Cundari Th.R. -- Computational Organometallic Chemistry-0824704789

108	Diedenhofen et al.

3.5.Calculation of Nuclear Magnetic Resonance Chemical Shifts of Transition Metal Compounds

There has been a stunning progress in the development of quantum chemical methods for calculating NMR chemical shifts of TM compounds in the last decade. Pioneering work in the field was carried out by Nakatsuji, who used Hartree–Fock/finite perturbation theory (HF/FPT) to predict TM chemical shifts of tetrahedral and octahedral 3d and 4d TM compounds (85). The ab initio values were generally in reasonable agreement with experimental values. However, the use of a common gauge origin at the metal center and the neglect of correlation energy precluded the extension of the method as a reliable tool for predicting chemical shifts of more complicated compounds and for ligand atoms. A breakthrough towards more accurate theoretical methods for the calculation of NMR parameters of TM compounds came when several groups developed methods for calculating NMR chemical shifts that are based on DFT. Different variants of the uncoupled DFT method with the IGLO (individual gauge for localized orbitals) (86) approach and with the GIAO (gauge including atomic orbitals) (87) method have been suggested (88). The most common methods presently used for TM compounds are the modified sum-over-states (SOS) density-functional perturbation theory (DFPT) IGLO approach by Malkin et al. (89) and the DFTGIAO work of Schreckenbach and Ziegler (90). Details about the methods can be found in the original publications. The scope and limitations of the methods have recently been reviewed in several papers (88,90,91). A review has also been published that focuses on the performance of DFT methods in predicting NMR parameters of TM compounds (92). The DFT-IGLO and DFT-GIAO methods are commonly used for TM compounds. While it seems that the GIAO approach is perhaps more robust than the IGLO method, it is too early to make a definite statement about the accuracy of the two methods. It is possible to obtain quite accurate results with IGLO and GIAO. The choice of the functionals, the basis set, and the method for calculating relativistic effects seems to be more important.

Although DFT methods for calculating NMR chemical shifts are still rather young, some standards have already been established. This became possible because systematic studies of the accuracy of the methods in the field have been made by Bu¨hl (91,93), by Kaupp (92,94), by Oldfield and coworkers (95), and by Schreckenbach, Ziegler, et al. (90,96). The most important conclusions of some representative papers shall shortly be summarized. We want to point out, however, that the calculation of NMR parameters for TM compounds is not a trivial task and that it is wise to consult an expert prior to running calculations. Also, much progress can be expected in the next couple of years, which may soon outdate the present recommendations. Yet, it is helpful to see what accuracy can already be expected from present standard methods.

QM Methods for Calculating TM Compounds

109

The choice of the method for calculating an NMR spectrum depends on whether one wants to know the chemical shifts of the ligand atoms or those of the metal atoms, which are usually more difficult to calculate. We will first focus on chemical shifts of the TMs. It is important to recognize that calculations of TM chemical shifts should not be carried out with ECPs for the metal, because the valence orbitals do not have the correct nodal behavior near the nucleus. This holds even when one is interested only in the relative shifts with respect to a standard compound, i.e., in the δ values of the chemical shifts for which some error cancellation may be expected. Thus, calculations of TM chemical shifts must be carried out with all-electron basis sets. It seems, however, that the effect of relativity on the predicted NMR chemical shifts can be neglected for 3d and perhaps even for 4d elements, but definitely not for the heaviest TM 5d elements. Table 18 shows calculated results of the absolute shielding and the chemical shifts of TM(CO)6 (TM Cr, Mo, W) at the nonrelativistic (NR) and quasirelativistic (QR) levels, which includes scalar-relativistic effects but not spinorbit coupling (95). It becomes obvious that relativity significantly influences the absolute values of the TM shielding. However, the chemical shifts at the NR and QR levels of Cr(CO)6 and Mo(CO)6 are very similar to each other. They are also in good agreement with experiment. The NR value for W(CO)6 clearly deviates from experiment, while the QR value is in much better agreement. We want to point out that the relativistic calculations were carried out with the frozen-core approximation; i.e., only the valence electrons have been treated with the QR approximation in the calculation of the molecules.

