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Molecular pseudopotential calculations on transition-metal complexes: Ni(CO)4, Pd(CO)4, and Pt(CO)4
Volume 39, number 1
CHEMICAL PHYSICS LETTERS
MOLECULAR PSEUDOPOTENTIAL Ni(C0)4, Pd(CC$, AND Ft(CO)4
1 April 1976
CALCULATIONS ON TRANSITION-METAL
Roman OSMAN, Carl S. EWIG and John R. VAN WAZER Department of Chemistry. Vanderbilt University. Nashville, Tennessee
37235,
COMPLEXES:
r~,!?_.j
Received 19 November 1975
The electronic structures of the transition-metal complexes Ni(CO)a. Pd(CO)a, and Pt(CO)a’are studied using ab initio molecular pseudopotentiaI theory. We report the valence-orbital energies For each compound. For Ni(C0)4, we also present the calculated equilibrium Ni-C bond length and the At vibrational stretching frequency. ‘The Ni(CO)G results are compared with conventional SCF calculations and with experiment and are found to be in excellent agreement.
2. Cakdational
1. Introduction Recent developments in molecular pseudopotential and effective-potential theory have permitted accurate SCF calculations using only the valence electrons to be performed on a variety of compounds_ However, an important class of molecules that have so far been inaccessible tG accurate va!encc-electron methods are those containing the transition elements. It has common!y been assumed [I-4] that a!1 such methods (which consider explicitly on!y the coordinates of the va!ence etectrons) must fail, due to mixing of the core and valence orbitals, for example the “valence” 3d and “core” 3p in Ni. In this paper we show that the suggested corevalence mixing causes no problems in the transitionmeta! compounds studied. Using recently developed ab initio molecular pseudopotentia! theory [5], we have carried out calculations and Pt(CO)q,
in Ni(CO),,
Pd(CO),,
using only the outermost s, p, and d valence orbit&. Where comparisons are available, the accuracy is found to be equiva!ent to a conventiona! all-electron self-consistent-field calculation using a comparable valence basis set. Of particular interest in the Pd and Pt compounds are the calculated deviations from the energy ordering of the two highest occupied sets of orbitals from that predicted by ligand-field theory.
details
I?le calculation on Ni(C0)4 was performed with three different Ni-C bond lengths: 1.74, I .84(equilibrium) [6], and 1.941% The Pd-C and Pt-C borid lengths were 1.84 and 2.08 A, respectively. The C-O bond length [6] was kept constant at 1.15 A in a!! ca!culations. The valence basis set for Ni consisted of the 3d, 4s and 4p functions and for C and 0 tie 2s and 2p. It wss constructed in such a way as to be comparable with a previous calculation [7], and each atomic orbital was described by an expansion in three gaussian functions [8]. A nickel 3d double-zeta orbital 1’71was contracted with atomic coefficients and again expanded in three gaussians. A parallel procedure was utilized for the Pd and pt atoms, resulting in the following Slater exponents; Pd: 4d -3.2933, 5s -1.5675,Sp -1.4000;Pt: 5d -3.4933, 6s -1.7919,6p
-1.7250.
The pseudopotentials and model potentials were generated using the NOCOR method as described previously [S] , with each core function being delineated by a four-gaussian expansion, and the model potential by six gaussians. The screening exponents used to describe the core potentials were found to have the following values for Ni, Pd, ad Pt, respectively:. 3.6534, 3.4041, and 3.6181 (au)-I. T!re NOCOR total energy
27
.voiu.mc.3q,number1 :. _’ ‘.._ t
-.
__
._
I
.-
CHEF&IA& PtiYSIC!ELETTERS
..I
lApril1976
..
_I:
was fitted to a qua_dratic potential in order to calcuIat+ the N&C bond length corresponding to the minimum-energy @r-dthe AI M-C stretching frequency.
