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Electronic structure and properties of transition metal complexes MCH2 and M5 CH2 (M = Fe, Ni, Cu;) by density functional methods
THEO CHEM
Journal
ELSEVIER
of Molecular Structure (Theochem) 394 (1997) 249-258
Electronic structure and properties of transition metal complexes MCHZ and M5 CH2 (M = Fe, Ni, Cu;) by density functional methods
Abstract The electronic
structure and properties ofcarbenes
methods (DF), particularly
ADF program of Bearends and collcaguea. the process MCHz -
basis set with frozen core orbit& methods and experimental
frequencies
Comparisons
values were carried out. Calculations
was studied dissociation
the non-planar
energies, distribution
Transition
model
for the Fe5 cluster.
were done using the triple-zeta
between our results and other calculations
using ab
were done for the ground doublet state of CuCH?, the
and singlet states for NiSCHZ were studied. considering and diagonal)
Optimization
metal carbens; Density
functional
of the position
of the CH?
gl-oup
in the cluster,
* Colsesponding author. e-mail: [email protected]
were
(Theory)
The interest in the subject considered in this report is due to the fact that in the Fischer-Tropsch synthesis CH 1 radicals are believed to be generated in the reduction of carbon monoxide by hydrogen, catalysed by transition elements; these radicals will remain attached to the metallic atoms, forming in this way metallic carbenes; these carbenes would be the precursors in the hydrocarbon synthesis [ 11. CuCH2 is
one of such compounds that has been isolated in an argon matrix and whose vibrational frequencies have been determined by FTIR 121. Density functional (DF) methods have become a very useful tool, due to both the accuracy of the results for several properties and the reduction in computational time. 2. Methods The calculations reported in this paper are based on the Kohn-Sham approach to density functional theory
0 1997 Elsevier Science B.V. All rights reserved
PI/ SO 166.1280(96)04840-3
planar and
for the CH? group. The triplet state for Fc5CH2
Science B.V.
1. Introduction
0166.1280/97/$I7.00
All the calculations
energies for by population
of‘ charges in the molecule and dipolar moments were also calculated and comparisons
made with the MCH? results. 0 1997 Elsevier Keywords:
Charge distributions
In order to compare our results with some references found in the literature
models for the MF clusters and two positions (parallel with
(NL) of Becke and Perdew and the
geometries and dissociation
in our study two states of the cation FeCHr.
In the second part of this report, doublet states for CuXH? non-planar
corrections
MCHz were calculated.
were also evaluated.
and the NL corrections.
singlet state of NiCHz and the triplet state of FeCH:. we have included
with the non-local
In the first part of this report the equilibrium
M + CH2 at the ground state of the compound
analysis, dipole moments and vibrational initio
MCH? and M $.IHZ (M = Fe, Ni, Cu) were studied using density functional
the local density approach (LDA)
(DFT) 131 with the methodology of Post and Baerends 141. The program used was the ADF (version 2.0. I, IS December 1995) [5]. Basically. the local density approach (LDA) was used for the calculation of the exchange energy Ex(LDA) derived from the original proposal made by Slater [6] (Xalpha approximation); the Vosko-Wilk-Nusair (VWN) version was used 171. An evaluation of the electron correlation energy was also included; thus we have: E,,(LDA)=E,(LDA)+E,(LDA). This is called the exchange correlation energy for a homogeneous electronic gas. Non-local corrections were introduced that signiticantly improve the results of calculation of several properties such as bonding energies and molecular geometries, dipole moments, etc; these corrections are: (a) a non-local term for the exchange energy Ex(NL) due to Becke [S]; (b) a similar correction for the correlation energy Ec(NL) due to Perdew [9]. The method is accordingly called LDA/NL. A Slater orbitals (STO) basis set was used for the molecular orbital expansion (LCAO method) and, for the transition elements in particular, an uncontracted triple-zeta was augmented by three (n + I ) p STO. The main elements (C in our case) were described by a double-zeta ST0 basis augmented by one 3d polarization ST0 and, in the case of hydrogen, one 2p was used; core orbitals (CO) were kept frozen. Core functions (CF) were introduced in order to establish the orthogonality of the valence molecular orbital!, (MO) on the CO; symmetry was considered in order to keep the overlap and Fock matrices block-diagonal by using symmetry-adapted linear combinations of the (C)BAS that we call (C)SBAS. A set of auxiliary s, p, d, f and g ST0 functions centred on each nucleus was used to tit the electronic density; for each metal atom 36 ST0 were used but this number was reduced to 20 for carbon and I I for hydrogen. In this way integrals involving electronic density (such as Coulomb potentials) were evaluated by using these auxiliary bases and then taking the linear combination of these integrals. The coefficients of these linear combinations are evaluated in each SCF cycle. The matrix elements of the overlap and Fock matrices were calculated by numerical integration. The success of the DFT methods is due, among
other reasons, to the existence of accurate and practical integration methods that now are available IlOl. Instead of total energies, bonding energies were calculated according to Ziegler’s procedure [II ]. These bonding energies are the difference between the total energy of a molecule (or atom) and those of the atoms (or fragments) in the established reference states. Optimization of the geometry in the LDA/NL method was done for all the geometrical parameters in the case of the MCHz compounds; C2V symmetry was used throughout. The ground state was studied in the CuCH? case in order to compare with the CASSCF (MRSADCI) calculations reported for this compound [ 121. Ground states were also considered for NiCH: and FeCHz in the singlet and triplet states, respectively. In all cases the energies of the M and CH1 fragments were obtained, and the dissociation energy was calculated in every case using the sum-of-fragment energies and the energy at the equilibrium geometry of MCH?. A Mulliken population analysis was made. and the charge distribution in the molecule and the related dipole moment were obtained as well as the vibrational frequencies of the normal modes. Referring to the MsCH~ compounds, we have two possibilities for the M5 clusters: Ni and Cu crystals have an fee (face centred cubic) elementary cell and the iron has a bee (body centred cubic) one. In the first two cases we have selected two cluster models: one that we call planar, symbolized by (5,0), with the five atoms (square vertices and centre) in the top face; and the other, called hollow and symbolized by (4.1), formed taking the four central atoms in the lateral cubic faces and the fifth atom at the centre of the bottom face. We have used the nomenclature given by Baerends [4]. The central M atom in (5.0). that we will call M 1, is shifted from the MJ plane by I .804 A for the Cu5 (4.1) cluster and 1.768 A for the Ni5 (4,l) 0
0 0
0
0
0 0
Fig. 1. HCH plane parallel to the side of the M, quare. Fe; 0 : H.
0: Cu. Ni,
R.M. Sosa, P. GnrdioWJoumal
of Molecular
0
o (Cu,Ni,Fe) 0
000
0 o
H
0 Fig. 2. HCH plane along one of the Cu, Ni, Fe: 0 : H.
diagonals of’the Ma square. 0:
cluster. In the case of the Fe5 cluster, the distance from Fe 1 to the Fe4 plane is 1.425 A. The CH:, group has its C2 axis normal and through the centre of the M1 square. We have investigated two situations: the first one in which the HCH plane is parallel to the side of the Mj square, that we call (5,O)p or (4,1)p; and the other one in which the HCH plane is along one of the diagonals of the Md square, that we call (5,O)d or (4,l)d; see Figs. 1 and 2.
3. Results
and discussion
3. I. CuCHz CuCHz was isolated in an Ar matrix by Chang [2] and its vibrational frequencies observed by FTIR spectroscopy. According to our calculations the ground state, in the group symmetry C2v, is the doublet 2B 1 and the first excited state is the doublet 2A 1, which is 43.1 kcal mol-’ higher in energy at the equilibrium geometries. Mochizuki et al. [12] report a CAS SCF (MRSDCI) ab initio study of this compound and arrive at the same conclusion, with an energy difference between the two states of 44.0 kcal mol-‘.
Structure
(Theochem)
251
394 (1997) 249-258
In the following we will consider only the ground state. The relevant geometrical parameters as well as the dissociation energy and dipole moments that we have obtained, and those of Ref. [ 121, are shown in Table 1; from these values we can conclude that the agreement between the two reported C-H distances and H-C-H angles is excellent but the difference between the Cu-C distances is 0.10 A, giving the ab initio method the largest values. This is a rather common situation: the HF method overestimates metalligand bond lengths and LDA underestimates them; with the NL corrections (such as with LDAPJL methods) it is possible to obtain the best concordance with experimental bond lengths [ 131. Now we will consider the energy change of the process CuCHz (2B 1) - Cu + CH2 that corresponds to the breaking of the Cu-C bond; in order to obtain this change we must consider the equilibrium energy for the ground state 2B 1; as we said before, we calculate not the total energy but the so-called bonding energy, that is the energy of the compound that we are considering relative to the elements in reference states that are well specified; the energy change that we are looking for is the difference between the sum of the bonding energies of the fragments Cu and CH> (to be called the sum-of-fragments energy, E,,,) and the bonding energy of CuCH?. These energies are shown in Table 1. In order to calculate E,,l we use the values given in Table 5: the lowest energy for the CH, fragment is - 0.438 155 a.u., corresponding to the equilibrium of the triplet 3B 1 state (C-H distance of 1.086 A and H-C-H angle of 135.98”). The lowest energy of the Cu atom in the doublet state is that of the symmetry C2v, which is the symmetry corresponding to the dissociation of the CuCHz molecule. This
Table I CuCH; (2BI) Geometrical
parameters distance (A) dz: C-H distance (A) (1: H-C-H angle (“) D: dissociation energy (kcal mol-‘) BE: Bonding energy (a.u.) E,,,: sum-of-fragments energy (a.u.)
d,: Cu-C
this work
[I21
dl
d?
