J. Phys. Chem. 1993,97, 7888-7893
7888
A Theoretical Study of the Singlet-Triplet Energy Gap Dependence upon Rotation and Pyramidalization for 1,2-Dihydroxyethylene. A Simple Model To Study the Enediol Moiety in Rubisco’s Substrate J. Andrb,’ V. S. Safont, and J. Queralt Departament de Cihcies Experimentals, Universitat Jaume I, Box 242, 12080 Castellb, Spain
0. Tapia’ Department of Physical Chemistry, Uppsala University, Box 532, S - 75121 Uppsala. Sweden Received: August 25, I992
A quantum chemical study is reported of the variation of the energy gap between the singlet ground (S)and first triplet (T) states for 1,2-dihydroxyethylene as a function of the rotational angle around the central double bond (4) and the pyramidalization angle of one CHOH group (a). R H F and U H F levels of theory are used; the ab initio calculations are made with three types of basis sets: 3-21G*, 4-31G, and 6-31G*. Correlation effects are estimated with different standard procedures (CISD and MP2) including multiconfiguration CASSCF. For the sake of completeness, potential energy surfaces for the singlet and triplet states are reported. AM1 calculations are also presented. The potentiality of different approaches to describe the gap is examined. The S-T energy gap is most sensitive toward 9. For a twisted system, this gap may be appreciably smaller than the one found for a planar conformer. Correlated and uncorrelated wave functions show similar trends in this respect. This S-T energy gap lowering can be used to help understand the electronic structure in the enediol moiety of the Rubisco substrate: D-ribulose 1,5-bisphosphate. There, at the active site, the conformation is cis out of plane. The carboxylationfoxygenationbifunctionality of Rubisco can then be given a relatively simple explanation.
Introduction Ethylene derivatives are still attracting the attention of theoreticianswho strive to understand their molecular properties both in the ground singlet (S)and first excited triplet (T) states.’ Thus, the cis-trans isomerization in 1,Zsubstituted derivatives has been extensively analyzed.2 The study of 1,2-dihydroxyethylene,in particular, has been stimulated by its presence as an intermediate species in some organic reaction mechanism.3 As a fragment, this molecule also appears in the enolized form of D-ribulose 1,5-bisphosphate, which is the substrate in the carboxylation and oxygenation reactionscatalyzed by Rubisco.” The importance of the enediol moiety in enzymatic processes goes beyond this particular case, as the triosephosphateisomerase (TIM) system sh0ws.89~ Although ab initio calculationsof this model enediol have been carried out using different basis sets,1”13 excited-stateproperties involvingthe first tripletare not yet fully understood. For example, Lin and Laidler14 focused on the cis-trans isomerization mechanism, for which two alternative pathways were proposed: (i) one involves an interconversion between triplet and singlet states and (ii) the other involves the singlet state crossing a barrier corresponding to a rotational angle of approximately 90°. In the present case the interest is centered upon the change of the singlet-triplet (S-T) energy gap with geometric variables. The study is based on the hypothesis that it is the lowering in the substrate singlet-triplet energy gap down to values accessible to thermal excitation which is responsible for the intersystem crossing in the reactive superm~lecule.~~J~ As the substrate in the active site has a nonplanar cis conformation, the range of interest for the rotational angle is between 0” and 60°. No attempt is made at describing a rotational barrier for this model system; the results around 90” are reported for the sake of completeness. The S-T energy gap is studied as a function of the angles 4 and a describing rotation around the C-C bond and pyramidalization of one C-center in 1,2-dihydroxyethylene, respectively. Ab initio molecular orbital theory is used with standard schemes: 0022-3654/93/2091-7888$04.00/0
restricted Hartree-Fock (RHF) for the singlet and unrestricted Hartree-Fock (UHF)” for the triplet. Three different basis sets are used: 3-21G*, 4-31G, and 6-31G*. The effect of electronic correlation is assessed also by using several procedures: a configuration interaction method with single and double excitations (CISD),18 MP2, and a multiconfiguration model. The AM1 semiempiricalmodel is employed to gauge its ability to reproduce the essential feature of the S-T gap change; this semiempirical procedure could be applied, for instance, to the study of more complex systems modeling the essential structural components in the active site of Rubisco.
