J. Phys. Chem. 1992, 96, 43'15-4381
4375
Theoretical Study on Metal NMR Chemlcal Shifts. Niobium Complexes Manabu Sugimoto, Mamoru Kanayama, and Hiroshi Nakatsuji* Department of Synthetic Chemistry, Faculty of Engineering, Kyoto University, Kyoto 606, Japan (Received: November 1, 1991; I n Final Form: January 16, 1992)
93Nbchemical shifts in 19 niobium complexes, NbX+,Y; (n = 0-6; X, Y = F, C1, and Br), are calculated by the ab initio Hartree-Fock method. The calculated values are in very good agreement with the experimental ones. Theoretical analyses reveal that the Nb chemical shifts are dominated by the paramagneticcontributionsand are due to the d-d* transition mechanism, in which the critical factor is a variation in the excitation energy AE. Based on an orbital interaction picture, AE is found to depend on the overlap interactions between the Nb 4d and ligand np orbitals. It is also observed that the Nb chemical shift is related to the electronegativity of the ligand atom, the Nb net charge, and the d-electron population of the central Nb atom. The origin of this correlation is also clarified.
Introduction A vast amount of experimental data has accumulated in recent years for transition-metal NMR chemical shifts.l For understanding the regularities and irregularities in the observed values, the need for knowledge on the electronic origin and the mechanism of the chemical shifts is ever increasing. In this series of studies,24 we systematically investigate NMR chemical shifts of metal nuclei, such as Cu, Ag, Zn, Cd38,b (dlos1-2po;class I), Sn? GeM(dl0sZp2;class 11), Mn,3CMO?"~Ti3g (d2-5~1-2; class 111). Recently, TosselS and Barfield et a1.6 have also studied the metal chemical shifts in Zn and Mo complexes, respectively. We have shown that the origins are classified into three types, depending on the occupations of the valence nd and (n l)p subshells. For the class I compounds, the d-hole or p-electron mechanism is the origin of the metal chemical shift. For the class I1 compounds, only the p-electron mechanism is important. For the class I11 compounds in which a metal has an open d subshell, the d-electron mechanism is dominant and is most clearly understood as a mixing of the magnetically allowed d-d* transitions from the perturbation theory point of view. We here report ab initio molecular orbital (MO) calculations of 93Nb NMR chemical shifts for 19 niobium complexes, NbX,+,,Y; (n = 0-6; X, Y = F, C1, Br), and elucidate the electronic origin and the mechanism of the chemical shifts. The Nb chemical shifts are expected to originate from the d-d* transition mechanism, because the Nb atom has an open d subshell as 4d45s1. In the complexes studied here, the shifts move monotonically downfield as the ligand is substituted into a less electronegative one. We will clarify that the interaction between the Nb 4d orbital and the halogen valence np orbital determines the
+
(1) (a) Harris, R. K., Mann, B. E., Eds. NMR and the Periodic Table; Academic: London, 1978. (b) Mason, J., Ed. Multinuclear NMR, Plenum: New York. 1987. (c) Mason, J. Chem. Rev. 1987,87, 1299. (d) Munakata, M.; Kitagawa, S.;Shibata, S.Introduction to the Multinuclear NMR, Approach to the State Analysis; KOdan-sya Scientific: Tokyo, 1991 (in Japanese). (2) (a) Nakatsuji, H. In Comparisons of A b Initio Quantum Chemistry with Experiment: State of the Art.; Bartlett, R. J., Ed.;Reidel: Dordrecht, The Netherlands, 1985. (b) Nakatsuji, H. In Modern Chemistry, Supplement 11, High Resolution NMR Spectroscopy; Saito, H., Morishima, I., Eds.; Tokyo Kagaku Dojin: Tokyo, 1987; p 237 (in Japanese). (3) (a) Nakatsuji, H.; Kanda, K.; Endo, K.; Yonezawa, T. J. Am. Chem. Soc. 1984,106,4653, (b) Nakatsuji, H.; Nakao, T.; Kanda, K. Chem. Phys. 1987, 115, 25. (c) Nakatsuji, H.; Nakao, T.; Inoue, T. Chem. Phys. Lett. 1990, 167, 1 1 1 . (d) Nakatsuji, H.; Nakao, T. To be submitted for publication. (e) Kanda, K.; Nakatsuji, H.; Yonezawa, T. J . Am. Chem. SOC.1984, 106, 5888. (f) Nakatsuji, H.; Sugimoto, M. Inorg. Chem. 1990, 29, 1221. (8) Nakatsuji, H.; Nakao, T. Chem. Phys. Left. 1990, 167, 571. (4) Nakatsuji, H.; Sugimoto, M.; Saito. S.Inorg. Chem. 1990, 29, 3095. (5) (a) Tossel, J. A. Chem. Phys. Lett. 1990, 169, 145. (b) Tossel, J. A. J . Phys. Chem. 1991, 95, 366. (6) (a) Combariza, J. E.; Enemark, J. H.; Barfield, M.; Facelli, J. C. J . Am. Chem. SOC.1989,111,7619. (b) Combariza, J. E.; Barfield, M.; Enemark, J. H. J . Phys. Chem. 1991, 95, 5463.
