J . Phys. Chem. 1989, 93, 5655-5660
5655
Ab Initio Molecular Orbital Configuration Interaction Study of Ni(PH,),(N,). Differences in Electron Correlation Effects between q'-End-On and q2-Side-On N2 Coordination Modes Shigeyoshi Sakaki* and Katsutoshi Ohkubo Department of Applied Chemistry, Faculty of Engineering, Kumamoto University, Kurokami, Kumamoto 860, Japan (Received: June 28, 1988; In Final Form: January 23, 1989)
Structure and bonding nature of Ni(PH3)2(v1-N2),Ni(PH3)2(72-N2)(9'-N2 = Vl-end-on N2, v2-N2= q*-side-on N2), and Ni( PH3)2(C2H4)are studied with ab initio MO Moller-Plesset (MP) perturbation and single-double configuration interaction (SD-CI) methods. Introduction of electron correlation effects is indispensable for investigating the relative stability of two coordination modes, TI-end-on and v2-side-on coordinations, of the N 2 complex. Although the binding energies of both coordination modes are almost the same on the Hartree-Fock level, introducing electron correlation effects with MP2, MP4(DQ), MP4(SDQ), and SD-CI methods yields much larger binding energy of the TI-end-on N2 coordination than that of the q2-side-on N2 coordination. Electron correlation effects on the Ni-N2 distance are also noticeable; in the TI-end-on mode, the Ni-N2 distance shortens by about 0.1 8, upon introducing electron correlation effects with MP2, MP4, and SD-CI methods, and the resultant Ni-N, distance agrees well with the experimental value. However, introducing electron correlation effects with the SD-CI method only slightly changes the Ni-N2 distance of Ni(PH3),(v2-N2) and slightly lengthens the Ni-C distance of Ni(PH3)2(C2H4),whereas both Ni-N and Ni-C bonds significantly lengthen by about 0.2-0.3 8, upon MP2 and MP4 calculations. A comparison of the optimized Ni-C distance and the calculated binding energy of the 7l-end-on N2 coordination with the experimental values suggests that the SD-CI method is more reliable than the M P method in these complexes. Differences in electron correlation effects between two coordination modes are easily explained in terms of nondynamical correlation that is characteristic of each coordination mode.
Introduction Transition-metal dinitrogen complexes have received considerable attention in the past decade.I Some of the impetus is, of course, activation of the nitrogen molecule via formation of transition-metal complexes and the subsequent N2 fixation into useful compounds.2 The presence of the dinitrogen coordination itself is also attractive from a viewpoint of molecular science of the chemical bond, because the nitrogen molecule is inert and its reactivity is very small. Furthermore, the coordination mode of dinitrogen complexes is interesting, as follows. The nitrogen molecule can interact with transition metals in two ways:3 one is the Vl-end-on coordination like CO, and another is the s2-side-on coordination like acetylene and ethylene (see 1 and 2 of Scheme I). Of these two coordination modes, the former has been isolated in many transition-metal dinitrogen c o m p l e ~ e swhereas ,~ the latter has been isolated only in a nickel cluster compound5 and proposed as a transition state or an intermediate of the N 2 linkage isomerization in [ R U ( N H ~ ) ~ ( N ~ ) W ] ~e' .wonder ~ why the q2-side-on coordination mode is very rare in the case of transition-metal dinitrogen complexes, in spite of many examples of ethylene and acetylene complexes that resemble the v2-side-on N, complex from ( I ) For example: (a) Olive, G. H.; Olive, S . Coordination and Catalysis; Verlag Chemie: Weinheim, 1977; p 289. (b) Chatt, J.; Dilworth, J. R.; Richards, R. L. Chem. Rev. 1978, 78, 589. (2) For example: Chatt, J.; da Camara Pina, C. L. M.; Richards, R. L., Eds. New Trends in the Chemistry of Nitrogen Fixation; Academic Press: London, 1980. (3) Goldberg, K. 1.; Hoffman, D. M.; Hoffmann, R. Inorg. Chem. 1982, 21, 3863, and references cited therein. (4) (a) Pombeiro, A. J. L., in ref 2, p 153. References cited therein. Following this review, subsequent papers have been published. (b) Yoshida, T.; Okano, T.; Thorn, D. L.; Tulip, T. H.; Otsuka, S.; Ibers, J. A. J . Organomet. Chem. 1979, 181, 183. (c) Thorn, D. L.;Tulip, T. H.; Ibers, J . A. J . Chem. SOC.,Dalton Trans. 1979, 2022. (d) Morris, R. H.; Ressner, J. M.; Sawyer, J. F.;Shiralian, M. J . A m . Chem. SOC.1984, 106, 3683. (e) Anderson, S . N.; Richards, R. L.; Hughes, D. L. J . Chem. SOC.,Dalton Trans. 1986, 245. (5) (a) Kruger, C.; Tsay, Y.-H. Angew. Chem., Int. Ed. Engl. 1973, 12, 997. (b) Jonas, K.: Brauer, D. J.; Kruger, C.; Roberts, P. J.;Tsay, Y.-H. Ibid. 1974, 12, 998. (6) Armor, J. A.: Taube, H. J . A m . Chem. SOC.1980, 92, 2560. (7) This problem has been discussed qualitatively in ref 3, based on the orbital interaction diagram.