Mechanism, Method, and Model (i) Mechanism. In Rubisco, once the substance D-ribulose 1,5-bisphosphateis enolized, two reactions may take place at the same C2-carbon center, namely, carboxylation (carbon dioxide fixation) and oxygenation.6 This very fact represents one of the mysteries surrounding the functioning of this enzyme. In the protein there is no transition metal to activate oxygen into a spin singlet. The problem is, therefore, the understanding of why two reactions involving molecules in different electronic spin states can take place with the same location in the substrate, while the products are all in a singlet spin state. One of the objectives of molecular genetic engineering experiments is to modify the catalytic action of Rubisco in view of improving efficiency in the natural fixing of C02 at the expense of the oxygenation reaction. In this respect, numerous experimental studies on the role played by the amino acid residues of which the activecenter is composedhave been completed in recent years7 but none of them has been successful. One of the aims in this and related works is to examine the electronicproperties of the enediol moiety in its first singlet and triplet states. In the real system the substratepresents a geometry around the putative double bond of out of plane cis. If one compares this with a substrate twisted in that way but in vacuum, 0 1993 American Chemical Society
Singlet-Triplet Energy Gap in 1,2-Dihydroxyethylene
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 7889
6
H7
I/
-t Figure 1. The numbering of the atoms of 1,2-dihydroxyethyleneand the rotation (4) and pyramidalization (a) angles.
one may then describe the situationas a molecule evolving under stressed conditions. (ii) Method. Analytical gradientsof the SCF HF energy with respect to the internal geometric parameters were calculated, and the optimallyconditioned minimization technique19was used to determine the points on the surfaces. The optimization was terminated after the overall average gradient length had been reduced to less than 5 X 10-4 mdyne. The programs MONSTERGAUSS20 and GAUSSIAN8821have been used with 4-3 1G,22 3-2 1G*,23 and 6-3 1G*24basis sets. The CISD calculations were made on the previously optimized structures at the MP2/6-3 1G* level.16 Singlet and triplet states were calculated by using restricted and unrestricted HF methods, respectively. The AM 1 semiempirical calculations were done with GAUSSIAN88. The geometries were optimized with the help of the Bemy analyticalgradientoptimization routinesF6 The requested convergence on the density matrix was l e 9 au, the threshold value of maximum displacement was 0.0018 A, and that of maximum force was 0.00045 hartree/bohr. For the triplet state, very low levels of spin contamination were found; typical values for spin multiplicity S(S + 1) at different points on the hypersurfaces range between 2.0001 and 2.0204. The CASSCF2' study was carried out with an active space of two orbitals (T and T * ) and two electrons for 1,2-dihydroxyethylene, using thegeometryobtained at the MP2/6-3 lG* level.16 Ethylene is examined to check the quality of the results obtained for the enediol. (iii) Model. The dihedral angles 4 and a are used to characterizehypersurfacesfor the rotation and pyramidalization processes related to the ethylenic fragment. They are depicted in Figure 1. The 4 angle was changed stepwise (10') from ' 0 to 180' and the a angle from -60' to +60°. On each one of the 8 surfaces about 247 points were examined. In every point all degrees of freedom, except those allowing the molecule to hold up the two planes showed in Figure 1, between which one can find 4 and a, were submitted to optimization. The conformation of 1,2-dihydroxyethylene is always ss, with the hydrogen atoms of the OH groups pointing away from the double bond. ResulQ
A. Energetics. ( i ) Ab Initio Hartree-Fock Level. In Table I is presented a selection of energy entries calculated for 1,2dihydroxyethylenein its singlet and triplet electronic states as a function of the rotational (4) and pyramidalization (a) angles. Results obtained with the three basis sets and AM 1 are reported. In general the energy contours (not reported) are fairly independent on the basis set used for calculating them. Just as it happens with ethylene28 and related compounds,29 rotation around the C-C bond destabilizes the singlet state and stabilizes the triplet one. Pyramidalizationhas a number of subtle effects on the shape of the hypersurface. This can more easily
