Prasad, R S

Singh, A K

IACS Institutional Repository

Iihd u m J . Phys. 7 6 B ( 2 ) ,  1 7 1 -1 7 6  (2 0 0 2 )U P  Ban intcmattonal journalMRINDO/S calculation on the electronic spectra of N2H2 isomersR S Prasad* fDepartment of Physics, Magadh University, Bodh-(|Bva-824 234, Bihar, Indiaand iA K SinghDepartment of Physics, D K College, Dumraoii, Buxar, Bihar, India E-mail : rsp phys( f^ediffmail*ieomReceived 26 September 2001, accepted 18 January 2002Abstract MRINDO/S calculations augmented by singly excited configuration interaction were performed on the isomers of N:l l2- Electronic configurations, ionization potentials and electronic spectra of the isomers arc presented The importance of outer (Rydberg) orbitals is stressed and It IS found that a number of singlet-singlet transitions of the isomers lead to excited states with considerable Rydberg charactersKeywords isomers, ionization potentials, electronic spectraPACS Nos. 31 15 Ne, 33.15 Ry, 33 20 Eg1. IntroductionDiazine (N2H2) has been the subject of numerous experimental and theoretical investigations f 1-5]. Its ground state is the planar singlet species which has a trans structure of CS/, symmetry. Trans-diazine is well characterized experimentally. Two other low-lying stable singlet species have been identified by theoretical studies; these are also planar and both have C2v symmetry. One is cis-diazine, while the second is iso-diazine (or amino nitrene). A very limited amount of experimental information is available for cis- and iso-diazine derived from gas phase and/or matrix isolation studies. Whitelegg and Woolley [5] have reported ionization potentials and vibrational frequencies spectra of these isomers. But there is scarcity of literature regarding their electronic spectra. This led us to consider these species. Here, we report the calculated electronic spectra of the isomers of diazine : trans-diazine, cis-diazine and iso-diazine. The optimized geometrical parameters, bond lengths in Angstrom and bond angles in degree, of the isomers were taken from W hitelegg and 'Voolley [5].Corresponding Author2. Outline of the workIn the present method, MRlNDO/S, we added H2s, H2p, N3j  and H3/7 Slater atomic orbitals to the basis. The details of the methodology have been given by Prasad and Rai [6].In the present calculation, the energy of the ground state was first minimized in the usual way. The configuration interaction was applied including the lowest thirty singly excited configurations for both the singlets and triplets. Jacobi diagonalization iterations were continued until all off- diagonai elements were smaller than 10"  ^ a.u. and the SCF (self-consistent field) procedure was terminated when all eigenvalues agreed within 10'^ a.u. between two successive iterations.3. ResultsTable 1 contains the Koopmans [7] theorem ionization potentials and the corresponding orbital symmetres. The ab initio value for IP'S (ionization potentials) and symmetry of orbitals are given in the first columns. These were taken from Whitelegg and Woolley fSj.O 2002 lACSTabic I. The lowest ionization potentials of N2H2 isomers (eV)172 R S  Prasad and A K SinghMolecule(symmetry)TraiiS’diazine(C2h)Cis-diazine(C2v)Iso-diazinc(Cl.)ab miticPIP10.8010 889 58Sym of orbitalMRINDO/SiP1.05 12.81 15.91 16.13 25.26 37 0911 7312 82 13 14 19 25 24 04 37 04 10 45 12.84 14.77 18.65 24 78 36.75Sym. of orbitalOgQubu««byhjbxa\Q\bia\bihibia\a,Typecr/r,naaCTacrjT,nrr,nacrcrajnn,nCTyflcrcrcr«Rcf [5JTable 2 contains the lower singlet-singlet excitation energies, oscillator strengths, and symmetries of the excited states as computed in the approximation used by Prasad and Rai [6]. The last columns of Table 2 contain the percentage Rydberg characters of the states. The first columns of Table 2 contain experimental transition energies [8,9], Table 3 gives transition energies, symmetries of