JOURNAL OF CHEMICAL PHYSICSVOLUME 113, NUMBER 18

8 NOVEMBER 2000

Electronic excitation spectra of furan and pyrrole: Revisitedby the symmetry adapted cluster–configuration interaction method
Jian Wan, Jaroslaw Meller, Masahiko Hada, Masahiro Ehara, and Hiroshi Nakatsujia)
Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering,
Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan

共Received 20 June 2000; accepted 17 August 2000兲
Electronic excitation spectra of furan and pyrrole are reinvestigated by the symmetry-adaptedcluster configuration-interaction method. The 47 and 46 lowest singlet and triplet electronic states
are computed for furan and pyrrole, respectively. Two series 共1a 2 and 2b 1 兲 of low-lying Rydberg
states and the valence ␲ – ␲* excited states strongly influence each other in both furan and pyrrole.
The present calculations give detailed and satisfactory theoretical assignments of the vacuum
ultraviolet spectra and the electron energy-loss spectra of the two molecules. The similarities anddifferences in the electronic excitations between furan and pyrrole are discussed in detail. The
accuracy and assignments of recent theoretical studies, i.e., complete active space second-order
perturbation, multireference Møller–Plesset perturbation, second-order algebraic-diagrammaticconstruction, multireference double configuration interaction, and CC3, are compared. © 2000
American Institute of Physics. 关S0021-9606共00兲30842-X兴
I. INTRODUCTION

obtained only by sophisticated electron-correlation methods
for ground and excited states. Third, dynamic polarization ofthe ␴ electrons occurs strongly for some electronic excitations. Fourth, all of the previous three factors interact rather
strongly in furan and pyrrole.
As observed from the experimental excitation spectra offuran and pyrrole 共Figs. 3 and 4兲, the peaks are broad andcomplicated for the existence of many valence- andRydberg-excited states and their vibrational structures. Generally band maxima and vertical excitation energies differ
substantially: even for Rydberg states the deviation exceeds
0.2 eV in some cases.27 This point should be kept in mind
when trying to do an assignment and judge the accuracy of
calculations.
Among the previous ab initio theoretical studies on furan
and pyrrole, the symmetry adapted cluster 共SAC兲 and SAC–
configuration interaction 共SAC–CI兲 study21 was a pioneering
work, but due to the computational resources available atthat time, the rather limited basis sets and relatively small
active space impaired the quality of the results. In the later
complete
activespace
second-order
perturbation
共CASPT2兲,22 multireference Møller–Plesset 共MRMP兲25 perturbation, second-order algebraic-diagrammatic construction
ADC共2兲,26,27 and a hierarchy of coupled cluster model
共coupled-cluster single double, CC3兲28,29 studies, fairly large
basis sets were used: the atomic natural orbital basis set contracted to 关 4s3 p1d/2s1p 兴 and augmented by ring-centereddiffuse s, p, and d functions in CASPT2, Dunning’s ccpVTZ basis set augmented by charge-centered 3s, 3 p, and
3d Rydberg functions in MRMP, cc-pVDZ augmented byatom-centered diffuse functions and molecule-centered diffuse functions in ADC共2兲, and cc-pVTZ augmented by atomcentered diffuse functions and molecule-centered diffuse
functions in CC3.
However, there are still many inconsistencies among theresults of these recent high-level theoretical studies with

Furan and pyrrole are so-called five-membered six
␲-electron aromatic ring molecules in which the heteroatoms
oxygen and nitrogen donate two ␲ electrons and each of thefour carbon atoms supplies one ␲ electron. The electronic
spectra of furan and pyrrole have been the subjects of many
experimental and theoretical studies.1–29 The interest in thesemolecules is not surprising, considering the importance of
these molecules as fundamental units in many important biological molecules. Further, recently, the calculations of theirelectronic excitation spectra have been considered as benchmarks for theoretical studies of excited states. The representative theoretical studies have been carried out so far by Nakatsuji et al.21 in 1985, Serrano-Andres et al.22 in 1993,
Palmer and co-workers23,24 in 1995 and 1998, Trofimov andSchirmer26,27 in 1997, and Christiansen and co-workers28,29
in 1998 and 1999.
On the experimental side,1–15,23,24 three types of electronic excitation spectra were measured for furan and pyrrole: the vacuum ultraviolet 共VUV兲 spectrum, electronenergy-loss 共EEL兲 spectrum, and ultraviolet photoelectron
spectrum. These spectra provide information regarding singlet valence- and Rydberg-excited states, optically forbidden
transitions such as triplet excitations, and ionization potentials, respectively.
On the other hand, the previous ab initio quantum theoretical investigations16–29 have demonstrated the underlying
difficulties in calculating vertical excited states of furan andpyrrole. One is strong valence-Rydberg mixing. Calculations
based only on the valence basis are obviously inadequate andthis is a main reason for the failure of early semiempiricalstudies and early ab initio studies. Second, the roles of electron correlations are crucial. Accurate and reliable results area兲

Author to whom correspondence should be addressed; electronic mail:hiroshi@sbchem.kyoto-u.ac.jp

0021-9606/2000/113(18)/7853/14/$17.00

7853© 2000 American Institute of Physics

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7854

Wan et al.

J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

FIG. 1. Furan and pyrrole 共C4H4X, X⫽O, NH兲.

large basis sets. For example, the CASPT2 and MRMP
methods, which use a complete active space self-consistent
field reference function, gave very similar computational results for furan and proposed a relatively reasonable interpretation of the singlet valence excitations lying lower than 7.8
eV, whereas, for pyrrole, they gave quite different results
共0.51 eV difference兲 for the lowest valence excitation of 1 B 2
symmetry, which was assigned to the first band of the VUVspectrum. For the same band, the ADC共2兲 studies made aconclusion that there was no valence excitation of 1 B 2 symmetry in this region, which was explained solely by the Rydberg transitions. Recently, the fourth ␲ – ␲* valence transition, V ⬘ ( 1 B 2 ), was identified by Palmer et al.23 as anabsorption peak at 8.7 eV in the VUV spectrum of furan withthe aid of multireference multiroot CI multireference double
configuration interaction 共MRDCI兲 calculations. CASPT2
calculated this state at 8.38 eV with an intensity of 0.27, and
MRMP did not visit this region. The CC3 estimated the corresponding state at an energy region higher than 9 eV.
On the other hand, since pyrrole differs from furan onlyby the substitution of an O atom by a N–H group, we would
expect the electronic structures and excitation spectra of thetwo molecules to be similar. For example, the general profiles of VUV spectra of the two molecules23,24 are very similar in that they have two main intense and broad bands; thefirst is located at around 5.5–7 eV, and the second is more
intense and located between 7.0 and 8.8 eV. However, anobvious difference exists in the spectra of pyrrole and furan,i.e., there is a weaker central band near 7 eV in the spectrumof pyrrole. The similarities and differences in the electronic
excitation spectra of furan and pyrrole, and the uncertainties
in the assignments of the valence and Rydberg excitations inthe spectra of furan and pyrrole have motivated us to reinvestigate them using the SAC/SAC–CI method. In Sec. II weoutline the computational details. Calculated results and discussion are presented in Sec. III. A summary is given in Sec.
IV.
II. COMPUTATIONAL DETAILSThe experimentally determined ground-state equilibriumgeometries30 for furan and pyrrole with C 2 v symmetry illustrated in Fig. 1 were commonly used for both ground andexcited states, so that the calculated excitation energies arevertical in nature.
In the present calculations, we have used Dunning’s augmented correlation consistent basis set AUG-cc-pVDZ31 for
O, N and C atoms, and cc-pVDZ32 for H atoms. For themolecule-centered Rydberg functions, we have used a set ofdiffuse functions (3s3 p3d) selected from the studies ofKaufmann et al.,33 and placed them on the molecular centerof gravity. These are the same as those used by Trofimov andSchirmer.26,27 The total number of basis functions is 175 infuran and 180 in pyrrole. This type of augmented basis isbelieved to be adequate for describing widely different electronic structures of molecules in the ground state, singlet andtriplet valence and Rydberg excited states, describing diffuse
character and differential correlation effects. The number ofHartree–Fock canonical orbitals, calculated by the GAUS34
SIN98 package, is 175, consisting of 18 occupied and 157
virtual orbitals in furan, and 180, consisting of 18 occupied
and 162 virtual orbitals in pyrrole. The self-consistent field
共SCF兲 occupied valence orbitals and some important virtual
orbitals of furan and pyrrole are shown in Table I, respectively, together with their orbital energies, symmetries, andcharacters.
The details of the SAC/SAC–CI theory have been presented elsewhere.35–41 The SAC/SAC–CI calculations weredone using the local version of the SAC–CI module.41 In allof the present SAC/SAC–CI calculations, the active spaceconsists of 13 occupied orbitals and 157 and 162 virtual
orbitals in furan and pyrrole, respectively: Only the 1s coremolecular orbitals are frozen. The details of the SAC/
SAC–CI calculations are exactly the same as those recently
reported for cyclopentadiene.42
Table II shows the previous21 and present SAC/SAC–CI
computational details on furan and pyrrole. Note that, 15
years ago, SAC/SAC–CI was the only sophisticated theory
for calculating the molecular excited states. The computational resources were quite different from those available
now: The available main memory, disk space, and computational time were very limited, although the previous calculations were certainly ‘‘big’’ by the standard of that time. But
now, we can use a much better basis set and a much larger
active space than those in the previous SAC/SAC–CI studies. This greatly improves the calculated results, even though
the basic method used is the same, i.e., the SAC/SAC–CI
method. Improvements in the SAC/SAC–CI program, algorithm, etc., are also important, but when we do the comparisons shown in Table II, we are strongly convinced that advances in computer technology over the past 15 years play
the greatest role in the present improvement.
III. RESULTS AND DISCUSSION

