Isomerization of stilbene using enforced geometry optimization

Isomerization of Stilbene Using Enforced

Geometry Optimization

JON BAKER,1 KRZYSZTOF WOLINSKI1,2

1Parallel Quantum Solutions, 2013 Green Acres Road, Suite A, Fayetteville, Arkansas 727032Department of Chemistry, Maria Curie-Sklodowska University, pl. Maria Curie-Sklodowska 3,

Lublin 20-031, Poland

Received 26 March 2010; Accepted 10 May 2010DOI 10.1002/jcc.21597

Published online 19 July 2010 in Wiley Online Library (wileyonlinelibrary.com).

Abstract: Using our recently proposed quantum chemical model to simulate the effect of external forces acting on

a molecule (Wolinski and Baker, Mol Phys 2009, 107, 2403), which we subsequently termed enforced geometry

optimization (EGO), we investigate structural isomerism in C14H12, starting from cis-stilbene. By applying an exter-

nal force to pairs of carbon atoms, one from each ‘‘half’’ of the molecule, we have generated 10 different structural

isomers. Each was characterized as a minimum by vibrational analysis. Not only can EGO generate potentially new,

metastable isomers it can also provide good initial guesses for transition states connecting the starting and final

structures, thus giving an estimate of the stability of the new isomers to rearrangement back to the starting material.

In addition to the new isomers, we provide a full set of vibrational fundamentals for cis- and trans-stilbeneand 4a,4b-dihydrophenanthrene. The agreement with experimental assignments is excellent, with mean average

deviations for the stilbenes of 5.0 cm21 or less.

q 2010 Wiley Periodicals, Inc. J Comput Chem 32: 43–53, 2011

Key words: isomerization; stilbene; enforced geometry optimization; transition state search

Introduction

Stilbene (1,2-diphenylethylene) is an important phosphorescent

hydrocarbon used in the manufacture of dyes, optical brighteners

and scintillators, as well as a source of optical gain in lasers.

Many stilbene derivatives occur naturally in plants and several

reportedly have a variety of health benefits, e.g., resveratrol, a

hydroxylated stilbene that is found in grapes.1

Stilbene has two principal conformers, trans (1) and cis (2).

The trans is the more stable of the two, although both its

ground-state geometry and the relative energy difference

between cis- and trans-stilbene have been somewhat controver-

sial, as has the barrier for the trans-cis interconversion. Trans-and cis-stilbene readily interconvert optically through a singlet

electronic excited state. On the excited state surface, the trans? cis barrier is 3.3 kcal/mol and the cis ? trans interconver-

sion is almost barrierless.2 On the ground state potential energy

surface (PES), an extensive high-level theoretical study from

Deleuze and coworkers3 at the CCSD(T) level extrapolated to

the basis set limit estimated the trans-cis energy difference at

2.8 kcal/mol. The same study also concluded that the transconformer was planar with C2h symmetry, although there is a

very weak torsional potential about the C��C bond to the phe-

nyl rings, and many calculations predict a C2 minimum. Calcu-

lations using density functional theory (DFT) with a range of

functionals routinely predict a planar, C2h structure, whereas

Hartree-Fock and MP2 typically predict nonplanar minima.3–5

The cis conformer has C2 symmetry (this is not in doubt) with

a torsional angle between the phenyl ring and the (formal)

C¼¼C double bond of some 348 to 448 depending on the level

of theory.3–5

Experimental studies initially also led to mixed conclusions.

It was apparent early on that trans-stilbene had a very flat tor-

sion potential, and at room temperature, the phenyl rings could

readily twist by 6308.6 Consequently, investigations at room

temperature (and higher) not surprisingly resulted in a range of

torsional angles. However, fluorescent spectroscopy studies

strongly suggested that trans-stilbene was essentially planar in

the liquid phase,7 and subsequent ultra cold (6 K) collision-free

molecular beam experiments ‘‘demonstrate unambiguously’’ that

the molecule is planar in both its S0 (ground) and S1 excited

states.8 The torsion angle in cis-stilbene obtained from electron

diffraction studies is 43.28.9

Correspondence to: J. Baker; e-mail: [email protected]

q 2010 Wiley Periodicals, Inc.

