Chemical Physics Letters 382 (2003) 217–225

www.elsevier.com/locate/cplett

Exploring the electronic structure of 2,6-stelladionefrom momentum space I: the p-dominant molecular

orbitals in the outer valence shell

Feng Wang a,*, Michael J. Brunger b, Ian E. McCarthy b, Dave A. Winkler c

a Centre for Molecular Simulation, Swinburne University of Technology, Hawthorn, Melbourne, Vic. 3122, Australiab School of Chemistry, Physics and Earth Sciences, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia

c Division of Molecular Sciences, CSIRO, Private Bag 10, Clayton South MDC, Vic. 3169, Australia

Received 17 June 2003; in final form 25 September 2003

Abstract

The p-electron dominant contributions to the outer valence shell of 2,6-stelladione (C8H8O2) are analyzed using

binding energy spectra and the orbital momentum distributions obtained by experimental and theoretical electron

momentum spectroscopy. The binding energy spectra are given for azimuthal angles / ¼ 0� and 10�, respectively, inorder to reveal information of the s- and p-electron dominant characteristics in these molecular orbitals. The wave-

functions in configuration space are directly mapped into momentum space using the plane wave impulse approxi-

mation. This work focuses on the interpretation of the electronic structural information and bonding mechanism of the

molecule in momentum space. In particular, p-electron dominant contributions of the strained organic compound are

used to support our findings.

� 2003 Elsevier B.V. All rights reserved.

1. Introduction

Tricyclo[3.3.0.03:7]octane-2,6-dione (C8H8O2),

also known as 2,6-stelladione, is a highly sym-

metric compound. It has been a key compound inthe synthesis of model structures for studying a

stepwise Cope rearrangement and also in the study

of long range interactions [1]. Additionally, 2,6-

* Corresponding author. Fax: +61392145075.

E-mail address: fwang@swin.edu.au (F. Wang).

0009-2614/$ - see front matter � 2003 Elsevier B.V. All rights reserv

doi:10.1016/j.cplett.2003.09.151

stelladione has served as a reference structure to

investigate energy transfer reactions as a function

of the strain energy of the r-frame between donor

and receptor substitutions [2]. However, as this

compound has been synthesized relatively recently[1], only limited X-ray crystallographic data [2]

and a photoelectron spectrum [1] are available in

the literature at this time to provide information

on its geometry and electronic structure. This sit-

uation is actually worse than it might otherwise

appear as the photoelectron spectrum provides us

with an incomplete range of the binding energies

in the outer valence shell of the molecule, only

ed.

218 F. Wang et al. / Chemical Physics Letters 382 (2003) 217–225

the first three molecular orbitals having been tab-

ulated [1]. Our most recent electron momentum

spectroscopy (EMS) study, the first EMS mea-

surement on this compound, attempted to address

(at least in part) some of this paucity in informa-

tion for this molecule [3]. For example, with thehelp of the EMS binding energy spectra, we were

able to reanalyze the photoelectron spectrum [1] to

give the complete binding energies of 2,6-stelladi-

one in the outer valence shell [3].

Theoretical studies of 2,6-stelladione have been

also limited, in this case by the size of the com-

pound, with only a few ab initio calculations using

Hartree–Fock (HF) method HF/3-21G [2], re-stricted HF (RHF) method RHF/6-31G* and a

single point calculation using the second order

M€ooller–Plesset perturbation theory (MP2) MP2/

6-31G*//RHF/6-31G* [1] being performed. These

rather low level calculations were able to provide

some reliable geometric information of the com-

pound, as confirmed by the X-ray crystallographic

data [2]. However electronic structural informationof this compound, depending on the specific mo-

lecular properties under study, needs the inclusion

of electron correlation energy. As a result, density

functional theory (DFT), together with the DGauss

DFT triple zeta with valence polarized (TZVP)

basis set [7], calculations were employed in the

present work to simulate the orbital momentum

distributions (MDs). In this work, we will focus onthe p-dominant atomic orbital (AO) contributions

to the molecular orbitals (MOs) of 2,6-stelladione

in the outer valence shell of its ground electronic

state (X1A1). Most of our analysis is conducted in

momentum space, which is the Fourier transform

analogue of the more familiar configuration space.

2. Molecule orientation

The ground electronic state of 2,6-stelladione

(X1A1) is highly symmetric, with a point group

symmetry of D2d. In this work, the tricyclo octane–

carbon skeleton of 2,6-stelladione is orientated in a

Cartesian coordinate system with the oxygen at-

oms located along the vertical z-axis. This is shownin Fig. 1, with the x-axis in the plane and the y-axisout-of-plane. Fig. 1 also gives the atom numbering

order of the eight carbon, two oxygen and eight

hydrogen atoms. The origin of the Cartesian co-

ordinate system coincides at the symmetry centre

of the molecule�s D2d point group.