the excited states, and splitings of the five lowest singlet-triplet transitions of each species.The results are compared mostly with the ab initio values cited in Tables 1 and 2; otherwise proper references are noted.4. Discussion4 .1. C h a rg e  d is tr ib u tio n  a n d  c is -tra n s  b a rr ie r  :The net charge distribution in diazine isomers is shown in Figure 1. According to general chemical intution, the higher the positive charge on H in a compound, the higher is its acidic character. So, more easily it may be replaced by metal. The higher the electron density on N, the higher is its donor character and hence the higher is its basic character. Due to increase in negative charge density on N, its size is slightly increased. If positive charge is developed on N, its donorMolecule(Symmetry)Experimental*''* MRlNDO/S % Rydberg characterTransitionenergyType of transitionTransitionenergy/ Syn of excited stateType of transitionH N TotalTrans-diaztne 3.54 1,97 0.000 B, cr- /^t* 0 0 0(Cih) 6.32 5.61 0.081 Bu 3 588.68 6.90 0.000 Bs a^rc* 0 0 07.23 0.000 Au cj^n* 0 0 . 07.67 0.132 Bu (7^0* 3 6 97 83 0.000 '•s a-XTfi* 36 54 908.17 0.000 Bt n->a* 5 12 178.18 0.000 43 52 958.64 0.005 Bu 30 60 908.76 0.002 Bu a^ CTfi* 39 58 97Cts-diazine 2.92 0.000 Bi 0 0 0iC^) 3.83 0.000 Ai 0 0 05.78 0.101 Bi 1 1 27.41 0.041 4 | cr^cf 4 4 87.88 0.000 Ai n->cj* 3 4 78.38 0.042 Bi a^ CTjK* 32 39 718.87 O.OOl Bj 30 59 899.15 0.000 Bi 30 42 729.19 0.000 Ax o*-*<r** 23 72 959.49 0.000 A\ 31 63 94MRINDO/S ccdculation on the electronic spectra of NfHj isomers 173Table 2. (Cont'd).Experimental*'^ MRINDO/S % Rydberg characterMolecule(Symmetry)TransitionenergyType of transitionTransitionenergy/  Syn. of excited stateType of transitionH N TotalIso-diazine(^ 2v)1.24 0.000 0 0 04.34 0.005 1 1 26.25 0.075 1 A, 0 0 06.59 0.000f Bi0 0 06.99 0.000 0 1 17.35 0.000 1 Bj 26 74 1007.96 0.000 ; *2 n-XX/i* 28 71 998.09 0.000 ' Ai 22 78 1008.13 0.000 A i 18 82 1008.40 0.000 Bi 31 68 99•Ref [8). *»Ref [9Jcharacter is d im in ish ed  a n d  h en ce  its b a s ic  ch a rac te r is decreased. O n th is  g ro u n d , th e  H  a tom s in  iso -d iaz ine  seem  to be m ore ac id ic  th an  in  tran s- an d  c is -d iaz ine . T h e  n itrogen  atom in iso -d iazine, a ttach ed  to  h y d ro g en  a tom s, lo ses its donor character, w h ile  th e  o th e r n itro g en  a tom  g e ts  m uch  more donor cha rac te r. In  tran s- an d  c is -d iaz in e , th e  b o n d in g  pair o f  e lec trons b e tw een  N  and  H  g e ts  sh ifted  to w ard s  N  making it sligh tly  n eg a tiv e ly  ch arg ed .I able 3. The five lowest singlet-triplet transitions in N2H2 isomers. All energies arc in cV.MRlNDO/S% Rydberg characterMolecule(symmetry)TransitionenergyS-TsplitSym. ofexcitedstateType of transitionH N ToUP  1 rans-diazinc 0.95 1.02 cr->ar* 0 0 01.80 3.87 0 0 0i 5.76 1.47 Au 0 0 0I 5.86 1.81 B. 7 13 201 6.37 0.53 B, 0 0 0m Cis-diazine 1.78 4.00 Bi rt —► /r* 0 0 01 1.89 1.03 By 0 0 01 2.79 1.04 Ai 0 0 0i 6.43 0.98 4\ 0 4 46.98 1.40 n-^<f 0 4 4Iso-diazinc 0.25 0.99 Ai 0 0 0(Cjv) 3.06 3.19 Ai 0 0 03.65 0.69 Bi 1 1 24.83 1.76 Bi n -^ i t 0 0 0— —5.29 1.70 Bt 0 1 1T'he com puted  the barrier h e i ^ tc is -tran s  b a rr ie r  is  a b o u t 2.21 eV , w hile  ca lc u la ted  a t th e  S C F  level o f  ab  in itioth eo ry  [5] is abou t 0 .1 1 h a rtree  ( -2 .9 7  eV ). T hus o u r ca lcu la tion  ag rees reasonab ly  w ith  th e  ab initio one.0.105-0.105trans-diaiine-0.105==:Nx0.094'H0.1050.094-0.094 =:N^-0.094ci»-diazma0.1180.1180.046.N =ifo-diaiitie-0.283:NFigure 1. The net charge distribution in diazines.4 .2 . Q u a n tu m  d e fe c t :T h e  en erg ies  o f  R ydberg  s ta tes, fo rm ed  by  ex ita tio n  o f  a  sing le  e lec tro n  to  a  R ydberg  o rb ita l can  b e  rep resen ted  in  a g ood  app ro x im atio n  by  a  R y d b erg  fo rm u la  tIO ]£ * ^ ____ —__■ ( " - 4 -w h ere  >4 is  th e  ion iza tion  p o ten tia l to w ard  w h ich  th e  se ries  co n v erg es a s  n  runs se ria lly  to  in fin ity , R  is th e  R y d b erg  constan t, an d  S  is ca lled  th e  qu an tu m  d efec t. F o r  m o lecu les174 R S Prasad and A K Singhbuilt-up from atoms of the first period, S  is small (^0.1) for states derived from nd electrons, somewhat larger (0.3-0.5) for np electrons and appreciably large (0.9-1.2) for ns electrons.4.3. Ionization potentials :The ab initio calculations predicted the following configurations for the stable singlet species :trans-diazine Og bu bu a^ "cis-diazine 0| 62 a\ aj b\iso-diazine : a\ a\ hi b\ a\Each of these orbitals is filled with two electrons. The present calculation predicts these configurations as follows.trans-diazine*>^2.hi.cis-diazineiso-diazineCl}flibuhiflia\hibuoifliCtub\'K>bi,bi.It is evident therefore that the present configurations are consistent with that of ah initio calculations except single reversal of states in trans- and iso-diazine. According to these configurations we infer that these species contain only one occupied s’MO associated with the orbital symmetries : a  ^ in trans-diazine and b\ in cis- and iso-diazine.The lowest occuped MO of these isomers is assigned an in-plane tj orbital. This is consistent with the ab initio calculation. In addition, the calculated Erst ionization potentials of the isomers are comparable with the ab initio prediction. The important aspect of the present calculation is that the second ionization potential of the isomers corresponds to the removal of an electron from a lone pair A-orbital. This ensures that the « -> transitions occurring in the spectra of these isomers must exhibit intensity. Such a situation is not found in higher azines : pentazine and isomers of s-triazine and j-tetrazine [6,11]. This aspect of the spectra will be discussed in succeeding section. We note that the first IP of the isomers follows the trendiso-diazine < trans-diazine < cis-diazine.This is again in accord with the ab initio calculation.4.4. Singlet excitations :(i) Trans-diazineThe n -¥  nP transitions cause weak bands in the visible or the near or the medium utraviolet; the overall energy region ranges from about 1.7 to 6.2 eV. We note only one « —> «* transition in trans-diazine at 5.67 eV. The overall symmetry of the state is B„ and hence it is electric dipole allowed with X and y  components of dipole moment vector. It has an oscillator strength of 0.081. The computed transition energy to n seems higher than experimental one [8].The n transition in pyridazine, pyrimidine and pyrazinc is observed [12] at 3.30, 3.85 and 3.82 eV with respective oscillator strength of0.0058,0.0069 and 0.01. The calculated [13] sequence of energy is 3.12, 4.01 and 3.53 eV whereas the sequence of oscillator strength is 0.016,0.015 and 0.014 In higher azines, s-triazine and s-tetrazine, weakly allowed nn* states have been predicted [6] while in pentazine and the isomers of i-triazine and s-tetrazine none of the n -> transitions exhibited intensity [6,11]. In this context the n -*  n* transition in trans-diazine seems to be more intense. The spectrum of trans-diazine does not comprise n jf> transition, for its configuration contains only one originating (occupied) n  MO which is assigned a lone pair MO. Trombetti [8] argued on his experimental observation that ;r r^* in trans-diazine is lost somewhere in the maze of absorption beyond 7000 cm ' (~8.68 eV). The maximum absorption in trans-diazine occurs at about 7.67 eV. The band associated with the maximum absorption is .cr-> a* which has an oscillator strength of 0.132.Series of Rydberg states in trans-diazine arise not only by taking an electron from the most loosely bound orbital (non-bonding orbital) but also by taking it from bonding orbital occuped in