(I
D
BE
E x,1
1.823 1.932
I .092 I.103
120 114
67.0 5 I .4
-0.554926
-0.448
103
of MolecultrrStructure
K.M. Sosa, P. Gurdiol/Joumul
252
energy is 0.009948 a.u., which is lower by 0.29 kcal mo1-’ than that corresponding to the configuration s2d 10 (0.009 484 a.u.); consequently E,,,, has the value given in Table 1 and our calculated dissociation energy is 67.0 kcal mol-‘, whereas the value reported in Ref. [12] is 51.4 kcal mol-’ (23%) lower. These results are quite different but unfortunately we have no experimental results to make the comparison possible. In general, the values given by the DFT methods when the NL corrections are included seem to be, in many cases, closer to the experimental values than the ab initio methods [ 141. Because CH? is common to all the compounds considered in this report, it is interesting to consider the results obtained from several methods applied to the theoretical study of the two lowest energy states: the ground 3B 1 and the first excited I Al; this calculation is also reported in Ref. [15] in which a method similar to ours was used. The results, for comparison, are in Table 6. We can conclude that our method and that used in Ref. [ 151 give the same results for the geometries and the energy difference between these two states. Comparing them with the experimental results, the geometries are very similar but the energy of excitation is too high; the RHF method gives a result that is much higher. The multireference CI method (CMRCI) gives a very good result, which is due to the fact that the ground state is well described with one configuration, but the excited state IA1 needs at least two configurations 1151. The results of the calculation of the vibrational frequencies that are shown in Table 2 are very important because we have experimental results to compare them with. Our stretching C-H frequency is 597 cm-’ with an intensity of 4 km mol-‘, agreeing quite well with the value of Ref. [12] (618 cm-‘) and the experimental one (614 cm-‘). The bending H-C-H frequency is 104 cm-’ lower than the experimental one and that of Ref. [ 121 is 61 cm-’ higher, but the concordance is acceptable. Our stretching C-H frequency is 72 cm-’ higher than the experimental Table 2 C&Hz (2BI) vibrational
this work [l21 121
frequencies,
cm-’
.f(C=C)
.AH-C-H)
597(4) 618 614
1241(69) 1406 I345
(intensity,
km mol-‘)
AC-H) 3033(22) 2868 2961
(Throchcm) 394 (1997) 249-258
Table 3 CuCH? (2BI 1 charge distribution L/KU)
and dipole moment DM iD) q(H)
L/(C)
this work
+O.?OO I
[I21
+0.230
-0.0573 -0.48 I
DM
-0.0714
I.952
+o.12s
353
value, and the value reported in [ 121 is 93 cm-’ lower than that value. The charge distribution and dipole moment are shown in Table 3 along with the results given in Ref. [ 121; we have no experimental results to compare them with. As we can see, there is a charge of 0.200 e transferred from the Cu atom to the CH: group; a similar result was given in Ref. 1121. But the charge distribution in the CH? group is completely different; according to our results, about the same negative charge is on the C and on each H atom, but in Ref. [ 121 the C atom carries a large negative charge and the H atoms a positive charge. Consequently the dipole moments are rather different; ours is much lower (1.95 D) than those of Ref. [ 121 (3.53 D). We do not have experimental data in order to make the comparisons. According to Ref. [14] the LDA method gives, in general, good results for dipole moments which are better when the NL correction is added. 3.2. NiCH2 As in the case of CuCH2, there are no reports on theoretical studies of this compound by DFT methods; there is, however, one report by Spangler et al. [ 161 in which the SCF method was used. and other by RappC et al. [17] where the GVB method with effective potentials was employed. Table 4 NiCHz (IAI) Geometrical parameters d,: Ni-C distance (A) dz: C-H distance (.&) n: H-C-H angle (“) D: dissociation energy (kcal mol-‘) BE: bonding energy (au.) I?,,,~: sum-of-fragments energy (a.u.) a D d, dz
BE
E \c,,
this work
1.698
1.101
-0.601 679
-0.466354
[I71
I .78
1.098
[I61
I.743
114.1 113.7 I II.6
84.9 65
R.M. Sosa, P. GardioWJoumal
Table 5 NiCHz (IAl)
atomic charger:
of Molecular
dipole moment DM (D); vlbrational
Structure
frequencies
(Thrachern)
25.7
394 (1997) 249-258
(cm-‘) (intensity in km mol-‘)
q(Ni)
q(C)
q(H)
DM
ANO
f(H-C-H)
AC-H)
+o. 1007
+0.0366
-0.0687
0.773
776(Y)
I293( 19)
2954(9)
The frequency f(Ni-C) is 179 cm-’ higher than f(Cu-H). and also f(H-C-H) is 52 cm - 1 higher than that corresponding to the CuCH? case; on the other hand, AC-H) is 68 cm-’ lower than in the CuCH 2 case.
The results of our calculations and those of these references are given in Table 4. The C-H distance and the H-C-H angle agree quite well, but our Ni-C distante is 0.08 A lower than in Ref. [17] and 0.04 A lower than in Ref. 1161; this situation is similar to the CuCH2 case. For the calculation of the dissociation energy we used the sum-of-fragments obtained from the bonding energy of the 3B 1 state of CH2, as was used in the case of the CuCH2 calculation, and that corresponding to the triplet Ni atom in the symmetry C2V (-0.028 199 a.u.); this value is 4.35 kcal mol-’ lower than that corresponding to the triplet in the sld9 configuration. The dissociation energy obtained was 84.9 kcal mol-’ and the value given in Ref. [ 171 is 65 kcal mol-‘, 23% lower than our result. Unfortunately we have no experimental values to assess which of these two values is better. In Table 5 our results for the atomic charges, dipole moments and vibrational frequencies are reported. From these results we conclude that the charge transferredfrom Ni to the CH2 group (0. IO 1 e) is much smaller than that corresponding to the CuCHz case, and that the C atom is positive while in the other case it was negative. The dipole moment (0.773 D) is also smaller than the one in the CuCH2 case. Table 6 FeCH* (3B2). FeCH; (4A2,4B
3.3. F&H2 As in the two previous cases, there are no reports of theoretical calculations using the DFT methodology; there is, however, a report by Veldkamp et al. [ 181 in which several compounds FeCH,, (n = 1,2,3) and their corresponding ( + 1) cations were studied using ab initio methods with effective core potential at the MP2 and MP4 post HF levels. Table 6 gives the results of our calculations as well as those of Ref. [18]. We have included the cation FeCHt because, for this compound, there are experimental data for the dissociation energy of the CH2 group that are missing for FeCH? [ 191. For the triplet state of FeCH? we found two states with almost the same energy: one with the configuration (in the symmetry group C2v) (6 1 2 3/5 0 2 3) (3A2 state), which is only 0.30 kcal mol-’ above the other with the configuration (6 1 2 3/5 1 2 2) (3B2 state) that is the ground state. In [18] this is also the
1)
Geometrical parameters distance (A) d?: C-H distance (A) a(H-C-H) angle (“) D: dissociation energy (kcal mol-‘) BE: bonding energy (ax) E,,,,: sum-of-fragments energy (a.u.) d ,: Fe-C
dl
FeCH, FeCH* FeCH ; FeCH ; FeCH; FeCH;
(3B2) (3B2) (4A2) (4B I ) (4B I) exp.
this work
[I81 this work this work
tta1 [I91
I.781 I.941 1.801 1.926 1.89-I .96
d2
n
D
BE
E \“f
I.096
116.1 113.2 116.0 112.4 122-123
x4.4 38.3 103.6 64.3 63.8 81.5
-0.7 I8 368
-0.583 843
-0.450 094 -0.387 469
-0.285 059 -0.285 059
I .090 I.099 I.103 1.09-1.10
254
R.M. Sosa, P. GurdioUJoumnl
C$ Molecular
Table 7 Bonding energy of fragments Cu(2) atom (2 3 5/2 3 4) (sld9) C”(2) atom (2 3 5/l 3 5) (s2dlO) C”(2) C2v (51 I 2/4 I 2 2) Ni( I) atom (2 3 4/2 3 4) (s2d8) Ni(l) atom (2 3 4/l 3 5) (sld9) Ni(l)C2v(4122/4122) Ni(3) atom (2 3 512 3 3) (s2d8) Ni(3) atom (2 3 5/l 3 4) (sld9) Ni(3) C2v (5 I 2 2/4 I I 2) Fe(l) Fe( 3) atom ( I 3 5/2 3 2) Fe(3) C2v (4 I 2 2/3 0 2 Fe(5) atom (2 3 S/l 3 2) Fe(5) atom (2 3 512 3 I) Fe(5) C2v Fe+(6) Fe+(4) CHZ(I) (1.123/100.63) CH2(3) (I .086/135.98)
(s I d7) 2) (sld7) (a2d6)
+O.OEI 208 a.“. -0.009484 a.“. -0.009948 a.u. +0.069 338 a.“. -0.014 869 a.“. -0.0165.57 a.“. +0.032689 a.“. -0.021 269 a.“. -0.028 I99 a.“. -0.000278 a.“. -0.104308 a.u. -0.119912a.u. -0.12691 1 a.u. -0.138017 a.“. -0. I45 688 a.“. +0.153 096 a.“. +0.160396 a.u. -0.413001 a.“. -0.438 I55 a.“.
