J. Phys. Chem. 1993, 97, 9986-9991
9986
Singlet- and Triplet-State Ni(CZH4): A Density Functional Study Imre Phpai' and Jdnos Mink Institute of Isotopes of the Hungarian Academy of Sciences, H-1525 Budapest, P.O.B. 77, Hungary
R e d Fournier Steacie Institute for Molecular Sciences, National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, KIA OR6 Canada
Dennis R. Salahub Dgpartement de Chimie et Centre &Excellence sur la Dynamique Moleculaire et Interfaciale, Universitt de Montrgal, C.P. 6128, Succursale A. Montrtal, Qugbec. H3C 3J7 Canada Received: March 30. 1993g Fully optimized geometries, harmonic frequencies, infrared intensities, and bond dissociation energies obtained from local and nonlocal density functional calculations are presented for the ground-state ('A') and a triplet excited-state Ni(C2H4). The ground-state complex has a CZ,equilibrium structure, whereas the symmetry is lowered to C,for the triplet state. The best estimation of the binding energy of the ground state is 38.9 kcal/mol, which is about 4 kcal/mol higher than the experimental value. The nickel-ethylene bond is much weaker in the triplet complex; the binding energy is estimated to be about 9 kcal/mol. The comparison of the theoretical infrared spectra, the shifts in the C C stretch, and CH2 scissor frequencies upon coordination and the H/D isotopic shifts with those from a recent matrix-isolation IR study shows a remarkable agreement for the groundstate Ni(C2H4). The effect of the nonlocal corrections to the exchange-correlation energy is discussed for each calculated property.
I. Introduction The implementation of analytical gradientsin density functional theory (DFT) based quantum chemical techniques' has made it possible to calculate fully optimized geometries and normal frequencies of transition-metal(TM) complexeswithin the density functional formalism. The first results, appearing in the past few years,2" are very promising, although only a limited number and type of complexes have been investigated so far. Theconclusionsemergingfrom thesestudiescan besummarized as follows. The calculated equilibrium geometries are generally in good agreement with experiment. It is shown that the metalligand (M-L) bond distances obtained by the local density approximation (LDA) are usually underestimated by an average of 0.05 A, which is consistent with the picture that LDA overestimatesthe bond strengths. If nonlocal corrections(NLC) are introduced to the exchange-correlationenergy, the bonds are lengthened, and the average discrepancy is reduced typically to 0.01 A.3-5 The vibrational frequenciesof TM complexes are also predicted reasonably well. Encouraging agreement between the DFT results and the exmrimentallv observed vibrational sbectra have been found for seieral first-row TM complexes at the' LDA le~e1.2.~.5The nonlocal corrections seem to reduce the M-L stretching frequencies by about lo%, as reported by Fan and Ziegler' for Ni(C0)4 and Cr(C0)6. Their work is in fact the first systematicstudy to present infrared (IR) intensities for TMligand systems using a DFT based method. The calculated intensities for Ni(C0)4 and Cr(C0)6 are found to be in good accordance with the experimental observations, at both LDA and NL levels of theory. Ni(CzH4) is a simple binary nickel-ethylene complex, first synthesized by coordinativereaction of Ni atoms with C2H4/Ar and C2H4 matrices.6.7 From their IR and UV-vis spectra, Ozin et ala6.'deduced that there is a weak metal-ligand interaction in Ni(CzH4). The low-temperatureexperimentshave been recently reinvestigated by Merle-Mejean et a1.8 using Raman, IR, and ~_____
Abstract published in Advunce ACS Absrrucrs, August IS, 1993.
UV-vis techniques,and the authors suggest a strongly perturbed CzH4 in Ni(C2H4). Kinetic studies of the gas-phase association reaction of Ni atoms with CzH4 at room temperature, in the pressure range 1-600 Torr, have also been reported recently, and the binding energy of Ni(CzH4) has been e ~ t i m a t e d . ~Ni(C2K) J~ has also been the subject of several theoretical investigations;ll-16 however, none of them attempted to present a full geometry optimization or a complete normal-coordinate analysis. The main objective of the present work was to calculate the fully optimized geometry and the IR spectrum of the Ni(C&) complex. For test purposes, we have already reported preliminary results on the equilibrium geometry and vibrational frequencies of the ground-state Ni(CzH4), at the local level of theory.? Here, we will apply various functionals (local and nonlocal) in the DFT approach, and we will consider the triplet state as well. The theoretical IR spectrum will be compared with the low-temperature matrix isolation IR data. The Ni-CzH4 bond dissociation energies for both states will also be presented.
