J. Phys. Chem. 1996, 100, 3359-3367
3359
Theoretical Study of 13C and 17O NMR Shielding Tensors in Transition Metal Carbonyls Based on Density Functional Theory and Gauge-Including Atomic Orbitals Yosadara Ruiz-Morales, Georg Schreckenbach, and Tom Ziegler* Department of Chemistry, UniVersity of Calgary, Calgary, Alberta, Canada T2N 1N4 ReceiVed: July 18, 1995; In Final Form: October 23, 1995X
A theoretical study has been carried out on 13C and 17O NMR shielding tensors in M(CO)6 (M ) Cr, Mo, and W), Fe(CO)5, and Ni(CO)4. The study was based on modern density functional theory (DFT) and gaugeincluding atomic orbitals (GIAO). The calculated shielding constants and tensors are in good agreement with the available experimental data. The difference in the isotropic shielding ∆δ ) σCO - σM(CO)n between free CO, σCO, and CO as a ligand, σM(CO)n was analyzed in detail. It was shown that the stretch of CO on coordination as well as the back-donation from dπ on the metal to π*CO of the CO ligand has a positive contribution to the coordination shift ∆δ whereas the donation from the σCO HOMO of CO to the metal orbitals has a negative contribution to ∆δ.
Introduction Nuclear magnetic resonance (NMR) is used extensively1 as a practical tool in chemical research. Many of its applications can be carried out on the basis of a simple effective Hamiltonian in which the observed shifts and spin-spin coupling constants are used as parameters without any further interpretation. However, an understanding of how these parameters are influenced by electronic and geometrical effects has not been established in detail except for a few classes of compounds,2-6 although such an understanding might enhance the amount of useful information obtained from NMR experiments. Computational methods based on molecular orbital theory can in principle provide the required insight.2-7 Calculations of the NMR shielding tensor have been carefully reviewed in an annual series.8 An overview of the state of the art can be found in a recent volume of conference proceedings,4 as well as in the newer reviews.5,6 The comparison between calculated and observed NMR spectra might further help in the identification of new species. With this in mind, several first principle methods capable of calculating NMR parameters have appeared over the last decade.4-7 One particular success of recently developed methods for the calculation of the chemical shift is the inclusion of electron correlation.4-6 The ab initio based methods are however very expensive and are thus restricted to small and medium size molecules. Another approach used in computational studies of the shielding tensor b σ is based on density functional theory (DFT).9,10 DFT accounts for electron correlation in an efficient manner. It should thus be particularly useful in the study of metal complexes and other heavy element compounds. The first DFT applications11 did not address the so-called gauge problem3,5 at all. Accordingly, the results are unreliable. Friedrich et al.12,13 were the first to combine the “gauge including atomic orbitals” (GIAO) method14,15 with DFT. However, their method is restricted by the use of the outdated XR approximation for the exchange-correlation (XC) energy functional9,10 and of minimal basis sets. Very recently, Malkin and co-workers have published a series of pioneering papers on the calculation of NMR properties, including shielding.7,16-21 They combine modern DFT with the “individual gauge for localized orbitals” X
Abstract published in AdVance ACS Abstracts, February 1, 1996.
0022-3654/96/20100-3359$12.00/0
(IGLO) method.22-24 We have recently presented a method in which the NMR shielding tensor is calculated by combining the GIAO approach with DFT. Our implementation makes full use of the modern features of DFT in terms of accurate exchange-correlation energy functionals and large basis sets.25-29 We present here calculations on the 13C and 17O shielding tensors for M(CO)6 (M ) Cr, Mo, W), Fe(CO)5, and Ni(CO)4 based on the GIAO-DFT approach.25-27,29 One objective of our study has been to test the accuracy and predictive power of the GIAO-DFT method by comparing theoretical results to the well established experimental values for this series of metal carbonyls. We shall in addition try to explain how the 13C and 17O shielding tensors of CO are changed as the molecule is complexed to a metal center. A comparison will also be made to the recent IGLO-DFT study by Kaupp and co-workers21 in which 13C NMR chemical shifts where presented for a number of organometallics including the metal carbonyls considered here. The interpretation of the chemical shift in binary metal carbonyls has been pioneered by Mahnke30 et al., Braterman31 et al., as well as Butler32 et al. However, the interpretations have been hampered by the lack of quantitative methods. Computational Details All calculations were based on the Amsterdam density functional package ADF.33-39 This program has been developed by Baerends et al. and vectorized by Ravenek. The adopted numerical integration scheme was that developed by te Velde et al.38,39 The metal centers were described by an uncontracted triple-ζ STO basis set40,41 for the outer ns, np, nd, (n + 1)s, and (n + 1)p orbitals whereas the shells of lower energy were treated by the frozen core approximation.33 The valence on carbon and oxygen included the 1s shell and was described by an uncontracted triple-ζ STO basis augmented by a single 3d and 4f function, corresponding to basis set V of the ADF package.33-39 A set of auxiliary42 s, p, d, f, and g STO functions, centered on all nuclei, was used in order to fit the molecular density and present Coulomb and exchange potentials accurately in each SCF cycle. The self consistent DFT calculations were carried out by augmenting the local exchange-correlation potential due to Vosko43 et al. with Becke’s44 nonlocal exchange corrections and Perdew’s45 nonlocal correlation correction (NL-SCF). The © 1996 American Chemical Society
3360 J. Phys. Chem., Vol. 100, No. 9, 1996
Ruiz-Morales et al.
3d and 4d complexes were treated without relativistic effects whereas both nonrelativistic and quasirelativistic46-48 (NLSCF+QR) calculations were carried out for the 5d complex W(CO)6. Experimental M-CO and C-O bond lengths were adopted for all systems.49 The inclusion of the frozen core approximation26 and quasirelativistic29 effects into the shielding calculations will be described elsewhere.
