A non-empirical SCF and CI study of the electronic spectrum of pyrrole

Volume 57. number 2

A NON-EMPlRICAL

CHEMICAL

PHYSICS LElTERS

15 July 1978

SCF ANLI Cl STUDY OF TEIE ELECIRXONICSPECTRUM OF PYRROLE

Werner BUTSCHER and KarI-Heinz THUNEMANN Lehntuhl jik Tieore,*the Chemie, Universft.2 Bonn. D 5303 Bonn. Gemmy Rccchd 7 February 1978 Revised manuscript received 28 February 1978

Various electronically excited states of pyrrole have been studied by ab initio SCF and CI calculations including rr-. n* and zr- Rydberg excitatiorz Optically allowed vaIenc= type transitions are found at energies higher Thea 65 eV_ whereas all the Iower singIet states are of Rydberg type. In addition to the experimental.& known tsiplet states at 4.23 and 5.10 eV, scverzd new triplet transitiors with energjes from 5.X to 7.10 eV are predicted In most cases good agieement with experimental data is found.

f.

Iutroduction

Optical absorption measurementsIn the W region of the mdecule pyrroIe have been performed for more than fifty years [l-7]. In 1971, *he photoelectron spectrum was measured by Derrick et aI_ [S] _ These authors revised the assignmentsof MuIIen and Orfoff [6] and explained most of the absorption bands by three Rydberg series, ohe of which Ieads to the second ionization potential Bavia et aI. [7], however, found no evidence for this latter Rydberg series from their absorption measurements.Recently, electron impact experimentshave been performed in order to study triplet excitations and electric dipole forbidden transitions 19, lo] _ Theoretical studies of the excited states of pyrrcle up to now have been based on semiempirical methods alone. They couId not give a consistentexpIauation of the spectrum [ l l -16]_ Non-empirical SCF calculationswere restricted to the study of the electronic structure of the pound state [17--191 or to the validity of the 0, ir separation [20]_ The recent progress in CI techniques deveIoped in our Iaboratory aIIows for an efficient handling of large basis sets and large configuration spaces.Thus moiec&s of this size can hopefully be studied routinely by ab initio Cl techniqueswithout o, z separation. The purpose of this work is to examine the experimental 224

assigumentsof the spectrum of this moIecuIe which has a considerable importance in biochemistry.

2_ Theoretical From microwave experiments [2 1] , pyrrole is expected to be planar and its symmetry is assumed to be C,, (fig_ 1) The fact that no n -+ nf transitionsare observed supports the quasiaromaticmodel according to which the nonbonding lone pair of the N atom contributes to the STelectron system of the heterocycIic ring. The observed spectrum is thus described by z * sr* vaIence and z * ns, np, nd Rydberg transitionsThe A0 basis used in the calculation consisted of a double zeta set of gaussian functions for the atornr N and C and two s groups for the hydrogens [22]. This basis set was augmented by five primitive bond s functions (exponent 1.4). In order to allow for a description of Rydberg states, one diffuse s and a set of diffuse p fimctions were placed in the center of mass of the mdecule both with exponents 0.03. The totat number of AO’s is 69. Table 1 contains the SCF results for the XIA, ground state. The ICMO’s have a2 and b, symmetry. In the present calculations the excited stateswiII be characterizedby excitations from the 5c2and 5~3MO’s to the lowest Rydberg and valence MO’s_ These states

CHEME4L PHYSICS LE’l-IERS

Volume 57, number2 i5

!

a $ y 6 E

120.7. 106_9*tC-N-C ANGLE) 108.V 107.6' 126-S*

15

July 1978

were calculated by the open-shell Roothaan procedure 1231 as starting point for the CI description. The SCF calculations were restricted to one muhiphcity per excitation (mostly triplets). For the CI calculations, the MRD CI program package was used 1245. A pilot CI based on ground state MO’s gave pre~hminaryinformation about the nature of the lowest states of each symmetry. The large number of basis functions and electrort required that at kast the ten lowest MO’s (1s and 2s core) were kept free from variable occupation in the CL Actually, the eleven lowest MO’s including 7al (see table 1) were used as core MO’s in our calculations_ Thnsstill resulted in up to 300000 generated and up to 5000 selected configurations. The influence of the configurations not included in the final secular equation on the total energy is estimated by an extrapolation procedure 125,261.