Table 1 Orbital e,nergiesof Ni(C0)4 (au)
3. Results
6al
MO St2
7al 6b le
The N&OR results are compared with the previous two-ab initio full-SCF calculations [7,9] in table I i The agreement is good, especially in the highest occupied molecular orbitals 2e and 9t2. Even in the very densely occupied region between orbit& 7a, and 8al, the order of the molecular orbit& is the same as in the previous calculations except for the 1t 1 and 8aI which according to ihe NOCOR results lie above the 8t2 set. . The overlappopulation analysis is shown in table 2. The sets of valence molecular orbitals St,, 6ai, 7a,, and 6t2 are composed of the 30 and 40 orbitals of the uncomplexed CO ligands slightly perturbed by bonding to the central atom. Likewise, orbital sets le, 7t-2 and It, zre similarly dominated by the-ligand In orbitals. OrbjtJs 8t, and 8a, are the main contributors to the u bonding between the ligand and rhe metal. These orbitals are formed as a result of the overlap of the lone pair (Scr) of the ligand with the 4s of the nickel to give 8a,, and with the Ni 3d and 4p to give 8t2. Orbitls 2k and 9t2 are populated largely by the 3d electrons of the nickel with a small contribution from its 4p orbitals. The bonding in the& orbitals consists mainly of a metal-to-figtid n* back-donation. Although there is appreciable u-bonding overlap in molecular orbital 9t, between the Ni 4p and the ligand, it is cancelled by equal cs-antibonding overlap betweea the Ni 3d and the ligand, thus leaving the bonding in this orbital to be dominated by the metal-to-n* backdonation. The total Ni-C and C-O overlap populations, shown in the bottom line of table 2, support this overall analysis of the bonding. Approximately 70%. of the Ni-C bonding is due to the iigand-tometal o donation and the rest to the metL.l-to-ligand back-donation. From the atomic population analysis, we fmd the ‘net charges on the.atoms to be: Ni W.44, C Hl.21, and 0 ;-d.3i;-+d these.values are in good agreement with those obtained in the previous calculations [7,9]. :28
7t2
8tz It1 8al
2e gt2
-NOCOR a)
Hillier[7]
Veillard [9]
11.533 -1.531 -0.859 -0.857 -0.687 -0.687 -0.682 -0.675 -0.671 -0.479 -0.391
-1.565 -1.574 -0.855 -0.830 -0.697 -0.797 -0.679 -0.686 -0.720 -0.496 -0.429
-1.530 -1.530 -0.809 -0.793 -0.665 -0.662 -0.644 -0.653 -0.693 -0.47 1 -0.395
a) Calculatedat the experimentalNi-C bond length 161.
_
Table 2
Overlap populationanalysisfor Ni(C0)4 a) MO St2
6al 7al
6t2
le 7t2 8tz 1t1 8a1 2e 9tz total
MD-Co
N&-Cn
CD-O0
-0.01 -0.00 0.02 -0.04 0 -0.01 0.21 0 -0.11 0 -0.00
-0.00
0.50 0.16 -0.03 -0.06
-0.02 -0.01 0 0 0.03 - 0.10
0.28
0.12
0
0 -0.00
0.02
0
-0.04 -0.16 0 -0.04 0 -0.01 0.32
G-0,
Natureb)
0.00 0
a(Q) o(Q)
0
a(Q) a(Q)
0.00
0.20
0.27 0.05 0.32 0 -0.02 -0.05
a(Q) a(Q) o(Q-m) n(Q) 0(Q+mj d(m)-in*(Q) p.d(m)-wr*(Q)
0.77
a) u and JToverlaps are defined with respect to the threefold axis Ni-C-O. b) Q= ligand;III= metal.
Since Ni(C0)4 is experimentally the better known molecule, we have also calculated the minimum-energy Ni-C bond length, as described in the previous section. The result is 1.8 1 A. This may be tompared with two different experimental values: the X-ray determined [6] bond length is 1.84A and the one measured by electron-diffraction [lO,l l] is 1.82 A. In both cases, the agreement is good. The A1 stretching frequency is calculated to be 418cm-1. as compared with an experimental value [ 121 of 370.8 cm-‘. In general, the calculated values tire in as good agreement with experiment as would be expected for a minimum basis set.
