J. Phys. Chem. 1995, 99, 9724-9729
9724
Multireference Configuration Interaction and Density Functional Study of the Azetidine Radical Cation and the Neutral Azetidin-1-yl Radical M. B. Huang,t H. U. Suter,# B. Engels," and S. D. Peyerimhoff Institut f i r Physikalische und Theoretische Chemie, Universitat Bonn, Wegelerstrasse 12, 0-53115 Bonn, Germany
S. Lune11 Department of Quantum Chemistry, Uppsala University, Box 518, S-75120 Uppsala, Sweden Received: December 15, 1994; In Final Form: April 6, 1995@
The geometry and the hyperfine structure of the four-membered rings azetidin-1-yl radical (CsH6N) and azetidine radical cation (C3H6NH+) have been studied. The geometries of both molecules were optimized using Mgller-Plesset perturbation theory as well as density functional approaches, while the hyperfine structure was calculated using the multireference configuration interaction with perturbational correction (MRD-CU BK)and density functional methods. The geometry of the radical cation was found to be planar, while the neutral radical is puckered with an optimized puckering angle of 22-23'. Employing a [6s3p/4s] A 0 basis the I4N isotropic hyperfine coupling constants (hfcc's) are 15.1 G in the neutral radical and 22.5 G in the radical cation, compared to the experimental values of 14.1 and 19.5 G. For the isotropic hfcc's of the p protons qualitative agreement between experiment and the present study was found. The influence of the molecular geometry and the theoretical treatment upon the values of the hfcc's has been studied, and some trends in the hfcc's of both molecules are discussed.
Introduction Radical cations and neutral radicals of saturated heterocyclic rings containing one nitrogen have attracted growing attention in recent years. Four- and five-membered rings containing one nitrogen atom both as radical cations and neutral radicals were recently studied by ESR experiment^'-^ and ab initio calculat i o n ~ . * .The ~ present paper is devoted to two four-membered rings, the azetidine radical cation, C3H6NH+, and the neutral azetidin- I-yl radical, C3H6N. The four-membered rings C3H6NH+ and C3H6N were studied by Qin and Williams' in 1986 using ESR experiments in different matrices, i.e. CF3Cl and CFCIZCF~CLIn 1991 Sjoqvist et aL2 reported ESR spectra of C3H6NH+ and the corresponding neutral species C3H6N in SF6 matrices. They also performed theoretical investigations using UHF/6-3 lG* calculations for the geometry optimization and SD-CI (CI including single and double excitations with respect to the Hartree-Fock configuration) calculations for the determination of the hyperfine coupling constants (hfcc's). All these experimental results are summarized in Table 1. For both compounds, Qin and Williams' found equal isotropic hfcc's for the four ,B protons. This behavior can be explained by the planar geometry indicated in Figure l a or by a doubleminimum potential with a puckered geometry (Figure lb), in which the energy of the populated vibrational state is above the planar structure. By studying both compounds at various temperatures Sjqvist et a1.* could show that the molecular structure of the radical cation seems to be planar, while the neutral radical has a puckered structure. For the neutral radical
* Author to whom correspondence should be addressed.
' On leave from National Synchronous Radiation
Lab, University of Science and Technology of China. Hefei 230029, People's Republic of Chjna. - Present address: Centro Svizzero di Calcolo Scientifico, CH-6928 Manno. Switzerland. @Abstractpublished in Advance ACS Abstracts, May 15. 1995.
TABLE 1: Previous Experimental and Theoretical Hyperfine Coupling Constants in the Acetidine Radical Cation (C3H6NH+) and the Neutral Azetidin-1-yl Radical (C3H6N) (in Gauss)" nucleus
T=90K1
T = 77 K2
theoryb
19.5 54.8
7.1 31.2 -0.3 -21.3
C&NH+ 19.1 54.2
23.4
22.6 Cd%N 13.6 38.4 38.4
14.1 49.0 29.2
3.1 32.4 19.4 -0.2 -0.4
a The sign cannot be determined by the experiments. See Figure 1 for the definition of the labels. SD-CI calculations reported in ref 2.