In the four ␲-orbital approximation, the two occupied
orbitals 2b 1 ( ␲ 2 ) and 1a 2 ( ␲ 3 ), and the two virtual orbitals
3b 1 ( ␲ *4 ) and 2a 2 ( ␲ 5* ) illustrated in Fig. 2 give rise to four
singlet ␲ – ␲* transitions: ␲ 3 → ␲ * (V) and ␲ 2 → ␲ * (V ⬘ ).
These four transitions V( 1 B 2 ), V ⬘ ( 1 A 1 ), V( 1 A 1 ), andV ⬘ ( 1 B 2 ) are expected to lie below the first ionization potential (IP1 ) 8.883 eV in furan and 8.21 eV in pyrrole, andwould give absorption bands in the range of 5.5–8.8 eV.
In order to distinguish valence and Rydberg-type transitions, we use some properties discussed in our recent
paper.42 First, we take advantage of the fact that the A 2 andB 1 Rydberg states are not perturbed by the valence ␲ – ␲*Downloaded 25 May 2001 to 130.54.33.33. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

Excitation of furan and pyrrole

7855

TABLE I. Hartree–Fock occupied molecular orbitals 共MOs兲 and some important unoccupied MOs of furan and pyrrole. ␴ and ␲ stand for valence character
and Ryd stands for Rydberg character.
Orbital energy 共eV兲

Symmetry
MOs

Furan

PyrroleFuran

PyrroleOccupied
Cores
6
7
8
9
10
11
12
13
14
15
16
17 共next highest occupied molecular orbital兲
18 共highest occupied molecular orbital兲

4a 1
5a 1
3b 2
4b 2
6a 1
7a 1
1b 1
5b 2
6b 2
8a 1
9a 1
2b 1
1a 2

4a 1
5a 1
3b 2
6a 1
4b 2
7a 1
8a 1
5b 2
1b 1
6b 2
9a 1
2b 1
1a 2

⫺39.820⫺29.602⫺27.409⫺22.032⫺21.314⫺20.170⫺17.230⫺16.621⫺15.694⫺15.451⫺14.732⫺10.835⫺8.702⫺35.263⫺28.470⫺26.621⫺21.711⫺20.913⫺20.074⫺16.181⫺15.888⫺15.430⫺14.861⫺14.411⫺9.454⫺8.054

Unoccupied
19 共lowest unoccupied molecular orbital兲
20
21
23
26
27
29
30
32
33
35
36
38
39
40
41
42
46
48
50
52
53
57
59
61
62
64
66

a1
b2
a1
a1
a2
a1
a1
b2
b1
b2
a1
a2
b1
b2
a1
b1
a1
b1
b1
b2
b2
a2
b1
a1
b1
a1
a2
b1

a1
a1
b2
a1
b1
a2
a1
b2
b1
a1
a1
b1
a2
a1
b2
b1
a1
b1
a1
b2
b1
a2
a1
b1
a2
b1
b1
a2

0.047
0.162
0.166
0.201
0.355
0.360
0.484
0.544
0.589
0.951
0.990
1.002
1.011
1.396
1.432
1.499
1.874
2.286
3.439
3.587
3.627
4.043
4.837
4.909
6.298
6.888
6.988
8.258

0.041
0.146
0.164
0.207
0.359
0.360
0.447
0.553
0.596
0.945
0.970
1.012
1.017
1.376
1.423
1.519
1.876
2.304
3.436
3.666
3.787
4.145
4.920
5.149
6.054
6.465
6.852
7.254

transitions due to the symmetry constraint. We then use theexpectation values of the second moments of the charge distribution 具 r 2 典 , and its components 具 x 2 典 , 具 y 2 典 , and 具 z 2 典 . In
addition, the oscillator strength has also been used by several
authors as an indicator to compare valence and Rydberg
characters.23,24,26,27 We will use all of them to analyze our
SAC–CI results.

A. Furan

The calculated SCF energy of furan is ⫺228.654 184
hartrees. The SAC ground-state energy is ⫺229.070 173 hartrees, and the correlation energy is ⫺0.415 988 hartrees. The

NatureFuran

Pyrrole␴ (1s)
␴ (2s)
␴ (2s)
␴ (2s)
␴ (2s)
␴ (2s)
␴ (2p)␲1
␴ (2p)
␴ (2p)
␴ (2p)
␴ (2p)
␲2
␲3

␴ (1s)
␴ (2s)
␴ (2s)
␴ (2s)
␴ (2s)
␴ (2s)
␴ (2p)
␴ (2p)
␴ (2p)␲1
␴ (2p)
␴ (2p)
␲2
␲3

s-Ryd
p y -Ryds/p z -Ryds/d-Rydd xy -Ryds/d-Ryds/d-Rydp y -Rydp x -Rydd yz -Ryds/d-Rydd xy -Rydd xz /p x -Rydp y -Ryds/p z -Rydp x -Ryds/d-Rydd xz /p x -Ryd␲*p y -Ryd␴ py␲*␲*␴ s /d-Ryd
␲*
␴s
␲*
␲*

s-Ryd
s/p z -Rydp y -Ryds/d-Rydd xz -Rydd xy -Ryds/d yz -Rydp y -Rydp x -Ryds/d-Ryds/d-Rydd xz /p x -Rydd xy -Ryds/p z -Rydp y -Rydp x -Ryds/d-Rydd xz /p x -Ryd
␴ s /d-Ryd
p y -Ryd␲*␲*␴ s /d-Ryd
␲*
␲*
␲*
␲*
␲*

corresponding previous values were ⫺228.557 15,⫺228.810 55, and ⫺0.253 40 hartrees, respectively.
The singlet vertical excitation energies calculated by the
SAC–CI method are given in Table III, which also shows theoscillator strength 关 f (r) 兴 and the second moment of each
excited state. In Table IV, the present SAC–CI singlet andtriplet excitation energies are compared with the experimental values, and with the results obtained by CASPT2,MRDCI, ADC共2兲, and CC3. Since for furan the MRMP results are quite similar to those for CASPT2, they are notgiven in Table IV. Figure 3 shows a comparison of the experimental VUV spectrum23 and the theoretical SAC–CI
spectrum of furan.

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7856

Wan et al.

J. Chem. Phys., Vol. 113, No. 18, 8 November 2000
TABLE II. Comparison of the previous and present SAC/SAC–CI computational conditions for furan andpyrrole.
Previous 共Ref. 6兲
Basis sets

Active space
Furan
PyrroleEnergy thresholdfor perturbation
selection 共PS兲DZ⫹Rydberg
O, N and C: 关 4s2p 兴
H: 关 2s 兴
Rydberg (2s2p1d) on themolecular center of gravity

AUG-cc-pVDZ⫹Rydberg
O, N and C: AUG-cc-pVDZ
H: cc-pVDZ
Rydberg (3s3p3d) on themolecular center of gravity

67a关5b,51c兴
69a关5b,53c兴

175a关5b,170c兴
180a关5b175c兴

␭ g ⫽4.0⫻10⫺5 , ␭ e ⫽5.0⫻10⫺5

␭ g ⫽1.0⫻10⫺5 , ␭ e ⫽1.0⫻10⫺6

Dimension of linked
operators after PS

Furan

PyrrolePresent

Singlet

TripletSinglet

TripletA 1 (G) d
A1
A2
B1
B2

2456
1896
2260
2352
1805

2496
2425
2017
2379

17 01061 28758 006106 049
60 29265 94269 32749 41659 803A 1 (G) d
A1
A2
B1
B2

2457
1841
1883
1913
1758

2515
2199
2487
2701

16 43767 16572 43389 00466 40471 06888 101
88 69065 683a

The total number of MOs.
The number of frozen orbitals. 5 means ‘‘1s core’’.
c
The size of the active space, 共occupied MO plus unoccupied MO兲.
d
SAC ground state.
b

1. Singlet valence excited states

The first band system occurs in the region of 5.5–7.0 eVof the VUV spectrum. The maximum of this band lies at 6.04
eV 共peak I in Fig. 3兲, which was assigned to the valence␲ – ␲* transition V( 1 B 2 ) by Palmer et al.23 In addition,
Flicker et al.8 observed the intensity maximum of a broadtransition at 6.06 eV using electron impact spectroscopy andassigned it to X̃ 1 A 1 → 1 B 2 . In our present SAC–CI calculations, the excitation energy of the 1 1 B 2 state is computed at
6.40 eV with an oscillator strength of 0.1852: it clearly represents the most intense feature of peak I. The second moment 具 r 2 典 is 92.5358 a.u.2, which defines it as a valence
excited state, even if it is somewhat more diffuse than the
ground state ( 具 r 2 典 ⫽64.6624 a.u.2 ) due to valence–Rydberg
mixing. The nature of the 1 1 B 2 state is mainly the ␲ 3 – ␲ *共18→48兲 excitations mixed with the Rydberg transitions
共18→41兲, 共18→32兲, and 共18→46兲, etc. We would like toassign the first peak at 6.06 eV to the 1 1 B 2 state. The exci-

FIG. 2. Two highest occupied ␲ orbitals and two lowest unoccupied ␲*
orbitals of furan and pyrrole.