CHEMICAL PHYSICS hTIFEkS
Volume 39, numb& 1 Table 3 Orbital energies of W(COk
9al 9t2 2e lot*
-1.520 -1.518 -0.926 -0.867 -0.745 -0.718 -0.684 -0.683
ItI llt2 3e
-0.668 -0.467 -0.300
‘7t2
? #aI 8ar -8t,
Table 4 Overlap popu1ations.h Ni(CO)a. Pd(C0)4 and Pt(CO),
and Pt(COI4 (au)
lot2 9al lOa, flt2
llal 12tz 3e 13t2
2t1 14t2 4e
1 April 1976
Pt(C0)4
Nature
M-C overlap
Ni(C0)4
Pd(CO)4
PmO)4
-1.504 -1.504 -0.868 -0.84 1 -0.728 -0.681 -0.664 -0.663 -0.656 -0.425 -0.259
a(Q) o(Q) o(Q) a(Q) o(Q-+m) ate-m)
a(Q-+m) m--a*(Q) total u overlap total TToverlap total (0 f a) overlap
0.324 0.132 0.275 0.121 0.396
0.161 0.130 0.096 0.138 0.234
0.157 0.133 0.273 0.138 0.311
a(Q) n(Q) n(Q) p,dh)+n*(Q) d(m)+n*(Q)
3.2. Pd{C0.14 and Pt(CO)4 The orbital energies of Pd(CO)4 and Pt(CO)d are presented in table 3. From a comparison of tables 1 and 3, we immediately see that in general the electronic structures of the Ni, Pd, and Pt tetracarbonyls are quite similar. In each case, the four most stable sets of valence molecular orbitals consist of the slightly perturbed ligand 30 and 4a orbitals.. Then, after the metal-carbon a-bonding orbit& [u(Q + m)], come the Iigand 7rorbitals. The important difference between the Pd or Pt and the Ni tetracarbonyls occurs in the two highest occupied sets of molecular orbitals. These orbitals are mainly populated by the metal d electrons split into the appropriate symmetries (e and t2) by the tetrahedral molecular geometry, with this splitting being reversed in Pd(CO), and Pt(CO), with respect to the prediction of the simple I&and-field approximation. The lack of experimental data on these two molecules concerning the ordering of the molecular orbitals makes it impossible to verify our calculations. However, photoelectron spectra on analogous compounds may be of use here. Two publications [13,14] have reported similar experimentaI results for the photoelectron spectra of PF3, Ni(PF& and Pt(PF3)4 but the interpretations were different. Hillier et aI. [ 141 assign the bands at 9.83 and 12.45 eV to the ionization of the highest t2 and e orbitals, respectively, in Pt(PF3)h. Consequent= ly the band at 14.54 eV is relegated to the ionization of the phosphorus lone pairs, an assignment which, when compared to the ionization potentials of the
same orbitais in Ni(PF3)4 and PF3 leads to the conclusion that Pt is a better (Tacceptor than Ni. On the other hand, Green et aI_ 1131 interpret the band at 9.8 eV as being of mixed e and t2 character due to the smaller Iigand-field splitting in Pt(PF3)4 and the 12.3 eV band to originate From the lone pair on the phosphorus atoms. This leads to a completely.opposite conclusion, namely that Pt is a poorer cr acceptor than Ni. Green’s results [IS] seem to support our calculated differences between Ni(C0)4 and Pt(C0)4 inasmuch as the ordering of the higher occupied orbitals is concerned. Moreover, their conclusions concerning the u-acceptor and n-donor abilities of Ni and Pt agree with our calculations. From the overlap-population analysis presented in table 4 we find that the u-acceptor ability is reduced and the r-donor ability practically does not change when going from Ni to Pt. This is also indicated by the atomic charges calculated for the central atoms: Ni, t0.44; Pd, +1.80; and Pt, +1.36. The last row in table 4 shows the total metalcarbon overlap, which would be expected to be proportiond to the metal-carbon stretching force constants. The experimental results [IS] for this stretch-’ ing are in fact in the same order as our calculated metal-carbon overlaps: Ni > Pt > Pd. The reason for the inversion of the outermost occupied t2 and e orbitals in Pd(CO)4 and Pt(C0)4 may lie in the ability of p(t2j and d(t?) to intermix. Molecules of tetrahedral geometry, since they lack a center of inversion, aIlow p-d mixing in the t2 but not in the e representation. Mixing p. with d, (u with respect to the three-fold axis) has the advantage of generating more bonding electron density in the region between the metal and the Iigand, while concentrating the antibonding combination on the opposite side of the metal. An alternative way of looking at p-d mixing is that the admixture of p character in the 29
-
,.
