J. Phys. Chem. 1995,99, 10213-10220
10213
Factors Affecting the Geometry (Pyramidal vs Planar) of Aminoxyl Radicals. An ab Initio Study I. Komaromi and J. M. J. Tronchet" Department of Pharmaceutical Chemistry, University of Geneva, Sciences II, CH-1211 Geneva 4, Switzerland Received: April IO, 1 9 9 9
Ab initio (UHF, W 2 ) and density functional calculations, basis sets from 6-31G to TZP, have been performed on a series of simple aminoxyls, either acyclic (Me2N0, (CF3)2NO) or cyclic (from aziridine-N-oxy1 to piperidine-N-oxyl) in order to assess their equilibrium geometry and the features of the nitrogen inversion. The results were in good agreement with the few available experimental results. The main problem that arises from the aminoxyl group is its variable geometry, even in apparently structurally close situations, e.g. planar in pyrrolidine-N-oxy1 and pyramidal in piperidine-N-oxyl. In an attempt to offer a rationalization of these unexplained differences, we applied to dimethylaminoxyl geometrical constraints concerning successively the C-N bond length, the C-N-C bond angle, and the H-C-N-C torsion angles Q, and Y on both sides of the aminoxyl group. Modifying the C-N bond length showed no effect on the out-of-plane deformation of the group. On the contrary, increasing the C-N-C angle diminished the out-of-plane deformation, thus explaining the planarity of the di(rerr-buty1)aminoxyl. Unexpectedly, the values of the torsion angles Q, and Y exerted an important influence upon the planarity-pyramidality preference, and the values imposed by the ring geometry in pyrrolidine-N-oxy1 and piperidine-N-oxy1 corresponded respectively to planar and pyramidal structures, as experimentally found.
Introduction The aminoxyl group is more frequently used than any other paramagnetic moiety in spin-labeling experiments. Spin-labeled analogues of biological molecules-especially when structurally close to their diamagnetic models1,2-can provide effective means of monitoring biological events. The EPR spectra of the free radicals, particularly their hyperfine coupling constants, afford informtion not only on the substitution of the aminoxyl group but also on its out-of-plane def~rmation.~ One general difficulty with highly reactive species, and particularly free radicals, is that their simplest representatives which are amenable to high level ab initio study are too unstable to allow reliable experimental measurements, whereas the stable members of the series have gained their stability at the price of profound structural modifications which deeply affect the geometry of their aminoxyl moiety. Moreover, for the only reasonably stable simple aminoxyl [(F3C)2NO] for which gas phase electron diffraction4(GED) and infrared5(JR) spectra were reported, the results concerning the planarity of the aminoxyl group were divergent: pyramidal from the GED experiments, planar by IR. From the few, stable aminoxyls for which GED6 and X-ray diffraction data are a ~ a i l a b l e , ~it- ' appears ~ that the aminoxyl group does not adopt a constant well-defined geometry. Generally planar when included in a five-membered ring, it becomes pyramidal in six-membered rings. Contrarily to the almost general rule of its pyramidality in N,N-dialkyl derivatives derived from EPR spectral parameters,I7 it appears planar in the stable di(tert-buty1)aminoxyl radicaL6 Theoretical calculations of the geometry of the parent aminoxyl radical (H2NO)'8-29 and of a few examples of its simply substituted derivative^^^,^^,^^ have shown this group to be very flexible. An out-of-plane motion of its N-0 bond from the H(C)-N-H(C) plane by f 3 0 ° can take place within a small (less than 1 kcaYmo1) energy range. This fact is certainly @
Abstract published in Advance ACS Abstracts, June 1, 1995.
responsible for the difficulties encountered in the experimental determination of geometrical parameters. None of the previous studies have proposed any rationalization of the geometrical variability of aminoxyls bearing the same type of substitution. In other words, no relationship, other than empirical in some cases, is known between the geometry (pyramidal or planar) of aminoxyls and other geometrical parameters of the molecule. We shall address this problem on the basis of the results of ab initio (SCF, MP2) and density functional calculations of aminoxyl (H2NO) itself?8 its dimethyl and bis(trifluoromethy1) derivatives, and the cyclic aminoxyls piperidine-, pyrrolidine-, azetidine-, and aziridine-N-oxyls,
