hk | H| h
3
2
[ Flk + (hh | lk) (mm | lk) + (ml | mk)
(hl | hk)]
1 l
1 lm
hk | H| h
3
2
(38)
[ Fmk + (hh | mk) (ll | mk) + (ml | lk)
(39)
(hm | hk)]
Procedure dodo.c
Interactions between the doubly excited configurations.
Type 1 - Type 1:
1 ll
1 mm
hh | H| kk 0
(40)
1 mm
1 mm
hh | H| kk (hk | hk)
(41)
1 ll
1 mm
hh | H| hh (lm | lm)
(42)
3
Type 1 - Type 2:
1 ln
1 mm
hh | H| kk 0
(43)
1 ln
1 mm
hh | H| hh 2 (lm | mn)
(44)
1 mn
1 mm
hh | H| kk 0
(45)
1 mn
1 mm
hh | H| hh 2 Fmn + (mm | mn) 2(hh | mn) + (hm | hn)
(46)
1 lm
1 mm
hh | H| hh 2 Fml + (mm | ml ) 2(hh | ml) + (hm | hl)
(47)
Type 1 - Type 3:
1 ll
1 mm
hh | H| jk 0
(48)
1 ll
1 mm
hh | H| jh 0
(49)
1 ll
1 mm
hh | H| hk 0
(50)
1 mm
1 mm
hh | H| jk
(51)
2 (jh | hk)
1 mm
1 mm
hh | H| hk 2 Fhk (hk | hh) + 2(hk | mm) (hm | km)
1 mm
1 mm
hh | H| hj 2 Fhj (hj| hh ) + 2(hj | mm) (hm | jm)
(52)
(53)
Type 1 - Type 4:
1 ln
1 mm
hh | H| jk 0
(54)
1 lm
1 mm
hh | H| jk 0
(55)
1 lm
1 mm
hh | H| hk 2(hk | lm) (kl | mh)
(56)
1 mn
1 mm
hh | H| hk 2(hk | mn) (kn | mh)
(57)
1 lm
1 mm
hh | H| jn 2(jh | ml) (jl | mh)
(58)
1 mn
1 mm
hh | H| jn 2(jh | mn) (jn | mh)
(59)
Type 1 - Type 5:
1 ln
1 mm
hh | H| jk 0
(60)
1 lm
1 mm
hh | H| jk 0
(61)
1 lm
1 mm
hh | H| hk 3 (kl | mh)
(62)
1 mn
1 mm
3 (kn | mh)
hh | H| hk
(63)
1 lm
1 mm
hh | H| jn
3 (jl | mh)
(64)
1 mn
1 mm
hh | H| jn 3 (jn | mh)
(65)
4
Type 2 - Type 2:
1 no
1 lm
hh | H| kk 0
(66)
1 no
1 lm
hh | H| hh (ln | mo) + (lo | mn)
(67)
1 lo
1 lm
hh | H| kk 0
(68)
1 lo
1 lm
hh | H| hh Fmo 2(hh | mo) + (hm | ho) + (ll | mo) + (lo | ml)
(69)
1 nl
1 lm
hh | H| hh Fmn 2(hh | mn) + (hm | hn) + (ll | mn) + (ln | ml)
(70)
1 mo
1 lm
hh | H| hh Flo 2(hh | lo) + (hl | ho) + (mm | lo) + (mo | ml)
(71)
1 mn
1 lm
hh | H| hh Fln 2(hh | ln) + (hl | hn) + (mm | ln) + (mn | ml)
(72)
1 lm
1 lm
hh | H| kk (hk | hk)
(73)
Type 2 - Type 3:
1 nn
1 lm
hh | H| jk 0
(74)
1 nn
1 lm
hh | H| hk 0
(75)
1 ll
1 lm
hh | H| hk 2(ml | hk) (mh | kl)
(76)
1 mm
1 lm
hh | H| hk 2(ml | hk) (hl | km)
(77)
1 ll
1 lm
hh | H| jh 2(ml | hj) (jl | hm)
1 mm
1 lm
hh | H| jh 2(ml | hj) (hl | jm)
(78)
(79)
Type 2 - Type 4:
1 no
1 lm
hh | H| jk 0
(80)
1 mn
1 lm
hh | H| jk 0
(81)
1 no
1 lm
hh | H| hk 0
(82)
1 mn
1 lm
hh | H| hk 2 (ln | hk) 0.5(hl | kn)
(83)
1 mo
1 lm
hh | H| hk 2 (lo | hk) 0.5(hl | ko)
(84)
1 nl
1 lm
hh | H| hk 2 (mn | hk) 0.5(hm | kn)
(85)
1 lo
1 lm
hh | H| hk 2 (mo | hk) 0.5(hm | ko)
(86)
1 mn
1 lm
2 (ln | jh) 0.5(hl | jn)
hh | H| jh
(87)
1 mo
1 lm
hh | H| jh 2 (lo | jh) 0.5(hl | jo)
(88)
5
1 nl
1 lm
2 (mn | jh) 0.5(mh | jn)
hh | H| jh
(89)
1 lo
1 lm
2 (mo | jh) 0.5(mh | jo)
hh | H| jh
(90)
1 lo
1 lm
hh | H| jh 2 (mo | jh) 0.5(mh | jo)
(91)
1 lm
1 lm
hh | H| jk
(92)
2 (hj| hk)
1 lm
1 lm