A very important point concerns the choice of the exchange and correlations functionals for the NMR calculations. The functionals should, in principle, depend on the current density induced by the magnetic field. Calculations using approximate current-DFT that have been published so far suggest that the currentdependent contributions to the chemical shifts are probably negligible (97). Thus, standard NL-DFT methods that do not depend on the current density are commonly used for the calculation of chemical shifts. No general trend has been established about the accuracy of the various functionals, although the results obtained with different functionals may vary significantly. The only general conclusion that can be made is that local DFT is insufficient for chemical shifts (92).

The most common functionals used in conjunction with the IGLO and GIAO approaches are BPW91, BP86, and B3LYP. A good example that shows the importance of the choice of the functionals is the study by Bu¨hl et al. (91) about the theoretically predicted 57Fe chemical shifts of various organometallic compounds. Table 19 shows the chemical shifts calculated at different levels of theory. It is obvious that the B3LYP-GIAO results are clearly superior to the SOS-DFPT-BPW91 data using the IGLO approach in conjunction with different

110

TABLE 18

Cr, Mo, W)

Calculated Metal Shieldings and
and in [WO	]	2	Using DFT-GIAO
4

Chemical Shifts (ppm) in

Transition Metal

Carbonyls

TM(CO)

6

(TM

				Calculated metal NMR
	Calculated metal shieldings				a
				chemical shifts
Compound	Nonrelativistic	Relativistic		Nonrelativistic	Relativistic	Experimental

Cr(CO)
		6
Mo(CO)
		6
W(CO)
[WO	]	6
		2
4

509	( 507)	451	( 449)	1831	( 1866)	1812	( 1846)	1795
1431	(1452)	1704	(1720)	1805	( 1814)	1804	( 1804)	1857
4900	(4892)	5834	(5767)	4075	( 4050)	3703	( 3615)	3505
825	(841)	2131	(2152)	0(0)		0	(0)	0

a Shifts are taken relative to the metal oxides Source: Ref. 96a.

[TMO4

2	.
]

.al et Diedenhofen

TABLE 19				57
				Fe Chemical Shifts Calculated with Various Density Functionals
Molecule						SOS-DFPT-PW91	SOS-DFPT-BP86	SOS-DFPT-DBP86	UDFT-GIAO-B3LYP Experimental
Fe(CO) (cyclo-C					H )	445	444	424	504	538
	3			4	4
Fe(CO)						0	0	0	0	0
	5
Fe(CO)		(H		CCCHCHCCH )		113	123	102	32	4
	3		2		2
Fe(CO)		(H CCCHCN)				102	90	104	210	303
	4		2
Fe(CO)		(H CCCHCHCO)				627	629	664	1237	1274
Fe(C	3		2
	H )		2			156	166	251	1485	1532
5	5
Source: Ref. 91.

Compounds TM Calculating for Methods QM

111

112	Diedenhofen et al.

FIGURE 5 Correlation between calculated and experimental 57Fe chemical shifts (ppm relative to Fe(CO)5) for two different functionals. The regression lines do not include the FeCp2 results. (From Ref. 92.)

TABLE 20 Comparison of Calculated and Experimental 13CO Chemical Shifts (ppm) Relative to TMS for Some First-Row Transition Metal Carbonyl Complexes

Compound	Exp.	ECP	AE-DZVP	AE-ext.
CO	185.3–187.1			175.0
H2CO	185.3			185.9
V(CO)6	225.7	216.8 (219.2)	215.5	215.7
Cr(CO)6	211.2–214.6	205.8 (207.7)	201.8	204.0 (205.1)
Mn(CO)5H cis	211.4	209.6 (210.3)	205.4	206.2 (207.4)
Mn(CO)5H trans	210.8	207.5 (207.9)	202.5	203.3 (204.0)
Ni(CO)4	191.6–193.0	197.6 (198.8)	192.3	192.9 (192.2)

Calculated at the SOS-DFPT-IGLO level using ECPs and all-electron basis sets with DZVP quality and extended basis sets.

