High-resolution spectroscopy of 4-fluorostyrene-rare gas van der Waals complexes: Results and comparison with theoretical calculations

High-resolution spectroscopy of 4-fluorostyrene-rare gas van der Waals complexes:

Results and comparison with theoretical calculations

N. M. Lakin, G. Pietraperzia, M. Becucci, E. Castellucci, M. Coreno, A. Giardini-Guidoni, and A. van der Avoird

Citation: The Journal of Chemical Physics 108, 1836 (1998); doi: 10.1063/1.475561

View online: http://dx.doi.org/10.1063/1.475561

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High-resolution spectroscopy of 4-ﬂuorostyrene-rare gas van der Waals

complexes: Results and comparison with theoretical calculations

N. M. Lakin,^a)G. Pietraperzia,^b)M. Becucci,^c)and E. Castellucci^b)

`

European Laboratory for non Linear Spectroscopy (LENS), Universita di Firenze, Largo E. Fermi 2,

50125 Firenze, Italy

M. Coreno

CNR-Istituto Metodologie Avanzate Inorganiche, Sede Staccata Area della Ricerca di Trieste, Padriciano

99, 34012 Trieste, Italy

A. Giardini-Guidoni

`

Universita di Roma ‘‘La Sapienza’’, Dipartimento di Chimica, Ple A. Moro 5, 00185 Roma, Italy

A. van der Avoird

Institute of Theoretical Chemistry, NSR Centre, University of Nijmegen, Toernooiveld 1, Nijmegen,

The Netherlands

͑Received 12 September 1997; accepted 24 October 1997͒

High-resolution laser excitation spectra of the S₁←S₀0⁰₀bands of the 1:1 van der Waals complexes

of 4-ﬂuorostyrene with atoms of argon and neon are presented. The rotational structure of each is

fully assigned using a rigid asymmetric rotor Hamiltonian. The rotational constants for the

complexes are used to extract effective coordinates for the rare-gas atoms which contain both

dynamic and geometric information. Semiempirical potentials for the clusters in the ground and

excited states are determined by ﬁtting to the rotational constants and vibrational frequencies from

three-dimensional quantum calculations to the experimental data. The effective coordinates are

interpreted by comparison with the results of these quantum calculations on the potential surfaces

I. INTRODUCTION

͑Refs. 2 and 3 ͑and references therein͒. In a series of papers,

Hollas and co-workers derived torsional potentials for ST

and 4FST in their ground and excited states.^4–6Both mol-

ecules have been classed as quasi-planar in the ground state:

The torsional barriers and ﬁrst vibrational intervals were es-

timated to be around 348 and 44 cm ^Ϫ1, respectively, for

4FST,⁴so that the molecule is subject to a large amplitude

zero-point torsional motion in the lowest vibrational level. In

their excited states ST and 4FST are far more rigid: The

torsional barrier and vibrational intervals have been esti-

mated at about 5190 and 170 cm^Ϫ1, respectively, in 4FST.⁴

As a prelude to the present study, we recorded the laser

excitation spectra of the S₁←S₀0⁰₀and 41₀¹42₀¹bands of the

bare 4FST molecule in a supersonic molecular beam.²Both

The van der Waals ͑vdW͒ complexes formed between

simple aromatic molecules and rare-gas atoms have been

much studied because of the importance of these systems in

developing an understanding of phenomena such as solva-

tion, nucleated growth, and matrix shifts in vibrational and

electronic spectra. In particular, rotationally resolved spectra

for these complexes provide a window onto their geometry

and internal dynamics. In a recent paper we presented the

laser excitation spectra of the S₁←S₀0⁰₀bands of the 1:1

vdW complexes of aniline with atoms of argon and neon

formed in a super-sonic molecular beam.¹Effective coordi-

nates determined for the rare-gas atoms were interpreted by

comparison with quantum-mechanical calculations. The

present paper describes the results of an equivalent study of

the complexes of the 4-ﬂuorostyrene ͑4FST͒ molecule. This

represents a step up in complexity: The lack of symmetry of

the complexes makes the interpretation of the effective coor-

dinates more difﬁcult and the low frequency of the torsional

mode in the ground state of 4FST makes coupling with the

vdW modes energetically more favorable.

bands were a/b-hybrids with the transition moment inclined

ϩ4

Ϫ5

at an angle of Ϯ(35 )° to the a-principal inertial axis. The

rotational constants obtained for the different vibronic states

were used to derive effective molecular geometries.