The experimental cis-trans energy difference based on heats

of combustion lies between 3.3 and 5.4 kcal/mol.10 A value of

4.59 kcal/mol was inferred from fluorescence excitation studies

in ultra cold molecular beams and argon clusters,11 and exactly

the same value was obtained based on the temperature depend-

ence of the cis-trans equilibrium in benzene, toluene, and

p-xylene.12 The latter study also provided an estimate for the

barrier for the cis-trans conversion (relative to the cis con-

former) on the ground state S0 surface of 48 6 2 kcal/mol.12

A structural isomer of C14H12 related to cis-stilbene is 4a,4b-

dihydrophenanthrene (DHP) (3), which can be obtained from it

by the action of light or heat. Its formation is a competing path-

way to cis-trans isomerization on the photoexcited S1 state PES

with a reported activation energy of 1–2 kcal/mol.13

The main purpose of this work is to investigate new struc-

tural isomers of C14H12 potentially obtainable from stilbene.

Starting from cis-stilbene, we apply an external force to pairs of

carbon atoms, one from each ‘‘half’’ of the molecule (Fig. 1),

acting along the line joining the two atoms so as to push them

together. Whatever force is applied to one atom, an equal and

opposite force is applied to the other; in this way, there is no

net force on the molecule as a whole and so no tendency for

the system to translate or rotate. In effect it remains in place

under simulated pressure. A standard geometry optimization is

then carried out in the presence of the applied external force.

The procedure described above has been termed enforced geom-

etry optimization (EGO)14 and is very likely to result in bond

formation between the two selected atoms. It has previously

been used to investigate related isomerizations starting from cis-azobenzene as well as conformational changes in pyranose

rings.15

Results and Discussion

The standard level of theory used in this work is DFT,16 using

the B3LYP hybrid exchange-correlation functional17 with the

6-31G* basis set.18 All calculations were performed using the

PQS program package incorporating the PQSMol graphical userinterface for postjob visualization and display.19 At the B3LYP/

6-31G* level, trans-stilbene (1) is essentially planar with full

C2h symmetry. We say essentially because a vibrational analysis

revealed a very small imaginary frequency (below 10i cm21)

which was ignored. The torsional angle between the C¼¼C

double bond and the phenyl ring in cis-stilbene (2) is 34.08,the cis-trans energy difference is 5.1 kcal/mol, and the barrier

height on the ground state PES is 40.3 kcal/mol. 4a,4b-dihy-

drophenanthrene (DHP) (3) lies 39.6 kcal/mol above cis-stil-bene with a barrier to interconversion, again on the ground

state energy surface, of 45.3 kcal/mol. (This latter reaction

appears to maintain C2 symmetry throughout.) All quoted rela-

tive energies are well-to-well and exclude zero-point effects.

These results are in generally good agreement with the known

experimental data.

To induce structural rearrangements, we applied a force of

0.1 au (�8200 pN) between all possible symmetry-unique pairs

of carbon atoms in cis-stilbene, one from each ‘‘half’’ of the

molecule. (Each ‘‘half’’ is defined by the C2 symmetry axis and

comprises the carbon atoms labelled from 1 to 7 in Figure 1 and

the corresponding symmetry-equivalent atoms labelled with a

prime.) This force was chosen based on our previous study of

cis-azobenzene15 and is normally easily sufficient to cause bond

formation between the two selected carbon atoms. It is by

no means the minimum force required, but that is not what

we are interested in here, as the focus is on the new isomers

themselves.

The enforced geometry optimizations were carried out start-

ing with a very slightly distorted structure so as to break the

original C2 symmetry. The majority of optimizations resulted in

a new structural isomer of C14H12, albeit one under considerable

stress. This stress was then removed, and each system was care-

fully reoptimized. One of two things then happened: either the

new structure was stable and remained essentially intact, relax-

ing to a lower energy, or it could not hold together once the

external force was removed and relaxed back to the starting

structure, cis-stilbene. The former occurred more often than the

latter, and we found no less than 10 different structural isomers

Figure 1. Atom labelling in cis-stilbene.

44 Baker and Wolinski • Vol. 32, No. 1 • Journal of Computational Chemistry

Journal of Computational Chemistry DOI 10.1002/jcc

Figure 2. Structures obtained by the application of external forces between various pairs of carbon

atoms in cis-stilbene (see Table 1) and their relative B3LYP energies in kcal/mol.

45Isomerization of Stilbene Using EGO


(as well as several chiral equivalents), all of which were charac-

terized as minima by a full vibrational analysis. They are

depicted in Figure 2, labelled according to the two atoms that

were pushed together to form them.

For each new structure found, we also looked for the transi-

tion state (TS) connecting it back to cis-stilbene in order to

give at least some idea as to its stability. If one looks at the

optimization history of a typical EGO calculation which

resulted in a stable isomer, then the energy (which is calcu-

lated on the ground state PES) first rises, reaches a maximum

and then falls as the new isomer forms. In effect a kind of

‘‘reaction path’’ results, and the highest energy structure on this

path was taken as an initial guess to the TS geometry. Some

examples of these ‘‘reaction paths’’ are given in schemes (4) to

(7), below. (These are extracted as .jpg images directly from

PQSMol.19)

Table 1. Relative Energies of All New Isomers of C14H12 and the Transition States Linking them Back to

cis-stilbene.

