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Molecular electrostatic potentials in transition-metal chemistry: an example
Volume 84, number 3
MOLECULAR
CHEMICAL PHYSICS LETTERS
ELECTROSTATIC
POTENTIALS
15 December 1981
lN TRANSITION-METAL
CHEMISTRY:
AN EXAMPLE Helge JOHANSEN Depzrtmcnt of Chemrcal Phyncs, The Technrcal Unnwnty
of Denmarh, DK-2300
Lyngby, Denmark
Rccelved 28 August 198 1
Usmg the protonation of Co(CO)i as an example, the apphubhty of the clectrostalc potenhal has been assessed by comparison with Hartrec-Fock calculahons It ISconcluaed that elcctrostatlc potentrals are useful for mapping the coordmation sphere of a transluon-metal atom, ~MII~ dlrectlons and distances, but that rclatrve cnerpes arc less rehable.
l_ Introduction
The reaction
Computational quantum mechamcs has reached a h3gh level of accuracy for molecules involvmg first and second row elements The extension to transltlonmetal compounds has been cumbersome, not m pnnc,.ple but m practice. The mam reasons are the followmg (1) The computation of Integrals with lughcr I quantum numbers are more time-consummg. (2) A
Co(CO),
“realistx” compound has many ligands, thus many integrals have to be computed and handled. (3) The systems usually have open shells. (4) There w1I1 be many levels close together III both hgands and metal,
thus large configuration interaction expansions are necessary. (5) With m,my hgands, there will be many degrees of freedom
to cope with m a geometry optimrzatlon. The use of pseudo-potential methods reduces the number of mtegrals to be computed and handled, but most of the abovementioned problems remam. First-pnnclple computatron of pathways m a cheml-
cai reactron involvmg a transItion-metal compound IS thus bound to be a maJor task for some tune. Lu77rted basis sets and small CI expansions WIU preva& and short-cuts WIU be welcome. The present study has Its emphasis on point (5) above, and usmg a sunple example, the aim is to assess the usefulness of molecular
electrostatic
poten-
teals irk the search for mtermehates and pathways in catalfic reactlons involvmg transition-metal atoms. 580
+ H’ -f HCO(CO)~
has been used as the example. It IS a sunple system, and we already have a geometry optunization ava& able from a study of the hydroformylation reaction [I] More detailed computational mformatlon may be found
m ref. [l] _ The basis set IS modest.
(C, O/7, 3) (H/4) contracted as (CO/~, 3,2) (C, O/3,2) (H/2) m a split-valence shell fashion. It was, however, Judged to be adequate for a prehmmary Investigation. Two pathways for the protonation of Co(CO), , calculated m the restricted Hartree-Fock approxunation, have been compared wth the correspondmg electrostatic potential for Co(CO), . Both Co(CO)z and HCo(CO)d have been the subject of a number of previous computational studies, SW e.g. ref. [?I. (Co/ 1 I, 8,4)
2. Results and discussion Frg. 1 shows the electrostatic potenhal (EP) for Co(CO), m a conformation as found by electron dtifraction for H$iCo(C0)4 [3]. This conformation was used prevJously for the Co(CO), fragment in various X-COG systems [l] _ The geometry of the ion Itself JS T,, and an EP has been calculated for this symmetry, but the present diagram is more informa-
0 009-26 14/81/0000-0000/C
02.75 0 198 1 North-Holland
Volume 84, number 3
CHEMICAL PHYSICS LElTERS
15 December 1981
,014 h F go12 s
SOlO i
h
au Fig. 1. Ele&ostatx potenti for Co(CO), in a plane containmg Co, an axnl and an equatorial CO group, Cs,, con-
formahon Contours are equllstant au, lowest deplcted contour IS-0.20 -0.11 au. Coordrnatcs are in au.
tive. Three types of minima axml position above cobalt,
Fig. 2 Comparison
of total energy (solid bne) and ekctrc(dash&l line) for the mcial approach The functions are depicted r&tive to their respective energy minima.
and separated by 0.01 au and the h&best
static potent&
are found: one in the one III connection with
the lone pair behind oxygen for each CO group, and one between the axial and two equatorial CO groups. There are three minima
(length)
of the last type, and they,
wrth 2.99 au found III the energy variahon calculation [ 11, and 2.94-2.97 au as determined expenmentaily [4,5] (wrth uncertainties of 0.03-0.08 au). Also the second 1
with the fist minimum, form four equiva111the Td conformation, corresponding to the four faces of a tetrahedron. The axral mimmum for the EP IS found at a dis-
derivatives
and fig. 2.
are very sxmilar as seen from table
The depth of the minimum IS, however,
together
much smaller for the EP (about one third). TMs in&-
lent muuma
cates that the shape of the potential energy curve is dominated by the electrostatic potential, and that the other components 111an energy decomposition analysrs [7] are large but add up to be relatively constant
tance of 3.02 au from cobalt.
