8308
J. Phys. Chem. 1996, 100, 8308-8315
Paramagnetic Exchange Spin-Catalysis of the Cis-Trans Isomerization of Substituted Ethylenes Olexandre Plachkevytch, Boris Minaev,† and Hans A° gren* Department of Physics and Measurement Technology, Linko¨ ping UniVersity, S-58183, Linko¨ ping, Sweden ReceiVed: NoVember 29, 1995; In Final Form: February 7, 1996X
Spin-catalysis of cis-trans isomerization reactions of substituted ethylenes by paramagnetic substances has been studied by ab initio calculations using an appropriate theoretical model: an internal rotation of the HCH group around the CdC double bond in the ethylene molecule in the presence of O2 or NO molecules. It is shown that spin-catalysis of this reaction is caused by paramagnetic exchange interactions. An adiabatic singlet-triplet intersystem crossing was traced to a stabilization in the transition of the lowest triplet state at the ethylene region by intermolecular exchange and charge-transfer mixings. The creation of a chemical intermediate was verified for the catalysis by nitric oxide. The NO catalyst, when the N atom forms a chemical bond, leads to a more pronounced lowering of the activation energy than does the O2 catalyst.
1. Introduction The transition states of many chemical reactions contain open electronic shells that are very sensitive to intermolecular exchange interactions. In such cases the reaction paths could be controlled by interaction with a paramagnetic substance (a catalyst). The importance of the electron spin for controlling these reaction channels in the region of an activation barrier can be explained in terms of spin-catalysis theory.1,2 Let us consider a reaction of cis-trans isomerization of substituted ethylenes. According to a suggestion of Eyring et al.,3 this reaction could pass through the singlet (path b in Figure 1) or the triplet (path a in Figure 1) electronic states when ethylenetype molecules isomerize from the cis to the trans form. It is well-known that this reaction is catalyzed by paramagnetic molecules such as O2, NO, NO2, S2, and Se2.3-7 The mechanism of this catalysis was treated by Eyring et al.8 from the viewpoint that a paramagnetic substance catalyzes isomerization Via the transition from the singlet (S0) to the triplet (T1) electronic state (path a in Figure 1) by providing “a nonhomogeneous magnetic field which will act differently on the two magnetic dipoles arising from spin of two electrons in the double bond”. However, the probability of the triplet path in the absence of a catalyst is small because of the small spin-orbit coupling (SOC) between the corresponding singlet S0 and triplet T1 states.3,9,10 It has been shown6,7,11,12 that the singlet mechanism is the only important thermal mechanism for the cistrans isomerization of pure simple olefins in the gas phase in the absence of a catalyst. However, one has to suspect the triplet mechanism as responsible for the lowering of activation energy of these reactions occurring in solution and for the catalytic and photosensitized cis-trans isomerization.3,12,13 According to Eyring et al.,3 the triplet reaction path for catalytic isomerization was supported by a magnetic interaction. This has, however, proved doubtful because the action of the nonhomogeneous magnetic field of the catalysts on the spins of two electrons in the double bond (the spin-spin interaction) is even weaker than the already mentioned small spin-orbit coupling. A qualitatively different explanation for the catalytic activity of paramagnetic substances has been put forward by McConnell.13 He suggested that a catalyst in an electronic state † Permanent address: Department of Chemistry, Cherkassy Engineering and Technological Institute, 257006, Cherkassy, Ukraine. X Abstract published in AdVance ACS Abstracts, April 15, 1996.