Method All the computations were performed using either the Gaussian 90,32 the GAUSSIAN 92/DR,33 or the ACES 234 program systems and the standard 6-31G,356-31G*,366-31G**,36 6-311G*,376-311G**,37DZP,38and TZP39bases. All HF and MP calculations used UHF and UMP2 wave functions, respectively (no ROHF references used). The MP2 calculations were usually performed using the frozen core approximation for the cyclic systems and the (F3C)2NO radical, whereas all the electrons were allowed to correlate for the dimethylaminoxyl radical. The density functional calculations have been performed using the Becke's gradient-corrected exchange functi0na1~~3~' combined with either the Lee-Yang-Pad2 or the per dew'^^^ gradient-corrected correlation functionals (respectively BLYP or BP86 methods in the GAUSSIAN 92" package). Becke's three-parametric hybrid exchange functi0na1~~ with the Lee-Yang-Parr correlation functional42has also been used (Becke 3LYP method in GAUSSIAN 92" and B3LYP hereafter). The inversional barriers, when present, were determined using the Baker's eigenvector-following algorithm45or assuming the appropriate symmetry of a planar radical. In many cases, the existence of energy minima and of transition states (TS) corresponding to first-order saddle points was proved by
0022-365419512099-10213$09.00/0 0 1995 American Chemical Society
10214 J. Phys. Chem., Vol. 99, No. 25, 1995
Komaromi and Tronchet
TABLE 1: Computed SCF, MP2, and DFT Energies @(tot), in hartrees), Energy Barriers and Zero-Point Vibrational Energies (E# and ZPVE, in k d m o l ) , and Main Geometrical Parameters at the Minimal Energies (Bond Lengths (r(XY)) in A, Bond Angles (a(CNC)) and Out-of-Plane Angles (z) in deg) for the (CH&NO Aminoxyl Radical symmetry
symmetry of the TS geometry
parameters
of the equil geometry
method
r(N0)
r(NO)#
1.2791 1.2637 1.2623 1.2635 1.2622 1.2620 1.2565 1.3079 1.2669 1.2665
1.2944 1.2591 1.2593 1.2590 1.2593 1.2592 1.2539 1.3039 1.2622 1.2619 planar pyramidal
1.4496 1.4477 120.84 1.4475 1.4438 118.90 1.4485 1.4453 118.93 1.4475 1.4438 118.98 1.4485 1.4453 118.95 1.4486 1.4454 119.04 1.4493 1.4462 118.82 1.4589 1.4566 120.35 1.4514 1.4476 118.55 1.4507 1.4468 118.52 56.339 kcaUmol 56.874 kcaUmol (corrected:"
1.2805 1.2855 1.2856 1.2857 1.2734 1.2769 planar pyramidal BLYP/D95 * 1.3078 1.3066 planar ZPVE(BLYPiD95 *) pyramidal BP86/D95* 1.2983 1.2977 ZPVE(BP86/D95*) planar pyramidal B3LYP/D95* 1.2902 1.2899 planar ZPVE(B3LYP/D95*) pyramidal
1.4562 1.4526 119.29 1.4579 1.4540 119.16 1.4567 1.4528 119.10 1.4566 1.4528 119.10 1.4570 1.4533 118.61 1.4583 1.4548 118.55 53.800 kcaUmol 54.523 kcal/mol (corrected:" 1.4797 1.4743 118.49 50.459 kcaUmol 50.869 kcal/mol (corrected:" 1.4707 1.4661 118.73 50.560 kcaUmol 5 1.036 kcaUmo1 (corrected? 1.4638 1.4587 118.68 52.131 kcaUmol 52.568 kcaUmol (corrected:"
HF/ 6-31G 6-31G* 6-31+G* 6-31G** 6-31++G* 6-3 1++G** 6-311+G** D95 D95* D95** ZPVE(HF/6-31G*) MP2/ 6-31G* 6-31+G* 6-31+G** 6-31++G** 6-311+G* TZP ZPVE(MP2/6-3 1G*)
1.2761 1.2800 1.2803 1.2803 1.2681 1.2728
r(NC)
r(NC)# a(CNC) a(CNC)# 121.34 120.65 120.51 120.72 120.53 120.59 120.34 121.19 120.46 120.46
t
E#
18.21 27.41 26.10 27.03 26.00 25.64 25.55 19.86 27.71 27.46
0.2260 1.0700 0.9578 1.0262 0.9391 0.91 13 0.9732 0.2503 1.0457 1.0127
-208.369 -208.459 -208.466 -208.469 -208.466 -208.476 -208.521 -208.413 -208.502 -208.513
0.9684 1.0953 1.0821 1.0632 1.1119 0.7154
-209.057 450 6 -209.074826 1 -209.122 855 0 -209.123 675 8 -209.216707 6 -209.255 678 1
&tot) 746 2 990 3 685 3 390 2 844 6 058 4 812 9 053 2 665 0 066 4
c2v
c2
Y
c2v CZV c 2
"
C2"
c2 c2 " c2v Y
C2"
56.451 kc:aUmol) 119.48 119.40 119.45 119.45 119.10 118.76
21.73 21.71 21.70 21.72 22.26 20.36
C2" C2" C2"
c2 c2 c2
Y Y Y
54.088 kcaUmo1) 120.15 24.58 0.9190 -209.678 046 5
c2
50.487 kcaUmo1) 119.76 23.21 0.9455 -209.758 6 4 0 7
c2
50.649 kcavmol) 119.73 23.83 0.8450 -209.757641 3
c2
52.181 kcaUmo1)
The N - 0 wagging contribution was subtracted from the ZPVE energy; see the text.
TABLE 2: Computed SCF, MP2, and DFT Energies @(tot), in hartrees), Energy Barriers and Zero-Point Vibrational Energies (E# and ZPVE,in kcaVmol), and Main Geometrical Parameters at the Minimal Energies (Bond Lengths (r(XY))in A, Bond Angles (a(CNC)) and Out-of-Plane Angles (z) in deg) for the (CF&NO Aminoxyl Radical symmetry of the equil geometry
method
r(N0)
