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

TABLE 3	Calculated and Experimental First Bond Dissociation Energies D							e	(kcal/mol) of Isoelectronic
TM Hexacarbonyls
Method	[Hf(CO) ]	2	[Ta(CO) ]		W(CO)		[Re(CO) ]				2
						6					[Os(CO) ]
	6		6						6		6
B3LYP	51.40		47.81		45.93			48.22			58.20
	(49.61)		(45.95)		(43.84)		(45.99)				(55.87)
BP86	54.86		50.94		49.43			52.25			62.57
	(53.18)		(49.08)		(47.34)		(50.02)				(60.24)
MP2			53.08		54.76			58.21			69.90
			(51.21)		(52.67)		(55.98)				(67.27)
CCSD(T)			47.94		48.02			50.57			60.95
			(46.07)		(45.93)		(48.34)				(58.62)
Experimental					46.0 2
ZPE corrected values are given in parentheses.
Source: Ref. 51.

78

[Ir(CO) ]	3
6
74.94
(72.59)
79.05
(76.70)
85.71
(83.36)
77.45
(75.10)

.al et Diedenhofen

TABLE	4	Calculated and Experimental Carbonyl Stretching Frequencies v			CO	(cm	1	) and Force Constants F	CO
	˚
(mdyn/A) of the Hexacarbonyl Complexes and CO
			t
			1u

Compound
[Hf(CO)		2
	]
6
[Ta(CO)	]
6
W(CO)
6
[Re(CO)	]
6
[Os(CO)			2
		]
6
[Ir(CO) ]	3
6
CO

v	CO	F	CO
1863.3		14.50
1798.5		13.49
1757
1969.7		16.22
1899.4		15.06
1896.4		14.75
1850
2074.2		18.00
1996.4		16.65
1977.7		16.35
1977			f
		17.0
2176.8		19.83
2088.8		18.24
2053.1		17.64
2085			f
		18.1
2267.5		21.50
2165.5		19.60
2113.9		18.67
2190			f
		19.8
2335.2		22.77
2223.5		20.65
2139.6		19.09
2254			f
		20.8
2211.6		20.21
2117.6		18.79
2118.9		18.81
2143		18.9

EgvCO

1873.8 1805.4

1988.7 1914.6 1882.9

2097.7 2017.3 1998.5 1998 2200.1 2112.4 2087.2 2122 2287.4 2187.0 2144.1 2218 2349.6 2240.4 2163.2 2276

A	1g	v	CO
1990.9
1910.3
2098.6
2015.6
2019.2
2191.8
2106.7
2095.1
2115
2271.9
2184.2
2148.1
2197
2333.1
2237.3
2172.7
2259
2373.4
2269.3
2167.9
2295

Method

B3LYP BP86 Experimental B3LYP BP86 MP2 Experimental B3LYP BP86 MP2 Experimental B3LYP BP86 MP2 Experimental B3LYP BP86 MP2 Experimental B3LYP BP86 MP2 Experimental B3LYP BP86 MP2 Experimental

Compounds TM Calculating for Methods QM

79

Source: Ref. 51.

80	Diedenhofen et al.

FIGURE 1 Trend of the calculated and experimental C-O stretching frequencies of the t1u mode of Hf(CO)62 , Ta(CO)6 , W(CO)6, Re(CO)6 , Os(CO)62 , Ir(CO)63 . (From Ref. 51.)

theoretical values are higher than given by experiment. Lupinetti et al. investigated the discrepancy between the CCSD(T) values and the experimental results. They carried out additional calculations using very large basis sets (53). The calculated bond energies did not change very much. BP86 and B3LYP give bond energies for the monoand dicarbonyls that are too high. The DFT methods also have problems with the relative FBDEs of Cu(CO) and Cu(CO)2 . CCSD(T) and even MP2, which notoriously gives bond energies that are too high, agree with the experimental observation that the FBDE of Cu(CO)2 is higher than that of Cu(CO) (Table 5). The bond energies predicted at BP86 are even higher than the MP2 values that are notoriously too high. The failure of the DFT methods for the monoand dicarbonyls of the group 11 metal ions is a warning against the indiscriminate use of DFT functionals without initial calibration calculations having been carried out.