S0022-3654(95)03534-9 CCC: $12.00
Figure 1. Possible mechanisms for the cis-trans isomerization reaction suggested by Eyring and Harman:8 (a) reaction path Via triplet potential energy surface with S-T intersystem crossing (“triplet path”); (b) reaction path Via singlet potential energy surface without S-T intersystem crossing (“singlet path”).
with multiplicity different from one (doublet, triplet, etc.) interacts with the singlet S0 and triplet T1 states of the isomer and that such an interaction forms new states of the complex, e.g. doublet states 2D and 2D′ together with a quartet 4Q state, if the catalyst is in a doublet state (Figure 2). Since both states 2D and 2D′ have the same multiplicity, an avoided crossing takes place which permits the nonadiabatic path, i.e. the S-T transition inside the isomer moiety. The same arguments are applicable for the explanation for the catalytic activity of a catalyst in a triplet state. No corresponding mechanism exists for catalysis of isomerization by substances in singlet states.13 The intrinsic ethylene “cis-trans” isomerization, with the ethylene molecule twisting around the CdC double bond, is the simplest model for cis-trans isomerization reactions of substituted ethylenes. This reaction is analogous to the thermal isomerization of 1,2-dideuterioethylene which occurs in the gas phase.3,4,6 It has been shown that the isomerization of this © 1996 American Chemical Society
Cis-Trans Isomerization of Substituted Ethylenes
Figure 2. Mechanism of catalysis of the cis-trans isomerization by paramagnetic substances suggested by McConnell.13
molecule is effectively catalyzed by the ground-state triplet molecules O2, S2, and Se2. Also nitric oxide has a very pronounced effect on the isomerizations of trans-dideuterioethylene6 and 2-butene.7 The present work has been carried out in order to investigate the catalytic effects of the paramagnetic oxygen and nitric oxide molecules in the model reaction of cis-trans isomerization of substituted ethylenes. In terms of the recently proposed classification of spin-catalysis phenomena1,2 the catalytic activity of these molecules serves as an example of homogeneous paramagnetic spin-catalysis of the second type. This type of catalysis has been denoted paramagnetic spin-catalysis because it is produced by paramagnetic substances. The nature of this catalysis has no relation to the magnetic field perturbations produced by catalysts,14 but is determined by intermolecular exchange interactions (electronic correlation effects) and by charge-transfer interactions,1,14 as will be demonstrated in the forthcoming. 2. Calculations Ab initio calculations of the potential energies of the intermolecular complexes of the ethylene molecule with oxygen or nitric oxide molecules have been carried out using the complete active space (CAS) configurational interaction (CI) and multiconfigurational self-consistent-field (MCSCF)15,16 approaches. Two different CAS models have been employed for the calculations of the ethylene-O2 complexes. In the CAS-1 model, the double-occupied 1ag, 1b1u, 2ag, 2b1u, 1b2u, and 3ag σ molecular orbitals (MO) of ethylene and the 1σg, 1σu, 2σg, 2σu, and 3σg orbitals of oxygen have been frozen. The occupied 1b3g and 1b3u and unoccupied 1b2g and 2b2u MOs of ethylene (the 1b3u and 1b2g MOs of ethylene are ordinarily called the π z xy and the π* molecular orbitals) and 1πzu, 1πxy u , 1πg, 1πg , and 3σu MOs of oxygen have been included in this active space. In the CAS-2 model, the 3σg orbital of oxygen is additionally included in the active space. The calculations of ethylene-nitric oxide complexes employ a third CAS model (CAS-3). The six, respectively four, lowlying σ orbitals of ethylene and nitric oxide were frozen. The active space included the occupied 1b3g and 1b3u and the unoccupied 1b2g, 2b2u, and 4ag MOs of ethylene and the doubly
J. Phys. Chem., Vol. 100, No. 20, 1996 8309
Figure 3. Geometrical model for the ethylene-oxygen (a, b) and ethylene-nitric oxide (c-f) molecular complexes calculated in the present work. The intermolecular distances R specified for the ethylene-O2 in Geo-1 (a) and Geo-2 (b) geometries refer to the distances between the C2 atom of ethylene and the O1 atom of molecular oxygen. In cases of the ethylene-nitric oxide complexes R refers to the distances between the C2 atom of ethylene and the N (c, d) or O (e, f) atoms of NO.