TABLE I: Relative Energies (in kcal/mol) of Relevant Points of the Singlet (S) and Triplet (T)State Energy Surfaces for Various Angles of Rotation around the Double Bond (+) and Pyramidalization (a) of 1,2-Dihydroxyethylene (both in deg). The Results of Four Different Methods of Calculation Are Compared: three ab initio Methods with tbe 3-21G* (I), 4-31G (11), and 6-31C* (111) Basis Sets and One AM1 Semiempirical Method (IV). Total Energies for the Reference Structure (+ = 180°, d = O", Singlet State) Are I, -226.465 594; 11, -227.405 791; In, -227.729 647; and IV, -0.120 385 au T
S
&/a o/o
I
2.76 0/*30 11.64 SO/-20 35.94 50/0 37.40 50/20 44.23 60/-20 49.08 60/0 51.78 60/20 58.72 90/0 106.90 90/30 96.76 90/-30 95.15 90/-20 99.67 130/-60 60.31 130/0 36.02 130/60 44.19 180/0 0.00 180/f30 8.68
I1 2.38 11.55 35.26 36.56 43.49 48.33 50.88 57.92 105.05 94.01 94.57 98.83 62.26 35.38 45.21 0.00 8.98
111 0.30 8.92 32.41 34.72 42.09 45.40 49.05 56.57 102.88 90.18 89.87 95.42 59.96 33.96 40.53 0.00 8.66
IV
I
I1
I11
IV
1.85 9.74 20.25 20.78 20.25 27.42 28.79 35.21 60.54 56.81 54.49 57.13 53.82 20.56 35.90 0.00 7.66
61.92 59.01 50.49 50.51 49.05 47.58 47.53 46.58 42.68 43.95 42.64 42.27 52.14 48.34 57.37 57.48 54.35
60.56 57.79 48.14 47.87 46.55 44.92 44.70 43.98 39.87 41.50 39.89 39.45 50.79 45.76 56.41 54.90 52.19
59.42 55.37 46.67 46.91 45.04 43.68 43.87 42.61 39.47 38.27 38.97 38.81 49.64 45.85 54.38 55.56 51.71
31.28 32.56 27.81 26.97 27.45 26.59 25.77 26.48 23.73 26.83 25.64 24.11 40.28 25.98 42.78 29.77 30.80
be seen in a three-dimensionalplot like the one shown in Figure 2 parts a and b. Here, the 6-3 1G* results are displayed. As expected, pyramidalization starting from either the cis or the trans conformer requires several kcal/mol. As the system is taken away from planar conformations, it becomes easier to pyramidalize the C-center. In particular, note that at around 4 = 50' the energy is lowered when 8 is about 20'. The important result is then that flexibility at the C-center is increased as the system is torsioned. It is worth noting that, although the difference in the value of the relative energies is important, all basis set results predict an energy crossing between the singlet and triplet states; the value of the rotational angle for which this fact m u r s is roughly the same, about 60'. Another crossing occurs near 4 = 120'. This feature can be easily seen in Figure 3. There, the geometriesare schematically displayed to help visualization. As it is well-known, at the HF-SCF level of theory, the region around 90' is not correctly represented.l2 Although in the present context this particular region is not of concern, it is important to assess correlation effects on the behavior of the S-T gap. (ii) Ab Initio HF Plus Correlation. MP2 and CISD calculations have been carried out for selected points, without taking into account the effect of pyramidalization. The results are listed in Table 11. For the MP2 and CISD representations, the crossing between the singlet and triplet states is produced with the same 4 values. This angle is larger than the one found at the HF level of theory. The shift is basically due to the energy of the triplet state, which is higher than the one found with the SCF method. Comparing the S-T gap found for the planar cis conformer with that in the region of interest around 60°, we find that the former is significantly smaller. This is an important outcome of these correlation calculations,i.e., one can get an energy difference of about 20 K cal/mol that is sensibly smaller than the one corresponding to planar conformers. (iii) CASSCFResults. A further check of correlationeffects on the S-T gap can be obtained with the use of a multiconfiguration reference wave function. The results for the singlet and triplet states obtained with the CASSCF (2,2) method are listed
And& et al.
