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Theoretical study of the molecular ions SiH−5 and SiH−3
Physics 8 (1975) 384 -390 0 North.Holland Publishing Company
Chcmicd
THEORETICAL
STUDY
01: THE MOLEClJLAR
IOKS SiHg AND SiH3
‘BH,
-
BzH6.
385
mum for the DJ, geometry. 3 short-lived
i.e.. !h
SiHf
may form
comples.
IIon $I!,‘) I$;),
since
(+R’ @‘lHl
$g’ *f’,
The product 2. hlethod
$A.$ I$:)
douhlc substitutions
=Ef)
f EL:).
conlains,
Ilowever.
311quadruples
bcsidcs the
ansing from SIIIIUI-
laneous double SU~SII~U~IO~Son system A and B. As
of electron correlarlon
For the treatment from ;! standard
Cl
according
Elccr ron corrclanon
treatment.
Tl~e canonical HF
HF computalmn.
hlOs nre then localized
Boys [6].
we sl;1rl
to the method 01
1s Jscounlcd
ry. w
Since only doubly sthst~~u~cd confjgll.
espcct lo xcounl
in an obvious
I~ICD-
3 Cl WI~II lhc
AIIS~LZ
(4).
In Ills prcsenl
work wc Iluve included
rl~c vA2nce
AE”)
irom
111[he lrealnienl
of rexiion
hciween
rhc tlcvlaIion
Anorher
l PNOsl of
by wlllch
IlIe
corrclarion
1l1e corrcspondmg
lrealmenl sIra!o
(2 ).
but consisienr
way rhe
WIIICII arc due to
and lligher substitutions
clusIers arising from rhe doubles.
This IS
(CEP.4) proposed by Meyer
p31r iurlc-
171. s,ec Aso [SLjl. In this
c3sc one 113s3clu311y (see. e.g.. ref. [JI): tcrl’!\
A*D
= EcI;P,\
A
+
EcEi’,~ II .
(8)
for the bulk of
(9)
it is still soniewl~31 uns2Iisfx~oQ
since c(2) has an incorrect of electrons
lo AEi of rexl1on
[7.R],
the Ansntz (4~ xcoun~ effects
IO 6.8 kcal/
done in the coupled elccrron par approsimalion
slldl noI concern us here. the reader
IO 111elirerature
Although
(7) it bus been shown 1113i
(6) and (7) miotms
way to avoid 111cproblem just discussed is
hon. I.e.. \ve perform 3. so callcd PNO Cl c0nipu131101i.
is referred
(7)
Ibc unlinked
of IIIC Cl cqua.
gL, and p,
For the delails Jnd more recllnical matIers of Ihis rnerhod. which
distance.
= E”,
quddruplc
HF lUOs <, and q, arc replaced 3s the pair
n3Iur31 orbilals
doubles only for lhc sys-
large in[crnuclcar
IO include in 3n approximaIc
only.
[ion we choose the orbitals
occupied
3 Cl wilh
lion of electron correlation (jl
IO redusc 111~ dunension
In order
manner
mol since in this cxc E,\2j, - (E.f) t f$)) = 6.8 kcal/ mol. corrcspondmg roughly lo 4.3’;;~of rile coniribu-
+ E(Z)_
shell correlaIion
lions and perform
Iems A + B at sufficien4y
,JEf’,
WIIICII y~eltls rhe encr: = El,,
1101
neglrct I~C quadruple subsr~tu-
NL’cun conswenlly
compute
noration.
(1)
fl2,
in penrr2l
Iiwe denote Ihe resulring energy by E.y.&,“!,,u’e rlwn
ior the bulk ofcorrclulion
cfcecrs by JUSI performmg
in E&is one an
rhaI rq. (5) yields reliable reaction rncrgieb. In
order IO Ireal AB and A f B in a compaable
for by ;I
rations contribulc’ irl firs! order of perlurlarion
Ilie lotler are negleclcd rxpccl
[-l.Sb].
which
of rexlioil
dependence
on tl~e number
may be quite ScrIouS in IlIe
sl~oulll be close to lhc rcsulls from cq. (7).
energies. In order lo dcmon-
this shortcoming we consider 3 reaction A + B -
AB. where A. B and AB have closed shell stxcs.
sponding wave functions Ilk2 Ansal or activarion
and energies obtained
(4). One may then c3lcul3te energ)’ M?(z)
according
Let
from
this way
AB on an unequal Ihe energy !$I)
one treats footing.
t ,!$)
he
the reaction
type functions
to
systems
A + B snd
This is due to the fact 11~1
corresponds
For Ihe present compuMions set of contrxted
(6) Proceeding
3. Basis set considerations
IO Ihe wavefunc-
we used an extended
gaussian lobe functions. were construcccd
[Ol. For silicon we starled with 3 HuzinJga 7pJ WI conlructed 3X!).
p-. d- and f-
as described in ref. (101 ( I Is,
lo a (7,-l) set nanielyf5.6X1/4.
This basis was IlIen augmented
by two com-
plete d sets w1tl17 = 0.69 and q = 0.73 and an fsct
with n = 0.48. For hydrogen we used ;1 Huzinaga 5s (3 I 1) and 3 P set with q = 0.4. This basis set for Si and H ~3s determined ;II optimizing 111s HF t valsnce shdl Codation energy ol’.%H4. It was used for SiHi ( D31, 3lld Qv
geome[ry)
-H-
and
computation.
for the
SiH4
For the H-
f’ragment
SitlOOlh
S fuM-
tion with 7j = 0.03 and 3150 usd rj = 0.1 (insrul Of 7 = 0.4) for the p Set on H. These sh3nges arr: nccess3ry to get an accuratr’ descrtptlon d H- \V~IK~ has 3 rather spread 0u1 electron distribution. Our HF and to131 encrgles ior H- xc Ellr(H) = -o.-%7j 3U 3nd E(2)
= -O.j’l
1 3~ \v[litjl n1.1)’ be comP.ircd
tu the COT-
respondmg +SZIC~vslues ol’-0.-%79!