3. Results and discussion Fiz- 1. Moleculargeometryof pynole used in the calculations. Distancesare givenin A.

Table 1 SCF resultsfor the X1 AI groundstate of pynole, ESCF = -208.7692 au 0rbitals used as fixed core in the CI calculations

Valenceorbitalswith v&able occupationin the CI and lowest virtualorb&Is

MO

orbitalenergies

orbitalenergies

Ial lb2

-15.61204 -11.26737 -11.26733 -11.22365 -11.22257 -1.29170 -1.04901 -0.98371 -0.79070 -0.77421 -0.73437

-0.59743 -057263 -0.56451 -0.55067 -054003 -0.35008 -0.29982

a1

3al 2bz 4al

2 % 4bz 7al

Table 2 contains information about the states caiculated by the open-shell SCF procedure. The type valence (V) or Rydberg (R) state is determined by the character of the MO into which the excitation occurs_ The identification of the MO’s as Rydberg or valence depends on their LCAO expansion and on their Coulomb integral (0.13-O. 15). Orbitals with Coulomb integrals of about 0.20 are expected to be of mixed Rydberg valence type (R, V). A few words seem to be in order about the u, ‘ITseparability. According to this approximation a change in the srelectron system should leave the o electrons unTable 2 SCF resultsfrom excited statescalculation

zq

x2 nj

State

X'A,

7b2

3bl llat 4bl 2a2

aE(eW V V R V

(Yr+ n*)
R

(Yr--t 3s)

0.0

0.07489

R(3s)

Al

0.09080 0.09434 0.10059 0.17319

ROp$

A2

ROPXI

B2

la2 4 7rg la2 + 3pb2 2bl -+ n$ la2 4 3s 2b1 --crr;

V

0 + rr*j

R(~Pz) ng

Al BI

la2-& 2bI 43s

&I)

(IT-r#) (ird3s)

0.22886

ng

la$

V

B2

31 1%

Excitatior

Azion

3.91 5.78

557 5.01 6.80 6.29 6.21 7.3

225

Volume 57, nxunbex 2

CZIiEEECAL PHYSICS

TaMe 3 Comparison of the occupied aI orbital energies in three different SCF CalcuIations

X0,

X’Ar

3B~

-15.6121 -11.2673 -11.2237 -1.2917 -1.0490 -0.7907 -0-7344 -0.5974 -0Li400

T2-Xe 4 Compah~n

(la2 + 3pW

-15_7055 -11.4046 -11.3339 -1-4053 -1.1571 -0.8859 -0.8384 -0.6989 -0.6432

-155484 -11.2481 -11.2453 -12711 -1.0487 -0.78 17 -0.7301 -05898 -0.5507

15 July 1978

LEITERS

afTected. In table 3, the orbital energies of the nine occupied o MO’s of al symmetry are compared for two different excitations. These numbers show that a R + n* excitation does affect the o MO’s, The successof a CI based on the o, z separation thus depends on a cancelIation of the Q MO reorganizatkn energies_The third column of table 3 shows that the orbitals which are at least approximately constant in a s--f IP excitztion undergo a strong reorganizationwhen a n + o excitation is performed_ ‘ibus it seems reasonable l bt those MO’s which are used as a fixed core in our CI calculations are determined for each state separately by an SCF calculation which allows for a reorganizationwithin the uncorrelated core. From previous experience with bu’adiene this reorganizationenergy amounts up to 0.4 eV [27] _

of experimentzl and theoretical singlet excitation energies obtained from CI

Theory

5.22 2, b)

assignment

type

dE(eW

state

type

‘AI

V V R

5.22

’ A2 (la2 + 3s)

R

Q32(3--*,+) 3 lB1 <* -* n+) d)

V

-

-

‘A1([=*;r*)a) * B1(la2 +

V R

6.05

(x-z*) a) + n*) b)

1A2h

*A2(lar +. 3s) C)

5.71 h&e)

5.88

a.b, e)

6.78 e. n 6.93

3pb2)f)

‘RI (la*

-33pbz)

R

rBr(2br -3sar)f)