u. All calculations in this study were performed with theaaussiantype orbital (GTO) based code, called "deMon".lFL9 The description of the LCGTO-DF formalism can be found in refs 2iL24; the technical details are given in refs 18 and 19. The calculations were carried out using three different energy functionals, labeled VWN, PW/P, and B/P. At the local level, the Vosko-Wilk-Nusair (VWN) parametrization25of the exchange-correlation potential has been used. In nonlocal calculations Perdew's26 corrections to the local spin density (LSD) correlation were added to the VWN potential, while the nonlocal exchange correctionsof Perdew and Wang2' (PW/P) or Beck@ (B/P) were chosen. The nonlocal correctionswere implemented self-consistently. All electron orbital basis sets were used for all atoms. We performed LSD calculations with two different basis sets which we will denote TZP-A and TZP-B. Basis set TZP-A consisted of orbital functions with the contraction patterns (63321/5211/
0022-3654/93/2097-9986$04.00/0 Q 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, NO. 39, 1993 9987
Singlet- and Triplet-State Ni(C2H4)
TABLE I: v b r i u m Geometry, Vibrational Frequencies (in cm-l), and IR Intensities (in km/mol) of C2)4 Obtained with Various Basis ts Using the VWN FUIIC~~OM~ DZa
TZP-A"
TZP-B"
TZPP
1.333 1.100 115.6 3150 1683 1323 1034 3155 1142 962 (124) 972 3203 (35.5) 784 (5.5) 3 102 (1 3.6) 1380 (18.8) 2.9 42
1.331 1.105 116.9 3074 1656 1315 1020 3143 1176 910 (91.7) 926 3168 (6.7) 789 (1.4) 3063 (7.7) 1384 (10.7) 3.6 33
1.331 1.100 116.6 3071 1660 1324 1023 3141 1177 921 (125) 923 3165 (9.7) 799 (2.9) 3059 (8.8) 1388 (14.2) 3.4 46
1.331 1.103 116.7 3074 1661 1324 1019 3144 1180 91 1 (95.7) 925 3167 (10.8) 197 (0.3) 3061 (11.5) 1395 (12.6) 3.5 28
ex9 1.339 1.085 117.8 3153 1655 1370 1044 3232 1245 969 (84.4) 959 3234 (26.0) 843 (0.03) 3147 (14.3) 1473 (10.4)
OOrbital bascsset notation: DZ: C(521/41), H(41/1);TZP-A: C(5211/411/1),H(41/1);TZP-B: C(6311/311/1), H(311/1);TZPP C(5211/ 41 1/1 l), H(41/11). Experimental geometries are taken from ref 37,the harmonic experimental frequencies are from ref 38,and the IR intensities arc from ref 39. Average percentage deviation from the experimental values. (010 has been excluded from the calculation of A,, because of its small
experimental value.)
41), (5211/411/1), and (41/1) for Ni,29 C,30 and H.30 The correspondingauxiliary basis sets, used in the fitting of the charge density (CD) and the exchange-correlation (XC) potential, were Ni(5,5;5,5),29 C(5,2;5,2),30and H(5,1;5,1).30 (In the notation (&l,k2;11,12), kl(l1) is the number of s-type Gaussians in the CD (XC) basisand &2(12)is the number of s-,p-, andd-type Gaussians constrained to have the same exponent in the CD (XC) basis.) Basis set TZP-B has the same functions for nickel but has orbital bases proposed by Hehre et al.37for C and H. These C and H orbital bases have slightly different contraction patterns, (63 11/ 31 1/1) and (31 l / l ) , respectively, and different exponents. The auxiliary bases in the TZP-B have the pattern (4,4;4,4) on C and (4,2;4,2) on H. Except wherecomparisons between bases TZP-A and TZP-B are made, all results reported here will refer to calculations performed with the TZP-A basis. The fit to the chargedensity is variational,22whereas a standard least-squares fit of the exchange-correlation potential evaluated at grid points was made. The grid includes 32 radial shells and 26 angular points per randomly rotated shell. At the end of each SCF procedure, the XC contribution to the total energy (and the energy gradients) was calculated by numerical integration3' on an augmented grid, having 50, 110, or 194 angular points per radial shell. The geometries were completely optimized, until the norm of the gradients became less than 0.0001 au, using the BFGS alg0rithm.3~ No symmetry constraint has been imposed in the geometry optimization. The harmonic frequencies were obtained by diagonalizing the Cartesian force constant matrix. The elements of this matrix are evaluatedby numerical differentiationof the analytical gradient23 using a displacement of A0.02 au from the optimized geometry for all 3N coordinates. The infrared absorption intensities were calculated from numerical derivatives of the dipole m0ment,3~ using the same displacements. The binding energies were computed for the equilibrium geometries with respect to the ground-state (4s13d9) Ni atom, using nonspherical atomic energies (Le., the constraint of the spherical charge density is removed by using integer occupation numbers for the 3d minority spin orbitals). The details of the atomic calculations are given in ref 35, with illustrations that nonspherical atomic energies are essential to obtain accurate binding energies. In. Results and Discussion A. IR Spectrum of the C f i Molecule. Before presenting the results obtained for Ni(CzH4), in order to judge the accuracy of