tation energies of the 1 1 B 2 state were calculated to be 6.04,
6.76, 5.95, 6.37, and 6.35 eV by CASPT2, MRDCI, MRMP,ADC共2兲, and CC3, respectively. The corresponding oscillator strengths are 0.1543, 0.183, 0.158, 0.148, and 0.144, respectively. When we estimate the accuracy of these theoretical results, we should take into account the difference
between the vertical excitation energy and the peak maximum. For example, it has been reported28 that the difference
between the vertical and the maximum peak excitation energies is at least 0.11 eV for the 1 B 2u valence excited state ofbenzene.
The region of greatest intensity in the VUV spectrum
occurs from approximately 7.2 to 8.4 eV, with an intensity
maximum at 7.8 eV 共peak II in Fig. 3兲, to which the valencetransition V( 1 A 1 ) has been assigned by most experimental
and theoretical studies. Our present results calculated the
6 1 A 1 state to lie at 8.34 eV above the ground state with anintensity of 0.4826. It is clearly related to the most intensefeature of peak II. Its second moment 具 r 2 典 is 97.5047 a.u.2,
which shows that it is a valence excited state, although it issomewhat more diffuse than the ground state due to slightvalence–Rydberg mixing. The nature of the 6 1 A 1 state is a
mixing of ␲ 3 – ␲ * 共18→53兲 and ␲ 2 – ␲ * 共17→48兲 excitations and the Rydberg transitions 共17→46兲 and 共17→38兲,
etc. Based on these results, we assign the 6 1 A 1 state as themain component of the V( 1 A 1 ) transition. Note that the nature of the 6 1 A 1 state is mixing of ␲ 3 – ␲ * and ␲ 2 – ␲ *Downloaded 25 May 2001 to 130.54.33.33. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

Excitation of furan and pyrrole

7857

TABLE III. Calculated excitation energies 共in eV兲, second moments, and main configurations by the SAC/
SAC–CI method for furan.
Second moment
State

a

Nature⌬E

1 1A 1
1 1A 2
1 1B 2
1 1B 1
2 1A 2
2 1A 12 1B 2
3 1A 2
2 1B 1
4 1A 2
3 1A 1
3 1B 1
5 1A 2
3 1B 2
4 1B 1
4 1B 2
6 1A 2
7 1A 25 1B 1
8 1A 2
4 1A 1
9 1A 25 1B 2
6 1B 1
5 1A 1
7 1B 1
6 1B 2
10 1 A 2
6 1A 18 1B 1
9 1B 1
10 1 B 1
7 1A 1
7 1B 28 1B 2
11 1 B 1
8 1A 1
12 1 B 1
9 1B 2
13 1 B 1

Ground3s⫺RV-mix
3p y ⫺R
3p z ⫺RV
3p x ⫺R
3d⫺R
3d yz ⫺R
3d⫺R
3d xy ⫺R
3s ⬘ ⫺R
4s⫺R
3d xz ⫺R
4p y ⫺R
4p x ⫺R
4p z ⫺R
4d⫺R
4d yz ⫺R
4d⫺R
4d xy ⫺R
5s⫺R
4d xz ⫺R
3p z⬘ ⫺R
3p x⬘ ⫺R
5p y ⫺R
5p x ⫺R
5p z ⫺R
V-mix
5d yz ⫺R
3d ⬘ ⫺R
3d ⬘ ⫺R
5d xy ⫺R
5d xz ⫺R⬘ ⫺R
3d xy
3d ⬘ ⫺R
4s ⬘ ⫺R
⬘ ⫺R
3d xz
V-mix
4 ⬘ p z ⫺R

0.0
5.99
6.40
6.45
6.66
6.79
6.82
7.04
7.14
7.27
7.36
7.45
7.50
7.51
7.67
7.71
7.72
7.85
7.89
7.93
7.99
8.04
8.07
8.07
8.14
8.18
8.19
8.21
8.34
8.47
8.54
8.67
8.69
8.75
8.79
8.87
8.95
8.95
9.08
9.15

1 3B 2
1 3A 1
1 3A 2
1 3B 12 3B 2
2 3A 2
2 3A 12 3B 1VV
3s⫺R
3p y ⫺R
3p x ⫺R
3p z /s⫺RV
3d yz ⫺R

4.39
5.63
5.98
6.52
6.66
6.68
7.10
7.21

b

Pol

y
x
z
y
x
z
x
y
x
y

x
z
y
x
z
x
y
z
x
x
x
z
y
y
x
x
z
y
x

f (r)

2

具x 典

具 y 2典

具 z 2典

具 r 2典0
Forbid0.18520.0313Forbid0.00000.0158Forbid0.0005
Forbid0.00010.0292
Forbid
0.01940.00080.0010ForbidForbid0.0000Forbid0.0002
Forbid
0.00690.00060.02050.00230.0016
Forbid
0.48260.00170.00950.02920.00350.02220.02430.00480.00360.07030.16620.000324.6628
42.5477
42.781737.042040.3748
25.988165.3598
41.610737.032052.6200
91.1382
45.5458
153.8467
108.2377
94.2931246.8240
104.4467
113.9521
79.7302121.5102211.5385
366.5189
225.2252
44.3096
83.4876
145.3949
389.8390147.3133
38.4469
54.9059
62.5576
57.9288
184.2435
168.8308
88.9270
38.4421135.2292
104.0758
56.3822111.3931

18.4772
34.803923.889365.4676
33.2618
20.0661
26.391268.772260.9984
30.071180.6382
47.8471
90.5160
40.0669226.6794
86.1320
91.4211256.0963
185.1881
76.7263200.0038
246.8423
78.9295
48.813939.7525
381.7329
133.7052
136.8059
26.9042120.4527
135.8883
47.8102173.1875
63.9795
68.644152.1882
98.2036
41.410341.892193.3319

21.5224
38.6635
25.8647
34.114175.043122.9068
37.741033.1252
64.9757
89.068340.2160
45.2990
99.9118
97.401890.712096.7509255.1376
75.7213190.2943
269.3098
80.1687
260.1989
209.5113
78.793037.0449
142.6457
144.3590
392.3236
32.1536
100.1038
117.9192
74.420371.3490157.0494
50.3966
72.9737
116.8031
97.6589
32.1471239.822164.6624116.0150
92.5358
136.6238
148.6797
68.9609129.4920
143.5080
163.0060
171.7594
211.9923
138.6919
344.2746
245.7064
411.6845
429.7070
451.0054
445.7697
455.2126
467.5463
491.7110873.5601
513.6660
171.9166
160.2850
669.7735
667.9031
676.4428
97.5047275.4624
316.3651
180.1593
428.7800
389.8597
207.9677
163.6040
350.2359
243.1450
130.4213
444.5471

¯
¯
¯
¯
¯
¯
¯
¯

25.0331
25.218143.0576
37.823373.504139.769929.0880
38.249718.3365
19.234434.1056
67.2748
29.523633.0344
22.2528
64.9995

22.606422.500237.2876
34.9733
34.641674.0609
23.5868
68.9878

65.9760
66.9527
114.4508
140.0714
137.6693
146.8652
74.9276172.2370ca

V and R denote, respectively, valence and Rydberg excited state. For details see the text.
Transition energy.
cPolarization direction of the transition moment.
btransitions, and the notation V( 1 A 1 ), based the simple four␲-orbital model, is inadequate because ‘‘V’’ denotes only
␲ 3 – ␲ * type transitions.
CASPT2 computed the 4 1 A 1 state at 7.74 eV with anintensity of 0.4159, and it was reported21 that the appearance
of intruder states in CASPT2 wave function renders an uncertainty of about 0.2 eV to this state. MRDCI computed thisstate at 8.324 eV with an intensity of 0.476. MRMP com-puted the 4 1 A 1 state at 7.69 eV with an oscillator strength of
0.494, ADC共2兲 at 8.16 eV with an oscillator strength of
0.308, CC3 at 8.35 eV with an oscillator strength of 0.350.
Recently, Palmer et al.23 assigned an absorption peak at
8.7 eV in their VUV spectrum 共peak III in Fig. 3兲 to thevalence excitation V ⬘ ( 1 B 2 ) with the aid of MRDCI calculated results: 9.422 eV with an intensity of 0.197. In theirstudies, the relative intensities were important for relating

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7858

Wan et al.

J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

TABLE IV. SAC–CI results compared with the experimental excitation energies and other theoretical results for furan.
CASPT2d

SAC–CIState
1Naturea

f (r)

⌬E b

CC3共CCSD兲e

State

5.92
6.04
6.46
6.59
6.16
6.48
7.00
7.15
7.22
7.31
7.21

1

1 A2
1 1B 2
1 1B 1
2 1A 2
2 1A 12 1B 2
3 1A 2
2 1B 1
4 1A 2
3 1A 1
3 1B 1

6.11
6.35
6.64
6.80
6.61
6.94
7.12

7.32
7.52

3d yz ( 1 B 1 )3s ⬘ ( 1 B 1 )

6.988
7.143

3d yz ( 1 B 1 )3s ⬘ ( 1 B 1 )7.13

3 1B 2

7.58
7.70
7.72

3d xy ( 1 A 1 )4s( 1 A 2 )3d xz ( 1 B 2 )

7.405
7.594
7.750

7.79

7.90
7.94

4p y ( 1 B 1 )4p x ( 1 B 2 )Nature1

1 A2
1 1B 2
1 1B 1
2 1A 2
2 1A 12 1B 2
3 1A 2
2 1B 1
4 1A 2
3 1A 1
3 1B 1
5 1A 2
3 1B 2
4 1B 1
4 1B 2
6 1A 2
7 1A 25 1B 1
8 1A 2
4 1A 1
9 1A 23s⫺RV
3p y ⫺R
3p z ⫺RV
3p x ⫺R
3d⫺R
3d yz ⫺R
3d⫺R
3d xy ⫺R
3s ⬘ ⫺R
4s⫺R
3d xz ⫺R
4p y ⫺R
4p x ⫺R
4p z ⫺R
4d⫺R
4d yz ⫺R
4d⫺R
4d xy ⫺R
5s⫺R

Forbid0.18520.0313Forbid0.00000.0158Forbid0.0005
Forbid0.00010.0292
Forbid
0.01940.00080.0010ForbidForbid0.0000Forbid0.0002
Forbid

5.99
6.40
6.45
6.66
6.79
6.82
7.04
7.14
7.27
7.36
7.45
7.50
7.51
7.67
7.71
7.72
7.85
7.89
7.93
7.99
8.04