0022-3654/89/2093-5655$01.50/0
SCHEME I N
II
i-
M
M
2
1
q
1
-end on
q2-side on
SCHEME I1
p
p,
T i I
N
i
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p/N'\.p
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p/"\p
P: PH3 3 I
4
-
P=PCy3
5
a point of view of metal-ligand interaction. M O studies including EH-M03,8and a b initio MO studies9J0 have been carried out on several transition-metal dinitrogen complexes. Information obtained from such MO studies is expected to be useful in understanding their electronic structure, bonding nature, coordination mode, and reactivity and also in finding transition-metal dinitrogen complexes to effect N2 fixation. Recently, rhodium(I)-dinitrogen complexes have been investigated (8) (a) Lauher, J. W.; Hoffmann, R. J . A m . Chem. Soc., 1976,98, 1729. (b) DuBois, D. L.; Hoffmann, R. Nouu. J. Chim. 1977, I , 479. (c) Hoffmann, R.; Chen, M. M.-L.; Thorn, D. L. Inorg. Chem. 1977, 16, 503. (9) (a) Veillard, H. N o w . J . Chim. 1978, 2, 215. (b) Murrell, J. N.; AI-Derzi, A,; Leigh, G. L.; Guest, M. F. J . Chem. SOC.,Dalton Trans. 1980, 1425. (c) Ondrechen, M. J.; Ratner, M . A,; Ellis, D. E. J . A m . Chem. SOC. 1981, 103, 1656. (d) Yamabe, T.; Hori, K.; Minato, T.; Fukui, K. Inorg. Chem. 1980, 19, 2154. Yamabe, T.; Hori, K.; Fukui, K. Ibid. 1982, 21, 2046. Hori, K.; Asai, Y.; Yamabe, T. Ibid. 1983, 22, 3218. (10) Sakaki, S.; Morokuma, K.; Ohkubo, K. J . A m . Chem. SOC.1985,107, 2686.
0 1989 American Chemical Society
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The Journal of Physical Chemistry, Vol. 93, No. 15, 1989
with the a b initio M O method,I0 which clarifies the reason that the 7’-end-on coordination mode is more stable than the q2-side-on mode, as follows: ( 1 ) the vi-end-on mode can receive greater stabilization from the electrostatic interaction, since the nitrogen molecule has a negative quadrupole moment and the rhodium(1) ion is positively charged in this complex, and (2) a donative ( N 2 Rh) interaction is stronger in the Vl-end-on mode than in the q2-side-on mode, whereas a a-back-donative (Rh d a N2 a*) interaction offers nearly equal contribution to both v2-side-on and ql-end-on modes. The above-mentioned analysis has been based on the Hartree-Fock calculation. A more detailed theoretical investigation including electron correlation effect is considered necessary in the case where the relative stability of two coordination modes are calculated to be very similar on the Hartree-Fock level. In the present work, the gl-end-on and V2-side-on coordination structures of Ni(PH,),(N,) (3 and 4 in Scheme 11) are investigated with a b initio MO Moller-Plesset perturbation ( M P ) ” and single-double configuration interaction (SD-CI) methods. Relative stability of these two coordination modes is predicted to be almost the same on the Hartree-Fock level for the following reasons: (1) The electrostatic interaction between N, and Ni(PH3)2would be very weak in both coordination modes, because the Ni atom in Ni(PH3),(N2) is zero-valent and neutral. (2) The donative (N, h i ) interaction would offer little stabilization to both coordination modes, since Ni(PH3)2is considered a strong Lewis base that substantially donates N i d a electrons to ligand.I2 Experimentally, however, only the 7’-end-on bridging type dinitrogen ( 5 in Scheme 11), has complex, (PCy3)2Ni-N=N-Ni(PCy3)2 been i ~ o l a t e d . ’ ~Therefore, it is reasonably anticipated that a detailed investigation including electron correlation effects is necessary to compare the relative stability of two coordination modes in Ni(PH,),(N,). This is the reason that Ni(PH3)2(N2) is examined here. The similar ethylene complex, Ni(PH3)*(C2H4), is also investigated with M P and SD-CI methods, since this complex resembles Ni(PH3)2(q2-N2)from a point of view of the metal-ligand interaction. Ni(PR,),(olefin) has been isolated and many experimental data have been reported, whereas Ni(PRJ2(v2-N2) has not been isolated and is considered not to be stable. Thus, we can compare calculated results with experimental ones not in the case of Ni(PH,),(s2-N2) but in the case of Ni(PH3)2(C2H4).Such a comparison would give us some information about the reliability of M P and SD-CI methods in these complexes. Through this theoretical work, we hope (a) to elucidate electron correlation effects on the relative stability and the coordinate bond distance of these two coordination modes, (b) to clarify the reason that the electron correlation effects differ between these two coordination modes, and (c) to compare reliability of the MP2. MP4, and SD-CI methods.
-
-
-
Computational Details The standard a b initio closed-shell Hartree-Fock calculations were carried out on a singlet state of Ni(PH3)*(N2)and Ni(PH3),(C2H4) with Gaussian 8214 and MELD program^.'^ Then, M P and SD-CI calculations were performed on these complexes with Gaussian 82 and MELD programs, respectively, using these molecular orbitals. Two types of basis sets were employed: In the first (BS I), a (3s2p5d) primitive setI6 contracted to [2s2p2d] and a (3s3p) primitive setI7 contracted to [2s2p] were used to represent the 3d, ( I I ) Pople. J . A.; Binkley, J. S.; Seeger, R. Int. J . Quantum Chem. Symp. 1976, 10. I . Krishnan, R.; Pople, J. A. I n t . J . Quantum Chem. 1978, 14, 91. (12) (a) Kitaura, K.; Sakaki, S.; Morokuma, K. Inorg. Chem. 1981, 20, 2292. (b) Sakaki, S.; Kitaura, K.; Morokuma, K. Ibid. 1982, 21, 760. (c) Sakaki. S.; Kitaura, K.; Morokuma, K.; Ohkubo, K. Ibid. 1983, 22, 104. (13) Jolly, P. W.; Jonas, K.; Kruger, C.; Tsay, Y.-H. J . Organomet. Chem. 1971. 33, 109. (14) Binkley, J. S.; Frisch, M.;Raghavachari, K.; DeFrees, D.; Schegel,
H. B.; Whiteside, R.; Fluder, E.; Seeger, R.; Pople, J. A . Carnegie-Mellon Quantum Chemical Archive, 1983. (15) Davidson, E. R.; McMurchie, L.; Elbert, S.; Langhoff, S. R.; Rawlings, D.; Feller, D. Program of MELD, IMS Computer Center Library No. 030. (16) Hay, P. J.: Wadt, W . R. J . Chem. Phys. 1985, 82, 270.