.
. .
clover-leaf&iped d makes it bend beIow its plane in the. two directions where it .is pdsitive and above its p?ane itj the two directions where it is negative. The physical sign&carrce of this distortion is a tendency to avoid the ligands (situated on four-of the eight corriers of a cube). Thus, an in&ease in tbc amount of p-d mixing will result in stabilization of the orbit& belonging to the t7 representatidn but will have no effect on the e or&t&. The population analysis shows that the percentage of p contribution to the highest occupied tz in Ni(CO)a, Pd(CO)4, and Pt(CO), is 16, 20, and 19, respectively.
of valence-electron energies alone.
calculatious. than do &&eorb&l :
Acknowledgement We wish‘to thank the Air Force Office of Scientific Research for partial support of this work-under grant AFOSR-72-2265 and Vanderbilt University for their contribution
of the computer
time and services..
References [I] E.C. Snow and J.H. Wood, Chem. Phys. Letters 25 (1974) 111.
4. Conclusions The accuracy of our calculated that the frozen-core approximation Factor in carrying out calculations
results indicates is not a limiting on transition-metal
compounds. To our knowledge, this work represents the first valence-only SCF calculation that seems to be generally equivalent tc an all-electron study, as applied to transition-metal compounds. Although other classes of molecules xxi&t pose a more .severe test than the carbonyl complexes, we feel that previously reported failures of valence-electron methods for transition-metal compounds most likely represent
simply shortcomings in the theoretica development employed. The accuracy of the calculated Ni(C0)4 bond lengths and vibrational frequencies is particularly encouraging, since a comparison of atomic SCF calculations of Ni, PC!, and Pt shows that the Ni valence-d orbitah are spatially and energetically closer to the core orbit& than in the other two atoms. Hence Ni compounds should exhibit the greatest core-valence mixing. Also, recently reported results [4] indicate that molec:-llar geometries may pose a more severe test
121 T.C. Chang, P. Habitz, B. Pittel and W.H.E. Schwarz, Theoret. Cbim. Acta 34 (1974) 263. j31 CF. Mclius, B.D. Oiafson and W.A. Goddard III, Chem. Phys. Letters 28 (1974) 457. [4] J-H. Yates sad R.M. Pitzer, Thirtieth Symposium on Molecule Structure and Spectroscopy, Columbus, Ohio, 1975. [S] C.S. Ewvig and 3-R. van Wazcr, J. Chcm. l%ys. 63 (1975), to be published. [61 J. Ladell, 5. Post and I. Faukuchen, Acta Cryst. 5 (1952) 79.5. 171 LH. Hillier and V-R. Saunders, Mol. Phys. 22 (1971) 1025.
[81 R-F. Stewart, J. Chem. Phys. 52 (1970) 431. P! 3. Demuynck and A. Veillard, Theoret. Chim.