5 1B 2
6 1B 14d xz ⫺R
3p z⬘ ⫺R

0.00690.0006

8.07
8.07

8.01
8.04

8.26
8.20

4d xz ( 1 B 2 )4d xy ( 1 A 1 )5 1A 1
7 1B 1
6 1B 2
10 1 A 2
6 1A 18 1B 1
9 1B 1
10 1 B 1
7 1A 1
7 1B 28 1B 2
11 1 B 1
8 1A 1
12 1 B 1
9 1B 2
13 1 B 1

3p x⬘ ⫺R
5p y ⫺R
5p x ⫺R
5p z ⫺R
V-mix
5d yz ⫺R
3d ⬘ ⫺R
3d ⬘yz ⫺R
5d xy ⫺R
5d xz ⫺R⬘ ⫺R
3d xy
3d ⬘ ⫺R⬘ ⫺R
3d xz
4s ⬘ ⫺RV-mix
4 ⬘ p z ⫺R

0.02050.00230.0016
Forbid
0.48260.00170.00950.02920.00350.02220.02430.00480.00360.07030.16620.0003

8.14
8.18
8.19
8.21
8.34
8.47
8.54
8.67
8.69
8.75
8.79
8.87
8.95
8.95
9.08
9.15

8.10
8.19
8.23

8.26
8.34
8.36

3p x⬘ ( 1 A 1 )5p y ( 1 B 1 )5p x ( 1 B 2 )

8.35
8.52
8.50

V( 1 A 1 )5d xz ( 1 B 2 )5d xy ( 1 A 1 )

8.7
8.96

8.38

1 3B 2
1 3A 1
1 3A 2
1 3B 12 3B 2
2 3A 2
2 3A 1VV
3s⫺R
3p y ⫺R
3p x ⫺R
3p z /s⫺R
V

¯
¯
¯
¯
¯
¯
¯

4.39
5.63
5.98
6.52
6.66
6.68
7.10

3.99
5.15

3.99
5.15
5.86
6.42

5.91
6.04
6.47
6.61
6.75

7.28
7.38
7.43
7.52
7.53

3s( A 2 )V( 1 B 2 )3p y ( 1 B 1 )3p z ( 1 A 2 )V( 1 A 1 )3p x ( 1 B 2 )3d z2 ( 1 A 2 )

7.70

7.8
8.32
8.34
8.46

7.74

4 1A 1

8.77

V 1B 2

⬎9

⬃6.5
⬃6.5

V( 1 B 2 )⌬E h

ADC共2兲i⌬E

Expt.c⌬E f

MRDCIg⌬E

Nature

5.86
6.37
6.35
6.50
6.70
6.73

3s( 1 A 2 )V( 1 B 2 )3p( 1 B 1 )3p( 1 A 2 )V ⬘( 1A 1)
3p( 1 B 2 )3d z2 ( 1 A 2 )4s( 1 A 2 )3d xy ( 1 A 1 )

6.89
6.98
7.22
7.05
7.80
7.11
7.30
7.35

3d( 1 A 2 )3d( 1 B 1 )3d( 1 A 1 )3s ⬘ ( 1 B 1 )4s( 1 A 2 )3d( 1 A 2 )4s( 1 A 2 )3d( 1 B 2 )7.824

4p x ( 1 B 2 )7.48

4p( 1 B 1 )7.652

4p y ( 1 B 2 )

7.563
8.581
8.844
8.148
8.040

4d z2 ( 1 A 2 )4d xy ( 1 A 1 )5s( 1 A 2 )3p x⬘ ( 1 A 1 )3p z⬘ ( 1 B 1 )8.324

V( 1 A 1 )

7.53
7.51
7.57
7.72
7.87
7.82
7.66
7.72
7.80
7.61
7.96
7.99
7.71
8.16

4p( 1 B 2 )4p( 1 A 2 )3 P ⬘( 1A 2)
4d( 1 B 1 )4d( 1 B 2 )4d( 1 A 1 )4d( 1 A 2 )4d( 1 A 2 )5s( 1 A 2 )3p ⬘ ( 1 B 1 )5p( 1 B 1 )5p( 1 B 2 )3p ⬘ ( 1 A 1 )V( 1 A 1 )

8.327
8.359

⬘ ( A 1)3d xz
⬘ 22 ( 1 B 1 )3d x⫺y

8.06
8.32
8.23

3d ⬘ ( 1 B 1 )3d ⬘ ( 1 B 2 )3d ⬘ ( 1 B 1 )

8.936
8.395

⬘ -( 1 B 2 )3d xy
3d z⬘ 2 ( 1 B 1 )8.51

3d ⬘ ( 1 A 1 )9.422

V ⬘( 1B 2)

8.64
8.41

V ⬘( 1B 2)
4s ⬘ ( 1 B 1 )Nature
1

5.950
6.759
6.659

3s( A 2 )V( 1 B 2 )3p x ( 1 B 2 )

6.024
6.633

V( 1 A 1 )3p y ( 1 B 1 )

3.931
5.282
8.682
9.077
6.313
8.733
6.648

1

4.31
5.50
5.81
6.31

a

V and R denote, respectively, valence and Rydberg excited state. For details see the text.
Transition energy 共in eV兲.
c
Experimental data were taken from Refs. 21–25 and references therein.
dReference 21.
eReference 25.
f
CC3 for valence and CCSD for Rydberg.
gReference 22.
hDifferent basis sets were used for valence and Rydberg.
iReference 24.
b

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J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

FIG. 3. VUV spectrum and SAC–CI theoretical spectrum of furan.

calculated results with experimental data when MRDCI results did not agree with the experimental data for the higher␲ – ␲* transitions. Our present results give the 9 1 B 2 state at
9.08 eV with an intensity of 0.1662 in this region. The second moment 具 r 2 典 of this state is 130.4213 a.u.2, whichclearly shows that this state has significant diffuse character.
Its nature is mainly due to the ␲ 2 – ␲ * 共17→53兲 and共17→64兲 excitations V ⬘ ( 1 B 2 ) mixed by the Rydberg transitions 共17→26兲 and 共17→36兲, etc. CASPT2 calculated thisstate at 8.38 eV with an intensity of 0.27. MRMP did notgive this state. ADC共2兲 computed this state at 8.64 eV withan oscillator strength of 0.116. CC3 estimated this state to be
above 9 eV and therefore outside of the energy range considered.
Finally, we discuss the valence excitation, V ⬘ ( 1 A 1 ),which is expected to occur in the first band. However, contrary to the V( 1 B 2 ) valence excitation which has been relatively well established, the V ⬘ ( 1 A 1 ) excitation is so complicated that it has not yet been reasonably assigned. There is a
progression of weak peaks at 5.70, 5.80, 5.89, and 5.91 eV in
the UV absorption spectrum. This was assigned to a Rydbergtransition and its vibronic lines by Robin,15 and to theV ⬘ ( 1 A 1 ) valence transition by Roebber et al.13 Palmer et al.
stated that their recent work23 supported the valence-type
assignment because their MRDCI calculations gave the energy order 1 A 1 ⬍ 1 B 2 for the two lowest valence transitions,although the numerical results for these two states changed
greatly with different basis sets. The 1 A 1 state was calculated
at 6.024 eV with an intensity of 0.011, and the 1 B 2 state wascalculated at 6.759 eV with an intensity of 0.183 using the
double zeta plus polarization 共DZP兲 basis, and these twostates were calculated at 6.63 and 6.88 eV, respectively, using the DZPR basis in a MRDCI study.23 Note that the natureof the 2 1 A 1 state in the MRDCI study is only ␲ 2 → ␲ * .

Excitation of furan and pyrrole

7859

CASPT2 computed the 2 1 A 1 state at 6.16 eV with an intensity of 0.0015, and its nature was reported to be a mixture of
the configurations 2b 1 →3b 1 and 1a 2 →2a 2 and the double
excitation of 关 (1a 2 ) 2 →(3b 1 ) 2 兴 . MRMP computed the 2 1 A 1
state at 6.16 eV with an intensity of 0.0035, and its nature
was almost the same as that by CASPT2, Rydberg mixing
was also found. ADC共2兲 computed this state at 6.70 eV withan oscillator strength of 0.003. CC3 computed it to be 6.61
eV with an oscillator strength of 0.000. Our present calculations give the 2 1 A 1 state at 6.79 eV with an oscillator
strength of 0.0000. Its second moment 具 r 2 典 is 68.9609 a.u.2,
which clearly defines it as a valence excited state, and its
nature is a mixture of ␲ 2 – ␲ * 共17→48兲 and 共17→61兲 and␲ 3 – ␲ * transitions 共18→53兲 and 共18→64兲. Double excitation makes a rather small contribution. Note that all of theabove-mentioned theoretical methods, except MRDCI, gavean energy order of 1 B 2 ⬍ 1 A 1 . This implies that the first 1 A 1
valence state should be located at a higher energy shoulder ofthe first band. Due to the very weak intensity of this valencetransition, there is no obvious experimental evidence to confirm the theoretical results, and vice versa. However, in thecase of thiophene, which will be discussed in a later paper,43
the 2 1 A 1 state has been well characterized with regard toboth excitation energy and oscillator strength, in comparison
with the experimental data of the VUV and magnetic circulardichroism spectra.
2. Singlet Rydberg states

The lowest singlet Rydberg transition has been assigned
to the 1a 2 →3s Rydberg series. Robin15 first assigned theweak feature at 5.94 eV to the dipole-forbidden 1 A 2 Rydberg
state, and later Roebber et al.13 also assigned the weak peakat 5.91 eV to the 1a 2 →3s Rydberg state using multiphoton
ionization spectroscopy 共MPI兲. In the present calculations,the 1 1 A 2 state is computed at 5.99 eV and its nature is a
3s-Rydberg transition. The CASPT2, MRDCI, MRMP,ADC共2兲, and CCSD methods computed this state at 5.92,
5.95, 5.84, 5.86, and 6.11 eV, respectively.
The group of transitions in the region 6.4–6.8 eV has
usually been assigned to the 1a 2 →3p Rydberg series. Derrick and co-workers5,6 assigned the band with a 0–0 origin at
6.475 eV to the transition 1a 2 →3pb 2 . Cooper et al.12 assigned 6.47 eV to the 3p Rydberg states in their MPI spectroscopy studies, which supported the results of Derrick andco-workers. Recently, the 3pb 2 ( 1 B 1 ) assignment was questioned by Palmer et al.,22 who assigned 6.472 eV to the 1 B 2state on the basis of their MRDCI calculations. Our present
calculations computed the 2 1 B 2 state at 6.82 eV, well separated from the 1 1 B 1 transition at 6.45 eV, which is consistent with the ADC共2兲 and CCSD results. Therefore, we assigned an observed transition at 6.47 eV to the 1a 2
→3p y (1 1 B 1 ) Rydberg series.
The nature of the transition observed at 6.75 eV has been
the subject of controversy.12,14,23 Cooper et al.12 assigned it
tentatively to the 1 A 1 valence-type transition. This was criticized by Robin,15 and more recently, this peak at 6.75 eV
was assigned to the 3p-Rydberg transition by Nyulaszi.14
Recently, Palmer et al.23 convincingly proved the
3p-Rydberg origin of the 6.75 eV band, but assigned it to

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7860

Wan et al.

