Lattice-Energy Calculations on Organometallic Compounds
Abstract
Lattice-energy calculations in the atom-atom approach have been performed for five organometallic com pounds of previously determined crystal structure. Minimization of energy in terms of positional, orienta tional, torsional and cell parameters gave satisfactory results. Computation of energy as a function of torsion angle gave two-dimensional cross sections which o108-7681/88/030259-04$03.00 present minimum-energy conformations at maximum deviations of 10° from the experimental conforma tions.
Full text
A. M. MILNE AND E. N. MASLEN 259
in e es ing ela ionship indica ed in Fig. 3. Fig. 3(a) is a
sec ion h ough he equa o ial plane con aining Fe,
N(18) and O(11), which also passes close o N(28) and
O(21). Figs. 3(b) and 3(c) a e sec ions pa allel o Fig.
3(a), bu 0.3 A close o he imidazole g oups con ain-
ing N(31) and N(41) espec i ely. I is clea om Fig.
3(b) ha wo o he e ahed al maxima a ound he Fe
a om a e close o he plane con aining he N(31)
imidazole g oup, e en hough one o he maxima does
no each ull heigh in he sec ion shown. Bo h maxima
a e close o ec o s linking he cen al Fe a om o
imidazole H a oms.
As seen in Fig. 3(c), he de o ma ion densi y is no
symme y ela ed o he imidazole g oup con aining
N(41). To b ing ha subsys em in o con o mi y wi h
he a angemen in Fig. 3(b) would equi e o a ion o
he N(41) imidazole g oup by app oxima ely 50 ° abou
he N(31)...N(41) ec o . A ha s age i would be a
igh angles o he N(31) imidazole g oup. In i s ac ual
con igu a ion wi hou ha o a ion, he N(4 l) imidazole
has he con igu a ion cha ac e is ic o he high-spin
o m o he ca ion, as iden i ied in [Fe(salen)(imd)2]PF 6
by Kennedy, McG a h, Mu ay, Skel on & Whi e
(1987).
We pos ula e ha in he ideal low-spin s uc u e he
imidazole ings a e a igh angles o each o he , and
coinciden wi h he planes bisec ing he O(ll)-Fe-
N(18) and he N(18)-Fe-N(28) angles espec i ely.
The ec o s om he Fe o he ou imidazole H a oms
would hen desc ibe a e ahed on simila o ha
de ined by he lobes o excess densi y in he spin
c osso e complex shown in Fig. 3. Howe e , only one
imidazole g oup is ac ually in he con igu a ion which
a ou s low spin. The o he is o ien ed so as o a ou
high spin, which is he eason o he ins abili y in his
s uc u e. I is clea om packing diag ams (no shown)
ha he imidazole g oups a e held in his mixed
con igu a ion by sol en molecules - accoun ing o
hei e ec on he spin ansi ion. This explains he
indi ec na u e o hei ole in he magne ic p ope ies o
he s uc u es con aining hese complexes no ed by
Kennedy, McG a h, Mu ay, Skel on & Whi e (1987).
Thanks a e due o A. H. Whi e, who sugges ed he
p oblem, o supe ising he da a collec ion. This wo k
was suppo ed by he Aus alian Resea ch G an s
Scheme.
Re e ences
DAVIS, C. L. & MASLEN, E. N. (1978).
Ac a C ys .
A34, 743-746.
In e na ional Tables o X- ay C ys allog aphy
(1~74). Vol. IV.
Bi mingham: Kynoch P ess. (P esen dis ibu o D. RCdel,
Do d ech .)
HIRSHEELD, F. L. (1977).
Theo . Chim. Ac a,
44, 129-138.
JOHNSON, C. K. (1965).
ORTEP.
Repo ORNL-3794. Oak R~ !ge
Na ional Labo a o y, Tennessee, USA.
KENNEDY, B. J., MCGRATH, A. C., MURRAY, K. S., SKELTON, B. S.
& WHITE, A. H. (1987).
Ino g. Chem.
26, 483-495.
MASLEN, E. N. & RIDOUT, S. C. (1987).
Ac a C ys .
B43, 352-356.