Sakaki and Ohkubo 4s, and 4p orbitals of Ni and the 3s and 3p orbitals of P, re-
spectively. The [Ar] core of N i and the [Ne] core of P were replaced with effective core potentials (ECP).I6ai7 For N and H atoms, the usual MIDI-4I8 and a (4s) primitive setIg contracted to a [2s] set were used, respectively. In the second basis set (BS II), the same basis sets as the BS I were used for N and H atoms but all-electron basis sets were employed for P and Ni atoms, as follows. For the P atom, the usual MIDI-4 set was used.i8b For the Ni atom, a ( 1 3s7p5d) primitive set, proposed for the state of Ni.18bwas incremented with a diffuse d primitive ({ = 0.10)2” and three p primitivesZobwhose exponents were taken to be the same as three most diffuse s primitives of Ni. The thus obtained (13sIOp6d) primitive set was contracted to [5s4p3d], Le., minimal for all core orbitals, double-{ for 4s and 4p orbitals, and triple-{ for the 3d orbital. The BS I set was used for preliminary M P calculations, and the BS I1 set was employed for M P and SD-CI calculations. A frozen-core approximation was applied to both M P and SD-CI calculations. In the case of the BS I set, the Is orbital of N and C atoms was considered a core orbital (note that core orbitals of Ni and P were replaced with ECP’s), and in the case of the BS I1 set, the I s - ~ s , 2p, and 3p orbitals of Ni, Is, 2s, and 2p orbitals of P. and Is orbital of N and C were excluded from the active space. In SD-CI calculations, the virtual orbitals were transformed to K orbitals to improve the C I convergence, as proposed by Davidson et aLzi In the case of Ni(PH3),(N2), about 101000 spin-adapted configuration functions were examined with perturbation selection (threshold = hartree) based on the second-order Rayleigh-Schrodinger perturbation theory.22 Resultant 7300-8 500 spin-adapted configuration functions, which include over 95% of the estimated single-double correlation energy, underwent the variational single-double configuration interaction calculation. In the case of Ni(PH3),(C2H4), the same perturbation selection (threshold = IO4 hartree) was applied to about 145 000 spin-adapted configuration functions, and then the variational SD-CI calculation was carried out on the resultant about 10 000-1 2 400 spin-adapted configuration functions which include over 92% of the estimated single-double correlation energy. The coefficient of the reference configuration, Co, is about 0.92 in all complexes examined. The variationally calculated limited S D correlation energy, E,,, SD.CI, was corrected by estimating the correlation energy arising from the discarded configuration functions, to yield E,,, SD.Ci,23 and then the correction of higher order CI expansions was carried out by the method of DavidsonZ4 to give E,,, full-CI. The geometry of Ni(PH3),(NZ) was taken from the experimental structure of [ N ~ ( P C Y , ) ~ ] ~ (inN which ~ ) , ~ ~the geometry of PH, was assumed to be the same as the PH3 molecule.25 The same N-N distance (R(N-N) = 1.12 ..&)I3 was assumed in both pi-end-on and v2-side-on N 2 modes of Ni(PH3)2(N2). Although this assumption seems arbitrary, a clear difference between two coordination modes is found, and therefore, semiquantitative discussion is expected to be possible, at least. In Ni(PH3)2(C2H4), the geometry of the Ni(PH,), part and the C=C distance were taken from the experimental structure of N i ( P R , ) , ( ~ l e f i n ) ,while ~~ (17) Wadt, W. R.; Hay, P. J. J . Chem. Phys. 1985, 82, 284. (18) (a) Tatewaki, H.; Hujinaga, S. J . Comput. Chem. 1980, I , 205. (b) Hujinaga, S.;Andzelm, J.; Klobukowski, M.; Radizio-Andzelm, E.; Sakai, Y.; Tatewaki, H. Gaussian Basis Sets f o r Molecular Calculations; Elsevier: Amsterdam, 1984. (19) Dunning, T . H.; Hay, P. J. Methods of Electronic Structure Theory; Schaefer, H . F., Ed.; Plenum: New York, 1977; p 1 . (20) (a) This exponent was estimated by even-tempered criterion. (b) These three primitives were added to represent the 4p orbital of Ni. (21) Feller, D.; Davidson, E. R. J . Chem. Phys. 1981, 84, 3997. (22) Langhoff, S. R. Davidson, E. R. Int. J . Quantum Chem. 1974, 8, 61. This computation is included in the MELD program. (23) Ee~tso-cl= €0 f ( E I ~ ~ S D- .€,)(I D I -k Ediscd/Ekspi), where Eo is the total energy of Hartree-Fock calculation, EdlSfd is the single and double correlation energy excluded from variational CI calculation, and ,Elrept is the SD correlation energy included in variational CI calculation. Edilod and ,Eiicp,are estimated by the second-order Rayleigh-Schrodinger perturbation method. (24) Davidson, E. R.; Silver, D. W. Chem. Phys. Lert. 1977, 52, 403. (25) Herzberg, G. Molecular Spectra and Molecular Structure; Academic Press: Kew York, 1974: Vol. 1. p 267.