3U (HF IlKlIt) [I I] and -0.fi177 j au [ I?]. respectively. \Vllllite and Spialtcr obtained E,,,(H-) = -0.-17.. Ti which is Jbour 9 kcai/mol above the HF limit whsreby one overestlmates iEr of reaction ( I) by roughly the s3me amount. The addittonai
smooth
5 functions
are oilittle
im-
portance in SIHJ. Addillon oi IIIM functions at the ~a1 H atoms In tllc Djh structure lowers the HF CYIerg? by 0.1 k~l/mol only which is clearly ne$lgible. The negative charge in SiH; IS more or kss drlocalircd over the whole molecule and IIIC 5s b3sij is obviousI> fleslble enough to give 3 proper dessriprlon of a shghtly charged hydrogen. For the SIH~ computation
X
( I .63 A);
@i-tlb,)
= I.55
.d
( I .63 .A).
lI(Si-H,,)
= I .57 A (not given).
SIH;
I C,,):
ill the Sill,
1111115lz~ttcr GIST we
augmented the buslj by XI additIona
= I.59
d(SiH,,)
The &H,,,SiH,, very littIc
was fised at 1Ol.j” [ I 1, since it IIJS on the energy. A comparison of
intlucnce
tllc ab inttio with the CNDO/z results shows that tllibond distances by rou_cllly 0.07 ,_I
latter ovcresrimates
on the avrrage. For SiH4 we used the esperimcntal SI-H disrance of I .-!S .a. which dtffers by less rhatl 0.00-l A front the one determined on the HF le~cl In order IO discuss reaction (3) we also had to detcrmlne IIIC stru;lure of SiH; for which no esperimental d2ta are wailable. It turns out Ihat SiHjr has ;Lpyr3n,i~~l structure with C;, symmetry. The Structure pardill. eters .IS obtained on the HF level for the C,, and II~C planar SlHj
case 3re as I’ollows:
D3b IC3,
1:
tl(Si-H1
=
I.575
2IHSiH
=
97”37’;
=
I .-El Ii.
SiWi
(DjhI:
r/iS~-Hj
(where one also expects
3 rath?r spread out b10 as discussed In the treatment of CHi (1311 we added 311addItional s and p set with either n = 0.03 and further a d;-: function with 7 = 0.1 at the silicon atom. In the H, computation required UI the discussion oireastion i;) we used 3 p set with 17= 0.65 (instead of n = 0.4). which is optimal for H,.
In table I we report our HF orbltal energies tor SiHi
and SIH~.
h10 is now lower d le;)
and Spialter
aroms
tion of the
which
allows
the structure parameters of
md Wlter
SiH,
(D3,,).
for CI more
different
is protisbl)’
3 full p set on III? byprecise
&scrlp.
IO this h!O. TIE
contribution
situ-
in PH, where the 7p- CL)D-
stabilizes the 211; more than in SiHi
II131 Ez3i’ = -0.3962
S$ In the &I, and C,, gcornetry WI~~MI tile HF apFrollmalion. The CKD0/3 r?jults obtained by \{‘llbite
and Spialter
we included
hydrogen
ation is somewhat trtbution
to Wilhitc
that
except that the 2ei
the ?a’,’ h10. The lowering oi
than
as compared
dro&cn
4. Results
The order of the c’s is in qremtwI
with that of Wilhite
due 10 the fact
We first redeternnnzd
A.
(note
in planar PH, as compared N
Ez3: = - 0.0083 in planar SiHi ). Consequcnrly Ill? ki’is lower than the Ze’, in PH, even ii p functions on H are not included
arc given in pZk?nllleses for comparison.
The computed HF.
PNO
energies
3s obtained
Cl and CEPA
method
are collected
2 for all systems
giirs for SiH; than
those
[ 141.
total
investigated.
are about reported
Our
computed
IO kcnl/mol=
in ref. [I
]. &hoUph
0.016
wthlrl
the
in tlble
HF ener. 3” kwr
We used an
387
--_____
.._._ ~
la1
-5
32, ?.tt ‘e 2c 5tr
_l--ll-
_.
I.
___.-..
_ ._-.
OS?1I -1.1680
-290.7x4 -290.7707 -291.3193 -291.9153 -291.9-709 -79 I.8929 distance
1’00XI
~-
_.-
I
cm1
-
I_..---..-
8700
-3.977 I -3.9771 - 3.9765 -0.363 1 -rLf334 -0.2314 -0.0605
lc
lc
Iwo Cl km)
_-
-685197
?a*
.
ktu)
. _- - -.
_I__-_-
-0.5111
-1.1680 -390.7429 -290.7847 -29 I.3599 -291.94?9 -29 I .9390 4919115
__“_
-
i3ut in tlic plewr
ewnple. From the RWJI~S CUIII~IIBI in t&k f we following inwrsion barriers -I~, for SiH_; :
obr3ln
tfle
kcai/nlol.
HI-‘:
xi
= ‘7.3
PWCl;
Xi
= 17.1 kcal/mol.