occupied πx, σz, and πy, the singly occupied π* y, and the unoccupied π*x MOs of nitric oxide. The minimal STO-6G17 and valence triple-ζ (TZV)18 basis sets have been used for the calculations. The geometry optimizations of the molecular complexes have been made with the restrictions of optimizing parameters in order to fix the positions of the O2 or NO molecules relative to the ethylene molecule at the two main points on the reaction path: (a) the starting point P which corresponds to the interaction of the ethylene molecule being in planar geometry of the groundstate S0 with the oxygen or nitric oxide molecules in the 2 corresponding 3Σg or Π ground states; (b) the transition-state point TS which corresponds to the interaction of the ethylene molecule being in twisted geometry of the transition state (biradical state) with the oxygen or nitric oxide molecules in the corresponding ground state. The geometry optimizations have been carried out at the restricted open-shell Hartree-Fock (ROHF)19-21 and at the MCSCF levels of theory. The “standard method”22-24 of the GAMESS program25 has been used for the geometry optimization. The ROHF optimized geometries of the molecular complexes have been used for the CAS CI calculations. At point P the geometry optimization was performed with triplet or doublet multiplicity corresponding to singlet ethylene in the ground state S0 with the triplet O2 or with the doublet NO molecules in their ground states. For the CAS CI calculations at the transition point TS the geometries of these complexes were optimized at the ROHF level with the maximum possible multiplicities (quintet or quartet) of the complexes composed from the twisted triplet ethylene molecule and the O2 or NO molecules in their ground states. Calculations have been carried out for the two different types of ethylene-O2 molecular complex geometries (Figure 3a,b) and for the four possible structures of the ethylene-nitric oxide complexes (Figure 3c-f). These types of geometrical structures could be subdivided into two main groups which differ from
8310 J. Phys. Chem., Vol. 100, No. 20, 1996
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TABLE 1: CAS CI Energies (Hartrees) of the 3(S0 + 3∑g-) and the 3(T1 + 3∑g-) States of Ethylene-Oxygen Molecular Complexes in Different Geometries (The Intermolecular Distance R (Å) Corresponds to the Distance between the C2 and O1 Atoms of These Molecules (Figure 3)) state 3
geometry RCO configuration
∞ (S0 + 3∑g) 3.8
2.8
3
∞ (T1 + 3∑g) 3.8
2.8
3
∞ (S0 + 3∑g) 3.8
2.8
3
∞ (T1 + 3∑g) 3.8
2.8
energy φ
CAS-1
CAS-2
TZV Basis set 0 -227.667 20 90 -227.583 00 Geo-1 0 -227.666 82 90 -227.584 93 Geo-2 0 -227.666 97 90 -227.585 00 Geo-1 0 -227.662 40 90 -227.582 51 Geo-2 0 -227.662 98 90 -227.58219 0 -227.476 92 90 -227.585 00 Geo-1 0 -227.475 92 90 -227.582 90 Geo-2 0 -227.475 35 90 -227.582 96 Geo-1 0 -227.472 92 90 -227.579 14 Geo-2 0 -227.474 23 90 -227.578 55
-227.675 67 -227.591 45 -227.667 03 -227.585 12 -227.667 18 -227.585 19 -227.662 69 -227.582 78 -227.663 22 -227.582 57 -227.485 39 -227.593 47 -227.476 29 -227.583 10 -227.475 73 -227.583 16 -227.473 39 -227.579 39 -227.474 61 -227.578 93
STO-6G Basis Set 0 -226.966 32 90 -226.862 94 Geo-1 0 -226.975 50 90 -226.869 74 Geo-2 0 -226.972 96 90 -226.871 96 Geo-1 0 -226.970 69 90 -226.874 69 Geo-2 0 -226.971 11 90 -226.871 23 0 -226.776 56 90 -226.863 80 Geo-1 0 -226.832 69 90 -226.861 65 Geo-2 0 -226.790 93 90 -226.870 24 Geo-1 0 -226.788 81 90 -226.825 14 Geo-2 0 -226.789 33 90 -226.868 82
-227.006 11 -226.902 73 -227.025 04 -226.876 33 -227.015 95 -226.872 88 -227.013 90 -226.874 69 -227.013 55 -226.873 39 -226.816 35 -226.903 59 -226.851 65 -226.868 24 -226.826 15 -226.871 24 -226.872 40 -226.872 40 -226.824 50 -226.871 03