The details of the GIAO-DFT method have already been described previously.25-27,29 However, we will have to stress a few points about NMR in general and the GIAO formalism in particular so as to facilitate the discussion in the next sections. The shielding tensor b σ is a sum of two contributions,
b σ)b σ +b σ
bd
(1)
The st-component of the diamagnetic tensor b σ d is given in the GIAO formalism as occ
σstd
)R
∑i ni
2
{〈
Ψi
|∑ν cνi0
〈[
0 0 cλi cνi χλ| ∑ λ,ν
1
〉
[b r N‚b r νδst - b r Ns‚b r νt]χν + 2rN3 b rν b rN R λ) ×∇ B χν × (R Bν - B 2 s r3 N t
] ( ) | 〉}
(2)
R occ 2
r B0 × b r ν)χν ∑i ∑ν nicνi0 Ψi(b)(B
(3)
induced by the constant external magnetic field B B0. The st-component of the paramagnetic tensor is given according to the GIAO formalism as
{
〈 | ( )| 〉 〈 |[ ] | 〉 〈 |[ ] | 〉}
occ b rN 1 0 0 cνi χλ (R Rν)s ×∇ B χν + Bλ × B σstp ) ∑ ni R2 ∑ cλi 2 i λ,ν rN3 t occ b rN ∑j RSij(1,s) Ψi 3 × ∇B Ψj + rN t unocc b rN ∑a Ruai(1,s) Ψi 3 × ∇B Ψa (4) rN t
where
〈
λ,ν
(5)
|[2 × (RB - BR )] |χ 〉
(1,s) (0) Spi ) R∑c(0) λp cνi χλ
{〈
|[ 2
(0) (1,s) χλ ) R∑c(0) Fai λa cνi λ,ν
b r
ν
λ
(6)
ν
s
-b rν
〈
×∇ B
]| 〉
χν +
|[2 × (RB - BR )] h(0)|χ 〉} (7)
χλ
s
b r
ν
λ
ν
s
The index i runs over orbitals occupied in the field free ground state, and the index a runs over the corresponding unoccupied orbitals. The paramagnetic shielding tensor b σ p of eq 4 is also set to be gauge invariant and an expectation value of Hermitian operators.2,13 The dominating contribution to σstp is given by the last term in eq 4. It represents a coupling between occupied, Ψi, and B0. The virtual orbitals, Ψa, due to the external magnetic field B coupling produces a current given by 3
Here the occupied molecular orbital Ψi has been expanded in terms of atomic functions χν and the coefficients c0νi. The zero superscript indicates that Ψi is calculated with zero magnetic field strength, as an eigenfunction to the Kohn-Sham operator rν ≡ br - R Bν denotes h(0) with the eigenvalue (0) i . The vector b the position of the electron relative to the nucleus at which the atomic orbital χν is centered, and brN is the position of the electron relative to the nuclear magnetic moment under consideration (relative to the NMR nucleus N). Further R is the dimensionless fine structure constant given as (approximately) 1/137. The diamagnetic shielding tensor b σ d of eq 2 is set in the GIAO scheme to be gauge invariant and an expectation value of Hermitian operators.2,13 It depends only on the unperturbed occupied orbitals for which ni * 0. The diamagnetic component σstd is dominated numerically by the first term in eq 2. This term is related to the diamagnetic current
B Jd )
with i * a
i(0) - (0) a
and
GIAO-DFT Method and Its Interpretation
bp
(1,s) (1,s) Fai - i(0)Sai
(1,s) uai )
occ unocc
B Jp ) R ∑ ∑ s)1
i
∑a uai(1,s)[Ψi∇BΨa - Ψa∇BΨi]B0,s
(8)
The magnitude of the coupling is given by u(1) ai . It is inversely (0) proportional to the energy gap (0) (eq 5) and for a large i a part directly proportional to the first term in eq 7 (1) ≈∝uai
R
(0) c(0) rν × ∇ B ]u|χν〉} ∑ λa cνi {〈χλ|[b 2 λ,ν
R ˆ u|Ψi〉 (9) ∝ - 〈Ψa|M 2 Within the GIAO formalism, the action of the magnetic operator M ˆ u on Ψq is simply to work with iLˆ νu on each atomic orbital χν. Here Lˆ νu is the u-component of the angular momentum operator with its origin at the center R Bν on which χν is situated. Tabulations for Lˆ νuχν are available in the literature.50,51 Results and Discussion We shall now provide a discussion of how the 13C and 17O NMR shielding tensors in CO are modified as the CO molecule is complexed to a metal center. The discussion will start with free CO and continue to the binary hexa-, penta-, and tetracarbonyls in the next sections. The coordinate systems are always chosen such that the z-axis points along the CO bond vector of the ligand probed by NMR. Complexation of a ligand to a metal is accompanied by changes in the chemical shifts of the ligand atoms. These effects are usually analyzed in terms of the coordination chemical shift. The coordination shift is defined as52
∆δ ) δcomplex - δligand
(10a)
In our attempts at a quantitative interpretation, the shielding terminology (σ) is employed instead of the chemical shift (δ). Given the opposite signs of σ (shielding) and δ (chemical shift),
13C
and
17O
NMR Shielding Tensors
J. Phys. Chem., Vol. 100, No. 9, 1996 3361
TABLE 1: Comparison between Experimentalg and Calculated Absolute 13C Chemical Shielding Tensor Components for the CO Molecule and Group 6 Metal Carbonyls (Numbers in ppm) system CO Cr(CO)6 Mo(CO)6 W(CO)6 rel.f
σxx (expt)a
σyy (expt)a
σzz (expt)a
anisotropy ∆σ (expt)a
isotropic shielding σ (expt)a
-149.4g (-132.3b) -174.5g (-167.6 ( 15c) -169.6g (-157.6 ( 15c) -167.9e -157.9f (-138.6 ( 15c)
-149.4 (-132.3) -174.5 (-167.6 ( 15) -169.6 (-157.6 ( 15) -167.9 -157.9 (-138.6 ( 15)
273.6 (273.4) 265.8 (255.4 ( 15) 267.6 (260.4 ( 15) 271.5 267.5 (256.4 ( 15)
423.0 (406(s) ( 1.4) 440.3 (423 ( 30) 437.5 (417 ( 30) 439.4 425.4 (395 ( 30)
-8.4 (1.0 (sr)) -27.7 (-26.6 ( 15(s, 1)) -23.9 (-17.6 ( 15) -21.4 -16.1 (-6.6 ( 15(s, 1))
other workd (absolute scalea)
-20.4 -19.4 -6.2
a The data originally reported in ppm relative to liquid TMS are converted to absolute shielding using the 13C absolute shielding scale in which σ(13C in liquid TMS) ) 185.4 ppm on the basis of 13C in CO(molecular beam) ) -42.3 ( 17.2 ppm, see ref 53. b References 3 and 57. c References 58 and 59. d Reference 21. e Nonrelativistic NL-SCF calculation. f Relativistic NL-SCF-QR calculation. g Experimental data are generally solid state data (s) or, as indicated, liquid (l), gas (g), or a combination of spin-rotation constants plus standard diamagnetic shieldings (sr).