3. The binding energy spectra of 2,6-stelladione

In molecular orbital theory anMO of a molecule

is considered as a linear combination of the com-

ponentAOs (LCAO),where this linear combination

does not change the nature of the AOs. As a result,

together with the MO coefficients in the wavefunc-

tion, the AOs essentially contain and reflect theelectronic structural information of the bonding

mechanism for the molecule under study (the con-

cept of �atoms-in-molecules� [5]). The �shape� ornature (s, p, d,. . .) of the AOs is determined by the

azimuthal quantum number l with l ¼ 0; 1; 2; . . . ;respectively, which relates to the EMS binding en-

ergy spectra and MDs through the azimuthal angle

/ (through momentum conservation).The EMS experiment is also called (e, 2e)

scattering in which an in-coming electron interacts

with the target (the sample molecule) leading to

ionization so that two electrons are scattered out

from the interaction region [6]. In the experiment,

the energies of the two outgoing electrons A and B

are equal and the polar angle is h ¼ 45� with re-

spect to the direction of the incident electronbeam. The total energy (sum of the energies of A

and B) is 1500 eV. The binding energy range of

interest (�f ¼ 7� 16 eV) is stepped through se-

quentially at each of a chosen set of azimuthal

angle / using a binning mode [4] through the

range of / ¼ 0�–30�. This is equivalent [3] to

sampling different target electron momenta P,

where

P ¼ ð2PA cos h

��P0Þ2 þ 4P2

A sin2 h sin2 /

2

� ��1=2:

ð1Þ

Note that for closed shell molecules the total

momentum is conserved so that both linear and

angular momenta should conserve in the (e, 2e)

scattering process. Therefore the angular momen-

tum of the system is correlated indirectly via

Fig. 1. The molecule orientation of 2,6-stelladione (C8H8O2, X1A1) in space.

F. Wang et al. / Chemical Physics Letters 382 (2003) 217–225 219

Eq. (1). For example when the azimuthal angle is

/ ¼ 0�, the corresponding momentum is P � 0

a.u., and the resulting binding energy spectrum of

the molecule indicates the MOs which are domi-

nated by the s-AOs (l ¼ 0) of the component at-

oms. Such electronic information thus provides

direct details for the bonding mechanism of themolecule.

In its electronic ground state, 2,6-stelladione

has component atoms with occupied s-AOs and

p-AOs. It is clear from our discussion above that

when the azimuthal angle in the EMS technique

is tuned to zero degree, the binding energy spec-

trum of 2,6-stelladione at this angle (/ ¼ 0�) in-

dicates s-electron domination status in the outervalence shell of the molecule. Alternatively, as

there are no l > 1 orbitals involved in the bond-

ing of this molecule, the binding energy spectrum

at / 6¼ 0� provides information of the p-electron

domination in the outer valence shell of the

molecule. Therefore, from the binding energy

spectra at zero and non-zero azimuthal angles,

bonding information for the p-dominant MOs in

the outer valence shell can be recognized. The

bonding mechanism information provided by theBES can be further identified in our later orbital

momentum distribution analysis using the EMS

experiment and simulation.

Fig. 2 shows the experimental BES for the

ground electronic state of 2,6-stelladione at a

total energy of 1500 eV [3]. The BES for / ¼ 0�and / ¼ 10� are shown in (a) and (b), respec-

tively. The vertical bars with numbers in Fig. 2agive the positions of the orbital energy and the

orbital number (the highest occupied MO is

numbered as 1), which also apply to Fig. 2b BES.

Fig. 2. The high resolution electron momentum spectroscopy (HREMS) binding energy spectra of 2,6-stelladione with: (a) / ¼ 0�; (b)/ ¼ 10�.

220 F. Wang et al. / Chemical Physics Letters 382 (2003) 217–225

F. Wang et al. / Chemical Physics Letters 382 (2003) 217–225 221

The MOs, such as 6b2 and 5b1 (their corre-

sponding positions are marked 4 and 10), with

peaks only apparent in the / 6¼ 0� spectrum are

almost certainly dominated by the p-electron

AOs. In addition, it has been observed that the

MOs are likely to be dominated by p-electrons, iftheir peak intensities in the binding energy spec-

tra experience large changes with respect to / 6¼0� and / ¼ 0� in the experiment. In the present

study the 4b3 & 3b2 and 5a MOs are thus also

likely to be p-dominant MOs.