they found the isotropic hfcc's of the /? protons split into two different sets of 49 and 29 G as the temperature was lowered from 110 to 77 K. This is similar to the azetidine molecule, for which a puckered structure was found by Gunther et al. using microwave spectroscopy and electron diffraction.4 For the radical cation a planar structure was proposed because the four hfcc's of the ,B protons do not change over a wide temperature range. The studies also show that the isotropic hfcc of the nitrogen center in the neutral radical is nearly independent of the puckering angle a because it remains constant with decreasing temperature. Both experimental studies show that the radical cation (C3H6NH+), on average, has larger isotropic hfcc's than the neutral radical (C&N) for both the nitrogen and the ring protons. By comparison with the dimethylamine radical cation ((CH3)2NH+)5 Qin and Williams concluded that also for C3H6N and C&NH+ the main part of the spin density is confined to the nitrogen center. To a first approximation in both C3H6N and c3H6NI-I' the unpaired electron occupies the 2p orbital of the
0022-3654/95/2099-9724$09.00/0 0 1995 American Chemical Society
Azetidine Radical Cation and Azetidin- 1-yl Radical H4
J. Phys. Chem., Vol. 99, No. 24, 1995 9725 the experimental data, a comparison of various methods is made in the present work. Also discussed in the paper are some interesting differences between the neutral radical and the radical cation. Besides these major topics the hfcc’s of the /3 hydrogens will be discussed. The influence of the molecular geometry and the theoretical methods used on these isotropic hfcc’s will also be investigated. Technical Details
H1
10) Hlt
N
H6
H5 H1
ib) Figure 1. Definition of the geometrical parameters used in (a) azetidine radical cation (C,NHi) and (b) azetin- 1-yl radical (C3NH6).
nitrogen atom which lies perpendicular to the molecular plane. The finding of Sjoqvist et al. that the isotropic hfcc’s of the nitrogen center are nearly independent of the puckering angle supports this assumption because for the given electronic structure the isotropic hfcc’s of the nitrogen center should be quite independent of the molecular geometry. A similar behavior was found for the NH26 radical, which, with respect to the singly occupied orbital, possesses an electronic structure similar to C3H6N and C3H6NHf. In order to test their conclusions regarding the molecular geometry and the electronic structure, Sjoqvist et al. also carried out ab initio calculations for C3H6N and C+16NHf. The geometries of both compounds were optimized with the UHF method using a 6-31G* A 0 basis set. For the radical cation the absolute minimum was found to be planar, while a puckered geometry was obtained for the neutral radical. The electronic structure proposed from the ESR results could also be c o n f i e d . For both compounds the singly occupied orbital (SOMO) was found to be essentially the 2p orbital of the nitrogen center lying perpendicular to the molecular plane. Despite these agreements, their efforts to describe the isotropic hfcc’s of the two compounds were quite unsuccessful. Although the A 0 basis sets and the methods used in the study of Sjoqvist et a1.* seemed to be of acceptable quality, their predicted isotropic hfcc’s for the nitrogen center deviate about 70-80% from the experimental values (see Table 1). For the p protons the discrepancy was about 30%. While the deviations found for the /3 protons are explainable, the large discrepancies obtained for the nitrogen center are astonishing since the unpaired electron is located at the nitrogen. Furthermore, uncertainties arising from the geometry are small because, as already discussed above, the isotropic hfcc of the nitrogen is expected to be insensitive to geometrical parameters. The present paper has two major aims. To test the conclusions regarding the electronic structure of both radicals made by Qin and Williams’ and Sjoqvist et a1.,* the isotropic hfcc’s of the nitrogen centers and the a hydrogen are investigated. These properties are well suited for this purpose because they are less influenced by uncertainties arising from the theoretical treatment (molecular geometry and correlation effects) and matrix effects than are the p hydrogen couplings. To study the reasons for the discrepancies between the previous theoretical predictions of the isotropic hfcc’s made by Sjoqvist et aL2 and