TABLE 2: Comparison of Experimentalf and Calculated Absolute 17O Shielding Tensor Components for the CO Molecule and Group 6 Metal Carbonyls (Numbers in ppm) system CO Cr(CO)6 Mo(CO)6 W(CO)6 rele
σxx (expt)a
σyy (expt)a
σzz (expt)a
anisotropy ∆σ (expt)a
isotropic shielding σ (expt)a
-307.3d (-267.6 ( 26(sr)c) -302.4d (-307.1 ( 10-20b) -295.6d (-277 ( 10-20b) -291.8d -268.7e (259.1 ( 10-20b)
-307.3 (-267.6 ( 26(sr)) -302.4 (-271.1 ( 10-20) -295.6 (-248.1 ( 10-20) -291.8 -268.7 (-228.1 ( 10-20)
410.6 (408.47 ( 26) 374.3 (401.9 ( 10-20) 362.9 (386.9 ( 10-20) 359.7 351.9 (374.9 ( 10-20)
717.9 (676.1 ( 26(sr)) 676.7 (691 ( 10-20) 658.5 (650 ( 10-20) 651.5 620.6 (619 ( 10-20)
-67.9 (-42.7 ( 17.2) -76.8 (-59.1 ( 10-20) -76.1 (-46.1 ( 10-20) -74.6 -61.8 (-40.1 ( 10-20)
a The experimental data originally reported in ppm relative to liquid H O are converted to absolute shielding using the 17O absolute shielding 2 scale in which σ(17O in liquid H2O) ) 307.9 ppm, see ref 53. b Reference 59. c Reference 57. d Nonrelativistic NL-SCF calculations. e Relativistic NL-SCF-QR calculations. f Experimental data are generally solid phase data (s) or, as indicated, liquid (l), gas (g), or a combination of spin-rotation constants plus standard diamagnetic shieldings (sr).
the coordination shift should be defined in terms of the shielding terminology as
∆δ ) σligand - σcomplex
(10b)
Thus, the coordination shift is defined as the difference in the shielding of the free ligand and the shielding of the ligand in the complex. We will use this terminology throughout the paper. Free CO. Tables 1 and 2 display the calculated as well as experimental 13C and 17O NMR shielding tensor components for free CO. It can be seen that the experimental values for σxx and σyy are negative for both nuclei. For these components the p (s ) x, y) of (usually) negative paramagnetic contribution σss eq 4 dominates over the (usually) positive diamagnetic contribud of eq 2. Our calculations reveal in addition that the tion σss leading paramagnetic contribution to σxx and σyy comes from the coupling between the σCO HOMO (1a) and the π* CO LUMO
ˆ s|π* (1b) of CO through the matrix elements 〈σ*CO|M CO〉 (s ) x, y), as defined in eq 9. It follows further from the discussion in the previous section that M ˆ xπ* CO (1c) is obtained from π* CO by
rotating50,51 each constituting atomic p-orbital χν around an axis in the x-direction, through the center on which χν is situated by 90°. The function M ˆ xπ* CO (1c) will have the form of a σ-type orbital and thus overlap with the HOMO 1a. The current induced by the coupling of the σCO HOMO with π* CO is shown in 1d. It corresponds to the perturbation of an external magnetic field in the x-direction. The σzz component in free CO is seen to be positive for both nuclei. It is dominated by the diamagnetic terms of eq 2. In fact the paramagnetic contribution to σzz is exactly zero due to ˆ z commutes with the Hamiltonian symmetry.53 This is so since M for linear molecules and thus is unable to couple different eigenfunctions, including occupied and virtual orbitals. Turning next to the calculated values, we note that the agreement between theory and experiment is excellent for the purely diamagnetic component σzz with respect to both nuclei. It seems that the GIAO-DFT formalism is well suited to evaluate d , as is almost any first principle NMR scheme.2,3,5 On the σss other hand, σxx and σyy are both calculated to be too negative d also is evaluated (Tables 1 and 2). We suggest that σss correctly by the GIAO-DFT scheme for these components and p , which is calculated to be too low that the error comes from σss (negative) by the GIAO-DFT method. The same error affords isotropic shielding constants σ ) 1/3(σxx + σyy + σzz) that are somewhat too low (negative) and shielding anisotropies ∆σ ) σzz - 1/2(σxx + σyy) that are too high. However, it should be pointed out that the experimental numbers are associated with some errors and that these errors at least for 17O are comparable to the deviation between theory and experiment. It is clear from Tables 1 and 2 that 13C and 17O have different shielding ranges. This conforms to well-known experimental facts.54-56 Thus, the totally diamagnetic σzz component in CO
3362 J. Phys. Chem., Vol. 100, No. 9, 1996
Ruiz-Morales et al.