The Journal of Physical Chemistry, Vol. 93, No. 15, I989
Ab Initio M O C I Study of Ni(PH3),(N2) r
I
I
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Figure 1. Binding energy (BE) calculated with M P method vs Ni-N2 distance in Ni(PH3)2!$-N2) and Ni(PH3),(v2-N2). The BS I (solid lines) and BS I 1 (dashed lines) sets were used. (a) The infinite separation is taken as a standard (energy 0), in which the ligand structure is not changed (see footnote c of Table I).
the C H 2 bending angle was assumed to be the same as the optimized value (26") of Ni(PH3)2(C2H4)on the Hartree-Fock level. I 2a
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-end o r Caard.rnrio? ( 0 1 .'-side on C o o r d i r a f ~ 0 n Figure 2. Binding energy (BE) calculated with M P method vs Ni-N2 distance in Ni(PH3),(o'-N2) and Ni(PH3)2(q2-N2). The BS I set was "
used, in which d polarization is added to the N basis set. (a) The infinite separation is taken as a standard (energy 0), in which the ligand structure is not changed (see footnote c of Table I).
Results and Discussion
Preliminary MP Calculations of Ni(PH3),(N2)and Ni(Pthe Hartree-Fock level, very shallow potential curves for the Ni-N2 distance are calculated with the BS I and BS I I sets in both coordination modes of Ni(PH,),(N,), as shown in Figure 1 .27 Furthermore, nearly equal binding energy of N 2 coordination is calculated in both coordination modes (see Table I), as predicted in the Introduction. Introducing electron correlation effects with MP2, MP4(DQ), and MP4(SDQ) methods, however, yields significant changes in the potential curves: (1) The potential curves become deep, and the binding energy of N 2 coordination increases in both coordination modes. (2) Two coordination modes exhibit considerably different binding energies on MP2 and MP4 levels; the binding energy of the VI-end-on mode is much larger than that of the q2-side-on mode, which is consistent with the experimental result that only the 7'-end-on mode has been isolated.20 (3) The Ni-N2 distance shortens in the VI-end-on mode but lengthens in the V2-side-on mode (see Figure 1 and Table I). The optimized Ni-N2 distance of the 7'-end-on mode agrees well with the experimentally reported Ni-N2 distance.20 These electron correlation effects are essentially the same in both the BS I and BS I I sets, whereas the binding energy and the optimized bond distance are only slightly different between the BS I and BS I1 sets. The binding energy of N 2 coordination would be estimated to be smaller than that of C2H4 coordination which has been reported to be 30 kcal/mol in Ni(PR3)2(C2H4),28 since the N 2 coordination is considered in general to be weaker than the C2H4coordination. In Ni(CO),(N2), the N 2 binding energy has been reported to be 21 kcal/mol (the relaxation of N i ( C 0 ) 3 is not ~ o r r e c t e d ) . ~ ~ Because C O is a better a-acceptor ligand than PH3, the C O ligand would weaken the a-back-bonding between Ni d a and N2 a * orbitals but would strengthen the electrostatic interaction and donative interaction. Thus, the N 2 binding energy is reasonably estimated to be not much exceeding 21 kcal/mol. The binding energies calculated on MP2 and MP4 levels seem too large, considering the above estimation. H3)2( C2H4).On
(26) Jolly, P. W.; Wilke, G. The Organic Chemisfry of Nickel; Academic Press: New York, 1974; Vol. I , p 267. (27) On the Hartree-Fock level, the BS I1 (all-electron) set tends to yield smaller binding energy than the BS I (ECP) set does, as shown in Figures 1 and 3. Although a general conclusion cannot be extracted from the limited number of calculations presented here, this result is worthy of note. (28) Tolman, C. A. J . Am. Chem. Sac. 1974, 96, 2780. (29) Turner, J. J.; Simpson, M. B.; Poliakoff, M.; Maier, W. B. J . Am. Chem. Sac. 1983, 105, 3898.
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Figure 3. Binding energy (BE) vs N i C 2 H , distance in Ni(PH3)2(C2H4). The BS I (solid lines) and BS I1 (dashed lines) sets were used. (a) The infinite separation is taken as a standard, in which the ligand takes the experimental structure. (b) The separation of R = 50.0 A is taken as a standard, in which the ligand has the experimental structure. (c) est SD-CI = correction of discarded single-double correlation energy. est full C I = correction of higher order C I expansions.
Recently, it has been reported that addition of a polarization function to a ligand basis set induces significant effects on a potential curve.3o Hartree-Fock and M P calculations were carried out, using the BS I set with a d-polarization function (( = 0.87)Iga added to the N basis set. As shown in Figure 2, the potential curves of two coordination modes are very similar to the corresponding modes calculated without the d-polarization function. Therefore, the d-polarization function was not added to the ligand basis set in rather detailed SD-CI and all electron M P calculations. Ni(PH3),(C2H4) is also investigated with the MP2 method, as shown in Figure 3A. The binding energies calculated with Hartree-Fock and MP2 methods roughly agree with the experimentally proposed value (about 30 kcal/mol),28 as shown in Table I. The optimized Ni-C distance is calculated to be 1.97 8, on the Hartree-Fock level, which agrees well with the experimentally reported value (1.99 The MP2 calculations, however, lengthen it to 2.34 i% in the case of the BS I set and to 2.29 8, in the case of the BS I1 set, which are too long. This electron correlation effect on the Ni-C distance is very similar to the result (30) (a) Marynick, D. S . Chem. Phys. Lert. 1987, 141, 455. (b) Dedieu, A., private communication.