Structure B3LYPa/6-31G* MP2a/6-311G** Structure B3LYPa/6-31G* MP2a/6-311G**

trans-stilbene 25.1 20.3b C3��C30 77.1 57.0

TS 40.3c TS 88.3 69.3

DHP 39.6 38.2 C4��C20 89.9 –d

TS 84.9 80.3 TS 90.0 –d

C6��C20 47.3 45.0 C5��C20; C6��C30 93.6 71.8

TS 54.2 50.9 TS 97.7 74.5

C7��C20; C7��C60 49.1 45.0 C7��C50 94.3 82.9

TS 63.0 56.6 TS 131.7 122.6

C1��C20; C6��C10 60.1 51.2 C7��C40 105.1 89.5

TS 83.0 73.8 TS 113.3 96.1

C4��C30; C4��C50 67.4 47.4 C6��C40 108.7 86.0

TS 80.2 57.8 TS 111.1 87.1

akcal/mol relative to cis-stilbene. bAssumed C2h.cThe cis ? trans TS was an open-shell singlet with considerable

bi-radical character (hS2i 5 1.064, multiplicity 5 2.293). dNot stable at the MP2 level.



The optimizations for C7��C20 (4) and C6��C20 (5) pro-

duced stable new isomers (see Fig. 2 for the resulting struc-

tures), whereas those for C3��C20 (6) and C2��C20 (7) did

not. The energy profiles are not completely smooth as occa-

sionally the optimization algorithm takes a slight mis-step but

they more-or-less are. If we take in each profile the highest

energy point found (this is shown by a small red dot) then in

(4) and (5), there is a clear energy lowering subsequent to

this, whereas in (6) and (7), the energy has reached a plateau,

and there is no real lowering. In fact, you can just about tell

in advance which final stressed structure will be stable after

relaxation (i.e., reoptimization after removal of the external

force) simply by looking at the optimization history: If the

energy profile looks like (4) or (5), the structure is very

likely to be stable, if it resembles (6) or (7), then it is likely

not to be.

Figure 3. Simulated SQM-scaled B3LYP/6-31G* IR spectra of cis-stilbene, trans-stilbene, 4a,4b-dihy-drophenanthrene, C1��C20 and C7��C50.



As noted, for all TS searches for those EGO calculations that

resulted in a new isomer, the highest energy structure (or close

to it) on the energy profile was used as the starting geometry. A

full analytical Hessian was computed at this geometry, and

thereafter, a standard EF geometry optimization20 was performed

with a Bofill Hessian update.21 In all cases bar one, the optimi-

zation converged smoothly to a transition state, which was veri-

fied by a full vibrational analysis. (The exception was C6��C40,the highest energy isomer found, which was so unstable that the

TS geometry involved only a minor distortion from the mini-

mum.) As with our previous study on azobenzene,15 all station-

ary points located at B3LYP/6-31G* were reoptimized at MP2/

6-311G** to check that the energetics remained stable.

The relative energies of all C14H12 isomers characterized in

this work at both B3LYP/6-31G* and MP2/6-311G** are given

in Table 1. All energies are relative to cis-stilbene and Table 1

includes both minima and the associated TS linking that struc-

ture back to cis-stilbene. The isomers are listed in relative

B3LYP energy ordering, lowest first.

Overall the B3LYP and MP2 energetics are pretty similar,

although there are clearly a few differences. Compared with

B3LYP, the MP2 energetics are somewhat compressed, i.e.,

energy differences of all structures compared with cis-stilbeneare greater at B3LYP/6-31G* than with MP2/6-311G**. This is

not a basis set effect (6-311G** versus 6-31G*) as additional

optimizations at B3LYP/6-311G** on several of the B3LYP/6-

31G* structures gave virtually identical relative energies. The

energy ordering of the new isomers is not precisely the same at

MP2 as it is at B3LYP: the third and fourth highest switch, as

do the last two (the ninth and tenth). In addition, one of the iso-

mers, C4��C20, is not stable at the MP2 level and could not be

located. This may seem to be a fairly substantial difference but

it is not at all, as the computed barrier height for rearrangement

of this isomer back to cis-stilbene at B3LYP is just 0.1 kcal/

mol, and so effectively this species does not exist.