The different approximations for all-electron relativistic calculations using one-component methods have recently been compared with each other and with relativistic ECP calculations of TM carbonyls by several workers (47,55). Table 6 shows the calculated bond lengths and FBDEs for the group 6 hexacarbonyls predicted when different relativistic methods are used. The results, which were obtained at the nonrelativistic DFT level, show the increase in the relativistic effects from 3d to 4d and 5d elements. It becomes obvious that the all-electron DFT calculations using the different relativistic approximations—scalar-relativ- istic (SR) zero-order regular approximation (ZORA), quasi-relativistic (QR) Pauli

TABLE 5		Calculated and Experimental TM–CO First Bond Dissociation Energies D					e	(kcal/mol) for [TM(CO)		]
Complexes (TM Cu, Ag, Au; n 1–4)									n
			MP2/I//	CCSD(T)/I//	CCSD(T)/I//	BP86/I//		B3LYP/I//
Compound			MP2/I	MP2/I	CCSD(T)/I	BP86/I		B3LYP/I	Experimental
[Cu(CO)]			38.1	32.3	32.9	51.7		43.3			37.4
[Cu(CO)			43.1	36.2	36.7	47.1		42.6			42.9
	]
2
[Cu(CO)			23.4	18.6	19.6	25.0		20.5			19.3
	]
3
[Cu(CO)			22.8	16.5	18.0	21.7		17.3			14.8
	]
4			23.3	21.8	22.0	35.2		29.5			22.0
[Ag(CO)]
[Ag(CO)	]		28.6	26.4	26.6	38.4		33.1			27.5
2
[Ag(CO)	]		13.9	12.6	12.8	16.4		13.8			13.6
3
[Ag(CO)	]		12.3	11.1	11.3	13.0		11.2			11.7
4			40.8	38.3	38.5	61.3		49.9			—
[Au(CO)]
[Au(CO)	]		51.0	47.0	47.3	57.2		51.9			—
2
[Au(CO)	]		9.2	6.4	6.9	11.5		7.2			—
3
[Au(CO)	]		9.3	6.7	7.3	10.1		7.1			—
4
Basis set I: 6–31G(d) for C, O; quasi-relativistic ECP with a valence basis set [311111/22111/411] for TM.
Source: Ref. 53.

Compounds TM Calculating for Methods QM

81

TABLE 6									˚							(kcal/mol) for
		Theoretical and Experimental Bond Lengths (A) and First Bond Dissociation Energies D													e
TM(CO)	6	(M Cr, Mo, W)
					Cr(CO)		6			Mo(CO)		6				W(CO)		6
Method			r (TM–C)		D	e	(TM–(CO))	r (TM–C)		D	e	(TM–(CO))	r (TM–C)			D	e		(TM–(CO))
DFT n.r.			1.908				41.6	2.079				37.2	2.106						37.5
DFT (SR)			1.904				42.0	2.068				39.6	2.062						45.0
ZORA
DFT QR			1.910				46.2	2.076				39.7	2.049						43.7
DFT DKH								2.068				39.3	2.063						46.9
DFT DPT			1.905				43.7	2.064				39.1	2.060						46.1
a			1.903				45.4	2.072				42.0	2.066						49.4
BP86
MP2			1.861				58.0	2.061				46.1	2.060						54.9
CCSD(T)//MP2							45.8					40.4							48.0
Experimental			1.918				36.8 2	2.063			40.5 2		2.058						46.0 2
a
BP86 values taken from Ref. 104.
Source: Ref. 54b.

82

.al et Diedenhofen

QM Methods for Calculating TM Compounds

83

Hamiltonian (PH), Douglas-Kroll-Hess (DKH), and direct perturbation theory (DPT)—give similar results as the much cheaper, quasi-relativistic ECP calculations. There is no reason for not using ECPs for the calculation of geometries, energies, and vibrational spectra of TM compounds. We want to point out that relativistic all-electron methods become important for the calculation of NMR chemical shifts and coupling constants, because the effect of the core electrons is not negligible anymore. This is discussed in more detail later.

The results shown in Table 6 seem to indicate that the different approximations for relativistic effects in all-electron calculations have a comparable accuracy. This is not the case. It has been found that the QR method using the Pauli Hamiltonian can lead to significant errors in the bond energy (55). An example will be given in the following section, about substituted carbonyl complexes.