TABLE 3: Contribution to the Calculated Shifta in the Isotropic Shielding of 13C for Complexed CO in M(CO)6 for M ) Cr, Mo, and W dist ∆δxx , ppmb
system
7.2c
Cr(CO)6 Mo(CO)6 W(CO)6 (NR)c W(CO)6 (rel)d
9.4c 11.1c 11.1d
dist ∆δyy , ppmb
dist ∆δzz , ppmb
p′ ∆δxx , ppme
p′ ∆δyy , ppme
p′ ∆δzz , ppme
∆δoc, ppmf
∆δoc-vir, ppmg
∆δ, ppma
7.2 9.4 11.1 11.1
0.0 0.0 0.0 0.0
3.2 -7.4 -12.1 -23.1
3.2 -7.4 -12.1 -23.1
35.7 31.1 31.4 35.9
-3.3 .4 -1.3 -1.5
18.8 11.7 9.8 4.0
15.5 12.1 8.5 2.5
p′ p′ 3 dist 3 p′ b Bdist a Coordination shielding: ∆δ ) σ oc 1 1 . Here CO is the free CO )b σ CO -b σ CO* CO - σM(CO)n or ∆δ ) ∆δ + /3∑s)1∆δss + /3∑s)1∆δss. ∆δ molecule and CO* the distorted ligand with the bond length it will have in the complex. The subscript p′ indicates that only contributions from p′ p′ ) σss,CO* the last term of eq 4 are taken into account. c Nonrelativistic NL-SCF calculations. d Relativistic NL-SCF-QR calculations. e ∆δss p′ p′ p′ f oc σss,M(CO)6 is the difference in the paramagnetic term of eq 4 between M(CO)6, σss,M(CO)6, and the distorted ligand CO*, σss,CO*. ∆δ is the contribution to the coordination shielding ∆δ from all the terms in eqs 2 and 4 that only depend on the occupied orbitals. g ∆δoc-vir is the contribution to the coordination shielding ∆δ from the last term in eq 4 that couples occupied and virtual orbitals.
TABLE 4: Contribution to the Calculated Shifta in the Isotropic Shielding of 17O for Complexed CO in M(CO)6 for M ) Cr, Mo, and W system
dist ∆δxx , ppmb
dist ∆δyy , ppmb
dist ∆δzz , ppmb
p′ ∆δxx , ppme
p′ ∆δyy , ppme
p′ ∆δzz , ppme
∆δoc, ppmf
∆δoc-vir, ppmg
∆δ, ppma
Co(CO)6 Mo(CO)6 W(CO)6c W(CO)6d
18.1c 23.8c 28.1c 28.1d
18.1 23.8 28.1 28.1
0.0 0.0 0.0 0.0
-34.7 -36.5 -46.1 -64.8
-34.7 -36.5 -46.1 -64.8
40.9 46.3 53.4 62.4
6.3 1.2 0.9 -2.4
2.6 7.0 5.8 -3.7
8.9 8.2 6.7 -6.1
a-g
See Table 3.
is larger for oxygen than for carbon. Also the σxx and σyy components dominated by paramagnetic contributions are larger for oxygen than carbon in absolute terms. These differences are not directly understandable from the way in which the Jp of eq 8 are made up through induced currents B Jd of eq 3 and B magnetic couplings, since these couplings are independent of the NMR nucleus N under consideration. The dependence on N comes from the full expression of the shielding tensors determined by
σNλν ) ∫
b r N × [J Bdν(b r N) + B J pν(b r N)]λ rN3
db rN
(11)
as expressed in detail in eqs 2 and 4. It involves an expectation value of rN-3 where rN is the distance to the NMR nucleus. For this reason the diamagnetic and paramagnetic contributions to the shielding constants of main group elements are roughly proportional54-56 to 〈a03/r3〉np, where np is the valence p-orbital of the NMR nucleus. Barnes and Smith54 have calculated 〈a03/ r3〉np for a number of elements. The 〈a03/r3〉2p values for carbon and oxygen were found to be equal to 1.23 and 4.3, respectively. Because of this, oxygen has numerically larger diamagnetic and paramagnetic contributions to the shielding constants. We shall draw on this point again in our discussion of the metal carbonyls. Cr(CO)6, Mo(CO)6, and W(CO)6. Table 1 displays calculated and experimental3,53,57-59 absolute 13C NMR shielding tensor components for the three hexacarbonyls M(CO)6 (M ) Cr, Mo, and W). A similar compilation is given in Table 2 for the 17O shielding. The calculated and observed tensor components σss (s ) x, y, z) compare well for both 13C and 17O, with differences almost within the experimental error limits. It is worth pointing out that the experimental σxx and σyy components should be equal for a single M(CO)6 molecule. The fact that they are different must be attributed to crystal effects. All hexacarbonyls have observed absolute isotropic shieldings, σ, that are negative for 13C as well as 17O. Further, σ decreases in absolute terms down the triad. For the 13C shielding, the largest drop occurs at the 5d element tungsten. Carbon as well as oxygen is seen to be deshielded in Cr(CO)6 and Mo(CO)6 compared to free CO. In W(CO)6 this deshielding is only marginal for carbon and changed to a shielding for oxygen. All of the experimental trends are reproduced by the GIAO-DFT
scheme after the inclusion of relativity (Tables 1 and 2). Kaupp21 et al. have recently published calculated isotropic 13C shielding constants for several transition metal complexes based on their IGLO-DFT scheme. It follows from Table 1 that their calculated isotropic carbon shieldings for the hexacarbonyls are in good agreement with experimental values and our estimates based on the GIAO-DFT method. We shall now turn to an interpretation of the observed changes ∆δ in the isotropic shielding of carbon and oxygen (eq 10) as CO is complexed to the metal center. Comment will also be provided on the observed trends for the individual components of the shielding tensor. The coordination shift ∆δ has contributions from the paramagnetic coupling between occupied and virtual orbitals, ∆δoc-vir, represented by the last term of eq 4 as well as contributions, ∆δoc, due to the remaining terms in eqs 2 and 4 that only depend on the occupied orbital. Thus:
∆δ ) ∆δoc-vir + ∆δoc
(12)
The components ∆δoc-vir and ∆δoc are displayed for carbon and oxygen of the hexacarbonyls in Tables 3 and 4, respectively. It is evident from the tables that ∆δoc-vir is predominant (trend setting), and we have in order to gain further insight into this term decomposed it as
∆δoc-vir )
1
3
∑∆δssdist +
3s)1
1
3
∑∆δssp′
3s)1
(13)
p′ p′ Bdist ) b σ CO -b σ CO* is the change in the contribution Here ∆δ from the last term of eq 4 due to the elongation (by ∼ 0.02 Å) of the bond vector in CO to the distance it will have in the dist (s ) x, complex, CO*. We display calculated values for ∆δss y, z) with respect to carbon and oxygen in Tables 3 and 4, dist respectively. The two terms ∆δdist xx and ∆δyy are positive and determined by an increase in the paramagnetic coupling (1c and d) between the σCO HOMO (1a) and the π* CO LUMO (1b) of CO as the energy gap between the two orbitals is diminished by the bond stretch. The RCO bond stretches are ∆RCO ) 0.013, 0.017, and 0.020 Å for chromium, molybdenum, and tungsten, dist (s ) x, y) increases respectively, and we note that ∆δss linearly with ∆RCO, as one would predict from our analysis.