The geometries of both molecules were reoptimized using the UMP2 method (unrestricted Moller-Plesset perturbation theory to the second order) in combination with a 6-31G* A 0 basis set. The calculations were performed with the Gaussian90 p r ~ g r a m . ~Additionally to the UMP2/6-3 lG* geometry optimization we performed geometry optimizations on the QCISD/ 4-3 lG* level and using density functional calculations (DFT). For the DFT calculations an A 0 basis set proposed by van Duijneveldt8 was used, consisting of a (13s8p) basis contracted to [8s5p] for the heavier atoms and a (9s) basis contracted to [7s] for the hydrogen atoms. This basis was augmented by two d functions (C: 1.097, 0.318, N: 1.654, 0.469) for the heavier centers and two p functions (1.407, 0.388) for the hydrogen centers. The density functional chosen was the Lee-YangParr functional9 with the gradient correction of Becke.Io This calculation will be abbreviated as BLYPDuij. In an additional calculation we used the B3-LYP functional, which as shown by Barone et al.29is superior to the BLYP functional for some compounds. These calculations are abbreviated as B3-BLYP/ Duij. All density functional calculations have been performed with the G92DFT program package.” The hyperfine coupling constants (hfcc’s) were obtained from large-scale configuration interaction (CI) calculations of several different levels of complexity (see below). The A 0 basis sets used in these calculations were selected according to Chipman. 12.13 For the heavier centers the starting point was Huzinaga’s (9s5p) basis seti4 contracted to [4s2p], while for the hydrogen centers the (4s) contracted to [2s] basis set was used. Each A 0 basis was augmented by diffuse s and p functions (C: 0.0479, 0.0358; N: 0.0667,0.0517; H: 0.0483). In a study by Bauschlicher et aLi5 it could be shown that the addition of one diffuse s function led to a saturation of the (sp) basis with respect to the calculated isotropic hfcc’s. A further enlargement of the A 0 basis, e.g. using even-tempered basis sets (ETG) as advocated by Feller and D a ~ i d s o n ,increased ~~.~~ A,,, by less than 1%. In addition to the diffuse functions, one tight s function was located at each center (C: 28191.9; N: 40030.9; H: 88.675). The total number of basis functions is 84 for C3H6N and 88 for C3H6NH’. On the basis of the experience of ab initio calculations for isotropic h f ~ c ’ s ~ ~ . ’ ~ . ’ ~ the neglect of polarization functions (d,f functions) on the heavier centers, not included due to software limitations, should yield spin densities for the nitrogen which are somewhat too large, as it will be shown later on. The influence of polarization functions was studied separately employing the CIS method (CI including only single excitations with respect to the HartreeFock determinant). For these calculations the original basis sets proposed by Chipmani2were used, which contain additional d polarization functions but no tight s functions. In order to investigate the influence of the correlation treatment on the isotropic hfcc’s, we performed SD-CI, individually selected multireference CI (MRD-CI), l 9 and MRD-CI/ BK*Ocalculations. In the MRD-CVBK method the BK*Itreatment is used for a perturbational correction of the MRD-CI wave function.*O While the SD-CI calculations were performed with SCF MOs, natural orbitals (NOS) obtained by a small preliminary MRD-CI calculation were used as the one-particle basis in the MRD-CI and MRD-CVBK calculations.
Huang et al.
9726 J. Phys. Chem., Vol. 99, No. 24, 1995
TABLE 2: UMPW4-31G* and UHF/6-31G* (in Parentheses) Optimized Geometries for C3NH,+ and C3NHsU
TABLE 3: QCISD/6-31G* and UHF-BLYP/Duij (in Parentheses) ODtimized Geometries for C3NH7' and C3NH8 ~
parameters
C3NH7' (C2,))
CiNH6 (c,)
WN-Ci) R(Ci-C3) R(Ci-Hi) R(Ci-Hd R(C3-Hj) R(C?-&) R(N-H7) R(Ci-Cd LCiNCz LClC3C2 LHlClN LHICIC? LHzCiN LHzCiC3 LHjC3C: LHsC3Cz
1.453 (1.473)' 1.548 (1.547) 1.098( I .083)
1.477 (1.469) 1.558 (1.541) 1.095 (1.084) 1.099 (1.087) 1.091 (1.083) 1.093 (1.083)
1.089 (1.079) 1.027 (1,010) 2.147 (2.163) 95.2 (94.5) 87.8 (88.7) 111.3 (110.7) 117.9 114.5
a (S3 ELMP?
0.767 -172.353 88
2.056 (2.071) 88.2 (89.7) 83.9 (84.5) 114.2 (1 13.3) 120.2 109.8 112.2 112.0 118.7 25.8 (15.4) 0.763 - 172.000 92
"See Figure 1 for the definitions of the labels and geometrical parameters. Distances in angstroms. Distances in angstroms and angles in degrees. Values in parentheses are the UHF/6-31G* results reported in ref 2.