hh | H| hk 2[(Fhk (hh | hk) + (ll | hk) 0.5(kl | hl) + (mm | hk)
0.5(hm | km)]
(93)
1 lm
1 lm
hh | H| hj 2 [Fhj (hh | hj) + (ll | hj) 0.5(jl | hl) + (mm | hj)
(94)
0.5(hm | jm)]
Type 2 - Type 5:
1 no
1 lm
hh | H| jk 0
(95)
1 nm
1 lm
hh | H| jk 0
(96)
1 no
1 lm
hh | H| hk 0
(97)
1 nm
1 lm
hh | H| hk
3
1 mo
1 lm
hh | H| hk
3
1 nl
1 lm
hh | H| hk
3
1 lo
1 lm
hh | H| hk
3
1 nm
1 lm
hh | H| jh
3
1 mo
1 lm
hh | H| jh
3
1 nl
1 lm
hh | H| jh
1 lo
1 lm
hh | H| jh
2
(lh | nk)
(98)
2
(lh | ok)
(99)
2
(mh | nk)
(100)
2
(mh | ok)
(101)
2
(hl | jn)
(102)
2
3
(hl | jo)
(hm | jn)
(104)
(hm | jo)
(105)
2
3
2
(103)
1 lm
1 lm
hh | H| jk 0
1 lm
1 lm
hh | H| hk
1 lm
1 lm
hh | H| hj
3
(106)
2
3
(hl | kl)
2
(hm | km)
(hl | jl) (hm | jm)
(107)
(108)
Type 3 - Type 3:
1 nn
1 mm
hk | H| gj 0
(109)
1 mm
1 mm
hk | H| gj (gh | jk) + (gk | hj)
1 nn
1 mm
hk | H| hj 0
(110)
(111)
6
1 mm
1 mm
hk | H| hj Fjk 2(mm | jk) + (km | jm) + (hj | hk) + (hh | jk)
(112)
1 mm
1 mm
hk | H| gh Fgk 2(mm | gk) + (km | gm) + (gh | hk) + (hh | gk)
(113)
1 mm
1 mm
hk | H| jk Fhj 2(mm | hj) + (hm | jm) + (kj| hk) + (kk | hj)
(114)
1 mm
1 mm
hk | H| gk Fhg 2(mm | hg) + (hm | gm) + (gk | hk) + (kk | hg)
(115)
1 nn
1 mm
hk | H| hk 0
(116)
Type 3 - Type 4:
1 ln
1 mm
hk | H| gj 0
(117)
1 ln
1 mm
hk | H| hj 0
(118)
1 mn
1 mm
hk | H| gj 0
(119)
1 mn
1
1 mm
hk | H| hj
2
(km | jn)
2(mn | jk)
(120)
1 mn
1
1 mm
hk | H| kj
2
(hm | jn)
2(mn | jh)
(121)
(hm | jn)
2(mn | jh)
(122)
1 mn
1
1 mm
hk | H| kj
2
1 mn
1
1 mm
hk | H| gh
2
(km | gn)
2(mn | gk)
(123)
1 mn
1
1 mm
hk | H| gk
2
(hm | gn)
2(mn | gh)
(124)
1 lm
1
1 mm
hk | H| hj
2
(km | jl)
2(ml | jk)
(125)
1 lm
1
1 mm
hk | H| kj
2
( hm | jl)
2( ml | jh )
(126)
1 lm
1
1 mm
hk | H| gh
2
(km | gl)
2(ml | gk)
(127)
1 lm
1 mm
hk | H| gk 2 (hm | gl) 2(ml | gh)
(128)
1 ln
1 mm
hk | H| hk 2 (ml | mn)
(129)
1 ln
1
1 mm
hk | H| hk
2
[2Fmn 2(hh | mn) + (hm | hn) 2(mn | kk)
+ (km | kn) + 2(mn | mm)]
1 lm
1
1 mm
hk | H| hk
2
[2Fml 2(hh | ml) + (hm | hl) 2(lm | kk)
+ (km | lk) + 2(lm | mm)]
(130)
(131)
Type 3 - Type 5:
1 ln
1 mm
hk | H| gj 0
(132)
1 ln
1 mm
hk | H| hj 0
(133)
1 mn
1 mm
hk | H| gj 0
(134)
1 lm
1 mm
hk | H| hj
3
2
(mk | lj)
(135)
7
1 lm
1 mm
hk |H| kj
3
1 lm
1 mm
hk | H| gh
3
1 lm
1 mm
hk | H| gk
3
1 mn
1 mm
hk | H| hj
3
1 mn
1 mm
hk | H| kj
3
1 mn
1 mm
hk | H| gh
3
1 mn
1 mm
hk | H| gk
3
2
(mh|lj)
(136)
2
(mk | lg)
(137)
2
(mh | lg)
(138)
2
(mk | nj)
(139)
2
(mh | nj)
(140)
2
(mk | ng)
(141)
2
(mh | ng)
(142)
1 ln
1 mm
hk | H| hk 0
1 mn
1 mm
hk | H| hk
3
1 lm
1 mm
hk | H| hk
3
(143)
2
(km | kn)
(hm | hn)
2
(hm | hl)
(km | kl)
(144)
(145)
Type 4 - Type 4
1 no
1 lm
hk | H| gj 0
(146)
1 no
1 lm
hk | H| gj 0
(147)
1 no
1 lm
hk | H| hk (ln | mo) + (lo | mn)
(148)
1 lo
1 lm
hk | H| hj (kj| mo) + 0.5(jo | mk)
(149)