the theory we applied, we felt it important to investigate how the calculated properties of the free ethylene molecule vary with respect to the basis sets and the energy functionals. Let us first examine the sensitivity of the properties to the basis sets. Table I shows the results obtained with four different basis sets. The basis set denoted as DZ has a double-zeta basis for C and a double-zeta basis with one polarization function for H. TZP-A denotes a triple-zeta plus polarization C and the same H basis set as above. TZP-B is another triple-zeta plus polarization C but with different number of Gaussians and exponents (see previous section). In calculations labeled TZPP we augmented the TZP-A basis sets with a second polarization function for both C and H, as described in ref 36, where it was shown that this basis set gives very accurate dipole moments and dipole polarizabilities. Table I indicates that the equilibrium geometry is fairly well converged already at the DZ level, although there is a difference of 1O in CYHCHbetween the DZ and TZP-A values. The TZP-A, TZP-B, and TZPP geometries are almost identical. It appears that the inclusion of the polarization function in the C orbital basis set has a considerable influence on the vibrational frequencies. The values are altered by 40-80 cm-' for several modes. However, the effect of the second set of polarization functions is negligible; the largest TZP-A - TZPP deviation is only 11 cm-' (for 4. It is also seen that the TZP-A and TZP-B frequencies are very similar. The average percentage deviation (4) from the experimentally deduced harmonic frequencies is always less than 3.6%, indicating an accuracy which is comparable to those of correlated ab initio methods. The calculated IR intensities seem to be more sensitive to the basis set. Both their absolute and relative valuesvary significantly in the DZ-TZP-TZPP series. Even bases TZP-A and TZP-B which are very similar give IR intensities that differ by 10-30%,. Nevertheless, the average percentage deviation (A,) from the experimental values is reduced by using larger basis sets. Again, the presence of the d polarizationfunction in the C basis is essential for the improvement. Although AIis reduced from 33% to 28% by the inclusion of the second polarization functions, the TZPP IR intensities do not always get closer to the experimental values with respect to the TZP-A results. On the basis of these findings, we decided to use the TZP-A basis set for further calculations. The calculated properties of CIH4 using the VWN, PW/P, and B/P functionals are presented in Table 11. It is seen that nonlocal corrections have little influence on the CH bond length (the discrepancy of 0.02 A with experiment still
9988 The Journal of Physical Chemistry, Vol. 97, No. 39, I993
TABLE Ik
E%R
dm(A) dc~(A)
1.331 1.105 116.9 3074 1656 1315 1020 3143 1176 910 (91.7) 926 3168 (6.7) 789 (1.4) 3063 (7.7) 1384 (10.7) 3.6 33
uilibrium Geometry, Vibratioaol Frequencies (in cm-I), and Intensities (in km/mol) of C f i Obtained with Various Energy Functionrls Using the TZP-A Basis Set VWN PW/P B/P =P(l aHCH (deg)
a1 W I
as w2
as w3 au0 4 bl, w bo w6 blu w7 b2s 08 b2u w9 bzUwio
b3u a11 bsuw12
Lb(%)
1.342 1.105 116.8 3065 1639 1333 1022 3128 1199 924 (81.6) 927 3155 (19.5) 810 (0.9) 3056 (16.0) 1419 (5.4) 3.1 22
1.340 1.103 116.7 3080 1640 1332 1023 3143 1196 925 (82.3) 922 3169 (17.5) 803 (0.7) 3069 (15.3) 1414 (6.6) 3.1 20
1.339 1.085 117.8 3153 1655 1370 1044 3232 1245 969 (84.4) 959 3234 (26.0) 843 (0.03) 3147 (14.3) 1473 (10.4)