each other by the angle between the O-O (N-O) bond of the catalyst and the C-C bond of the ethylene. These two groups are denoted below as Geo-1 (Figure 3a,c,e) and Geo-2 (Figure 3b,d,f). The pyramidalization angles θ1 and θ2 are correspondingly the angles between the C1C2 axis and the H1C1H2 plane and between the C1C2 axis and the H3C2H4 plane. The rotational angle φ is determined as the angle between the plane of the ethylene molecule in the ground state and the plane H1C1H2 which is rotating in our model, projected to the condition of θ1 ) θ2 ) 0. 3. Discussion 3.1. Potential Energy and Basis Set Dependencies. The potential energies of the intermolecular complexes of ethylene with the O2 or NO molecules at the starting point P and at the TS point have been calculated by varying the intermolecular distances R from 2.4 to 4.2 Å at the different geometries of the complexes (Figure 3). The results of these calculations are shown in Table 1 for the ethylene-O2 complexes and in Table 2 for the ethylene-NO(ON) complexes. The results of the geometry optimization at the starting point P show shallow minima for both the ethylene-O2 and the
ethylene-NO complexes. The dissociation energies of these intermolecular complexes are in the range 0.6-1.6 kcal/mol, and the equilibrium distances (Re) vary from 3.58 to 3.66 Å depending on the geometry configuration of the molecular complex. Comparable behavior of the potentials has been obtained for the calculations using both STO-6G and TZV basis sets. The results of the calculation using the STO-6G basis set, employed here for qualitative analysis, are, however, afflicted with enhanced basis set superposition error (BSSE)26-28 and increased sensitivity to the choice of the active space. An accurate determination of the intermolecular equilibria and of the complex dissociation energies would require an account of the full van der Waals interaction, which is beyond the scope of this study. Using the different CAS models, we have investigated the influence of the correlation effects on the main energetic parameters of the cis-trans isomerization reaction. For the TZV basis set calculations the change of the active space by including the 3σg orbital of oxygen (CAS-2) for the ethyleneoxygen complexes gave only slight changes (0.02-0.06 kcal/ mol) of the S0-T1 transition energy of ethylene, the activation energy of the cis-trans isomerization, and the S-T energy gap at the TS point (Table 3). The variations of the values of the activation energy, energy gap, and S0-T1 transition energy calculated using the different CASs are practically independent of the geometry configuration for the ethylene-O2 complexes and depend on the orientation of nitric oxide to ethylene in the ethylene-nitric oxide complexes starting from R less than 3.6 Å. When the oxygen atom of NO is closest to the ethylene, the activation energy and the energy gap dependence are practically the same as for the ethylene-O2 complexes (Table 3), while when the nitrogen atom of NO points to ethylene, the energy gap is steeply increased to 8.0-8.2 and 15.1-15.2 kcal/ mol at the 2.8 and 2.4 Å intermolecular distances, respectively, and the activation energy drops to 36.7-37.8 kcal/mol at R ) 2.4 Å. One should note that 2.4 Å is a quite short intermolecular distance at which one can assume an onset for the chemical reaction between the compounds. In this case one should expect the energy lowering and creation of the C-O or C-N covalent bond. This can be characterized by large occupational numbers of the MOs constructed by mixing of the corresponding atomic orbitals. But the mixing of the MOs of the complexes does not exceed 