7890 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993
TABLE Ik Relative Ene es (in kcal/mol) of Selected Points of tbe Singlet and let (Triplet Values in Parentbeses) States of 1,2-D%ydroxyetbylene as a Function of the Rotational Angle (4). In All Cases, tbe Value for tbe PyramidalizationAngle (a) is O.Oo. "be Results Obtained witb tbe Tbree Calculation Methods Are Presented. Total Energies for the Point 4 = 180.0°, d = O.Oo, Singlet State, are MP2/631C* = -228.352 372, CISD = -228.365 726, and CASSCF(2,Z) -227.755 359 au I$ (deg) HF/6-31GS MP2/6-31G* CISD CASSCF(2,2)
#
0
30 60 70 80 90 180
0.3 (59.42) 12.37 (53.78) 49.05 (43.87) 65.39 (41.52) 83.45 (40.02) 102.88 (39.47) 0 (55.56)
0 (82.24) 10.99 (75.63) 41.76 (64.71) 55.44 (63.76) 70.29 (60.74) 85.89 (60.23) 0.01 (78.99)
1.74 (79.10) 11.10 (72.68) 41.38 (62.00) 54.8 1 (59.58) 69.33 (58.07) 84.50 (57.54) 0 (75.77)
2.27 (82.97) 12.24 (76.97) 42.49 (66.51) 53.92 (64.02) 62.7 1 (62.45) 65.37 (61.85) 0 (78.98)
4
6
.
1
, 0
TABLE IIk Relative Ewr es (in kcal/mol) of Selected Points of tbe S i e t and plet (Triplet Values in Parentbeses) States of Etbylene as a Function of tbe Rotatio~lAngle (4). In All Cases, tbe Value for tbe Pyramidalhation Angle (a) is O.Oo. Tbe Results Obtained witb tbe Tbree Calculation Methods Are Presented, Total Energies for tbe Point 4 = 180.0°, d = O.Oo, Singlet State, are: HF/631G* = -78.031718, MP2/631G* = 78.294286, CISD = -78.314139, and CASSCF(2,2) = -78.060006 au d (deg) HF/6-31G* MP2/6-31G* CISD CASSCF(2.2) 0
LOP 30 60 70 80 90
Figure 2. Three-dimensionalrepresentationsof the energy hypersurface for rotation around the double bond in and the pyramidalizationof 1,2dihydroxyethylene(a) in its singlet state and (b) in its triplet state. The hypersurface arising from the 6-31G* basis set for the ab initio method of calculation is given. The topology of the hypersurfaces corresponding tothe4-31Gand3-21G* basissetsand theAM1 methodis thesamethat of the 4-31G one.