AP(1) OExperimental geometries are taken from ref 37, the harmonic experimental frequencies are from ref 38, and the IR intensitiesarc from ref 39. Average percentage deviation from the experimental values. (WIIJ has bcen excluded from the calculation of A,, because of its small experimental value.) remains) and the HCH bond angle, but they increase the CC distance by about 0.01 A, which is closer to the experimental value. This is in line with the conclusions of other DFT studies on several small organic and inorganic molecule^.^.^^ Both PW/P and B/P functionals give a slightly improved as compared to the VWN value, and this is mostly because the calculated frequencies shift closer to the experimental values by about 20-30 cm-1 for a few modes (wg and 0 1 2 for instance). It is perhaps interesting to note that the absolute values of the calculated frequencies are very similar for the two nonlocal functionals, indicating their similar quality for this property. The improvement in the calculated IR intensities as a result of the nonlocal corrections is worth mentioning. The average deviation is reduced from 33% to 22% and 20% for PW/P and B/P, and all values shift closer to the correspondingexperimental data, except the 012 mode. Since the eigenvectors of the Hessian matrix show only a minor dependence on the applied functional, the improvement in the IR intensities is mostly due to the fact that more accurate dipole moment derivatives are obtained with nonlocal functionals. These results show quite conclusively that the experimentalIR spectrum of the ethylene molecule is reproduced reliably at this level of theory. The overall agreement is certainly good enough to guide interpretations. B. Cnnad-StateNi(Cfi). It followsfrom previoustheoretical studies on Ni(C2H4)11-16 that the first question we have to ask is, what is thegroundstateoftheNi(C2H4)complex? The present method predicts the singlet ('Al) state to be the ground state, in agreement with a CASSCF calcualtion by Widmark et al.I4 and in contrast to two other studies.12.13 The bond dissociation energies of Ni(C2H4) will be discussed in subsection E. Here, we shall examinethe optimized structure and the theoretical IR spectrum of the ground-statecomplex. The results are summarized in Table 111. The geometry optimization yielded a C, symmetry (two equivalent NiC bonds) for the ground-state Ni(C2H4), with an elongated CC bond and a nonplanar C2H4, in which the H atoms are tilted away from the Ni atom. The experimental geometry of Ni(C2H4) is unknown; however, the obtained structure is consistent with the experimentalobservation for other transition metal-ethylene complexes.42-44 It is seen from Table I11 that the NiC distance, optimized with the nonlocal functionals, is about 0.04 A longer than the VWN value. Very similar effects have been found for Ni(CO)4 and Cr(C0)6 by Fan and Ziegler? for Fe(CO)5 and Mn(C0)4NO
PBpai et al. by Sosa et a1.,5 and for CrCO, NiCO, and CuCO by Fournier." The effect of the nonlocal correctionson the internal geometrical parameters of the C2H4 ligand is very similar to that found for the free ethylene. We note that the NiC distance was calculated to be much longer (1.972 A) in the CASSCF study,l4 likely because of the limited inclusion of electron correlation in the CASSCF method. The comparison between the TZP-A and TZP-B VWN frequencieslisted in Table I11 reveals that for some modes (CH stretch, CC stretch, CH2 scissor, and NiC stretch) the calculated frequencies are insensitive to the bases, while for other modes the frequencies differ by 30-40 cm-l (CH2 wag and CH2 twist). In going from LSD to NLC functionals, we see that: (1) The frequencies corresponding to the C2)4 internal modes usually shift to higher values, except for 0 3 and 011. (2)The wag and CH stretch frequenciesstay within 1%, and the other frequencies shift by 15-90 cm-I. (3) The nonlocal NiC stretch frequencies ( 0 5 and 012) are reduced considerably with respect to the local values, in line with the fact that the nonlocal correctionsweaken the M-L interaction. This effect appears to be more prominent for the PW/P functional. (4) Most of the PW/P and B/P frequencies have very similar values, except for the 0 5 mode. (They differ by 49 cm-l.) As we already observed for the free C2H4 molecule, the IR intensities may vary notably with the basis set and by the inclusion of nonlocal corrections. This seems to be true for Ni(C2b) as well. The CH stretching vibrations (01, 0.5, and 09) 0 3 and 0 4 become stronger, and the w10 and 0 1 2 modes become weaker with nonlocal functionals. In spite of this, the general characteristics of the predicted IR spectra are quite similar. According to the NLC results, the strongest band correspond to the bl CH2 wag mode at around 920cm-*,no other strong bands appear between 1600 and 900cm-l, and there are several relatively intense bands in the 600-500-cm-1 region. C. Triplet Ni(Cz&). Previous studies on the triplet state of Ni(C2Hd) led to contradictory conclusions. Widmark et aI.l4 found an unbound triplet Ni(CzH4) with a repulsive E = E(&~+H,) potential energy curve, whereas