All of the new isomers derived from cis-stilbene are thermo-

dynamically less stable than the three known compounds: cis-and trans-stilbene and 4a,4b-dihydrophenanthrene (DHP). Nearly

all of them have fairly low barriers for decomposition back to

cis-stilbene (14 kcal/mol or less at B3LYP/6-31G* and even

lower at MP2/6-311G**), and so most are not kinetically stable.

The two isomers which may be stable are the third highest (this

is the fourth highest at MP2), C1��C20 (C6��C10) which lies

60.1 (51.2) kcal/mol above cis-stilbene with a reverse barrier

height of 22.9 (22.6) kcal/mol (B3LYP with MP2 values in

parentheses), and C7��C50 which lies 94.3 (82.9) kcal/mol

above cis-stilbene with a reverse barrier height of 37.4 (39.7)

kcal/mol. Compare these values with DHP, which lies 39.6

(38.2) kcal/mol above cis-stilbene with a reverse barrier height

of 45.3 (42.1) kcal/mol.

Note that, despite being the most stable non-stilbene isomer,

DHP was not formed in any of our initial EGO calculations. If

atoms C2 and C20 are pushed together maintaining C2 symmetry

throughout, a somewhat distorted DHP forms, but this is appa-

rently under too much stress as on relaxation it collapses back

to cis-stilbene. (Its energy profile is given in (7)). The lowest

energy new isomer found, C6��C20, is clearly related to DHP,

except that the hydrogens on the two joined carbon atoms (C6

and C20) are on the same side of the molecule (cis), whereas in

DHP, they are on opposite sides (trans). It lies just 7.7 kcal/mol

higher in energy than DHP (6.8 kcal/mol at MP2). However, the

reverse barrier for rearrangement back to cis-stilbene is only 6.9

(5.9) kcal/mol, and so it is unlikely to be stable.

DHP can be formed by pushing together atoms C6 and C20

while simultaneously pulling atoms C3 and C50. (Like several of

the other isomers reported here, it is chiral.) Indeed further iso-

mers, different from those discussed here but with even higher

energy, can be formed by applying external forces to multiple

pairs of atoms at the same time. The more interesting of these

will be described elsewhere, along with related structures formed

from cis-azobenzene.22

The simulated infrared (IR) spectra for cis-stilbene, trans-stil-bene, 4a,4b-dihydrophenanthrene, and the two potentially kineti-

cally stable new isomers C1��C20 and C7��C50 are shown in

Figure 3. These were obtained directly from the computed

B3LYP/6-31G* force constant (Hessian) matrix, scaled using the

five standard precomputed scaled quantum mechanical (SQM)

scale factors23 shown in Table 2 and visualized using the

PQSMol graphical user interface available with PQS.19 All spec-

tra have been partially standardized to aid comparison.

Although all five IR spectra are clearly different and could

be used to identify each isomer if observed in isolation, there

are no major distinguishing features that would help detect any

of the other isomers at low concentration in a mixture of mainly

cis- and trans-stilbene. The fairly strong band at 2738 cm21

could perhaps be used as a fingerprint for DHP, as there is noth-

ing at all in this region in the IR spectrum of either cis- or

trans-stilbene, and only a much weaker signal at 2807 cm21 in

C1��C20. Similarly the bands just after this, and just before the

main C��H stretching region (at 2916 and 2961 cm21) might be

used to show the presence of the C7��C50 isomer assuming its

concentration were high enough.

The corresponding standardized simulated Raman spectra are

shown in Figure 4. Note that the intensity scale is up to an order

of magnitude greater than for the IR spectra. and is less by a

factor of three for the two new isomers (C1��C20 and C7��C50)than for the other three.

DHP has a very intense band at 1481 cm21 that is a good

candidate for identifying this isomer (see later). This band,

which is due to a coupled stretching and compression of the

C��C bonds in the various rings together with corresponding

ffCCH bends, is so intense that it has been truncated (i.e., its in-

tensity is greater than the maximum (1200) given in the plot).

Unfortunately, although cis-stilbene has few, if any, features in

Table 2. Standard B3LYP/6-31G* SQM Scale Factors Relevant to

C14H12.