triplet state, which is reported as the ground state. As we can see, the agreement of the distance d(C-H) and the angle a(Fe-C-H) between the result of [18] and ours is quite good, but our distance d(Fe-C) is 0. I6 A lower than that reported there; this is a common situation for the distances M-C between the transition element M and the C atom, as we said before. For the cation FeCHz + we report two states: the ground state, according to our calculations, is the 4A2; and the state 4B 1, that is reported in [ 181 as the ground state, is, according to our results, 39.3 kcal mol-’ higher, as we can deduce from Table 6. The Esof energy was obtained from Table 7, considering the CH2 group in the triplet state 382 and the Fe atom in the quintuplet state with C2v symmetry (that is, 4.81 kcal mol-’ below the quintuplet in the s2d6 -0.583 gziu??ze E,zite harlkZ a ~~~~iati~~ energy of 84.4 kcal mol-‘. The value reported in [ 181 is 38.3 kcal mol -‘, which is 55% lower than ours; that is indeed a large difference, much larger than the 23% that we had in the CuCH2 and NiCHz cases. Table 8 F&HZ (3B2) atomic charges; dipole moment DM (D); vibrational
Structure
(Theochem)
394 (I 997) 249-258
Unfortunately, we have no experimental values to make the comparison possible, but Ref. [ 181 quotes, for the cation FeCHl, an experimental value of 81.5 kcal molK’ taken from Ref. [ 191. We therefore decided to calculate its dissociation energy. As stated earlier, we found the 4A2 as the ground state instead of the 4B1, so we report in Table 6 our results for these two states. The geometry and the dissociation energy that we obtained for the 4Bl state was almost the same reported in [18]. This is quite curious, because in the case of FeCH? our values were significantly larger than those reported in [ 181; on the other hand, the value of the dissociation energy that we obtained for our ground state 4A1 was 103.6 kcal mol-‘, which is 30% larger than the experimental value of 81.5 kcal mol-‘. However, our value for the state 4B1, which, as stated above, is almost the same as the one reported in [ 181, was 22% lower than the experimental one. The E,,,r used in the FeCH; calculations was obtained with the bonding energy of CH2 (3Bl) and Fe’(6); we have used this multiplicity for the Fe’ cation because its bonding energy is lower (by 4.6 kcal mol-‘) than that of Fe+ (4); as a check on our result, the experimental value for this difference is 5.3 kcal mol-‘, as quoted in [18]. The conclusion is that our calculated values for the energy of the metal-carbon transition, in the case of carbenes, are not as bad as might be considered at first sight. Furthermore, analysis of several cases reported in the literature and our experience with transition metal carbonyls [20] support the idea that the LDA/ NL calculations give good results in comparison with experimental values [ 141. From Table 8 we can observe that the charge transferred from the Fe atom to the CH2 group is 0.154 e, a value between those corresponding to the CuCHz and NiCH2 cases; as in the case of CuCH2, the C atom is negative. The dipole moment is 1.095 D, a value between those of the CuCH2 and NiCH2 cases. The frequencies f(H-C-H) and f(C-H) reported in the same table are similar to the NiCH, case; in fact
frequencies
(cm-‘) (intensity in km mol.‘)
q(Fe)
q(C)
q(H)
DM
f(Fe-C)
0.1540
-0.0370
-0.0585
1.095
649( 19)
AH-C-H) l303(41)
AC-H) 293 I(30)
R.M. Sosa, P. GurdioWJoumal of Moleculur Structure (Theochern) 394 (1997) 249-258
f(H-C-H) is 10 cm-’ higher andf(C-H) is 23 cm-l lower, but the fIFe-C) frequency is 127 cm-l lower than f(Ni-C) and 52 cm-l higher thanf(Cu-C). Table 9 gives the geometrical parameters for CH>.
255
only the most stable state for each of the four combinations of the kinds of cluster (5,0), (4,l) and the orientation of the CH2 group, p or d. In the case of iron, we have only the one case (4,l) and the orientations p and d. The distances from C to the M4 plane, d, are given in Tables lo- 12; in order to obtain the distances from C to the fifth M atom (that we call Ml) in the (4,l)
3.3.1. MjCH2 (M = Fe, Ni, Cu) cases Tables lo- 17 show the relevant parameters that we have calculated in this report. We have considered Table 9 CH2
Geometrical parameters d: distance C-H (A) a: angle H-C-H (“) E,,: energy difference between the singlet (IA]) and triplet (3Bl) states (kcal maI_‘) 3Bl IAI d
a
d
a
Et,
this work
I .09
PO1
1.09 I .07 I .08 I .07
136 140 130 133 134
1.12 I.14 I.10 I.1 I I.11
IO1 100 I04 102 102
15.8 15.0 25.0 9.4 9.1
RHF CMR-CI exp.
Table IO CUSCHZ distance from C to the CUE plane: d (A); bonding energy: (kcal mol-‘f
BE (ax.):
sum-of-fragments
energy: E,,~ (a.~.); dissociation
Molecule/State
d
BE
E roi
D
CuW,
1.85 I .85 0.10 0.20
-0.750 687 -0.722 673 -0.704 142 -0.697 I7 I
4.682 472 -0.682 472 4.612091 -0.612091
42.80 25.22 57.76 53.39
VA]) (W) p
Cu&H2 (2B2) (5,O) d CusCHz (2Bl) (491) p CuSCH? (2Bl) (4,l) d
Table
energy: D
II
NicCH2 distance (kcal mol.‘)
from C to the NiJ plane: d (A); bonding
Molecule/State NiJHl ([AI) Ni5CHz (IAI) Ni5CH,(IB2) Ni5CH, (IAI)
(5,O) (5,O) (4.1) (4.1)
Table I2 Fe&Hz distance (kcal mol-‘)
p d p d
energy:
d
BE
I .70 I .70 I .30 1.20
-0.92 I -0.940 -0.779 -0.796
from C to the Fe4 plane: d (A); bonding
energy:
BE (ax.):
sum-of-fragments
energy:
E \“f 304 206 62 I I76
BE (ax);
-0.792 4.792 -0.726 -0.726
sum-of-fragments
E,,f ,dU,; dissociation
energy:
D
D 603 603 902 902
80.76 92.62 33.08 43.26
energy: E,,, (a.u.); dissociation
Molecule/State
d
BE
E \Ol
D
Fe&H, (3Al) (4.1) p Fe5CH2 (3A2) (4,l) d
I .30
1.30
- 1.459 900 -I ,588 328
-1.368653 -1.368 653
57.25 137.8
energy: D
256
R.M. Sosrr, P. Gnrdiol/Joumtrl
c~Molrculur
S~rucrure (Them-hem) 394 (1997) 249-258
Table 13 CuKH2 atomic charges and dipole moment: DM (D) Molecule/State Cu$ZH2 CulCHz CujCH2 CulCH:
(2Al) (5.0) (2B2) (5.0) (2Bl) (4,l) (2B I ) (4, I)
y(Ml) p d p d
-0.2285 -0.2566 0.3019 0.2447
q(M2. M4)
q(M3. MS)
0.0538 0.0795 -0.008.5 -0.067 I
0.0538 0.0233 -o.oaso PO.0993
cases, we have to add to d the distance from M 1 to that plane which is, as stated earlier, I.804 A, 1.768 A and 1.425 A for the Cu, Ni and Fe clusters, respectively. In Tables 13-15, Ml is the central or shifted atom in the case of cluster (5,O) or (4,1), respectively; M2 and M4 are the M atoms of the Mj square close to the H atoms in the d case, and M3, M5 are the other two; in the p case the four M1 atoms are equivalent. The sum q(C) + 2q(H) must be opposite to the sum q(M1)+2q(M2.
q(C)
q(M) -0.0 I33 -0.05 12 0.2679 0.1803
0.2032 0.2 132 0.0083 -0.0181
q(H)
DM
-0.0949 -0.0810 -0.1381 -0.08 1 I
I.009 0.512 1.660 I.610
to about 43 and 25 kcal mol-’ for the p and d cases, respectively. The interaction of the Cud ring with the CuCHz molecule is, as a consequence, destabilizing, and therefore it would be easier to remove the CH2 group in the case of the crystal than in the case of the isolated molecule if we take, as a model for the crystal, the cluster Cus (5,O). The dissociation energies were calculated using the E,,,,- energies also given in Table 10; these E,,r are calculated in the same way as in the case of the case of the MCH? compounds, that is, adding the bonding energies of the fragments; the fragment CH2 has been given earlier (we are using the 3B1 state) and the fragments Mi are given in Table 17. It is interesting to note the big reduction in the dissociation energy produced by a 45” rotation of the CH2 group in order to shift from the p to the d position. In the (4,l) case we have a C-Ml equilibrium distance of 1.90 A for the p case and 2.00 A for the d, because the distances d are 0.10 and 0.20 A, respectively; these are a little bit higher that in the (5,O) case. The dissociation energies are also reduced, but to a much smaller amount than in the (5,O) case, which
M4)+2q(M3,M5)
and any of these sums gives the amount of charge transferred from the MS cluster to the CH2 fragment. The symmetry of the states is established from the occupations of the orbitals given in Table 16. 3.4. C’ll_jCHz In the case of Cu2CHz (5,0) p or d, the distance d, which is also the distance from the C to the central Cu atom, is almost the same as the distance Cu-C in CuCH? (2Bl); the effect of the other four Cu atoms is to lower the dissociation energy from 67 kcal molK’
Table I4 NI JJHz atomic charges and dipole moment: DM (D) Molecule/State Ni,CHz (IAI) (S,O) p Ni;CH? (I Al) (-5.0) d Ni,CH,(lB2)(4,l)p Ni5CH2 (IAI) (4.1) d
q(M1) -0.0989 -0.0947 0.0095 -0.0223
y(M2, M4) 0.0385 0.0993 0.0656 0.0769
q(M3, M5) 0.0385 -0.0264 0.0656 0.0703
q(M) 0.0553 0.0512 0.2717 0.2719
q(C) 0.1607 0.1242 -0.0647 -O.llSS
q(H) PO.1080 -0.0877 -0.1035 -0.0782
DM 0.948 1.198 0.3 I3 0.679
Table IS Fc$ZH? atomic charges and dipole moment: DM (D) Molecule/State Fe&H: (3Al) (4,1) p FeTCH2 (3A2) (4,l) d
y(Ml) -0.0434 -0.1657
q(M2, M4) 0.0625 0.0365
y(M3, M5) 0.062.5 0. IS45
y(M) 0.2066 0.2 I63
q(C) 0.0726 0.0343
q(H) -0.1397 -0.1253
DM I.872 3.240
R.M. Sosa.