I IO)
CEPA:
xj
= 26.1 kc~l/ntoi.
tx,
IIS)
R:o~h et 31. [ISI qtw~ed an irrvcrsinn barrizr or’>0 6 k~~l/mol without Tl~c dcvistion
giving details of their con~pu[~ti~R.
tiorn our result could be dtv IO the
tkt thst these ~utltors ernpfofed ;i too restr~& (see. e.g.. the discussion in ref. [ 131). \Ye lirsr note the snwll effect of corr~lallon barrier which is analogous to rlle results
for
b3slj un tile
111epseuri~~.
rmtion for SiHT 1or the corresponding harrirrs ior Pli~ ,CH, . NH3 . OHS [ I 7, f 9 I. TIIC ntwrston bxncr in SiHi
is about 8.8 kcrtl/lnol
srxaller tktn for PH,
I~~i
= 35 kcrtllrnnt. dS. [ 1‘).10)). .~l~llOU~l Ill? IllW~ sion bxriers in the second per!od 3x cons~dwbl~ Iargr than in the first period (CHj: _I~~ = I 2 k~i/ rnol, NH3:5-6 kcal/n~ol [1.171) WClind tile SJIW trend in both wes: the barrier decrcxscs in gome from
the
nelnd
t0 th? nQ3tkv IOJJ energy of SiH) is 5 4 I\&‘Iw~
SySIenl
T[le correlation
kirger Ifian for SiHl ~ltllou~il IOO different
in electronic
horh rn~tlca~lzs 315 noi
strtxlure.
The rason ior
tlus is essentially the increased differential
over13Pb+
tween the rather difiuse lone pair and 111~St--H bond pairs in SiH, which results in 3n incrrawd JntrrPfir correlation energy. Due to the snlaller +M-i 67.6’ in SiHi versus 109.5” III SiH4 ) ant aisn IinJj 3n increase in the interbond
ioter3ct~on which appc3rstD
be less imporkmt.
however.
With reference
RlCk. IA comparison
lo rrilclion
ior llle rcxhon
ing results
AEf
IIF:
L’tlcrg~ M,:
= t 5.6 kcul/mol.
AL-(
CEPA:
(3) we ol1t~111tl,e iollo\+
For ihis reaction
(II)
= + 6.3 kcd/moI. WC lid
(12)
311dmos~ ul23nirlgl~js
ClTeClS. 1n cuntrJs1
ence ofcorrddtion
ior rcac‘rion ( I). SCC Cqs.( 13)-t 15). In boll1 reuctikins 1~2 increase tile number of nest negllbour bond InIcr-
aslions which lrcnds lo stabrlits 111o Ml; but due lo lilt unusually large corwhtton SIH~.
3s jus1 discussed.
ior rextion
(3).
tron correlation
TINScsampk
oII ALE’,
if energy
wit11 chuical
differ-
of correl2lion
3ccur32y
by analoflcs
is still
is not stabk
IlIe possiblllry
minimum
beeu shown metry
lhar
by HoTfmunu
allo\rcd
c1 A.
~3111s cxibt
;comc~ry.
[ 2 I 1 IILII
symmetry
small Iwrier
Tl~e endotlwrnliciry
oi rcaclion
sn131lcr than
kcal/mol
tron .i-center 1l1e central
bond
tl1an in PH5. iA = PH3. potential planar
SiHi
tSIHj
PH3
result
jxentcr
) dcpcnds
) = 0.0083
The
smaller
;I”. czaitPHJ
srrongcr is the S-center
since
Ii--A-
h10 of tllC c3js 1112~2,
isoh1hlO 01‘
111eIP - EZ~‘,
b = 0.796::
ilu - ihC
E = 0.0305
II inlruIly ulwur
3u 1n all systelns
cncrgy
of IIIC Ion? p3ir
7:; is still
01’31)out
~onAlcr~blc
(or inlcrbonil) runce from
1101
I7 ;III ISIII,,
0.001
XI (SItI-Sill
SIII,
iu SiH,)
in
10 0.0107
). WC h~vc wriiicd
HU
ly
011 tl~c
cllargc 01’Ills: corrcspondm~ 15 csssntially
vir1ually
IIMI
on tll;
due 10 the chnges
tincr_pics siikc In order
Ilic mtrapar
to cslimlte
terms one could
Icruls
311’
kinds 01
tllc cf’fecl
of Il;l:
iti a iirst upproxi1113~1o~~ as-
1lw1r sum is propor11onaI
pjirb of xljxrn1
rC;tctton
in lhc imcr.
JI ICISI for ~hc d1t’fcrcnr
constwl
I I~oiI&.
orhlrals.
O~CICC~~WI correhtton
pair corrcla11on Si -I
ot’ 1hc
cncr_ck!r E,,. i *i.
t Ini tlic magnitude dc,, . i + j. dcpcnds distmse hwccu the wutrords of
cwntiully
sncrp.3
devi~hons
correlation
- lone p3ir irl SIH~
IU 1hc number
bonds or lone pairs. This would
plum tl~c el‘iw~ of corrclatioil
011 AL-f
of cs-
for reaction
(I I
of ( 21wlicre one Ills 3n iucrcssc of nest nc1gMour bond 1111crxt1ons.
Due to the ~~nusually large 1111cr.
pair conlrihution
in Sll-1,. ws find. I~ow~v~r. no net
cl’fccr 0i clcclrun
correl311011
on AE,
ior rc3cliun
(3).
intcrcskd
in
5. Conclihions
In 11~2pr2S2lll work we were mainly IWO kinds oi problems.
rat)’ ofa CEPA
pair corrh silicon
hydrides. to be localized IiF
01 rcx1ion cncrpics [like rcx( I 1and (3) or hxrrcrs for inversion.
cc)nlpuI:lIIon
see eqs. ( I j)-(
eii for the various
Tllc Eij are defined with reference
S1
hiarc
mallcr (6 = 0 027s 3~) tlhu Lx 311
U’c ;i~;d. Iwwcvcr.
