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"11-‘1 “1316‘“? 1. -. $1.1, "écfi- "‘L 1‘31; 1. 1,1 . -. 1 1 ". 1 1‘ :- . 35""213i1fffl \ 3.2.1.1234 - . . . _1,.r r‘ 1.1, -. ~27 mfi-” 4 .1, 11*"; 351:2- 13""! "-11-. - “’23 .l 2m.4 "" ‘. 4’.) I 1 15:11: ., ..1 ~5“1‘1"1"~~1w~h'31‘:31'13"“\:1:23 i“ f} ‘1}:,’,LL,'1';:7; $1.11 13;:- . 1 ‘4‘ "if: “211$,“ d'i'n- "~. 1“” 11-111 1 C X '33; ‘3 ~< ~. 11 ’kad.fi, fikfigqi‘d, “33,. " "I U , , 1: , a -, , mm Date 0-7 639 memm Michigan State 3 University This is to certify that the thesis entitled Vibrational Analysis of o—Benzyne presented by Hak—Hyun Nam has been accepted towards fulfillment of the requirements for M. S . degree in Chemi stry 1W 2M; 0 Major p iofessor George E. Leroi 9/12/85 MS U is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES 4132-. RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. VIBRATIDNAL ANALYSIS OF O‘BENZYNE By Hak-Hyun Nam A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemistry ISBS / (_ ABSTRACT VIBRATIONAL ANALYSIS OF o-BENZYNE By 'Hak-Hyun Nam The infrared spectrum of o~benzyne was obtained via uv photolysis of matrix isolated phthalic anhydride. Two additional frequencies, 1355 and 1395 cm‘l, which matChes the normal coordinate calculation well were found in addition to all of the frequencies previously reported by Dunkin and MacDonald. Attempts to obtain Raman spectra of this transient species were not successful. The normal coordinate calculation was performed for o-CbHa and o—CéD4 with the experimental data , and with the G~matrix based on a theoretically~ca1culated molecular geometry. The proposed vibrational force field reproduces experimental infrared frequencies within 2% for in~plane motions and 0.4% for out- of—plane fundamentals. In general the stretches of the strained ring system are stiffer and the bends are more pliant than those of benzene. Bond length/bond strength correlations are not strictly followed; this is explicable in terms of pinelectron overlap populations. ACKNOWLEDGMENTS It would have been impossible to complete this thesis without the help of my advisor, Dr. G. E. Leroi. I am grateful to my guidance committee members, Dr. J. F. Harrison and Dr. D.‘ G. Nocera, for their generous understanding of the difficulties I encountered. I would also like to thank Dr. H. Hart for his helpful disCussions about this project. I wish to thank my wife for her patience and encouragement throughout my graduate work. Financial support from MSU and a fellowship from SUHID are gratefully acknowledged. ii TABLE OF CONTENTS LIST OF TABLES.. .......................... .. iii VLIST OF FIGURES .......................... ............. 1. Introduction..... ................... ............... 2. Experimental ................. . ..... ........... ..... 3. Normal Coordinate Analysis of o~Benzyne........... 3.1 Coordinates and Structural parameters.... ..... 3.2 Method of Calculation ............. ..... ........ 3.3 Results and Discussion ........................ A. Infplane vibrations.. ............. . ........ .... B. Dutwof~plane vibrations ............. . .......... Appendix 1 ............................................... Appendix 2........ ......................... ..... ...... Table l"-J M U! Page LIST OF TABLES The observed wavenumbers of o—benzyne in this work Symmetry coordinates for o-benzyne Internal coordinate force constants for the in—plane vibrations of o-benzyne Isotopic product rule for ofbenzyne Calculated and observed wavenumbers of in-plane vibrations of o-benzyne Force field for out—of—plane vibratios of owbenzyne Calculated and observed wavenumbers of infrared-active (B1) outuof—plane vibrations of o-benzyne iv Figure 1 i=3 I'_.-.