13C
and
17O
NMR Shielding Tensors
J. Phys. Chem., Vol. 100, No. 9, 1996 3363 shift ∆δ in W(CO)6 is negative as opposed to the positive values in Cr(CO)6 and Mo(CO)6 (Table 4). The interaction between σCO and the metal orbitals represents a donation of charge from the CO ligand to the metal center. We see that this bonding mode tends to shield 13C and 17O by shifting ∆δ to lower values, in particular for the 5d element. The complexed CO ligand has as opposed to free CO a paramagnetic contribution to the zz-component of the shielding p′ tensor in terms of ∆δzz (Tables 3 and 4). The M ˆ Z operator of eq 9 does not commute with the Hamiltonian in M(CO)6 and can as a consequence couple occupied and virtual orbitals. There are two main categories of couplings. The first involves the occupied πCO type orbitals 1t1u, 1t2u, 1t2g, 1t1g (Figure 1) and the virtual π*CO type orbitals 3t1u, 2t2u, 3t2g, 2t1g (Figure 1). As an example, the occupied 1t1u-y orbital (3a) is primarily πCO
Figure 1. Schematic orbital level diagram for M(CO)6.
Note that the effect is larger for oxygen than for carbon. This is a consequence of 〈1/r3〉2pO > 〈1/r3〉2pC; see discussion in dist is zero due to connection with free CO. The term ∆δzz symmetry, as discussed above. The second part of eq 13 deals with the change in the coupling between occupied and virtual orbitals as CO* is complexed to p′ (s ) x, y, and z) the metal. The individual components of ∆δss can be found for carbon and oxygen in Tables 3 and 4, p′ respectively. The two components ∆δp′ xx and ∆δyy are again determined by the paramagnetic coupling (1c and d) between the σCO HOMO (1a) and the π* CO LUMO (1b) of CO*. The σCO HOMO (1a) is now involved in the 2t1u, 1eg, and 1a1g σ-orbitals of the M(CO)6 complex (Figure 1). They are all shifted to lower energy than σCO in free CO due to the bonding interactions with the (n + 1)s (1a1g), ndσ (eg), and (n + 1)p (2t1u) orbitals (Figure 1). The π* CO LUMO (1b) is on the other hand involved in the 2t1g, 3t1u, 2t2u, and 3t2g orbitals of M(CO)6 (Figure 1). Of these, 3t2g and 3t1u are shifted to higher energies than π*CO of free CO due to interactions with metal orbitals. All these interactions widen the effective energy gap between σCO and π* CO with the result that the paramagnetic coupling is reduced p′ 13C and ∆δp′ xx as well as ∆δyy are negative in all cases but the shielding in Cr(CO)6. Again, the effect is more pronounced for oxygen than for carbon, in line with our previous discussion. The reduction is especially noticeable for W(CO)6 after relativity has been included. Relativistic effects will lower the energy of 6s and 6p and thus make them more accessible for interactions with σCO. The result is a stabilization (2) of 1a1g
and 2t1u which will reduce the paramagnetic σCO to π*CO coupling. This reduction is primarily responsible of the facts that the coordination shift ∆δ of W(CO)6 is smaller than that in Cr(CO)6 and Mo(CO)6 (Table 3) and that the 17O coordination
based with some admixture from σCO. It can couple with the ˆ z|2t2u-x〉 (3c) has a σ-type empty 2t2u-x orbital (3b) since M component that facilitates an overlap with 1t1u-y and makes the ˆ z|2t2u-x〉 different from zero. The coupling element 〈1t1u-y|M second and more important category arises from a coupling between the 2t2g HOMO of M(CO)6 (4a), which is dπ based
with an in-phase bonding contribution from π* CO, and the empty ˆ z|2t1g-x〉 2t1g orbitals (4b), which are purely π* CO based. Again, M (4c) will overlap with 2t2g-y (4a) through the common π* CO lobes on 4a and 4c. The interaction between dπ and π* CO represents the back-donation of density from the metal to CO. We see that it tends to deshield 13C and 17O by shifting ∆δ to higher values (Tables 3 and 4). The picture that emerges from our analysis is that the metal to CO back-donation as well as the bond stretch of the coordinated CO ligand has a positive contribution to the coordination shift ∆δ for carbon as well as oxygen whereas the contribution from the CO to metal donation is negative for the two nuclei. We shall finally comment on the observed trends in the σss shielding matrix components (Tables 1 and 2). The experimental σzz components for complexed CO in M(CO)6 (M ) Cr, Mo, W) are positive for both nuclei as in the case of the free ligand. For carbon, σCzz of M(CO)6 is reduced compared to that of the free ligand by about the same amount for all three metals. The σOzz component of complexed CO is also reduced compared to that of free CO and decreases further down the triad. The observed trends in σzz are well reproduced by the GIAO-DFT scheme, and we can correlate the reduction in σCzz and σOzz with the emergence of the negative paramagnetic contribution - ∆δp′ zz in the hexacarbonyls (Tables 3 and 4).