(i) Th
6ond.
3 we have summarized
cuiiw-
II
4.3. Pair correluliorr ericryies In table
wllicli
bul this deviation
tion cncrfiea
lion energies [7,8b]
Cl ~‘a
\vliicli
OII tlw wnwtwu
occupied
(in the prescn1
or SiHi).
bond
crucially
and
st.~ble In SIH~
more
IS. of course. expcc1sd
of the highest
molecule
Icvcl 2nd
IWO
too l;ll”C
SIIIW
[ I G] The 4clcc~
tlie a’i131 Iiytlro;c’us
of :1 klectron
(IP)
ed cen1raI
Si- Ii I~I~iIil
imcrpalr
is. howcvcr.
OII the IiF
15 considerably
Tlus
he stability
between
atlIe:
de~ompos~l~o~~ 01
ior the CEPA
atoms
WC clpccts
ior lliis cw.
wluc
1s 4lglitly
Tl~e cfrect
mok-
\Vc bud to CIIOOS~
the interprttt21ion. cncrgics
311 avcrugc
pJlr
may desow
(3)
for tlie corresponding
-, ’ ticul/mol where SE = 4_._ = 36.2
311 ABj
Aon_r whicll
into .AB, + B,. For this mson
PHj.
1’: from
(Ilontl
IWO syw
no1 provide arc. 01 Courw.
of slcctrons
lrs~cd in tal~le 3. Tl~e 1ntrupdir
over 0.0061
II 1~~
hi&
lllc sm3ll cl1angcs of Ilir
p31r rorrelulion
TIIC latter
tlw poLenli31 surl’xC
no or at most 3 ratlier
X
U’e firs1 nolc hd
SIH;)
respect ICI (3).
wtl~
ior the DQ
zulc. with either D3t, or C,, pox
qucnrly would olwurc
inspection SiHj
AIIIIOII~II tllere
on lhc to131 numl)cr
(a11
10 ~eh-
10 llic c3110nic31
would
in tllcse mol~~lcs.)
II,
ed moksulcs.
has 3 local
depend
iiitcrpair
siuce it is too d311gcro1h
r’rror of ;I few kcd/molb. the efl;ct
cncrgy 01
refcrrlng
tllc CEPA c’s for this purpose SIIICC flit
111SIlli
shows ;IgJin that L’LX.
has lo be included
encch arc lo bc compulcd estimate
cowph.
tlbxc IS no ncI ell;-sI
quiIc dificrcnt
~rltlu-
1~ the results
oft,,
hlOs of Sill, _Sil I, and SIII, . . . muA Inlorrn3tlon slncc 1I1cx
for
17). and pscudorotation]
few kcal/mol
11)’ 211d some propertics
In order of SiH<
w1tl1 317 XW-
lo dcrcmiine and SiHi
parisonof ~llescresul1s wit11 those of rchcd pounds Ilke PH,. PHJ . CHI.
Ille skhilsnd comCOIII-
References D.L. H’ilflitc and L. SPiaitcr. J. Am. Chem. Sac. 95 (1973) 2100. A. Rauk, LG. ALICIIand Ii. Clrmenti, J. Chcm. PhYc 52 (1970)4133. A. Dcdwi. A. Vc~fl~d and B. Rooq, in: thcmfc3f sn,f biocl~emiC3t reactivity. The Jcrus&m symposra on 4usn, turn chcmisrry and biochemistry. Vol. VI (fsracf ~~c~,lG_ my OI Scicnccs. Jerusalem. 197-I) p. 371. R. ~Ihlrichs, Thcorcr. Chim. Acts 35 11974159. IS\ C.W. Msppr’s, S.A. Friedman and T.P. Fchlner. J. pfr!, Them. 74 (1970) 3307, see 3Jso J.H. 1fall. D.S. Xtlryniek and 1Y.N. Ltpwomb. Inor: Chtm. 1 I If 97% 3 IX. (61 J.M. Foswr and SF. BOYS.Rev. Uod. Phys. 32 (196(l)
300. i?f W. Skyerr J. Chcm. Phys. 58 (1973) 1017. ISJ a. R. Ahltichr snd F. Driesslq
Throrc!. Chim, ..jctl
36 r1975) 775. b. R. Ahlrichr, H. Lischks, V. Sra~mmler and \\‘. ~ur~~f. nigg. J. Chem. Ph~s. 62 (1975) 1225. 191 F. Drlcsslrr and R. Ahlrichs, Chrm. Phys. LclrL\rb 33 11973) 571. f 101 S. Huzinqa. ~ppro~irn~t~ a10m1c junctions 1, II. Technical Report, Division oi Thcorelical Chenisfr~. Tie Unrvcr~tp of‘Alberta f 1971). f I I { C.J.Roothxin. t&. Sachs 2nd A.W. Wcis,. Rev. !fod Phys. 32 11970) 186. \I?_) C.L. P&ws. Phys. Rev. I I? (1958) 1649. [ 131 F. Dricsslcr, R. Xhlrichs. V. Slxmnrlcr and W. Kurzcl. nig Thcorrt. Chim. Act3 30 (1973) 315. J141 A. Rauk, L.C. Men and K. Mirlow. J. Rm. Chcm. So<. 94 (1971) 3035. [IS\ A. Sttich snd A. Vciflxd. J. Am. Chcm. Sot. 95 (1973) w1. [ 161 r. MI ssd W. Kurzelnigg. J. Am. Chem. Sot.. In press. [ 171R. Ahlrichs. F. Dricssfrr, H. Lischka. V. Stacmmfcr and it’. butz&4gg.
3. AmChem.
Sot. 062 (1975) 1135.
j 181 A. Rwli. C. Allen and i;. Misbw, Angw. Chcmrs 81 I 1970) 453.