Acta 28 (1972) 242. IlO1 L. Brockway and P.C. Cross, J. Chcm. Phys..3 (1935) 828. 1111B. Crawford and J. Horowitz, J. Chem. Phys. 16 (1948) 147. [I21 L.H. Jones, RS. McDowell and hi. Goldblatt, J. Chem. Phys. 48 (1968) 2663. f131 J.C. Green, D-I. King and J.H.D. Etand. Chem. Commun. (1970) 1121. 1141 1-H. Hillier, V.R. Saunders, M.J. Ware, P-J. Bassett, D-R. Lloyd and W. Lynaugh, Chem. Commun. (1970) 1316. [15j E.P. Kiindig, D. McIntosh, M. hioskovits and G.A. Ozin, J. Am. Cbem. Sot. 95 (1973) 7234.
CHEMICAL PHYSICS LETTERS
MOLECULAR PSEUDOPOTENTIAL Ni(C0)4, Pd(CC$, AND Ft(CO)4
1 April 1976
CALCULATIONS ON TRANSITION-METAL
Roman OSMAN, Carl S. EWIG and John R. VAN WAZER Department of Chemistry. Vanderbilt University. Nashville, Tennessee
37235,
COMPLEXES:
r~,!?_.j
Received 19 November 1975
The electronic structures of the transition-metal complexes Ni(CO)a. Pd(CO)a, and Pt(CO)a’are studied using ab initio molecular pseudopotentiaI theory. We report the valence-orbital energies For each compound. For Ni(C0)4, we also present the calculated equilibrium Ni-C bond length and the At vibrational stretching frequency. ‘The Ni(CO)G results are compared with conventional SCF calculations and with experiment and are found to be in excellent agreement.
2. Cakdational
1. Introduction Recent developments in molecular pseudopotential and effective-potential theory have permitted accurate SCF calculations using only the valence electrons to be performed on a variety of compounds_ However, an important class of molecules that have so far been inaccessible tG accurate va!encc-electron methods are those containing the transition elements. It has common!y been assumed [I-4] that a!1 such methods (which consider explicitly on!y the coordinates of the va!ence etectrons) must fail, due to mixing of the core and valence orbitals, for example the “valence” 3d and “core” 3p in Ni. In this paper we show that the suggested corevalence mixing causes no problems in the transitionmeta! compounds studied. Using recently developed ab initio molecular pseudopotentia! theory [5], we have carried out calculations and Pt(CO)q,
in Ni(CO),,
Pd(CO),,
using only the outermost s, p, and d valence orbit&. Where comparisons are available, the accuracy is found to be equiva!ent to a conventiona! all-electron self-consistent-field calculation using a comparable valence basis set. Of particular interest in the Pd and Pt compounds are the calculated deviations from the energy ordering of the two highest occupied sets of orbitals from that predicted by ligand-field theory.
details
I?le calculation on Ni(C0)4 was performed with three different Ni-C bond lengths: 1.74, I .84(equilibrium) [6], and 1.941% The Pd-C and Pt-C borid lengths were 1.84 and 2.08 A, respectively. The C-O bond length [6] was kept constant at 1.15 A in a!! ca!culations. The valence basis set for Ni consisted of the 3d, 4s and 4p functions and for C and 0 tie 2s and 2p. It wss constructed in such a way as to be comparable with a previous calculation [7], and each atomic orbital was described by an expansion in three gaussian functions [8]. A nickel 3d double-zeta orbital 1’71was contracted with atomic coefficients and again expanded in three gaussians. A parallel procedure was utilized for the Pd and pt atoms, resulting in the following Slater exponents; Pd: 4d -3.2933, 5s -1.5675,Sp -1.4000;Pt: 5d -3.4933, 6s -1.7919,6p
-1.7250.
The pseudopotentials and model potentials were generated using the NOCOR method as described previously [S] , with each core function being delineated by a four-gaussian expansion, and the model potential by six gaussians. The screening exponents used to describe the core potentials were found to have the following values for Ni, Pd, ad Pt, respectively:. 3.6534, 3.4041, and 3.6181 (au)-I. T!re NOCOR total energy
27
.voiu.mc.3q,number1 :. _’ ‘.._ t
-.