Type Scale factor

Stretch rCC 0.9207

Stretch rCH 0.9164

Bend ffCCC 1.0144

Bend ffCCH 0.9431

Torsion all 0.9523



this region of the Raman spectrum, trans-stilbene—which after

all is the most stable conformer—does have a band here. There

are far more intense bands in the trans-stilbene spectrum, but it

might well be sufficient to hide the formally intense band from

DHP in low concentration. A careful comparison would have to

be made with the spectrum of pure trans-stilbene.In addition to this extremely intense band for DHP, the same

bands in the C��H stretching region that could potentially be

used to detect the presence of non-stilbene isomers in the IR

spectrum are also present in the Raman spectra, namely the

band at 2738 cm21 in DHP and the bands at 2916 and 2961

cm21 in C7��C50. Unfortunately, although C1��C20 has a fairly

distinctive spectrum in the fingerprint region, the average inten-

sity, although high, is noticeably less than in the stilbenes and

DHP, and unless present in high concentration it is likely to be

swamped by signals from the more stable species. Compared

with the other isomers, C7��C50 is almost Raman inactive apart

from the C��H stretches.

Figure 4. Simulated SQM-scaled B3LYP/6-31G* Raman spectra of cis-stilbene, trans-stilbene, 4a,4b-dihydrophenanthrene, C1��C20 and C7��C50.



Finally, we consider 13C NMR chemical shifts in the three

non-stilbene isomers. Predicted B3LYP/6-31G* absolute 13C

NMR chemical shifts for selected carbon atoms in the various

C14H12 isomers are shown in Table 3. The carbons (and also the

protons) in cis- and trans-stilbene are in similar chemical envi-

ronments, and all have very similar computed B3LYP/6-31G*

chemical shifts (spanning a range of only around 10 ppm). In

DHP, C1��C20, and C7��C50, there are several signals shifted to

much higher field, particularly for the atoms involved in forming

new bonds. If we arbitrarily take the mid-point of the 13C sig-

nals in cis-stilbene as our reference (roughly 65.0 ppm), then in

DHP the computed shift upfield for atoms C6 and C20 (identicalby symmetry) is almost 83 ppm; in C1��C20 the shifts are �70

and �76 ppm, respectively, with two more signals shifted (rela-

tively) by �69 and �96 ppm, whereas in C7��C50 the relative

shifts upfield are �84, �86, �91 and �109 ppm, respectively.

Any observed shifts of this magnitude should in principal be de-

tectable and would clearly indicate a non-stilbene isomer if one

was present in sufficient concentration. It should even be possi-

ble to distinguish between the isomers, there being just one high

field signal in DHP, four with a 27 ppm split in C1��C20 andfour with a similar split (25 ppm) but shifted upfield on the av-

erage by more in C7��C50.

Comparison With Experiment for Vibrational Fundamentals

Tables 4 and 5 compare the SQM B3LYP/6-31G* predicted

vibrational fundamentals for trans- and cis-stilbene, respectively,with experimental values from the literature. We have quoted

data from two groups: A joint experimental and SQM theoretical

study of the vibrational spectra of both stilbene conformers from

Otero and coworkers24 (this was subsequently reinvestigated

somewhat by Choi and Kertesz5), and a later vibrational analysis

of trans-stilbene in the ground and excited singlet states by

Fuyura and coworkers.25

Overall, our SQM results are in excellent agreement with the

experimental fundamentals for both trans- and cis-stilbene, andbased on our results, we are able to propose some corrections

and reassignments for the trans conformer. The accuracy one

Table 3. Predicted B3LYP/6-31G* 13C NMR Chemical Shifts (Absolute)

for Selected Carbon Atoms in the Various C14H12 Isomers.

13C Atom trans-stilbene cis-stilbene DHP C1��C20 C7��C50

C1 60.0 60.0 58.2 133.9 54.1

C6 65.2 66.1 147.7 141.2 67.3

C7 68.1 64.7 69.7 161.0 151.4

C20 73.5 68.6 147.7 135.3 51.8

C50 67.8 68.0 68.8 70.3 149.2

C60 65.2 66.1 65.7 71.7 173.7

C70 68.1 64.7 69.7 63.7 156.3

Table 4. Predicted (SQM) and Experimental Fundamentals for trans-stilbene.

Expt.a Expt.b SQM Expt.a Expt.b SQM Expt.a Expt.b SQM

– \10i au 854 bg 848 bg 858 bg 1332 bu 1327 bu 1325 bu– 57 au 866 ag 869 ag 866 ag 1338 ag 1336 ag 1337 ag– 64 bg 909 au 907 au 896 au 1337 bu 1346 bu– 81 bu 912 bg 914 bg 907 bg 1445 ag 1448 ag 1448 ag

198 ag 203 ag 203 ag – au 938 au 1450 bu 1453 bu 1458 bu227 bg 227 bg 216 bg 939 bg 1491 ag 1492 ag 1495 ag268c au 286 au 280 au 966 au 959 au 963 au 1494 bu 1497 bu 1502 bu(336) ag 291 ag 285 ag 969 bg 969e bg 968 bg 1573 ag 1577 ag 1574 ag

