An analysis of the through-bond interaction using the localized molecular orbitals with ab initio calculations—II Lone-pair orbital energies in bicyclo compounds: 7-azabicyclo[2.2.1]heptane and 2-azabicyclo[2.2.2]octane, and their n-methyl

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An analysis of the through-bond interaction using the localized molecular orbitals with ab initio calculations—II Lone-pair orbital energies in bicyclo compounds: 7-azabicyclo[2.2.1]heptane and 2-azabicyclo[2.2.2]octane, and their n-methyl

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  Tttr~h ~ Vol. 37. pp 2191 IO 2195. I 1 Pnnwd in Gnat Brilain Al rights reserved m4ado2ab3~itt2t9b0ss02.m~o Copyrighl @l9Sl Pcrgamon Press Lid AN ANALYSIS F THE THROUGH-BOND INTERACTION USING THE LOCALIZES OLECULAR ORB~TALS ITH AB ~~~~~ CALCULATION~I LONE-PAIR RBITAL NTERACTIONS N C1S- AND TRANS-HYDRAZINES KIR MAMURA* ~Pa~ment of Chemistry, Shiga University of Medical Science, Seta~sukinowa~ho, Otsu, Shiga 52&2l, Japan and MASARU OHSAKU Department of Chemistry, Faculty of Science, Hiroshima University, Higashisenda-machi, Hiroshima 730, Japan (Receked in Japnn 26 Ju 1980; occepled I4 October MO) Abst@et-Ab inifio SCF MO calculations using ST@3G basis set were ~~orrned on the cis- and fruns- hydra es. The cannonical MOs obtained by these calculations were then transformed into the localized MOs. With the use of the localized MOs thus obtained, the variation in the lone-pair orbital energies of the molecules were pursued in the light of the through-space and/or the through-bond interactions between the specified localized MOs. As a result of this analysis, it was found that; (a) the effect of the inner shell orbitals, I s electrons of N atoms,is not negligibly small, cb) the effect of the through-bond interaction is not so larger than the through-space interaction, and (c) the large contribution of the through-space interaction is caused from the indirect as well as direct interactions between two lone-pairs. The concept of the through-space and the through-bond interactions was first introduced by Hoffmann et al. in connection with the discussions on the height of the energy levels of the lone-pair orbitals (LPOS).‘,~ This concept has been applied to many fields such as chemical reactivity, electron spin distribution and so on. Heil- bronner et at. developed a method for the quantitative calculation of the throu~-spare and the through-end interactions by using the symmetry adapted localized orbitals and applied to bicycle compounds with semi- empirical MOS.~ We have also developed a method3 to evaluate the through-space and the through-bond inter- actions by making use of the LMOs and this method has been successfully applied to explain the long-range hype~ne spin coupling consents in alkyl radicals,s*6 o explain lone-pair orbital interaction in azines,“? and to explain the long-range effect of the LPO to optical rotatory strength of the CO n + 7r* transition in keto- piperidines.’ In these papers,‘.‘” the procedure is to estimate quantitatively the through-bond and/or the through-space interaction by using the semi-empirical method.9.‘0 70” was used. The LMOs were obtained from the CMOS by the procedure of Edmiston-Ruedenberg.‘2 The SCF calculations based on the LMOs were carried out in order to evaluate various types of the through- bond/space interaction energies. Theory. For the analysis of the throu~-~nd~space inte~~tions, Fock matrix elements ~tween LMOs are obtained. These Fock matrix elements are easily cal- culated by the following convenient procedure. First, the LMOs &.,. $LbilrI.s, , are expressed by eqn (I) from the CMOS 4,. $2,. . . , which are obtained from the usual SCF MO calculation, Together with the CMOS, the orbital energies cl, e2,. * . 1 c;, can be obtained from the SCF calculations. Second, we now define a new datrix D Id,) by using the t~nsformation matrix as in eqn (2), I In the present work, in order to confirm and to support the validity of the previous procedure, and to obtain This matrix D is nothing but the Fock matrix represen- ted on the basis set of the LMOs, since the orbital separately new information, we have developed the energies, I~, e2 . , . , en, are the matrix elements between method by the aid of ob initio SCF MO calculations. the CMOS. Method of calculation The srcinal CMOS were Off-diagonal matrix elements in the matrix D cor- obtained from the ab inifio SCF calculations. Tbe basis set used was the STO-3G and the program GAUSSIAN respond to the interaction