Chcmicd
THEORETICAL
STUDY
01: THE MOLEClJLAR
IOKS SiHg AND SiH3
‘BH,
-
BzH6.
385
mum for the DJ, geometry. 3 short-lived
i.e.. !h
SiHf
may form
comples.
IIon $I!,‘) I$;),
since
(+R’ @‘lHl
$g’ *f’,
The product 2. hlethod
$A.$ I$:)
douhlc substitutions
=Ef)
f EL:).
conlains,
Ilowever.
311quadruples
bcsidcs the
ansing from SIIIIUI-
laneous double SU~SII~U~IO~Son system A and B. As
of electron correlarlon
For the treatment from ;! standard
Cl
according
Elccr ron corrclanon
treatment.
Tl~e canonical HF
HF computalmn.
hlOs nre then localized
Boys [6].
we sl;1rl
to the method 01
1s Jscounlcd
ry. w
Since only doubly sthst~~u~cd confjgll.
espcct lo xcounl
in an obvious
I~ICD-
3 Cl WI~II lhc
AIIS~LZ
(4).
In Ills prcsenl
work wc Iluve included
rl~c vA2nce
AE”)
irom
111[he lrealnienl
of rexiion
hciween
rhc tlcvlaIion
Anorher
l PNOsl of
by wlllch
IlIe
corrclarion
1l1e corrcspondmg
lrealmenl sIra!o
(2 ).
but consisienr
way rhe
WIIICII arc due to
and lligher substitutions
clusIers arising from rhe doubles.
This IS
(CEP.4) proposed by Meyer
p31r iurlc-
171. s,ec Aso [SLjl. In this
c3sc one 113s3clu311y (see. e.g.. ref. [JI): tcrl’!\
A*D
= EcI;P,\
A
+
EcEi’,~ II .
(8)
for the bulk of
(9)
it is still soniewl~31 uns2Iisfx~oQ
since c(2) has an incorrect of electrons
lo AEi of rexl1on
[7.R],
the Ansntz (4~ xcoun~ effects
IO 6.8 kcal/
done in the coupled elccrron par approsimalion
slldl noI concern us here. the reader
IO 111elirerature
Although
(7) it bus been shown 1113i
(6) and (7) miotms
way to avoid 111cproblem just discussed is
hon. I.e.. \ve perform 3. so callcd PNO Cl c0nipu131101i.
is referred
(7)
Ibc unlinked
of IIIC Cl cqua.
gL, and p,
For the delails Jnd more recllnical matIers of Ihis rnerhod. which
distance.
= E”,
quddruplc
HF lUOs <, and q, arc replaced 3s the pair
n3Iur31 orbilals
doubles only for lhc sys-
large in[crnuclcar
IO include in 3n approximaIc
only.
[ion we choose the orbitals
occupied
3 Cl wilh
lion of electron correlation (jl
IO redusc 111~ dunension
In order
manner
mol since in this cxc E,\2j, - (E.f) t f$)) = 6.8 kcal/ mol. corrcspondmg roughly lo 4.3’;;~of rile coniribu-
+ E(Z)_
shell correlaIion
lions and perform
Iems A + B at sufficien4y
,JEf’,
WIIICII y~eltls rhe encr: = El,,
1101
neglrct I~C quadruple subsr~tu-
NL’cun conswenlly
compute
noration.
(1)
fl2,
in penrr2l
Iiwe denote Ihe resulring energy by E.y.&,“!,,u’e rlwn
ior the bulk ofcorrclulion
cfcecrs by JUSI performmg
in E&is one an
rhaI rq. (5) yields reliable reaction rncrgieb. In
order IO Ireal AB and A f B in a compaable
for by ;I
rations contribulc’ irl firs! order of perlurlarion
Ilie lotler are negleclcd rxpccl
[-l.Sb].
which
of rexlioil
dependence
on tl~e number
may be quite ScrIouS in IlIe
sl~oulll be close to lhc rcsulls from cq. (7).
energies. In order lo dcmon-
this shortcoming we consider 3 reaction A + B -
AB. where A. B and AB have closed shell stxcs.
sponding wave functions Ilk2 Ansal or activarion
and energies obtained
(4). One may then c3lcul3te energ)’ M?(z)
according
Let
from
this way
AB on an unequal Ihe energy !$I)
one treats footing.
t ,!$)
he
the reaction
type functions
to
systems
A + B snd
This is due to the fact 11~1
corresponds
For Ihe present compuMions set of contrxted
(6) Proceeding
3. Basis set considerations
IO Ihe wavefunc-
we used an extended
gaussian lobe functions. were construcccd
[Ol. For silicon we starled with 3 HuzinJga 7pJ WI conlructed 3X!).
p-. d- and f-
as described in ref. (101 ( I Is,
lo a (7,-l) set nanielyf5.6X1/4.
This basis was IlIen augmented
by two com-
plete d sets w1tl17 = 0.69 and q = 0.73 and an fsct
with n = 0.48. For hydrogen we used ;1 Huzinaga 5s (3 I 1) and 3 P set with q = 0.4. This basis set for Si and H ~3s determined ;II optimizing 111s HF t valsnce shdl Codation energy ol’.%H4. It was used for SiHi ( D31, 3lld Qv
geome[ry)
-H-
and
computation.
for the
SiH4
For the H-
f’ragment
SitlOOlh
S fuM-
tion with 7j = 0.03 and 3150 usd rj = 0.1 (insrul Of 7 = 0.4) for the p Set on H. These sh3nges arr: nccess3ry to get an accuratr’ descrtptlon d H- \V~IK~ has 3 rather spread 0u1 electron distribution. Our HF and to131 encrgles ior H- xc Ellr(H) = -o.-%7j 3U 3nd E(2)
= -O.j’l
1 3~ \v[litjl n1.1)’ be comP.ircd
tu the COT-
respondmg +SZIC~vslues ol’-0.-%79!