(971) au410 au 408 au 402 au 984 au 980 au 988 au 1577 bu 1581 bu 1580 bu

985 bg 985e bg412 bg 406 bg 403 bg 998 ag 1001 ag 996 ag 1593 ag 1600 ag 1599 ag466 bg 464 bg 466 bg 1001 bu – bu 998 bu 1597 bu 1603 bu 1607 bu

(419d) bu 469 bu 473 bu 1026 ag 1028 ag 1024 ag 1639 ag 1639 ag 1644 ag528 au 526 au 531 au 1028 bu 1031 bu 1026 bu 3020 ag541 bu 538 bu 547 bu 1071 bu 1071 bu 1079 bu 3020 bu 3027 bu616 ag 620 ag 627 ag 1093 ag – ag 1082 ag 3029 ag 3040 ag620 bu – bu 631 bu 1155 bu 1155 bu 1157 bu 3031 bu 3040 bu640 ag 641 ag 650 ag 1156 ag 1157 ag 1157 ag 3040 ag 3047 ag686 bg – bg 683 bg 1182 bu 1179 bu 1179 bu 3047 bu692 au 691 au 688 au 1184 ag 1183 ag 1180 ag 3056 bu 3056 bu734 bg 736 bg 735 bg 1193 ag 1194 ag 1185 ag 3057 ag764 au 760 au 764 au 1220 bu 1214 bu 1221 bu 3062 ag 3066 ag824 bu – bu 811 bu 1264 bu 1262 bu 1261 bu 3066 bu838 bg 821 bg 827 bg 1289 ag 1293 ag 1302 ag 3076 bu 3073 bu

1300 bu847 au – au 828 au 1326 ag 1320 ag 1323 ag 3082 ag 3073 ag

arefs. 24 and 5. bref. 25. cTaken from ref. 28. dTaken from ref. 29. eBased on an analysis of combination bands.



would typically expect from the SQM method is an average

error of less than 10 cm21 over the entire vibrational spectrum

with a maximum error (usually in the C��H stretch region) of

around 30 cm21. If any vibrational fundamentals differ from the

SQM prediction by significantly more than this maximum, then

it is far more likely in our opinion that the mode has been mis-

assigned experimentally than the SQM prediction is wrong.26,27

Most of the misassignments are in the work of Otero and co-

workers.24 The first one is an ag mode at 336 cm21. The SQM

prediction is 285 cm21 and this is supported by Fuyura and co-

workers who have assigned this mode at 291 cm21. Next is a bumode at 419 cm21 for which the SQM prediction is 469 cm21

which is again supported by the Japanese group (473 cm21).

The third is an au mode at 971 cm21. In Table 2 in ref. 25, the

four highest au bands are given at 980, 959, then a gap (no

mode assigned), then 907 cm21. The three quoted bands are al-

ready assigned to SQM fundamentals at 988, 963, and 896

cm21. The location of the gap suggests that the unassigned aumode is certainly expected to be less than 959 cm21. There is

just no room for a fundamental at 971 cm21 and our opinion is

that this feature has simply been misassigned. A similar argu-

ment applies to the bu mode at 1300 cm21. (The first three of

the frequencies noted above which we consider to have been

misassigned are in parentheses in Table 4.)

The last of our proposed reassignments is not so clear cut.

These concern the three bg modes observed between 900 and

1000 cm21. By symmetry, none of the bg modes is IR active

and virtually all are listed as very weak in the Raman spectrum.

The two experimental groups assign these three fundamentals at

985, 969, and 912 (914) cm21. The SQM predictions are 968,

939, and 907 cm21. The lowest of these is clear, but if the two

others are simply assigned to the two experimental values in

order, then the errors are 17 and 30 cm21, respectively. This is

not impossible of course, but we prefer the alternative of

assigning the SQM mode at 968 cm21 to the experimental

band at 969 cm21, leaving the feature at 985 cm21 misas-

signed. In considering this reassignment, it should be noted

that Fuyura and coworkers assigned both of these modes based

on an analysis of combination bands, and the SQM mode at

939 cm21 has a very low predicted Raman intensity (much

lower than for the two other bg modes), which might explain

why it was not observed.

Not all the bands in the spectrum of cis-stilbene were

assigned experimentally (this applies in particular to the b

modes), and we have no proposed reassignments. If the assign-

ments given in Tables 4 and 5 are taken ‘‘as is’’ and comparison

is made between the SQM frequencies and the experimental

value that is closest to it, then the average deviation between

theory and experiment is just 4.6 cm21 for trans-stilbene and

5.0 cm21 for the cis conformer, with maximum errors of 19 and

16 cm21, respectively. These very low errors lend strong support

to our theoretical predictions for the other potential C14H12 iso-

mers discussed in this work.