J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

1a 2 →3p y ( 1 B 1 ) based on their MRDCI results. Taking into
account the discussion on the 6.47 eV transition, we believe
the 2 1 B 2 state is a better candidate for the observed 6.75 eVtransition, which is consistent with the ADC共2兲 and CCSD
results. CASPT2 computed the 1 1 B 1 and 2 1 B 2 states at 6.46
and 6.48 eV, respectively, and assigned both of them to the
6.47 eV transition. MRMP computed the 1 1 B 1 and 2 1 B 2state at 6.40 and 6.50 eV, respectively, and also assigned
both of them to the 6.47 eV transition. Apparently, the observed 6.75 eV transition was overlooked by the CASPT2
and MRMP studies, which is rather misleading because noevidence for a second transition at 6.48 eV can be found in
the experimental spectrum. In addition, we computed thedipole-forbidden 2 1 A 2 state at 6.66 eV, which is a 1a 2
→3p z Rydberg series.
Following the above-mentioned three 3p-Rydberg
states, there is an experimentally identified Rydberg transition at 7.28 eV. This transition was interpreted as the
3d-Rydberg series,5,7,14 however, the spatial symmetry designation of this series is again not fully secure. Derrick andco-workers5,6 experimentally assigned the transition at 7.28
eV to the 3 1 A 1 state. CASPT2 calculations gave the 2 1 B 1
state at 7.15 eV and the 3 1 A 1 state at 7.31 eV, and followed
the assignment of Derrick and co-workers MRMP and
ADC共2兲 also followed the choice of CASPT2: the 2 1 B 1 and
3 1 A 1 states were computed at 7.10 and 7.26 eV by MRMP,
and at 6.98 and 7.22 eV by ADC共2兲, respectively. Recently,
however, Palmer et al.22 assigned the observed 7.28 eV transition to the 3d( 1 B 1 ) state according to their MRDCI results:
the 2 1 B 1 state at 6.988 eV and the 3 1 A 1 state at 7.75 eV.
CCSD calculated the 3d yz ( 1 B 1 ) state at 7.32 eV and followed the assignment by Palmer et al. Our present results
computed the 2 1 B 1 (3d yz ) state at 7.14 eV, and the
3 1 A 1 (3d xy ) state at 7.36 eV. The assignment to the
3d xy ( 1 A 1 ) state seems more natural, and therefore we assign
the 7.28 eV transition to the 3 1 A 1 (3d xy ) Rydberg series, aswith CASPT2, MRMP, and ADC共2兲.
The next transition at 7.38 eV has usually been assigned
to the 1b 1 →3s Rydberg series (3s ⬘ ). 5,12,23 Our present calculations gave the 3 1 B 1 (3s ⬘ ) state at 7.45 eV. CASPT2,MRDCI, MRMP, ADC共2兲, and CCSD calculations gave thisstate at 7.21, 7.143, 7.31, 7.05, and 7.52 eV, respectively.
Regarding the transitions at 7.43, 7.52, and 7.53 eV,
MRDCI calculations assigned them to the dipole-forbidden
transitions 1a 2 →3d ( 1 A 2 , 7.405 eV兲, 1a 2 →4s ( 1 A 2 , 7.594
eV兲 and the dipole-allowed transition 1a 2 →3d ( 1 A 1 , 7.750
eV兲 states, respectively. ADC共2兲 studies assigned these threetransitions to the 3d ( 1 A 2 , 7.22 eV兲, 4s ( 1 A 2 , 7.30 eV兲, and3d ( 1 B 2 , 7.35 eV兲 states, respectively. However, according
to our present results, we prefer to tentatively assign them to
3 1 B 2 (3d xz , 7.51 eV兲, 4 1 B 1 (4 p y , 7.67 eV兲, and 4 1 B 2(4 p x , 7.71 eV兲. Our present assignment of Rydberg transitions lower than 7.53 eV is consistent with the energy orderand gap of the experimental data.
In the energy region higher than 7.53 eV, Rydberg transitions become increasingly dense, and the assignment of
individual Rydberg transitions is more difficult. Therefore,
the assignments of the experimental data higher than 7.53 eV
given in Table IV are tentative.

3. Triplet excited states

The two lowest triplet transitions of furan have been
well
identified
byelectronenergy-loss
共EEL兲
spectroscopy8–10,23 at 3.99 and 5.2 eV, which are assigned tothe 3 B 2 and 3 A 1 valence transitions, respectively. Ourpresent calculations computed the 1 3 B 2 state at 4.39 eV witha second moment of 65.9760 a.u.2, and 1 3 A 1 at 5.63 eV witha second moment of 66.9527 a.u.2. The second moments ofthese two states clearly characterize them as valence excitations. The main configurations of 3 B 2 are 共18→48兲,
共18→61兲, 共18→57兲, etc., and those of 3 A 1 are 共17→48兲,
共18→64兲, 共18→53兲, 共17→61兲, etc.
Recently, Palmer et al.23 observed two higher triplet
transitions at around 6.5 eV in their EEL spectrum study andassigned them to the 2 3 A 1 and 2 3 B 2 states. Our present
calculations gave the 3p series of triplet Rydberg states inthis energy region, 1 3 B 1 (3p y ) at 6.52 eV, 2 3 B 2 (3p x ) at
6.66 eV, and 2 3 A 2 (3p z ) at 6.68 eV. The valence triplet excited state 2 3 A 1 was given at 7.10 eV with the main configurations of 共17→48兲, 共18→53兲, 共18→64兲, etc. Thesestates are related to the two higher triplet transitions in the
EEL spectrum.
B. Pyrrole

The SCF energy of pyrrole is -208.838 068 hartrees. The
SAC ground-state energy is ⫺209.218 937 hartrees, and thecorrelation energy is ⫺0.380 869 hartrees. The corresponding previous values were ⫺208.754 72, ⫺208.993 36, and⫺0.238 64 hartrees, respectively.
The principal SAC–CI results for the singlet and triplet
vertical excitation energies are shown in Table V, along withthe oscillator strength 关 f (r) 兴 and second moment of each
excited state. In Table VI, the present SAC–CI singlet andtriplet excitation energies are compared to the experimental
values, and to the results obtained by CASPT2, MRMP,ADC共2兲, and CC3. Figure 4 shows a comparison of the experimental VUV spectrum24 and the theoretical SAC–CI
spectrum of pyrrole. Additionally, to interpret the similarities
and differences between the VUV spectra of pyrrole and furan, the excitation energies, oscillator strengths, second moments, and main configurations of the valence excitations of
the two molecules are compared in Table VII.
1. The first intense and broad band (5.2 – 6.6 eV) of
the VUV spectrum

Our present calculations show that the first three 1 B 2states are computed at 5.88, 6.48, and 6.76 eV, respectively,
with oscillator strengths of 0.0805, 0.0475 and 0.0789, respectively. The second moments of the three excited statesare 132.1, 146.3, and 224.7 a.u.2, respectively. It is difficult
to distinguish these three states as valence excitation or Rydberg excitation by the second moments and oscillator
strengths. However, we can use a simple hybrid model togive an interpretation. Since there are three configurations
1 1 B 2 (1a 2 →3p x ), 2 1 B 2 共valence 1a 2 → ␲ * 兲, and3 1 B 2 (1a 2 →3d xz ) which are close in energy, we can assume that these three configurations (1a 2 →3p x , ␲*, and3d xz 兲 are strongly mixed with each other and then construct
three
new
hybridexcitedstates
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J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

Excitation of furan and pyrrole

7861

TABLE V. Calculated excitation energies 共in eV兲, oscillator strengths, and second moments of pyrrole.
Second moment
State

Naturea⌬E b

1 1A 1
1 1A 2
1 1B 1
2 1A 2
1 1B 2
2 1B 1
3 1A 2
3 1B 1
2 1A 1
4 1A 2
2 1B 2
3 1A 1
4 1B 1
5 1A 2
3 1B 2
4 1A 15 1B 1
6 1A 2
4 1B 2
7 1A 2
8 1A 2
6 1B 1
5 1A 1
7 1B 15 1B 2
9 1A 28 1B 1
10 1 A 2
9 1B 1
6 1B 2
6 1A 1
7 1B 2
10 1 B 1
11 1 B 1
7 1A 1
8 1A 18 1B 2
9 1A 1
12 1 B 1
9 1B 2
10 1 A 1
10 1 B 2
11 1 A 1