1 mo
1 lm
hk | H| hj (kj| lo) + 0.5( jo | lk)
(150)
1 nl
1 lm
hk | H| hj (kj| mn) + 0.5(jn | mk)
(151)
1 nm
1 lm
hk | H| hj (kj| ln) + 0.5(jn | lk)
(152)
1 lo
1 lm
hk | H| gh (kg | mo) + 0.5(go | mk)
(153)
1 mo
1 lm
hk | H| gh (kg | lo) + 0.5(go | lk)
(154)
1 nl
1 lm
hk | H| gh (kg | mn) + 0.5(gn | mk)
(155)
1 nm
1 lm
hk | H| gh (kg | ln) + 0.5( gn | lk)
(156)
1 lo
1 lm
hk | H| gk (hg | mo) + 0.5( go | mh)
(157)
1 mo
1 lm
hk | H| gk (hg | lo) + 0.5(go | lh)
(158)
1 nl
1 lm
hk | H| gk (hg | mn) + 0.5(gn | mh)
(159)
1 nm
1 lm
hk | H| gk (hg | ln) + 0.5(gn | lh)
(160)
1 lo
1 lm
hk | H| kj (hj| mo) + 0.5(jo | mh)
(161)
8
1 mo
1 lm
hk | H| kj (hj| lo) + 0.5(jo | hl)
(162)
1 nl
1 lm
hk | H| kj (hj| mn) + 0.5(jn | hm)
(163)
1 nm
1 lm
hk | H| kj (hj| ln) + 0.5 (jn | hl)
(164)
1 lm
1 lm
hk | H| gj (kj| lj) + 0.5(hj| gk)
1 lo
1 lm
hk | H| hk Fmo (hh | mo) (kk | mo) + 0.5(hm | ho) + 0.5(km | ko)
+ (ll | mo) + (ml | ol)
(165)
(166)
1 mo
1 lm
hk | H| hk Flo (hh | lo) (kk | lo) + 0.5(hl | ho) + 0.5 (kl | ko)
(167)
+ (mm | lo) + (ml | om)
1 ln
1 lm
hk | H| hk Fmn (hh | mn) (kk | mn) + 0.5(hm | hn) + 0.5(km | kn)
+ (ll | mn) + (ml | nl)
(168)
1 mn
1 lm
hk | H| hk Fln (hh | ln) (kk | ln) + 0.5(hl | hn) + 0.5(kl | kn)
(169)
+ (mm | ln) + (ml | mn)
1 lm
1 lm
hk |H| hj Fkj (hh|kj) (hk|hj) + 0.5 (kl| jl) + 0.5 (km| jm)
(170)
+ (ll|kj) +(mm|kj)
1 lm
1 lm
hk | H| gh Fgk (hh | gk) (hk | gh) + 0.5 (kl | gl) + 0.5 (km | gm)
+ (ll | gk) + (mm | gk)
1 lm
1 lm
hk | H| jk Fhj (kk | hj) (hk | jk) + 0.5(hl | jl) + 0.5(hm | jm)
+ (ll | hj) + (mm | hj)
1 lm
1 lm
hk | H| gk Fhg (kk | hg) (hk | gk) + 0.5(hl | gl) + 0.5(hm | gh)
+ (ll | gh) + (mm | gh)
(171)
(172)
(173)
Type 4 - Type 5
1 no
1 lm
hk | H| gj 0
(174)
1 no
1 lm
hk | H| hj 0
(175)
1 no
1 lm
hk | H| hk 0
(176)
1 lo
1 lm
hk | H| hj
3
1 mo
1 lm
hk | H| hj
3
2
(km | oj)
(177)
2
(kl | oj)
(178)
1 ln
1 lm
hk | H| hj
3
1 mn
1 lm
hk | H| hj
3
1 lo
1 lm
hk | H| gh
3
1 mo
1 lm
hk | H| gh
1 ln
1 lm
hk | H| gh
1 mn
1 lm
hk | H| gh
2
(km | nj)
(179)
2
(kl | nj)
(180)
2
(km | go)
(181)
(kl | go)
(182)
(km | gn)
(183)
3
3
3
2
2
2
(kl | gn)
(184)
9
1 lo
1 lm
hk | H| gk
3
1 mo
1 lm
hk | H| gk
1 ln
1 lm
hk | H| gk
(hm | go)
(185)
(hl | go)
(186)
(hm | gn)
(187)
2
3
3
2
1 mn
1 lm
hk | H| gk
3
1 mo
1 lm
hk | H| jk
3
1 ln
1 lm
hk | H| jk
2
2
(hl | gn)
(188)
2
(hl | oj)
(189)
3
2
(hm | nj)
(190)
1 lm
1 lm
hk | H| gj 0
1 no
1 lm
hk | H| gj
3
(191)
(km | ko)
(hm | ho)
(192)
2
(kl | ko)
(hl | ho)
(193)
2
(hm | hn)
2
1 mo
1 lm
hk | H| hk
3
1 ln
1 lm
hk | H| hk
3
1 mn
1 lm
hk | H| hk
3
1 lm
1 lm
hk | H| hj
3
1 lm
1 lm
hk | H| gh
3
1 lm
1 lm
hk | H| jk
3
1 lm
1 lm
hk | H| gk
3
1 lm
1 lm
hk | H| hk
3
(km | kn)
2
(hl | hn)
2
(jm | km)
2
(kl | gl)
2
(jm | hm)
2