electronic structures of the Nb complexes and thereby their chemical shifts. We will see the existence of the parallelism between N b chemical shifts and some other quantities in these complexes.
Computational Details The Nb magnetic shielding constant u and the N b chemical shift 6 are calculated for 19 hexahalogenoniobates, NbX6,,Y[ (n = 0-6; X, Y = F, C1, Br). The geometrical isomers for the compounds of n = 2-4 are also investigated. We use the finite perturbation method for calculating the paramagnetic term of a magnetic shielding constant' as in this series of ~tudies.~J The unperturbed Hartree-Fock wave function is calculated by the H O N program.8 ~ The gauge origin is placed at the position of the N b atom. This choice is very natural and is expected to reduce errors in such highly symmetrical molecules. This is also anticipated from the work of Snyder and Parr, who showed that the contribution of the continuum states in the sum-over-states formula grows large when the gauge origin is moved away from the position of the nucleus? The basis sets are all taken from the Huzinaga's book;I0 the Nb basis is (16slOp7d)/[6~3p3d]augmented with the two diffuse p functions ({ = 0.074,0.023) representing 5p orbitals. The basis sets for F, C1, and Br atoms are (7s4p)/[2slp], (lOs7p)/[3s2p], and (13slOp4d)/[4~3pld],respectively. Our previous studies have concluded that the dominant contribution mainly comes from the metal atom concerned, and those of the ligands are negligibly smalL3 This suggests that the basis set for the central metal atom should be more accurate, and those for the ligands are less important. In addition, we have checked the ligand basis set dependence for the Nb magnetic shielding constants of NbFL and N b Q - using a split valence set augmented with a polarization d function. The results are discussed in the Appendix. The geometries are as follows: the Nb-F, N W l , and Nb-Br lengths are assumed to be constant for all the molecules studied here and are taken from the geometries of the neutral molecules NbF5, NbC15, and NbBr5,I1Le. d(Nb-F) = 1.88 A, d ( N W 1 ) = 2.28 A, and d(Nb-Br) = 2.45 A, respectively. The bond angles (7) (a) Cohen, H. D.; Roothaan, C. C. J. J . Chem. Phys. 1965,43, S34. (b) Cohen, H. D. J. Chem. Phys. 1965.43.3558. (c) Cohen, H. D. J . Chem. Phys. 1966, 45, 10. (d) Pople, J . A.; McIver, J. W.; Ostlund, N . S.Chem. Phys. Lett. 1967, 1 , 465. (e) Pople, J. A.; McIver, J. W.; Ostlund, N . S.J . Chem. Phys. 1968,49, 2960. ( 8 ) Dupuis, M.; Watts, J. D.; Villar, H. 0.;Hurst, G . J. B. Program Library HOND07 (No. 1501), Computer Center of Institute for Molecular Science, 1989. (9) Snyder, L. C.; Parr, R. G. J . Chem. Phys. 1961, 34, 837. (10) Huzinaga, S.;Andzelm, J.; Klobukowski, M.; Radzio-Andzelm, E.; Sakai, Y . ; Tatewaki, H. Gaussian Basis Sets for Molecular Calculations; Elsevier: Amsterdam, 1984. (1 1) Hellwege, K.-H., Hellwcge, A. M., Eds. Lnndolr-Bbrnstein; Spring er-Verlag: Berlin, 117, 1115:
0022-3654/92/2096-4375$03.00/00 1992 American Chemical Society
4316 The Journal of Physical Chemistry, Vol. 96,No. 11, 1992
Sugimoto et al.