During the final preparation of this article we found a paper

on the resonance Raman spectra of DHP from Myers and co-

workers.30 This claimed, likely correctly, to be the first pub-

Table 5. Predicted (SQM) and Experimental Fundamentals for cis-stilbene.

IRa Ramana SQM IRa Ramana SQM IRa Ramana SQM

29 b 844 a 846 a 840 a 1336 b 1333 b 1326 b

31 a 863 b 863 b 859 b 1332 a

74 a 912 a 908 a 1406 b 1405 b 1416 b

166 a 154 a 925 919 b 1444 a 1443 a 1446 a

157 b 945 b 1449 1456 b

248 b 947 a 1490 a 1490 a 1495 a

261 a 262 a 966 a 965 a 967 a 1495 1498 b

403 a 401 a 983 971 b 1576 a 1573 a 1574 a

404 b 992 976 a 1578 b

407 a 1001 a 1001 a 995 a 1600 a 1599 a 1602 a

443 b 449 b 451 b 998 b 1605 b

502 508 b 1029 a 1029 a 1025 a 1629 a 1635 a

519 a 519 a 523 a 1025 b 2999 b

561 a 561 a 564 a 1074 1076 a 3012 a 3014 a 3020 a

619 b 619 b 628 b 1082 b 3024 b 3030 b 3040 b

629 a 1149 a 1146 a 3040 a

682 b 684 b 1156 b 3048 b

694 a 1156 a 1157 a 3048 a

698 b 699 b 698 b 1176 b 3054 b 3049 b 3057 b

732 b 731 b 735 b 1180 a 1182 a 1177 a 3058 a

752 a 752 a 749 a 1203 b 1203 b 1198 b 3069 b

771 a 769 a 768 a 1234 a 1241 a 3061 a 3070 a

781 b 782 b 787 b 1293 b 3082 b

837 b 1305 a 1317 a 3079 3083 a

aref. 24.



lished vibrational spectra for this species. The experiment is not

an easy one, but they managed to observe nine bands by excit-

ing the Raman spectrum within the absorption band of DHP at

436 and 477 nm. The spectra at both wavelengths is dominated

by a strong band at 1474 cm21 which the authors state is pre-

sumably the mostly in-phase stretch of the double bonds in the

conjugated polyene chain. This compares extremely well with

the simulated Raman spectrum for DHP presented in this work

(see the discussion above) where this band—predicted to have

an intensity almost an order of magnitude greater than the next

most intense band—occurs at 1481 cm21.

Given that there is at least one partial experimental spec-

trum for DHP,30 we present in Table 6 all predicted SQM fun-

damentals for 4a,4b-dihydrophenanthrene, together with their

IR and Raman intensities and Raman depolarization ratios as

an aid to further experimental studies. (It should be noted that

predicted intensities in the C��H stretching region, both IR and

Raman, are often greater than those observed experimentally.)

Also given are the nine experimental frequencies reported in

ref. 30.

As can be seen from Table 6, almost all of the tentative

experimental values map very nicely onto a calculated fre-

quency and furthermore one with either a very high predicted

Raman intensity (typically [100) or an intensity that is the

highest in its vicinity. The only experimental frequency we

would query is the one at 1035 cm21 as the closest SQM fre-

quency is at 1077 cm21, which is 42 cm21 too high. There is

a moderately intense ag band in the Raman spectrum of trans-stilbene found experimentally at 1028 (1026) cm21 (see Table

4): could this have been the band observed and misassigned?

An earlier SQM study from Zhou and Liu31 (done at RHF/4-

31G) which concluded that the observed frequencies at 1555

and 1534 cm21 were not fundamentals of DHP looks clearly

to be in error.

Table 6. Predicted (SQM) and Experimental Fundamentals for 4a,4b-dihydrophenanthrene, Together With

Raman and IR Intensities and Raman Depolarization Ratios.