3364 J. Phys. Chem., Vol. 100, No. 9, 1996
Ruiz-Morales et al.
TABLE 5: Comparison between Experimentalf and Calculated Absolute 13C and 17O Chemical Shielding Tensor Components for Fe(CO)5 and Ni(CO)4 (Numbers in ppm) system
σxx (expt)a
Fe(CO)5d
-178.5 (ax)e -175.4 (eq)e -176.6 (av)g (169.6 ( 15b) -147.9e (-140.6 ( 15b)
Ni(CO)4
anisotropy ∆σ (expt)a
isotropic shielding σ (expt)a
13C Chemical Shielding Tensor Components -178.5 (ax) 211.8 (ax) -171.9 (eq) 245.7 (eq) -174.5 (av) 232.1 (av) (-169.6 ( 15) (255.4 ( 15) -147.9 252.0 (-140.6 ( 15) (254.4 ( 15)
390.3 (ax) 419.4 (eq) 407.8 (av) (425 ( 30) 399.9 (395 ( 30)
-48.2 (ax) -33.8 (eq) -39.6 (av) (-27.6 ( 15) -14.6 (-8.6 ( 15) -120 (ax) -84.5 (eq) (-80.1 ( 8(l)c) -65.1 (-54.1(l)c)
σyy (expt)a
σzz (expt)a
Fe(CO)5d
-302.5 (ax)e -260.0 (eq)e
17O Chemical Shielding Tensor Components -302.5 (ax) 244.9 (ax) -337.4 (eq) 341.6 (eq)
547.4 (ax) 640.6 (eq)
Ni(CO)4
-265.5e
-265.5
601.2
335.7
a 13C: The data originally reported in ppm relative to liquid TMS are converted to absolute shielding using the 13C absolute shielding scale in which σ(13C in liquid TMS) ) 185.4 ppm on the basis of 13C in CO(molecular beam) ) -42.3 ( 17.2 ppm, see ref 53. 17O: The experimental data originally reported in ppm relative to liquid H2O are converted to absolute shielding using the 17O absolute shielding scale in which σ(17O in liquid H2O) ) 307.9 ppm, see ref 53. b References 58, 60, and 61. c Reference 62. d The CO ligand probed by NMR could be in axial (ax) or equatorial (eq) positions. e Nonrelativistic NL-SCF calculation. f Experimental data are generally solid state data (s) or, as indicated, liquid (l), gas (g), or a combination of spin-rotation constants plus standard diamagnetic shieldings (sr). g Weighted average (av).
TABLE 6: Contribution to the Calculated Shifta in the Isotropic Shielding of 13C and 17O for Complexed CO in Fe(CO)5 and Ni(CO)4 system
dist ∆δxx , ppmb
dist ∆δyy , ppmb
dist ∆δzz , ppmb
p′ ∆δxx , ppme
p′ ∆δyy , ppme
Fe(CO)5 equatorial Fe(CO)5 axial Ni(CO)4
13.4c,d 13.4c,d 7.2c
13.4 13.4 7.2
0.0 0.0 0.0
13C 3.6 -2.4 -14.8
-0.2 -2.4 -14.8
Fe(CO)5 equatorial Fe(CO)5 axial Ni(CO)4
33.9c,d 33.9c,d 18.1c
33.9 33.9 18.1
0.0 0.0 0.0
17O -33.8 -34.4 -73.6
-69.3 -34.4 -73.6
p′ ∆δzz , ppme
∆δoc, ppmf
∆δoc-vir, ppmg
∆δ, ppma
53.2 84.2 41.5
-2.5 4.3 -2.6
27.9 35.5 8.8
25.4 39.8 6.2
91.5 185.9 85.6
-2.1 -9.5 5.7
18.7 61.6 -8.5
16.6 52.1 -2.8
1 3 p′ p′ oc a Coordination shielding: ∆δ ) σ 3 p′ b dist 1 Bdist ) b σ CO - b σ CO* . Here CO is the free CO molecule CO - σM(CO)n or ∆δ ) ∆δ + /3∑s)1∆δss + /3∑s)1∆δss. ∆δ and CO* the distorted ligand with the bond length it will have in the complex. c Nonrelativistic NL-SCF calculations. d The CO ligand probed by p′ p′ p′ NMR could be in the axial (ax) or equatorial (eq) position. e ∆δss ) σss,CO* - σss,M(CO) is the difference in the paragmagnetic term of eq 4 n p′ p′ f oc between M(CO)n, σss,M(CO) , and the distorted ligand CO*, σ . ∆δ is the contribution to the coordination shielding ∆δ from all the terms in ss,CO* n eqs 2 and 4 that only depend on the occupied orbitals. g ∆δoc-vir is the contribution to the coordination shielding ∆δ from the last term in eq 4 that couples occupied and virtual orbitals.