of MolecularSrructurr(Throchm)
P. Gnrdinl/Joumd
Table I6 Electronic
configurations
of the M&H?
compounds
(group symme-
)
try c2v
(5.0) p
(16 IO 13 12115 IO 13 12)
(S,O) d
(187
(4.1) p
(16 IO 13 l2/16
(431) d
(197
(LO) p (5,O) d
(18711
(4, 1) p
(IS79
(4, 1) d
(188 II
(4.1) p
(IS I I 10113 I I 8 IO)
(4.
13 lYl87 I3 lZ/lY
I3 12) IO I2 12) 7 I2 12)
12/187ll
12)
(177 12 12/17 7 12 12)
I 1d
I2 l2/169 12/1X7
I? II) II
12)
(176101111651011)
means that the interaction with the Cul group is lower in this case. From Tables 3, and 13 we can see the influence of the interaction of the Cul group with the CuCH2 molecule in relation to the charge transferred to the CH2 group and the dipole moment. In the (5,O) cases about 0.20 and 0.2 I e are transferred from the C atom to the Cug cluster and the H atoms, in cases p and d respectively, which is very different from the case of the CuCH? molecule. Also, the dipole moments are changed by a great amount, from 1.95 D in the CuCH? case to 1.O and 0.5 D in cases p and d respectively. 3.5. NijCH? In the (S,O) case the distance d is the same as that corresponding to NiCHz, as is seen from Table 11; the dissociation energies of the two cases p and d are similar to those of the NiCHz molecule: we have 85 kcal molK’ for this molecule and, by interaction with the Nil ring, this is reduced to 81 kcal mol-’ in the p case and increased to 91 kcal mol-’ in the d case. In the (4,l) case the distances rl are much longer than in the similar case for CuSCH2, and the dissociation energies are reduced to 33 kcal mol-’ in the p case and 43 kcal mol-’ in the d case: this means that the inter-
Table
17
Bonding cui
energy (au.) of fragments
(5.0)
cu5 (4.1) Ni
T(5.0)
Cui. Nti,
-0.244
3 I7
-0. I73 936 -0354448
NIP (4.1)
-0.288
Fe; (4.1)
-0.930498
747
CH? (3Bl)
-0.438
I55
Fe,
394 (1997)
249-258
251
action of the Ni, ring on the NiCHl molecule is relatively small in the (5,O) case but important in the (4,l) case. In this last case it is easier to remove the CH2 group from the cluster, especially in the p case. From Tables 5, and 14 we conclude that the charge transferred from the NiS cluster to the CH? group in the (5,O) case, for both the p and d cases, is about onehalf that corresponding to the NiCHz case, but the charge on the C atom increases; the dipole moment also increases as a consequence of the increase in the polarity of the C-H bonds, but this increase is only moderate (from 0.77 D to 0.95 D in the p care and I .20 D in the d case). In the (4,l) case, on the other hand, the charge transferred from the NiS cluster to the CH1 group is multiplied by a factor of almost three relative to the NiCH2 molecule. but the charge on the C atom becomes negative in both p and d cases. The reduction in the dipole moment is more important in the (4, I) p case than in the (4,l) d case, which is also the case in which the change in the dissociation energy is most important. 3.6. Fe jCHz From Tables 6, and I2 we observe that the distance C-Fe1 for both p and d cases is much longer than in the case of FeCH? (similarly to the NiiCHz (4,l) cases). The dissociation energy in the p case is reduced from 84 kcal mol-’ (for the FeCH 2 molecule) to 57 kcal mol-’ but increased to 138 kcal mol-’ in the d case; this means that the interaction between the H atoms and the Fe atoms of the Fel ring is much larger in the d case, corresponding to an important stabilization of the CHL group in the field of the cluster, than in the p case in which it is easier to remove the CH2 group from the cluster than in the FeCH2 case. The results from Tables 8, and 15 allow us to conclude that the transfer of charges from the Fes cluster in both cases is increased from 0.15 e (in the FeCH? case) to about 0.20 e; this is only a modest change, but the polarization of the C-H bonds is significantly increased because the C atom changes from negative to positive and the H atoms become more negative: as a consecuence the dipole moment increases in both cases from 1.1 D in the FeCH 1 case to 1.9 D for the (4,l) p case and 3.2 D in the (4,l) d one. The big change in the dipole moment is parallel to the change in the dissociation energy.
258
R.M. Saw, P. GardioUJoumal
of Molecular Structure (Theochem) 394 (1997) 249-258
4. Conclusions The DFT method, in the version LDA/NL of the program ADF (version 2.0.1) used in this report, is a very practical and computationally economical procedure for the theoretical study of molecular properties such as equilibrium geometries, dissociation energies, charge distributions, dipole moments, vibrational frequencies etc. Comparison between our results and CASSCF (MRSDCI) ones reported for CuCH2 in the ground state is very positive and the agreement with experimental vibrational frequencies is very good. This calculation was therefore extended to other carbenes such as NiCH2 and FeCH2 that are considered important in theoretical studies in the field of heterogeneous catalysis. These calculations were generalized by considering clusters of the elements Fe, Ni and Cu with five atoms. Calculations of several properties such as the equilibrium position of the CH2 group with respect to the cluster, dissociation energy, electrical charge distributions and dipole moments were carried out and compared with the results obtained with the MCH2 compounds. Acknowledgements This work was supported by CONICYT (Consejo Investigaciones Cientificas y National de Tecnologicas) of Uruguay.
References [I] R.C. Beady III and R. Pettit. J. Am. Chem. Sot.. 102 (1980) 6182. [2] S. Chang, Z.H. Kafafi, R.H. Hauge. W.E. Billups and J.L. Margrave. J. Am Chem. Sot.. 109 (1987) 4508. [3] W. Kohn and L.J. Sham, Phys. Rev. A. 140 (1965) 1133. [4] D. Post and E.J. Baerends, J. Chem. Phys.. 78 (1983) 5663. [Sl ADF 2.0.1 (12/15/95), SCM, Theorettcal Chemistry. Wrije Universiteit, Amsterdam, The Netherlands; E.J. Baerends, D.E. Ellis and P. Ross, Chem. Phys.. 2 (1973) 41: G. te Velde and E.J. Baerends. J. Comp. Phys.. 99 (1992) 84. [6] J.C. Slater. Phys. Rev.. 81 (1952) 381. [7] S.J. Vosko, L. Wilk and M. Nusair, Can. J. Phyj.. 58 (1980) 1200. [8] A.D. Becke, Phys. Rev.. A38 (1988) 309X. [9] J.P. Perdew, Phys. Rev., B33 (1986) 8822: errata: B34 (1986) 7406. [IO] P.M. Boerrigter, G. te Velde and E.J. Baerends, Int. J. Quantum. Chem., 33 (1988) 87. [I I] T. Ziegler and A. Rauk, Theor. Chim. Acta, 46 (1977) I. [ 121 Y. Mochizuki. K. Tanaka, K. Ohno, H. Tatewaki and S. Yamamoto, Chem. Phys. Lett., 152 (1988) 457. [I31 L. Fang and T. Ziegler, J. Chem. Phys., 95 (1991) 7401. [I41 T. Ziegler, Chem. Rev., 91 (1991) 651. 1151 A. Selmain and D.R. Salahub. J. Chem. Phys.. 89 (1988) 1529. [I61 D. Spangler. J.J. Wendoloski, M. Dupuia, M.M.L. Chen and H.F. Schaeffer III, J. Am. Chem. Sot.. 103 (1981) 3985. [ 171 A.K. RappC and W.A. Goddard III, J. Am. Chem. Sot.. 99 ( 1977) 3966. [ 181A. Veldkamp and G. Frenking. J. Compt. Chem, I3 (1992) 1184. [ 191 R.L. Hettich and B.S. Freiser, J. Am. Chem. Sot., I08 (1986) 2537. [20] R. Sosa and P. Gardiol, Int. J. Quantum Chem. Quant. Chem. Symp. 30,60 (1996) 1429.