the ground state. Out of thirty SCF states, excluding valence states, most arise by taking an electron from bonding orbital and few of them are weakly allowed by symmetry. Rydberg stales which arise due to the removal of an electron from non-bonding orbital are all symmetry forbidden. The overall symmetry state of allowed Rydberg bands is By.Rydberg excitations in trans-diazine set in at 7.83 eV; this in pyrimidine and pyrazine sets in at 6.97 and 6.83 eV respectively. Rydberg excitations in pyridazine have not been observed [12]. The first two members of Rydberg band in trans-diazine at 7.83 and 8.18 eV possess respective quantum defects (S) of 0.95 and 0.83 and hence correspond to the members of ns Rydberg series. Thus the first m Rydberg band is in a reasonable agreement with experiment [9]. The next band at 8.64 eV with S  = 0.63 forms the member of np Rydberg series and agrees well with experimental one [9]. This is then followed by a number of closely spaced Rydberg bands and hence we discuss the spectrum no further.(ii) Cis-diazineWe note a forbidden (f® 0.00) n - ^  zi* transition at 3.83 eV and thus this energy value agrees well with experimental one for trans-diazine. The forbiddance arises due to the feet that the overall symmetry of the ntP state is y A2 = A i^ ^  none of the componets of dipole moment vector M has symmetry Af, consequently the matrix element of the transition moment vanishes. In general, Ai -  A\ transitionsMRJNDO/S calculation on the electronic spectra o f N2H2 isomers 175of t ’n,, are rigorously forbidden for electric dipole radiation can occur as magnetic dipole radiation. On the other hand,note another nrt* state of state symmetry Bj at 5.78 eV ttliich is allowed with they component of the dipole moment vector. It has an oscillator strength of 0.101. Similar to trans- (jia/ine, the spectrum of cis-diazine does not reveal rc-^ trattsitions. The maximum absorption in cis-diazine occurs at about 9.88 eV. The band associated with the maximum absorption is rt -+ o* which has an oscillator strength of 0 248 .As to the Rydberg excitations, the first two bands at 8.38 anti 8.87  eV have respective quantum defects of 0.99 and 0 83 and thus from the members of ns Rydberg series. The members at 9.15 and 9 .19 eV with respective 5 values of 0.71 ,vid 0.69 belong to np Rydberg series. Thus we note some Liilianced values for ns and np Rydberg bands as compared to the bands in trans-diazine. This is then followed by a number of Rydberg excitations. In cis-diazine Rydberg bands with state symmetry Bi seem to be allowed and the one at 8.38 eV is the most intense which has an oscillator strength of0.042, This lies about t .5 eV below the maximum absorption band.uiil iso-diazineHie number of occupied lone pair orbital increases as we move from trans-diazine to iso-diazine ; one in trans-, two ill eis-, and three in iso-diazine. Consequently, to all of the excitations in iso-diazine the originating orbital is a lone pair orbital. We note the lowest singlet A2 {n n*) state at 1.24 eV which is forbidden by symmetry. The next n ti* transition at 6.25 eV is intense ( f  -■ 0.075). The overall symmetry of the state is A\ and hence this is allowed with c component of dipole moment vector. Thus, the allowed n-^ n* transition in the isomers is predicted at higher energy than experiment. The third nn* state with state symmetry B\ IS predicted to be forbidden ( f=  0.00) which voilets the general selection rule. The B\ electronic state of C2v is allowed with x component of dipole moment vector. The reason of forbiddenness might be due to the neglect of vibronic interactions, for the general selection rule is valid when vibronic interactions are not neglected. None of the transitions is assigned n -¥  The maximum absorption in iso-diazine occurs at about 10.32 eV; the band associated is n~^ a* with an