MASLEN, E. N., RIDOUT, S. C. & WATSON, K. J. (1988).
Ac a
C ys .
B44, 96--101.
STEWART, J. M. & HALL, S. R. (1983).
XTAL Use 's Manual.
Compu e Science Cen e , Uni . o Ma yland, College Pa k,
Ma yland, USA.
STEWART, R. F., DAVIDSON, E. R. & SIMPSON, W. T. (1965). J.
Chem. Phys.
42, 3175-3187.
Ac a C ys .
(1988). B44, 259-262
La ice-Ene gy Calcula ions on O ganome allic Compounds
BY J. SANZ-APARICIO, S. MARTiNEZ-CARRERA AND S. GARCiA-BLANCO
UEI de C is alog a ia, Ins i u o 'Rocasolano', CSIC, Se ano
119, 28006
Mad id, Spain
AND A. CONDE
Depa amen o de Fisica del Es ado SSlido, Ins i u o de CC de los Ma e iales de Se illa, Uni e sidad de Se illa,
CSIC,
41080
Se illa, Spain
(Recei ed 5 Oc obe
1987;
accep ed
21
Janua y
1988)
Abs ac
La ice-ene gy calcula ions in he a om-a om app oach
ha e been pe o med o i e o ganome allic com-
pounds o p e iously de e mined c ys al s uc u e.
Minimiza ion o ene gy in e ms o posi ional, o ien a-
ional, o sional and cell pa ame e s ga e sa is ac o y
esul s. Compu a ion o ene gy as a unc ion o o sion
angle ga e wo-dimensional c oss sec ions which
0108-7681/88/030259-04503.00
p esen minimum-ene gy con o ma ions a maximum
de ia ions o 10 ° om he expe imen al con o ma-
ions.
In oduc ion
Packing analysis ollowing he a om-a om app oach
(Ki aigo odsky, 1973) has been used in de e mining he
c ys al s uc u e o a la ge a ie y o o ganic com-
© 1988 In e na ional Union o C ys allog aphy
260 LATTICE-ENERGY CALCULATIONS ON ORGANOMETALLIC COMPOUNDS
Table 1.
Non-bonded po en ial unc ion coe icien s
Fo mixed in e ac ions, he geome ic ule o a ac i e and
epulsi e e ms sepa a ely is:
Aab = (AaAb) u2, Bab = (BaBb) /2, Ca , = (C a + Cb)/2.
In e ac ion A (kJ A 6) B(kJ) C(A-~)
Ta-Ta 27713.1 728721 2.92
Nb-Nb 27713.1 728721 2.92
Fe-Fe 11437.3 275299 3.03
CI-CI 5977.4 922944 3.62
S-S 4552.0 216386 3.30
P-P 5982.9 923602 3-62
Si-Si 5982.9 923602 3.62
O-O 836.0 779152 4.55
N-N 3176.8 4405572 3.60
C-C 1759.8 299288 3.68
H-H 121.2 20482 4.29
pounds, including molecules con aining a oms o he
han C, H o O (Villa es, Jim nez-Ga ay, Conde &
M~quez, 1976; Es ada, Conde & Mh quez, 1983).
Minimiza ion o ene gy in e ms o he o sional
angles is cu en ly being pe o med in con o ma ional
analysis wi h he aim o elucida ing s uc u e-ac i i y
ela ionships in compounds possessing some chain
lexibili y.
In he p esen pape , he alidi y o he a om-a om
model o he po en ial ene gy o in e ac ion be ween
molecules o o ganome allic compounds is in es i-
ga ed. Fo his pu pose, i e compounds, whose
s uc u es ha e been p e iously sol ed, we e chosen:
(I), [Fe( /5-CsHs){SP(=S)(OP i)2 }(CO)2] (Sanz-
Apa icio, Ma inez-Ca e a & Ga cia-Blanco, 1986a);
(II), [Fe( -CsMes){SP(=S)(OP ~)2 }(CO)2] (Sanz-
Apa icio, Ma inez-Ca e a & Ga cia-Blanco, 1986b);
(III) [Fe( /5-C 5Hs){SP(=S)(OE )2 }(CO)2] (Sanz-
Apa icio, Ma inez-Ca e a & Ga cia-Blanco, 1987);
(IV), [Nb{N(SiMea)2}(NSiMe3)(g-OCH3)C1] (An i-
iolo, O e o, U banos, Ga cia-Blanco, Ma inez-
Ca e a & Sanz-Apa icio, 1988); (V), [Ta( /5-CsMes) -
{CHEP(Ph)2Me}CI 4] (Fandos, G6mez, Royo, Ga cia-
Blanco, Ma inez-C a e a & Sanz-Apa icio, 1987).