the GVB-CI calculation12 predicted a bound structure, with a binding energy of 14.2 kcal/mol. According to our calculations, the triplet state is bound with respect to the ground-state asymptotes, although the Ni-ethylene bond is much weaker than in the ground-state complex. We found two stationary points on the triplet potential energy surface (PES). Starting froma Cbinitialstructure, thegeometry optimization yielded a CZ, stationary point for all functionals. (The norm of the gradient vector was less than 0.0003au.). The vibrational analysis, carried out at this geometry, resulted in an imaginary frequency (about 200i cm-I), corresponding to the asymmetricNiC(q2) stretchmode. In other words, theobtained structure is a saddle point, and the C, symmetry tends to break. Indeed, we obtained a second stationary point by continuing the geometry optimization from a slightly distorted Cb structure. This stationary point is a minimum on the PES, since all normal frequencies are real at this geometry. It is important to mention here that the triplet PES between the Cb and C, stationary points (along the asymmetric NiC stretching normal coordinate) is extremely flat. The difference in the C, and C, total energies is about 1 kcal/mol for all functionals. In our experience, the structures corresponding to the stationary points on a flat PES might be very sensitive to the grid used for the fitting and the numerical integration. In order to check whether it is the case for the triplet Ni(C2H4), we have repeated the geometry optimizationwith an extended grid, where the number of radial shells was increasedfrom 32to 64. Thegrid effect is clearly illustrated in Table IV. It is obvious that the triplet equilibrium parameters did not reach their "final" values with the generally used FINE grid. In the most extreme case (PW/P functional), one of the NiC bond lengths varies by more than 0.3A when going from 32-to 64-
Singlet- and Triplet-State Ni(C2H4)
The Journal of Physical Chemistry, Vol. 97. No. 39, I993 9989
TABLE IIk Equilibrium Geometry (4 a,t in A and deg), Vibrational Frequencies (01 in cm-I), and IR Inteusities (in km/mol, in Parentheses) of the Ground-State Ni(C&) Obtained with Various Eaergy Function& VWN TZP-A dNic dcc dcH
VWN TZP-B
PW/P TZP-A
BIP TZP-A
1.840 1.428 1.111 114.5 112.2
1.846 1.423 1.107 114.1 112.6
1.884 1.440 1.108 115.0 111.2
1.878 1.439 1.108 114.4 112.1
2981 (14.6) 1443 (0.0) 1174 (0.8) 901 (0.6) 582 (5.7)
2981 (13.1) 1445 (0.0) 1184 (1.1) 933 (4.4) 576 (4.3)
2985 (21.6) 1458 (0.3) 1151 (2.0) 903 (1.3) 490 (5.2)
2995 (21.3) 1461 (0.3) 1158 (2.3) 910 (2.4) 539 (5.9)
ol CHI rock wg CH2 twist
3066 (7.6) 742 (0.0) 575 (20.3)
3066 (6.4) 763 (0.2) 613 (20.2)
3073 (16.7) 761 (0.0) 603 (17.9)
3077 (16.0) 757 (0.0) 595 (21.4)
w9 CH stretch WIO CHI scis~ W I I CHZwag w12 NiC stretch
2978 (14.3) 1354 (5.4) 925 (38.1) 527 (5.7)
2973 (13.5) 1358 (5.9) 959 (28.8) 530 (4.8)
2982 (22.3) 1392 (1.9) 920 (32.9) 484 (3.5)
2991 (22.8) 1388 (2.2) 923 (35.3) 510 (4.4)
~ 1 CH 3 stretch WI) CHI rock ~ 1 CH2 5 twist
3049 (0.0) 1136 (0.0) 808 (0.0)
3047 (0.7) 1150 (0.0) 830 (0.0)
3052 (0.0) 1157 (0.0) 817 (0.0)
3059 (0.0) 1155 (0.0) 822 (0.0)
aHCH (NICH
aIc
CH stretch CC stretch' w3 CH2 scissd w4 CHI wag 405 NiC stretch w1 02
a2 06
CH stretch
exIP
expb
1465 1156 901 498
2960 1496 1158 900 376
bi
b2
From ref 8. From refs 6 and 45. The normal modes are classified into Cb symmetry representations. The w2 and w3 modes are both mixtures of CC stretch and CH2 scissor; the amplitude of the CC stretch motion is nearly q u a l in these two modes.
TABLE Iv: Equilibrium Geometry (4 a,e in A and deg), Vibrational Frequencies (06 in cm-1) and IR Intensities (in km/mol) (in Parentbeses) of the Ground-State Ni(C&) Obtained with Various Energy F~nctionals;Optimized Geometrical Parameters
Obtained with the &Shell Grid Are Listed in Parentheses VWN TZP-A dNic( 1
1.940 (1.961) 2.042 (2.012) 1.387 (1.387) 1.107 (1.108) 1.106 (1.107) 115.1 (115.5) 116.3 (1 16.0) 106.4 (106.6) 107.4 (107.2)
1.935 2.027 1.388 1.105 1.101 114.6 116.1 107.4 107.7
0 3 CHI sciss 0 4 CHI wag w5 NiC stretch
3046 (6.1) I501 (14.1) 1245 (24.5) 913 (8.5) 406 (6.0)
3049 (8.4) 1489 (15.0) 1249 (32.6) 938 (6.7) 392 (9.8)
CH stretch CH2 rock wg CH2 twist
3137 (0.1) 760 (1.1) 473 (0.8)
3142 (0.0) 775 (1.4) 528 (2.4)
09 CH
3016 (1.8) 1371 (6.5) 857 (23.4) 152 (59.9)
3008 (2.6) 1370 (9.3) 841 (35.4) 218 (62.9)
3097 (0.4) 1150 (0.0) 850 (2.0)
3094 (0.6) 1162 (0.0) 901 (1.4)
d~ic(2)
dcc dcH(1) dcH(2) aHCH( 1 aHCH(2) CNiCH( 1 (NiCH(2) 81.