The σCxx, σCyy and σOxx, σOyy components remain negative as CO is complexed. For carbon, σCxx and σCyy are lower (more negative) in the complex compared to those for free CO and decrease in absolute terms down the triad. A similar decrease in absolute terms is seen for oxygen, where σOxx, σOyy starts out for M ) Cr at lower (more negative) values than in free CO and ends up for M ) W at a higher (less negative) value. Again, the observed trends in σss for s ) x, y, and z are reproduced well by the GIAO-DFT scheme, and we can correlate the p′ decrease of σxx and σyy to the trends in - ∆δp′ xx and - ∆δyy (Tables 3 and 4). Fe(CO)5. Iron pentacarbonyl has three equatorial and two axial CO ligands. The two sets of ligands are inequivalent and should in principle be distinguishable by NMR. However, Fe(CO)5 interchanges axial and equatorial sites rapidly60 and this fluxional behavior makes the interpretation of the experimental NMR data complex.60 Table 5 presents experimental58,60-62 and calculated absolute 13C and 17O NMR shielding tensor components for Fe(CO) . 5 The shielding tensor components σss in Fe(CO)5 were calculated for both the equatorial and axial 13C17O ligands. The experimental tensor components58,60-62 were obtained by NMR powder spectroscopy53 and correspond most likely to an average of the axial and equatorial sites. Averaged theoretical values are included in Table 5 as well for comparison. We have analyzed the calculated coordination shift, ∆δ, in
the isotropic shielding of carbon and oxygen as CO is complexed at either the equatorial or axial sites. The coordination shift52 is according to eq 12 made up of the two components ∆δoc-vir and ∆δoc. It follows from Table 6 that the contribution from the paramagnetic coupling between occupied and virtual orbitals, ∆δoc-vir, dominates over the contribution, ∆δoc, from the occupied orbitals. dist p′ and ∆δss A further decomposition of ∆δoc-vir into ∆δss according to eq 13 is provided in Table 6 as well. The dist contribution ∆δss comes from the stretch of CO to the distance it has in the complex. The stretch amounts to 0.024 Å for both axial and equatorial ligands. The two terms dist ∆δdist xx and ∆δyy are positive and determined as in the case of the hexacarbonyls by an increase in the paramagnetic coupling (1c) between the HOMO (1a) and the π* CO LUMO (1b) of CO as the energy gap between the two orbitals is diminished by dist the bond stretch. The term ∆δzz is zero by symmetry. We dist dist note again that ∆δxx and ∆δyy are larger for oxygen than for carbon because 〈1/r3〉2pO > 〈1/r3〉2pC. p′ signify changes in the paramagnetic couThe terms ∆δss pling between occupied and virtual orbitals as the stretched CO* ligand is complexed to the metal center. The two components p′ ∆δp′ xx and ∆δyy are determined by the coupling 1c, between the σCO HOMO (1a) and the π* CO LUMO (1b) of CO*. The σCO HOMO (1a) is stabilized by interactions with the (n + 1)s, ndσ,
13C
and
17O
NMR Shielding Tensors
Figure 2. Schematic orbital level diagram for Fe(CO)5.
and (n + 1)p orbitals on iron whereas the π* CO LUMO (1b) is destabilized by interactions with the ndπ metal orbitals (Figure 2). As a consequence of all these interactions the effective energy gap between σCO and π* CO is enhanced, yielding a decrease of the paramagnetic coupling. Because of this, p′ ∆δp′ xx and ∆δyy are, in general, negative. The effect is particularly noticeable for oxygen, again due to the larger 〈1/r3〉2p value. Also the reduction in the coupling between σCO and π* CO is largest at the axial site due to the strong stabilization of the axial σCO orbital 1a′1 (Figure 2) from interactions with dσ, in particular in the oxygen case (Table 6). The coordination of CO introduces a paramagnetic contribup′ , to the shielding tensor component σzz along the CO tion, ∆δzz bond vector in both the equatorial and axial sites of Fe(CO)5. The contributions are substantial in absolute terms and responsible for the large positive coordinations shifts ∆δ (Table 6). p′ term in the axial site gives We note further that the larger ∆δzz rise to corresponding larger downfield shifts, ∆δ, for the axial carbon and oxygen atoms. p′ comes from couplings beThe main contribution to ∆δzz tween the dπ HOMO (Figure 2) and the empty π* CO orbitals. The coupling in the equatorial site involves the 2e′ HOMO (5a) and the empty 3e′′ orbital (5b). Here 2e′ (5a) is a bonding
J. Phys. Chem., Vol. 100, No. 9, 1996 3365 axial and equatorial π* CO combination strongly destabilized from p′ interactions with dπ in the axial plane. The axial ∆δzz contribution arises from a coupling between the same 2e′ HOMO (5a) and the vacant 3e′ orbital (5d), where 3e′ is a nonbonding π* CO combination involving the axial ligands. Since the strongly antibonding vacant orbital 3e′′ (5b) in the equatorial coupling is of higher energy than the virtual nonbonding 3e′ p′ to the orbital (5d) in the axial coupling, the contribution ∆δzz p′ equatorial ligand is smaller than the ∆δzz contribution to the p′ is larger for oxygen than for carbon, axial ligand. Again ∆δzz as expected. The fluxional behavior of Fe(CO)5 makes it difficult to interpret its experimental NMR spectrum. There are two studies in which both the axial and equatorial isotropic shifts of 13C have been reported.60,63 Both have the axial carbons more deshielded, σ ) -38.763 and -30.660 ppm, than the equatorial carbons, σ ) -2163 and -22.760 ppm. This trend is reproduced well by our calculations, although the deshielding seems to be somewhat overestimated by the GIAO-DFT method. Ni(CO)4. We shall finally