| U! page 10*12 l4 17 18 LIST OF FIGURES Sample cell for matrix isolation experiment Spectra of phthalicanhydride and photolysed products Spectrum after annealed at 55 K Sample cell for matrix iso: -ion experiment Internal valence coordinates for owbenzyne IR its Raman Structural parameters for ofbenzyne (from reference 5) Relations between displaced and equilibrium vectors for a rocking mode 1. Introduction Benzyne, or bisdehydrobenzene (CéHa), is of great chemical interest because of its likely participation as a transient intermediate in organic reactions.1 Only the ortho isomer (1,2fdehydrobenzene) has been isolated for spectroscopic studyf'z‘4 although theoretical calculations of all three isomers at several levels of sophistication have been reported.”“9 There is now general agreement that the ortho isomer is the most stable, and that it has a singlet ground electronic state. A normal coordinate analysis of o- benzyne has been reported10 which is in moderately good agreement with the observed vibrational data. The first infrared spectrum of o-benzyne (hereafter simply termed benzyne) was reported by Chapman and coworkers in ‘1973.2 They photolyzed the precursor benzocyclobutenedione, isolated in an Ar matrix at 8 H, with UV light to obtain eight bands in the 400 — 1700 cm"1 range which were attributable to benzyne. One additional band (2085 cm"1 ) was found two years later by the same group,3 following short wavelength photolysis of 3— diazobenzofuranone under similiar matrix conditions. On the basis of those results, Laing and Berry proposed a structure and a set of force constants for benzyne.1° Badger’s rule was used to deduce the Cay symmetry geometry, and the complete vibrational spectra of the normal and perdeuterated molecules were calculated. Among the significant predictions was the expectation of two C~C ring stretching modes of A1 symmetry in the 2000 - 2500 cm“1 region for each isotopomer. Subsequently, Dunkin and McDonald obtained improved IR spectra of benzyne and tetradeuteriobenzyne by UV photolysis of phthalic anhydride and its perdeuterated analog, isolated in N2 matrices at 12 H.‘ The C¢H4 spectrum reported by the Chapman grout was generally confirmed, with the addition of a C—H stretch at 3088 cm“1 and the exception of a band previously observed at 1627 cm“1 . Eleven bands were reported for 8604; agreement between observed4 and predicted10 frequencies was reasonably good below 2000 cm"1, but rather poor in the critical higher wavenumber region. Reevaluation of the bensyne force field was suggested,4 and the normal coordinate analysis of reference 10 was criticized in an independent MNDO study by Dewar, et al. published in the same year.11 Indeed, fatal mistakes were found in ref. 10 by Nam and Leroilz: (1)an incorrect proposed geometry for ombenzyne ~ the sz hexagon was not properly closed; (2) illogical methodology in the calculation (e.g. arbitrary change in force constants from known models, inconsistent calculations of the 6 matrix); (3) inconsitencies in the isotopic product rule between calculated CaH4 and 56D4 vibrations. The physical data pertaining to benzyne are rather sparese in view of its importance and also the vibrational spectra are not yet complete . This thesis describes further experimental and theoretical work on owbenzyne; two additional bands of benzyne in mid-infrared region obtained by the photolysis of phthalic anhydride (reproduction of Dunkin and MacDonald’s work ) and a complete reanalysis of the normal coordinate calculation for this important molecule has been made. Measurement of Raman fundamentals was attempted unsuccessfuly. 