VWN TZP-B
01 CH stretch w2 CC stretch
au 06
w7
a1
stretch
w10 CHI Sci~s w11 CHI w a s 012 NiC stretch
au 013
CH stretch
W14 CHZrock ~ 1 CHI 5 twist
PW/P TZP-A
BIP TZP-A
2.005 (2.035) 2.523 (2.203) 1.399 (1.393) 1.106 (1.107) 1.102 (1.103) 115.0 (115.4) 116.9 (116.6) 100.9 (104.8) 108.6 (106.4)
1.997 (2.010) 2.158 (2.129) 1.394 (1.394) 1.105 (1.105) 1.102 (1.103) 115.1 (115.3) 116.5 (1 16.3) 105.4 (105.8) 106.9 (107.0)
#The normal modes are classified into C, symmetry representations. The sequence of the normal modes is the same as in Table 111. Harmonic frequencies are calculated with the 32-shell radial grid; therefore there might be large uncertainty on their values.
shell grid. This effect is far less pronounced for the VWN and B/P results, but the NiC bond distances still vary by 0.01-0.03 A, which is not reassuring. Although we listed the calculated VWN/TZP-A and VWN/TZP-B harmonic frequencies in Table IV, we warn the reader that because they have been obtained with the 32-shell grid, there might be a large uncertainty on the values. Also, the triplet frequencies appear to be more sensitive to the bases than the ground-state frequencies, particularly for the low-frequency modes.
The question arises as whether the ground-state propertiesare converged with respect to the grid. To answer this question, we have performed a geometry optimization and a vibrational analysis for the ground-state Ni(C2H4) with the extended grid using both nonlocal functionals. (The VWN results were the least sensitive to the grid.) We found that for the B/P functional the NiC distance was altered by less than 0.003 A, the CC and CH bond lengths were altergd by less than 0.001 A, and the bond angles were identical to within 0.lo with those obtained with the 32-
Pdpai et al.
9990 The Journal of Physical Chemistry, Vol. 97, No. 39, I993 TABLE V Frequency Shifts (in cm-1) for the CC Stretch (02) and the C H 2 Scissor (03) Mode upon the Coordination of C2H4 - . with Ni PW/P
B/P
tripletb VWN
181 182 363
179 174 353
154 70 224
singleta
Aoz(CCstretch) A03(CH2scissor) total(Awz+
Au3)
exp
expd VWN
158 186 344
127 184 311
213 141 354
Using the data from Tables I1 and 111. Using the data from Tables I1 and IV.e The experimental shifts are obtained using the Ni(C2H4)
data from ref 8 and thegas-phaseexperimentaldata from ref 38. From ref 6 and ref 38.
shell grid. The grid effect on the vibrational frequencies was less than 6 cm-1. For most of the modes, the IR intensities were essentially unchanged; the largest differences were found for the two CH2 wag modes. (The intensity decreased from 2.4 to 1.4 for w4 and increased from 35.3 to 37.9 for 011.) Theground-state properties are somewhat more sensitive to the grid for the PW/P functional,just as we found for the triplet state. The grid effects are 0.010 A for d N i c , 0,001 A for ~ C and C d C H , and 0.3' and 0.7' for QCH and C N ~ C H .Most of the frequencies were altered by only a few cm-I; however, three low-frequency modes (OS, wg, and 0 1 5 ) shifted by more than 10 cm-I (3 1,17, and 15 cm-I, respectively). The largest changes in the IR intensities were found for the tog and wI1modes; they shifted from 17.9 and 32.9 to 21.2 and 40.1. These values should be therefore considered as error bars on the calculated ground-state properties listed in Table 111. It is clear that they are far less significant than those for the triplet state. A detailed discussion of the relation between the grid effect and functionals will be published elsewhere.49 Finally, we wish to point out that the optimized NiC bonds of the triplet Ni(C2H4) are considerably longer than those obtained for the ground-state complex. In addition, the geometry of the ethylene molecule is less distorted, indicating a weaker metalligand bond. D. Comparison with the Experimental IR Spectrum. Two detailed analyses of the IR spectra of the matrix-isolated Ni(C2H4). (n = l, 2, 3) complexes have been reported in the literature. The first was reported by Ozin et a1.6in 1976 and the second by Merle-Mejean et al.8 last year. Ozin et al. associated four bands in the low-temperature IR spectra with the Ni(C2H4) product; they were observed at 2960, 1496, 1158, and 900 cm-l and were assigned to the CH stretch, CC stretch, CH2 scissor, and CH2 wag modes, respectively. An additional band in the far-infrared region at 376 cm-1 has been later attributed to the same comple~.