__
._
I
.-
CHEF&IA& PtiYSIC!ELETTERS
..I
lApril1976
..
_I:
was fitted to a qua_dratic potential in order to calcuIat+ the N&C bond length corresponding to the minimum-energy @r-dthe AI M-C stretching frequency.
Table 1 Orbital e,nergiesof Ni(C0)4 (au)
3. Results
6al
MO St2
7al 6b le
The N&OR results are compared with the previous two-ab initio full-SCF calculations [7,9] in table I i The agreement is good, especially in the highest occupied molecular orbitals 2e and 9t2. Even in the very densely occupied region between orbit& 7a, and 8al, the order of the molecular orbit& is the same as in the previous calculations except for the 1t 1 and 8aI which according to ihe NOCOR results lie above the 8t2 set. . The overlappopulation analysis is shown in table 2. The sets of valence molecular orbitals St,, 6ai, 7a,, and 6t2 are composed of the 30 and 40 orbitals of the uncomplexed CO ligands slightly perturbed by bonding to the central atom. Likewise, orbital sets le, 7t-2 and It, zre similarly dominated by the-ligand In orbitals. OrbjtJs 8t, and 8a, are the main contributors to the u bonding between the ligand and rhe metal. These orbitals are formed as a result of the overlap of the lone pair (Scr) of the ligand with the 4s of the nickel to give 8a,, and with the Ni 3d and 4p to give 8t2. Orbitls 2k and 9t2 are populated largely by the 3d electrons of the nickel with a small contribution from its 4p orbitals. The bonding in the& orbitals consists mainly of a metal-to-figtid n* back-donation. Although there is appreciable u-bonding overlap in molecular orbital 9t, between the Ni 4p and the ligand, it is cancelled by equal cs-antibonding overlap betweea the Ni 3d and the ligand, thus leaving the bonding in this orbital to be dominated by the metal-to-n* backdonation. The total Ni-C and C-O overlap populations, shown in the bottom line of table 2, support this overall analysis of the bonding. Approximately 70%. of the Ni-C bonding is due to the iigand-tometal o donation and the rest to the metL.l-to-ligand back-donation. From the atomic population analysis, we fmd the ‘net charges on the.atoms to be: Ni W.44, C Hl.21, and 0 ;-d.3i;-+d these.values are in good agreement with those obtained in the previous calculations [7,9]. :28
7t2
8tz It1 8al
2e gt2
-NOCOR a)
Hillier[7]
Veillard [9]
11.533 -1.531 -0.859 -0.857 -0.687 -0.687 -0.682 -0.675 -0.671 -0.479 -0.391
-1.565 -1.574 -0.855 -0.830 -0.697 -0.797 -0.679 -0.686 -0.720 -0.496 -0.429
-1.530 -1.530 -0.809 -0.793 -0.665 -0.662 -0.644 -0.653 -0.693 -0.47 1 -0.395
a) Calculatedat the experimentalNi-C bond length 161.
_
Table 2
Overlap populationanalysisfor Ni(C0)4 a) MO St2
6al 7al
6t2
le 7t2 8tz 1t1 8a1 2e 9tz total
MD-Co
N&-Cn
CD-O0
-0.01 -0.00 0.02 -0.04 0 -0.01 0.21 0 -0.11 0 -0.00
-0.00
0.50 0.16 -0.03 -0.06
-0.02 -0.01 0 0 0.03 - 0.10
0.28
0.12
0
0 -0.00
0.02
0
-0.04 -0.16 0 -0.04 0 -0.01 0.32
G-0,
Natureb)
0.00 0
a(Q) o(Q)
0
a(Q) a(Q)
0.00
0.20
0.27 0.05 0.32 0 -0.02 -0.05
a(Q) a(Q) o(Q-m) n(Q) 0(Q+mj d(m)-in*(Q) p.d(m)-wr*(Q)
0.77
a) u and JToverlaps are defined with respect to the threefold axis Ni-C-O. b) Q= ligand;III= metal.