2. Experimental Phthalic anhydride was isolated in Na matrices by simple sublimation into a Displex cryogenic refrigerator as shown in Figure 1. The ratio of phthalic anhydride to nitrogen gas could not be measured Jexactly, but it is believed to be higher than about 1:300. To determine this ratio pure phthalic anhydride was sublimed for 90 minute and deposited onto the cold Csl window. The weight of the substrate was measured before and after deposition. The weight increase gives the iuantity of phthalic anhydride deposited in the inert gas matrix for a compared deposition time. The flow of nitrogen gas was regulated at 2 mM per minute. In this manner matrix~to~solute ratio could be measured approximately. After recording the infrared spectrum of pure phthalic anhydride isolated in N2 matrix with a Bomem model DAB FT-IR, subsequently it was photolyzed with a 200 w mercury— Xenon arc lamp through a water filter . The spectrum of the photolyzed sample was then recorded under the same conditions as its precusor. After about 30 minute of photolysis the matrix began to develop a pale yellowish color matrix and the IR showed a remarkable increase in intensity at 2348 cm“1,the stretching frequency of carbondioxide, yet no other bands were appreciably enhanced. Frequency at 2140 cm“1, corresponding to the carbonmonoxide - the product of photolysis, was appeared visibly after an hour later. At this time the band at 2082 cm"1, corresponding to carbon-carbon triple bond stretch of o- benzyne, began to show- up. Figure 2 shows the spectra of phthalicanhydride/Nz matrix and its photolyzed products after 2 hours of irradiation. The bands due to benzyne are marked by a triangle at the top of the spectra. Identification of those bands made from comparison with the spectrum of the annealed sample (Figure 3), and with the values given by normal coordinate analysis (Tables 4, 6). In general all the bands reported by Dunkin and MacDonald were confirmed, with the addition of bands at 1355 and 1395 cm”1 which agree very well with the normal coordinate calculation. Among five bands over 2000 cm‘i, only two bands, at 2082 and 2090 cm“1 were reproducible for all experiments. Small peaks at 20o0, 2067 and 2110 cm“1 may be attributable to site splitting of the two strong bands at 2082 and 2090 cm‘l. The band at 2090 cm“1 may be due to a ketene species, which is one of the possible products of the photolysis.” To find the A2 frequencies of benzyne, a very crucial source of information to understand the character of C-C triple bond, Raman different type of Unfortunately, no extremely weak signals for 5 experiments were performed with two sample cell as shown in Figure 4. attemps were successful due to the matrix isolated species. Table 1. The observed wavenumbers o"henzyne waygnumger _Qfl# Ch** ** *%¥r 470 739 848 1038 1055 355 1395 1448 1596 2082 Reference Reference Section 472 743 847 1039 1056 t“...- 1448 1598 2084 469 735 849 1038 1053 1451 1607 2085 743 845 1039 1052 1360 1391 1450 1599 2092 in this work d"m”“---—-—_ ca1c*** . 482 QUARTZ WINDOW 1.0. ‘ m>zvrm amp... mom {Ear—x .m0r>._._oz :N MXVMEINZA .zmxa o>m _z_.m._. . . . _ u . mzcaamm m>§vrm IOromm do----—- O s 0 A -O------—-4- no. $22002 .. 050x <>OCCI oozzmoaom r-O—C—.—._.-.--P_--.--- Dav—.mx Im>o FIG. 2 SPECTRA OF PHTHALICANHYDRIDE AND ITS PHOTOLYZED PRODUCTS The bands due to o-bonzyne are marked by triangle while cross indicates the bands due to other products. 1 1:1 .mmm 38 11 l: (V (V oo . . .35 xx du- l3 .osm .aos .ofiaw .owma .oWaa _ -r- J:- ~1- x on ._.< omu bonds attached to the ith C~C~C—C frame. within the Bay point group, the twenty“ four fundamental vibrations of benzyne transform as follows: 901 + 402 + 381 + 882. Al and 8: species represent in-plane normal modes, whereas A: and B1 belong to out of plane vibrations; all of the normal modes are Raman—active, but only A1, 81 and .82 can be observed in the infrared. The symmetry coordinates of benzyne in terms of these four symmetry species are given in Table 2.1-3 163 Table 2 Symmetry coordinates for gfbenzyne ‘ Al. A2 31 52 1'. 'At 0t) I" 3-1—1 - ) I" n—"—( o ) 1'- -_.l_(t -t) 15 ,2- 1 s 14 ”HM 14 5*174 IS ”.1 s o 1 - l T -:-(t+c) 1‘ -—(Y-Y) 0.1 '.1 - 24 fi 2 4 23 '12- 2 3 ['23 3(12013) T24 th t4) 9 l - l - I 73 " ‘3 A15 ' 7—;(61’55) A15 ' 7545145) 514 ' #‘1"4’ 0» 1 - 1 - 1 T1% ' ‘6 A24 ' #52’54) A2.1 ' 72-46244) 523 ' 3‘32"!) 