4. Momentum distributions of the p-dominantmolecular orbitals

The p-electron dominant MOs, namely, 6b2,

5b1, 4b3 & 3b2 and 5a, of 2,6-stelladione can be

uniquely identified by their MDs, obtained from

both experimental and quantum mechanical sim-

ulation techniques. Under the Born–Oppenheimer

approximation for the target and ion wavefunc-tion, the EMS cross section for randomly-orien-

tated molecules is given in the plane-wave impulse

approximation by [4],

r ¼ KZ

dXjhPWN�1f jWN

i ij2; ð2Þ

where the terms in this equation are defined in our

previous study [3]. The overlap of the initial andfinal electronic wavefunctions is a one-electron

quantity known as the Dyson orbital. It may be

approximated by an MO, wjðPÞ, using the same

independent-particle model for the target and ion.

Eq. (2) reduces to,

r ¼ KSðf Þj

ZdXjwjðPÞj2; ð3Þ

where the spectroscopic factor Sðf Þj is the proba-

bility of one-hole configuration j being in the ion

wavefunction WN�1f [6].

5. Analysis for the p-dominant molecular orbitals

Details of the quantum mechanical calculationsand the transform of the wavefunction for the 2,6-

stelladione molecule have been reported elsewhere

[3]. To further extract information for the p-elec-

tron dominant MOs in the outer valence shell,

RHF/6-31G** calculations are performed using

GAMESS [8] and the molecular point group

symmetry information has been imposed in the

calculations. Table 1 gives the Mulliken atomicpopulation analysis on each of the p-dominated

MOs, based on the RHF/6-31G** calculations. As

these MOs are p-dominated and in the outer va-

lence shell of the molecule, it is clear from Table 1

that the oxygen and carbon atoms, possibly their

2p-AOs, are dominant. Hydrogen atoms make

important secondary contributions to some of the

MOs, such as 5b1 and 4b3, but are virtually elim-inated in 6b2. Indeed compared to the other MOs

in Table 1, 6b2 is the only MO where the hydrogen

1s-AO contributions are apparently negligible. As

a result, the bonding in 6b2 can be considered as

being due to �pure� p-contributions and its MD in

Fig. 3 supports this finding. Furthermore, as can

also be seen from this table, b2 is dominated by the

two ketone oxygen atoms, Oð1Þ and Oð2Þ (0.34), andthe two methylene carbon atoms (CH2), i.e., Cð9Þand Cð10Þ (0.23), with the central four equivalent

carbon atoms, i.e., Cð5Þ, Cð6Þ, Cð7Þ and Cð8Þ (0.17),

making some secondary contributions. This is be-

cause Oð1Þ, Oð2Þ, Cð3Þ, Cð4Þ, Cð9Þ and Cð10Þ are con-

fined in the same plane by symmetry, pz- (of Oð1Þand Oð2Þ) and px-AO (Cð9Þ and Cð10Þ) contributions

of the appropriate atoms are therefore expected(the distance between, say, Oð1Þ to Cð9Þ is 3.19 �AA).

Further analysis of the 6b2 orbital wavefunction

shows that the py-AOs of the methylene carbons

Cð9Þ and Cð10Þ overlap with px-AOs of Cð6Þ, Cð6Þ and

Cð7Þ and Cð8Þ, where Cð7Þ and Cð8Þ locate in the back

side (negative y) of the xz-plane and Cð7Þ and Cð8Þlocate in the front side (positive y) of the xz-plane,contributing to the strained six-ring r-bond of thecarbon skeleton.

The contributions from the s-AOs to the rest of

the p-dominant MOs can not be neglected, indi-

cating the possible effects of hybridization. As

Fig. 3 shows, all the orbital MDs of the p-domi-

nant MOs exhibit a local minimum in the MD at

small P before they start to climb (that is, the sign

of its second derivative changes), except for the 6b2

MO. This indicates that those MOs except for 6b2

are dominated by the carbon p-AOs. Fig. 3 also

Table 1

Mulliken atomic population analysis of the p-dominated MOs in the outer valence shell of 2,6-stelladione (C8H8O2, X1A1) using RHF/