Journal
ELSEVIER
of Molecular Structure (Theochem) 394 (1997) 249-258
Electronic structure and properties of transition metal complexes MCHZ and M5 CH2 (M = Fe, Ni, Cu;) by density functional methods
Abstract The electronic
structure and properties ofcarbenes
methods (DF), particularly
ADF program of Bearends and collcaguea. the process MCHz -
basis set with frozen core orbit& methods and experimental
frequencies
Comparisons
values were carried out. Calculations
was studied dissociation
the non-planar
energies, distribution
Transition
model
for the Fe5 cluster.
were done using the triple-zeta
between our results and other calculations
using ab
were done for the ground doublet state of CuCH?, the
and singlet states for NiSCHZ were studied. considering and diagonal)
Optimization
metal carbens; Density
functional
of the position
of the CH?
gl-oup
in the cluster,
* Colsesponding author. e-mail: [email protected]
were
(Theory)
The interest in the subject considered in this report is due to the fact that in the Fischer-Tropsch synthesis CH 1 radicals are believed to be generated in the reduction of carbon monoxide by hydrogen, catalysed by transition elements; these radicals will remain attached to the metallic atoms, forming in this way metallic carbenes; these carbenes would be the precursors in the hydrocarbon synthesis [ 11. CuCH2 is
one of such compounds that has been isolated in an argon matrix and whose vibrational frequencies have been determined by FTIR 121. Density functional (DF) methods have become a very useful tool, due to both the accuracy of the results for several properties and the reduction in computational time. 2. Methods The calculations reported in this paper are based on the Kohn-Sham approach to density functional theory
0 1997 Elsevier Science B.V. All rights reserved
PI/ SO 166.1280(96)04840-3
planar and
for the CH? group. The triplet state for Fc5CH2
Science B.V.
1. Introduction
0166.1280/97/$I7.00
All the calculations
energies for by population
of‘ charges in the molecule and dipolar moments were also calculated and comparisons
made with the MCH? results. 0 1997 Elsevier Keywords:
Charge distributions
In order to compare our results with some references found in the literature
models for the MF clusters and two positions (parallel with
(NL) of Becke and Perdew and the
geometries and dissociation
in our study two states of the cation FeCHr.
In the second part of this report, doublet states for CuXH? non-planar
corrections
MCHz were calculated.
were also evaluated.
and the NL corrections.
singlet state of NiCHz and the triplet state of FeCH:. we have included
with the non-local
In the first part of this report the equilibrium
M + CH2 at the ground state of the compound
analysis, dipole moments and vibrational initio
MCH? and M $.IHZ (M = Fe, Ni, Cu) were studied using density functional
the local density approach (LDA)
(DFT) 131 with the methodology of Post and Baerends 141. The program used was the ADF (version 2.0. I, IS December 1995) [5]. Basically. the local density approach (LDA) was used for the calculation of the exchange energy Ex(LDA) derived from the original proposal made by Slater [6] (Xalpha approximation); the Vosko-Wilk-Nusair (VWN) version was used 171. An evaluation of the electron correlation energy was also included; thus we have: E,,(LDA)=E,(LDA)+E,(LDA). This is called the exchange correlation energy for a homogeneous electronic gas. Non-local corrections were introduced that signiticantly improve the results of calculation of several properties such as bonding energies and molecular geometries, dipole moments, etc; these corrections are: (a) a non-local term for the exchange energy Ex(NL) due to Becke [S]; (b) a similar correction for the correlation energy Ec(NL) due to Perdew [9]. The method is accordingly called LDA/NL. A Slater orbitals (STO) basis set was used for the molecular orbital expansion (LCAO method) and, for the transition elements in particular, an uncontracted triple-zeta was augmented by three (n + I ) p STO. The main elements (C in our case) were described by a double-zeta ST0 basis augmented by one 3d polarization ST0 and, in the case of hydrogen, one 2p was used; core orbitals (CO) were kept frozen. Core functions (CF) were introduced in order to establish the orthogonality of the valence molecular orbital!, (MO) on the CO; symmetry was considered in order to keep the overlap and Fock matrices block-diagonal by using symmetry-adapted linear combinations of the (C)BAS that we call (C)SBAS. A set of auxiliary s, p, d, f and g ST0 functions centred on each nucleus was used to tit the electronic density; for each metal atom 36 ST0 were used but this number was reduced to 20 for carbon and I I for hydrogen. In this way integrals involving electronic density (such as Coulomb potentials) were evaluated by using these auxiliary bases and then taking the linear combination of these integrals. The coefficients of these linear combinations are evaluated in each SCF cycle. The matrix elements of the overlap and Fock matrices were calculated by numerical integration. The success of the DFT methods is due, among
other reasons, to the existence of accurate and practical integration methods that now are available IlOl. Instead of total energies, bonding energies were calculated according to Ziegler’s procedure [II ]. These bonding energies are the difference between the total energy of a molecule (or atom) and those of the atoms (or fragments) in the established reference states. Optimization of the geometry in the LDA/NL method was done for all the geometrical parameters in the case of the MCHz compounds; C2V symmetry was used throughout. The ground state was studied in the CuCH? case in order to compare with the CASSCF (MRSADCI) calculations reported for this compound [ 121. Ground states were also considered for NiCH: and FeCHz in the singlet and triplet states, respectively. In all cases the energies of the M and CH1 fragments were obtained, and the dissociation energy was calculated in every case using the sum-of-fragment energies and the energy at the equilibrium geometry of MCH?. A Mulliken population analysis was made. and the charge distribution in the molecule and the related dipole moment were obtained as well as the vibrational frequencies of the normal modes. Referring to the MsCH~ compounds, we have two possibilities for the M5 clusters: Ni and Cu crystals have an fee (face centred cubic) elementary cell and the iron has a bee (body centred cubic) one. In the first two cases we have selected two cluster models: one that we call planar, symbolized by (5,0), with the five atoms (square vertices and centre) in the top face; and the other, called hollow and symbolized by (4.1), formed taking the four central atoms in the lateral cubic faces and the fifth atom at the centre of the bottom face. We have used the nomenclature given by Baerends [4]. The central M atom in (5.0). that we will call M 1, is shifted from the MJ plane by I .804 A for the Cu5 (4.1) cluster and 1.768 A for the Ni5 (4,l) 0
0 0
0
0
0 0
Fig. 1. HCH plane parallel to the side of the M, quare. Fe; 0 : H.
0: Cu. Ni,
R.M. Sosa, P. GnrdioWJoumal
of Molecular
0
o (Cu,Ni,Fe) 0
000
0 o
H
0 Fig. 2. HCH plane along one of the Cu, Ni, Fe: 0 : H.
diagonals of’the Ma square. 0:
cluster. In the case of the Fe5 cluster, the distance from Fe 1 to the Fe4 plane is 1.425 A. The CH:, group has its C2 axis normal and through the centre of the M1 square. We have investigated two situations: the first one in which the HCH plane is parallel to the side of the Mj square, that we call (5,O)p or (4,1)p; and the other one in which the HCH plane is along one of the diagonals of the Md square, that we call (5,O)d or (4,l)d; see Figs. 1 and 2.
3. Results
and discussion
3. I. CuCHz CuCHz was isolated in an Ar matrix by Chang [2] and its vibrational frequencies observed by FTIR spectroscopy. According to our calculations the ground state, in the group symmetry C2v, is the doublet 2B 1 and the first excited state is the doublet 2A 1, which is 43.1 kcal mol-’ higher in energy at the equilibrium geometries. Mochizuki et al. [12] report a CAS SCF (MRSDCI) ab initio study of this compound and arrive at the same conclusion, with an energy difference between the two states of 44.0 kcal mol-‘.
Structure
(Theochem)
251
394 (1997) 249-258
In the following we will consider only the ground state. The relevant geometrical parameters as well as the dissociation energy and dipole moments that we have obtained, and those of Ref. [ 121, are shown in Table 1; from these values we can conclude that the agreement between the two reported C-H distances and H-C-H angles is excellent but the difference between the Cu-C distances is 0.10 A, giving the ab initio method the largest values. This is a rather common situation: the HF method overestimates metalligand bond lengths and LDA underestimates them; with the NL corrections (such as with LDAPJL methods) it is possible to obtain the best concordance with experimental bond lengths [ 131. Now we will consider the energy change of the process CuCHz (2B 1) - Cu + CH2 that corresponds to the breaking of the Cu-C bond; in order to obtain this change we must consider the equilibrium energy for the ground state 2B 1; as we said before, we calculate not the total energy but the so-called bonding energy, that is the energy of the compound that we are considering relative to the elements in reference states that are well specified; the energy change that we are looking for is the difference between the sum of the bonding energies of the fragments Cu and CH> (to be called the sum-of-fragments energy, E,,,) and the bonding energy of CuCH?. These energies are shown in Table 1. In order to calculate E,,l we use the values given in Table 5: the lowest energy for the CH, fragment is - 0.438 155 a.u., corresponding to the equilibrium of the triplet 3B 1 state (C-H distance of 1.086 A and H-C-H angle of 135.98”). The lowest energy of the Cu atom in the doublet state is that of the symmetry C2v, which is the symmetry corresponding to the dissociation of the CuCHz molecule. This
Table I CuCH; (2BI) Geometrical
parameters distance (A) dz: C-H distance (A) (1: H-C-H angle (“) D: dissociation energy (kcal mol-‘) BE: Bonding energy (a.u.) E,,,: sum-of-fragments energy (a.u.)
d,: Cu-C
this work
[I21
dl
d?