8‘ "i(8 ‘5) A 8 6 A- I—l-( -a) 14 - ,2— 1 4 3 3 16 ”fl 6 S. I —£{s 0: ) A a 6 A” . -$( - ) 23 ,2- 2 3 6 6 25 a“: s A. - gm «3 ) A' . 1 2 16 l 6 34 -—(a3-a) If a 4 AT 3 l“: +0. ) 3. g .145 ’8' J 25 5 2 S 14 a} l 4 0 l 4* l A.14 ' Equz) B23 ' *{32‘533 -—:—.a_.__._ .- 17 FIG. 5 INTERNAL VALENCE COORDINATES FOR O-BENZYNE 18 6 1.2263. 1 ‘j127.2° @895 0 1.08013. 5 )1105 2 1-1, 122.3 1.3898. 49 3 / 1.420Z\\ H3 H2 FIG. 6 STRUCTURAL PARAMETERS FOR O-BENZYNE (FROM REFERENCE 6). The structural parameters utilized for the benzyne 8 matrix were taken from the careful review of the calculated geometries of all three isomers published by Noell and Newtong° the adopted values are shown in Figure 6. Although there have been numerous theoretical studies of benzyne before and since, the singlerdeterminant 4~318 extended basis geometry given in reference 6 was chosen as most reliable. Other reported structures provided improper ring closure,7 were predicated on the benzene hexagonal carbon skeleton,‘3 or did not specify the bond angles.” 3.2 Method of Calculation The normal coordinate analysis of benzyne was separated into two parts: the in—plane and out~of~plane vibrations. For the planar oscillations the modified valency force field chosen as a model for the in~plane vibrations of benzene by Duinker and Mills14 was first adopted. Although the benzene parameters are of course not directly applicable to benzyne, the rough calculation of the benzyne in~plane fundamentals from the force constants of Cbe and the geometry of C¢H4 enables one to identify which experimental frequencies reported by Dunkin and MacDonald4 are most likely attributable to in~plane vibrations. There are 17 in-plane modes (981, 882); however of 34 vibrations thus predicted for the two isotopomers studied in reference 4 only 14 2 C) observed bands could be readily assigned to inmplane motions. We therefore tried to minimize the number of force constants utilized in succeeding steps. Again the model force field suggested in reference 14 was chosen, but different force constants were admitted for each bond stretch and angle bend of the ring, consistent with the constraints of Csv symmetry. Interaction force constants were separated into two groups with respect to whether or not they involved the strained bond t2, and/or “2 or db (see Figure 1); further distinctions would be required in a detailed analysis. Even with these simplifications, 26 different internal coordinate force constants remain to be specified. First the 13~parameter force field of benzenewas assumed, although some of the force constants reported by Duinker and Mills14 (De, F103, 8) were altered to better fit the benzyne observed frequencies. From this initial force field (Table 3, last column) band assignments could be made after diagonalization of the Wilson GF matrix. The force constants were then refined to provide a best least-squares fit of the experimental and calculated frequencies, according to an extensively modified computer program (see Appendices) originally written by the Shimanouchi group.15 The definitions of the in~plane force constants in terms of the internal coordinates and their final values are given in Table 3. internal coordinate force constantsa Table 3. for the in-pianc vibrations of gfbcnzyne' ForcafConstant Definitionb Final Valuec Initial valued 01 2,6,. 7.790 (0.144) 7.015 02 czcz 6.569 (0.114) 7.015 03 :32, 6.677 (0.112) 7.015 06 2626 15.950 (0.105) 14.0000 11.0 t1t£° (126) 0.660 (0.062) 0.551 a. 2,2: (ifié) -0.450 (0.050) -o.551 dp I :£619.(126) 0.147 (0.227), 0.551 a; t6t1° 0.255 (0.060) 0.551 a; ‘6F1' -0.100 (0.271) - -0.s51 ‘2 266,9' 0.125 (0.294) 0.551 10 cia:(aga1 or “61 0.551 (0.071) 0.226 ‘3 tin (6-6,. or '6) 0.026. (0.126) 0.226 1; 66¢? 