The heo e ical equilib ium s uc u e o all o hese
compounds was de e mined by la ice-ene gy mini-
miza ion, he ene gy being calcula ed wi hin he
a om-a om app oach. Compa isons be ween expe i-
men al and calcula ed s uc u es we e used o assess he
eliabili y o he me hod.
The shape o he c ys al ene gy su ace in he
su oundings o he minimum was also s udied, by
ca ying ou la ice-ene gy calcula ions as a unc ion o
o sional angle.
Desc ip ion o he calcula ions
La ice-ene gy calcula ions we e pe o med using he
compu e p og am
PCK6
(Williams, 1972), in which
he la ice ene gy o a c ys al is app oxima ed by a
pai wise sum o e non-bonded in e a omic po en ial
unc ions o a oms in di e en molecules, ollowing he
Buckingham o m
U( ) = -A -6 + B
exp(-C ); a dis-
ance o 6 A was se as he summa ion limi . The
a iables conside ed in he calcula ions we e six
igid-body deg ees o eedom and he pa ame e s o he
uni cell. Some molecula lexibili y was allowed in he
o m o in e nal o a ions abou bonds (sub o a ions),
and in amolecula con ac s we e e alua ed using
sub o a ion po en ials o he cosEe ype, o allow o
conjuga ion ene gy. The o a ions conside ed wi hin
each compound a e shown below.
g I
CH 3 CH 3 CH 3 CH 3
R! R,
CHj-Si~ l 3 Si-CH]
2
R,~ R, / o..)_R, N~"
: , I l / CHs
Fe ~S~P_ CI-Nb=N-.~Si ~CH 3
/ u~°-) -R2 I c~,
CO CO S h OCH s
(I): R l = H, R 2 = P I (IV)
(II): R l = Me, R 2 = P I
(III): R 1 = H, R 2 = E
Ta
C1 C~ 2- CI
Ph~'~Ph
l- l | 3
CH3
( )
S a ing om he expe imen al c ys al s uc u e, he
s uc u al pa ame e s we e op imized o gi e a heo e i-
cal equilib ium s uc u e o checking agains he
expe imen al one. Fo he po en ial unc ions co -
esponding o Ta, Nb, Fe, Si and P a oms, pa ame e s
de e mined by Mason & Rice (1954a) o he co -
esponding noble gases we e used wi h he assump ion
ha he an de Waals adii a e simila . Ene gy alues
ob ained in his way a e meaningless in an absolu e
sense and hey a e no gi en. Fo he Cl...Cl
in e ac ions, pa ame e s we e aken om Mason &
K ee oy (1955) and o S...S in e ac ions, om
Rinaldi & Pawley (1973). Fo O and N a oms,
coe icien s i ed by Giglio, Liquo i & Mazza ella
(1969) and Go e s (1975) espec i ely we e applied.
Finally, C...C and H...H in e ac ions we e e alua ed
by Mi sky (1976) po en ial unc ions. Fo mixed
in e ac ions, he geome ic mean ule o sepa a e a ac-
i e and epulsi e e ms (Mason & Rice, 1954b) was
used. This ule leads o he ollowing exp essions:
A,~ b = (AaAb)u2, Bah =
(BaBb) u2
and
Cab = (C a + Cb)/2.
All he independen pa ame e s a e lis ed in Table 1.