Source: Ref. 98b.

QM Methods for Calculating TM Compounds

113

DFT options. In particular, the calculated IGLO values for ferrocene are dramatically in error by more than 1300 ppm, while the GIAO result concurs with experiment. However, the differences are caused mainly by the functionals used and not by the NMR methods. It has been shown that the GIAO results strongly depend on the functional being used. Figure 5 displays a correlation of experimental and calculated 57Fe chemical shifts predicted using the B3LYP and BPW91 functionals in conjunction with GIAO. The regression lines have slopes of 0.65 for BPW91-GIAO and 0.97 for B3LYP-GIAO. Thus, there is a dramatic improvement of the theoretically predicted 57Fe chemical shifts when the hybrid functional B3LYP is used. A comparison of the two methods for the calculation of 103Rh chemical shifts in various rhodium compounds showed a similar situation, but the slopes of the regression lines were 0.90 at BPW91-GIAO and close to 1 at B3LYP-GIAO (93a).

The calculation of the NMR chemical shifts of ligand atoms of TM complexes is somewhat easier than the metal chemical shifts, because the use of quasi-relativistic small-core ECPs for the metal-core electrons leads to negligible errors for complexes of 3d and 4d elements. The errors for complexes of the 5d elements caused by neglecting spin-orbit effects may become larger, but trends are usually reproduced correctly. Thus, calculations of 1H, 13C, 15N, 17O, 31P, and other chemical shifts of TM ligands can be carried out analogous to molecules composed of main group elements (94b,d,e,95d,96,98). Table 20 shows a comparison of theoretically predicted 13C chemical shifts of carbonyl ligands using ECPs and all-electron (AE) basis sets (98b). The calculations were carried out at the SOS-DFPT-IGLO level. It becomes obvious that the AE basis set does not lead to better results than the ECP method. The same paper reports a large number of calculated 13C chemical shifts of TM carbonyl and cyanide complexes, which demonstrates the good performance of the method (98b).

The quantum chemical methods may be used to predict not only chemical shifts but also the tensor components of the chemical shielding. Table 21 shows the experimental and calculated 13C and 17O shielding tensor components predicted by the NL-DFT-GIAO method of the transition metal hexacarbonyls of Cr, Mo, and W (96b). The experimental values have a rather large error bar, which makes it difficult to estimate the accuracy of the calculated absolute values. However, the trend of the observed data is well reproduced. Unusually large differences between the vector components of the chemical shifts have recently been reported for phosphido complexes (65). Table 22 gives experimental anisotropies and calculated values using GIAO and IGLO of model complexes with smaller substituents. Both methods predict the record-high differences between the tensor components quite well.