This 1s to be compared
Table 1 Comparison
of t&d
cobalt atom, &_:
energy and ele~t~ost&~ potential for two duections of approach x0: position Of the! mirdnllll’n r&tie energy/potenti mmimum (for Etot relative to Co(CO)& All values are in au
-
X0
---_I_ axial direction HCo(C0)4 Co(COxi
(C~V). Etot (C3”h CP
experunent
Gin
t0 the
Curvature
299
-0.623
0.12
3.02
-0.198
0.10
294 a), 3.00 b,
-
0.14 =)
7.45
-0.425
0.65
7.73
-0.208
0.23
carbonyl dxection HCo(C014 Co(C% a) Ref. [4] (1.556(18)
A).
(T&, EtOt ud),
EP
b, Ref. [S] (L59 f 0.04 A)_
c) Ref. [6] (222 md/A).
581
over the region of mterest.
A slmrlar result for the
shape of the EP curve was proton affiity for anunes,
found In a study of the
alcohols and ethers [8]. The EP mmirna behmd the oxygen atoms are shghtly lower than the axial mrurnum, but the protonation does not occur at these positlons (the skucture of HCO(CO)~ has been dlscussed extensively m the Literature. see e.g. ref. [4] and references therem).
To mvestigate this pomt further, Hartree-Fock type calculations were performed for a proton approactung the cartonyl group in tetrahedral Co(CO), along the duectlon of a C-O bond The muwnum for the change UI total energy IS found to be only 68% of that for the axial approach, thus confirming the expenmental structure [4,5] _ But when the total energy 1s compared with the EP, taole 1, it IS seen that both the
supply quahtative reformation about the posstbihties involved It 1s the shape of the potential and not the absolute value which appears to be most useful.
References
111 N. Fonnesbech, J. HJortkJaer and H. Johanscn, intern. 3. Quantum Chem. 12 SuppL 2 (1977) 95. N. Fonncsbech, LIC Techn
versrty of Denmark, [21 W-C Nieuwpoort. EJ. Baerends and
the shape of the curve. electrostatic potential IS already useful m the study of crystal packmg [9], and In bm-orgamc
stu&es of protonation, hydration, catlon bmdmg. etc. [lo]. The present mvestlgahon mdlcates that the electrostatic potential 1s also useful m mappmg out the immediate coordmation sphere of a transItIonmetal atom tn a complex, predctmg possible pathways for reactlons and geometries of compounds.
The dxect hnk of hydrogen to the metal atom IS surpnsmgly well described,, and the spcclal nature of the d orbltals may play an important part m tbs. A more formal energy decomposltlon analysis should be undertaken m order to settle this question. For the two cases studled, the EP accounted for respectively 32% and 49% of the total energy. The
potent&
582
can therefore
a pamcular
not be used alone to single or pathway, but they
conformation
Tbeas, The Techrucal (1979).
Urn-
met. Chem. 129 (1977) 221; D.A. Pensak and R.J. McKmney, Inorg Chem. 18 (1979) 3407, B.D. El-Issa and A. Hmchbffe, I. MoL Struct 69 (1980) 305, V. BeUagamba, R. Ercoh, A. Gamba and GEX. Suffnti,
Chem. 190 (1980) 381. Roblctte, GM Shcltick, R.N.F. SiiqWin, B.1. Aylett and J.A. Campbell, J. Organomet. Chem. 14
domrnate The
Lyngby
Philips Res Rept 20 SuppL (1965) 6, P. ROS MoL Phys 30 (1975) 1735. J.P. Gnma, F. Chophn and G. Kaufmann, J. Organo-
location of the muumum and the curvature differ considerably for thus case. Here the EP does not alone
out
15 December 1981
CHEMICAL PHYSICS LETTERS
Volume 84, number 3
J. Organomet.
131 AX.
(1968)
279. McNeill and F.R. Scholcr, J. Am. Chcm. Sot 99 (1977) 6243. GM. Sheldnck, Chem Commun (1967) 751. W-F. EdgcU and R Sumrmtt, J. Am Chcm. Sot 83 (1961) 1777 K_ ~it;l~n and K- Morokuma_ Intern J. Quantum Chem. 10 (1976) 325. H. Umcyama and K. Morokuma, J Am. Chem Sot 98 (1976) 4400. H. Johansen, S. Rcttrup and B. Jensen, Thcoret Chun. Acta 55 (1980) 267. E. Scrocco and J. Tomask Advan. Quantum Chem. 11 (1978) 115, and references thercm. H. Berthod and A. Pullman, J. Comput. Chcm. 2 (1981) 87, and references thcrcm.
[41 EA.