(hl | gl)
2
(mk| mk) + ( hl| hl)
(194)
(kl | kn)
(195)
(kl | jl)
(196)
(gm | km)
(197)
(hl | jl)
(198)
(gm | hm)
(199)
(kl| kl) (hm| hm)
(200)
Type 5 - Type 5:
1 no
1 lm
hk | H| gj 0
(201)
1 no
1 lm
hk | H| hj 0
(202)
1 no
1 lm
hk | H| hk (ln | mo) (lo | mn)
(203)
1 lo
3
1 lm
hk | H| hj 2 (jo | mk) (jk | mo)
(204)
1 mo
1 lm
hk | H| hj
(205)
1 ln
1 lm
hk | H| hj
3
3
2
2
(jo | kl) + (jk | lo)
(jn | km ) + (jk | mn)
(206)
1 mn
3
1 lm
hk | H| hj 2 (jn | kl) (jk | ln)
1 lo
1 lm
hk | H| gh
3
2
(go | km) + (gk | mo)
(207)
(208)
1 mo
3
1 lm
hk | H| gh 2 (go | kl) (gk | lo)
1 ln
3
1 lm
hk | H| gh 2 (gn | km) (gk | mn)
(209)
(210)
10
1 mn
1 lm
hk | H| gh
3
2
(211)
(gn | kl) (gk | ln)
1 lo
3
1 lm
hk | H| gk 2 (go | hm ) (gh | mo)
(212)
1 mo
1 lm
hk | H| gk
3
1 ln
1 lm
hk | H| gk
3
2
(go | hl) (gh | lo)
(213)
2
(gn | hm) (gh | mn)
(214)
1 mn
3
1 lm
hk | H| gk 2 (gn | hl) (gh | ln)
(215)
1 lo
1 lm
hk | H| jk
(216)
3
2
(jo | hm) (hj| mo)
1 mo
3
1 lm
hk | H| jk 2 (jo | hl) (hj| lo)
(217)
1 ln
3
1 lm
hk | H| jk 2 (jn | hm) (hj| mn)
(218)
1 mn
1 lm
hk | H| jk
(219)
3
2
(jn | hl) (hj| ln)
1 lm
1 lm
hk | H| gj (gh | jk) (hj| gk)
(220)
1 lo
3
3
1 lm
hk | H| hk Fmo (hh | mo) + 2 (hm | ho) (kk | mo) + 2 (km | ko)
+ (ll | mo) (lo | lm)
1 mo
1 lm
hk | H| hk Flo (hh| lo)
3
2
(hl| ho) (kk| lo)
3
2
(kl| ko)
(mm | lo) + (mo | lm)
1 ln
1 lm
hk | H| hk Fmn + (hh | mn)
3
2
(hm | hn) (kk | mn)
3
2
(km | kn)
(ll | mn) + (ln | lm)
1 mn
3
3
1 lm
hk | H| hk Fml (hh| ln) + 2 (hl| hn) (kk| ln) + 2 (kl| kn)
+ (mm| ln) (mn| lm)
1 lm
3
3
1 lm
hk | H| hj Fjk (hh | jk) + 2 (kl | jl) (mm | jk) + 2 (jm | km)
(ll | mn) (hk | hj)
1 lm
1 lm
hk | H| gh Fgk (hh | gk)
3
2
(kl | gl) + (mm | gk)
3
2
(gm | km)
(ll | gk) + (hk | hg)
1 lm
1 lm
hk | H| jk Fhj (kk | hj)
3
2
(hl | jl) + (mm | hj)
3
2
(jm | hm)
+ (ll | hj) + (hk | jk)
1 lm
3
3
1 lm
hk | H| gk Fgh + (kk | gh) + 2 (hl | gl) (mm | gh) + 2 (gm | hm)
(ll | gh) (hk | gk)
(221)
(222)
(223)
(224)
(225)
(226)
(227)
(228)
Procedure h.c
Computation of the (ij | kl) integrals with the molecular orbitals and the electron electron repulsion matrix.
11
REFERENCE
1.
P.A. Straub, personal communication.
12
Tel: (01) 632 2901
FAX: (01) 632 1280
e-mail: [email protected]
Supplementary Material
Semiempirical Computation of Large Organic Structures and their UV/vis Spectra:
Program Discription and Application to Poly(triacetylene) Hexamer and Taxotere
by Harold Baumann*, Rainer E. Martin and François Diederich
Laboratorium für Organische Chemie der Eidgenössischen Technischen Hochschule,
Universitätstr. 16, CH-8092 Zürich
(9. 12. 1997)
Procedure sido.c 1
Interactions between the doubly and singly excited configurations and between the
doubly excited and the ground configuration.