3.2. Substituted Transition Metal Carbonyl Complexes

The accuracy of DFT methods and ab initio calculations has also been investigated for substituted TM carbonyl complexes TM(CO)nL. Two papers focused on group 6 and group 10 carbonyls with the formula TM(CO)5L (TM Cr, Mo, W) and TM(CO)3L (TM Ni, Pd, Pt), respectively (56,57). Table 7 shows a comparison of the calculated bond lengths and (CO)nTM-L BDEs of some complexes at the BP86, MP2, and CCSD(T) levels of theory. The BP86 calculations were carried out with all-electron basis sets and first-order relativistic corrections estimated by direct perturbation theory (57), while the MP2 and CCSD(T) results have been obtained using quasi-relativistic ECPs for Mo and W and nonrelativistic ECPs for Cu (56).

The results shown in Table 7 span a range between weakly (N2) and very strongly (NO ) bonded ligands. It becomes obvious that the bond lengths of the molybdenum and tungsten complexes calculated with BP86 and MP2 are very similar, while the BDEs predicted at MP2 are clearly higher than the BP86 values. Since the BP86 values for the bond energies are very similar to the data obtained at CCSD(T) it can be concluded that BP86 gives rather accurate bond lengths and bond energies for these systems.

It is frequently said that present DFT methods are not reliable enough to calculate weakly bonded systems. An important work by Ehlers et al. (58) about TM–noble gas complexes TM(CO)5NG (TM Cr, Mo, W; NG Ar, Kr, Xe) showed that the NL-DFT methods BP86 and PW91 have a comparable accuracy for calculating TM–NG bond energies as the CCSD(T) method. Table 8 shows the theoretical and experimental bond energies. The calculated values have been corrected for the basis set superposition error (BSSE). The large all-electron triple-zeta Slater-type basis set III augmented by polarization functions and diffuse functions was used in the DFT calculations. The basis set II for the CCSD(T) calculations employed DZ P valence basis sets for the TMs and QZ P

TABLE 7								˚					(kcal/mol) for TM(CO) L complexes
		Calculated Bond Lengths (A) and Dissociation Energies D
												e				5
			r (TM-(CO)		cis	)		r (TM-(CO)	trans	)		r (TM-L)				D	e	(TM-L)
L
			MP2/II	BP86				MP2/II	BP86			MP2/II	BP86	MP2/II				CCSD(T)/II	a
											Cr(CO) L
N		1.870		1.907				1.803	1.877		5		1.961	33.9				24.8
											1.936
2
CO		1.861		1.905										58.0				45.8
CS		1.860		1.907				1.920	1.930		1.804		1.869	84.9				65.8
NO		1.900		1.948				2.055	1.994		1.761		1.749	126.0				106.7
											Mo(CO) L
N		2.060		2.062				1.996	2.017		5		2.128	26.3				22.0
											2.164
2
CO		2.061		2.064										46.1				40.4
CS		2.066		2.068				2.119	2.095		1.985		2.024	70.0				60.8
NO		2.119		2.102				2.233	2.157		1.877		1.888	123.6				104.4
											W(CO) L
N		2.057		2.059				2.013	2.022		5		2.099	32.6				26.4
											2.126
2
CO		2.060		2.061										54.9				48.0
CS		2.063		2.063				2.094	2.085		2.006		2.025	80.3				70.7
NO		2.107		2.093				2.178	2.144		1.891		1.887	129.2				110.0
a
Using MP2 optimized geometries.
Source: MP2 and CCSD(T) values are taken from Ref. 56; the BP86 data are taken from Ref. 57.

84

BP86

22.5 43.7 59.5 103.0

19.8 39.0 54.5 101.8

25.6 46.1 63.1 109.0 Diedenhofen

al et .