5% even at the 2.4 Å intermolecular distance for the ethylene-O2 and ethylene-ON complexes. This underlines the fact that the intermolecular interaction in these complexes does not result in a chemical product. However, the CAS CI energy of the ethylene-NO complexes at the transition point TS is 11 kcal/mol lower than that for the ethylene-O2 and ethylene-ON complexes at the intermolecular distance R ) 2.4 Å. Also, the S-T energy gap at the TS point for this kind of ethylene-nitric oxide complex is more than 2 times larger in comparison with the ethylene-O2 and ethylene-ON complexes. This proves that this geometry configuration creates the possibility of “realizing” a free valence29 for NO orswhich is practically the same in this casesan unpaired electron localized on the nitrogen atom. 3.2. Geometry Optimization. The results discussed above show that the effectiveness of intermolecular interactions in ethylene-O2 or -NO molecular complexes depends strongly on the geometrical configuration. The geometry optimizations of these complexes have been carried out with freezing of the intermolecular distance and angles C1C2O1 and C2O1O2 for the ethylene-O2 complexes and the intermolecular distance and angles C1C2N(O) and C2NO(ON) for the ethylene-nitric oxide
Cis-Trans Isomerization of Substituted Ethylenes
J. Phys. Chem., Vol. 100, No. 20, 1996 8311
TABLE 2: CAS CI Energies (Hartree) of the 2(S0 + 2Π) and the 2(T1 + 2Π) States of Ethylene-Nitric Oxide Molecular Complexes in Different Geometries (The Intermolecular Distance R Is Given in Angstroms) ethylene-NO complex state
R
φ
Geo-1
Geo-2
ethylene-ON complex Geo-1
Geo-2
TZV Basis Set
2(S 0 2(T 1 2 (S0 2(T 1 2(S 0 2 (T1 2(S 0 2 (T1 2(S 0 2(T 1 2 (S0 2(T 1
+ 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π)
∞
0
∞
90
3.8
0
3.8
90
2.4
0
2.4
90
2(S 0 2 (T1 2 (S0 2 (T1 2(S 0 2(T 1 2(S 0 2 (T1 2(S 0 2(T 1 2(S 0 2(T 1
+ 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π) + 2Π)
∞
0
∞
90
3.8
0
3.8
90
2.4
0
2.4
90
-207.258 25 -207.067 63 -207.172 79 -207.170 50 -207.239 57 -207.064 19 -207.181 11 -207.156 86
-207.300 86 -207.110 58 -207.216 64 -207.218 65 -207.259 18 -207.258 74 -207.068 83 -207.067 84 -207.172 98 -207.174 13 -207.170 68 -207.172 08 -207.241 96 -207.241 07 -207.072 47 -207.048 27 -207.171 78 -207.164 04 -207.157 62 -207.155 74
-207.259 34 -207.068 43 -207.174 00 -207.171 88 -207.242 02 -207.053 58 -207.167 00 -207.154 68
STO-6G Basis Set
-206.720 83 -206.531 07 -206.588 16 -206.542 44 -206.703 15 -206.530 00 -206.605 58 -206.559 72
complexes in order to save the relative disposition of the molecules inside the complexes (Figure 3). All intramolecular distances and angles of the molecules within these complexes have been optimized. Geometry optimizations have also been carried out separately for the ethylene, O2, and NO molecules without any restrictions for the optimizing parameters. The geometry optimization of ethylene (Table 4) in the ground S0 state has been done at the restricted Hartree-Fock (RHF) level of theory. As seen in Table 4, the results for the STO-6G and TZV calculations are reasonably close to each other and to the experimental values.30 The geometry optimization of ethylene in the triplet T1 state has been carried out at the ROHF and MCSCF levels of theory. For comparison we list in Table 4 also the results of the geometry optimization by the MCSCF calculations in various basis sets of the triplet ethylene from ref 10. A general good concordance between these results and the present results can be noted. In the optimized geometry the ethylene is found to be twisted at φ ) 90°. The ROHF and MCSCF geometry optimizations of the T1 state of ethylene (Table 4), with the TZV basis