I is gene ally accep ed ha he elec os a ic ene gy
has a small in luence on he molecula posi ion o
c ys als, because i is a a he slowly a ying unc ion
SANZ-APARICIO, MART NEZ-CARRERA, GARCIA-BLANCO AND CONDE 261
o he s uc u e pa ame e s. This asse ion was es ed in
ou o ganome allic compounds by conside ing Coulom-
bic ene gy. The e ec i e cha ge on each a om was
e alua ed empi ically by means o an exp ession
(Sko czyk, 1976) which akes accoun o he pe -
cen age ionic cha ac e , depending on he di e ence in
elec onega i i y be ween bonded a oms. All he a oms
we e conside ed o be in an oxida ion s a e o 0.
Since H a oms a e c i ical in de e mining molecula
in e ac ions, hey we e included in he calcula ions, bu
hei posi ions we e shi ed o a C-H bond leng h o
1.08 ]k, keeping he expe imen al angles. All a emp s
using expe imen al H-a om posi ions led o poo e
esul s.
To in es iga e he ene gy su ace in he icini y o he
minimum, he la ice ene gy o each compound was
compu ed as a unc ion o he abo e-men ioned
sub o a ions and mapped as he wo-dimensional c oss
sec ions o he h ee-dimensional ene gy su ace. I he
p oposed ene gy app oach is alid, hen he su ace
mus ha e a minimum in he neighbou hood o he
expe imen ally de e mined con o ma ion. Sub o a ions
o a om g oups we e ca ied ou by means o he
o a ion ma ix
(In e na ional Tables o X- ay C ys-
allog aphy,
1972):
[cos~+Ll2(1--cosc ) L1L2(1-coso + L3sina)
R = IL~L2(1--cosa)--L3sina
cosa + L22(1--cos ~)
LLaLl(1-cosc ) + L2sin x
L2La(1-cosa)-L~sina
L3L
l( 1-cosc )-L2sina "]
L#3(1-cosa) + L~sina|
COS~ + L32(1--cos~ )
J
whe e
L IL2L a
a e he Ca esian di ec ion cosines o he
o a ion axis, which is aken coinciden wi h he bond
joining he subg oup o he molecule, and c is he angle
o o a ion abou ha axis, coun e clockwise being
posi i e. Calcula ions o ene gy we e pe o med wi h-
ou conside ing Coulombic in e ac ions.
Resul s and discussion
Resul s o ene gy minimiza ion o he expe imen al
s uc u e a e gi en in Table 2, bo h wi hou and wi h
conside a ion o elec os a ic in e ac ions. The molecu-
la posi ion and o ien a ion a e exp essed in e ms o
he displacemen o he cen e o mass (A m) and he
magni ude o he molecula o a ion (A0), which is
gi en by he o a ion ma ix e e ed o he ine ia axes
o he molecule. The inc emen s on each o he
sub o a ion (d /) and he cell pa ame e s ob ained a he
end o he p ocess a e gi en as well. Also a ac o is
included, o mula ed as:
R = Y.{[X e]
-[X ]}/~.[X
e]
which exp esses he ag eemen be ween he expe imen-
al coo dina es
(X e)
and he heo e ical coo dina es
calcula ed by he minimiza ion p ocess
(X ).
Table 2.
Resul s o ene gy minimiza ion
T ansla ion, (a)
~,a ,~ (A) (b)
Ro a ion, (a)
~a01 (o) (b)
Sub o a ions
IA , I (o) (a)
iA 21 (o)
I
A 31 (o)
(b)
Cell pa ame e s
Obse ed
a (A)
b (A)
c (A)
#(°)
Calcula ed
a (h)
b (h)
c (h)
#(o)
(I) (II) (III) (IV) (V)
O. 15 O. 13 0.49 0-03 0.00
O- 16 O. 16 0-40 0-00 0.00
3.4 3-9 2-9 2-2 1-7
2.9 3.1 2-3 0.0 2-1
4-5 1-6 2.2 0.5 0.1
3.4 20.9 2-9 0.5 0.3
31.4 18.2 5.6 0.3 0.0
3.3 2.8 0.7 0-1 0.0
0.0 23.9 1.9 0.0 0.1
31.1 20.2 3.8 0.0 0-0
13.189(4) 13.718(1) 7.440(1) 10.236(i) 13.247(1)
8.636(2) 11.090(1) 14.545(1) 9.789(1) 20.335(3)
16-113 (4) 14.985 (l) 14-454 (l) 21.201 (3) 9.492 (2)
94.19(4) 98.162(2) 94.415(3) 102.67(1)
(a) 13.111 13.614 7.226 10.247 13.249
8.526 10.982 14.279 9.788 20.336
16.039 14.918 14.203 21.191 9.490
98.03 98.69 96.07 104.06
(b) 13. I05 13.544 7.169 10.237 13.248
8.525 I 1.004 14.153 9.789 20.336
16-031 14.936 14.225 21.200 9-491
97.40 97.72 95.24 103.54
(a) 0.05 0.03 0-06 0.01 0.01
(b) 0.05 0.03 0.04 0.00 0.01
No es: (a) Coulombic in e ac ions we e no conside ed, (b) Coulombic
in e ac ions we e conside ed.