0.154 (0.111) 0.226 50 216° 0.505 (0.015) 0.510 e s1:i 5.155 (0.019) 5.125 2 ‘1“141 -0.244 (0.157) -0.009 2, 31¢, 0.708 (0.045) 0.800' 52 02“: 0.290 (0.074) 0.500~ 53 53a: 0.595 (0.019) 0.950° f0 gin: (121 or 6) -0.052 (0.015) -0.095 t; a,a,° (1-1 or 6) .0.165 (0.010) -0.098 no “15° 0.025 (0.011) 0.065 0 gig, 0.752 (0.055) 1.000- (continued) ”1)"? 2.5:. Table 3. (continued) Force Constant Definitionb Final'Valuec Initial Valued to 8,0,o 0.021 (0.056) 0.020 0. 8181' -0.050 (0.056) -0.022 p _ ‘ _ 0,, 01101 0.025 (0.054) 0.052 astretching force constants - ndyne/X stretching-bending interactions - ndyne/rad bending force constants - ndyne.K/rad2 bDefinitions xix1°5 xixi. , x. xi? indicate the interaction force constants between coordinates x1 and its ortho or neta or para position. clhe values.¢iven in parentheses are dispersions of the final values, given in the sane units. dInitial values from reference 13, except the.force constants indicated by ‘. ('1? Six experimental frequencies remained to be assigned, three each for O‘CaH4 and o-CaDa.4 Their values satisfy the isotopic product rule for the infrared~ and Raman* active 81 out~of~plane vibratins within 0.4%. Table 4 summarizes the isotopic product rule expectations .for the symmetry representations of benzyne, as well as the values according to the assignments of reference 10 and our assignment of the B; vibrations in the experimental spectra. The constraints method16 for the F matrix was 'then utilized to determine a mathematically correct (although not necessarily unique) force field for the B; representation. A 8 matrix can be written in diagonal form by means of a similarity transformation 14133 = T (1) whereupon the F matrix can be estimated by the following equation F = {ATT7§;"1 C‘1I\’E;1 (AT1’2)*1, (2) where C is any orthogonal constraint matrix for F and/\.is the eigenvalue matrix of the experimentally observed frequencies. For a group with n degrees of internal freedom the F matrix contains n(n+1)/2 elements, and the C matrix depends on n(n-1)/2 independent parameters. The F matrix constraints are determined by the choice of the C matrix parameters, for which several methods have been proposed.16 we chose to set C=E, the identity matrix, which corresponds .,4_ .1"... .a~ accouowou no «auxnuca ouacavuooo aaaua: on» xn vouuuucou nouu:o:¢ouu sauna .v oocououou scum a .o oucououou uo xuuoaoou uuoauouoosu on» scum .N ouauam cu =o>uu nuouoe«uaq «aunuusuun ogu aoum vouu~=u~ao oaua>u -o--- -4--- o~o.n w” 1* .~.2~N Anna: .vm3.... ems Na 33.... :3 o~3 m~3 v~3 2:... on»; 2»; TL Team”. .2 a...“ :vLIrJI an H.....Ou es l.... .. s 3. .Ln... .. o.u~au m.~umxm nousuosuum rounnoumxm couuuuconoumox oaun> onxucoanm now can» unavoum camouonn 4? «Anne I") L7: .IL. s... to the assumption that the normal coordinates are defined in PUFEly kinematic terms.1e There are four symmetry coordinates in the B. group, while only three vibrational frequencies are allowed. In order to use equation (2 the redundancy was eliminated by use of the transformation U matrix, which has the following properties:17 A- UU = 1 (3); UR = S (4); UGJJ = [3... <5); URI? = F- (.5). Here R and subscript r represent the coordinate system which has redundancy and matrices which are defined in R coordinates, respectively; B and subscript s represent the coordinate system without redundancy and matrices which are defined in the S coordinate, respectively. From permutations of the three experimental E. frequencies for CbH4 six possible trial force fields were obtained. These force fields were substituted in turn into the equation for CbD4: GFL = LA. (7) CL = (AT1/2)C (8)] and their eigenvalues were compared to the E1 experimental frequencies for the perdeuterated species. One of the permutations predicted each CaD4 fundamental within 25 cm"1 of the observed value, without any adjustments. That particular force field was chosen as