6-31G** calculations

No. orbital Atoms 6b2 5b1 4b3 3b2 5a

Energy/eV 13.18 15.33 16.28 16.60 19.50

1 Oð1Þ 0.34 0.02 0.35 0.46 0.53

2 Oð2Þ 0.34 0.02 0.35 0.46 0.53

3 Cð3Þ 0.06 0.06 0.16 0.24 0.12

4 Cð4Þ 0.06 0.06 0.16 0.24 0.12

5 Cð5Þ 0.17 0.03 0.15 0.07 0.11

6 Cð6Þ 0.17 0.03 0.15 0.07 0.11

7 Cð7Þ 0.17 0.03 0.15 0.07 0.11

8 Cð8Þ 0.17 0.03 0.15 0.07 0.11

9 Cð9Þ 0.23 0.46 0.01 0.09 0.05

10 Cð10Þ 0.23 0.46 0.01 0.09 0.05

11 Hð11Þ 0.01 0.18 0.00 0.02 0.01

12 Hð12Þ 0.01 0.18 0.00 0.02 0.01

13 Hð13Þ 0.01 0.18 0.00 0.02 0.01

14 Hð14Þ 0.01 0.18 0.00 0.02 0.01

15 Hð15Þ 0.00 0.01 0.10 0.02 0.03

16 Hð16Þ 0.00 0.01 0.10 0.02 0.03

17 Hð17Þ 0.00 0.01 0.10 0.02 0.03

18 Hð18Þ 0.00 0.01 0.10 0.02 0.03

222 F. Wang et al. / Chemical Physics Letters 382 (2003) 217–225

illustrates a tendency that as more s-character isadded to an MO, the lower in momentum will the

primary peak in the MD be observed. This phe-

nomenon may be qualitatively understood from

Eq. (1). In the EMS experiment, the initial mo-

mentum P0, the momentum of scattered electron

PA and the polar angle h (here h ¼ 45�) are given,

so that in symmetric non-coplanar kinematics

P / / for / 2 ½0�,30�]. Hence with more s char-acter (as / ¼ 0� for �pure� s-AOs) contribution, the

more the peak of the MO cross section moves

further toward the lower momentum region. Fi-

nally, molecular orbital theory points out that

hybridized orbitals form stronger bonds. By defi-

nition (Eq. (3)), the intensity of the cross section

and the peak position of an orbital MD provide an

indication of the bond strength and bond naturefor the MO. For example, the �pure� p-like 6b2

orbital (Fig. 3a) exhibits the lowest peak magni-

tude in cross-section, with the peak intensity lo-

cating at about P ¼ 1:1 a.u. the largest

momentum in the group of MOs.

For the unresolved orbitals 4b3 and 3b2 (Fig. 3c),

with some hydrogen s-AO contribution and

therefore some hybridization feature, the MD peak

position locates in the lower momentum region ofP ¼ 0:90 a.u. Orbital 5b1 (Fig. 3b) involves even

more hydrogen s-AO character (see Table 1), and

thus has an intense MD peak with the peak posi-

tion locating in the smaller momentum region than

either 6b2 or 4b3 and 3b2. MO 5a obviously dem-

onstrates a very strong bond and locates on the far

left side (P � 0:70 a.u.) of the distributions among

theMOs in Fig. 3d. The bonding mechanism of thisMO is, however, quite different as its s character is

not from the contributions made by the hydrogen

1s-AOs like the other MOs. Instead, it comes from

the oxygen 2s-AOs which overlap with the carbon

2pz-AOs in the ketone groups. This will be dis-

cussed further later. Consequently, relative inten-

sities of the MD primary peaks exhibit

an order of 5að6:1� 10�4 a:u:Þ > 5b1ð3:6� 10�4

a:u:Þ > 4b3 & 3b2ð3:2� 10�4a:u: eachÞ > 6b2

ð2:5 � 10�4 a:u:Þ, so that it is predicable that the

order of the bonds strength formed by those

MOs may have the same order as the peak inten-

sities.

Orbital 5b1 is dominated by contributions

from the 2pz- and 2px-AOs of the carbon atoms

in the methylene groups (0.46), i.e., Cð9Þ and

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3

(e,2

e) c

ross

sec

tio

n (

x 1

0-4 a

.u.)

p(a.u.)

Orbital 46b

2 orbital

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5 3(e

,2e)

cro

ss s

ecti

on

( x

10-4

a.u

.)p(a.u.)

Orbital 105b

1orbital

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5 3

(e,2

e) c

ross

sec

tio

n (

x 1

0-4 a

.u.)

p(a.u.)

Orbitals 11,124b

3 + 3b

2 orbitals

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5 3

(e,2

e) c

ross

sec

tio

n (

x 1

0-4 a

.u.)

p(a.u.)