(I
D
BE
E x,1
1.823 1.932
I .092 I.103
120 114
67.0 5 I .4
-0.554926
-0.448
103
of MolecultrrStructure
K.M. Sosa, P. Gurdiol/Joumul
252
energy is 0.009948 a.u., which is lower by 0.29 kcal mo1-’ than that corresponding to the configuration s2d 10 (0.009 484 a.u.); consequently E,,,, has the value given in Table 1 and our calculated dissociation energy is 67.0 kcal mol-‘, whereas the value reported in Ref. [12] is 51.4 kcal mol-’ (23%) lower. These results are quite different but unfortunately we have no experimental results to make the comparison possible. In general, the values given by the DFT methods when the NL corrections are included seem to be, in many cases, closer to the experimental values than the ab initio methods [ 141. Because CH? is common to all the compounds considered in this report, it is interesting to consider the results obtained from several methods applied to the theoretical study of the two lowest energy states: the ground 3B 1 and the first excited I Al; this calculation is also reported in Ref. [15] in which a method similar to ours was used. The results, for comparison, are in Table 6. We can conclude that our method and that used in Ref. [ 151 give the same results for the geometries and the energy difference between these two states. Comparing them with the experimental results, the geometries are very similar but the energy of excitation is too high; the RHF method gives a result that is much higher. The multireference CI method (CMRCI) gives a very good result, which is due to the fact that the ground state is well described with one configuration, but the excited state IA1 needs at least two configurations 1151. The results of the calculation of the vibrational frequencies that are shown in Table 2 are very important because we have experimental results to compare them with. Our stretching C-H frequency is 597 cm-’ with an intensity of 4 km mol-‘, agreeing quite well with the value of Ref. [12] (618 cm-‘) and the experimental one (614 cm-‘). The bending H-C-H frequency is 104 cm-’ lower than the experimental one and that of Ref. [ 121 is 61 cm-’ higher, but the concordance is acceptable. Our stretching C-H frequency is 72 cm-’ higher than the experimental Table 2 C&Hz (2BI) vibrational
this work [l21 121
frequencies,
cm-’
.f(C=C)
.AH-C-H)
597(4) 618 614
1241(69) 1406 I345
(intensity,
km mol-‘)
AC-H) 3033(22) 2868 2961
(Throchcm) 394 (1997) 249-258
Table 3 CuCH? (2BI 1 charge distribution L/KU)
and dipole moment DM iD) q(H)
L/(C)
this work
+O.?OO I
[I21
+0.230
-0.0573 -0.48 I
DM
-0.0714
I.952
+o.12s
353
value, and the value reported in [ 121 is 93 cm-’ lower than that value. The charge distribution and dipole moment are shown in Table 3 along with the results given in Ref. [ 121; we have no experimental results to compare them with. As we can see, there is a charge of 0.200 e transferred from the Cu atom to the CH: group; a similar result was given in Ref. 1121. But the charge distribution in the CH? group is completely different; according to our results, about the same negative charge is on the C and on each H atom, but in Ref. [ 121 the C atom carries a large negative charge and the H atoms a positive charge. Consequently the dipole moments are rather different; ours is much lower (1.95 D) than those of Ref. [ 121 (3.53 D). We do not have experimental data in order to make the comparisons. According to Ref. [14] the LDA method gives, in general, good results for dipole moments which are better when the NL correction is added. 3.2. NiCH2 As in the case of CuCH2, there are no reports on theoretical studies of this compound by DFT methods; there is, however, one report by Spangler et al. [ 161 in which the SCF method was used. and other by RappC et al. [17] where the GVB method with effective potentials was employed. Table 4 NiCHz (IAI) Geometrical parameters d,: Ni-C distance (A) dz: C-H distance (.&) n: H-C-H angle (“) D: dissociation energy (kcal mol-‘) BE: bonding energy (au.) I?,,,~: sum-of-fragments energy (a.u.) a D d, dz
BE
E \c,,
this work
1.698
1.101
-0.601 679
-0.466354
[I71
I .78
1.098
[I61
I.743
114.1 113.7 I II.6
84.9 65
R.M. Sosa, P. GardioWJoumal
Table 5 NiCHz (IAl)
atomic charger:
of Molecular
dipole moment DM (D); vlbrational
Structure
frequencies
(Thrachern)
25.7
394 (1997) 249-258
(cm-‘) (intensity in km mol-‘)
q(Ni)
q(C)
q(H)
DM
ANO
f(H-C-H)
AC-H)
+o. 1007
+0.0366
-0.0687
0.773
776(Y)
I293( 19)
2954(9)
The frequency f(Ni-C) is 179 cm-’ higher than f(Cu-H). and also f(H-C-H) is 52 cm - 1 higher than that corresponding to the CuCH? case; on the other hand, AC-H) is 68 cm-’ lower than in the CuCH 2 case.
The results of our calculations and those of these references are given in Table 4. The C-H distance and the H-C-H angle agree quite well, but our Ni-C distante is 0.08 A lower than in Ref. [17] and 0.04 A lower than in Ref. 1161; this situation is similar to the CuCH2 case. For the calculation of the dissociation energy we used the sum-of-fragments obtained from the bonding energy of the 3B 1 state of CH2, as was used in the case of the CuCH2 calculation, and that corresponding to the triplet Ni atom in the symmetry C2V (-0.028 199 a.u.); this value is 4.35 kcal mol-’ lower than that corresponding to the triplet in the sld9 configuration. The dissociation energy obtained was 84.9 kcal mol-’ and the value given in Ref. [ 171 is 65 kcal mol-‘, 23% lower than our result. Unfortunately we have no experimental values to assess which of these two values is better. In Table 5 our results for the atomic charges, dipole moments and vibrational frequencies are reported. From these results we conclude that the charge transferredfrom Ni to the CH2 group (0. IO 1 e) is much smaller than that corresponding to the CuCHz case, and that the C atom is positive while in the other case it was negative. The dipole moment (0.773 D) is also smaller than the one in the CuCH2 case. Table 6 FeCH* (3B2). FeCH; (4A2,4B
3.3. F&H2 As in the two previous cases, there are no reports of theoretical calculations using the DFT methodology; there is, however, a report by Veldkamp et al. [ 181 in which several compounds FeCH,, (n = 1,2,3) and their corresponding ( + 1) cations were studied using ab initio methods with effective core potential at the MP2 and MP4 post HF levels. Table 6 gives the results of our calculations as well as those of Ref. [18]. We have included the cation FeCHt because, for this compound, there are experimental data for the dissociation energy of the CH2 group that are missing for FeCH? [ 191. For the triplet state of FeCH? we found two states with almost the same energy: one with the configuration (in the symmetry group C2v) (6 1 2 3/5 0 2 3) (3A2 state), which is only 0.30 kcal mol-’ above the other with the configuration (6 1 2 3/5 1 2 2) (3B2 state) that is the ground state. In [18] this is also the
1)
Geometrical parameters distance (A) d?: C-H distance (A) a(H-C-H) angle (“) D: dissociation energy (kcal mol-‘) BE: bonding energy (ax) E,,,,: sum-of-fragments energy (a.u.) d ,: Fe-C
dl
FeCH, FeCH* FeCH ; FeCH ; FeCH; FeCH;
(3B2) (3B2) (4A2) (4B I ) (4B I) exp.
this work
[I81 this work this work
tta1 [I91
I.781 I.941 1.801 1.926 1.89-I .96
d2
n
D
BE
E \“f
I.096
116.1 113.2 116.0 112.4 122-123
x4.4 38.3 103.6 64.3 63.8 81.5
-0.7 I8 368
-0.583 843
-0.450 094 -0.387 469
-0.285 059 -0.285 059
I .090 I.099 I.103 1.09-1.10
254
R.M. Sosa, P. GurdioUJoumnl
C$ Molecular
Table 7 Bonding energy of fragments Cu(2) atom (2 3 5/2 3 4) (sld9) C”(2) atom (2 3 5/l 3 5) (s2dlO) C”(2) C2v (51 I 2/4 I 2 2) Ni( I) atom (2 3 4/2 3 4) (s2d8) Ni(l) atom (2 3 4/l 3 5) (sld9) Ni(l)C2v(4122/4122) Ni(3) atom (2 3 512 3 3) (s2d8) Ni(3) atom (2 3 5/l 3 4) (sld9) Ni(3) C2v (5 I 2 2/4 I I 2) Fe(l) Fe( 3) atom ( I 3 5/2 3 2) Fe(3) C2v (4 I 2 2/3 0 2 Fe(5) atom (2 3 S/l 3 2) Fe(5) atom (2 3 512 3 I) Fe(5) C2v Fe+(6) Fe+(4) CHZ(I) (1.123/100.63) CH2(3) (I .086/135.98)
(s I d7) 2) (sld7) (a2d6)
+O.OEI 208 a.“. -0.009484 a.“. -0.009948 a.u. +0.069 338 a.“. -0.014 869 a.“. -0.0165.57 a.“. +0.032689 a.“. -0.021 269 a.“. -0.028 I99 a.“. -0.000278 a.“. -0.104308 a.u. -0.119912a.u. -0.12691 1 a.u. -0.138017 a.“. -0. I45 688 a.“. +0.153 096 a.“. +0.160396 a.u. -0.413001 a.“. -0.438 I55 a.“.