3U (HF IlKlIt) [I I] and -0.fi177 j au [ I?]. respectively. \Vllllite and Spialtcr obtained E,,,(H-) = -0.-17.. Ti which is Jbour 9 kcai/mol above the HF limit whsreby one overestlmates iEr of reaction ( I) by roughly the s3me amount. The addittonai
smooth
5 functions
are oilittle
im-
portance in SIHJ. Addillon oi IIIM functions at the ~a1 H atoms In tllc Djh structure lowers the HF CYIerg? by 0.1 k~l/mol only which is clearly ne$lgible. The negative charge in SiH; IS more or kss drlocalircd over the whole molecule and IIIC 5s b3sij is obviousI> fleslble enough to give 3 proper dessriprlon of a shghtly charged hydrogen. For the SIH~ computation
X
( I .63 A);
@i-tlb,)
= I.55
.d
( I .63 .A).
lI(Si-H,,)
= I .57 A (not given).
SIH;
I C,,):
ill the Sill,
1111115lz~ttcr GIST we
augmented the buslj by XI additIona
= I.59
d(SiH,,)
The &H,,,SiH,, very littIc
was fised at 1Ol.j” [ I 1, since it IIJS on the energy. A comparison of
intlucnce
tllc ab inttio with the CNDO/z results shows that tllibond distances by rou_cllly 0.07 ,_I
latter ovcresrimates
on the avrrage. For SiH4 we used the esperimcntal SI-H disrance of I .-!S .a. which dtffers by less rhatl 0.00-l A front the one determined on the HF le~cl In order IO discuss reaction (3) we also had to detcrmlne IIIC stru;lure of SiH; for which no esperimental d2ta are wailable. It turns out Ihat SiHjr has ;Lpyr3n,i~~l structure with C;, symmetry. The Structure pardill. eters .IS obtained on the HF level for the C,, and II~C planar SlHj
case 3re as I’ollows:
D3b IC3,
1:
tl(Si-H1
=
I.575
2IHSiH
=
97”37’;
=
I .-El Ii.
SiWi
(DjhI:
r/iS~-Hj
(where one also expects
3 rath?r spread out b10 as discussed In the treatment of CHi (1311 we added 311addItional s and p set with either n = 0.03 and further a d;-: function with 7 = 0.1 at the silicon atom. In the H, computation required UI the discussion oireastion i;) we used 3 p set with 17= 0.65 (instead of n = 0.4). which is optimal for H,.
In table I we report our HF orbltal energies tor SiHi
and SIH~.
h10 is now lower d le;)
and Spialter
aroms
tion of the
which
allows
the structure parameters of
md Wlter
SiH,
(D3,,).
for CI more
different
is protisbl)’
3 full p set on III? byprecise
&scrlp.
IO this h!O. TIE
contribution
situ-
in PH, where the 7p- CL)D-
stabilizes the 211; more than in SiHi
II131 Ez3i’ = -0.3962
S$ In the &I, and C,, gcornetry WI~~MI tile HF apFrollmalion. The CKD0/3 r?jults obtained by \{‘llbite
and Spialter
we included
hydrogen
ation is somewhat trtbution
to Wilhitc
that
except that the 2ei
the ?a’,’ h10. The lowering oi
than
as compared
dro&cn
4. Results
The order of the c’s is in qremtwI
with that of Wilhite
due 10 the fact
We first redeternnnzd
A.
(note
in planar PH, as compared N
Ez3: = - 0.0083 in planar SiHi ). Consequcnrly Ill? ki’is lower than the Ze’, in PH, even ii p functions on H are not included
arc given in pZk?nllleses for comparison.
The computed HF.
PNO
energies
3s obtained
Cl and CEPA
method
are collected
2 for all systems
giirs for SiH; than
those
[ 141.
total
investigated.
are about reported
Our
computed
IO kcnl/mol=
in ref. [I
]. &hoUph
0.016
wthlrl
the
in tlble
HF ener. 3” kwr
We used an
387
--_____
.._._ ~
la1
-5
32, ?.tt ‘e 2c 5tr
_l--ll-
_.
I.
___.-..
_ ._-.
OS?1I -1.1680
-290.7x4 -290.7707 -291.3193 -291.9153 -291.9-709 -79 I.8929 distance
1’00XI
~-
_.-
I
cm1
-
I_..---..-
8700
-3.977 I -3.9771 - 3.9765 -0.363 1 -rLf334 -0.2314 -0.0605
lc
lc
Iwo Cl km)
_-
-685197
?a*
.
ktu)
. _- - -.
_I__-_-
-0.5111
-1.1680 -390.7429 -290.7847 -29 I.3599 -291.94?9 -29 I .9390 4919115
__“_
-
i3ut in tlic plewr
ewnple. From the RWJI~S CUIII~IIBI in t&k f we following inwrsion barriers -I~, for SiH_; :
obr3ln
tfle
kcai/nlol.
HI-‘:
xi
= ‘7.3
PWCl;
Xi
= 17.1 kcal/mol.