Ground3s⫺R
3p y ⫺R
3p z ⫺R
3p x ⫺R
3s ⬘ ⫺R
3d⫺R
3d yz ⫺R
V
3d⫺R
V-3d xz ⫺R
3d xy ⫺R
3p z⬘ ⫺R
4s⫺R
3d xz ⫺R
3p x⬘ ⫺R
4p y ⫺R
4p z ⫺R
4p x ⫺R
4d⫺R
4d⫺R
4d yz ⫺R
4d xy ⫺R
3d ⬘ ⫺R
4d xz ⫺R
5s⫺R
3d ⬘ ⫺R
5p z ⫺R
5p y ⫺R
5p x ⫺R
⬘ ⫺R
3d xz
⬘ ⫺R
3d xy
4s ⬘ ⫺R
5d yz ⫺R
4 ⬘ p x ⫺R
V-mix
5d xz ⫺R
5d xy ⫺R
4d ⬘ ⫺R
⬘ ⫺R
4d xy
⬘ ⫺R
4d xz
V-mix
5 ⬘ p x ⫺R

0
5.11
5.80
5.81
5.88
6.05
6.38
6.39
6.41
6.44
6.48
6.64
6.68
6.71
6.76
6.86
6.93
6.95
6.99
7.11
7.13
7.14
7.26
7.26
7.26
7.27
7.34
7.44
7.44
7.45
7.49
7.55
7.63
7.75
7.83
7.88
7.93
7.99
8.02
8.14
8.20
8.25
8.32

1 3B 2
1 3A 2
1 3A 1
1 3B 1V
3s⫺R
V
3p y ⫺R

4.58
5.08
5.60
5.82

Polc

x
y
x
x
z
y
z
x
y
z
x
y

x
z
x
y
x
x
y
z
y
x
x
z
z
y
z
x
y
z
y
z

f (r)

具 x 2典具 y 2典

具 z 2典

具 r 2典0
Forbid
0.0211
Forbid
0.08050.0005
Forbid
0.00370.0002
Forbid
0.04750.00000.0266
Forbid
0.07890.01460.0029Forbid
0.0020ForbidForbid0.00010.00410.00180.0119Forbid
0.0092
Forbid
0.00480.00200.06790.00520.00000.00020.00200.32520.01270.08140.0001
0.04450.07580.25530.001426.309338.5385
40.1805
44.0000
70.6606
39.1957
42.189940.0846
29.5900
70.1989
68.327895.7588
44.3956112.8202
103.2229
81.7840
103.5279
131.9602
244.7481
167.1016
105.1136
86.5404
216.4420
49.2432
209.6781
296.8269
63.3648
195.3911
142.7447
390.0070
88.5856
100.2877
115.5165
83.3076
243.7424
113.6843
184.2486
161.1558
105.1475
198.4062
195.4445
69.5117398.9488

20.6830
31.6834
69.3496
38.944231.570737.240978.462564.5531
24.3270
31.998130.0456
83.849844.7269
79.8926
41.5147
39.3594254.7510
107.6015
87.0448189.0867
149.2357
203.5861
205.8745
59.817675.2864230.0584
73.0189
177.9971
373.8345
135.3600
41.1360
91.348280.3642190.2939
93.9043
66.9987
67.3410144.0513
189.7472
188.6370
73.8492
56.0848141.0667

18.333444.499335.1595
56.7104
29.904143.752147.3118
64.3982
19.428157.5656
47.941037.421461.0966
147.4559
79.998132.4668
99.6378
177.5677
89.8109
88.1108231.5695
194.1834
77.9965
59.5719199.8960
330.6280
33.5406
371.4336
138.7340
136.3607
73.484737.2567149.7550
187.5531
89.394870.1911173.6527
66.2029184.0334
71.1856
177.7282
33.4018
139.610965.3256
114.7213
144.6895
139.6547
132.1354
120.1888
167.9642
169.0359
73.3451
159.7626
146.3143
217.0300
150.2190
340.1687
224.7356
153.6102457.9166
417.1295
421.6038
444.2990
485.9187
484.3100
500.3131168.6327
484.8605
857.5133
169.9242
744.8217655.3133
661.7277
203.2063
228.8926
345.6358
461.1546
427.0415
250.8741
425.2423
371.4099
478.9280
458.2288
447.0220158.9982
679.626526.7894
38.941727.3228
40.091720.9241
31.5646
22.2646
67.9226

19.4356
42.5046
18.899034.3289

67.1491
113.011068.4864142.3432aV and R denote, respectively, the valence and Rydberg excited state. For details see the text.
Transition energy.
cPolarization direction of the transition moment.
b→3px ,␲*,3d xz ), 2 1 B 2 共valence 1a 2 → ␲ * , 3p x , 3d xz 兲 and3 1 B 2 (1a 2 →3d xz , ␲ * ,3p x ) that are moderately separated inenergy. Thus, an attempt to assign pure Rydberg or purevalence excitations in this case is meaningless. In our present
calculations, we found that one valence transition configuration, 1a 2 → ␲ * (18→52), is included in all three 1 B 2 states,
and its contributions 共absolute value of the coefficient ofconfiguration兲 to the three 1 B 2 states are 0.35, 0.48 and 0.53,
respectively. This further shows that the intensity of this energy region can be attributed mostly to valence excitation,and explains why Rydberg transitions (1a 2 →3p x , ␲*, 3d xz
and 1a 2 →3d xz , ␲*, 3p x 兲 show strong intensity in this energy region. Our present calculated excitation energies, oscillator strengths, and second moments for the three 1 B 2states are very similar to those by CC3 calculations. Assignment of the first 1 B 2 valence excitation in this energy region
has been controversial in other theoretical studies.22,24,25,26,29
Although the 2 1 B 2 state was calculated and assigned to be
the valence excitation and was the major source of intensity
for this energy region in CASPT222 and MRMP25 studies,

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7862

Wan et al.

J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

TABLE VI. SAC–CI results compared with the experimental excitation energies 共in eV兲 and other theoretical results for pyrrole.
SAC
State
1

Naturea

CASPT2d

SAC–CIf (r)⌬E bExpt.c
⬃5.22
⬃5.7

1 A2
1 1B 1
2 1A 2
1 1B 2
2 1B 1
3 1A 2
3 1B 1
2 1A 1
4 1A 2
2 1B 2
3 1A 1
4 1B 1
5 1A 2
3 1B 23s⫺R
3p y ⫺R
3p z ⫺R
3p x ⫺R/V
3s ⬘ ⫺R
3d⫺R
3d yz ⫺R
V
3d⫺R
V/3d xz ⫺R
3d xy ⫺R
3p z⬘ ⫺R
4s⫺R
3d xz ⫺R/V

Forbid
0.0211
Forbid
0.08050.0005
Forbid
0.00370.0002
Forbid
0.04750.00000.0266
Forbid
0.0789

5.11
5.80
5.81
5.88
6.05
6.38
6.39
6.41
6.44
6.48
6.64
6.68
6.71
6.76

4 1A 15 1B 1
6 1A 2
4 1B 2
7 1A 2
8 1A 2
6 1B 1
5 1A 1
7 1B 15 1B 2
9 1A 28 1B 1
10 1 A 2
9 1B 1
6 1B 2
6 1A 1
7 1B 2
10 1 B 1
11 1 B 1
7 1A 1
8 1A 18 1B 2
9 1A 1
12 1 B 1
9 1B 2
10 1 A 1
10 1 B 2
11 1 A 1
1 3B 2
1 3A 2
1 3A 1
1 3B 1

3p x⬘ ⫺R
4p y ⫺R
4p z ⫺R
4p x ⫺R
4d⫺R
4d⫺R
4d yz ⫺R
4d xy ⫺R
3d ⬘ ⫺R
4d xz ⫺R
5s⫺R
3d ⬘ ⫺R
5p z ⫺R
5p y ⫺R
5p x ⫺R
⬘ ⫺R
3d xz
⬘ ⫺R
3d xy
4s ⬘ ⫺R
5d yz ⫺R
4 ⬘ p x ⫺R
V-mix
5d xz ⫺R
5d xy ⫺R
4d ⬘ ⫺R
⬘ ⫺R
4d xy
⬘ ⫺R
4d xy
V-mix
5 ⬘ p x ⫺R
V
3s⫺RV
3p y ⫺R

0.01460.0029Forbid
0.0020ForbidForbid0.00010.00410.00180.0119Forbid
0.0092
Forbid
0.00480.00200.06790.00520.00000.00020.00200.32520.01270.08140.0001
0.04450.07580.25530.0014

6.86
6.93
6.95
6.99
7.11
7.13
7.14
7.26
7.26
7.26
7.27
7.34
7.44
7.44
7.45
7.49
7.55
7.63
7.75
7.83
7.88
7.93
7.99
8.02
8.14
8.20
8.25
8.32
4.58
5.08
5.60
5.82

⬃5.86
⬃6.42

6.2–6.5
6.5–6.7
6.78
7.0–7.1
7.0–7.1

MRMPe⌬E

Nature

5.08
5.85
5.83
5.78
5.97
6.40
6.42
5.92
6.51
6.00
6.54
6.62

1

⌬E

1 A 2 -3s
1 1 B 1 -3p
2 1 A 2 -3p
1 1 B 2 -3p
2 1 B 1 -3s ⬘3 1 A 2 -3d
3 1 B 1 -3d
2 1 A 1 -V
4 1 A 2 -3d
2 1 B 2 -V
3 1 A 1 -3d
4 1 B 1 -3p ⬘