TABLE	8		Dissociation Energies and Enthalpies (kcal/mol) of the Noble Gas Complexes TM(CO)																		–NG (TM Cr, Mo,
W; NG Ar, Kr, Xe)																				5
					CCSD(T)/II						BP86/III						PW91/III
				∆E	∆H		∆H	298		∆E	∆H		∆H	298		∆E	∆H		∆H	298		Experimental
						298	BSSE corr					298	BSSE corr					298	BSSE corr			∆H	298
Cr(CO)	Ar			4.9	6.3		3.5		1.9		3.3		3.0		3.8		5.2		4.8
5
Cr(CO)	Kr			6.2	7.5		4.7		3.0		4.3		4.0		5.0		6.3		5.9
5
Cr(CO)	Xe			7.2	8.5		5.0		5.4		6.7		6.4		7.6		8.9		8.5			9.0 0.9
5
Mo(CO) Ar				5.4	6.8		2.2		2.7		4.1		3.6		4.0		5.4		4.9
	5
Mo(CO)		Kr		6.9	8.2		4.4		3.9		5.2		4.7		5.1		6.4		5.9
	5
Mo(CO)		Xe		8.2	9.5		4.7		7.0		8.3		7.9		8.6		9.9		9.4			8.0 1.0
W(CO)	5																					3
	Ar			8.0	9.4		4.3		3.6		5.0		4.6		5.2		6.6		6.1
5
W(CO) Kr				10.0	11.3		6.7		5.1		6.4		6.0		7.0		8.3		7.8			6
5
W(CO)	Xe			11.9	13.2		7.6		7.6		8.9		8.8		9.8		11.1		10.7			8.2 1.0
5
Source:	Ref. 58.

Compounds TM Calculating for Methods QM

85

86	Diedenhofen et al.

valence basis sets for the noble gas elements. The authors also calculated the electric polarizabilities of the noble gases, because the TM-NG bonding is mainly due to dipole-induced dipole interactions. Table 9 shows the calculated results.

The data in Table 9 show that the larger basis sets used for the DFT calculations yield atomic polarizabilities in good agreement with experiment. The DFT values are even slightly too high. The polarizabilities predicted by the ab initio methods are clearly too low, which is caused by the significantly smaller basis sets. This is partly corrected by the contribution of the basis set superposition of the TM(CO)5 fragment orbitals to the calculated polarizabilities, which leads to ab initio results that are 75–80% of the experimental values. Table 8 shows that the theoretically predicted TM-NG BDEs (CCSD(T)/II, BP86/III, and PW91/ III) after BSSE correction are in reasonable agreement with experiment. The BSSE corrections at the DFT levels are very small. PW91 gives always larger bond energies than BP86. The error range of the experimental values is too large to discriminate among the methods. The CCSD(T)/II energy calculations used geometries optimized at MP2/II. The bond lengths calculated at MP2/II, BP86/ III, and PW91/III were found to be very similar (58). The message of this study is that NL-DFT methods may also be used for TM complexes with weakly bonded ligands.

Another class of substituted carbonyl complexes that has been investigated to test the accuracy of theoretical methods are phosphine complexes TM(CO)5PR3. The theoretical studies focused on the results obtained when different approximations for the treatment of relativistic effects are used (47,55). Table 10 shows the W–P bond lengths and bond energies of the complexes (CO)5W– PR3 (R H, CH3, F, Cl) that have been calculated with the BP86 functional

TABLE 9 Calculated and Experimental Electric Polarizabilities of the Noble Gas Atoms (10 24 cm3)

Method	Basis Seta	Ar	Kr	Xe
HF	II	0.716	1.086	2.352
MP2	II	0.723	1.064	2.340
CCSD(T)	II	0.730	1.068	2.364
HF	II W(CO)5 ghost functions	1.254	2.019	3.388
BP86	III	1.737	2.597	4.188
PW91	III	1.787	2.666	4.250
Experimental	Experimental	1.64	2.48	4.04

a Basis set II: ECP with [3111/3111/1] valence basis set. Basis set III: Triple-zeta Slater functions augmented by two s, p, d diffuse functions.

Source: Ref. 58.

TABLE	10 Calculated Bond Lengths r							˚					(kcal/mol) of W–PR				Bonds of
								(A) and Bond Dissociation Energies D				e				3
Octahedral W(CO)			PR	3	Complexes Using Different Approximations for Relativistic Effects
		5
						r(W-P)								D	(W-P)
														e
								BP86	BP86								BP86
R	BP86/II	a				BP86 (QR)	b	c	(DPT)	BP86/II	a			BP86 (QR)	b	(ZORA)		c
								(ZORA)
									d
H	2.515				2.496			—	2.518	35.3			37.2				—
F	2.409				2.374			—	2.399	43.3			39.6				—
Cl	2.442				2.431			—	2.442	32.6			33.3				—
Me	2.543				2.460			2.553	2.542	45.5			75.7				43.8
a
Quasi-relativistic ECPs.
b
Quasi-relativistic Pauli Hamiltonian.
c
ZORA approximation.
d
Direct perturbation theory.
Source: Ref. 55.

BP86 (DPT)d

33.0 35.1 29.2 43.5

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87