R

6.13

‘B1 (2bI * 3s)


‘Bt(2bI 4352r)f) ur vikation

R

633

%(l

R

*Al (122 - 3da2) fi

R

6.73

rAr 42%(2br-+ 1~qt)

-

b)

22

-

3pW

27%(la+ --,I& -

-

V -

f)

R

-

7.22 b. e, f, 9)

‘Br(la2 -4pb2) f) VI viiration

R

-

-

7.43 2. b, 6

‘Ai (122~4~2)

R

754 b, 0

rAr (?a* --,Sp&) f)

7.69 G b, r)

‘Ar

7_i2eL&

‘B,

(la2

(i22

44pW

-

5d22)

7.86 h b, r)

‘BI (2b: +4s)

8.21 f)

2A2 ion

a)

Ref. [6]_

226

b) Ref. [?I_

r)

r)

0

c) Ref. 1281.

-

-

R

-

-

-

R

7.70

l&z(la2 + Gf)

R

-

-

V -

V

7.71

d) Ref. [7]_

e) Ref. [4]_

‘As ion f) Ref_ (81.

g) Ref. 121.

Volume 57. number 2

cY3EMIcAL

For most states, the f?naICI was based on natural orbitals. The difference in the extrapolated energies between a NO CI and a SCF MO CI is small, however. The resultingtransitionenergiestogether with the correspondingexperimental data and assignmentsare collected in table 4 for the singletsand table 5 for the triplets_ In their electron impact experiments, Flicker et al. [9] found a peak at 5.22 eV. From the angulardependence of the scatteringintensity they conclude that this peak corresponds to an electric dipole forbidden singlet transition. Because the ground state is totally symmetric this means, that the upper state should have IA2 symmetry. On the other hand, the same authors arguewith the help of the quasiaromaticmodel that the 5.22 eV peak should correspond to a ST+ a* transition. This is not consistent, however, since no state of A2 symmetry can be formed from a s + IT-fexcitation (for the symmetries of the n MO’s see table 1). The calculatedverticalenergy difference of 5.22 eV sup ports the assumption of an electric dipole forbidden singlet state and is in agreementwith Robin’s assignment of a Rydberg transition [28]. No calculated excitation energy, however, can be assignedto the absorption peak at 5.71 eV. According to the most recent assi@rnent of Baviaet al_ [7], this energy should correspond to a transition to a 1B, valence state. The electron impact experiments of Flicker et al. [9], however, gave no evidence for a state at 5.71 eV. Their lowest singlet transition above 5.22 eV lies at 5.89_ + 0.04 eV_ The absorption band with origin at 5.88 eV has been assignedby Derrick et al. [S] as the frrstmember of ‘he Rydberg series la, + npb2 leading to the first Table 5 Comparison

15 July 1978

PHYSICS LETrERs

ionization potential of 8.21 eV. The calculatedvertical energy of 6.05 eV for this excitation obviously supports this assignment. The two peaks at 6.23 eV and 6.32 eV have been interpretedby the same authors as the origin and the u1 vibration of ‘the Rydberg series lB, (2bl atEsal) leading to the second ionization potential (2Br ion). The calculationsagreewith this assignmentof the 6.23 eV peak. The assumed vibrationallevel at 6.32 eV, however, can also be explained as the origin of the Rydberg series lB2(la2 +npbl) leading to fiit ionization potential. The transitionat 6.78 eV is accorclIngto Derrick et al_ [S] the origin of the Rydberg d series la2 + nda,. ‘This type of Rydberg states could not be calculated, because the A0 basis did not contain diffuse d functions_ The calculated excitation energy of 6.73 eV oE fers the alternativepossibility of a transitionto a IAl (rr+ 5c+)valence state which cannot be describedby one dominant configuration alone. In the region of 7-l-7.9 eV severalbands have been observed both by absorption and electron impact experiments_Derrick et al. [S] explain these bands by Rydberg transitionwith quantum numbers n > 3. Based.on the assumption that the 6.?8 eV transition actually corresponds to our calculatedvalence state at 6.73 eV, one expects the Rjrdberg3d series to be among these bands. Typical term values for Rydberg d seriessuggest to place this state at the lowest transition. Actually, recent n electron CI calculationsby Tanaka et al. [29] with an excitation energy of = 7.1 eV for a (1 a2 + 3da2) transitionconGrm these argumen& The closely spaced bands in the 7.1-7.9 eV region