an approximate solution for the B1 vibrations, and was refined by least—squares ”'5 4.53 adjustment. The outmof~plane force constants generated by :2." this procedure are listed in Table a. 3.3 Results and Discussion A. ln~plane vibrations The infplane (A1, 82) vibrational fundamentals predicted for o—C6H4 and obeDq by the force field given in the third column of Table 3 are listed in Table 6, where they are compared to tie experimental results.2*4 Agreement between observed and calculated wavenumbers is very good (within 2%), although a definitive test of the force field cannot be made until additional bands are experimentally observed. The refined force constants (Table 3) indicate that in general the ring stretching motions become stiffer, and the ring bending motions more pliant, in comparison with typical aromatic systems.15 This is in good agreement with theoretical expectation for a strained ring system,19 here due to the strong, short Ce—C1 bond (t6 in Figure 5). Unlike the previous normal coordinate analysis,1° only one benzyne ring stretching vibration above 2000 cm“1 is calculated in this work [Table 5: 2094 cm—1 (C6H4), 2084 cm"1 (CaD4)]. The MNDD study also predicted only one such mode.11 Inspection of the force constant potential energy "“I .- .. p] .8— Calculctcd and observed wavcnunbcrs (cn'l) of ln-plane vibrations Table 5 of 3-bcnzync 2:56“4 Cclc. Obs.a Atb P.E.D.c Assignment 3031 son: .o.23 $3362 sf‘ss Al cu stretch 3074 SI‘7S $5324 82 CH stretch 3059 51,63 s;337 Al ca stretch 3050 $2376 $1424 32 cu stretch 2092 2084(2085) -o.ss That 1:517 Al ring stretch 1657 (1627) 13,41 1:543 32 ring stretch 1599 1598(1607) -o.oe 31,54 82328 A1 cu bending 1549 ”$316 1354: 32 on bond o ring stretch O ISLO 1&466 {334‘ A, ring stretch 1450 1443(1451) -o.14 a{‘37 1;,17 32 cu bend o ring stretch 1391 . 32376 31‘37 A1 CH-bending 1360 TE440 TI539 82 ring stretch 1245 7:552 7319 Al ring stretch 1052 1056(1053) .o.2s 7346 TISZQ A1 ring stretch 339 A1653 A3413 3, c-c-c bend 452 472(469) -2.12 A3475 A1621 3, c-c-c bend O O 395 A2538 A3418 A1 c-c-c bend (continued) Table 5 (continued) 2&3 Cs1c. 0bs.a 43° P.E.o.° Assignment 2296 2293 -0.13 85348 sI‘As Al CD strctch 2206 si471‘53323 02 co stretch 2257 5:443 5534a A1 co stretch '2237 $3375 si‘zs 02 c0 stretch 2034 2093 .0.43 7683 1:514 Al ring stretch 1640 11554 73447 32 ring stretch 1403 1483 0.00 1347a 7345 A1 ring stretch 1360 13,51 T;537 .32 ring stretch 1291 129; .0.1s 1:543 7316 Al ring stretch 1107 1103 +0.01 33361 31435 02 to bend 1102 0i447 33332 A, c0 bend 1029 1029 0.00 8:466 03337 32 c0 bend 1011 1341 T;521 Al ring stretch 1002 85369 Bi44$ Al to bend 322 822 0.00 AibSZ Ag413 32 c-c-c bend 462 471 +1.91 Ag47s AI6ZO 32 c-c-c bend 331 A5537 A;418 Al c-c-c bend a . From reference 4; values in parentheses are from references 2 bPercent deviation: 100 (obs-calc)/obs. cPotential energy distribution, with major symmetry coordinate in percent. and 3. contributions, 29 distribution shows that this band is dependent primarily on the ta bond stretching torce constant. De. The magnitude ot this Force constant. Da = 13.95 mdyne/A, indicates that the CémCl bond is very nearly triple bond in character. It is slightly lower than the theoretically calculated value (1&.9 mdyne/A), consistent with the trend exhibited by symmetric CwC stretching force constants For other unsaturated systems.19 The experimentally observed trequencies can thus be cited as evidence of the strained ring structure oF benzyne, as first claimed by Chapman, et al.;3 their inverted positions4 [Table 5: 2084 cm"1 (CbH4), 2093 cm“1 (CbDa)J may reflect interaction between t6 and the C-D displacements (51, 54, 61, e4), which were not taken into consideration in these calculations. In the theoretical structure of benzyneé (Figure 2) the adjacent bond lengths, t1 and t; as well as t4 and t5, are identical and close