1 = (hl | hl)
1 llhhl | H|
0
1
1
lm
hh | H| 0 =
(1)
2 (hl | hm)
(2)
2 (hm | km)
(3)
1
1 mm
hk | H| 0
1
1 lm
hk | H| 0 (hm | kl) + (hl | km)
(4)
1
1 lm
hk | H| 0 3 (hm | kl) (hl | km)
(5)
1 s 0
1 llhh | H|
r
(6)
1 l
1 llhh | H|
r
(7)
2 (hl | hr)
1 s 2 (hl | ls)
1 llhh | H|
h
1 l =
1 llhh | H|
h
(8)
n
2 H hl + 2
2(ii | hl)
(ih | il) +
i
(9)
2 (ll | hl) (hh | hl)
1
1 s
lm
kk | H| r 0
(10)
1 l
1 lm
kk | H| r (km | rk)
(11)
1 m
1 lm
kk | H| r (kl | rk)
(12)
1 s
1 lm
kk | H| k (kl | ms) + (km | ls)
(13)
1 m
1 lm
kk | H| k Flk + (mk | lm ) (kl | kk) + (kl | mm)
(14)
1 l
1 lm
kk | H| k Fmk + (lk | lm ) (km | kk) + (km | ll)
1 s
1 mm
hk | H| r 0
(15)
(16)
1 m
1 mm
hk | H| r (km | hr) + (mh | kr)
(17)
1 s
1 mm
hk | H| k (mh | ms)
(18)
1 s
1 mm
hk | H| h (mk | ms)
(19)
1 m
1 mm
hk | H| k Fmh + (mk | hk ) + (mh | kk) (mh | mm)
(20)
1 m
1 mm
hk | H| h Fmk + (mh | hk) + (mk | hh) (mk | mm)
(21)
1 s
1 lm
hk | H| r 0
(22)
1 m
1
1 lm
hk | H| r
2
(kr | hl) + (hr | kl)
(23)
2
1 l
1
1 lm
hk | H| r
2
1 s
1 lm
hk | H| h
1
1 s
1 lm
hk | H| h
1
(kr | hm) + (hr | km)
(24)
2
(mk | ls ) + (lk | ms)
(25)
2
(mh | ls) + (lh | ms)
(26)
1 m
1
1 lm
hk | H| k
2
Flh (mh | ml) + (lh | kk) (lh | mm) + (lk | hk)
1 l
1
1 lm
hk | H| k
2
[ Fmh ( lh | ml) + (mh | kk)
(27)
(28)
(mh | ll) + ( mk | hk)]
1 m
1
1 lm
hk | H| h
[ Flk ( mk | ml) + (lk | hh )
2
(29)
(lk | mm ) + (lh | hk)]
1 l
1
1 lm
hk | H| h
2
[ Fmk ( lk | ml) + (mk | hh)
( mk | ll) + (mh | hk)]
1 s
1 lm
hk | H| r 0
1 m
1 lm
hk | H| r
3
1 s
1 lm
hk | H| h
3
1 s
1 lm
hk | H| k
1 m
1 lm
hk | H| k
(31)
(lh | kr)
(hr | lk)
(32)
2
(mh | kr)
(hr | mk)
(33)
2
(ms| kl)
(sl | mk)
(34)
(ms| hl) (sl | mh)
(35)
3
1 l
1 lm
hk | H| r
(30)
2
3
2
3
2
[ Flh + (kk | lh) (mm | lh) + (ml | hm)
(36)
(kl | hk)]
1 l
1 lm
hk | H| k
3
2
[ Fmh + (kk | mh) (ll | mh) + (ml | hl )
(37)
(km | hk)]
1 m
1 lm
hk | H| h
3
2
[ Flk + (hh | lk) (mm | lk) + (ml | mk)
(hl | hk)]
1 l
1 lm
hk | H| h
3
2
(38)
[ Fmk + (hh | mk) (ll | mk) + (ml | lk)
(39)
(hm | hk)]
Procedure dodo.c
Interactions between the doubly excited configurations.
Type 1 - Type 1:
1 ll
1 mm
hh | H| kk 0
(40)
1 mm
1 mm
hh | H| kk (hk | hk)
(41)
1 ll
1 mm
hh | H| hh (lm | lm)
(42)
3
Type 1 - Type 2:
1 ln
1 mm
hh | H| kk 0
(43)
1 ln
1 mm
hh | H| hh 2 (lm | mn)
(44)
1 mn
1 mm
hh | H| kk 0
(45)
1 mn
1 mm
hh | H| hh 2 Fmn + (mm | mn) 2(hh | mn) + (hm | hn)
(46)
1 lm
1 mm
hh | H| hh 2 Fml + (mm | ml ) 2(hh | ml) + (hm | hl)
(47)
Type 1 - Type 3:
1 ll
1 mm
hh | H| jk 0
(48)
1 ll
1 mm
hh | H| jh 0
(49)
1 ll
1 mm
hh | H| hk 0
(50)
1 mm
1 mm
hh | H| jk
(51)
2 (jh | hk)
1 mm
1 mm
hh | H| hk 2 Fhk (hk | hh) + 2(hk | mm) (hm | km)
1 mm
1 mm
hh | H| hj 2 Fhj (hj| hh ) + 2(hj | mm) (hm | jm)
(52)
(53)
Type 1 - Type 4:
1 ln
1 mm
hh | H| jk 0
(54)
1 lm
1 mm
hh | H| jk 0
(55)
1 lm
1 mm
hh | H| hk 2(hk | lm) (kl | mh)
(56)
1 mn
1 mm
hh | H| hk 2(hk | mn) (kn | mh)
(57)
1 lm
1 mm
hh | H| jn 2(jh | ml) (jl | mh)
(58)
1 mn
1 mm
hh | H| jn 2(jh | mn) (jn | mh)
(59)
Type 1 - Type 5:
1 ln
1 mm
hh | H| jk 0
(60)
1 lm
1 mm
hh | H| jk 0
(61)
1 lm