I IO)
CEPA:
xj
= 26.1 kc~l/ntoi.
tx,
IIS)
R:o~h et 31. [ISI qtw~ed an irrvcrsinn barrizr or’>0 6 k~~l/mol without Tl~c dcvistion
giving details of their con~pu[~ti~R.
tiorn our result could be dtv IO the
tkt thst these ~utltors ernpfofed ;i too restr~& (see. e.g.. the discussion in ref. [ 131). \Ye lirsr note the snwll effect of corr~lallon barrier which is analogous to rlle results
for
b3slj un tile
111epseuri~~.
rmtion for SiHT 1or the corresponding harrirrs ior Pli~ ,CH, . NH3 . OHS [ I 7, f 9 I. TIIC ntwrston bxncr in SiHi
is about 8.8 kcrtl/lnol
srxaller tktn for PH,
I~~i
= 35 kcrtllrnnt. dS. [ 1‘).10)). .~l~llOU~l Ill? IllW~ sion bxriers in the second per!od 3x cons~dwbl~ Iargr than in the first period (CHj: _I~~ = I 2 k~i/ rnol, NH3:5-6 kcal/n~ol [1.171) WClind tile SJIW trend in both wes: the barrier decrcxscs in gome from
the
nelnd
t0 th? nQ3tkv IOJJ energy of SiH) is 5 4 I\&‘Iw~
SySIenl
T[le correlation
kirger Ifian for SiHl ~ltllou~il IOO different
in electronic
horh rn~tlca~lzs 315 noi
strtxlure.
The rason ior
tlus is essentially the increased differential
over13Pb+
tween the rather difiuse lone pair and 111~St--H bond pairs in SiH, which results in 3n incrrawd JntrrPfir correlation energy. Due to the snlaller +M-i 67.6’ in SiHi versus 109.5” III SiH4 ) ant aisn IinJj 3n increase in the interbond
ioter3ct~on which appc3rstD
be less imporkmt.
however.
With reference
RlCk. IA comparison
lo rrilclion
ior llle rcxhon
ing results
AEf
IIF:
L’tlcrg~ M,:
= t 5.6 kcul/mol.
AL-(
CEPA:
(3) we ol1t~111tl,e iollo\+
For ihis reaction
(II)
= + 6.3 kcd/moI. WC lid
(12)
311dmos~ ul23nirlgl~js
ClTeClS. 1n cuntrJs1
ence ofcorrddtion
ior rcac‘rion ( I). SCC Cqs.( 13)-t 15). In boll1 reuctikins 1~2 increase tile number of nest negllbour bond InIcr-
aslions which lrcnds lo stabrlits 111o Ml; but due lo lilt unusually large corwhtton SIH~.
3s jus1 discussed.
ior rextion
(3).
tron correlation
TINScsampk
oII ALE’,
if energy
wit11 chuical
differ-
of correl2lion
3ccur32y
by analoflcs
is still
is not stabk
IlIe possiblllry
minimum
beeu shown metry
lhar
by HoTfmunu
allo\rcd
c1 A.
~3111s cxibt
;comc~ry.
[ 2 I 1 IILII
symmetry
small Iwrier
Tl~e endotlwrnliciry
oi rcaclion
sn131lcr than
kcal/mol
tron .i-center 1l1e central
bond
tl1an in PH5. iA = PH3. potential planar
SiHi
tSIHj
PH3
result
jxentcr
) dcpcnds
) = 0.0083
The
smaller
;I”. czaitPHJ
srrongcr is the S-center
since
Ii--A-
h10 of tllC c3js 1112~2,
isoh1hlO 01‘
111eIP - EZ~‘,
b = 0.796::
ilu - ihC
E = 0.0305
II inlruIly ulwur
3u 1n all systelns
cncrgy
of IIIC Ion? p3ir
7:; is still
01’31)out
~onAlcr~blc
(or inlcrbonil) runce from
1101
I7 ;III ISIII,,
0.001
XI (SItI-Sill
SIII,
iu SiH,)
in
10 0.0107
). WC h~vc wriiicd
HU
ly
011 tl~c
cllargc 01’Ills: corrcspondm~ 15 csssntially
vir1ually
IIMI
on tll;
due 10 the chnges
tincr_pics siikc In order
Ilic mtrapar
to cslimlte
terms one could
Icruls
311’
kinds 01
tllc cf’fecl
of Il;l:
iti a iirst upproxi1113~1o~~ as-
1lw1r sum is propor11onaI
pjirb of xljxrn1
rC;tctton
in lhc imcr.
JI ICISI for ~hc d1t’fcrcnr
constwl
I I~oiI&.
orhlrals.
O~CICC~~WI correhtton
pair corrcla11on Si -I
ot’ 1hc
cncr_ck!r E,,. i *i.
t Ini tlic magnitude dc,, . i + j. dcpcnds distmse hwccu the wutrords of
cwntiully
sncrp.3
devi~hons
correlation
- lone p3ir irl SIH~
IU 1hc number
bonds or lone pairs. This would
plum tl~c el‘iw~ of corrclatioil
011 AL-f
of cs-
for reaction
(I I
of ( 21wlicre one Ills 3n iucrcssc of nest nc1gMour bond 1111crxt1ons.
Due to the ~~nusually large 1111cr.
pair conlrihution
in Sll-1,. ws find. I~ow~v~r. no net
cl’fccr 0i clcclrun
correl311011
on AE,
ior rc3cliun
(3).
intcrcskd
in
5. Conclihions
In 11~2pr2S2lll work we were mainly IWO kinds oi problems.
rat)’ ofa CEPA
pair corrh silicon
hydrides. to be localized IiF
01 rcx1ion cncrpics [like rcx( I 1and (3) or hxrrcrs for inversion.
cc)nlpuI:lIIon
see eqs. ( I j)-(
eii for the various
Tllc Eij are defined with reference
S1
hiarc
mallcr (6 = 0 027s 3~) tlhu Lx 311
U’c ;i~;d. Iwwcvcr.
(i) Th
6ond.