~S Merle-Mejean et al. proposed several changes in the assignment of the Ni(CzH4). spectra. According to their analysis, the bands at 1496 and 376 cm-I are not related to Ni(C2H4) but rather to Ni(CzH4)2 and N ~ ( C Z H ~respectively, )~, and they propose that the Ni(C2H4) CC stretch and NiC stretch frequencies should be at around 1465 and 498 cm-1. We compiled both assignments in Table I11 next to our calculatedground-state harmonic frequencies. When we compare the experimental and theoretical values, it becomes evident that the agreement is much better for the assignment suggested by Merle-Mejean et a1.8 The average percentage deviation of the PW/P and B/P frequencies from those given in ref 6 and 8.4% and 11.796, whereas from those given in ref 8 are 0.7% and 2.4%. Although we do not expect our calculated IR intensities to be very precise, we mention that the calculated low intensity of the CC stretch is also in line with the findings of ref 8; i.e., the absorption at 1465 cm-1 is extremely weak, if it is observed at all. Note that the theoretical frequencies are harmonic, and if we want to be strict they should be compared with harmonic experimental values, which are not available. Nevertheless, we can make a more convincing comparison by calculating the theoretical and experimental frequency shifts upon the coordination. The shifts for the CC stretch and the symmetric CH2 scissor modes are given in Table V. Our analysis of the
TABLE VI: Hannonic Frequencies (in em-') and IR Intensities (in k d m o l ) for the S let- and Triplet-State Ni(CS4) . - .. Obtained with the VWN ~ n c t i 0 ~ 1 singlet tridet Ni(C2D4) AH/P Ni(CzD4) AH/^ ex@ ~
WI
012 ~3 04 US
06 ~7
ws
wg WIO
WII
012 ~ 1 3 W I ~
WIS
2181 (7.3) 1290 (0.3) 898 (0.4) 720 (0.7) 526 (3.8) 2279 (2.6) 530 (0.2) 425 (12.4) 2151.(5.9) 1005 (4.1) 776 (19.8) 460 (2.9) 2272 (0.0) 904 (0.0) 582 (0.0)
1.37 (1.37)c 1.12 (1.15) 1.31 (1.27) 1.25 (1.29) 1.11 (1.07) 1.35 (1.35) 1.40 (1.40) 1.35 (1.36) 1.38 (i.38j 1.35 (1.35) 1.19 (1.22) 1.14 (1.15) 1.34 (1.34) 1.26 (1.26) 1.39 (1.39)
i"f,
2231 (13.2) 1380 (25.5) 923 (4.0) 659 (17.6) 389 (4.6) 2335 (0.0) 547 (0.8) 344 (0.9) 2184 (0.4j 1012 (4.4) 710 (19.1) 139 (51.3) 2306 (0.0) 922 (1.5) 610 (0.1)
1.37 1.09 1.35 1.39 1.04 1.34 1.39 1.38 1.38 1.35 1.21 1.09 1.34 1.25 1.39
1.15 1.25 1.47 1.02
a AH/D = wI(N~(C~H~))/~~(N~(C~D,). Using the data from Table I in ref 8. Corresponding B/P values.
TABLE W: Calculated Bond Dissociation Energies (in kcal/mol) for the Singlet and Triplet Ni(C34) VWN PW/P B/P expo singlet
70.4
42.2
44.4 (39.8)b
35.5 i 5
triplet 32.4 16.1 17.3 (13.2)b a Reference 9. Values corrected for BSSE and ZPVE. For the triplet state, the same BSSE correction is assumed as for the ground state (3.6 kcal/mol). eigenvectors of these two modes revealed that the CC stretch and al CH2 scissor motions are strongly coupled in both C2H4 and Ni(C2H4); therefore, their shifts must be examined together. Considering the shifts listed for the ground-state Ni(C2H4) we see that: (i) The theoretical Aw2 Aw3 shifts are very close to that obtained with data from ref 8. (This is not true for data from ref 6.) (ii) The same tendency is observed if the Aw2 and A03 are considered separately. (iii) The NLC functionals yield better estimates for Aw2 and Aw3. We can clearly conclude at this point that our ground-state results are more consistent with the assignment suggested by ref 8 than with that by ref 6. Also given in Table V are the theoretical shifts for the triplet Ni(C2H4) obtained at the LSD level. The calculated Aw2 Aw3 shift is about 60% of that for the ground-state Ni(C2H4), in line with a weaker metal-ligand bond in the triplet complex. On the basis of the comparison of the singlet and triplet shifts with those from experiment, even if we recall the uncertainty in the triplet frequencies, wecan likely rule out the possibility of the formation of the triplet Ni(C2H4) in the matrix-isolation experiments. The deuterated complexes (Ni(CzD4).) have also been investigated by Merle-Mejean et al., and four IR bands have been associated with theNi(CzD4) species. These frequencies arelisted in Table VI along with the singlet B/P values. This table shows that the experimentally determined isotope shifts are remarkably well reproduced for the CC stretch and CH2 scissor modes; however, there is a significant discrepancy for the CH2 wag and NiC stretch modes. The experimentally estimated AHIDfor w4 is surprisingly high (1.47), while it is rather small for 05 (1.02). In light of the theoretical results, it would be perhaps worthwhile to reinvestigate these regions in the IR spectra of the deuterated complexes. Also, the results of our current calculations on the Ni(C2H& and Ni(C2H4)3 might give further information. E. Bond Dissociation Energies. It is of particular interest to determine the stability of the singlet and triplet Ni(CzH4); therefore, we have calculated the Ni-ethylene bond dissociation energies for both states. The results are collected in Table VII. Most apparent from this table is the large discrepancy between the VWN and NLC results. The overestimation of the binding energies by LSD calculations is well known (see for example ref
