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

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calculation of vibrational properties requires full geometry optimizations to a high degree of accuracy, the PW91 DFT method is anticipated to be an appropriate theoretical tool, especially for metal-containing systems. We have recently shown that this method can be used with good success to calculate the vibrational modes of Pa(Cot)2 (15). Here we will extend these studies to the calculations and assignments of the vibrational spectra to the other An(Cot)2 (An Th–Am) systems, with comparisons to the available experimental data. The present work represents the first comprehensive theoretical study of the vibrational spectra and assignments of the actinocenes.

Based on standard group theoretical analysis (103), among the 93 vibrational modes of actinocenes with D8h symmetry, only the 4 A2u and 6 E1u modes are IR active, whereas 4 A1g, 5 E1g, and 6 E2g modes are Raman active. Table 6 lists the calculated LDA and PW91 frequencies, infrared intensities, and assignments for the vibrational modes of Th(Cot)2. The vibrational frequencies and IR intensities for the other actinocenes are listed in Table 7.

The simple linear-three-mass model for XYX systems (104) can be applied to the An(Cot)2 sandwich complexes when treating the Cot rings as rigid mass points. Using this model, three vibrational modes involving An–Cot interactions are apparent: (1) the symmetric ring–metal–ring stretching mode (A1g), (2) the asymmetric ring–metal–ring stretching mode (A2u), and (3) the ring–metal–ring bending mode (E1u). These three modes represent the lowest-frequency Raman and IR vibrations of actinocenes. As expected, the symmetric ring–metal–ring stretching causes a large change in the molecular polarizability, leading to a strong Raman absorption, observed at 225 cm 1 for Th(Cot)2. The asymmetric ring–metal–ring stretching mode of Th(Cot)2 is observed as a strong IR absorption at 250 cm 1. For the ring–metal–ring bending mode, which has not been observed experimentally for any actinocene, the potential energy surface is so flat that the calculated frequency of this mode becomes imaginary even when a very stringent numerical integration accuracy (INTEGRATION 8.0) is employed. By increasing the accuracy of the numerical integration even more (to INTEGRATION 10.0), we have obtained this frequency as 57 cm 1 for Th(Cot)2. Based on the experimental estimation, this band should appear around 125 cm 1 (102).

The C8H8 rings are, of course, neither structureless point masses nor rigid rings. In addition to the modes involving the metal–ring interactions (for which the rings are largely rigid), there are numerous modes corresponding to C–C and C–H stretching and in-plane ( ) and out-of-plane ( ) C–H bending. We will not detail the descriptions of these modes but only summarize the results in Table 6. We will examine more closely the ring-centered modes that lead to experimentally observed IR and Raman bands with strong intensities.

In addition to the previously mentioned strong absorption at 250 cm 1, the IR spectrum of Th(Cot)2 exhibits strong absorptions at 695, 742, and 895 cm 1.

TABLE 6			Calculated LDA and PW91 DFT Vibrational Frequencies (cm							1	) and Absolute IR Intensities (km/mol, in
parenthesis) for the IR and Raman Active Modes of Th(Cot)
								2
Mode			Exptl.		a	LDA		PW91			Assignment	b
A		2u	250	(s)		246	(72.7)	220	(76.9)		Asymmetric ring–metal–ring stretching
			695	(vs)		666	(457)	633	(446)		Asymmetric C–H bending ( )
			742	(s)		762	(17.2)	747	(0.7)		Asymmetric in-plane C–C stretching
			3005	(m)		3059	(0.4)	3079	(0.1)		Asymmetric C–H stretching
E	1u		(125)			8	(7.7)	57	(8.9)		Asymmetric ring–metal–ring bending
						225	(0.0)	235	(0.2)		Asymmetric in-plane C–C stretching
						743	(35.1)	745	(23.2)		Asymmetric C–H bending ( )
			895	(s)		915	(69.4)	895	(84.1)		Asymmetric ring–metal–ring tilting
			1315	(m)		1406	(1.5)	1430	(0.2)		Asymmetric C–H bending ( )
			2920	(m)		3052	(0.1)	3072	(8.3)		Asymmetric C–H stretching
A		1g	225	(s)		227		138			Symmetric ring–metal–ring stretching
						680		683			Symmetric C–H bending ( )
						770		809			Symmetric in-plane C–C stretching
			3045	(m)		3059		3058			Symmetric C–H stretching
E	1g		242	(s)		265		260			Symmetric ring–metal–ring tilting
						768		762			Symmetric C–H bending ( )
						911		898			Symmetric C–C stretching
			3022			1405		1426			Symmetric C–H bending ( )
				(m)		3052		3068			Symmetric C–H stretching
E	2g					237		235			Symmetric CCC bending	( )
			391	(m)		388		365			Symmetric in-plane C–C stretching
			775	(s)		817		819			Symmetric C–H bending ( )
						1187		1177			Symmetric C–H bending ( )
						1498		1500			Symmetric in-plane C–C stretching
			2905	(m)		3038		3066			Symmetric C–H stretching
a
The experimental intensities are shown as very strong (vs), strong (s), and medium (m) based on Ref. 100.
b
The and are referred to the Cot plane.