TABLE 21 Comparison Between Experimental and Calculated Absolute												13	C and		17	O Chemical Shielding Tensor
Components (ppm) for the CO Molecule and Group 6 Transition Metal Carbonyls
			CO				Cr(CO)6						Mo(CO)6										W(CO)6
	13	C	17	O	13		C	17	O	13		C				17	O	13		C				17	O
σxx	149.4		307.3			174.5		302.4			169.6					295.6			167.9				a	291.8			a
	( 132.3)		( 267.6 26(sr))			( 167.6 15)		( 307.1 10–20)			( 157.6 15)			( 277 10–20)					157.9				b	268.7			b
																			( 138.6 15)					( 259.1 10–20)
σyy	149.4		307.3			174.5		302.4			169.6					295.6			167.9				a	291.8			a
	( 132.3)		( 267.6 26(sr))			( 167.6 15)		( 271.1 10–20)			( 157.6 15)			( 248.1 10–20)					157.9				b	268.7			b
																			( 138.6 15)					( 228.1 10–20)
σzz	273.6		410.6		265.8			374.3		267.6						362.9		271.5			a			359.7		a
	(273.4)		(408.47 26)			(255.4 15)		(401.9 10–20)			(260.4 15)			(386.9 10–20)				267.5			b			351.9		b
																			(256.4 15)					(374.9 10–20)
Anisotropy ∆σ	423.0		717.9		440.3			676.7		437.5						658.5		439.4			a			651.5		a
	(406(s) 1.4)		(676.1 26(sr))			(423 30)		(691 10–20)			(417 30)				(650 10–20)			425.4			b			620.6		b
																			(395 30)					(619 10–20)
Isotropic	8.4		67.9			27.7		76.8			23.9					76.1			21.4			a		74.6		a
shielding σ	(1.0 (sr))		( 42.7 17.2)			( 26.6 15(s,l))		( 59.1 10–20)			( 17.6 15)			( 46.1 10–20)					16.1		b			61.8		b
																			( 6.6 15(s,l))					( 40.1 10–20)
Calculated values at BP86. Experimental values in parentheses. 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).
a
Nonrelativistic NL-DFT calculation.
b
Relativistic NL-DFT-QR calculation.
Source: Ref. 96b.

114

.al et Diedenhofen

TABLE 22	Experimental and Theoretical Anisotropies of the Calculated	31	P Chemical Shifts (ppm)

Compound
[Mo(P)(NH ) ]
	2	3
[W(P)(NH ) ]
2	3
[Mo(PS)(NH ) ]
		2	3
[W(PS)(NH ) ]
	2	3
[Mo(P)(NH ) (NH )]
	2	3		3
[W(P)(NH ) (NH )]
2	3		3
[Mo(P)(N N)]
3
[W(P)(N N)]
3
[Mo(PS)(NH ) (NH					)]
		2	3	3
[W(PS)(NH )			NH	]
	2	3	3
a
No convergence.
Source: Ref. 65.

δ

181.0211.7292.6267.3204.5295.9

nc	a
nc
nc
nc

IGLO

δ

1676.6 1395.9 769.8 667.1 1755.9 1825.8 nc nc nc nc

δ	δ
1857.6
1607.6
1062.4
934.4
1960.4
2121.7
	nc
	nc
	nc
	nc

δ

144.8187.9268.4247.8253.7240.196.0136.3402.0385.5

GIAO

δ

1707.6 1402.7 711.7 613.1 1948.5 1764.9 1823.2 1495.0 679.4 598.2

δ	δ
1852.4
1590.6
980.1
860.9
2202.2
2005.0
1919.2
1631.3
1081.4
983.7

		Experimental
δ		δ	δ	δ
324		1987	2311

—— —

—— —

—— —

—— —

—— —

267	2125	2392
280	1728	2008

—— —

—

—

—

Compounds TM Calculating for Methods QM

115

116	Diedenhofen et al.

4. SUMMARY AND CONCLUSION

The progress that has been made in the development of quantum chemical methods for accurate calculations of TM compounds in the last decade is truly impressive. The account given here is not comprehensive, but the examples presented reflect the already high accuracy of presently available methods. The review focused on methods for calculating geometries, energies, vibrational frequencies, and NMR chemical shifts, because they are probably the most important properties of a molecule. Theoretical methods for other properties are also available but not reviewed here. Standard levels of theory have been established that complement experimental techniques that aim at gaining insight into the structure and reactivity of TM compounds. Chemistry is no longer a purely experimental science. This has already been accepted in recent decades by organic chemists. Inorganic chemistry, particularly TM chemistry, appeared to be a much more difficult challenge. New theoretical methods, particularly NL-DFT techniques, have helped to conquer the field. Method development in TM chemistry has not come to an end yet. In particular, methods for calculating relativistic effects are a field where further progress can be expected in the near future. Theoretical TM chemistry is a booming field with a bright future.

ACKNOWLEDGMENTS

This work was financially supported by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. The HRZ Marburg, HLRZ Darmstadt, and HLRS Stuttgart provided computer time and excellent service.

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