in value to ta; they differ little from the benzene C—C bond length. Yet the force constants ditfer markedly from «one another, alternating in strength as one goes around the ring. This departure from the bond length/ bond strength (Badger’s rule) correlation is explicable in terms ot the theoretical electron population analysis, which shows that the awcontribution remains tairly constant, but' that the c—electron overlap alternates stronglyé'lq in the strained ring system. Tit") B. Dut~ofrplane Vibrations In the absence of data for the A: vibrations, which are Hanan-active only, the out~of~plane Vibrational potential for benzyne is necessarily incomplete. The frequencies predicted for the B; out~of~plane modes by the force field given in TAble 4 are compared to the observed frequencies in Table 7. The agreement (within 0.4%) is excellent. As is well known, although the B; force field generated by the procedure given in section 3.2 is mathematically correct, it is not unique.20 However, one can apply some general criteria to check its likely applicability. For example, one Fl expects the C~H (or —D> out~of~plane wagging force constants to be little changed from benzene. If the J1J4 interaction force constant is assumed to be negligible (it is actually a very small negative number), then the benzyne -h C~H wagging orce constant is 0.49 mdyne A/*ad2. This value is close to the reported experimental and theoretical values for benzn.r.=:ne,"*‘1 0.44"0.45 mdyne A/radz. Unfortunately, the torsional force constants cannot be similarly compared, since they are not separable in the 8; symmetry block alone. The individual torsional force constants (8’s) can be estimated only after the Ag, Raman~ active out~of~plane vibrations are available. Moreover, the B1 block potential constants do not include the torsion about the ta bond, which is most critical for the 31 Table 6. Force Field for out-of-plane vibrations of g-benzyne Forcetonstanta ' Valueb £7171 + £7174 0.493 fylyz + fYIYS ' -0.018 fY151 - £7155 ' ' -0.333 £7151l- £¥1§4. ' 0.33s £Y2Y2 + £Y2Y3 0.317 £Y25~1 - £7255 ' i 0.212 £7252 - ff264 -0.o13 £5151 - £5i55 . ' 0.341 £6162 - £6164 -0.658 £6262 - £6264 0.593 aUnits: mdyne K/rad2 bDispersions are not included since this force field was transformed directly from the Fr matrix. -r r3 .3 .0 '...' .1— Table 7 Calculated and observed watenunbers (ca ) of infrared-active ('1’ out-of-plane vibrations of o-benzyne Cale. 00s.‘ M" P.3.0.° 7 Assignment “1039 1039(1033) 0.00 3253 r 33 cu wag 3 ring torsion 84$ 847(849) 00.24 P2353 6:523 CH tag 9 ring torsion 2306114 743 743035) 0.00 1'l ‘ 122 cu wag 788 792 00.50 hiszs 62412 Ring torsion 730 730 0.00 PL?! 1‘; 351 CD wag . 9:37.604 616 616 0.00 r, 411713327 c0 wag ‘Fron reference 4; values in parentheses_frou reference 2. bPercent deviation: 100 (obs-calc)/obs. cPotential energy distribution, with Iajor symmetry coordinate contributions, in percent. “-1": ’n-. .w. calculation of the strained ring structure of benzyne. On the basis of frequency shifts of bands attributed to benzyne out~of~plane deformations from the positions of corresponding bands in benzenoid systems, Chapman, et al.2 concluded that benzyne is less rigid with respect to out—of— plane distortion. The bands used in that comparison were not specified, and we feel that it is therefore more prudent to postpone discussion of the flexibility of the benzyne ring until the A; vibrations are observed. Then the torsional force constants can be compared to other aromatic systems. In addition, the results can be used to test Anno’s criteria,22 developed by Hydd,23 relating the torsional force constant to the product of the c bond order and the carbon 2pc orbital overlap integral. APPEND I CES Appendix 1 Computer program for the calculation of the torsional coordinate s vector according to Hildebrandt’s method. More than one terminal atom, m atoms on j and n atoms on k, constitute m x n torsional motions around one axis jfk. Contributions from all these motions to axis j~k can be taken into account by taking a normalized linear combinations of the m x n four atom configurations as was used by Snyder and Schachtschneider.24 Hildebrandt, however, proved computationally that this method of normalization does not give a correct reduced moment of inertia from the inverted S matrix and proposed new formulas for the calculation of the torsional coordinate s vector.”