Hyperfine coupling constants were also calculated using the DFT method. Here the same approach as used for the geometry optimization was taken. The MRD-CI and MRD-CIIBK calculations were performed with various numbers of reference configurations, which were selected according to their coefficients and their contributions to the spin density matrix. The size of the total MR-CISD space varied from about 8 000 000 to 22 000 000 configurations depending on the symmetry of the molecules (C, or CzV)and the size of the reference space. The number of selected configurations variationally treated in the MRD-CI was around 25 000-30 000. All single excitations with respect to the main configurations were included in the BK correction. The relaxation of the coefficients of higher excitations is less important, so that inclusion of those configurations having coefficients larger than 0.04 in the BK treatment was found to be sufficient.20.22A theoretical discussion of the MRD-CVBK method may be found in,20 while a comparison with other methods may be found in ref 22. Since experimental values of the isotropic hfcc's are only available for the nitrogen and the hydrogen centers, the present study will focus on these properties. Therefore, it was possible to keep the 1s orbitals of the carbon centers frozen in the MRDCVBK calculations, leaving a total of 25 electrons to be correlated. Carbon hfcc's are, however, reported from the DFT calculations. Results and Discussion Geometries. Four-membered rings are known to have a double-minimum potential with a relatively small barrier, which for cyclobutane is approximately 1 kcal/m01.*~.~~ From ESR experiments a puckered structure was suggested for the azetidinyl radical (C&N), while a planar structure was proposed for the azetidine radical cation (c3H6NHf). The geometry used in the previous theoretical study by Sjoqvist et aLz was obtained from an UHF/6-31G* geometry optimization. To study the influence of electron correlation, we decided to reoptimize the geometry using the UMP2 method in combination with a 6-3 lG* A 0 basis set. The reoptimized geometry is compared with the UHF/6-31G* one in Table 2. Due to correlation effects, the intemuclear distances change by about 0.02 A, and for the neutral radical the puckering angle increases by about 10" from
~~~
parametersa WN-C I 1 N C I-C3) R(Ci-Hi) R(Ci -Hd R(C3-Hj) R(C3-Hd R(N-N7) R(CI-Cd LCiNC2 LCIC3C2 LHlClN LHICIC~ LH2ClN LH~CIC~ LH~C~CZ LH6C3Cz
a (9) EUQCISD (EBLYP)
CINH~' (C?,.) 1.461 (1.454) 1.550 (1.561) 1.099 (1.105) 1.091 (1.092) 1.027 (1.027) 2.155 (2.155) 95.0 (95.3) 88.1 (87.0) 111.3 (112.2) 117.8 (118.1) 114.4 (1 14.6)
0.767 (0.753) -172.221 47 (-172.934 03)
C3NH6 (CS) 1.483 (1.488) 1.541 (1.556) 1.096 (1,100) 1.101 (1.103) 1.094 (1.094) 1.094 (1.095) 2.070 (2.094) 88.5 (89.4) 84.4 (84.6) 113.8 (1 13.0) 119.6(118.8) 110.0 (1 10.7) 112.9 (1 14.2) 112.4 (1 13.4) 118.3 (117.3) 22.1 (23.2) 0.763 (0.753) -171.862 80 (-172.577 67)
"See Figure 1 for the definitions of the labels and geometrical parameters. Distances in angstroms. Distances in angstroms and angles in degrees.
15.4" in the UHF calculation to 25.8" in the UMP2 treatment. The geometries obtained from the QCISD/4-31G* and DFT calculations are given in Table 3. Both methods show geometries very similar to the UMP2/6-31G* calculation. The strong dependence of the puckering angle on the method of optimization (UHF 15.4"; UMP2 25.8"; QCISD 22.1"; DFT 23.2') is understandable because of the very low barrier height found for the neutral radical, being 0.81 kcaVmol at the UMP2/ 6-31G* level and 0.42 kcaYmol at the QCISD/4-31G* level. This is close to the value given in the literature for the azetidine molecule (1.0 kcaUm~l).'~The barrier height is strongly influenced by electron correlation; that is, a barrier of less than 0.1 kcaUmol is found in the UHF calculation.