4.92
5.70
5.74
5.87
5.81
6.45
6.38
5.98
6.44
6.51
6.52
6.48

6.53
7.31
6.65

3 1 B 2 -3d
6 1 A 2 -3d ⬘4 1 A 1 -3p ⬘

6.61
7.25
6.62

6.77

5 1 A 2 -3d ⬘

6.70

7.39
7.72

6 1 B 1 -3d ⬘5 1 B 2 -4d

7.23

7.32

5 1 B 1 -3d ⬘7.14

7.0–7.1

⬃7.35
⬃7.4

ADC共2兲f

CC3g⌬E

Nature⌬E

Nature

5.03
5.68
5.71
5.86
5.77
6.25
6.27
6.66
6.37
6.48
6.54
6.43
6.55
6.71

1

3s( A 2 )3p( 1 B 1 )3p( 1 A 2 )3p( 1 B 2 )3s ⬘ ( 1 B 1 )3d( 1 A 2 )3d( 1 B 1 )V ⬘( 1A 1)
3d( 1 A 2 )3d( 1 B 2 )3d( 1 A 1 )3p ⬘ ( 1 B 1 )4s( 1 A 2 )V( 1 B 2 )

6.42
6.78
6.78
6.88
6.98
6.99
7.00
7.12
6.97
7.14

3p ⬘ ( 1 A 1 )4p( 1 B 1 )4p( 1 A 2 )4p( 1 B 2 )4d( 1 A 2 )4d( 1 A 2 )4d( 1 B 1 )4d( 1 A 1 )3d ⬘ ( 1 B 1 )4d( 1 B 2 )

5.20
5.95
5.94
6.04
6.12
6.51
6.55
6.37
6.57
6.57
6.87
6.82
6.92
6.90
6.97
7.04
7.17
7.16
7.20
7.34
7.36
7.37
7.48
7.41
7.48

3s( 1 A 2 )3p y ( 1 B 1 )3p z ( 1 A 2 )3p x ( 1 B 2 )3s ⬘ ( 1 B 1 )3d( 1 A 2 )3d yz ( 1 B 1 )V( 1 A 1 )3d( 1 A 2 )V( 1 B 2 )3d xy ( 1 A 1 )3p z⬘ ( 1 B 1 )4s( 1 A 2 )3d xz ( 1 B 2 )3p ⬘y ( 1 A 2 )?
3p x⬘ ( 1 A 1 )4p y ( 1 B 1 )4p z ( 1 A 2 )4p x ( 1 B 2 )4d( 1 A 2 )4d( 1 A 2 )4d yz ( 1 B 1 )4d xy ( 1 A 1 )3d ⬘ ( 1 B 1 )4d xz ( 1 B 2 )7.09

3d ⬘ ( 1 B 1 )7.47

3d ⬘ ( 1 B 1 )

⬃7.54
⬃7.7
⬃7.85
⬃7.95
7.5–8
⬃8.0
⬃8.1

7.36
7.43

5 1 A 1 -3d ⬘4 1 B 2 -3d ⬘

7.20
7.36

7.23
7.26
7.24

3d ⬘ ( 1 A 1 )3d ⬘ ( 1 B 2 )4s ⬘ ( 1 B 1 )7.46

6 1 A 1 -V

7.48

7.75

V( 1 A 1 )7.88¯
and more Ryds
¯

7.91

¯
and more Ryds¯

7 1 A 1 -4d ⬘

8.31
4.2
5.10

4.21
5.04
5.16
5.82

V( 1 A 1 )V( 1 B 2 )

4.59
5.00
5.55
5.63

a

V and R denote, respectively, valence and Rydberg excited state. For details see the text.
Transition energy.
cExperimental data are taken from Refs. 3, 7, 9, and 22, and references therein. Those for valence excitations are chosen as the bands’ maximum; those for
Rydberg transitions are 0–0 excitation energies.
dReference 21.
eReference 23.
f
Reference 24.
g
Reference 25.
b

the difference in the calculated vertical excitation energy ofthe 2 1 B 2 state between CASPT2 and MRMP studies is aslarge as 0.51 eV. In recent ADC共2兲 studies,26 however, thefirst 1 B 2 valence excitation was suggested to be outside thisenergy region, and the intensity for this region was ascribed
mostly to the 1a 2 →3 p(1 1 B 2 ) Rydberg transition.
A weak singlet excited state has been observed at about

5.22 eV and assigned to one 1 A 1 state in the VUV absorption
spectrum by Mullen and Orloff.3 However, this assignment
was disputed by Robin15 and experimentally assigned to a
Rydberg state. The present calculations compute the 1 1 A 2
state with 1a 2 →3s nature at 5.11 eV, which supports thenotion that the lowest singlet state might be due to the vibrational structure of the dipole-forbidden 1a 2 →3s Rydberg

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J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

Excitation of furan and pyrrole

FIG. 4. VUV spectrum and SAC–CI theoretical spectrum of pyrrole.

transition, since the present calculations, together with previous high-level calculations,22,26,29 show that there is noother singlet state in this energy region.
Next, we discuss the valence excitation, V ⬘ ( 1 A 1 ), whichis expected to occur in the first band. As we discussed for the
2 1 A 1 state of furan, a similar situation occurs in the 2 1 A 1
state of pyrrole. Our present calculations give the 2 1 A 1 state
at 6.41 eV with an oscillator strength of 0.0002. Its second
moment 具 r 2 典 is 73.3451 a.u.2, which clearly characterizes it
as a valence excited state, and its nature is a mixture of␲ 2 – ␲ * 共17→52兲 and ␲ 3 – ␲ * transitions 共18→53兲 and共18→66兲. Double excitation makes a rather small contribution. CC3 computed it to be 6.37 eV with an oscillator
strength of 0.001. ADC共2兲 computed this state at 6.66 eVwith an oscillator strength of 0.017. CASPT2 computed the2 1 A 1 state at 5.92 eV with an intensity of 0.0195, and its
nature was reported to be a mixture of the single excitation

7863

2b 1 →3b 1 and 1a 2 →2a 2 configurations in combination
with a large fraction 共25%兲 of double excitations (1a 2 ) 2→(3b 1 ) 2 . MRMP computed this state at 5.98 eV with anintensity of 0.0098, and its nature was almost the same asthat of CASPT2. Note that here there is again a discrepancy
between SAC–CI, CC3, and CASPT2, MRMP results. However, in the case of thiophene, which will be discussed in alater paper,43 the 2 1 A 1 state 共lowest excited state兲 has been
well characterized to be predominantly single excitation byboth SAC–CI and CASPT2 with regard to both excitationenergy and oscillator strength, in good accordance with theexperimental data of the VUV and magnetic circular dichroism spectra. Generally speaking, the SAC–CI SD-R method
used here, together with the CCSD/CC3 and EOM-CCSD共T兲
methods, is best applied to states that are largely single excitation in nature, and may give a relatively high excitationenergy estimate for the state of significant doubly excitedcharacter. Therefore, the doubly excited characters of the
2 1 A 1 states of this series of five-membered ring compounds
deserve to be further investigated by the SAC–CI general-R
method,44 which is suitable for two- and many-electron processes.
In the VUV spectrum of Mullen and Orloff,3 absorption
peaks are observed at around 5.71 and 5.88 eV, and a question arises as to whether these two absorption peaks represent two separate electronic transitions or one transition withan associated vibrational structure. In the later UV spectrumof Bavia et al.,7 absorption peaks were reported at around5.82 and 5.86 eV, however, an obvious absorption peak ataround 5.7 eV was ignored. In the latest VUV spectrum ofPalmer et al.,24 absorption peaks were reported at around5.698 and 5.861 eV and assigned to the 1 1 B 2 (1a 2 →3p ␲ )and 1 1 B 1 (1a 2 →3p y ) states, respectively. The 5.861 eVtransition is the most intense and shows obvious vibrational
structures in the first band. Other nearby peaks, e.g., 5.82 and5.88 eV, are interpreted as part of the vibrational structure ofthis transition. Palmer et al.,24 by comparing this with theenvelope of the first band in PES,5 confirmed that the 5.861
eV absorption arises from the excitation of a 1a 2 →3p Rydberg state associated with IP1 共8.21 eV兲. Our present calculations support this general experimental assignment, but thecalculated excitation energy orders and oscillator strengths
prefer the assignment of the 5.861 eV transition to
1 1 B 2 (1a 2 →3p x , ␲ * ) and the 5.698 eV transition to

TABLE VII. Comparison of electronic transition mechanisms in pyrrole and furan.
Pyrrole
State
1

1 A1
1 1B 2
2 1A 12 1B 2
3 1B 2
8 1A 1
10 1 B 2aNatureGround3p x ⫺R⬃V
V
V-3d xz ⫺R
3d xz ⫺R⬃V
V-mix
V-mix

⌬E
0
5.88
6.41
6.48
6.76
7.88
8.25

Furan
a

f (r)

SM

0.081
0.000
0.048
0.079
0.325
0.255

⫺65.3
⫺132.1⫺73.3⫺146.3⫺224.7⫺250.9⫺159.0MCb

1a 2 ⫺3p x , 1a 2 ⫺ ␲ *2b 1 ⫺ ␲ * , 1a 2 ⫺ ␲ *1a 2 ⫺ ␲ * , 1a 2 ⫺3d xz
1a 2 ⫺3d xz , 1a 2 ⫺ ␲
1a 2 ⫺ ␲ * , 2b 1 ⫺ ␲ *2b 1 ⫺ ␲ *State

Nature

⌬E

f (r)

SM

MC

1

GroundV-mix
V
3p x ⫺R
3d xz ⫺R
V-mix
V-mix

0
6.40
6.79
6.82
7.51
8.34
9.08

0.185
0.000
0.016
0.019
0.483
0.166

⫺64.7
⫺92.5
⫺69.0
⫺129.5⫺245.7⫺97.5⫺130.4

1a 2 ⫺ ␲ *2b 1 ⫺ ␲ * , 1a 2 ⫺ ␲ *1a 2 ⫺3p x
1a 2 ⫺3d xz
1a 2 ⫺ ␲ * , 2b 1 ⫺ ␲ *2b 1 ⫺ ␲ *1 A1
1 1B 2
2 1A 12 1B 2
3 1B 2
6 1A 1
9 1B 2

SM denotes second moment.
MC denotes main configuration.

b

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7864

Wan et al.

