Haque, W

Singh, A N

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Indian J. Phy,s. 5IB. 218-222 (1977)Use of the INDO method in spectroscopy : alkenesA. N. S ingh and W. HaqueDepartment o f  Physics, Muf^adh University, Bodh Goya, Bihar 1. [ ntro o uctio nThe CNDO method as developed by Poplc and coworkers^ results in a complete intenningling of cr and ti levels in benzenoid hydrocarbons-. To overcome this difliculty l>cl Bene and JafTe used different bonding parameters for and cr,o- interactions^. Jug suggests the use of different orbital exponents for cr and tc orbitals*^As these modifications prejudice the preconceived ideas regarding cr-T: separability, Salahub and Sandorfy opine that a  and t: clctirons should be Ircaitcd on equal footing in order to distinguish tt, and cr*<—crtransitions from one another in unsaluraled molecules'*. So, they use the same bo»nding parameters 3 “ab for both and cr,tr inleiactions in theirvalence shell (CNDO and INDO) and extended basis set (RCND O) calculations.Before the suitability of these methods to interpret the electronic spectra of simple molecules is CsStablished. we require an extensive application of these methods. The present paper is one in this direction,Wc have also observed that the RCNDO mclhod, in its original para- metri/ation, gives siomewhat less satisfactory description of tl^ e ground state as well as the triplet excited stale*’. Wc have, therefore, changed the bonding parameters slightly and have also considered the atomic exchange integrals.2. T heoryThe elements of the INDO HF (Hartee-Fock) matrix FAFpp == Upp + 2  P y y [ ( p p l y y )  —  i i )  i p y l p y ) ]  + S  (P.m — Z,, p on aIV-'“■ Ppq f(«) (PA/PQ) --- (4) (pP/Q^l)]»Fp,, -  Sp and(i)  Prq "^ AH»p q both on A p on A, q on BUpp = ( i )  ( I ,  + A„ ) -  [Z* -  (k )] Y,A. N. Singh and W. HaqueThe F matrix under the RANDO approximations'’ areFp.i ”  Upp + s ’ p^  ^ [(pp/’Y'V) —  ( i  (p7/pr)]y2 1 9+ 2n. An,A7^ n,n,A  A1r "+ 21L n. Pn,Bn.jn B~ Pp(1 [ (3/2) (pq/pq) -  (J)  (pp/qq) 1. P9^ =q both on An,F,„, = e“n,n,j S,,y — (J) pp„ 7n, n, , p on An, and q on Bn,A H  A  Bwhere the symbol pan A stands for atomic orbital Op on atom A and belongs n lto the principal quantum number ni, andUp,, -  (4) ( I . + A, ) -  (Z, -  1) 7n. n, - -  ( i)  7n,n.A A  A  Awhere the symbols have their usual meanings'.Using such F matrices the Hartrcc- Fock-Rcx>lhaan equation^ *'.FC =r eSC'were first solved and the excitalion energies were computed in the so-called virtual orbital approximation. 1'his was followed by a configuialion inicractioa procedure for the lowest thirty singly excited configurations. 7'he details r f the procedure are given elsewhere^.3. R e su i.ts and DisrnssioNWe sumimerise the results of our INIX) calculations on tlx; S-S-transitions in alkenes in table 1. The lowest singlel-singlet transitions in ethylene is that is fallowed by The lowest S-S ti*ansition of the alkyiderivataves of ethylene is also found to be Tt-xr*. R IN D O  and R C N D O  calculations^* on ethylene indicate that these are valence-shell transitioTiS7A2 2 0 INDO method in spectroscopyTable 1. Singlet—Singlet transitions in alkenesMolecule Experimental Values INDO-ClA'^ o-o(ev)AEmax(ev)f AE f sym. Type7.6a 7.58b 0 3a 7.76“ 0.008.7.SC 7 la 8.27a 0.00 or—>71*8%f S) 8 46a 0.00 B;.u 71—>or’^(Rn-2)9.62c 7.45a 0  ^la 0 lOa 0.14 Bxu TC—>TC*16.72b 7.15b 0 32b 6.9^ ) 0.00 TT—XT’"(R ^N ) (V<_N)7.1d 7.84 0.01 A" Tt—X7*8,24*1 8.07 0.00 A"8.82d 8 27 0.01 A" 7:—>0**8.37 0.15 A' 1 7t-»7l’^i O'—XT*, 6.62® 7.04f 0 36* 6.97 0.01 A'^ 7C—XT*(R<-N) (V^N )0.36 111 0 05 A" 7C--XT*7 94 0.00 A" or—>71:*8.28 0.02 A" Tt-^ CT*8.34 0.08 A' f TT-^ TT*1 o-~>cr*6,03b.e.