=5 This was confirmed algebraically by Nilliams.26 Since Shimanouchi’s program also uses the same method as Snyder and Schachtschneider, the calculation of the torsional 5 vector had to be modified according to Hildebrandt's method of normalization. Modification was made without changing the format of the original program. For one torsional axis this program 35 distinguishes the type of terminal atoms and calculates them separately by calling subroutines TORSI and TDRSE. Source programs are listed on the following pages. For more complete descriptions of the mathmatical treatment, see reference 25 and 26. (10(1(}0(1 36 THIS TORSIONAL 3 MATRIX ELEMENTS CALCULATION uAs HOOIFIEO COMPLETELY ACCORDING TO HILOEBRANO'S NORMALIZATION. NEH SUBROUTINES TORSl AND TORSZ uan CREATED FOR THIS PART INSTEAD OF OLD suanour1xe ronsn. FOR COMPLETE DISCRIPTION OF PROGRAHsSEE THE REF. CAN.J.CHEfl 33.1239.197a AND NOTE OF AUTHOR H-H NAH.‘ 337 IF (MOTOR .50. 01 GO TO 363 00 332 HTOR - 1. NOTOR NI - NITR(HTOR) NL - NLTR(HTOR) T1-1.0/N1 TL-i.O/NL JA - JTOR(HTOR) KA a KTOR=OATBcTL 330 CONTINUE 361 CONTINUE NEB(NJ+l) = MED e x1e3 + NLn3 + 3 n3 = NJ + 1 332 CONTINUE oDECK TORS SUBROUTINE TORSI THIS SUDROUTINE COMPUTES THE B HATIX ELEHENTS FOR THE I‘TYPE TORSION ACCORDING TO HILDEDRAND’S NORMALIZINO SCHEME. THIS HAS CREATED BY HAK-HYUN NAN 0.1 4/3/84. TO UNDERSTAND THIS PROGRANe SEE REF. J. HOL. SPEC 440 599.1972 AND DESCRIPTION OF PROGRAM NRITTEN BY H-H NAM. NHICH IS IN DR. LEROI’S GROUP. It END ATOHS NHICH IS ON CENTRAL ATOM J. DIMENSION RIJ‘3’0RJK(3’0 EIJ(3)o Ev .K(3,OX(5033’9NCB(603’ BEL‘boO). +CI(3 CONNON NOAT. Xe NCO. BEL. IA: JA: KA. LA. JOKER IF(IA. GT. NOAT OR. JA .OT. NOAT .OR. KA .OT. NOAT) GO TO 380 DIJSOBO. O DJKSG'0.0 DO I70 "'1: 3 RIJ(H)-X(N.JA)-X(N.IA) RJK(N)IX(N:KAQ-X(N.JA) DIJSG=DIJSQ+RIJ(H)¢&2 170 DJKSG=DJKSG+RJK(N)9§2 DIJ= SGRT(DIJSG) DJK=SGRT(DJKSO) COSJ=O. 0 DO 240 Hal. 8 EIJ(N)=RIJ(H)IDIJ EJK(N)=RJK(N)/DJK 240 COSJ=COSJ-EIJ(H)‘EJK(H) IF(ABS(COSJ) .GT. 1.0) GO TO 400 SINJ=SORT(1.0-COSJI§2) C1(1)=EIJ(2)*EJK(3)-EIJ(3)*EJK(2) Cl(2)=EIJ(3)*EJK(1)-EIJ(11*EJK(3) C1(3)=EIJ(1)*EJK(2)-EIJ(2)IEJK(1) DO 360 "=1. 3 - NCB(1. H)=(IA-l)*3+fi NCB(2.H)=(JA-l)o3+fl NCB(3.N)=(KA-l)§3+fl BEL(1.N)=-Cl(N)/(DIJ*SINJI*2) BEL(2.M)= C1(H)*(DJK-DIJ*COSJ)/(DIJ*DJK*SINJ**2) BEL(3.N)8 61¢“)!COSJ/(DJK*SINJ**2) 360 CONTINUE GO TO 420 380 JOKER'l , GO TO 420 400 JOKER=2 420 RETURN END 000000 38 . SUBROUTINE TOR52 C THIS SUBROUTINE COMPUTES THE B MATRIX ELEMENTS OF J-TYPE C TORSION. L STANDS FOR THE END ATOM ON J. DIMENSION RLK(3).RKJ(3) ELK(O). EKJ(3) NCD(6.8). BEL(6.3). +X(3.30).C2(3) COMMON NOAT:X:NCB.BEL.IAoJAoKAoLATJOKEN IF(JA .OT. NOAT .OR. KA .GT. NOAT .OR. LA . ' DLKSG=0.0 DKJSO=0.0 DO 170 Na1. 3 RLK(M)=X(M.KA)-X(M.LA) RKJ(H)=X(M.JA)-Xe32 DLK=SORT 1 (r; — r:cos¢;)e; + (r2 - rscos¢1)ez E ' 71r25in¢1 (r2 ~ racos¢5)ez + (r; — rzcos¢2)e31 F2F35IF¢2 J .1. (A-14) In (A~14), each coefficient corresponds to the s vectors for the particular atom. Thus: S; a: cos¢ses - e: risin¢s 82 :: -sin¢se1 + sin(¢1 - ¢2)e2 + sin¢1e3 rzsi n¢ssi nfiz 5:: :2 COE¢223 - 2: So 2: "( 31 + 52 + S; ) (9-15) The Shimanouchi's normal coordinate program was extended to include treatment of the rocking coordinates by this formulas according to subroutine ROCKM, for which the source code follows. 363 366 370 376 377 IF(NOROC .E0. 00 376 Ndsl. IA- IROC