+
+
Singlet- and Triplet-State Ni(C2H4) 48); thus, the nonlocal values should be regarded as better predictions. The PW/P and B/P binding energies appear to be very close to each other for both states. In order to estimate the basis set superposition error (BSSE) in our calculations, the counterpoise correctionM has been calculated at the equilibrium geometry of the ground-state Ni(C2H4) at the B/P level. This correction lowers the binding energy by 3.6 kcal/mol. The zero-point vibrational energy (ZPVE) corrections for the singlet and triplet states are 1.O and 0.5 kcal/ mol. If both correctionsare taken into account, the B/P estimate for the binding energy of the ground-state complex is 39.8 kcal/ mol, which is about 4 kcal/mol higher than the experimental value (although it is within the experimental error bars) and about 12 kcal/mol higher than the results obtained with extended coupled-cluster and coupled-pair functional calculations.16 We note that a similar overestimation has been found recently in the binding energy of NiC0,47using the same method as in the present work. Likewise, we probably overestimatethe binding energy of the triplet Ni(C2H4). Lowering our best estimate (13.2 kcal/ mol) by the discrepancy between the B/P and the experimental values for the ground state (4.3 kcal/mol), we obtain 8.9 kcal/ mol for the binding energy of the triplet state. (The molecule is still clearly bound, even if this value is decreased by the error bar given in the experimental binding energy estimation? i.e. by 5 kcal/mol.) Our finding that the triplet Ni(C2H4) is bound is consistent with recent kinetics datal0 for the gas-phase reaction of Ni with C2H4, which suggest that the reaction may occur on both ground-state and triplet excited-state potential energy surfaces.
IV. Summary and Conclusions The basic aim of our work was to calculate the equilibrium properties of the Ni(C2H4) complexusingthe LCGTO-DF method and compare them to available experimental data. Our conclusions are summarized as follows. Besides the ground state (lAl), a triplet excited state is found to be bound as well. While the equilibrium structureof the ground state has C, symmetry, the triplet state has two inequivalent equilibrium NiC bonds (C, symmetry). The calculated Ni-CzH4bond dissociation energy of the ground state, obtained with the nonlocal functionals, is overestimatedby about 4 kcal/mol (10%) with respect to the experimental value when corrections for BSSE and.ZPVE are included. This error might result from the incompletetreatment of either the Ni atom or the metal-ligand bond in DFT calculations. Correcting the calculated binding energy of the triplet state for this discrepancy, and also taking into account the correctionsfor BSSE and ZPVE, the triplet Ni(C2H4) is found to be bound by about 9 kcal/mol. The calculated frequencies and their shifts upon coordination have been compared with two sets of matrix-isolationdata (refs 6 and 8), and we found a close agreement between our results and those from ref 8, supporting the new assignment proposed by Merle-Mejean et al. The effect of the nonlocal corrections on the calculated propertieshas also been examined. In summary, the equilibrium NiC bond distance is lengthened by 0.04-0.06 A, the NiC stretchingfrequencies decreaseby 10-20%, and the IR intensities are altered considerably by the inclusion of nonlocal corrections in the LDA functional. As for the binding energies, it is essential to use nonlocal functionalsto obtain reasonable estimates. These conclusionsare in line with the general experience. The calculated properties of the ground-state Ni(C2H4), obtained with two nonlocal functionals(PW/P and B/P), are very similar; however, we found significant differences between the PW/P and B/P equilibrium structures for the triplet state. Using an extended grid in the calculations, these differencesbecame less important. We think this work demonstrates that the present quantum chemical treatment of the transition metal-ligand systems can provide much useful information to complement and rationalize
The Journal of Physical Chemistry, Vol. 97, No. 39, 1993 9991 the experiments. What is clear, however, is that further benchmarks are needed to be more confident in the conclusions.
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