* Hyperfine Structure. The dependence of the isotropic hfcc's on the theoretical method, basis set, and geometry is shown in Tables 4-6. We will initially focus on the radical cation and later extend the discussion to the neutral radical. Let us first concentrate on the isotropic hfcc of the nitrogen center, A,,,(I4N), for which Sjoqvist et al. found the largest deviation from the experimental results (7.1 G versus 19.5 G). Because the unpaired electron occupies a nitrogen 2p orbital perpendicular to the molecular plane, A,,,('4N) is determined solely by polarizatiodcorrelation effects. The large effect of the basis set can be seen by comparing given by Sjoqvist et al. (Table 1) and our SD-CI value (Table 4). Using the more appropriate basis described above, A,,,(I4N) is shifted by about 6 G toward the experimental value. A similar behavior was already found by Chipmani2.I3and Bauschlicher et al.,I5 who could show that diffuse functions, which are missing in the basis set used by Sjoqvist et aL2 are very important for the description of spin polarization effects in nitrogen. For both the p hydrogens (HI) and the a hydrogen (H7), the influence of the A 0 basis set is less pronounced. In Table 5 the effects of the missing polarization function are estimated using the CIS treatment. In many cases CIS calculation gives quantitative agreement with the experimental results. However, as shown in previous studies, the success of CIS is due to error ~ a n c e l l a t i o n ,which ~ ~ in some cases fails.22 Nevertheless, the CIS treatment is very inexpensive, which opens the possibility to check larger basis sets. The effect of polarization functions in the A 0 basis can be estimated from Table 5. One can see that for the present system also the CIS
J. Phys. Chem., Vol. 99, No. 24, 1995 9727
Azetidine Radical Cation and Azetidin- 1-yl Radical
TABLE 4: Energies of the Variationally Handled Space (MRD-CI), of the MRD-CVBKMethod Based on the Same Space, and the Isotropic Hyperfine Coupling Constants (in Gauss) for the Azetidine Radical Cation (C3NH,+) UHF geometry“ UMP2 geometrya energy C,C2 f
N HI
Hs H7
SD-CIb
MRD-CI‘
Bwb
MRD-CI‘
-171.02008 0.8935 13.7 31.4 -0.2 -23.3
-172.060 05 0.8966 15.8 35.9 0.1 -22.7
-172.075 42 0.8968 22.7 37.2 -0.2 -25.9
-172.060 88 0.8948 15.5 39.3 0.2 -22.33
Bd
MRD-CId
-172.076 14 -172.061 07 0.8950 0.9013 22.2 15.6 40.8 39.3 0.2 0.0 -25.5 -22.3
B$ -172.078 09 0.9015 22.5 41.7 -0.1 -25.6
MRD-CI‘
B vd
-172.061 15 -172.078 88 0.9049 0.9052 15.6 22.5 39.3 42.1 0.2 -0.2 -22.4 -25.6
a See ref 2 for the UHF geometry and Table 3 for the UMP2 geometry. SD-CI calculation using the basis set of the present investigation. 24 reference configurations. 50 reference configurations. e 72 reference configurations. f Sum over the squared coefficients of the reference space. See Figure 1 for the definition of the labels:
TABLE 5: Comparison of the A 0 Basis Set Used in the MRD-CI/BKCalculations (Bl) with the Standard Chipman Basis Set Including Polarization Functions (B2)12for C&NH+, Using CIS Calculations basis B1 B2
exptl
N 23.3 18.3 19.5
HI
H7
37.7 36.6
-28.1 -26.3
54.8
23.4
TABLE 6: Hyperfine Coupling Constants of C3HsNH+ and C&N for All Atoms Obtained Using the BLYPDuij Method (Upper Line) and the B3-LYPDuij Method (Lower Line)” 1 1.o (1 1.2) 15.0 -10.2 (-10.0) - 10.0 -0.1 (0.0) 0.5 66.9 (65.7) 59.5 5.0 (5.1) 1.9
9.8 (9.9) 12.1 -10.3 (-10.3) -11.6 3.8 (3.3) 4.9 51.2 (48.7) 49.4 32.9 (33.3) 29.9 0.5 (0.6) -0.2 0.5 (0.6) -1.0
-17.8 (-18.0) -21.6
The geometry was the one optimized on the same level, while the values in parentheses were calculated at the UMP2/6-3 1G* geometry. (‘