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TABLE 7 PW91 Vibrational Frequencies (cm 1) and Absorption Intensities (km/mol) for IR and Raman Active Modes of An(Cot)2 (An Pa–Am)

Mode	Pa(Cot)2	U(Cot)2	Np(Cot)2	Pu(Cot)2	Am(Cot)2
A2u	239	232	216	203	195
	683	735	741	734	722
	771	751	748	741	746
	3065	3072	3073	3076	3072
E1u	38	36	45	67	72
	220	236	235	235	235
	761	760	759	757	755
	895	908	910	907	909
	1438	1438	1438	1438	1439
	3064	3066	3066	3070	3064
A1g	328	385	252	192	87
	530	586	700	705	699
	839	756	716	708	765
	3090	3133	3125	3125	3072
E1g	253	233	221	221	216
	787	783	780	778	772
	902	902	903	901	903
	1427	1430	1432	1433	1435
	3063	3063	3065	3067	3065
E2g	219	143	235	250	253
	410	404	380	376	371
	823	829	828	831	824
	1161	1171	1174	1173	1176
	1513	1516	1518	1516	1516
	3046	3040	3041	3045	3051

All of these vibrational frequencies are reproduced with reasonable accuracy in the DFT calculations. The 695-cm 1 band is the strongest in the spectrum. The calculated frequencies, 666 cm 1 at the LDA level and 633 cm 1 at the PW91 level, are only in fair agreement with the experimental value. However, the mode is calculated to have the strongest absolute intensity, which is in complete accord with the experimental observation. We are therefore confident in assigning this mode as asymmetric C–H bending, which differs from a previous assignment of it as the asymmetric ring–metal–ring tilting mode (102). The 742-cm 1 and 895cm 1 modes are reproduced with remarkable accuracy at the PW91 level (Table 6). These bands are due to C–C stretching and asymmetric ring–metal–ring tilting, respectively.

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In addition to the strong band at 225 cm 1, the Raman spectrum of Th(Cot)2 shows two other strong absorptions at 242 and 775 cm 1, which are assigned as symmetric ring–metal–ring tilting and a C–C bending. These vibrational frequencies of these bands have been reproduced with reasonable accuracy at both the LDA and PW91 levels of calculation.

Table 6 demonstrates that the PW91 frequencies and IR intensities are overall in fair agreement with the experimental spectra. These theoretical results can be further improved by increasing the quality of the optimized geometry via the use of larger basis sets. By combining the calculated IR intensities and the frequencies, the PW91 theoretical calculations can provide reliable predictions of the positions and absorbency of the IR transitions. Therefore, theoretical calculations of IR spectra can be very useful in helping experimentalists to identify the IR bands and their microscopic origins, even for molecules as large as the actinocenes.

Because the geometric structures and bonding are very similar for the entire series of actinocenes, we might expect their vibrational frequencies to be very similar as well. Table 7 lists the PW91 calculated frequencies for the An(Cot)2 complexes, with An Pa–Am. We see a smooth trend in the vibrational frequencies across the series, with similar values to those discussed earlier for Th(Cot)2. The ability to calculate the predicted changes in the vibrational frequencies across a series of homologous complexes is certainly a strength of the application of DFT to vibrational problems.