set, results in pyramidalization angles of less then 0.1°. The data of Table 4 show that the value of the pyramidalization angle decreases drastically with the increase of the correlating active space and the size of the basis set. Obviously, the twisted ethylene in the excited T1 state should be more reactive compared with ethylene in the ground state because of the two unpaired electrons localized on the degenerate (or near-degenerate for the partially twisted ethylene) π and π* MO orbitals which are localized on the different carbon atoms of ethylene. The interaction of two unpaired electrons of the oxygen molecule (or the unpaired electron of nitric oxide) with the unpaired electrons on the carbon atoms of ethylene should mostly be due to paramagnetic exchange interactions. One can expect the creation of the chemical C-N bond in the interaction between ethylene and NO through the nitrogen atom because of the localization of the unpaired electron on this atom. The geometry optimization of molecular complexes (Table 5) of singlet planar ethylene in the ground state (N′ state in
-206.780 15 -206.590 39 -206.676 77 -206.677 63 -206.721 11 -206.721 02 -206.531 10 -206.531 16 -206.588 28 -206.588 38 -206.542 64 -206.542 65 -206.709 34 -206.706 11 -206.531 35 -206.519 97 -206.607 36 -206.586 44 -206.566 46 -206.542 37
-206.721 17 -206.531 16 -206.588 42 -206.542 67 -206.711 00 -206.523 61 -206.607 36 -206.566 46
terms of ref 12) with the O2 or NO molecules at the intermolecular distance R ) 3.8 Å gave values of the bond distances and angles which are practically equal to the calculated parameters of the separated molecules. This reflects the weakness of the intermolecular interaction at such a long intermolecular distance. Even an approach of ethylene in the S0 state connected to the oxygen (or nitric oxide) molecule up to the intermolecular distance R ) 2.4 Å results only in small changes (less than 0.0005 Å) of the intramolecular distances and shows a slight pyramidalization of ethylene (less than 1.1°). The geometry optimization of the molecular complex of the twisted ethylene in the T1 state (or T state in terms of ref 12) with the O2 or NO molecules at the intermolecular distance R ) 3.8 Å also gave practically the same results for the bond distances and the HCH angles as for the separated molecules. The main differences in these results are the values of the pyramidalization angles θ1 and θ2 and the rotational angle φ; see Table 5. The small values of the pyramidalization angle (up to 4-6° for the ethylene-O2 and ethylene-ON complexes and up to 14-16° for the ethylene-NO complexes) should be due to intermolecular exchange interaction. The chemical process of creation of the C-N bond for the ethylene-NO complexes leads to a change of geometry of the interacting CH2 radical group of twisted ethylene to one which is close to a geometry of the CH3 group in C2H6. The rotational angle φ is found to be less than 90° for the molecular complexes. This indicates a change of equilibrium geometry of triplet ethylene due to the interaction with the catalyst. Obtained values of the rotational angles in the range from 79° to 89° are close to the expected values to those corresponding to the maxima of the lowest potential energy curve; see Figure 2. Taking into account the pyramidalization of the ethylene and these values for the rotational angle, one notes that a many-dimensional avoided crossing has been created by the geometry optimization. A slight increase of the C-C bond (by 0.001-0.002 Å) and a small shortening of the C-H bonds (by 0.0005-0.001 Å) are also found. The calculated values for the HCH angles at the intermolecular distance R ) 3.8 Å are slightly smaller.