gives quite accurate values. Using the same basis set as employed in the MRD-CI/BK calculation, the hfcc’s differ by 2-5 G from the MRD-CI/BK results. As expected, the hfcc of the nitrogen center decreases if polarization functions (basis B2) are added. The hfcc’s of the p protons (HI) remain nearly unchanged. However, because the CIS does not properly account for the higher excitations, the effect on the’p protons might be larger in MRD-CVBK calculations. For the radical cation also the influence of the correlation treatment and the molecular geometry on the isotropic hfcc’s can be studied in Tables 4 and 5. Let us first concentrate on the correlation effects. Comparing the various treatments used in the present work, the influence of the correlation treatment on A,,,(14N) is obvious. As already shown in several other s t ~ d i e s , ~the~ -inclusion ~~ of higher than double excitations is important. Furthermore, within the framework of truncated MRCI treatments the influence of the neglected configurations has to be taken into account.20 For the UMP2 geometry of the radical cation we performed calculations with three different reference spaces consisting of 24, 50, and 72 reference configurations. If the truncated MR-CI treatment is used, the influence on A,,, is negligible for all centers. If the BK correction is taken into account, the isotropic hfcc’s of the p
protons (A,,,(Ht)) improve by 1-2 G, while A,,,(14N) and A,,,(H7) keep nearly constant. A similar pattern is found if the CIS treatment is compared to the MRD-CI/BK calculations. Using the more elaborate MRD-WBK treatments, the isotropic hfcc’s increase by 4-5 G, which indicates that missing higher excitations are one reason for the two low spin density at the p protons (HI). These findings are consistent with a previous study on H2CN and H2COf.22,28The work on HzCN and HZCOf also showed that an enlargement of the configuration space handled variationally does not change the isotropic proton hfcc’s to a large extent ( 5 2 % ) . On the basis of our experience from these systems, the error in Also(H~)due to an incomplete correlation treatment can be estimated to be 3-5 G, while the error in A,,,(I4N) and A,,,(H7) is much smaller. The DFT method has been used successfully by several groups to calculate h f c ~ ’ s . ~To ~ -use ~ ~the possibilities given by the DFT theory, we decided to perform a BLYPDuij and B3-BLYP calculation for the hfcc’s. The results given in Table 6 emphasize that the hfcc’s of the present systems are very difficult to obtain. Using the BLYPDuij approach for the cation, the hfcc’s of the nitrogen center and the a proton are seriously underestimated, while the hfcc’s calculated for the p protons are overestimated. For the neutral radical the nitrogen value is also too small, but the values of the p protons are very where it good. This finding is in line with a previous was shown that with the given functionals the DFT is not able to describe n centers correctly. The calculated hfcc’s of p protons are often in better agreement with the experimental values because a large direct contribution is calculated within the DFT approach. This seems to work for the neutral radical but breaks down in the radical cation. Using the B3-BLYP functional, the calculated hfcc’s improve noticeably, although the general trend still can be found. Altogether the B3-BLYP functional gives more reliable values than the BLYP functi~nal.*~ Previous experimental studies indicate that only the isotropic hfcc’s of the /3 proton (AIs,(Hl)) should depend strongly on the equilibrium geometry. This finding is confirmed by Table 4. The table shows that uncertainties in the calculated equilibrium geometry of the molecule have to be considered only for the isotropic hfcc’s of the ,8 proton (Also(H~)), while the isotropic hfcc’s of the a proton (H7) and of the nitrogen center are relatively insensitive to molecule geometry changes. Going from the UHF geometry to the UMP2 geometry, only minor changes in the geometrical parameters are found for the radical cation (Table 2 ) . However, already from these small changes an increase of 3-4 G is found for AIS,(Hl), while the isotropic hfcc’s of all other centers remain nearly constant. Comparing the DFT results obtained at the geometry optimized on the DFT level with those obtained at the UMP2/6-31G* level (see Table 6) in the neutral radical, A,$,(Hl) again changes by about 2-3 G, although the differences in both geometries (cf. Tables 2 and 3) are very small.
Huang et al.