triplet state, which is reported as the ground state. As we can see, the agreement of the distance d(C-H) and the angle a(Fe-C-H) between the result of [18] and ours is quite good, but our distance d(Fe-C) is 0. I6 A lower than that reported there; this is a common situation for the distances M-C between the transition element M and the C atom, as we said before. For the cation FeCHz + we report two states: the ground state, according to our calculations, is the 4A2; and the state 4B 1, that is reported in [ 181 as the ground state, is, according to our results, 39.3 kcal mol-’ higher, as we can deduce from Table 6. The Esof energy was obtained from Table 7, considering the CH2 group in the triplet state 382 and the Fe atom in the quintuplet state with C2v symmetry (that is, 4.81 kcal mol-’ below the quintuplet in the s2d6 -0.583 gziu??ze E,zite harlkZ a ~~~~iati~~ energy of 84.4 kcal mol-‘. The value reported in [ 181 is 38.3 kcal mol -‘, which is 55% lower than ours; that is indeed a large difference, much larger than the 23% that we had in the CuCH2 and NiCHz cases. Table 8 F&HZ (3B2) atomic charges; dipole moment DM (D); vibrational
Structure
(Theochem)
394 (I 997) 249-258
Unfortunately, we have no experimental values to make the comparison possible, but Ref. [ 181 quotes, for the cation FeCHl, an experimental value of 81.5 kcal molK’ taken from Ref. [ 191. We therefore decided to calculate its dissociation energy. As stated earlier, we found the 4A2 as the ground state instead of the 4B1, so we report in Table 6 our results for these two states. The geometry and the dissociation energy that we obtained for the 4Bl state was almost the same reported in [18]. This is quite curious, because in the case of FeCH? our values were significantly larger than those reported in [ 181; on the other hand, the value of the dissociation energy that we obtained for our ground state 4A1 was 103.6 kcal mol-‘, which is 30% larger than the experimental value of 81.5 kcal mol-‘. However, our value for the state 4B1, which, as stated above, is almost the same as the one reported in [ 181, was 22% lower than the experimental one. The E,,,r used in the FeCH; calculations was obtained with the bonding energy of CH2 (3Bl) and Fe’(6); we have used this multiplicity for the Fe’ cation because its bonding energy is lower (by 4.6 kcal mol-‘) than that of Fe+ (4); as a check on our result, the experimental value for this difference is 5.3 kcal mol-‘, as quoted in [18]. The conclusion is that our calculated values for the energy of the metal-carbon transition, in the case of carbenes, are not as bad as might be considered at first sight. Furthermore, analysis of several cases reported in the literature and our experience with transition metal carbonyls [20] support the idea that the LDA/ NL calculations give good results in comparison with experimental values [ 141. From Table 8 we can observe that the charge transferred from the Fe atom to the CH2 group is 0.154 e, a value between those corresponding to the CuCHz and NiCH2 cases; as in the case of CuCH2, the C atom is negative. The dipole moment is 1.095 D, a value between those of the CuCH2 and NiCH2 cases. The frequencies f(H-C-H) and f(C-H) reported in the same table are similar to the NiCH, case; in fact
frequencies
(cm-‘) (intensity in km mol.‘)
q(Fe)
q(C)
q(H)
DM
f(Fe-C)
0.1540
-0.0370
-0.0585
1.095
649( 19)
AH-C-H) l303(41)
AC-H) 293 I(30)
R.M. Sosa, P. GurdioWJoumal of Moleculur Structure (Theochern) 394 (1997) 249-258
f(H-C-H) is 10 cm-’ higher andf(C-H) is 23 cm-l lower, but the fIFe-C) frequency is 127 cm-l lower than f(Ni-C) and 52 cm-l higher thanf(Cu-C). Table 9 gives the geometrical parameters for CH>.
255
only the most stable state for each of the four combinations of the kinds of cluster (5,0), (4,l) and the orientation of the CH2 group, p or d. In the case of iron, we have only the one case (4,l) and the orientations p and d. The distances from C to the M4 plane, d, are given in Tables lo- 12; in order to obtain the distances from C to the fifth M atom (that we call Ml) in the (4,l)
3.3.1. MjCH2 (M = Fe, Ni, Cu) cases Tables lo- 17 show the relevant parameters that we have calculated in this report. We have considered Table 9 CH2
Geometrical parameters d: distance C-H (A) a: angle H-C-H (“) E,,: energy difference between the singlet (IA]) and triplet (3Bl) states (kcal maI_‘) 3Bl IAI d
a
d
a
Et,
this work
I .09
PO1
1.09 I .07 I .08 I .07
136 140 130 133 134
1.12 I.14 I.10 I.1 I I.11
IO1 100 I04 102 102
15.8 15.0 25.0 9.4 9.1
RHF CMR-CI exp.
Table IO CUSCHZ distance from C to the CUE plane: d (A); bonding energy: (kcal mol-‘f
BE (ax.):
sum-of-fragments
energy: E,,~ (a.~.); dissociation
Molecule/State
d
BE
E roi
D
CuW,
1.85 I .85 0.10 0.20
-0.750 687 -0.722 673 -0.704 142 -0.697 I7 I
4.682 472 -0.682 472 4.612091 -0.612091
42.80 25.22 57.76 53.39
VA]) (W) p
Cu&H2 (2B2) (5,O) d CusCHz (2Bl) (491) p CuSCH? (2Bl) (4,l) d
Table
energy: D
II
NicCH2 distance (kcal mol.‘)
from C to the NiJ plane: d (A); bonding
Molecule/State NiJHl ([AI) Ni5CHz (IAI) Ni5CH,(IB2) Ni5CH, (IAI)
(5,O) (5,O) (4.1) (4.1)
Table I2 Fe&Hz distance (kcal mol-‘)
p d p d
energy:
d
BE
I .70 I .70 I .30 1.20
-0.92 I -0.940 -0.779 -0.796
from C to the Fe4 plane: d (A); bonding
energy:
BE (ax.):
sum-of-fragments
energy:
E \“f 304 206 62 I I76
BE (ax);
-0.792 4.792 -0.726 -0.726
sum-of-fragments
E,,f ,dU,; dissociation
energy:
D
D 603 603 902 902
80.76 92.62 33.08 43.26
energy: E,,, (a.u.); dissociation
Molecule/State
d
BE
E \Ol
D
Fe&H, (3Al) (4.1) p Fe5CH2 (3A2) (4,l) d
I .30
1.30
- 1.459 900 -I ,588 328
-1.368653 -1.368 653
57.25 137.8
energy: D
256
R.M. Sosrr, P. Gnrdiol/Joumtrl
c~Molrculur
S~rucrure (Them-hem) 394 (1997) 249-258
Table 13 CuKH2 atomic charges and dipole moment: DM (D) Molecule/State Cu$ZH2 CulCHz CujCH2 CulCH:
(2Al) (5.0) (2B2) (5.0) (2Bl) (4,l) (2B I ) (4, I)
y(Ml) p d p d
-0.2285 -0.2566 0.3019 0.2447
q(M2. M4)
q(M3. MS)
0.0538 0.0795 -0.008.5 -0.067 I
0.0538 0.0233 -o.oaso PO.0993
cases, we have to add to d the distance from M 1 to that plane which is, as stated earlier, I.804 A, 1.768 A and 1.425 A for the Cu, Ni and Fe clusters, respectively. In Tables 13-15, Ml is the central or shifted atom in the case of cluster (5,O) or (4,1), respectively; M2 and M4 are the M atoms of the Mj square close to the H atoms in the d case, and M3, M5 are the other two; in the p case the four M1 atoms are equivalent. The sum q(C) + 2q(H) must be opposite to the sum q(M1)+2q(M2.
q(C)
q(M) -0.0 I33 -0.05 12 0.2679 0.1803
0.2032 0.2 132 0.0083 -0.0181
q(H)
DM
-0.0949 -0.0810 -0.1381 -0.08 1 I
I.009 0.512 1.660 I.610
to about 43 and 25 kcal mol-’ for the p and d cases, respectively. The interaction of the Cud ring with the CuCHz molecule is, as a consequence, destabilizing, and therefore it would be easier to remove the CH2 group in the case of the crystal than in the case of the isolated molecule if we take, as a model for the crystal, the cluster Cus (5,O). The dissociation energies were calculated using the E,,,,- energies also given in Table 10; these E,,r are calculated in the same way as in the case of the case of the MCH? compounds, that is, adding the bonding energies of the fragments; the fragment CH2 has been given earlier (we are using the 3B1 state) and the fragments Mi are given in Table 17. It is interesting to note the big reduction in the dissociation energy produced by a 45” rotation of the CH2 group in order to shift from the p to the d position. In the (4,l) case we have a C-Ml equilibrium distance of 1.90 A for the p case and 2.00 A for the d, because the distances d are 0.10 and 0.20 A, respectively; these are a little bit higher that in the (5,O) case. The dissociation energies are also reduced, but to a much smaller amount than in the (5,O) case, which
M4)+2q(M3,M5)
and any of these sums gives the amount of charge transferred from the MS cluster to the CH2 fragment. The symmetry of the states is established from the occupations of the orbitals given in Table 16. 3.4. C’ll_jCHz In the case of Cu2CHz (5,0) p or d, the distance d, which is also the distance from the C to the central Cu atom, is almost the same as the distance Cu-C in CuCH? (2Bl); the effect of the other four Cu atoms is to lower the dissociation energy from 67 kcal molK’
Table I4 NI JJHz atomic charges and dipole moment: DM (D) Molecule/State Ni,CHz (IAI) (S,O) p Ni;CH? (I Al) (-5.0) d Ni,CH,(lB2)(4,l)p Ni5CH2 (IAI) (4.1) d
q(M1) -0.0989 -0.0947 0.0095 -0.0223
y(M2, M4) 0.0385 0.0993 0.0656 0.0769
q(M3, M5) 0.0385 -0.0264 0.0656 0.0703
q(M) 0.0553 0.0512 0.2717 0.2719
q(C) 0.1607 0.1242 -0.0647 -O.llSS
q(H) PO.1080 -0.0877 -0.1035 -0.0782
DM 0.948 1.198 0.3 I3 0.679
Table IS Fc$ZH? atomic charges and dipole moment: DM (D) Molecule/State Fe&H: (3Al) (4,1) p FeTCH2 (3A2) (4,l) d
y(Ml) -0.0434 -0.1657
q(M2, M4) 0.0625 0.0365
y(M3, M5) 0.062.5 0. IS45
y(M) 0.2066 0.2 I63
q(C) 0.0726 0.0343
q(H) -0.1397 -0.1253
DM I.872 3.240
R.M. Sosa.