SQM Raman Depol IR ref. 30 SQM Raman Depol IR ref. 30

62 a 1.8 0.680 – 1077 a 255 0.309 1.9 1035

81 b 0.1 0.750 0.3 1097 a 135 0.312 0.5 1080

192 a 11.4 0.550 – 1146 a 94.3 0.215 1.3 1147

194 b 2.2 0.750 0.5 1147 b 4.7 0.750 22.7

216 a 9.2 0.426 0.5 1158 b 15.6 0.750 9.8

367 b 0.2 0.750 6.8 1175 b 25.2 0.750 5.3

374 a 35.6 0.260 – 1995 a 10.6 0.212 4.9

380 b 8.1 0.750 6.1 1210 a 239 0.195 0.1 1201

382 a 0.8 0.268 1.3 1237 b 57.6 0.750 3.0

455 b 5.1 0.750 4.4 1262 a 22.6 0.318 1.3

461 a 9.4 0.218 5.1 1276 b 1.5 0.750 21.8

488 b 5.4 0.750 4.1 1318 a 75.9 0.331 1.1 1298

530 a 14.3 0.364 1.1 1339 b 14.6 0.750 2.7

548 a 14.2 0.074 – 1367 a 205 0.352 3.5

584 b 4.6 0.750 9.5 1376 b 17.7 0.750 18.1

629 a 17.3 0.717 1.2 1383 a 12.7 0.290 0.2

639 b 8.0 0.750 6.2 1430 b 26.0 0.750 0.5

686 a 8.9 0.493 3.3 1434 a 98.4 0.194 0.5

687 b 5.7 0.750 38.9 1481 a 4365 0.264 0.3 1474

701 b 6.0 0.750 31.8 1542 b 120 0.750 2.7 1534

776 a 25.7 0.403 1.5 769 1563 a 130 0.750 4.1 1555

783 b 7.5 0.750 1.0 1603 b 78.4 0.750 6.2

799 a 9.4 0.251 4.1 1641 a 335 0.416 3.6

809 b 0.8 0.750 3.2 1649 b 54.2 0.750 0.1

856 b 1.5 0.750 52.4 2725 a 180 0.368 1.7

907 a 40.4 0.345 – 2738 b 16.2 0.750 59.3

910 a 13.8 0.334 0.2 3030 b 36.8 0.750 12.4

939 b 1.7 0.750 3.1 3035 a 51.7 0.200 0.7

945 a 3.5 0.398 0.2 3035 b 16.0 0.750 31.7

950 b 5.1 0.750 1.1 3040 b 259 0.750 0.4

958 a 5.1 0.722 2.5 3042 a 37.8 0.256 13.4

961 b 2.5 0.750 1.1 3046 a 198 0.261 49.7

962 a 27.9 0.354 1.2 3056 b 56.4 0.750 5.0

969 b 0.1 0.750 1.4 3063 a 227 0.512 30.3

1003 a 8.3 0.190 52.4 3068 b 10.2 0.750 67.2

1069 b 5.9 0.750 – 3070 a 589 0.110 15.9



Conclusions

Using what we have termed enforced geometry optimization

(EGO) in which equal and opposite external forces are applied

to pairs of atoms in a molecule along the line joining their

centres (acting in this case so as to push the atoms together), we

have discovered several potentially new metastable isomers of

C14H12 starting from cis-stilbene. Taking the energy profiles for

the EGO optimizations as a kind of reaction path, we have

located transition states for rearrangement of all of the new iso-

mers back to cis-stilbene, starting from the geometry corre-

sponding to the highest energy point on the EGO energy profile.

All stationary points found, both minima and transition states,

were characterized by a full vibrational analysis at B3LYP/6-

31G* and the energetics were checked by reoptimization at

MP2/6-311G**.

Most of the new C14H12 isomers have low barriers for rear-

rangement and are consequently kinetically unstable. We have pro-

vided simulated IR and Raman spectra as well as 13C NMR chemi-

cal shifts for the two new isomers which we consider, based on ki-

netic considerations, to be the most stable as an aid to their

possible detection. The excellent agreement between the computed

and observed vibrational fundamentals of cis- and trans-stilbene(mean average deviations of 5.0 cm21 or less) and likewise the

agreement with the nine observed fundamentals for DHP provide

strong support for our predictions for the new isomers.

Enforced geometry optimization is a very powerful tool for

discovering new chemical structures. The highest point along the

EGO energy profile (the optimization history) provides a good

starting geometry for a standard TS search and makes it straight-

forward to determine the barrier height for rearrangement back

to the starting material, giving at least an idea of the kinetic sta-

bility of any new compounds formed. This approach worked for

nine of the 10 isomers found in this study, including several

with very low reverse barriers, and could prove to be a viable

replacement for an optimized potential scan (i.e., driving a

‘‘reaction coordinate’’ through a range of values while simulta-

neously optimizing all other degrees of freedom) for the location

of difficult transition states.

Acknowledgments

We thank Dr. Peter Pulay (University of Arkansas, Fayetteville)

for locating the unrestricted open-shell singlet (UB3LYP) transi-

tion state for the cis- to trans-stilbene rearrangement.

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Isomerization of stilbene using enforced geometry optimization

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