9728 J. Phys. Chem., Vol. 99, No. 24, 1995 TABLE 7: Isotropic Hyperfine Coupling Constants (in Gauss) for the Azetidine Radical Cation (C3NH7+) and the Neutral Azetidin-1-yl Radical, Calculated on the QCISD/ 6-31G* Geometries“ nucleus RHF BLYP MRDCI BK exptl N
0.0
HI H5
25.6
H7
0.0 0.0
N
0.1
HI H2 H5 H6
23.5 9.1 0.7 0.3
CjNH7’ (C?,)’ 15.5 11.2 39.3 65.7 5.1 0.2 -18.0 -22.4 C3NH6 (Cs)‘ 10.1 9.9 36.6 48.7 16.5 33.3 -0.6 0.6 0.3 0.6
22.5 42.1 -0.2 -25.6
19.5 54.8
15.1 38.1 18.4 -1.5 0.3
14.1 49.0 29.2
23.4
See Figure 1 for the definition of the labels. Experimental data in a SF6 matrix (77 K); only absolute values given (see ref 1). Experimental data in a CF2ClCFCI2 matrix (77 K) (see ref 1). See Figure la,b for the assignment of the hfcc’s. The hfcc’s of the p protons are most strongly influenced by geometrical changes which brings them closer to the radical center, For example a small distortion of the CCCN ring by changing the C3N distance (see Figure 1) by about 0.05 A shifts the isotropic hfcc’s of the p protons by as much as 5 G. To judge the uncertainties arising from the theoretically determined equilibrium geometry, one has to keep in mind that for the same change in the C3N distance the total energy increases by less than 1 kcaVmol (in the UHF calculation). A similar behavior is found with respect to the variations of the puckering angle a (Table 8). The isotropic hfcc of H2 changes by about 7 G if the puckering angle is changed from the optimal value of about 23-24” to a value of 10’. For the same distortion the energy changes by less than 0.4 kcal/mol. The calculated barrier for the puckering motion (a = 0) is less than 0.5 kcaYmo1. Furthermore, because of the floppy nature of the molecule, differences between the molecular geometry in the gas phase and in the matrix can result. However, vibrational averaging will not change the isotropic hfcc’s to a large extent, because the dependence on the geometrical distortions is nearly linear. In our opinion an uncertainty in the isotropic hfcc’s of the p protons of at least 5-7 G has to be assumed due to uncertainties in the theoretically determined equilibrium geometry. Comparison between C3H6NH+ and C3H& A summary of the isotropic hfcc’s of C3H6N and C & , N H + calculated at the UMP2/6-31G* geometry is given in Table 7. It is obvious that we have managed to remove the large discrepancies between theory and experiment found for the nitrogen centers (see Table 1) in a previous study.2 For the isotropic hfcc of the a proton in the radical cation a value of -25.5 G is obtained in the present study. The results of the present investigation confirm the conclusions about the electronic structure made by Qin and Williams. I The isotropic hfcc’s of the p protons of the radical cation were calculated to be %42-43 G, while ~ 3 and 8 19 G were found in the neutral radical. These values are in qualitative agreement with experiment, although the absolute errors are larger than for the nitrogen centers. In agreement with experimental findings the isotropic hfcc’s of the y protons (H5, H6) are found to be nearly 0. Since experimental values of the isotropic hfcc’s are only available for the nitrogen and the hydrogen centers, the present study concentrates on these properties. The hfcc’s of the carbon center can be taken from Table 6, but the values could be less accurate, as discussed above. One interesting feature of the hyperfine structure is the difference in the isotropic hfcc’s of the two compounds. While
TABLE 8: Isotropic Hyperfine Coupling Constant Values (in Gauss) for HI and Hz in the C3HsNH+ and C3H6N Radicals, Calculated with the CIS Method at Fixed Puckerine Angles9
33.7 34.6 32.2 28.1 41.5 43.7 36.7 15.6 13.5 22.1 22.6 28.1 29.9 36.7 a The other geometrical parameters were optimized at the UMP2I 6-31G* level (a,in degrees). The calculation has been performed using the original Chipman basis,I2 with two d functions and without tight s functions. See Figure 1 for the definition of the labels. bUMP2/631G* geometry. HI H?
the qualitative picture (relative magnitudes for the various centers and the signs of the hfcc’s) is equal in both compounds, the isotropic hfcc’s of the radical cation are found to be significantly larger than those for the neutral radical. To explain the differences between the two molecules, the contributions to the spin densities at the various nuclear centers were analyzed. Let us first focus on the nitrogen center itself. Because the spin density at the nitrogen center is insensitive to variations of the molecular geometry,2 the electronic structure has to be the reason for the difference between both molecules. As already discussed in the work of Sjoqvist et al.,2 the singly occupied molecular orbital (SOMO) closely resembles the nitrogen p orbital lying perpendicular to the molecular plane (pl). Therefore, for both molecules the isotropic hfcc’s of the nitrogen center are determined solely by spin polarization effects. For the radical cation a strong contribution to the spin density at the nitrogen center arises from the spin polarization of the electrons occupying the orbitals describing the N-Ha 0 bond. Since the hydrogen center is absent in the neutral radical, these orbitals resemble a slightly distorted p in-plane orbital at the nitrogen center, which cannot contribute to the isotropic hfcc of the nitrogen center due to its shape. The same