between the two specified LMOs which concentrate in the specified bond/atom. 2191  2 92 A. IMAMURA nd M. OHSAKU Consequently, we can detect the contribution of the through-bond/space interactions to the orbital energies by dropping the relevant matrix element followed the diagonal~tion to obtain orbital energies. When the two LMOs localized on the two adjacent bonds, the cor- responding off-diagonal elements should be responsible for the through-bond interaction, while the two LMOs localized on two remote parts of the molecule, this matrix element should relate to the through-space inter- action. By combining appropriate off-diagonal matrix elements, we can evaluate a relevant throu~-~~d~space interaction. It should be noteworthy that the trans- formation matrix obtained by the a~ve-mentioned pro- cedure for the analysis of the through-bond/space inter- actions is orthogonal, so that the density matrix as well as the total energy is invariant under this transfor- mation.16 In the preceding series of the papers,3 we have evaluated the through-bond/space interactions by drop- ping the relevant core resonance integrals and the two- electron integrals were not varied. This definition may be rationalized because of the approximation of the neglect of differential overlaps used in the semi-empirical method. However in the ab initio method, this definition is very difficult, since differential overlaps are included explicitely in the calculation. Accordingly, in the present paper, the through-space/bond interactions are evaluated by dropping the relevant Fock matrix elements instead of the core resonance integrals. A~~~ic~tion to fttc uc~uu~ ~oi~c~~~~. The procedure developed is now applied to the actual molecules cis- and truns-hydrazines. Molecular geometries used are shown below: r(N-N) = 1.47 I%, r(N-H) = 1.04 bi; angles around N atoms were assumed tetrahedral. Although molecular structures of hydrazine and related com- pounds have been estimated spec~oscopically,‘~‘s we have treated here hydrazine in the typical cis- and truns- forms only. There are two LPOs, ni and n2, in the molecules treated here. These two LPOs, n and nz, can lx classified into a symmetric, nl n2, or an anti-symmetric, nl - n2, combination from their symmetry properties. We will pursue the orbital energies of these two com- binations in the present work. RESULTS AND IMSCUSSION cis-I ?ydruzirre. Figure 1 shows the variation in the lone-pair orbital energy (LPOE) of cis-hydrazine. The LPOEs are raised up by interacti~ with ne~~~~ N-H bonds (a and b). By compa~ng with the diae;rams b and c, we can see that the effect of the inner shell orbitals, Is electrons of N atoms, is not negligibly small, although the effect is not so large. This cannot be recog- nized by the previous procedure with the semi-empirical methode3 To examine the diagrams a, c, and d, we can notice that the through-bond interaction is rather small. This result differs from the case of p~d~ine~.’ af- though the sit~tions are somewhat different between the cis-hydra&e and pyridazine. From the diagrams a. c, e, and I, we can see that the through-space interaction is responsible for the energy difference between the two LPOs. This is also true in the case of pyridazine.3*7 We will now discuss in more details the through-bond interaction using Fig. 2. From the diagrams E and g, it is CT _____ ~- _--_ h _ _____ Fig. 2. LPO through-bond interaction diagram or cis-hydrazine. The figures n parenthesis show the difference in orbital energies between the diagram c and each diagram. The larger value indicates the larger effect in the interaction. The diagram c is the starting one. The other notations : see Fig. 1. c and d: see Fig. 1. g: in addition to the diagram c, the through-bond interaction between the LPOs via the central N-N bond is allowed, and in this diagmm 1s electrons of N atom are not included in the interaction, h: in addition ot the diagram g, the N-H bonds are allowed to interact with the central N-N bond, and in this diagram also Is electrons on N atom are not included in the interaction. d e 5 06 0 5486 A Fig. 1. Typical LPO interaction dim for cis-hydrazine. The part surrounded by broken line is allowed to interact with each other. Nitrogen: 8, 1s electrons are not included in the inte~ction, and 0, they are included. -‘-: inte~ction allowed path. In the interaction diagram includi~ N-H bonds to avoid complexity only single line as a whole is used to represent the interaction with two N-H bonds. a: LPOs are cut off from all the types of interactions, b: interactions in the N-H bonds and LPO are allowed in each NH2 group except Is electrons of N atom. c: interactions are allowed between the LPO and N-H bonds including Is electrons of N atom in each NH2 group, d: in addition to the diagram c. all the types of through-bond interactions between the two NH1 groups are allowed, and Is electrons of N atom are included in the interaction, e: in addition to the diagram c, all the types of through-space interactions between the two NH2 groups are allowed, but the through-bond interactions are not allowed, f: full interaction case.  