8312 J. Phys. Chem., Vol. 100, No. 20, 1996
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TABLE 3: Energy of the S0-T1 Transition in Ethylene (kcal/mol), the S-T Energy Gap at the TS Point (kcal/mol), and the Activation Energy (kcal/mol) of the Cis-Trans Isomerization Reaction of Ethylene in Catalyzed Complexes with the O2 and NO Molecules for the Different Geometries of these Molecular Complexes (The Intermolecular Distance R (Å) Corresponds to the Distance between the O2 or NO Molecules and the C2 Carbon Atom of Ethylene) type of molecular complex ethylene ethylene-O2
geometry active configuration space
Geo-1
Geo-2
ethylene-NO
Geo-1 Geo-2
ethylene-ON
Geo-1 Geo-2
ethylene ethylene-O2 ethylene-NO
ethylene-ON
R
activation S0-T1 energy energy energy gap
TZV Basis Set ∞ CAS-1 3.8 2.8 CAS-2 3.8 2.8 CAS-1 3.8 2.8 2.4 CAS-2 3.8 2.8 2.4 CAS-3 3.8 2.8 2.4 CAS-3 3.8 2.8 2.4 CAS-3 3.8 2.8 2.4 CAS-3 3.8 2.8 2.4
STO-6G Basis Set ∞ Geo-2 CAS-1 3.8 2.8 2.4 Geo-1 CAS-3 2.8 2.4 Geo-2 CAS-3 2.8 2.4 Geo-1 CAS-3 2.8 2.4 Geo-2 CAS-3 2.8 2.4
52.85 51.39 50.13 51.40 50.15 51.43 50.70 54.99 51.45 50.61 54.52 53.63 47.16 36.68 54.09 48.33 37.76 53.09 51.78 48.34 53.56 52.20 47.08
119.40 1.26 119.79 1.27 118.90 2.11 119.69 1.27 118.79 2.13 120.24 1.28 118.44 2.28 118.44 6.91 120.14 1.28 118.35 2.28 118.35 6.92 119.61 3.48 117.87 8.19 110.05 15.22 119.44 3.63 113.92 8.03 106.35 15.16 119.79 4.51 120.92 4.93 120.99 6.62 119.79 4.45 120.35 5.10 118.25 8.24
64.87 63.38 62.67 59.87 80.39 61.22 81.78 63.99 81.52 75.09 81.46 65.03
119.07 114.22 114.06 86.86 116.66 108.65 117.71 111.69 118.70 116.81 119.17 117.59
0.54 1.07 1.51 5.31 29.93 28.78 28.64 25.67 28.11 27.65 27.41 25.67
3.3. Catalysis of the Cis-Trans Isomerization Reaction. Let us consider the main macroeffects of the intermolecular interaction of ethylene with the paramagnetic O2 and NO molecules. The calculated values of the activation energy, the energy of the S0-T1 transition in ethylene, and the S-T energy gap at the transition point TS are shown in Table 3. We can see that a catalytic effect of this reaction is the lowering of the activation barrier at this point. The energy separation of the singlet and the triplet states of ethylene (S-T energy gap) at the TS point is very small in the absence of the catalyst and grows rapidly with the decrease of the intermolecular distance R. The triplet state of ethylene has the lower potential energy at the transition point TS. This state is stabilized by the intermolecular exchange interaction with the catalyst, which also results in the avoided crossing (Figure 2) between the S0 and T1 states of ethylene. The origin of the near-degeneration of the S0 and T1 states of pure ethylene at the TS point (N′ state, respectively, T state) is a degeneracy of the π and π* orbitals of the twisted ethylene, which results in two singly occupied degenerate orbitals (i.e. biradical).12 The calculated potential energy difference between these states at the TS point is very small (about 1.3 kcal/mol; see Table 3), and the triplet state is found below the singlet state. Previous ab initio results by Buenker and Peyerimhoff31
(1.5 kcal/mol) and by Kollman and Staemmler32 (about 1 kcal/ mol) show that the singlet state is the lowest one but that the S-T energy gap is still small. A singlet lowest state is a violation of Hund’s rules which has been explained qualitatively by the “dynamic spin polarization”.32 Disagreement in the order of the triplet and singlet states in twisted ethylene indicates a problem which could be related with the performance of CI calculations. We agree with Kollman and Kohn33 that inclusion of electron correlation could lower the energy of the singlet state more than that of the corresponding triplet due to the fact that correlation of electrons with parallel spins is already included in the open-shell HartreeFock scheme without CI. It