TABLE I: Calculated Nb Magnetic Shieldlag Constants and Their Breakdown into Core and Valence MO Contributions (ppn) fla
molecule NbFLNbFiCltruns-NbF4CI2cis-NbF4C1, mer-NbF3C1< fUc-NbF,Cl< trans-NbF2Cl4cis-NbF2C1c NbFCIjNbClC NbC15Brtrans-NbCl4BrC cis-NbCI,Br< mer-NbC1,BrC fuc-NbCI,Br,truns-NbC12Br4cis-NbCl2BrL NbCIBr5NbBrC
core 3939.3 3969.1 3998.9 3998.9 4028.6 4028.7 4058.3 4058.4 4088.1 4117.7 4183.3 4248.8 4248.8 4314.3 4314.3 4379.8 4379.8 4445.4 4510.9
valence 193.2 188.2 183.4 183.3 178.5 178.4 173.9 173.8 169.2 164.6 163.2 161.9 161.9 160.5 160.5 159.1 159.1 157.8 156.4
omla
total 4132.6 4157.3 4182.2 4182.1 4207.1 4207.1 4232.2 4232.1 4257.2 4282.4 4346.5 4410.7 4410.6 4474.8 4474.8 4539.0 4538.9 4603.1 4667.3
"The definition of chemical shift is u(NbC1L)
E a
.
0
- u.
shift 149.8 125.1 100.2 100.3 75.3 75.3 50.2 50.3 25.2 0.0 -64.1 -128.3 -128.2 -192.4 -192.4 -256.6 -256.5 -320.7 -384.9
core -477.4 -476.6 -474.8 -480.4 -480.7 -487.3 -480.1 -488.2 -486.6 -481.8 -474.1 -465.6 -465.6 -456.3 -456.3 -446.0 -446.1 -434.9 -422.7
valence -1303.8 -1524.2 -1765.8 -1777.5 -2053.9 -2060.1 -2363.7 -2365.6 -2696.8 -3047.4 -3223.1 -3404.9 -3407.2 -3597.6 -3598.4 -3796.9 -3796.4 -4002.3 -4215.2
total -1781.2 -2000.7 -2239.9 -2257.9 -2534.6 -2547.4 -2843.7 -2853.7 -3183.5 -3529.2 -3697.2 -3870.5 -3872.7 -4053.8 -4054.6 -4242.9 -4242.4 -4437.2 -4637.9
shift -1748.0 -1528.5 -1289.3 -1271.3 -994.6 -981.8 -685.5 -675.5 -345.7 0.0 168.0 341.3 343.5 524.6 525.4 713.7 713.2 908.0 1108.7
o(tota1) 2351.4 2156.6 1942.3 1924.2 1672.5 1659.6 1388.5 1378.4 1073.7 753.2 649.3 540.1 537.9 421.0 420.1 296.1 296.5 166.0 29.4
8" calc exptlb -1598.2 -1490 -1403.4 -1189.1 -1171.0 -919.3 -906.4 -635.3 -625.2 -320.5 -258 0.0 0 103.9 126 213.1 246 215.3 253 332.2 371 333.1 378 457.1 492 456.7 497 587.2 616 723.8 735
A value of a positive sign means the downfield shift. bReferences 12 and 13.
t I I -1000 Theoretical
I
,'
1
1
0 ppm
Figure 1. Correlation between the calculated and experimental values of the Nb chemical shifts in the NbX6,Y; series (X,Y = F, CI, Br; n = 0-6). The open circles indicate the lack of the experimental values. 0
are all assumed to be 90'; Le., all complexes are octahedral or pseudooctahedral.
Theory-Experiment Correlation and Suggested Trends The calculated results of the Nb magnetic shielding constant u and chemical shift 6 are summarized in Table I. The definition of the chemical shifts utilized here is 6 = u(ref) - u
(1)
The reference molecule is NbC16-. The experimental values are from Tarasov et al.Iz for NbCl&,Br;. For NbF, and NbFC15-, the data from Kidd and Goodfellow are converted by using the relationI3 6(refNbC16-) = b(refNbF6-) - 1490 ppm
(2)
Figure 1 shows the correlation between the theoretical and experimental values of the Nb chemical shifts. The experimental values for the NbF6,C1; series with n = 1 4 are not available to the best of our knowledge. For the other compounds, our (12) Tarasov, V. P.; Privalov, V. I.; Buslaev, Yu. A. Mol. Phys. 1978, 35,
1047.
(13) Kidd, R. G.; Goodfellow, R. J. In ref la, Chapter 8. (14) Nakatsuji, H.; Saito, S.J . Chem. Phys. 1990, 93, 1865. (15) (a) Kidd, R. G.; Spinny, H. G. Inorg. Chem. 1973, 22, 1967. (b) Kidd, R.G.; Spinny, H. G. J . Am. Chem. SOC.1W1,103,4759.