An analysis of the through-bond interaction 2193 found that the direct through-bond interaction via the central N-N bond raises up the symmetric LPOE con- siderably to lead to the large difference in energy for the two LPOs. When we include the indirect” throu~-end interaction via the N-H bonds as well as the direct one, the energy difference in the two LPOs decreases remarkably as shown in the diagram b. This tendency is straightened by including the indirect through-bond in- teraction via the inner-shell Is orbitals of two N atoms as shown in the diagram d. Thus, the coupling between the direct through-end interaction and the indirect through- bond interactions lead to small energy difference be- tween the two LPOsas the whole through-end interaction. k Fig. 3. LPO through-space interaction diagram for cti-hydrazine. The figures in parenthesis show the difference in orbital energies between the diagram c and each diagram. The larger value indicates the larger effect in the interaction. The diagram c is tbe starting one. The other notations: see Fig. I. c and e: see Fig. I. i: in addition to the diagram c, the through-space interaction be- tween the LPOs is allowed. j: in addition to the c diagram, the throu~-space interactions between the LPOs and N-H bonds are allowed, k: n addition to the c diagram, the trout-space interactions between the N-H bonds of the two NH:, groups are allowed, I in addition to the c diagram, the through-space inter- action between Is electrons of N atoms is allowed, m: in addition to the c diagram, the through-space interactions between Is electron of N atom and LPO are allowed, II: in addition to the c diagram, the through-space interactions between Is electron of N atom and the N-H bonds are allowed. We will then discuss in more details the through-space interaction by using Fig. 3. In Fig. 3, we list different kinds of through-space interaction diagrams. From these we can easily see that the dominant ones to determine the through-space interaction are the interactions written in the diagrams I and j. These two diagrams cover over 90% of the whole through-space interaction (see diagrams I, j and e). That is, the direct through-space interaction between the two LPOs and the indirect through-space interactions via the N-H bonds are res- ponsible for the magnitude of the whole through-space ~nteractjon. trans-~y~~ffz~~e. Figure 4 shows the variation in the LPOE levels of truns-hydrazine. From the diagrams a to d, it is found that the situations of the truns-hydrazine are similar with those of the cis-hydrazine. By compar- ing the diagrams e and f, the order of the LPOEs is in reverse order from that of cis-hydrazine. By the more detailed analysis of the throu~-end interaction shown in Fig, 5, it is also found that the sit~tion of the trans- hydrazine is quite similar with that of ci~-hydrazine. As for the through-space interaction, by comparing Figs. 3 and 6, difference appeared in the diagrams of i, j, k, m, and e. Among these, the largest one is the diagram j. but not in the diagram i. This is very interesting, because we can usually expect that the direct through-bond in- teraction ~dia~am i) should be the most dominant one. For reader’s information, the values of the interaction matrix elements (&I are listed in Table I. GENERAL ISCU~ION We have now turned again to the energy levels of the LPOs. The reverse of the energy level ordering for the symmetric and the anti-symmetric combinations of the LPOs for cis- and ~~~~~-hydrazines is caused from the direction of LPOs, which determine the magnitude and the sign of the throu~-space interaction. Among many c,____, r--_ II__..___ _----- -0 3009 (0 6291 -0.36 36 (0 Ooool Fig. 5. LPO through-bond interaction diagram for trans-hydra- zinc. Notations: see Fig. 2, VI -04 g -0s .==+,-04466A -044664, 5 -06 -0 5526 A Fig. 4. Typical LPO interaction diagram for frun~-hyd~ne. Notations: see Fig. 1.  