Since Ni(C0)4 is experimentally the better known molecule, we have also calculated the minimum-energy Ni-C bond length, as described in the previous section. The result is 1.8 1 A. This may be tompared with two different experimental values: the X-ray determined [6] bond length is 1.84A and the one measured by electron-diffraction [lO,l l] is 1.82 A. In both cases, the agreement is good. The A1 stretching frequency is calculated to be 418cm-1. as compared with an experimental value [ 121 of 370.8 cm-‘. In general, the calculated values tire in as good agreement with experiment as would be expected for a minimum basis set.
CHEMICAL PHYSICS hTIFEkS
Volume 39, numb& 1 Table 3 Orbital energies of W(COk
9al 9t2 2e lot*
-1.520 -1.518 -0.926 -0.867 -0.745 -0.718 -0.684 -0.683
ItI llt2 3e
-0.668 -0.467 -0.300
‘7t2
? #aI 8ar -8t,
Table 4 Overlap popu1ations.h Ni(CO)a. Pd(C0)4 and Pt(CO),
and Pt(COI4 (au)
lot2 9al lOa, flt2
llal 12tz 3e 13t2
2t1 14t2 4e
1 April 1976
Pt(C0)4
Nature
M-C overlap
Ni(C0)4
Pd(CO)4
PmO)4
-1.504 -1.504 -0.868 -0.84 1 -0.728 -0.681 -0.664 -0.663 -0.656 -0.425 -0.259
a(Q) o(Q) o(Q) a(Q) o(Q-+m) ate-m)
a(Q-+m) m--a*(Q) total u overlap total TToverlap total (0 f a) overlap
0.324 0.132 0.275 0.121 0.396
0.161 0.130 0.096 0.138 0.234
0.157 0.133 0.273 0.138 0.311
a(Q) n(Q) n(Q) p,dh)+n*(Q) d(m)+n*(Q)
3.2. Pd{C0.14 and Pt(CO)4 The orbital energies of Pd(CO)4 and Pt(CO)d are presented in table 3. From a comparison of tables 1 and 3, we immediately see that in general the electronic structures of the Ni, Pd, and Pt tetracarbonyls are quite similar. In each case, the four most stable sets of valence molecular orbitals consist of the slightly perturbed ligand 30 and 4a orbitals.. Then, after the metal-carbon a-bonding orbit& [u(Q + m)], come the Iigand 7rorbitals. The important difference between the Pd or Pt and the Ni tetracarbonyls occurs in the two highest occupied sets of molecular orbitals. These orbitals are mainly populated by the metal d electrons split into the appropriate symmetries (e and t2) by the tetrahedral molecular geometry, with this splitting being reversed in Pd(CO), and Pt(CO), with respect to the prediction of the simple I&and-field approximation. The lack of experimental data on these two molecules concerning the ordering of the molecular orbitals makes it impossible to verify our calculations. However, photoelectron spectra on analogous compounds may be of use here. Two publications [13,14] have reported similar experimentaI results for the photoelectron spectra of PF3, Ni(PF& and Pt(PF3)4 but the interpretations were different. Hillier et aI. [ 141 assign the bands at 9.83 and 12.45 eV to the ionization of the highest t2 and e orbitals, respectively, in Pt(PF3)h. Consequent= ly the band at 14.54 eV is relegated to the ionization of the phosphorus lone pairs, an assignment which, when compared to the ionization potentials of the
same orbitais in Ni(PF3)4 and PF3 leads to the conclusion that Pt is a better (Tacceptor than Ni. On the other hand, Green et aI_ 1131 interpret the band at 9.8 eV as being of mixed e and t2 character due to the smaller Iigand-field splitting in Pt(PF3)4 and the 12.3 eV band to originate From the lone pair on the phosphorus atoms. This leads to a completely.opposite conclusion, namely that Pt is a poorer cr acceptor than Ni. Green’s results [IS] seem to support our calculated differences between Ni(C0)4 and Pt(C0)4 inasmuch as the ordering of the higher occupied orbitals is concerned. Moreover, their conclusions concerning the u-acceptor and n-donor abilities of Ni and Pt agree with our calculations. From the overlap-population analysis presented in table 4 we find that the u-acceptor ability is reduced and the r-donor