The Journal of Physical Chemistry, Vol. 93, No. 15, 1989
5658
Sakaki and Ohkubo
TABLE I: Optimized Bond Distance between Ni and L (L = N2 or C 2 H I )and Binding Energies (BE)"
BE, basis set
BS I
BS I I
expt
BS I
BS 11
R(Ni-L),b 8,
method
Ni(pH3)2(q'-N2) HF 1.94 MP2 1.81 I .so M P4( DQ) 1.81 MP(SDQ) HF I .92 MP2 1.78 1.78 M P4( DQ) MP4(SDQ) 1.78 1.85 lim SD-CI est SD-CI 1.84 1.82 est full-CI 1.78g Ni(PH3)2(a2-N2) HF 2.03 MP2 2.21 MWDQ) 2.29 MP4(SDQ) 2.36 HF 2.05 MP2 2.16 MP4(DQ) 2.2 MP4(DQ) 2.4 MP4(SDQ) 2.2 MP4(SDQ) 2.4 lim SD-CI 2.13 est SD-CI 2.06 est full-CI 2.04
BS I BS I I
MP2 HF MP2 lim SD-CI est SD-CI est full-CI
2.24 1.81 2.18 1.89 I .85 1.89 1 .86h
expt
kcal/mol 8c 37
51 73 5d 38 56e 80' 7 14 16
6c 15 16 20 Id
13 13' 13' 15' 17' -3 5 4 3af 34 29d 35 17 33 35 30'
"These values are estimated from parabolic fitting of total energies. The Hartree-Fock energies (hartrees) near the minimum are as follows: E , of Ni(PH3)2(q1-N2)= -163.6672 with BS I, -163.7306 with BS I d polarization on N for R(Ni-N) = 1.78 A, -2298.1062 with BS I1 for R(Ni-N) = 1.81 A; E , of Ni(PH3),(q2-N2) = -163.6643 with BS I, -163.4366 with BS I d polarization on N for R(Ni-N,) = 2.0 A, -2298.1 104 with BS I1 for R(Ni-N2) = 2.03 A; and E , of Ni(PH3),(C2H4) = -132.8611 with BS I, -2267.3100 with BS I1 for R(Ni-C2H4) = I .8 A. R is the distance between Ni and the coordinating N atom in the q' end-on N 2 complex and the distance between Ni and the center of the X-X bond ( X = C or N ) in the q2 side-on N 2 and C2H4complexes (see R in Figures 1-4). CThe infinite separation is taken as a standard, because the size consistency is satisfied in M P calculation in general. At infinite separation, the structure of the ligand is not changed, because the lengthening of the N-N distance is very small (only 0.026 A). dThe separation of 50.0 A between N i and the ligand is taken as a standard, in which the ligand takes the equilibrium structure. 'This is not an optimized value but is compiled here for a comparison between BS I and BS 11. f T h e sum of total energies of two fragments is taken as a standard, in which the ligand takes the equilibrium structure. gFrom ref 13. *From ref 26. 'From ref. 27.
+
+
obtained in the q2-side-on N, complex. The disagreement found in the N, binding energy of the 7'-end-on Ni(PH3),(N2) and the optimized Ni-C distance of Ni(PH3),(C2H4)between M P calculations and experiments suggests that the M P method would not be appropriate in the Ni(0)-N2 and Ni(0)-C2H, complexes. Limited SD-CI Calculations of' N i ( P H 3 ) , ( N 2 )and Ni(PH3)2(C2H4). Both coordination modes of dinitrogen complexes have been investigated with the limited SD-CI method. In the case of the 7'-end-on mode, the binding energy increases and the optimized Ni-N, distance slightly shortens by 0.07 A upon introducing electron correlation effects with the SD-CI method, as shown in Table I and Figure 4. Extrapolation to full CI calculation yields further shortening of the Ni-N2 distance, and the resultant Ni-N, distance agrees well with the experimental value.13
Figure 4. Binding energy (BE) calculated with SD-CI method vs Ni-N2 distance in Ni(PH3),(q1-N2) and Ni(PH3)2(q2-N2). The BS I1 set was used. (a) The separation of R = 50.0 A is taken as a standard, in which the ligand structure is not changed. (b) est SD-CI = correction of discarded single-double correlation energy. est full CI = correction of higher order C1 expansions.