1 2 3 4 5 6 Number of Heavier Atoms n
Figure 2. The dependence of the calculated and experimental Nb chemical shifts on the number of the heavier ligands.
theoretical results well reproduce the experimental values. This shows that the theoretical method used in the present study is reliable for the calculation of the Nb chemical shifts in these complexes. Relativistic and correlation effects seem to be small or to cancel for the Nb chemical shifts studied here. For each of the compounds NbF&,Cl; and NbC16,Br; with n = 2-4, there are two geometrical isomers. Our results show that the trans (meridional for n = 3) isomers have an upfield shift relative to the cis (facial) isomers except for NbC1,Br; whose cis and trans isomers have nearly equal shifts. For the NbCbBr; series, this trend is in accordance with the assignment of Tarasov et a1.I2 Our calculations indicate that the splitting between the isomers seems to become smaller as the ligand is substituted with a heavier atom. The dependence of the experimental and theoretical chemical shifts on the number of heavier ligands n is nearly linear as depicted in Figure 2. It is interesting to see that the slopes of the two series of complexes, NbF6,Cl; and NbCl+,Br;, are different, implying a difference in the effects of the substitution. A smaller slope for the NbCl,,Br; series reflects that the substitution of C1 with F brings larger effects on the electron distribution than the substitution with Br. In exaggerated terms, the theoretical plot for the NbF6,Cl,- series shows a small U-
The Journal of Physical Chemistry, Vol. 96, No. 11, 1992 4377
93NbChemical Shifts in Niobium Complexes TABLE II: A 0 Contributions to the Nb Mamgwtic Term uy. in ppm niobium molecule S P d total s NbF; 1916.4 1407.9 524.8 3849.1 19.5 1916.1 1407.8 526.1 3850.0 19.5 NbFiCI19.5 19.5 1407.7 527.8 3851.1 1915.6 trans-NbF,CIY 19.5 527.6 3851.0 1915.7 1407.8 cis-NbF,CIT 19.5 19.6 1407.7 529.5 3852.3 1915.1 mer-NbF,Cl,19.5 19.6 529.2 3852.2 1407.8 1915.2 foc-NbF,ClF 19.5 1407.6 531.6 3853.8 1914.6 trans-N bF2CIi 19.6 3853.7 1914.7 1407.7 531.3 cis-NbF2C1,
fluorine, bromine P d total' 27.7 47.2 27.6 47.1 (ax) 27.6 47.2 (eq) 47.1 27.6 47.1 (ax) 27.6 27.5 47.1 (eq) 47.0 (ax) 27.5 27.5 47.1 (eq) 47.0 27.5 47.0 27.5 47.0 27.4
NbFClC
1914.1
1407.7
533.5
3855.2
19.6
27.4
NbCIc NbC1,Br-
1913.5 1913.2
1407.7 1407.7
535.8 536.4
3856.9 3857.3
30.4
66.2
38.2
trans-N b C 4 B r ~ 1913.0 1913.0 cis-NbCI4Br2-
1407.8 1407.8
536.9 536.9
3857.7 3857.7
30.4 30.4
66.2 66.2
38.2 38.2
mer-NbC1,BrC
1912.7
1407.9
537.5
3858.1
fac-NbCI,Br; trans-N bCI2Br[ cis-NbCI2Br,-
1912.7 1912.5 1912.5
1407.9 1407.9 1407.9
537.5 538.1 538.1
3858.1 3858.5 3858.5
N bC1Br,-
1912.2
1408.0
538.7
3858.9
NbBr(-
1912.0
1408.1
539.3
3859.4
30.4 30.4 30.4 30.4 30.4 30.4 30.4 30.4 30.4
66.2 66.1 66.2 66.1 66.1 66.1 66.1 66.1 66.1
38.2 38.2 38.2 38.2 38.2 38.2 38.2 38.2 38.2
chlorine P total'
,dh
24.3
47.2
71.5
total 41 32.6 4157.3
24.3 24.3
47.0 47.1
71.3 71.4
4182.2 4182.1
24.3 24.3 24.3 24.3 24.3 24.3 24.3 46.9 24.3 24.3 134.8 24.3 24.3 24.3 134.7 24.3 134.8 24.3 24.3 134.7 (ax) 134.7 (3) 24.3 134.7 24.3 24.3 134.7 24.3 134.7 (ax) 134.7 (eq) 24.3 134.7 (ax) 134.7 (eq) 134.7
47.0 46.9 47.0 46.8 46.8 46.9 46.8 46.7 46.6 46.6 46.6 46.6 46.6 46.6 46.6 46.6 46.6 46.6 46.5
71.3 (ax) 71.2 (eq) 71.3 71.1 71.1 (ax) 71.2 (eq) 71.1 (ax) 71.0 (eq) 70.9 70.9 (ax) 70.9 (eq) 70.9 70.9 (ax) 70.9 (eq) 70.8 (ax) 70.8 (eq) 70.8 70.9 70.8
4207.1
46.5
70.8
4603.1
S
4207.1 4232.2 4232.1 4257.2 4282.4 4346.5 4410.7 4410.6 4474.8 4414.8 4539.0 4538.9
4667.3
'The parentheses indicate the position of a ligand; ax, axial; eq, equatorial.