of MolecularSrructurr(Throchm)
P. Gnrdinl/Joumd
Table I6 Electronic
configurations
of the M&H?
compounds
(group symme-
)
try c2v
(5.0) p
(16 IO 13 12115 IO 13 12)
(S,O) d
(187
(4.1) p
(16 IO 13 l2/16
(431) d
(197
(LO) p (5,O) d
(18711
(4, 1) p
(IS79
(4, 1) d
(188 II
(4.1) p
(IS I I 10113 I I 8 IO)
(4.
13 lYl87 I3 lZ/lY
I3 12) IO I2 12) 7 I2 12)
12/187ll
12)
(177 12 12/17 7 12 12)
I 1d
I2 l2/169 12/1X7
I? II) II
12)
(176101111651011)
means that the interaction with the Cul group is lower in this case. From Tables 3, and 13 we can see the influence of the interaction of the Cul group with the CuCH2 molecule in relation to the charge transferred to the CH2 group and the dipole moment. In the (5,O) cases about 0.20 and 0.2 I e are transferred from the C atom to the Cug cluster and the H atoms, in cases p and d respectively, which is very different from the case of the CuCH? molecule. Also, the dipole moments are changed by a great amount, from 1.95 D in the CuCH? case to 1.O and 0.5 D in cases p and d respectively. 3.5. NijCH? In the (S,O) case the distance d is the same as that corresponding to NiCHz, as is seen from Table 11; the dissociation energies of the two cases p and d are similar to those of the NiCHz molecule: we have 85 kcal molK’ for this molecule and, by interaction with the Nil ring, this is reduced to 81 kcal mol-’ in the p case and increased to 91 kcal mol-’ in the d case. In the (4,l) case the distances rl are much longer than in the similar case for CuSCH2, and the dissociation energies are reduced to 33 kcal mol-’ in the p case and 43 kcal mol-’ in the d case: this means that the inter-
Table
17
Bonding cui
energy (au.) of fragments
(5.0)
cu5 (4.1) Ni
T(5.0)
Cui. Nti,
-0.244
3 I7
-0. I73 936 -0354448
NIP (4.1)
-0.288
Fe; (4.1)
-0.930498
747
CH? (3Bl)
-0.438
I55
Fe,
394 (1997)
249-258
251
action of the Ni, ring on the NiCHl molecule is relatively small in the (5,O) case but important in the (4,l) case. In this last case it is easier to remove the CH2 group from the cluster, especially in the p case. From Tables 5, and 14 we conclude that the charge transferred from the NiS cluster to the CH? group in the (5,O) case, for both the p and d cases, is about onehalf that corresponding to the NiCHz case, but the charge on the C atom increases; the dipole moment also increases as a consequence of the increase in the polarity of the C-H bonds, but this increase is only moderate (from 0.77 D to 0.95 D in the p care and I .20 D in the d case). In the (4,l) case, on the other hand, the charge transferred from the NiS cluster to the CH1 group is multiplied by a factor of almost three relative to the NiCH2 molecule. but the charge on the C atom becomes negative in both p and d cases. The reduction in the dipole moment is more important in the (4, I) p case than in the (4,l) d case, which is also the case in which the change in the dissociation energy is most important. 3.6. Fe jCHz From Tables 6, and I2 we observe that the distance C-Fe1 for both p and d cases is much longer than in the case of FeCH? (similarly to the NiiCHz (4,l) cases). The dissociation energy in the p case is reduced from 84 kcal mol-’ (for the FeCH 2 molecule) to 57 kcal mol-’ but increased to 138 kcal mol-’ in the d case; this means that the interaction between the H atoms and the Fe atoms of the Fel ring is much larger in the d case, corresponding to an important stabilization of the CHL group in the field of the cluster, than in the p case in which it is easier to remove the CH2 group from the cluster than in the FeCH2 case. The results from Tables 8, and 15 allow us to conclude that the transfer of charges from the Fes cluster in both cases is increased from 0.15 e (in the FeCH? case) to about 0.20 e; this is only a modest change, but the polarization of the C-H bonds is significantly increased because the C atom changes from negative to positive and the H atoms become more negative: as a consecuence the dipole moment increases in both cases from 1.1 D in the FeCH 1 case to 1.9 D for the (4,l) p case and 3.2 D in the (4,l) d one. The big change in the dipole moment is parallel to the change in the dissociation energy.
258
R.M. Saw, P. GardioUJoumal
of Molecular Structure (Theochem) 394 (1997) 249-258
4. Conclusions The DFT method, in the version LDA/NL of the program ADF (version 2.0.1) used in this report, is a very practical and computationally economical procedure for the theoretical study of molecular properties such as equilibrium geometries, dissociation energies, charge distributions, dipole moments, vibrational frequencies etc. Comparison between our results and CASSCF (MRSDCI) ones reported for CuCH2 in the ground state is very positive and the agreement with experimental vibrational frequencies is very good. This calculation was therefore extended to other carbenes such as NiCH2 and FeCH2 that are considered important in theoretical studies in the field of heterogeneous catalysis. These calculations were generalized by considering clusters of the elements Fe, Ni and Cu with five atoms. Calculations of several properties such as the equilibrium position of the CH2 group with respect to the cluster, dissociation energy, electrical charge distributions and dipole moments were carried out and compared with the results obtained with the MCH2 compounds. Acknowledgements This work was supported by CONICYT (Consejo Investigaciones Cientificas y National de Tecnologicas) of Uruguay.
References [I] R.C. Beady III and R. Pettit. J. Am. Chem. Sot.. 102 (1980) 6182. [2] S. Chang, Z.H. Kafafi, R.H. Hauge. W.E. Billups and J.L. Margrave. J. Am Chem. Sot.. 109 (1987) 4508. [3] W. Kohn and L.J. Sham, Phys. Rev. A. 140 (1965) 1133. [4] D. Post and E.J. Baerends, J. Chem. Phys.. 78 (1983) 5663. [Sl ADF 2.0.1 (12/15/95), SCM, Theorettcal Chemistry. Wrije Universiteit, Amsterdam, The Netherlands; E.J. Baerends, D.E. Ellis and P. Ross, Chem. Phys.. 2 (1973) 41: G. te Velde and E.J. Baerends. J. Comp. Phys.. 99 (1992) 84. [6] J.C. Slater. Phys. Rev.. 81 (1952) 381. [7] S.J. Vosko, L. Wilk and M. Nusair, Can. J. Phyj.. 58 (1980) 1200. [8] A.D. Becke, Phys. Rev.. A38 (1988) 309X. [9] J.P. Perdew, Phys. Rev., B33 (1986) 8822: errata: B34 (1986) 7406. [IO] P.M. Boerrigter, G. te Velde and E.J. Baerends, Int. J. Quantum. Chem., 33 (1988) 87. [I I] T. Ziegler and A. Rauk, Theor. Chim. Acta, 46 (1977) I. [ 121 Y. Mochizuki. K. Tanaka, K. Ohno, H. Tatewaki and S. Yamamoto, Chem. Phys. Lett., 152 (1988) 457. [I31 L. Fang and T. Ziegler, J. Chem. Phys., 95 (1991) 7401. [I41 T. Ziegler, Chem. Rev., 91 (1991) 651. 1151 A. Selmain and D.R. Salahub. J. Chem. Phys.. 89 (1988) 1529. [I61 D. Spangler. J.J. Wendoloski, M. Dupuia, M.M.L. Chen and H.F. Schaeffer III, J. Am. Chem. Sot.. 103 (1981) 3985. [ 171 A.K. RappC and W.A. Goddard III, J. Am. Chem. Sot.. 99 ( 1977) 3966. [ 181A. Veldkamp and G. Frenking. J. Compt. Chem, I3 (1992) 1184. [ 191 R.L. Hettich and B.S. Freiser, J. Am. Chem. Sot., I08 (1986) 2537. [20] R. Sosa and P. Gardiol, Int. J. Quantum Chem. Quant. Chem. Symp. 30,60 (1996) 1429.