The binding energy with the correction of higher order C I expansions (Eestfull.cr) is about 16 kcal/mol for the reference state being taken a t the 50.0-A separation between N i and N,.3' It is noted that although these electron correlation effects on the Ni-N2 distance and the binding energy of N2 coordination are qualitatively the same as those obtained by M P calculations, the binding energy calculated with the SD-CI method is much smaller and seems more reasonable than the value calculated with the M P method (note the above-mentioned estimation of the binding energy). In the case of the V2-side-on coordination mode, on the other hand, the binding energy increases slightly and the optimized Ni-N, distance scarcely changes upon introducing electron correlation effects with the SD-CI method. As a result, the binding energy of the ql-end-on mode is greater than that of the q2-side-on mode, which is consistent with the experimental result. Again, inclusion of electron correlation effects with the SD-CI method yields a meaningful difference in the relative stability of two coordination modes. Other attention is drawn here to the Ni-N2 distance, because a critical difference is found in the optimum Ni-N, distance between M P and SD-CI calculations; although M P calculations considerably lengthen the optimized Ni-N, distance in the q2-side-on mode, the SD-CI calculations scarcely change it. Since the presence of Ni(PH3),(v2-N2) has not been known, it is still ambiguous which of the two, the M P and SD-CI methods, is correct concerning the bond distance of the q2-side-on N, complex. The well-known complex Ni(PH3),(C2H,) is again examined with the SD-CI method. SD-CI calculations lengthen the Ni-C distance to a much lesser extent than M P calculations do, as shown in Figure 3B and Table I. Important results are that the binding energy (35 kcal/mol) and the Ni-C distance (2.02 A) calculated with the SD-CI method agree well with experimental values (about 30 kcal/mol and 1.99 A)26,28and that M P calculations yield too long Ni-C distance (vide supra). These results suggest that the SD-CI method can be considered reliable, at least semiquantitatively, and that the M P method seems inappropriate in Ni(0)-q2-N2 and Ni(0)-C2H, complexes. Hereafter, we will discuss electron correlation effects, based on the SD-CI calculations. (31) The binding energy after correction of higher order CI expansion is calculated to be 1 1 kcal/mol for the reference state being taken at the infinite separation between Ni and N1. If both corrections of higher order CI expansion and perturbation selection are perfectly carried out, the binding energy depends little on the reference state. A difference of 4 kcal/mol between two estimations is not negligible. Of these two estimated values, the larger 16 kcal/mol value seems more reliable, because the reference state includes the quadruple excitations and the perturbation selection is carried out similarly in both the reference state and the complex.
A b Initio MO CI Study of Ni(PH3),(N2)
The Journai of Physical Chemistry, Vol. 93, No. 15, 1989 5659
TABLE 11. Occupation Numbers of Natural Orbitals' of Ni(PH3)2(N2)and Ni(PH&(C2H4).
N~(PHMv~-N~)~ 3a2 19al lobl
6b2 1 Ib, 12b1 7b2 20al 4a2
1.98
1.98 1.98 1.97 1.96 0.05
0.04 0.03 0.02
Ni 3d, Ni 3dz2-x2 (Ni 3d,, + N2 aJb N2 (Ni 3d,, + N2 A$ (N2 r X *+ Ni 3d,,)a (N2 ry* + Ni dJae Ni 4d,2,2 Ni 4d,
Ni(PH3)2(?2-N2)' 3% 17al 18al 6b2 12b, 13bl 4a2 19a, 7b2
1.98 1.98 1.97 1.97 1.96 0.05
0.04 0.02 0.02
Ni(PH3)2(C2Hdd
Ni 3d, Ni 3d,z N2 A~ N2 (Ni 3d,, + N2 A , * ) ~ (N2 A?* + Ni 4d,,)ae N2 A ~ * Ni 4d,z Ni 4dy,
17al 6b2 482 18a1 12bl 13bl 19al 5a2 7b2
1.98 1.98 1.98 1.98 1.95 0.06 0.02 0.02 0.02
C2H4 A C2H4 u C2H4u C2H4u (Ni 3d, + C2H4A * ) ~ (C2H4 A* + Ni 3d,,)a Ni 4d: Ni 4dy, Ni 4d:
'Orbitals with occupation number of 0.02-1.98 are compiled here. See ref 32 for superscripts a and b. bR(Ni-N2) = 1.81 A. cR(Ni-N2) = 2.03 A. dR(Ni-C2H4) = 1.90 A. 'This d,, orbital is a mixing of 3d,, and 4d,, orbitals. 'This d orbital is a mixing of dx2~y2and dzz orbitals.
Differences in Electron Correlation Effects between Two Coordination Modes. It is interesting that the electron correlation effect on the Ni-N2 distance is different between ql-end-on and q2-side-on coordination modes; in the former, the Ni-7'-N2 distance shortens upon introducing electron correlation effects, but in the latter, the Ni-v2-N2 distance scarcely changes and the Ni-C2H, distance slightly lengthens. Occupation numbers of several important natural orbitals are given in Table 11. In the 7'-end-on mode, nonbonding 3d and 4d orbitals of Ni, (Ni 3d,, + N 2 a,)b*32(Ni 3d,, + N, ax)", ( N 2 a x * + Ni d,,)", N 2 a,,, and (N, a,,* + Ni d,,,)" 3 3 make important contributions to electron correlation effects (see Figure 5 for the x and z axes, and see ref 32 for superscripts a and b). In the V2-side-on N 2 complex, the (Ni 3d,, + N 2 n,)" 32 interaction disappears because of the symN, a,*)b and metry constraint (vide infra), and the ( N i 3d,, ( N 2 a,* + Ni d,,)a 3 3 appear as important orbitals in addition to the N 2 ayand ay* orbitals and the Ni nonbonding 3d and 4d orbitals. A difference in electron correlation effects between two coordination modes is considered to result primarily from the orbitals in which the dinitrogen ligand directly interacts with the Ni atom. In the Tl-end-on mode, the N 2 a, and ax* orbitals and the N i d, orbital belong to the b, representation of the C,, symmetry. As shown in Figure 5A, the d, orbital, the H O M O of Ni(PH3),, can interact with the N2 T , orbital in an