ability practically does not change when going from Ni to Pt. This is also indicated by the atomic charges calculated for the central atoms: Ni, t0.44; Pd, +1.80; and Pt, +1.36. The last row in table 4 shows the total metalcarbon overlap, which would be expected to be proportiond to the metal-carbon stretching force constants. The experimental results [IS] for this stretch-’ ing are in fact in the same order as our calculated metal-carbon overlaps: Ni > Pt > Pd. The reason for the inversion of the outermost occupied t2 and e orbitals in Pd(CO)4 and Pt(C0)4 may lie in the ability of p(t2j and d(t?) to intermix. Molecules of tetrahedral geometry, since they lack a center of inversion, aIlow p-d mixing in the t2 but not in the e representation. Mixing p. with d, (u with respect to the three-fold axis) has the advantage of generating more bonding electron density in the region between the metal and the Iigand, while concentrating the antibonding combination on the opposite side of the metal. An alternative way of looking at p-d mixing is that the admixture of p character in the 29
-
,.
.
. .
clover-leaf&iped d makes it bend beIow its plane in the. two directions where it .is pdsitive and above its p?ane itj the two directions where it is negative. The physical sign&carrce of this distortion is a tendency to avoid the ligands (situated on four-of the eight corriers of a cube). Thus, an in&ease in tbc amount of p-d mixing will result in stabilization of the orbit& belonging to the t7 representatidn but will have no effect on the e or&t&. The population analysis shows that the percentage of p contribution to the highest occupied tz in Ni(CO)a, Pd(CO)4, and Pt(CO), is 16, 20, and 19, respectively.
of valence-electron energies alone.
calculatious. than do &&eorb&l :
Acknowledgement We wish‘to thank the Air Force Office of Scientific Research for partial support of this work-under grant AFOSR-72-2265 and Vanderbilt University for their contribution
of the computer
time and services..
References [I] E.C. Snow and J.H. Wood, Chem. Phys. Letters 25 (1974) 111.
4. Conclusions The accuracy of our calculated that the frozen-core approximation Factor in carrying out calculations
results indicates is not a limiting on transition-metal
compounds. To our knowledge, this work represents the first valence-only SCF calculation that seems to be generally equivalent tc an all-electron study, as applied to transition-metal compounds. Although other classes of molecules xxi&t pose a more .severe test than the carbonyl complexes, we feel that previously reported failures of valence-electron methods for transition-metal compounds most likely represent
simply shortcomings in the theoretica development employed. The accuracy of the calculated Ni(C0)4 bond lengths and vibrational frequencies is particularly encouraging, since a comparison of atomic SCF calculations of Ni, PC!, and Pt shows that the Ni valence-d orbitah are spatially and energetically closer to the core orbit& than in the other two atoms. Hence Ni compounds should exhibit the greatest core-valence mixing. Also, recently reported results [4] indicate that molec:-llar geometries may pose a more severe test
121 T.C. Chang, P. Habitz, B. Pittel and W.H.E. Schwarz, Theoret. Cbim. Acta 34 (1974) 263. j31 CF. Mclius, B.D. Oiafson and W.A. Goddard III, Chem. Phys. Letters 28 (1974) 457. [4] J-H. Yates sad R.M. Pitzer, Thirtieth Symposium on Molecule Structure and Spectroscopy, Columbus, Ohio, 1975. [S] C.S. Ewvig and 3-R. van Wazcr, J. Chcm. l%ys. 63 (1975), to be published. [61 J. Ladell, 5. Post and I. Faukuchen, Acta Cryst. 5 (1952) 79.5. 171 LH. Hillier and V-R. Saunders, Mol. Phys. 22 (1971) 1025.
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