gives a more accurate description of the high-spin state compared to the corresponding low-spin state, which tends to diminish the singlet-triplet energy gap or even invert the order of the energy levels. A good example of this is given in ref 34, in which a minimal two-electron CI gives an inverted order of the N′ and T states, while this order is reversed back by a 12-electron CI calculation. However, this effect is diminished in the present work since both the singlet and the triplet states of ethylene have been calculated in molecular complexes with paramagnetic open-shell molecules taking into account this bias of CI against triplet states, although the results of our calculations of ethylene itself also show a correspondence to Hund’s rules. Lets us consider now the wave functions of the low-lying states of the molecular complexes. The analysis of the coefficients of the CI expansion, energies, and optimized geometries shows that the origin of the intermolecular interactions in the ethylene-NO complexes (case B) is completely different from those for the ethylene-O2 and ethylene-ON complexes (case A). So, we shall consider these two main types of intermolecular interactions in the ethylene-nitric oxide complexes separately. The principal structure of the CI expansions in case A is quite similar for both ethylene-O2 and ethylene-ON complexes and for all geometry configurations of these complexes (the CI coefficients are similar for the STO6G and TZV basis sets). The two lowest states of the ethyleneO2 complexes in the TS point are mainly constituted by the singlet N′ state of ethylene and the triplet ground state of oxygen or by the triplet T state of ethylene with the triplet ground state of oxygen, respectively. These complex states have been calculated as triplet states. Both of them are constructed by linear combinations of the same determinants: z z x xy z z x xy z z xy c1|πxy g πgpC1pC2| + c2|πg πgpC1pC2| + c3|πg πgpC1pC2| + z z x c4|πxy g πgpC1pC2| (1)
z z xy in which πxy g and πg are the oxygen MOs and pC1 and pC2 are z xy* degenerate former π and π MOs of twisted ethylene. The coefficients c1 ) 0.975, c2 0.497, c3 ) -0.006, and c4 ) -0.472 of the lowest state at the intermolecular distance R ) 3.8 Å show that the intermolecular paramagnetic exchange interaction stabilizes the triplet state of ethylene with a large admixture of the singlet state. The values of the coefficients of the CI expansion of the second state at R ) 3.8 Å are the following: c1 ) -0.332, c2 ) 0.675, c3 ) 0.343, and c4 ) 0.686. This state is constructed by the intermolecular paramagnetic exchange interaction admixing of the triplet state of ethylene to the singlet. The mixing of the triplet and singlet states could be denoted as “spin polarization”, although the mixing is only the result of paramagnetic exchange interactions between the catalyst and the isomer, which here is taken into
Cis-Trans Isomerization of Substituted Ethylenes
J. Phys. Chem., Vol. 100, No. 20, 1996 8313
TABLE 4: Results of the Geometry Optimization of Ethylene (Interatomic Distances Are Given in Angstroms, Angles in Degrees)a method
φ
C1C2
C1H1
C2H3
H3C2H4
θ1
θ2
ethylene, S0, expt, ref 30 ethylene, STO-6G, RHF, S0 state ethylene, TZV, RHF, S0 state ethylene, STO-6G, ROHF, T1 state ethylene, TZV, ROHF, T1 state ethylene, STO-6G, MCSCF, CAS44, T1 state ethylene, TZV, MCSCF, CAS44, T1 state ethylene, SZ, MCSCF, CAS22, T1 state, ref 10 ethylene, DZ, MCSCF, CAS22, T1 state, ref 10 ethylene, TZP, MCSCF, CAS22, T1 state ref 10 ethylene, TZP, MCSCF CAS44, T1 state, ref 10
0 0 0 90 90 90 90 90 90 90 90
1.339 1.305 1.319 1.481 1.468 1.516 1.492 1.569 1.479 1.467 1.490
1.086 1.078 1.073 1.078 1.074 1.079 1.073 1.186 1.076 1.087 1.086
1.086 1.078 1.073 1.078 1.074 1.079 1.073 1.185 1.076 1.086 1.085
117.6 115.7 116.2 117.6 117.4 116.1 117.8 115.4 117.6 117.3 117.9
0.0 0.0 0.0 0.0