oscillator strength of 0.328. Thus, it seems obvious that the n o* or a  o* transitions are the cornerstone of the spectra of N2H2 isomers.Contrary to trans-diazine and cis-diazine, we note only one member of ns Rydberg series at 7.35 eV with S=  0.92.first member of np Rydberg series appears at 7.96 eV with S= 0.66. This is then followed by a number of closely spaced Rydberg bands. The Rydberg bands are very weakas compared to the bands in trans- and cis-diazine. We note that the ns and np Rydberg bands in iso-diazin are in a reasonable agreement with experimental ones for trans- diazine.4.5. Triplet excitations :The experimental benchmarks of the calculations are the separation^ between the lowest singlet n-zr and n -x  states, the separ^ions between the lowest singlet and triplet n -x  states, an^ the intensities of allowed n-x*  transitions. As discussed| in the preceding sections, the spectra of the isomers » e  devoid of x - x  states and hence question of separatioi|B of the lowest singlet x - x  and n -x  states does not arise. Tl^ intensities of allowed n-/r* transitions have already bieen discussed. To the remaining part, we predict the separations between the lowest singlet and triplet h tt states as follows. This is about 3.87 eV in trans-diazine, 4.00 eV in cis-diazine, and 0.99 cV in iso-diazine. The low value of the separation in iso-diazine may be attributed to its structure in which the two hydrogen atoms are attached to a single nitrogen atom. However, this separation in iso- diazine is comparable to the corresponding separations in higher azines [6,11 ]. Triplet Rydberg bands are also predicted whose S-T splits are too small.5. ConclusionThe presence of nitrogen atoms causes the appearance of lone pair level which is characterized by very high coefficients of 2Si  ^ and IPjsi in the molecular orbital. These orbitals clearly cannot be termed non-bonding since the first ionization potential of any isomers is > 10 eV. The total populations in the isomers based upon a Mulliken population analysis show that the nitrogen atoms are over all sp^ hybridized. The n n* transitions in the isomers exhibit intensity. In going from trans- to iso-diazine, the maxima in the absorption bands show hyperchromic effect. These bands, on account of their high intensity, can be easily observed. On the other hand, Rydberg bands in the isomers are less intense which may be observed under appropriate experimental conditions.AcknowledgmentsThe calculations were performed at the computer centre, Banaras Hindu University, Varanasi. The helping attitude of the staff of this centre is gratefully acknowledged.Referencesll] J A Popic, K Raghavachari, J J Frisch, J S Bmkelcy and P V R  Schleyr J. Am. Chem. Soc, 105 6389 (1983)[2] W J Hchre, L Random, P V R  Schleyr and J A Pople Ah initio M olecular O rbital Theory (New York ; Wiley) (1986)[3] H J A Jensen, P Jorgensen and T Hclgakcr/ Am Chem. Soc 109 2895 (1987)176 R S  Prasad and A K SinghHI S P Walsh J. Chem. Phys. 91 389 (1989)[5] D Whitcicgg and R G Woolley J. Mol. Struct 209 23 (1990) f6) R S Prasad and B N Rai Theo. Chim. Acta  77 343 (1990)(7J T Koopmans Phystca I 104 (1933)18] A Trombetti Can. J. Phys. 46 1005 (1968)[9] S N Foncr and R L Hudson J. Chem. Phys. 28 719 (1958)[lOJ G Herzberg M olecular Spectra a n d  E lectronic Structure // E lectronic Spectra  a n d  E lectronic Structure o f  Polyato,^  ^M olecules (New York : Van Nostrand) (1966)[11] R S Prasad and A K Singh Theo. Chem. Acc. 103 434 (2ooo[12] K K innes, J P Byrne and I G Ross J. Mol. Spectrosc. 22 12 (1967)[13] J Ridley and M Zerner Theo. Chim. A cta  32 111 (1973)

MRINDO/S Calculation on the Electronic Spectra of N2H2 Isomers

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MRINDO/S Calculation on the Electronic Spectra of N2H2 Isomers

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