[5]
161 [71 F-U 191 1101
MOLECULAR
CHEMICAL PHYSICS LETTERS
ELECTROSTATIC
POTENTIALS
15 December 1981
lN TRANSITION-METAL
CHEMISTRY:
AN EXAMPLE Helge JOHANSEN Depzrtmcnt of Chemrcal Phyncs, The Technrcal Unnwnty
of Denmarh, DK-2300
Lyngby, Denmark
Rccelved 28 August 198 1
Usmg the protonation of Co(CO)i as an example, the apphubhty of the clectrostalc potenhal has been assessed by comparison with Hartrec-Fock calculahons It ISconcluaed that elcctrostatlc potentrals are useful for mapping the coordmation sphere of a transluon-metal atom, ~MII~ dlrectlons and distances, but that rclatrve cnerpes arc less rehable.
l_ Introduction
The reaction
Computational quantum mechamcs has reached a h3gh level of accuracy for molecules involvmg first and second row elements The extension to transltlonmetal compounds has been cumbersome, not m pnnc,.ple but m practice. The mam reasons are the followmg (1) The computation of Integrals with lughcr I quantum numbers are more time-consummg. (2) A
Co(CO),
“realistx” compound has many ligands, thus many integrals have to be computed and handled. (3) The systems usually have open shells. (4) There w1I1 be many levels close together III both hgands and metal,
thus large configuration interaction expansions are necessary. (5) With m,my hgands, there will be many degrees of freedom
to cope with m a geometry optimrzatlon. The use of pseudo-potential methods reduces the number of mtegrals to be computed and handled, but most of the abovementioned problems remam. First-pnnclple computatron of pathways m a cheml-
cai reactron involvmg a transItion-metal compound IS thus bound to be a maJor task for some tune. Lu77rted basis sets and small CI expansions WIU preva& and short-cuts WIU be welcome. The present study has Its emphasis on point (5) above, and usmg a sunple example, the aim is to assess the usefulness of molecular
electrostatic
poten-
teals irk the search for mtermehates and pathways in catalfic reactlons involvmg transition-metal atoms. 580
+ H’ -f HCO(CO)~
has been used as the example. It IS a sunple system, and we already have a geometry optunization ava& able from a study of the hydroformylation reaction [I] More detailed computational mformatlon may be found
m ref. [l] _ The basis set IS modest.
(C, O/7, 3) (H/4) contracted as (CO/~, 3,2) (C, O/3,2) (H/2) m a split-valence shell fashion. It was, however, Judged to be adequate for a prehmmary Investigation. Two pathways for the protonation of Co(CO), , calculated m the restricted Hartree-Fock approxunation, have been compared wth the correspondmg electrostatic potential for Co(CO), . Both Co(CO)z and HCo(CO)d have been the subject of a number of previous computational studies, SW e.g. ref. [?I. (Co/ 1 I, 8,4)
2. Results and discussion Frg. 1 shows the electrostatic potenhal (EP) for Co(CO), m a conformation as found by electron dtifraction for H$iCo(C0)4 [3]. This conformation was used prevJously for the Co(CO), fragment in various X-COG systems [l] _ The geometry of the ion Itself JS T,, and an EP has been calculated for this symmetry, but the present diagram is more informa-
0 009-26 14/81/0000-0000/C
02.75 0 198 1 North-Holland
Volume 84, number 3
CHEMICAL PHYSICS LElTERS
15 December 1981
,014 h F go12 s
SOlO i
h
au Fig. 1. Ele&ostatx potenti for Co(CO), in a plane containmg Co, an axnl and an equatorial CO group, Cs,, con-
formahon Contours are equllstant au, lowest deplcted contour IS-0.20 -0.11 au. Coordrnatcs are in au.
tive. Three types of minima axml position above cobalt,
Fig. 2 Comparison
of total energy (solid bne) and ekctrc(dash&l line) for the mcial approach The functions are depicted r&tive to their respective energy minima.
and separated by 0.01 au and the h&best
static potent&
are found: one in the one III connection with
the lone pair behind oxygen for each CO group, and one between the axial and two equatorial CO groups. There are three minima
(length)
of the last type, and they,
wrth 2.99 au found III the energy variahon calculation [ 11, and 2.94-2.97 au as determined expenmentaily [4,5] (wrth uncertainties of 0.03-0.08 au). Also the second 1
with the fist minimum, form four equiva111the Td conformation, corresponding to the four faces of a tetrahedron. The axral mimmum for the EP IS found at a dis-
derivatives
and fig. 2.
are very sxmilar as seen from table
The depth of the minimum IS, however,
together
much smaller for the EP (about one third). TMs in&-
lent muuma
cates that the shape of the potential energy curve is dominated by the electrostatic potential, and that the other components 111an energy decomposition analysrs [7] are large but add up to be relatively constant
tance of 3.02 au from cobalt.