3 we have summarized
cuiiw-
II
4.3. Pair correluliorr ericryies In table
wllicli
bul this deviation
tion cncrfiea
lion energies [7,8b]
Cl ~‘a
\vliicli
OII tlw wnwtwu
occupied
(in the prescn1
or SiHi).
bond
crucially
and
st.~ble In SIH~
more
IS. of course. expcc1sd
of the highest
molecule
Icvcl 2nd
IWO
too l;ll”C
SIIIW
[ I G] The 4clcc~
tlie a’i131 Iiytlro;c’us
of :1 klectron
(IP)
ed cen1raI
Si- Ii I~I~iIil
imcrpalr
is. howcvcr.
OII the IiF
15 considerably
Tlus
he stability
between
atlIe:
de~ompos~l~o~~ 01
ior the CEPA
atoms
WC clpccts
ior lliis cw.
wluc
1s 4lglitly
Tl~e cfrect
mok-
\Vc bud to CIIOOS~
the interprttt21ion. cncrgics
311 avcrugc
pJlr
may desow
(3)
for tlie corresponding
-, ’ ticul/mol where SE = 4_._ = 36.2
311 ABj
Aon_r whicll
into .AB, + B,. For this mson
PHj.
1’: from
(Ilontl
IWO syw
no1 provide arc. 01 Courw.
of slcctrons
lrs~cd in tal~le 3. Tl~e 1ntrupdir
over 0.0061
II 1~~
hi&
lllc sm3ll cl1angcs of Ilir
p31r rorrelulion
TIIC latter
tlw poLenli31 surl’xC
no or at most 3 ratlier
X
U’e firs1 nolc hd
SIH;)
respect ICI (3).
wtl~
ior the DQ
zulc. with either D3t, or C,, pox
qucnrly would olwurc
inspection SiHj
AIIIIOII~II tllere
on lhc to131 numl)cr
(a11
10 ~eh-
10 llic c3110nic31
would
in tllcse mol~~lcs.)
II,
ed moksulcs.
has 3 local
depend
iiitcrpair
siuce it is too d311gcro1h
r’rror of ;I few kcd/molb. the efl;ct
cncrgy 01
refcrrlng
tllc CEPA c’s for this purpose SIIICC flit
111SIlli
shows ;IgJin that L’LX.
has lo be included
encch arc lo bc compulcd estimate
cowph.
tlbxc IS no ncI ell;-sI
quiIc dificrcnt
~rltlu-
1~ the results
oft,,
hlOs of Sill, _Sil I, and SIII, . . . muA Inlorrn3tlon slncc 1I1cx
for
17). and pscudorotation]
few kcal/mol
11)’ 211d some propertics
In order of SiH<
w1tl1 317 XW-
lo dcrcmiine and SiHi
parisonof ~llescresul1s wit11 those of rchcd pounds Ilke PH,. PHJ . CHI.
Ille skhilsnd comCOIII-
References D.L. H’ilflitc and L. SPiaitcr. J. Am. Chem. Sac. 95 (1973) 2100. A. Rauk, LG. ALICIIand Ii. Clrmenti, J. Chcm. PhYc 52 (1970)4133. A. Dcdwi. A. Vc~fl~d and B. Rooq, in: thcmfc3f sn,f biocl~emiC3t reactivity. The Jcrus&m symposra on 4usn, turn chcmisrry and biochemistry. Vol. VI (fsracf ~~c~,lG_ my OI Scicnccs. Jerusalem. 197-I) p. 371. R. ~Ihlrichs, Thcorcr. Chim. Acts 35 11974159. IS\ C.W. Msppr’s, S.A. Friedman and T.P. Fchlner. J. pfr!, Them. 74 (1970) 3307, see 3Jso J.H. 1fall. D.S. Xtlryniek and 1Y.N. Ltpwomb. Inor: Chtm. 1 I If 97% 3 IX. (61 J.M. Foswr and SF. BOYS.Rev. Uod. Phys. 32 (196(l)
300. i?f W. Skyerr J. Chcm. Phys. 58 (1973) 1017. ISJ a. R. Ahltichr snd F. Driesslq
Throrc!. Chim, ..jctl
36 r1975) 775. b. R. Ahlrichr, H. Lischks, V. Sra~mmler and \\‘. ~ur~~f. nigg. J. Chem. Ph~s. 62 (1975) 1225. 191 F. Drlcsslrr and R. Ahlrichs, Chrm. Phys. LclrL\rb 33 11973) 571. f 101 S. Huzinqa. ~ppro~irn~t~ a10m1c junctions 1, II. Technical Report, Division oi Thcorelical Chenisfr~. Tie Unrvcr~tp of‘Alberta f 1971). f I I { C.J.Roothxin. t&. Sachs 2nd A.W. Wcis,. Rev. !fod Phys. 32 11970) 186. \I?_) C.L. P&ws. Phys. Rev. I I? (1958) 1649. [ 131 F. Dricsslcr, R. Xhlrichs. V. Slxmnrlcr and W. Kurzcl. nig Thcorrt. Chim. Act3 30 (1973) 315. J141 A. Rauk, L.C. Men and K. Mirlow. J. Rm. Chcm. So<. 94 (1971) 3035. [IS\ A. Sttich snd A. Vciflxd. J. Am. Chcm. Sot. 95 (1973) w1. [ 161 r. MI ssd W. Kurzelnigg. J. Am. Chem. Sot.. In press. [ 171R. Ahlrichs. F. Dricssfrr, H. Lischka. V. Stacmmfcr and it’. butz&4gg.
3. AmChem.
Sot. 062 (1975) 1135.
j 181 A. Rwli. C. Allen and i;. Misbw, Angw. Chcmrs 81 I 1970) 453.