antibonding way and with the N2 a,* orbital in a bonding way.34 The resultant orbital, 11b,, includes a weakly antibonding interaction between Ni and N,,35 and its occupation number is about 1.95e, as shown in Table 11. The 12bl is an antibonding counterpart of the lib', and its occupation number is about 0.05e. Also, the a,, and a,,* orbitals of N, and the dy, orbital of Ni belong to the b2 representation. However, the mixing among these orbitals is small on the occupied level; Le., the 6b2 orbital mainly consists of the N 2 a? orbital into which the Ni d,,, orbital mixes slightly in an antibonding way. On the other hand, its antibonding counterpart, 7bz, includes significant mixing between N, a,,* and Ni d,,, orbitals. The 6bz and 7b2 orbitals have occupation numbers of 1.97 and 0.04, respectively. Therefore, excitations from 1 l b l and 6bz to 12bl and 7b2 seem to contribute significantly to the electron correlation effects. This means that the back-donative interaction between Ni d a and N, a * orbitals cannot be described well on the Hartree-Fock level and would be improved by the introduction of electron correlation effects. These excited configurations correspond to either an excitation from an antibonding orbital to an antibonding orbital or an excitation from a nonbonding orbital to an anti-bonding orbital, which would not significantly influence the bond distance between Ni and NZ. The other excited configurations, including Ni 3d 4d, N, lone pair a*, and many dynamical correlations, would probably shorten the Ni-N, distance, since these excitations would weaken the exchange repulsion arising from the overlap
4
Ai
x P'
P'
-
+
-
-
(32) The superscripts a and b mean the antibonding and bonding interactions, respectively. ( 3 3 ) This d,, orbital is mixing of 3d,, and 4d,, orbitals. (34) This kind of orbital mixing has been reported in ref 8b,c. (35) The Hartree-Fock canonical orbital of 1 Ib, is nearly nonbonding between Ni and N1. In the natural orbital, this becomes weakly antibonding, perhaps due to the improvement of the back-bonding interaction.
2
1
LNTN
( B ) ?*-Side o n
(Ni\p
Figure 5. Characteristic interactions found in several important natural orbitals. between tight electron clouds of two Lewis bases. Therefore, the sum of these electron correlations yields the shortening of the Ni-N, distance in the Vl-end-on mode. In the V2-side-on mode, only the N, a,* orbital belongs to the same representation as the Ni d,, orbital and forms 12bl and 13bl orbitals. The occupation numbers of the 12bl and 13bl are about I .96e and about 0.05e, respectively, which suggests the importance of the excitation from 12bl to 13bl. Again, it is reasonably concluded that this a-back-donative interaction is not described well on the Hartree-Fock level but is improved by introducing electron correlation effects. Here, a difference between the VI-end-on and V2-side-on modes is noted: the Vl-end-on mode has two a-back-donative interactions (a strong one in the bl representation and a weak one in the b2 representation) that are improved by the introduction of electron correlation effects, whereas the $-side-on mode has only one (note that the N, A,,* orbital cannot overlap well with the Ni d, orbital in the a, representation). Probably, this is one of the important reasons that introducing electron correlation effects yields greater energy improvement in the ql-end-on complex than in the V2-side-on complex. In the T2-side-on mode, the N 2 a, orbital cannot mix into the Ni d,-N2 az*bonding interaction because of symmetry constraint (see Figure 5B), and as a result, the bonding interaction of 1 2bl
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T h e Journal of Physical Chemistry, Vol. 93, No. 15. 1989
is not weakened, unlike the 1 1bl orbital of the VI-end-on mode. Thus, the excitation from 12bl to 13bl of the T2-side-on mode corresponds to an excitation from a bonding orbital to an antibonding orbital, which would induce the lengthening of the Ni-N2 distance. The lengthening of the Ni-N2 distance caused by this nondynamical correlation would be compensated for by the shortening of the Si-N, distance that arises from the other many excited configurations including dynamical correlation, and as a result, the S i - N 2 distance scarcely lengthens upon SD-CI calculations. Thus, the difference in electron correlation effects between the 7'-end-on and v2-side-on modes is easily explained in terms of nondynamical correlation that is characteristic in each coordination mode. The electron correlation effects found in Ni(PH3)2(C2H4)are very similar to those found in Ni(PH3),(q2-N2). The 12bl and 1 3bl orbitals include bonding and antibonding interactions between Ni d,, and C2H4a* orbitals, and their occupation numbers are 1.95e and 0.06e, respectively. Thus, the 12b, 13bl excited configuration is important in the electron correlation of Ni(PH3)2(C2H4)as in Ni(PH3,),(v2-N2), which lengthens the Ni-C distance. The 12b, in N I ( P H ~ ) ~ ( C has ~ H a~ )slightly smaller occupation number than in the g2-side-on N2 complex, and the I 3bl in the former has a slightly larger occupation number than in the latter. This means that nondynamical electron correlation effect lengthens the Ni-C distance, to a greater extent, than it does the i ii-N2 distance in Ni(PH3),(v2-N2). This lengthening would be compensated for to some extent by the shortening of the Ni-C distance which is induced by the other many excited configurations, and consequently, the Ni-C distance slightly lengthens upon introducing electron correlation effect.