1 mm
hh | H| hk 3 (kl | mh)
(62)
1 mn
1 mm
3 (kn | mh)
hh | H| hk
(63)
1 lm
1 mm
hh | H| jn
3 (jl | mh)
(64)
1 mn
1 mm
hh | H| jn 3 (jn | mh)
(65)
4
Type 2 - Type 2:
1 no
1 lm
hh | H| kk 0
(66)
1 no
1 lm
hh | H| hh (ln | mo) + (lo | mn)
(67)
1 lo
1 lm
hh | H| kk 0
(68)
1 lo
1 lm
hh | H| hh Fmo 2(hh | mo) + (hm | ho) + (ll | mo) + (lo | ml)
(69)
1 nl
1 lm
hh | H| hh Fmn 2(hh | mn) + (hm | hn) + (ll | mn) + (ln | ml)
(70)
1 mo
1 lm
hh | H| hh Flo 2(hh | lo) + (hl | ho) + (mm | lo) + (mo | ml)
(71)
1 mn
1 lm
hh | H| hh Fln 2(hh | ln) + (hl | hn) + (mm | ln) + (mn | ml)
(72)
1 lm
1 lm
hh | H| kk (hk | hk)
(73)
Type 2 - Type 3:
1 nn
1 lm
hh | H| jk 0
(74)
1 nn
1 lm
hh | H| hk 0
(75)
1 ll
1 lm
hh | H| hk 2(ml | hk) (mh | kl)
(76)
1 mm
1 lm
hh | H| hk 2(ml | hk) (hl | km)
(77)
1 ll
1 lm
hh | H| jh 2(ml | hj) (jl | hm)
1 mm
1 lm
hh | H| jh 2(ml | hj) (hl | jm)
(78)
(79)
Type 2 - Type 4:
1 no
1 lm
hh | H| jk 0
(80)
1 mn
1 lm
hh | H| jk 0
(81)
1 no
1 lm
hh | H| hk 0
(82)
1 mn
1 lm
hh | H| hk 2 (ln | hk) 0.5(hl | kn)
(83)
1 mo
1 lm
hh | H| hk 2 (lo | hk) 0.5(hl | ko)
(84)
1 nl
1 lm
hh | H| hk 2 (mn | hk) 0.5(hm | kn)
(85)
1 lo
1 lm
hh | H| hk 2 (mo | hk) 0.5(hm | ko)
(86)
1 mn
1 lm
2 (ln | jh) 0.5(hl | jn)
hh | H| jh
(87)
1 mo
1 lm
hh | H| jh 2 (lo | jh) 0.5(hl | jo)
(88)
5
1 nl
1 lm
2 (mn | jh) 0.5(mh | jn)
hh | H| jh
(89)
1 lo
1 lm
2 (mo | jh) 0.5(mh | jo)
hh | H| jh
(90)
1 lo
1 lm
hh | H| jh 2 (mo | jh) 0.5(mh | jo)
(91)
1 lm
1 lm
hh | H| jk
(92)
2 (hj| hk)
1 lm
1 lm
hh | H| hk 2[(Fhk (hh | hk) + (ll | hk) 0.5(kl | hl) + (mm | hk)
0.5(hm | km)]
(93)
1 lm
1 lm
hh | H| hj 2 [Fhj (hh | hj) + (ll | hj) 0.5(jl | hl) + (mm | hj)
(94)
0.5(hm | jm)]
Type 2 - Type 5:
1 no
1 lm
hh | H| jk 0
(95)
1 nm
1 lm
hh | H| jk 0
(96)
1 no
1 lm
hh | H| hk 0
(97)
1 nm
1 lm
hh | H| hk
3
1 mo
1 lm
hh | H| hk
3
1 nl
1 lm
hh | H| hk
3
1 lo
1 lm
hh | H| hk
3
1 nm
1 lm
hh | H| jh
3
1 mo
1 lm
hh | H| jh
3
1 nl
1 lm
hh | H| jh
1 lo
1 lm
hh | H| jh
2
(lh | nk)
(98)
2
(lh | ok)
(99)
2
(mh | nk)
(100)
2
(mh | ok)
(101)
2
(hl | jn)
(102)
2
3
(hl | jo)
(hm | jn)
(104)
(hm | jo)
(105)
2
3
2
(103)
1 lm
1 lm
hh | H| jk 0
1 lm
1 lm
hh | H| hk
1 lm
1 lm
hh | H| hj
3
(106)
2
3
(hl | kl)
2
(hm | km)
(hl | jl) (hm | jm)
(107)
(108)
Type 3 - Type 3:
1 nn
1 mm
hk | H| gj 0
(109)
1 mm
1 mm
hk | H| gj (gh | jk) + (gk | hj)
1 nn
1 mm
hk | H| hj 0
(110)
(111)
6
1 mm
1 mm
hk | H| hj Fjk 2(mm | jk) + (km | jm) + (hj | hk) + (hh | jk)
(112)
1 mm
1 mm
hk | H| gh Fgk 2(mm | gk) + (km | gm) + (gh | hk) + (hh | gk)
(113)
1 mm
1 mm
hk | H| jk Fhj 2(mm | hj) + (hm | jm) + (kj| hk) + (kk | hj)
(114)
1 mm
1 mm
hk | H| gk Fhg 2(mm | hg) + (hm | gm) + (gk | hk) + (kk | hg)
(115)
1 nn
1 mm
hk | H| hk 0
(116)
Type 3 - Type 4:
1 ln
1 mm
hk | H| gj 0
(117)
1 ln
1 mm
hk | H| hj 0
(118)
1 mn
1 mm
hk | H| gj 0
(119)
1 mn
1
1 mm
hk | H| hj
2
(km | jn)
2(mn | jk)
(120)
1 mn
1
1 mm
hk | H| kj
2
(hm | jn)
2(mn | jh)
(121)
(hm | jn)
2(mn | jh)
(122)
1 mn
1
1 mm
hk | H| kj
2
1 mn
1
1 mm
hk | H| gh
2
(km | gn)
2(mn | gk)
(123)
1 mn
1
1 mm
hk | H| gk
2