discuss Ni(CO)4. Table 5 displays calculated and experimental58,62 13C and 17O shielding tensor components. In the case of 17O, experimental data are only available for the isotropic shielding. The fit between calculated and experimental tensor components is in general good with differences within the experimental error limits. Oxygen has numerically larger tensor components than carbon for reasons explained previously. An analysis of the coordination shift for Ni(CO)4 is provided in Table 6. The stretch of the CO bond in this complex is a dist modest 0.013 Å. Thus ∆δdist xx and ∆δyy are small compared to those for some of the other carbonyls and as expected, positive. p′ The paramagnetic changes, ∆δp′ xx and ∆δyy, to the xx- and yyshielding tensor components are negative and numerically large. p′ The contributions from ∆δp′ xx and ∆δyy in Ni(CO)4 are only surpassed in absolute terms by those in W(CO)6. They are numerically large because all four σCO combinations in Ni(CO)4 are strongly stabilized by interaction with 3d, 4s, and 4p metal orbitals. Thus, the effective energy gap between the σCO HOMO (1a) and the π*CO LUMO (1b) of CO* is large and the corresponding coupling between the two orbitals (1c) reduced compared to that for free CO*. p′ component is positive for both 13C and 17O (Table The ∆δzz 6). It arises mainly from a coupling between the dπ based occupied 1t2 orbital (6a) and the empty π*CO type orbital 2t2
(6b). The coupling is possible because of the in-phase bonding contributions to 1t2 (6a) from π*CO. These contributions ensure ˆ z|2t2〉 (6c) through the common an overlap between 1t2 and |M π*CO lobes. The large negative contribution from ∆δp′ xx + results in a rather small carbon coordination shift ∆δ for ∆δp′ yy Ni(CO)4 and a corresponding oxygen shift that actually is negative. Concluding Remarks orbital between dπ in the equatorial plane and a combination of axial as well as equatorial π* CO orbitals whereas 3e′′ (5b) is an
We have studied the change of the coordination shift ∆δ for M(CO)6 (M ) Cr, Mo, W), Fe(CO)5, and Ni(CO)4. The
3366 J. Phys. Chem., Vol. 100, No. 9, 1996
Ruiz-Morales et al.
TABLE 7: Calculated and Experimental Coordination ShieldingssA Correlation with Other Properties of Metal Carbonyls compound Co(CO)6 Mo(CO)6 W(CO)6 Fe(CO)5 Ni(CO)4 a
∆δ for 13C, ppm calc expt 19.3 15.5 7.7 25.4 (eq) 39.8 (ax) 6.2
27.6 18.6 7.6 22.0 (eq) 37.0 (ax) 9.6
b
∆δ for 17O, ppm calc expt 8.9 8.2 -6.1 16.6 (eq) 52.1 (ax) 30.8 (av) -2.8
c
k(C-O), mdyn Å-1
∆R(C-O), Å
π*CO occupation per CO ligand
D(M-CO), kcal/mol
k(M-C), mdyn Å-1
17.2a 17.3a 17.2a
0.019b 0.017c 0.020c 0.024d
0.45 0.43 0.47 0.48 (eq) 0.50 (ax)
37f 41f 46f 42f
2.08a 1.96a 2.36a
0.38
25g
2.02a
16.4 3.4 -2.6 37.4 (av)
17.9a
11.4
d
e
0.013e f
g
Reference 68. Reference 64. Reference 65. Reference 66. Reference 67. Reference 69. Reference 70.
p′ TABLE 8: Correlation between ∆σzz and the Population of π*CO in the HOMO of M(CO)n
system
p′ ∆σzz in 13C shielding, ppm
p′ ∆σzz in 17O shielding, ppm
population of π* CO in HOMO
Cr(CO)6a Mo(CO)6a W(CO)6a W(CO)6 relb Ni(CO)4a Fe(CO)5a equatorial Fe(CO)5a axial
35.9 31.1 31.4 35.9 41.5 53.2 84.2
41.5 46.3 53.4 62.4 85.6 91.5 185.9
0.76 0.79 0.80 0.85 0.95 1.40 1.40
a Nonrelativistic NL-SCF calculation. b Relativistic NL-SCF-QR calculation.
calculated and experimental values are summarized in Table 7. It is clear that the GIAO-DFT method reproduced the observed trends in ∆δ for carbon as well as for oxygen. There have been attempts to correlate ∆δ in metal carbonyls to properties that are characteristic for this type of compound. Perhaps the most obvious is the metal to σ* CO back-donation. This property can be related to the CO stretch,64-67 ∆R(C-O), the CO force constant in the metal complex, k(C-O),68 or the π* CO population per CO ligand. All three measures for π* CO backdonation correlate well with each other, as shown in Table 7. However, neither of the measures correlates with the observed or calculated coordination shift ∆δ, nor would we expect such a correlation from our analysis in the previous section. Another possible property would be the first D(M-CO)69,70 dissociation energy or the related k(M-CO)68 force constant. Again, no correlation is apparent from Table 7. We have found in our analysis of the paramagnetic contribution to ∆δ that three terms are important. The first, ∆δdist xx + , from the stretch of the CO bond vector in complexed ∆δdist yy carbon monoxide is positive and directly proportional to ∆R(Cp′ is also O) and the π*CO back-donation. The second term ∆δzz positive. It comes from the paramagnetic coupling between the occupied dπ orbital and vacant π* CO combinations. It correlates with the bonding contributions from π* CO to the occupied dπ orbital, since such contributions increase the coupling to the vacant π* CO combinations. The correlation is illustrated in Table p′ 8. The last term ∆δp′ xx + ∆δyy, is negative and represents a decrease in the paramagnetic coupling (1c) between the CO HOMO σCO (1a) and the CO LUMO π* CO (1b) as the effective gap between the two orbitals is increased on coordination by interactions with the nd, (n + 1)s, and (n + 1)p orbitals. None of the three terms mentioned above are by themselves determining the trend in ∆δ, nor are they influenced by a common factor. It is for this reason not surprising that it is difficult to correlate ∆δ with any single property of the M(CO)n complexes. Acknowledgment. This work has been supported by the National Sciences and Engineering Research Council of Canada
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