in Table 11. In so far as this energy gap is concerned, the results are comparable with those obtained previously at an MP2 and CISD level of theory. At 60°, the gap lowers by about 70% of the initial value, namely, ca. 24 kcal/mol. It can be seen that all the HF-like results overestimate this reduction effect. The point is, however, the significantly lower energy requirement to move from the ground singlet to the first triplet state when the system is out of plane. (iv)AM1 Study. The data is reported in Table I. It is apparent that AM 1 semiempiricalresults for the singlet are quite different from the ab initio outcomes. With respect to ab initio results with and without correlation the deformation energy in the S state is clearly underestimated by AMI. A similar result is obtained for the triplet. The S-T energy gap around SOo is much smaller than those obtained with ab initio techniques. Differences of energy entries between AM1 and ab initio
0 (56.96) 12.98 (53.41) 50.79 (46.07) 68.33 (44.07) 87.99 (42.76) 109.44 (42.30)
0 (85.89) 11.69 (81.59) 45.65 (72.68) 61.28 (70.28) 78.57 (68.70) 97.06 (68.15)
0 (82.10) 10.96 (77.96) 41.83 (69.39) 55.08 (67.08) 68.18 (65.56) 78.32 (65.04)
0 (80.03) 11.55 (76.11) 42.65 (68.17) 54.51 (66.04) 63.66 (64.65) 66.45 (64.18)
calculations have been noted recently in the study of carbonic anhydrase30 when compared with a similar AM1 study.3' B. Structures. Selected bond distances and angles of 1,2dihydroxyethylene in both states are showed in Table IV. Rotation makes the double bond longer in the singlet state (Table IV), this result being independent of the method and the basis set level. On the other hand, the length of this double bond is slightly overestimated when the AM1 semiempirical method is used. Also important to note is that the AM1 values for all the angles are systematically lower than the corresponding ones of the three ab initio calculations, by amounts that are oscillating between 2O and 8 O . In the singlet state, the geometricparameters are well reproduced by AM 1. In triplet state (Table IV) ab initio and AM1 geometric parameters display a rather similar behavior. The C-C bond distance tends to decrease as 4 increases. AM1 slightly underestimate this change. Pyramidalization does not affect the geometric parameters too much. This result is valid for all HF-like calculations. The structural parameters are then well represented with the AM1 parameterized method. C. HOMOS and LUMOS. To get more detailed insight into the electronic reorganization taking place as a function of pyramidalization and rotation, the highest occupied and lowest
Singlet-Triplet Energy Gap in 1,ZDihydroxyethylene
The Journal of Physical Chemistry, Vol. 97, No. 30, I993 7891
Figure 3. Schematic representation of ab initio results for the singlet and triplet surfaces. Regions of minima, maxima, and intercrossing points arc depicted, showing structure and energy gaps obtained by different basis sets.
unoccupied molecular orbitals, HOMOs and LUMOs, are presented diagrammatically in Figure 4. We have selected the 4-31Gresults;similartrendsareobtained with 3-21G* and6-31GS basis sets. In Figure 4a the HOMO in the singlet state for the points 4 = O", a = Oo, and 4 = 180°, a = 0" is depicted. In the ethylene moiety, it corresponds to the a bond associated to the double bond CI-C2and lone pairs of oxygen atoms are in the anti phase. For the point 4 = Oo, a = 90°, the HOMO is associated to a nonbonding C& interaction and a* interactions C1-0~and C d , keep the phase; this and the raise in energy observed in the twisted geometry explain the rotational barrier by means of breaking the double bond. The behavior is archetypal of the ethylenic bond. From the LUMOs, shown in Figure 4b for the singlet state, it can be observed that for the point 8 = O", dJ = 90° the orbital energyis much smaller than that in the other two planar structures.