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Concluding Remarks In the present theoretical work, a b initio M O M P and SD-CI calculations were carried out on Ni(PH3)2(q'-N2), Ni(PH3),(v2-N2),and Ni(PH3),(C2H4). Although the relative stability of two coordination modes of Ni(PH3),(N2) is calculated to be almost the same on the Hartree-Fock level, introducing electron correlation effects with MP2, MP4(DQ), MP4(SDQ), and SD-CI methods yields a significant difference in the stability of the two coordination modes. At the above-mentioned correlated levels, the calculated binding energy of the gl-end-on mode is much greater than that of the u2-side-on mode, which is consistent with the experimental result that only the 7'-end-on coordination has been found in [ K \ ; ~ ( P C Y ~ ) ~ ] ~ ( N ~ ) . In the VI-end-on mode, M P and SD-CI calculations shorten the Ni-N2 distance by about 0.1-0.13 A and the resultant Ni-N2 distance agrees well with the experimental value. In the q2-side-on mode, however, the M P calculations considerably lengthen the Ni-iV2 distance, while the SD-CI calculations change it only slightly. M P and SD-CI calculations were also carried out on Ni(PH3),(C2H4),which includes the v2-side-on coordination like Ni(PH3)2(72-N2). The M P calculations, again, significantly lengthen the Ni-C distance, and the resultant Ni-C distance is much longer than the experimental value. On the other hand, the SD-CI calculations slightly lengthen it, and the resultant Ni-C distance agrees well with the experiment. Thus, the M P method does not seem appropriate in investigating Ni(O)-$-N, and Ni(O)-C,H, complexes. The calculated binding energy of the 7'-end-on coordination is 37 (BS I ) and 38 (BS 11) kcal/mol on the MP2 level, 51 (BS I) and 56 ( B S 11) kcal/mol on the MP4(DQ) level, and 73 (BS I)and 80 (BS 11) kcal/mol on the MP4(SDQ) level. These values seem too large, considering the binding energy of the C2H4 coordination in Ni(PR3)(C2H4)28and that of the N2 coordination in Ni(C0)3(N2).29 The SD-CI calculation yields the binding energy of 16 kcal/mol after correction of discarded singledouble correlations and higher order C I expansions. This value seems much more reasonable than the values estimated with the M P method.
Sakaki and Ohkubo Introduction of electron correlation effects improves the aback-bonding interaction in both coordination modes. The 7'end-on mode has two a-back-bonding interactions in the bl and b2 representations, whereas the q2-side-on mode has only one in the b, representation. This difference is probably one of the important reasons that the energy improvement by introducing electron correlation effects is greater in the VI-end-on mode than in the g2-side-on mode. The electron correlation effects on the Ni-N2 distance is also noted here, because it is different between the 7'-end-on and V2-side-on modes (vide supra). In the VI-end-on mode, the excitations from the weakly antibonding 1 1b, and nearly nonbonding 6b2 orbitals to the antibonding 12bl and 7b2 orbitals mainly contribute to the electron correlation effects, which would not influence significantly the Ni-N2 distance. In the g2-side-on mode, the excitation from the bonding 12b, to the antibonding 1 3bl considerably contributes to the electron correlation effects, which lengthens the Ni-N, distance. An important difference is found a t the occupied level: the 1 I b l and 6b2 of the $-end-on N2 complex are weakly antibonding and nearly nonbonding, respectively, but the 12bl of the v2-side-on N2 complex is strongly bonding. The symmetry properties of these two coordination modes yield this difference. The Vl-end-on N2 coordination mixes the Ni da-N2 a antibonding overlap into the N i da-N2 A* bonding overlap, to yield 1 1bl and 6b2 orbitals in which the Ni da-N2 a* bonding overlap is weakened by the above-mentioned mixing of the antibonding overlap. In the q2-side-on mode, the mixing of the N2 a orbital into the h'i dr-N2 a* bonding interaction (1 2bl) cannot occur due to the symmetry constraint, and the 1 2bl is a strongly bonding orbital. This difference leads to a difference in nondynamical correlation between the two coordination modes: in the 7'-end-on mode, the excitations from 11b, and 6b2 to 12bl and 7b2 do not significantly influence the Ni-N2 distance, but in the q2-side-on mode, the 12bl 13bl excitation lengthens it. The other type of excited configurations including dynamical correlation would shorten the Ni-N2 distance, because they would weaken the exchange repulsion between two Lewis bases. As these result, introduction of electron correlation effects shortens the Ni-N2 distance in the sl-end-on mode but scarcely changes it in the V2-side-on mode. It is helpful to offer a general proposal regarding which type of coordination bond is sensitive to electron correlation. From a limited investigation presented here, it is not easy and seems rather dangerous to offer such a general proposal. However, several comments are possible: ( I ) When two complexes have different numbers of a-back-bonding interactions, their relative stability is sensitive to electron correlation. (2) When two complexes have different types of H O M O and L U M O at the H F level, the discussion of relative stability and coordinate bond distance is also sensitive to electron correlation. (3) Especially when the H O M O of one complex is bonding and the H O M O of the other complex is nonbonding, introducing electron correlation effect is indispensable for comparing their relative stability and coordinate bond distance. To obtain a general conclusion regarding electron correlation effects on the transition-metal chemistry, we must carry out many theoretical studies on various types of transition-metal complexes.
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Acknowledgment. S.S. thanks Prof. K. Morokuma for his generous support and encouragement, Drs. U. Nagashima and N . Koga for stimulating discussion, and Drs. K. Kamiya and K. Yamashita for their helps in carrying out SD-CI calculations. The authors gratefully acknowledge the Computer Center, Institute for Molecular Science, Okazaki National Institute, for the use of Hitac M-680H and S 8 I O / IO computers and library programs MELD and Gaussian 82. This work was partially supported by a grant from the Ministry of Education, Culture and Science through Grant-in-Aids for Co-operative Research (No. 62303002). Registry N o Ni(PH,),(a2-N2), 118907-47-4; Ni(PH,)2(C2H,), 63995-33-5; N I ( P H ~ ) ~ ( ~ ' - N 121173-88-4 ~),