« 7.10b 0.59® 6 48 0.00 A. Tt-^a*(R<_N) (V4_N)7.7b 6.95 0 05 Bo 7t—>cr*1.52 O.Ol B._. t: - » o'*7.61 0.29 B,’ i TC—>Tt*1 CT—>cr*- 6.57h 7 01b 0 38 7.08 0.01 7U—XJ"(R4-.N) (V<-N)7.92 0.06 A" 7t—X T8.17 0.00 A" O'—>7t8.23 0.32 A' / 0* -> 0 '1 O'—»7I: Ref. 8 ; c :  Ref. 9 : d : Ref. 10; e : Ref. 11 ; f : Ref. 12; g : Ref. 13;rH.=r.CH2(C, )Cis-CHCH,,(C, )h : Ref. 14.A . N . Singh an d  W . H aq u e 2 2 1Transiftion t:— in alkenes usually undergoes rcd-shifl that is accompanied by a decrease in intensity. However, we also find a blue-shift in the case of 1-pentene and an increase in intensity for cis-2- bulcne. The cnplanation of these effects is as follows :— Transitions cr—>ar* generall appear later than transitions. The former transitions, arc associated with larger intensity as compared to the latter. Also the latter transitions arc usually miA(."d with with the former as a result of configuration interactions.The singlet-triplet transitions as obtained by JNDO and RINDO methods are summarised in table 2. The first two transitions are found to consist essentially of a single configuration and llie S-T splitting decreases upov alkylation.Table 2. Singlet— Triplet transitions in alkenesMolecule “Expcrimtntal Theoretical TypeAE S-Tsplitting MetluxlHA S-1splittingsymmetryC H .=C H o 4 6a 3.f)a INDO-C'I 5 1 1 ^ 1 33 7^1—>7r*)D , i .  ) 6.6C 1.42a 6.53b 1 2^ (Tu->cr*)R lN D O -n 4.60 35 32 1 4?7 64 1 V) t a’—>cr'*‘)C R -C H C H ^ 2.%<i INIX)-CT 5 2 84 A '(C ) 1.23a 5 S5 1 0^ A" (7t-»cr*)7 0^) 07S A " (t:—>C7*)CH.^=CHC2Hr, INOO-CI 5 7S 2 59 A ' (Tr->7t:*)(C. ) 5 97 1 (M) A" (tt:—>cr2)7 0^ 0 72 A " Ctc—>cr*)Cis- 3.39« INDO-Cl 5 16 245 Hi (ti:—»7r*)0 .70a 5 66 0 82 A . (ti:—XT*)(C2„ ) 6 57 0 B.» (tt:—XT*)INDO-Cl 5 % 111 A' (■n—>Tt*)6 15 0 93 A"1A9 0.73 A " (7t—> ff* )a : Ref. 15 ; b . Ref. 7 c : Ref. 9 ; d : Ref. 16 ; c : Ref.222 IN D O  m ethod in spectroscopyWc remark that the entended basis set calculations ( R IN D O  &  R C N D O )  describe the excited stales of ethylene and higher alkenes belter than valence basis ( IN IX ) )  calculaion However, the TN D O  calculation, would assume better rcic in interpreting the spectra of larger molecules where the formet cannot simply be carried out.RKFH<RhN('ESI Popic, 1 A. & Beveridge, D. L , Approximate Molecular Orhital Theory, New York :2. Del Bone. & Jaffe. H-1I„ J. Chem. Phys. 48, 1807. 4050 (1968).3 Jug K., Theorot C'hini, Ada, 14, 91 (1%9)4. Salahi'b, D. R. & Sandorfy. ( ’., Thcoret. Chem. Acta. 20, 227 (1971)..5 Haque, W', Ph.D. Thesis, Magadh University, Bcnlh-Claya (India), 1974.6. Roothan. C. C. J., Rev. Mod. Phy.s., 23, 69 (151).7. Salaiiiib, D. R., lech Report TC 7007 ■ 19728. Salahub, D. R., Tech Report TC 7002 Svwi-Empiruul AU-Vakttce-hlectron SCI- LCAO-MO-CT calculations of Electronic Spectra., Laboratory dc spc*ctroscop e Molccu'.aire ct chimi Theorique, Universiie dc Montreal, Quebec, Canada : l ‘)72.9. ITubin-Fianskin. M. J , & J E. collin, Int. J. Mass Spcctrom. Ion. Phys., 5, 163 (1970) 10 Herzberg (J., Molecular Spectra and Molecular Structure III. E.leclroni( Spectra andEdectronit Structure of Polyatomic Molecules, Princeton- New Jersey- Toronlo- Mclbiiurne- London : D Van Nosirand : I9S7II Gtay. J. 1.. & I W Pickett, ibid. 22, .W (2954),12. Sampson, J.A R., F.F Marmo & K Watanaba, ibid, 36, 783 (196i2)13. Me iJi.innid, R.. Ibid, 50, 2.328 (%9)14. Seinenow, D„ A. J. Harn.son & E. P. carr, J Chem. Phys.. 22, 638 (.954)'5. Merer, A J., & R. S Mulliken. Chem Rev 69, 639, (]%9)Ih Itoh, M., & R. S. Mulliken, J Phys. Chem. 73, 4332 (1%9).17. Scmeluk, G P & Stevens. R D S , Can. J C'hcm. 49, 2452 (1971) ,

Use of the INDO Method in Spectroscopy : Alkenes

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Use of the INDO Method in Spectroscopy : Alkenes

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