This, in conjunction with the energy increase which is observed at this point in the HOMOs, makes the HOMO-LUMO energy gap smaller in the perpendicular geometry;this fact is typical for the ethylene fragment and explains the possibility of promoting one electron and obtaining the molecule in the triplet state. As for the influence of pyramidalization in orbital pattern, it is important when the system is rotated out of plane, as overlap between the p-orbitals is increased. For the planar system the opposite effect is produced. This simple description rationalizes the more sophisticated numerical results reported in this paper. D. Comparison with Ethylene: A Multiconfigurational Ap proach. As an accuracy check of the results reported so far, a well-known system, ethylene, is examined. The energies of the singlet and triplet states as a function of rotation angle (6)around the C-C bond for selected values of dJ have been calculated. The results are reported in Table 111. Comparing entries for the different levels of theory we can see that for HF and MP2 the
7892 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993
TABLE I V Selected Geometric Parameters for the Singlet and Triplet States of 1,2-DihydroxyethyleneAt Various Rotational (6)and Pyramidalization (d) Angles. The Results of Four Different Methods of Calculation are Compared: Three ab initio Methods with the 3-21G* (I), 4-31G (11), and 6-31C* (111) Basis Sets and One AM1 Semiempirical Method (IV) bond distances (A) bond angles (deg) 418 Cic2 c103 c204 03C1c2 Cic204 HsO3C1
o/o
I I1 111 IV
0/130
I I1 111 IV
90/0
I I1 111 IV
90/30
I I1 111 IV
90/-30
I I1 111 IV
180/0
I I1 111 IV
180/130 I I1 111
IV
o/o
I I1 111
IV 0/130
I I1 111
IV 90/0
I I1 111
IV 90/30
I I1 111
IV 90/-30
I I1 111
IV 180/0
I I1 111
IV 180/130 I I1 111 IV
1.3093 1.3099 1.3143 1.3476 1.3182 1.3109 1.3233 1.3586 1.3793 1.3783 1.3857 1.4007 1.3850 1.3828 1.3868 1.4002 1.3836 1.3803 1.3851 1.3976 1.3072 1.3077 1.3125 1.3481 1.3158 1.3162 1.3211 1.3588 1.5301 1.5172 1.5250 1.4631 1.5307 1.5171 1.5241 1.4703 1.4480 1.4404 1.4483 1.4394 1.4603 1.4517 1.4609 1.4494 1.4595 1.4507 1.4595 1.4514 1.5225 1.5080 1.5158 1.4651 1.5226 1.5083 1.5155 1.4723
Singlet 1.3868 1.3868 1.3752 1.3750 1.3580 1.3580 1.3779 1.3779 1.3790 1.4036 1.3680 1.3901 1.3501 1.3716 1.3739 1.3832 1.4014 1.4014 1.3906 1.3906 1.3666 1.3659 1.3635 1.3631 1.3739 1.3947 1.3641 1.3808 1.3357 1.3650 1.3615 1.3569 1.3785 1.4005 1.3715 1.3867 1.3442 1.3701 1.3600 1.3585 1.3929 1.3929 1.3839 1.3839 1.3648 1.3647 1.3821 1.3820 1.3870 1.4106 1.3781 1.4001 1.3582 1.3794 1.3783 1.3873 Triplet 1.3817 1.3817 1.3720 1.3719 1.3547 1.3547 1.3497 1.3497 1.3819 1.3845 1.3718 1.3751 1.3547 1.3559 1.3492 1.35 15 1.3919 1.3919 1.3828 1.3827 1.3622 1.3622 1.3559 1.3562 1.3891 1.3984 1.3798 1.3896 1.3596 1.3664 1.3539 1.3592 1.3921 1.3961 1.3825 1.3866 1.3622 1.3648 1.3570 1.3575 1.3862 1.3862 1.377 1 1.3771 1.3576 1.3576 1.3526 1.3526 1.3863 1.3894 1.3772 1.3811 1.3581 1.3598 1.3523 1.3544
122.29 122.64 123.04 120.20 122.39 122.86 123.08 120.04 121.55 121.21 121.97 116.21 118.51 118.51 1 18.64 116.53 126.12 125.26 127.30 1 19.99 120.19 119.87 120.94 1 17.36 120.53 120.29 121.47 1 17.57
122.29 122.66 123.06 120.20 117.48 118.11 118.17 1 16.36 121.56 121.22 122.00 1 16.30 128.38 127.39 128.80 121.24 130.52 129.75 131.98 123.97 120.19 1 19.87 120.94 1 17.42 1 15.46 1 15.36 116.21 1 13.97
111.84 114.14 110.13 106.61 1 12.27 1 14.50 110.41 106.88 111.30 1 13.67 109.62 107.73 1 12.27 1 14.46 110.44 107.57 113.14 1 15.32 111.15 109.1 1 1 1 1.77 114.12 109.96 106.48 1 12.22 114.53 1 10.28 106.84
1 15.22 1 16.46 115.91 1 16.42 1 15.59 1 16.72 1 16.26 1 16.47 1 17.93 1 17.45 1 18.08 116.41 117.69 117.33 1 17.80 1 16.46 1 16.86 116.39 117.28 1 15.67 113.12 1 13.05 1 13.70 113.91 113.10 113.23 114.08 114.14