of experimentaland theoreticalkipIet excitationenergiesobtainedfrom CI

Experiment

Theory

aE(ev)

assignment

aE(ev)

assignment

4.21 a) 5.10 b) -

3t5r-+ %*) a) 3(zr+ n*) b) -

4.42 5.25 5.71 5.99 691 7-10

‘BZ (la2 + ~2) 3A2 (la2 + 3s) 3A1 (2514 &) 3B1
V R V R V V

a) Ref. 191. b, Ref. [lo].

227

Volume 57. number 2

and the estimated uncertainty of our excitation energies (0.1-0.3 eV) do not allow to give a definite assignment of the calculated 7.70 eV state to one of the remaining experimental transitions. Furally our calculated ion is 0.5 eV too low compared with experiment. This is consistent with our experience from calculations of ionization potentials for other malecul~ with basis sets of this size_ Contrary to the optically allowed transitions which have been measured for many decades, only two very recent experiments are available which identify the two lowest triplet transitions (table 5). The calculated triplet state located 4.42 eV above the ground state can obviously be identified with the observed triplet transition at 4.23 eV. ‘Ibus the assignment of a ~(YZ+ n*) transition by the experimental&s is correct.The theoreticaldata show in addirion that ihe symmetry of this lowest triplet state is 3B2. The triplet state detected by van Veen [IO] at 5.1 e’V does not result from a 3(rr + rP) excitation_ This is a Rydberg state arising from a rr + 3s excitation. Consistent with the small singlet triplet splitting Gf Rydberg states, this triplet state is the partner of the IA2 Rydberg state calculated at 5-22 eV_ The explanati@n why our triplet lies slightly higher than the corresponding singlet state is that for the triplet, the CI calculation had not the same quality as for the singlet state, because a configuration which contributes tG the final wavQ&u’Mion with one percent (Gn the basis Gf the cc) had not been included in ‘the set of main con&rmti0n.S. Since no further tripler excitation energies are available from experiments, we predict at S-71 eV a 3A1 (2br + rrz) valence state. The Rydberg state 3Br (la2 + 3pb2) is again the &seIy spaced partner state of the calculated 6.05 eV IB, transition. The singlet partners of the two uiplet valence states located at 6.91 eV and 7.1 eV will probably be among the super-excited singlet states of pyrrole. ‘Ihe semiempirical calculations in the past failed to explain the spectrum of pyrrole consistently. One reason is that Rydberg states cannot be described in a valence basis set The other source of error results from the approximation of the integrals. In table 6, the excitation energies obtained from a non-elmplrIcal SCF procedure are compared with CI energies and where possiiIe, with experiment. These numbers demonstrate that a mm-empirical SCF together with a Rydberg and 228

15 July 1978

CHEMICAL PHYSICS LEZTERS

6 Comparisonof SCF and CI excitationenergieswith experiment

TzbIe

State

3B2 (la2

Excitationenergies(ev)

+

6)

3Aa (la2 + 3s) ‘BI (Ia2 + 3pbd

3Ar (2bl --csr;) ‘B2 (2bl + 3s)

SCF

CI

e_xperiment

3.91 5.01

4.42 5.22 5.99 5.71 6.13

4.21

5.78 557 6.21

5.10

6.23

valence basis can give reasonable excitation energies_ Howe&r,

since the majority

of the SCF

calculations

restricted to triplet excitations, no more states could be compared.-

were

4_ Conciusion A final look at the calculated data clearly shows that the MRD CI procedure can successfully be used to obtain theoretical infGmMion cGncerning electronic spectra of molecules as large as pyrrole. The calculated transition energies are in good agreement with the pertinent experimental data and fall in a region of 0.1 to 03 eV, a fact cornm~nly observed in similar calculations. The rnGre impOrtant PGiRt in our G@liGll is that we could give a clear destinction between the Rydberg and valence type transitions of that molecule. The “5-l/5.2 eV’ problem is simply solved by having the small multiplet splitting of an otherwise optically forbidden 1 A2 Rydberg transition_ There is a good chance that the MRD CI can tind its application in calculations on other five-me&n&red rings with equal success. After completion of this work we became aware of a related work by Tanaka et al. [29].