This 1s to be compared
Table 1 Comparison
of t&d
cobalt atom, &_:
energy and ele~t~ost&~ potential for two duections of approach x0: position Of the! mirdnllll’n r&tie energy/potenti mmimum (for Etot relative to Co(CO)& All values are in au
-
X0
---_I_ axial direction HCo(C0)4 Co(COxi
(C~V). Etot (C3”h CP
experunent
Gin
t0 the
Curvature
299
-0.623
0.12
3.02
-0.198
0.10
294 a), 3.00 b,
-
0.14 =)
7.45
-0.425
0.65
7.73
-0.208
0.23
carbonyl dxection HCo(C014 Co(C% a) Ref. [4] (1.556(18)
A).
(T&, EtOt ud),
EP
b, Ref. [S] (L59 f 0.04 A)_
c) Ref. [6] (222 md/A).
581
over the region of mterest.
A slmrlar result for the
shape of the EP curve was proton affiity for anunes,
found In a study of the
alcohols and ethers [8]. The EP mmirna behmd the oxygen atoms are shghtly lower than the axial mrurnum, but the protonation does not occur at these positlons (the skucture of HCO(CO)~ has been dlscussed extensively m the Literature. see e.g. ref. [4] and references therem).
To mvestigate this pomt further, Hartree-Fock type calculations were performed for a proton approactung the cartonyl group in tetrahedral Co(CO), along the duectlon of a C-O bond The muwnum for the change UI total energy IS found to be only 68% of that for the axial approach, thus confirming the expenmental structure [4,5] _ But when the total energy 1s compared with the EP, taole 1, it IS seen that both the
supply quahtative reformation about the posstbihties involved It 1s the shape of the potential and not the absolute value which appears to be most useful.
References
111 N. Fonnesbech, J. HJortkJaer and H. Johanscn, intern. 3. Quantum Chem. 12 SuppL 2 (1977) 95. N. Fonncsbech, LIC Techn
versrty of Denmark, [21 W-C Nieuwpoort. EJ. Baerends and
the shape of the curve. electrostatic potential IS already useful m the study of crystal packmg [9], and In bm-orgamc
stu&es of protonation, hydration, catlon bmdmg. etc. [lo]. The present mvestlgahon mdlcates that the electrostatic potential 1s also useful m mappmg out the immediate coordmation sphere of a transItIonmetal atom tn a complex, predctmg possible pathways for reactlons and geometries of compounds.
The dxect hnk of hydrogen to the metal atom IS surpnsmgly well described,, and the spcclal nature of the d orbltals may play an important part m tbs. A more formal energy decomposltlon analysis should be undertaken m order to settle this question. For the two cases studled, the EP accounted for respectively 32% and 49% of the total energy. The
potent&
582
can therefore
a pamcular
not be used alone to single or pathway, but they
conformation
Tbeas, The Techrucal (1979).
Urn-
met. Chem. 129 (1977) 221; D.A. Pensak and R.J. McKmney, Inorg Chem. 18 (1979) 3407, B.D. El-Issa and A. Hmchbffe, I. MoL Struct 69 (1980) 305, V. BeUagamba, R. Ercoh, A. Gamba and GEX. Suffnti,
Chem. 190 (1980) 381. Roblctte, GM Shcltick, R.N.F. SiiqWin, B.1. Aylett and J.A. Campbell, J. Organomet. Chem. 14
domrnate The
Lyngby
Philips Res Rept 20 SuppL (1965) 6, P. ROS MoL Phys 30 (1975) 1735. J.P. Gnma, F. Chophn and G. Kaufmann, J. Organo-
location of the muumum and the curvature differ considerably for thus case. Here the EP does not alone
out
15 December 1981
CHEMICAL PHYSICS LETTERS
Volume 84, number 3
J. Organomet.
131 AX.
(1968)
279. McNeill and F.R. Scholcr, J. Am. Chcm. Sot 99 (1977) 6243. GM. Sheldnck, Chem Commun (1967) 751. W-F. EdgcU and R Sumrmtt, J. Am Chcm. Sot 83 (1961) 1777 K_ ~it;l~n and K- Morokuma_ Intern J. Quantum Chem. 10 (1976) 325. H. Umcyama and K. Morokuma, J Am. Chem Sot 98 (1976) 4400. H. Johansen, S. Rcttrup and B. Jensen, Thcoret Chun. Acta 55 (1980) 267. E. Scrocco and J. Tomask Advan. Quantum Chem. 11 (1978) 115, and references thercm. H. Berthod and A. Pullman, J. Comput. Chcm. 2 (1981) 87, and references thcrcm.
[41 EA.
[5]
161 [71 F-U 191 1101