1 15.22 1 16.46 1 15.89 1 16.42 115.15 1 16.28 1 15.92 1 15.07 117.93 1 17.46 1 18.08 1 16.44 115.51 115.15 115.71 114.32 1 15.26 114.92 1 15.68 114.52 113.12 113.05 1 13.68 1 13.92 113.15 112.82 113.40 112.87
1 12.06 1 14.29 109.86 107.35 112.17 1 14.46 1 10.00 107.48 1 12.03 1 14.47 110.12 107.54 1 12.06 1 14.46 110.1 1 107.39 1 12.27 1 14.78 110.35 107.76 1 12.66 1 15.08 1 10.44 107.25 112.73 115.14 110.47 107.49
trends are very similar. The behavior of the CISD electronic energy is also comparableexcept that the singlet state of ethylene at 90' is slightly more dependentupon configuration mixing than the singlet of 1,2dihydroxyethylene.TheS-T energy gap behaves more or less the same in both systems.
Andrh et al.
a
I
&O BtO. E--0.3 I89
a=o 0480. E=-0.3198
Figure 4. (a) Highest occupied molecular orbitals and (b) lowest unoccupied molecularorbitalscorresponding to the planar geometriescis and trans and to the twisted to 90°one. HOMO and LUMO are depicted for the singlet state of 1,2-dihydroxyethyIene. Energies are given in au.
At this stage, it is interesting to check the rotational barrier in the ground electronic state. Experimentally, its rotational barrier in the singlet state is about 65 K cal/m01.~~ The rotational barrier obtained with the inclusion of CISD is still far from the experimental figure. For CASSCF the rotational barrier is now very similar to the experimental value. Since the trends obtained for the S-T gap with CASSCF are the same as those obtained with the other correlated wave functions, it follows that this quantity is not critically dependent on the wave function form, namely, one determinant with correlation or multiconfigurational.
Discussion A quantum chemicalstudy is reported examiningthe variation of the energy gap between the singlet ground and first triplet states for 1,Zdihydroxyethyleneas a function of the rotational and pyramidalization angles. Thus, for a conveniently deformed enediol, the S-T energy gap may be appreciably smaller than the one found for a planar conformer. Correlated and uncorrelated wave functions show similar trends; the latter exaggerate the effect. The geometric parameters calculated with AM 1 behave fairly similarly to those calculated with the three basis sets used in the present study. The energy entries for the singlet state are below those obtained with correlated wave functions. The AM1 procedure may turn out to be most useful to describe the geometries in more complex model systems. The results concerning the S-T gap can be used to discuss some aspects of the enzymatic reaction mechanism. The X-ray data of the substrateand a transition state analog show a nonplanar cis conformationaround the C2-C3 bond in the enolized ribulose 1,5-bispho~phate.~~.~~ Under these geometrical conditions and accordingto the results herein reported,the triplet state of oxygen can interact with the triplet state of the deformed enediol to give a reactive supermolecule~5(see below). This simple fact provides a rationale to help in analyzing the bifunctionalityin Rubisco and allows for a simultaneousdiscussion of the mechanisms for carboxylation and oxygenation reactions. Carboxylation at the center C2 of enolized ribulose 1,5bisphosphate is a standard reaction taking place on the singlet reactive energy hypersurface. The carboxylation transition structure15has a geometry superposable with a transition state analog3jthereby showing that the substrate has a cis out of plane conformation around the C 2 4 3 bond. Oxygen is in a triplet state but also attacks the center C2 in the supermolecule. In Scheme I the elements of the argument
Singlet-Triplet Energy Gap in 1,ZDihydroxyethylene
SCHEME I’
-
3[02...~U~q
t
30*
’RuBP
thermal activation a
1[~2..q~U~~]
intersystem crossing
RuBP = D-ribulose 1,s-bisphosphate.