All ansla ional shi s a e unde 0.2 A excep hose
o compound (III), which a e la ge (0-49 and 0.40 A
espec i ely); o a ional angles a e small, wi h a
maximum alue o 4 ° in compound (II). Sub o a ions
i well; only [A 3] o compound (I) is abou 30 ° and
[A E] and JA 3] o compound (II) a e abou 20°. Cell
pa ame e s a e ep oduced wi h be e han 4%
accu acy and disag eemen be ween obse ed and
calcula ed coo dina es is unde 6% in all cases.
In iew o he esul s ob ained, and since he la ges
de ia ions co espond o sub o a ions, all calcula ions
we e epea ed wi h pa ame e s ixed
(i.e.,
ene gy was
minimized wi h espec o ansla ion, o a ion and cell
cons an s). Howe e , hese condi ions led o a wo se i
o he calcula ed s uc u e o he expe imen al one,
including hose cases whe e sub o a ions did no
p esen such a la ge de ia ion, as in compound (III). In
pa icula , ansla ion and cell pa ame e s exhibi
no ably la ge inc emen s, he las eaching a shi o
13%.
Since empe a u e e ec s and la ice ib a ions we e
no aken in o accoun , he ene gy minimiza ion led, as
expec ed, o dec eases o cell olumes in all cases excep
compound (V), whe e a ia ions a e insigni ican .
As can be deduced om Table 2, he in luence o he
Coulombic in e ac ions on he op imized pa ame e s is
no e y clea . While some pa ame e s a e sligh ly
imp o ed, o he s p esen la ge shi s when elec o-
s a ic ene gy is included in he calcula ion. In gene al,
ag eemen is simila in bo h cases, bu he e is a end o
262 LATTICE-ENERGY CALCULATIONS ON ORGANOMETALLIC COMPOUNDS
a be e i wi h conside a ion o Coulombic con-
ibu ions, pa icula ly in compound (IV). The esul s
a e, howe e , good enough wi hou conside ing elec o-
s a ic ene gy o jus i y i s omission, especially as i s
e alua ion inc eases no ably he compu a ion ime
equi ed.
The mo e sa is ac o y esul s ob ained o com-
pounds (IV) and (V) han o compounds (I), (II) and
(III) may depend on he ac ha hea y a oms a e mo e
sc eened in (IV) and (V), which could be a ibu ed o
he high b anching o he SiMe 3 ligands in compound
(IV), o o he la ge coo dina ion a ound he Ta a om in
compound (V).
Fig. 1 shows he wo-dimensional c oss sec ions o
he ene gy su ace o each compound, in he h ee main
p ojec ions. Con ou s a e calcula ed wi h an accu acy
o 5 ° o he angles l, 2 and z" 3 a ying wi hin he
ange +15 ° om he poin co esponding o he
expe imen ally obse ed con o ma ions [poin (0,0,0) in
T 3
~3
0-5~ 0 5 10 15 -5 0 5 10 15
L ,o ,o
~' (I) , (II)
5
T 3
0 5 10 15
,
%2
(III)
~3
-5 0 5 10 15 -10-5 0 5 10
,1''°
0 - - 5
i
• , (i ) ~, ( )
Fig. 1. C oss-sec ion U( , 2, 3), h ough he ene gy su ace
minimum poin , o compounds (I), (iI), ill), (IV) and (V).
he maps]. Nea he minimum, calcula ions ha e been
pe o med wi h an accu acy o 1 ° . The minimum
posi ion on each sec ion is designa ed by a c oss.