effect was described for the dimethylamino radical ((CH3)2N) and its protonated cation ((CH3)2NH+).5.34Also the isotropic hyperfine coupling constants have been found to be similar to the azetidines. The neutral dimethylamino radical has an isotropic hyperfine coupling constant around 14 G, while for the radical cation the value was around 20 G. The difference in the isotropic hfcc’s of the p hydrogens of the two compounds is well reproduced by the present work even though the absolute errors are larger than for the nitrogen centers. Parts of the differences in the isotropic hfcc’s of the p protons of both compounds are already described at the RHF level (Table 7 ) . On the other hand, the geometry of the molecules influences the isotropic hfcc’s of the p protons considerably. To distinguish between the influence of the puckering angle a and other reasons, the hfcc’s of the protons of both compounds were calculated at various puckering angles using the CIS method (including only single excitations). The results are given in Table 8. As already shown in Table 5 for the present molecule, the CIS approach gives qualitative agreement with the experimental results. Comparing the a = 0 geometries, the spin densities at the /?protons are still larger for the radical cation. Studying different effects, the shape of the SOMO in the radical cation was found to be the most important reason for the differences in the hyperfine structure of the /3 protons of both compounds. However, the geometry is also important. The distances between the nitrogen and tbe p hydrogen in the radical cation are slightly smaller (e0.02 A) than in the neutral radical, which increases the direct contribution to A ~ ~ W I ) . For the neutral radical the p hydrogen values are different, but, surprisingly, the hydrogens beneath the CCC plane (HI,
Azetidine Radical Cation and Azetidin- 1-yl Radical
Hi
(1)
(11)
Figure 2. View of the azetidinyl radical along the C I - C ~bond.
H3), e.g. opposite to the nitrogen, have larger isotropic hfcc's. Again, the reason lies in'the shape of the SOMO. It is also consistent with the finding that the distances from the nitrogen to the hydrogens located beneath the CCC plane (HI, H3) are smaller (=0.03 A) than from the nitrogen to those above the CCC plane (H2, H4). The situation is depicted in Figure 2. Starting from the planar form (I), both CH2 groups twist to reduce the repulsion between the nitrogen and the two hydrogens above the CCC plane. Conclusion The main emphasis of the present work was to remove the large discrepancies between theoretically2 and experimentally' obtained isotropic hfcc's of the nitrogen centers in the fourmembered rings C&N and C3H6NH+. These large deviations were not understandable in terms of uncertainties arising from geometrical structure of the molecules and the matrices, since these effects should be small for these coupling constants. However, due to this discrepancy the conclusions about the electronic structure were less certain. In the present work the geometry and the hyperfine coupling constants of the fourmembered rings azetidin- 1-yl radical (C3H6N) and azetidine radical cation have been studied with various methods. While a planar geometry was found for the radical cation, a puckered equilibrium geometry was calculated for the neutral radical. The size of the puckering angle depends rather strongly on the computational model used in the geometry optimization: UHF/ 6-31G* 15.4"; UMP2/6-31G* 25.8; QCISD/4-31G* 22.1"; BLYPDuij 23.2". This is understandable because a very low barrier height is found for the neutral radical. The barrier height is 0.8 1 kcaVmo1 employing the UMP2/6-3 1G* treatment and 0.42 kcaVmol if the QCISD/4-31G* level of sophistication is used, while being less than 0.1 kcal/mol in the UHF calculation.2 The isotropic hyperfine coupling constants were calculated using various methods (CIS, SD-CI, MRD-CI, MRD-CVBK,and DFT). For the nitrogen centers values of e 2 2 G for the cation and 15 G for the neutral radical were obtained. This is in good agreement with the experimental values of 19.5 and 14.1 G. For the /3 protons the calculated values deviate more from the experimental results, i.e. ~ 2 5 %in the case of A,so(H~). Deficiencies in the correlation treatment (3-5 G) and uncertainties in the geometrical equilibrium structure (5-7 G) were found to be the main causes of the strong deviation. Although the absolute errors in the isotropic hfcc's of the /3 protons (A,so(H,))are larger than for the nitrogen centers, their relative magnitudes comparing the two molecules under consideration are reproduced well by the present work. Therefore, it w a s possible to study some interesting trends in the hyperfine structure of both molecules, e.g. the larger spin density in the radical cation and the difference between the two /3 protons in the neutral radical. In the case of the nitrogen center, spin polarization of the doubly occupied orbitals describing the N-H o bond was found to be responsible for the larger spin density in the radical cation, while the shape of the singly occupied orbital (SOMO) is the main reason in the case of the /3 protons. The shape of the SOMO and the distances between the /3 protons and the nitrogen center also explain the differences in the isotropic hfcc's of the /3 protons in the neutral radical.
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