t
shaped relationship as observed for Si and Sn chemical shifts of halogen-containing complexes. Origin of the Nb Chemical Shifts As is well-known, a magnetic shielding constant u is composed of two terms: a diamagnetic term d"and a paramagnetic term e, which are fmt-order and second-order quantities, respectively, in the perturbation theory. Table I shows the component analysis of the calculated chemical shift. We observe that the dominant contribution is from the paramagnetic term uprarather than the diamagnetic term dip. The sign of Adia is even different from that of Ad- and the observed shifts. Thus,A e is the dominant factor for the Nb chemical shift. It corresponds to an electronic response against an external magnetic perturbation and is represented by a mixing of excited states of the unperturbed system into the ground state. Therefore, it is necessary to investigate what state mixes in this way for giving rise to the paramagnetic term. Table I also shows the analysis of ad" and uprainto core and valence MO contributions. The valence MOs are the higher 18 occupied MOs composed of the Nb 4d, 5s and ligand np AOs. It is observed that the variations in the valence MO contributions of the paramagnetic term result in the chemical shifts. This is natural since the variations in the electronic states due to the ligand substitution are governed by the valence electrons. Tables I1 and I11 show the analyses of the qdla and upra,respectively, into atomic orbital (AO) contributions. The A 0 analysis is defined previ~usly,'~ similar to the Mulliken population analysis. For the diamagnetic term, the well-established Pascal-rule-like formula3ais also satisfied for the present Nb complexes.
din= dia(Nb atom) + XnLuLdia
(3)
This relation is derivable from the Flygarffioodisman equation16 when we neglect variations of M-L bonds. Thus,& is determined solely by the structural factors. The average of the of Nb atom is calculated to be 3855 ppm in this study, while the free (16) Flygare, W. H.; Goodisman, J. J. Chem. Phys. 1968,49, 3122.
-4000
E, a
.
2
1 - '0''0
t 0
1 2 3 4 5 6 Numher of Heavier Atoms n
Figure 3. The dependence of the Nb paramagnetic shielding constants and their Nb d components on the number of the heavier ligands.
atom value by Malli and Froese is 3870.35 ppm." For uprP,the contributions from the d orbitals of Nb are evidently the most significant. The contributions of the ligands themselves are negligibly small. In Figure 3, we plot the dependence of upra and the Nb d component of upraon the number of heavier ligands n. The apM is clearly dominated by the d component. We also see that the dependence is almost linear. The difference in the slopes of the two series of compounds is also observed. The tendency of deviation from the linearity is also seen for NbF+,,Cl;. This is the reason why the n dependence of 6 shown in Figure 2 deviates from (17) Malli, G.; Froese, C. Int. J . Quantum Chem. 1967, 1 , 95.
4378 The Journal of Physical Chemistry, Vol. 96, No. 11, I992
Sugimoto et al.
TABLE 111: A 0 Contributions to the Nb Paramagnetic Term upn in ppm
molecule NbFANbFiCl-
P -178.5 -231.1
niobium' d -1570.6 -1737.8
total -1749.1 -1968.8
f~c-NbF,Cl,trum-NbF,Cl,cis-NbF2C1c
-355.8 -372.3 -400.8
-2160.3 -2441.2 -2422.3
-2516.1 -2813.4 -2823.1
-1.7 -1.8 -1.7
fluorine, bromine P d totalb -3.4 -5.3 -3.3 -5.1 (ax) -3.5 -5.4 (4 -3.5 -5.3 -3.5 -5.4 (ax) -3.3 -5.0 (q) -4.9 (ax) -3.2 -3.5 -5.3 (eq) -3.2 -5.0 -3.5 -5.3 -4.9 -3.2
P~tts-N bF4ClC cis-NbF4C12-
-266.9 -289.9
-1941.7 -1936.4
-2208.6 -2226.3
mer-NbF3Cl