From Tables 6 and 7, we see that the lowest A1g vibration (i.e., the symmetric Cot–An–Cot stretch) and the lowest A2u vibration (the asymmetric Cot–An– Cot stretch) show nearly the same trend across the actinide series: the frequencies increase slightly from Th to Pa and then decrease from U to Am. This trend is entirely consistent with the trends in the group orbital overlap integrals mentioned earlier and the An–C8H8 bond energies. Because the frequencies of fully symmetric vibrations are rigorously independent of the mass of An, the changes of the vibrational frequencies of the A1g mode from Th to Am directly reflects the An– Cot bonding strength. For the asymmetric Cot–An–Cot stretching mode, the frequency changes from Th to Am agree well with the increase of the atomic mass from Th to Am and the decrease of the symmetric stretching frequencies.

In conclusion, the calculated PW91 vibrational frequencies are in reasonably good agreement with the experimental data. As we discussed earlier, augmentation of the basis sets can improve the molecular geometries of the actinocenes. We can therefore expect that better agreement with experiments can be achieved if the vibrational frequencies are calculated with larger basis sets. The assignments of the IR and Raman vibrational modes will help us to understand the vibrational spectra of other actinocenes and their microscopic origins. Our calculations in this work indicate that gradient-corrected density functional meth-

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ods, especially the PW91 functional, not only can be used to elucidate the bonding and electronic structure, but can also be of great value in interpreting and predicting the vibrational properties of actinide complexes. Because the symmetric vibrational frequencies are not sensitive to the mass of the central metal, the present vibrational analysis and mode assignments will also be useful in understanding the vibrational spectra of lanthanocenes (105).

7. CONCLUSIONS

Relativistic density functional theory, especially with the inclusion of nonlocal exchange and correlation corrections, has become a powerful predictive tool in actinide chemistry. The methodology is sufficiently efficient to allow experimentally important properties, such as the geometry, vibrational frequencies, and infrared absorption intensities, to be calculated even for large organoactinide systems such as those discussed here. Inasmuch as many aspects of actinide chemistry are experimentally challenging because of the difficulty in handling of the elements, reliable theoretical calculations provide a valuable adjunct to experimental studies.

State-of-the-art DFT methods can provide theoretical interpretations of experimental results and are becoming more and more reliable in predicting physicochemical properties of actinide compounds. In spite of the current shortcomings of the method, new developments and future advances in density functional theory, such as the hybrid exchange-correlation functionals (106), meta-GGA functionals with high-order gradient corrections and kinetic energy density included (107), and time-dependent DFT (108), promise to provide even greater utility with respect to the study of ground-state and excited-state properties of actinide and organoactinide complexes (109).

ACKNOWLEDGMENTS

We gratefully acknowledge support for this research from the Division of Chemical Sciences, U.S. Department of Energy (Grant DE-FG02-86ER13529 to BEB), from Los Alamos National Laboratory, and from the Ohio Supercomputer Center and the Environmental Molecular Sciences Laboratory at Pacific Northwest National Laboratory for grants of computer time.

ABBREVIATIONS

An	actinide element
BLYP	Becke 1988–Lee-Yang-Parr
BP86	Becke 1988–Perdew 1986
Bz	benzene, C6H6

Relativistic DFT and Organoactinide Complexes		373
Cht	cycloheptatrienyl, C7H7
Cot	cyclooctatetraene, C8H8
Cp	cyclopentadienyl, C5H5
Cp*	pentamethylcyclopentadienyl, C5Me5
DFT	density functional theory
DZP	double-ζ basis set with polarization function
GGA	generalized gradient approach
HFS	Hartree–Fock–Slater
LDA	local density approach
NR	nonrelativistic
PW91	Perdew–Wang functional (1991)
RKS	spin-restricted Kohn–Sham
SO	spin-orbit
SOCI	spin-orbit configuration interaction
SR	scalar relativistic
TBB	1,3,5-tri-tert-butylbenzene, C6H3-tBu3
TZ2P	triple-ζ basis set with two polarization functions
UKS	spin-unrestricted Kohn–Sham

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