Acknowledgement The authors want to express their thanks to RJ- Buenker and SD_ Peyerimhoff for use of the Bonn SCF CI program package and also for their helpful comments.For the evaluation of integrals the IBMOL integral program of E. Clementi was used. The services of the computer centre of the University of Bonn are gratefully acknowledged.

Vofume 57, number 2

CHEhffCAL

PHYSICS LETTERS

References [l] S. hfenczel, 2. Physfk. Chem. 125 (1927) 161. [2] G. Schelbe and H. Grieneisen, 2. Physik. aem. B 25 (1934) 52. [ 3) W-C- Priceand AD. Walsh, Proc. Roy. Sot. A 179 (1941) 206. [4] L.W. Picket& M-E. Corning,G-hf. Wieder, D.A. Semenow uld J-M. Buckley, J. Am. Chem. Sot. 75 (1953) 1618. [5] G. Hotith and A.f. Kiss, Spectrochim. Acta A 23 (1967) 921. [61 PA Mullen and MX. Orloff, J. C&em. J3y.s. 51(1969) 2276. 171 F- Bavia,F- Bertinelli,C. Talianiand C. Z&&i, Mol. Wys. 31(1976) 479. PI PJ. Derrick,L. Asbrink, 0. Edqvist, B-6. Jonssonand E. Lindholm, Intern.J. Xfass Spectrom. Ion Phys. 6

(1971) 197. Flicker,0-k IMkher and A Kuppermann,J. 191 W-LMI. Chem. Phys. 64 (1976) 1315. I101 E-H. van Veen, Chem. Phys. Letters41(1976) 535. 1111 J-P- Dabl and AB. Hansen,Theoret. Chim. Acta 1 (1963)

199.

1121 N- Solony, F.W. Birssand J.B. Greenshields,Can. J_ Chem. 43 (1965) 1569. 1131 H. Hartmann and K-Jug, Theoret CXim. Acta 3 (1965) 439. 1141 P. Chiorlzoli, k RasteRi and F. Momicchioli, Theoret. Chim. Acta 5 (1966) 1.

15

July 1978

[15] J. Del Bene and H-H. Jaffg, J. Chem. Phys.48 (1968) 4050. jl65 K. Ohno, in: Quantum aspects of heterocycliccompoundsin chemistryand biochemistry,eds. D. Bergmann and B. Pullmann(JerusalemAcademic Press,Jerusalem, 1970) p_ 139. [ 171 E. Clementi, H. Clementiand D.R. Davis,J. Chem. Phys. 46 (1967) 4725. [ 181 M-H. Palmerand AK. GaskeJJ,Theoret. Chim. Acta 23 (1971) 52. [19j M-H. Palmerand JJ. Gaskell,Theoret. Chim. Acta 26 (1972) 357. [20] R.W. Kram&g and E.L. Wagner,Theoret. Chim. Acta 15 (1969) 43. [21) B. Bak, D. Christensen, L. Hansen and J. Rastrup-

Anderson,J. Chem. Phys. 24 (1955) 720.

1221 S. Hutiaga, 3. Chem_Phys.42 (1965) X293_ (231 CCJ. Roothzin, Rev. Mod_ Phys. 32 (1960) 179. 1241 R6. Buenker,S.D. Peyerimhoffand W. Butscher,Mol.

Phys.. to be published_ 12.5] R-J. Buenkerand SD_ Peyerimhoff,Theoret- Chim. Acta 35 (1974) 33. [26] R-J. Buenker and S-D. Peyerimhoff, Theoret. Chhn. Acta 39 (1975) 217. /27] S. Shih, R-J. Buenkerand S.D. Peyerimhoff,Chem. Phys. Letters 16 (1972) 244. [28] hf_B. Pobin, Higherexcited statesof polyatomic molecules (AcademicPress,New York, 1975). 1291 K. Tanaka,T- Nomura, T. Noro, H. Tatewaki,T. Takada, & Kashiwagi,F. Sasakiand K. Ohno, preprint.

229