leading from a triplet supermolecule to an excited singlet supermoleculeare summarized. For the supermolecule,a thermal excitationis possible from the ground triplet state, where oxygen orbitals are responsible for spin multiplicity, toward an excited triplet state where the enediol *-orbitals and oxygen support a supermolecule triplet. Four electronsparticipate in this process. They can form three types of spin multiplicity: singlet, triplet, and quintuplet states. The idea is that a singlet state is in a neighborhood of the excited triplet of the supermolecule when the enediol is twisted. Therefore, intersystem crossing might be a likely process to explain the irreversibletransformation into a singlet reactive supermolecule. The possibility of a change in the electronic state of 3 0 2 to become ‘02prior to forming a supermoleculeand thereafter react with the singlet state of the enolized substrate bound to Rubisco seems to have a small probability. Theoretically,such a change in the electronic state of oxygen needs an amount of energy around 53 kcal/mol when the 6-31G* basis set is used. It is difficult to figure out where this energy may come from. The alternative discussed above seems more simple and therefore attractive.
Acknowledgment. The calculations were performed in three computer facilities: an IBM 3090/150 computer of the Centre d‘lnformatica de la Universitat de Valbncia, a CRAY XMP 14 at the Construcciones Aeroniuticas S.A. computer center, and a HP Apollo 9000/730 workstation at the Centre de Processament de Dades de la Universitat “Jaume I” de Caste116 We especially thank Fernando Sinchez Zabala for his generous help at the Construcciones Aeronauticas S.A. This work was supported by research funds of the University “Jaume I” of Caste116 O.T. thanks NFR for financial support. References and Notes (1) (a) Nebot-Gil, I.; Malrieu, J. P. J . Am. Chem. Soc. 1982,104,3325. (b) Wang, S.Y.; Borden, W. T. J. Am. Chem. Soc. 1989, I l l , 7282. (c) Morais, J.; Ma, J.; Zimmt, M. B. J . Phys. Chem. 1991, 95, 3885. (2) (a) Buenker, R. J. J . Chem. Phys. 1968,48,1368. (b) Kaldor, U.; Shavitt, I.J. Chem.Phys. 1968,48,191. (c) Buenker,R. J.; Bonacic-Koutecky, V.; Pogliani, L. J. Chem. Phys. 1980, 73, 1836. (d) Doany, F. E.; Heilweil, E. J.; Moore, R.; Hochstrasser, M. J. Chem.Phys. 1984,80,201. (e) Favini, G.; Gamba, A,; Todeschini, R. J . Chem. Soc., Perkin Trans. ZZ 1985,915. (3) (a) Lasne, M. C.; Ripoll, J. L. Tetrahedron Lett. 1982,23,1587. (b) Duhamel, L.; Launay, J. C. Tetrahedron Lett. 1983,24,4209. (c) Turecek, F.; Havlas, Z. J. Org. Chem. 1986, 51, 4066. (4) (a) Jaworowski, A,; Hartman, F. C.; Rose, I. A. J . Biol. Chem. 1984, 259,6783. (b) Pierce, J.; Lorimer, G. H.; Reddy, G. S.Biochemistry 1986, 25, 1636. (c) Van Dyk, D. E.; Schloss, J. Biochemistry 1986, 25, 5156. (5) Andrews, T. J.; Lorimer, G. H. The BiochemistryofPIants;Academic Press: Orlando, FL, 1987; Vol. 10, pp 131-210.
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