(hm | gn)
2(mn | gh)
(124)
1 lm
1
1 mm
hk | H| hj
2
(km | jl)
2(ml | jk)
(125)
1 lm
1
1 mm
hk | H| kj
2
( hm | jl)
2( ml | jh )
(126)
1 lm
1
1 mm
hk | H| gh
2
(km | gl)
2(ml | gk)
(127)
1 lm
1 mm
hk | H| gk 2 (hm | gl) 2(ml | gh)
(128)
1 ln
1 mm
hk | H| hk 2 (ml | mn)
(129)
1 ln
1
1 mm
hk | H| hk
2
[2Fmn 2(hh | mn) + (hm | hn) 2(mn | kk)
+ (km | kn) + 2(mn | mm)]
1 lm
1
1 mm
hk | H| hk
2
[2Fml 2(hh | ml) + (hm | hl) 2(lm | kk)
+ (km | lk) + 2(lm | mm)]
(130)
(131)
Type 3 - Type 5:
1 ln
1 mm
hk | H| gj 0
(132)
1 ln
1 mm
hk | H| hj 0
(133)
1 mn
1 mm
hk | H| gj 0
(134)
1 lm
1 mm
hk | H| hj
3
2
(mk | lj)
(135)
7
1 lm
1 mm
hk |H| kj
3
1 lm
1 mm
hk | H| gh
3
1 lm
1 mm
hk | H| gk
3
1 mn
1 mm
hk | H| hj
3
1 mn
1 mm
hk | H| kj
3
1 mn
1 mm
hk | H| gh
3
1 mn
1 mm
hk | H| gk
3
2
(mh|lj)
(136)
2
(mk | lg)
(137)
2
(mh | lg)
(138)
2
(mk | nj)
(139)
2
(mh | nj)
(140)
2
(mk | ng)
(141)
2
(mh | ng)
(142)
1 ln
1 mm
hk | H| hk 0
1 mn
1 mm
hk | H| hk
3
1 lm
1 mm
hk | H| hk
3
(143)
2
(km | kn)
(hm | hn)
2
(hm | hl)
(km | kl)
(144)
(145)
Type 4 - Type 4
1 no
1 lm
hk | H| gj 0
(146)
1 no
1 lm
hk | H| gj 0
(147)
1 no
1 lm
hk | H| hk (ln | mo) + (lo | mn)
(148)
1 lo
1 lm
hk | H| hj (kj| mo) + 0.5(jo | mk)
(149)
1 mo
1 lm
hk | H| hj (kj| lo) + 0.5( jo | lk)
(150)
1 nl
1 lm
hk | H| hj (kj| mn) + 0.5(jn | mk)
(151)
1 nm
1 lm
hk | H| hj (kj| ln) + 0.5(jn | lk)
(152)
1 lo
1 lm
hk | H| gh (kg | mo) + 0.5(go | mk)
(153)
1 mo
1 lm
hk | H| gh (kg | lo) + 0.5(go | lk)
(154)
1 nl
1 lm
hk | H| gh (kg | mn) + 0.5(gn | mk)
(155)
1 nm
1 lm
hk | H| gh (kg | ln) + 0.5( gn | lk)
(156)
1 lo
1 lm
hk | H| gk (hg | mo) + 0.5( go | mh)
(157)
1 mo
1 lm
hk | H| gk (hg | lo) + 0.5(go | lh)
(158)
1 nl
1 lm
hk | H| gk (hg | mn) + 0.5(gn | mh)
(159)
1 nm
1 lm
hk | H| gk (hg | ln) + 0.5(gn | lh)
(160)
1 lo
1 lm
hk | H| kj (hj| mo) + 0.5(jo | mh)
(161)
8
1 mo
1 lm
hk | H| kj (hj| lo) + 0.5(jo | hl)
(162)
1 nl
1 lm
hk | H| kj (hj| mn) + 0.5(jn | hm)
(163)
1 nm
1 lm
hk | H| kj (hj| ln) + 0.5 (jn | hl)
(164)
1 lm
1 lm
hk | H| gj (kj| lj) + 0.5(hj| gk)
1 lo
1 lm
hk | H| hk Fmo (hh | mo) (kk | mo) + 0.5(hm | ho) + 0.5(km | ko)
+ (ll | mo) + (ml | ol)
(165)
(166)
1 mo
1 lm
hk | H| hk Flo (hh | lo) (kk | lo) + 0.5(hl | ho) + 0.5 (kl | ko)
(167)
+ (mm | lo) + (ml | om)
1 ln
1 lm
hk | H| hk Fmn (hh | mn) (kk | mn) + 0.5(hm | hn) + 0.5(km | kn)
+ (ll | mn) + (ml | nl)
(168)
1 mn
1 lm
hk | H| hk Fln (hh | ln) (kk | ln) + 0.5(hl | hn) + 0.5(kl | kn)
(169)
+ (mm | ln) + (ml | mn)
1 lm
1 lm
hk |H| hj Fkj (hh|kj) (hk|hj) + 0.5 (kl| jl) + 0.5 (km| jm)
(170)
+ (ll|kj) +(mm|kj)
1 lm
1 lm
hk | H| gh Fgk (hh | gk) (hk | gh) + 0.5 (kl | gl) + 0.5 (km | gm)
+ (ll | gk) + (mm | gk)
1 lm
1 lm
hk | H| jk Fhj (kk | hj) (hk | jk) + 0.5(hl | jl) + 0.5(hm | jm)
+ (ll | hj) + (mm | hj)
1 lm
1 lm
hk | H| gk Fhg (kk | hg) (hk | gk) + 0.5(hl | gl) + 0.5(hm | gh)
+ (ll | gh) + (mm | gh)
(171)
(172)
(173)
Type 4 - Type 5
1 no
1 lm
hk | H| gj 0
(174)
1 no
1 lm
hk | H| hj 0
(175)
1 no
1 lm
hk | H| hk 0
(176)
1 lo
1 lm
hk | H| hj
3
1 mo
1 lm
hk | H| hj
3
2