Calcula ions o he ene gy su ace as a unc ion o he
h ee sub o a ions led o minima a poin s (7,4,-3),
(-3,1,10), (-1,7,-2), (-1,9,-10)and (-8,-8,3) o
l Eh.angles o compounds (I), (II), (III), (IV) and (V)
espec i ely.
In summa y, la ice-ene gy calcula ions as a unc ion
o o sion angle lead o sa is ac o y esul s, as ene gy
minimiza ion does, when he ene gy is e alua ed in he
a om-a om model. This unexpec ed ac , in iew o he
oughly app oxima ed po en ial unc ions used, could
be explained in e ms o he hea y a oms being
sc eened. In ac , packing ene gy due o he me al a om
is abou 20% o he o al ene gy in compounds (I), (II)
and (III) and less han 10% in compounds (IV) and (V).
Al hough addi ional wo k is needed, he esul s gi en in
his pape sugges ha he a om-a om app oach may
be used o o ganome allic compounds when limi ed
accu acy is needed.
We hank P o esso M. Ma inez-Ripoll o
assis ance in p og amming and P o esso J. Fayos o
aluable discussions.
Re e ences
ANTX~OLO, A., OTERO, A., URBANOS, F., GARCiA-BLANCO, S.,
MARTiNEZ-CARRERA, S. & SANZ-APARICIO, J. (1988). J.
O ganome . Chem. In
he p ess.
ESTRADA, M. D., CONDE, A. & M.~RQUEZ, R. (1983).
Ac a C ys .
B39, 739-742.
FANDOS, R., GOMEZ, M., ROYO, P., GARCiA-BLANCO, S.,
MARTiNEZ-CARRERA, S. & SANZ-APARICIO, J.
(1987).
O ganome allics,
6, 1581-1583.
GIGLIO, D., LIQUORI~ A. M. & MAZZARELLA, L. (1969).
Le .
Nuo o Cimen o,
1, 135-139.
GOVERS, H. A. J. (1975).
Ac a C ys .
A31, 380-385.
In e na ional Tables o X- ay C ys allog aphy
(1972). Vol. II, p.
62. Bi mingham: Kynoch P ess. (P esen dis ibu o D. Reidel,
Do d ech .)
KITAIGORODSKY, A. ]. (1973).
Molecula C ys als and Molecules.
New Yo k, London: Academic P ess.
MASON, E. A. & KREEVOY, M. M. (1955). J.
Am. Chem. Soc.
77,
5808-5814.
MASON, E. A. & RICE, W. E. (1954a).
J. Chem. Phys.
22, 843-851.
MASON, E. A. & RICE, W. E. (1954b).
J. Chem. Phys.
22, 522-534.
MIRSKY, K. (1976).
Ac a C ys .
A32, 199-207.
RINALDI, R. P. & PAWLEY, G. S.
(1973).
Nuo o Cimen o
B,
16,
55-62.
SANZ-APARICIO, J., MARTiNEZ-CARRERA, S. & GARCiA-BLANCO, S.
(1986a).Ac a C ys .
C42, 1121-1123.
SANZ-APARICIO, J., MARTiNEZ-CARRERA, S. & GARCiA-BLANCO, S.
(1986b).
Z. K is allog .
175, 195-202.
SANZ-APARICIO, J., MARTiNEZ-CARRERA, S. & GARCiA-BLANCO, S.
( 1987).
A c a C ys .
C 43, 2009-2011.
SKORCZYK, R. (1976).
Ac a C ys .
A32, 447-452.
VILLARES, P., JIMI~.NEZ-GARAY, R., CONDE, A. & Mh, RQUEZ, R.
(1976).
Ac a C ys .
B32, 2293-2296.
WILLIAMS, D. E. (1972).
Ac a C ys .
A28, 629-635.