Orbital 165a orbital

(a) (b)

(d)(c)

Fig. 3. Comparison of MDs of the p-dominant MOs in the outer valence space of 2,6-stelladione obtained from our HREMS with

Run A (the solid circles) and Run B (white circles), with the simulated using DFT-BP/TZVP. Here (a) the 6b2 MO, (b) the 5b1 MO, (c)

the 4b3 & 3b2 MOs and (d) the 5a MO.

F. Wang et al. / Chemical Physics Letters 382 (2003) 217–225 223

Cð10Þ as well as the connected hydrogen atoms

(0.18). This MO is in fact a linear combination

of equivalent bond orbital (LCBO) [10], made bythe four equivalent methylene C–H bonds. Or-

bitals 4b3 and 3b2 of 2,6-stelladione are nearly

degenerate in energy, 16.28 and 16.60 eV, re-

spectively, given by our RHF/6-31G** calcula-

tions. The energy difference between them is

0.32 eV which is well within the experimental

resolution of 0.52 eV. However, this near degen-

eracy may be considered as an accidental one,

for the bonding mechanism forming these two

MOs is not the same in nature. Even thoughboth orbitals 4b3 and 3b2 are dominated by the

ketone carbon and oxygen atoms, the secondary

contributions to 4b3 and 3b2 are quite different:

with another LCBO from the central four C�s(0.15) and their connected H�s (0.10) contribut-

ing to orbital 4b3. Note that the contribution

from the methylene groups here is negligible.

224 F. Wang et al. / Chemical Physics Letters 382 (2003) 217–225

Hence, the bonding mechanism for orbital 4b3

appears to be from through-bond interactions

[9]. On the other hand, the secondary contribu-

tions to orbital 3b2 are from the six-ring carbon

frame with the central four carbons of Mulliken

population 0.07 and the methylene carbons of0.09. The role of the two hydrogen groups, that

is, the methylene hydrogens Hð11Þ, Hð12Þ, Hð13Þ &

Hð14Þ and the central hydrogens Hð15Þ, Hð16Þ, Hð17Þ& Hð18Þ, is nearly equivalent, yielding the Mul-

liken population of approximately 0.02, respec-

tively. As a result, in 3b2, the LCBO of the

methylene carbons seems to interact with the

ketone groups by through-space interactions [9].The MD of the 5a orbital is quite different

from the other MOs in Fig. 3. The intensity of

its MD peak is apparently higher than those of

the other p-dominant MOs, almost twice as

much as the rest of the MOs in this Figure.

Additionally its MD peak position is at the

lowest momentum (see Fig. 3). Although a sec-

ondary contribution from groups of LCBO ofthe central carbons is observed in Table 1, the

primary contribution forming 5a is from the

overlap between 2s-AOs and 2pz-AOs of both

oxygen and carbon in the ketone groups, so that

this MO is dominated by the 2pz-AOs and 2s-

AOs �head-on� r-bond. As a result, the 5a orbital

exhibits a strong bond nature (high intensity)

and s-character (low momentum location).

6. Conclusions

The p-electron contribution is dominant in

several molecular orbitals in the outer valence

shell, namely, orbitals 6b2, 5b1, 4b3 & 3b2 and

5a of the 2,6-stelladione molecule. Our workindicated that the binding energy spectra at zero

and non-zero azimuthal angles / provided pre-

liminary information on the s- and p-contribu-

tions to the valence MOs of the compound,

which could be confirmed by an orbital based

momentum distribution analysis using both ex-

periment and simulation. Detailed MO analysis

of the p-dominant MOs of 2,6-stelladione hasbeen given using experimental binding energy

spectra, experimental and simulated momentum

distributions of the molecular orbitals, and has

been also assisted by the Mulliken atomic orbital

population analysis. In conclusion, it was evident

that EMS observes the behavior of the molecular

orbitals through the azimuthal angle, and there-

fore, reflects the momentum based informationof the molecular orbitals, which is not always

obvious in configuration space. As the p-domi-

nated molecular orbitals such as 6b2 and 5a can

be r bonds, depending on the direction of the

bonding, the orbital momentum distributions

obtained from EMS can describe the atomic

orbital nature from which the molecular orbitals

are determined. This work also has attempted tointerpret the EMS binding energy spectra and

momentum distributions using standard molecu-

lar spectral analysis, that is, indicating that the

electronic structure and the bonding mechanism

of the molecule link to the peak position in

momentum and intensity of the orbital momen-

tum distributions.

Acknowledgements

One of the authors (FW) would like to ac-knowledge the Australian Partnership for Ad-

vanced Computing (APAC) for using the Compaq

SC AlphaServer Cluster National Facilities. FW

also acknowledges the HPCCC group of CSIRO

for computer resources.

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