J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

1 1 B 1 (1a 2 →3p y ), which is opposite the assignments ofPalmer et al.22 Except for CASPT2, all previous theoreticalstudies, i.e., CC3, MRMP, and ADC共2兲, gave similar trends
for excitation energy orders and oscillator strengths to ourpresent results, however, all of them followed Bavia et al.7
and ignored the 5.7 eV peak, and assigned the 5.861 eVtransition to 1 1 B 2 (1a 2 →3 p x ) and the 5.82 or 5.88 eV transition instead of the 5.7 eV transition to 1 1 B 1 (1a 2 →3p y ).
The next peak in the VUV spectrum is observed ataround 6.2 eV. This peak was assigned experimentally to the2b 1 →3s Rydberg transition by Derrick et al.5 On the other
hand, this peak, together with other peaks at slightly higher
energies, was assigned experimentally to a vibrational structure of the 1a 2 →3p x Rydberg state by Bavia et al.7 Our
present calculations support an alternative assignment forthis group of peaks, and associates them with the V(2 1 B 2 )state calculated at 6.48 eV and its vibrational structure. Additionally, the 1a 2 →3d yz (3 1 B 1 ) Rydberg states, etc., arealso predicted to be in this region. Note that the absorption
peaks were reported at around 6.42 eV and assigned to the1a 2 →3d Rydberg state in the UV spectrum of Bavia et al.7
2. The second weak central band (6.6 – 7.1 eV) in the
VUV spectrum

A relatively intense absorption peak was observed ataround 6.78 eV in the VUV spectrum by Palmer et al.,24 andassigned to the 1a 2 →3d Rydberg transition instead of 1a 2
→4s, 7 which is dipole forbidden. Two other weaker bands
at 7.021 and 7.044 eV were assigned to the excitations of the2b 1 →3p series of Rydberg transitions.24 Our present calculations support the above-given general assignments of thisenergy region. The 3 1 B 2 state (1a 2 →3d xz ) is computed at
6.76 eV with an oscillator strength of 0.0789, which is themost intense absorption peak in this energy region and hence
is reasonably associated with the absorption peak at around6.78 eV in the VUV spectrum. It is easy to understand why
this Rydberg transition is intense via the above-mentioned
hybrid model. It is mixed with valence transition and hence it‘‘borrows’’ the intensity from the valence transition. Most of
the intensity of the first and second bands can be attributed tothe same valence transition. Additionally, the 2b 1 →3p series of Rydberg states are also predicted in this region, andthe 1a 2 →4p series of Rydberg states are predicted at thehigh-energy tail of this energy region. Note that CC3 calculations predicted very similar results in this energy region
and also supported the assignment. However, CASPT2 and
MRMP assigned the 6.78 eV peak to the 2b 1 →3 p series ofRydberg transitions according to their calculations.
3. The third strong intense and broad band (7.1 – 8.2eV) in the VUV spectrum

A strong intense and broad absorption superimposedwith a few sharp peaks was observed at 7.1–8.2 eV in the
VUV spectrum. Our present calculations computed the 8 1 A 1
state at 7.88 eV with an oscillator strength of 0.3252 and the
10 1 B 2 state at 8.25 eV with an oscillator strength of 0.2553.
The nature of the 8 1 A 1 state is a strong mixture of the
␲→␲* transitions 共18→53兲 and 共17→52兲 with the Rydbergtransitions 共17→26兲 and 共18→38兲, etc., which are respon-sible for the rather large second moment 共250.9 a.u.2兲 of thisstate. The nature of the 10 1 B 2 state is of strong mixture of
␲→␲* transitions 共17→53兲, 共17→66兲, and 共18→52兲 with
Rydberg transition 共17→27兲, etc., which is responsible forthe large second moment 共159.0 a.u.2兲 of this state. The
strong mixture of ␲→␲* excitations with Rydberg excitations reflects the strong interactions between valence and Rydberg excited states. Note that these interactions in pyrrole
are stronger than those in furan. The two states mentioned
previously are defined as energetically high valence states of
A 1 and B 2 symmetries, respectively, considering oscillator
strengths, main configurations, and second moments. Ourpresent calculations show that a significant portion of theelectronic absorption intensity in this region is due to the twoenergetically high valence excitations mentioned previously.
We also predict that the 1a 2 →4d series, 1a 2 →5p series,
2b 1 →3d series, 1a 2 →5d series, 2b 1 →4d series, etc., Rydberg states are located in this energy region, and some ofthem have relatively large oscillator strengths. There are somany Rydberg states in only a 1 eV range, and therefore it isdifficult to make an accurate assignment of Rydberg transitions in this energy region. For vibrational and geometricalrelaxations, Rydberg transitions can easily overlap, and thus
the absorption in this region becomes very complicated.
However, we believe that it is reasonable to associate thevalence and Rydberg excitations mentioned previously to thefine structure in the region 7.1–8.2 eV.
4. Triplet excited states

The two lowest triplet transitions of pyrrole have been
identified by the electron energy-loss 共EEL兲8–10,24 spectrum
at 4.2 and 5.1 eV, which are assigned to the 3 B 2 and 3 A 1
valence transitions, respectively. Our present calculations
computed the 1 3 B 2 state at 4.58 eV with a second momentof 67.1 a.u.2, and the 1 3 A 1 state at 5.60 eV with a second
moment of 68.5 a.u.2 The second moments of these twostates 共listed in Table V兲 clearly characterize them as valence
excitations. The main configurations of 1 3 B 2 are 共18→52兲,
共18→62兲, 共18→59兲, 共18→64兲, etc., and those of 1 3 A 1 are
共17→52兲, 共18→66兲, 共18→53兲, 共17→62兲, etc. In the sameenergy region, we found two Rydberg excited states
1 3 A 2 1 3 A 1 and 1 3 B 2 , which are given at 5.08 and 5.82 eV,
respectively.
C. Comparison of furan and pyrrole

Comparing the present calculations of furan with thoseof pyrrole, it is obvious that a similar electronic excitation
mechanism occurs in both molecules. There are two valence
excitations in B 2 and A 1 symmetry, respectively, which areresponsible for most of the intensity of the electronic absorption bands, and hence span the general profiles of the VUVspectra in the energy region up to around 8.2 eV in pyrrole
and 8.8 eV in furan. From the main configurations listed inTable VII, we can see that both 1a 2 and 2b 1 series ␲→␲*valence transition configurations contribute to the two valence excitations of A 1 symmetry in both molecules. However, the 1a 2 series ␲→␲* valence transition configurations
predominantly contribute to the lowest valence excitation of

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J. Chem. Phys., Vol. 113, No. 18, 8 November 2000

B 2 symmetry and the 2b 1 series ␲→␲* predominantly contribute to the higher-energy valence excitation of B 2 symmetry in both molecules. At the same time, these valence excitations are more or less influenced by low-lying Rydbergtransitions. In the case of pyrrole, due to the lower first ionization potential 共1IPs兲, the Rydberg states are expected to bein the lower energy region, which is proven by our present
calculations. In furan, the lowest excited state is the valence
excitation of B 2 symmetry except for the dipole-forbidden
3s Rydberg transition, whereas in pyrrole the energies of the
3 p series Rydberg transitions are lower than that of the lowest valence excitation of B 2 symmetry, which gives rise tostronger interactions between valence and Rydberg excitations than in furan. It is also clear from the second momentsof these states that the interactions between valence and Rydberg transitions in pyrrole are much stronger than those infuran, which is responsible for the more complicated VUVfine structure of pyrrole.
Comparing the present SAC–CI results with those obtained by the CCSD and CC3 methods, we find that thegeneral trends are very similar, and the difference in excitation energies is very small, less than 0.1 eV 共maximum兲 forvalence excitations and 0.25 eV 共maximum兲 for Rydbergtransitions. These similar results are natural since the basic
theories are quite similar and the difference lies only in computational methodology: the former uses perturbation selection schemes and the latter adopts integral-direct strategies.
The present results, comparing with CCSD/CC3 results,
show that the perturbation selection scheme in the SAC–CI
SD-R method is very effective and reserves a high accuracy
at the same time.
IV. CONCLUSIONSThe SAC/SAC–CI theory was applied to furan and pyrrole to reinvestigate their electronic excited states in moredetail, including the singlet and triplet valence and Rydberg
excited states. The SAC/SAC–CI method with a sufficiently
extended basis set and a large active space gave a quantitatively satisfactory result to make reliable assignments for theelectron excitation spectrum of furan and pyrrole. The
present results show good agreement with various experimental data measured by VUV and EEL spectroscopies. The
mixing of valence and Rydberg states was stronger in pyrrole
than in furan.
In the case of furan, four singlet valence ␲ – ␲* excitations 共two A 1 states and two B 2 states兲, which span the general profile of the VUV spectrum, agree well with the latest
experimental data by Palmer et al.23 In particular, ourpresent results strongly support the notion that valence excitation exists in the 8.7 eV energy region. In addition, many
Rydberg excitations were determined in the present calculations, and the corresponding assignments in this work should
constitute a useful theoretical reference for experimental
chemists in this field.
In the case of pyrrole, 43 low-lying singlet excited states
were obtained theoretically and reliable assignments for the
VUV spectrum up to 8.2 eV were made using the calculated
energies and oscillator strengths. Valence and Rydberg excited states were discussed separately in detail. For the first

Excitation of furan and pyrrole

7865

intense band and second weak band of the VUV spectrum,
our present calculated results show a strong mixture of valence and Rydberg excitations in the first three 1 B 2 excitedstates. For the third strong and broad band, the present calculations give two valence excited states, 8 1 A 1 and 10 1 B 2 ,which are strongly influenced by Rydberg transitions. Thesevalence excitations, together with Rydberg excitations, span
the general profile of the VUV spectrum observed by Palmer
et al.24
ACKNOWLEDGMENTS

This research was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science,
Culture and Sports. The authors are grateful to K. Toyota for
helpful discussions on this subject.
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