2194 A. IMAMURA nd M. OHMKU Table 1. Interaction matrix elements (d& for trans-hydrazine 1s His Nls NLPO N-N NLPO Nls HIS His 1 2 3 4 5 6 7 El 9 la -0.7530 0.1793 0.7190 -0.2074 0.1562 0.0221 2 -0.7530 -0.7190 0.2074 -0.1562 -0.0221 3 -15.1260 1.2220 -0.6293 0.0206 4 -0.5528 0.1912 -0.0642 5 -0.7989 -0.1912 6 -0.5528 8 9 a LMO nunberinqs are shown below. I __.___ ______ m-_____ ___. A -04174 t-005361 S -0.3657 (-0.0019) A -0.3619 ~00019) s A -0.3572 (000661 -0.3697 (-000591 S -0.2780 (00858) A -04406 t-008481 Fig. 6. LPO through-space interaction diagram for truns- hydrazine. Notations: see Fig. 3. types of the through-space interactions, the direct through-space interaction between the two LPOs play an important role. Moreover, it should be stressed that the indirect through-space interactions via the N-H bonds also contribute to the energy separation of the two LPOs. Actually the molecular conformation is not the cis- or the frons- one,‘“.15 but it is in the intermediate conformation between these two forms, that is the dihe- dral angle between lone-pairs is about 90-I lo”. Therefore in the actual molecule, the interactions between the LPOs may be somewhat different from those now analyzed in the present paper. Nevertheless, the present result is very interesting as the model for the analysis of the typical through-bond/space interactions between two remote lone-pair orbitals. In conclusion, the present procedure is very helpful to analyse the interaction between or among definite orbi- tals (chemical bonds) in the other molecules with very clear chemical images. In the present procedure, we can also treat the inner shell electrons, Is electrons of N -0.0787 -0.0510 0.0787 -0.0095 0.0104 0.0787 -0.0206 0.0221 -0.6293 -0.1562 -1.2220 -0.2074 -15.1261 -0.7190 -0.7530 0.0095 0.0510 0.0787 0.0221 -0.1562 -0.2074 -0.7190 -0.1793 -0.7530 atom, explicitely which is not taken into consideration in the previous semi-empirical method.3*7 The present pro- cedure will also be used for the analysis of the chemical reaction processes. Acknowledgements-This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, for which we express our gratitude. We would like to acknowledge the continuing encouragement of Professor Hiromu Murata of Hiroshima University. We are also sincerely indebted to the Associate Professor Shinichi Yamabe and DE.. Tsutomu Minztto nd Yoshihiro Osamura or their help to our use of the GAUSSIAN 70 program package. The computations were car- ried out on FACOM Ml90 and M200 of the Data processing Center, Kyoto University. REFERENCES ‘R. Hoffmann, A. Imamura and W. J. Hehre, J. Am. Gem. Sot. 90 1499 1968). ‘R. Hoff mann, Act. Chem. Res. 4. 1 (197 ); R. Gleiter, Angew. Chem. 86.770 (1974). ‘M. Ohsaku, A. Imamura and K. Hirao, Bull. Chem. Sot. Jpn. a,3443 (1978). ‘E. Heilbronner and A. Schmelzer. He/u. Chem. Acta S8 936 (1975). ‘M. Ohsaku, A. Imamura, K. Hirao and T. Kawamura. Term- he&on 35,701 (1979). 6M Ohsaku, H. Murata, A. Imamura and K. Hirao, Ibid. 36, (1980). ‘hi. Ohsaku, H. Murata, A. Imamura and K. Hirao, Ibid. 35, 1595 1979). 8A. Imamura and K. Hirao, Ibid. 35, 2243 (1979). %J A. Pople, D. P. Santry and G. A. Segal, 1. Chem. Phys. 43 Sl’29 (1965); *J. A. Pople and G. A. Segal. Ibid. 43. S136 (1965): ‘J. A. Pople and Cl. A. Segal, Ibid. 44 3289 (1966). ‘OJ. A. Pople, D. L. Beveridge and P. A. Dobosh, Ibid. 47 2026 (1967). “W J Hehre, W. A. Lathan, R. Ditchfield, M. D. Newton and J. A.‘Pbple, GAUSSIAN 70, Program No. 216, Quantum Chem- istry Program Exchange, Indiana University, Bloomington, In- diana. ‘T. Edmiston and K. Ruedenberg, Reu. Mod. Phys. 35, 457 (1963). “K. Kohata, T. Fukuyama and K. Kuchitsu, Chem. tilt. 257 (1979). “N S. Chiu, H. L. Sellers, L. SchHfer and K. Kohata. J. Am. hem. SM. 101, 5883 1979).  An analysis of the through-bond interaction 2195 lS”K. Kimura and K. Osafune, Bull. C’hcm. SW. J’n. 48. 2421 (1975); bK. Kimura, Private communication. 16C. C. J. Roothaan, Rev. Mod. Phys. 23,69 (1951). “In the present paper, the direct through-bond interaction is denoted for the interaction of two lone-pair orbitals through the central N-N bond, while the indirect one is for the interaction of two lone-pair orbitals through two N-H bonds as well as the centraal N-N bond. The direct through-space interaction is for the interaction of two lone-pair orbitals without any intervening orbitals while the indirect one is for the through-space inter- action between two lone-pair orbitais via two N-H bonds, inner shell orbitals and so on.
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