(km | oj)
(177)
2
(kl | oj)
(178)
1 ln
1 lm
hk | H| hj
3
1 mn
1 lm
hk | H| hj
3
1 lo
1 lm
hk | H| gh
3
1 mo
1 lm
hk | H| gh
1 ln
1 lm
hk | H| gh
1 mn
1 lm
hk | H| gh
2
(km | nj)
(179)
2
(kl | nj)
(180)
2
(km | go)
(181)
(kl | go)
(182)
(km | gn)
(183)
3
3
3
2
2
2
(kl | gn)
(184)
9
1 lo
1 lm
hk | H| gk
3
1 mo
1 lm
hk | H| gk
1 ln
1 lm
hk | H| gk
(hm | go)
(185)
(hl | go)
(186)
(hm | gn)
(187)
2
3
3
2
1 mn
1 lm
hk | H| gk
3
1 mo
1 lm
hk | H| jk
3
1 ln
1 lm
hk | H| jk
2
2
(hl | gn)
(188)
2
(hl | oj)
(189)
3
2
(hm | nj)
(190)
1 lm
1 lm
hk | H| gj 0
1 no
1 lm
hk | H| gj
3
(191)
(km | ko)
(hm | ho)
(192)
2
(kl | ko)
(hl | ho)
(193)
2
(hm | hn)
2
1 mo
1 lm
hk | H| hk
3
1 ln
1 lm
hk | H| hk
3
1 mn
1 lm
hk | H| hk
3
1 lm
1 lm
hk | H| hj
3
1 lm
1 lm
hk | H| gh
3
1 lm
1 lm
hk | H| jk
3
1 lm
1 lm
hk | H| gk
3
1 lm
1 lm
hk | H| hk
3
(km | kn)
2
(hl | hn)
2
(jm | km)
2
(kl | gl)
2
(jm | hm)
2
(hl | gl)
2
(mk| mk) + ( hl| hl)
(194)
(kl | kn)
(195)
(kl | jl)
(196)
(gm | km)
(197)
(hl | jl)
(198)
(gm | hm)
(199)
(kl| kl) (hm| hm)
(200)
Type 5 - Type 5:
1 no
1 lm
hk | H| gj 0
(201)
1 no
1 lm
hk | H| hj 0
(202)
1 no
1 lm
hk | H| hk (ln | mo) (lo | mn)
(203)
1 lo
3
1 lm
hk | H| hj 2 (jo | mk) (jk | mo)
(204)
1 mo
1 lm
hk | H| hj
(205)
1 ln
1 lm
hk | H| hj
3
3
2
2
(jo | kl) + (jk | lo)
(jn | km ) + (jk | mn)
(206)
1 mn
3
1 lm
hk | H| hj 2 (jn | kl) (jk | ln)
1 lo
1 lm
hk | H| gh
3
2
(go | km) + (gk | mo)
(207)
(208)
1 mo
3
1 lm
hk | H| gh 2 (go | kl) (gk | lo)
1 ln
3
1 lm
hk | H| gh 2 (gn | km) (gk | mn)
(209)
(210)
10
1 mn
1 lm
hk | H| gh
3
2
(211)
(gn | kl) (gk | ln)
1 lo
3
1 lm
hk | H| gk 2 (go | hm ) (gh | mo)
(212)
1 mo
1 lm
hk | H| gk
3
1 ln
1 lm
hk | H| gk
3
2
(go | hl) (gh | lo)
(213)
2
(gn | hm) (gh | mn)
(214)
1 mn
3
1 lm
hk | H| gk 2 (gn | hl) (gh | ln)
(215)
1 lo
1 lm
hk | H| jk
(216)
3
2
(jo | hm) (hj| mo)
1 mo
3
1 lm
hk | H| jk 2 (jo | hl) (hj| lo)
(217)
1 ln
3
1 lm
hk | H| jk 2 (jn | hm) (hj| mn)
(218)
1 mn
1 lm
hk | H| jk
(219)
3
2
(jn | hl) (hj| ln)
1 lm
1 lm
hk | H| gj (gh | jk) (hj| gk)
(220)
1 lo
3
3
1 lm
hk | H| hk Fmo (hh | mo) + 2 (hm | ho) (kk | mo) + 2 (km | ko)
+ (ll | mo) (lo | lm)
1 mo
1 lm
hk | H| hk Flo (hh| lo)
3
2
(hl| ho) (kk| lo)
3
2
(kl| ko)
(mm | lo) + (mo | lm)
1 ln
1 lm
hk | H| hk Fmn + (hh | mn)
3
2
(hm | hn) (kk | mn)
3
2
(km | kn)
(ll | mn) + (ln | lm)
1 mn
3
3
1 lm
hk | H| hk Fml (hh| ln) + 2 (hl| hn) (kk| ln) + 2 (kl| kn)
+ (mm| ln) (mn| lm)
1 lm
3
3
1 lm
hk | H| hj Fjk (hh | jk) + 2 (kl | jl) (mm | jk) + 2 (jm | km)
(ll | mn) (hk | hj)
1 lm
1 lm
hk | H| gh Fgk (hh | gk)
3
2
(kl | gl) + (mm | gk)
3
2
(gm | km)
(ll | gk) + (hk | hg)
1 lm
1 lm
hk | H| jk Fhj (kk | hj)
3
2
(hl | jl) + (mm | hj)
3
2
(jm | hm)
+ (ll | hj) + (hk | jk)
1 lm
3
3
1 lm
hk | H| gk Fgh + (kk | gh) + 2 (hl | gl) (mm | gh) + 2 (gm | hm)
(ll | gh) (hk | gk)
(221)
(222)
(223)
(224)
(225)
(226)
(227)
(228)
Procedure h.c
Computation of the (ij | kl) integrals with the molecular orbitals and the electron electron repulsion matrix.
11
REFERENCE
1.
P.A. Straub, personal communication.
12