Several studies of complexes between ST derivatives

and small molecules or rare-gas atoms have been performed

using resonant two photon ionization ͑R2PI͒ processes in a

supersonic molecular beam. The S₁←S₀one color ͑1C͒-

R2PI spectra of ST-Ar and 4FST-Ar are shifted to the red of

the corresponding spectra of the bare molecule by about 31

and 42 cm^Ϫ1, respectively.⁷These shifts are of the magni-

tude expected for a mainly dispersive bonding interaction,

which strengthens on excitation of the complexes to their S₁

states. The vibrational structures of these spectra are domi-

nated by the ‘‘internal’’ modes of the aromatic molecule,

with weaker satellite bands assigned to excitation of the vdW

Over the past thirty years there have been numerous

spectroscopic studies of styrene ͑ST͒ and its derivatives

a͒

¨

Present address: Institut fur Physikalische Chemie, Universitat Basel, Klin-

gelbergstrasse 80, CH 4056, Basel, Switzerland.

b͒

`

Also, Dipartimento di Chimica, Universita di Firenze, Via G. Capponi 9,

50121 Firenze, Italy.

c͒

Author to whom correspondence should be addressed. Electronic mail:

becucci@lens.uniﬁ.it

1836

J. Chem. Phys. 108 (5), 1 February 1998

0021-9606/98/108(5)/1836/15/$15.00

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Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

1837

modes. The disappearance of band structure for vibrational

excitation exceeding 0⁰₀ϩ410 cm^Ϫ1for ST-Ar^3,8,9and 0₀⁰

ϩ496 cm^Ϫ1for 4FST-Ar⁷has been taken as indication of

dissociation of these complexes in their excited states. The

vdW intervals and dissociation energies of these complexes

were reasonably well reproduced by modeling the atom–

aromatic potential using a pairwise summation of atom–

atom potentials of the Lennard-Jones 6-12 type.^3,10,11The

equilibrium position of the argon atom was calculated to be

approximately above the center of the aromatic ring but sub-

ject to large amplitude vdW oscillations parallel to the ring.

Analogous spectra were recorded for the 4FSTX ͑XϭNe, Kr,

and Xe͒ complexes, where the spectral shift increases with

the atoms polarizability as expected from the dispersive na-

ture of bonding interaction.^7,12

In this paper, we describe the measurement of the

S₁←S₀0⁰₀bands of the 4FST-X ͑XϭAr and Ne͒ vdW com-

plexes ͑Sec. II͒ and the analysis of their rotational structure

͑Sec. III͒. Effective coordinates for the rare gas atom are

extracted from the rotational constants in Sec. IV. In Sec. V

rotational and vibrational eigenvalues are calculated from a

parameterized form of the 4FST-X potential-energy surface

and the potential is optimized by least-squares ﬁtting to the

experimental data. The role of the effective coordinates in

judging the empirical potentials is also demonstrated. The

results are then discussed ͑Sec. VI͒ in comparison with

analogous molecular systems and ﬁnally the main points of

the work are summarized ͑Sec. VII͒.

FIG. 1. Comparison between the experimental ͑exp͒ and simulated spectra

for a-type ͑a͒ and c-type ͑c͒ components of the S₁←S₀0⁰₀transition in

4FST-Ar. The simulated spectra were convoluted with a Lorenzian function

of 33 MHz linewidth.

are determined by recording the trace from a 150 MHz free

´

spectral range etalon.

Commercially available 4FST ͑Aldrich, purity 99%͒ was

used without further puriﬁcation. The sample was main-

tained at a temperature around 40 °C, which provides a con-

venient vapor pressure without signiﬁcant thermal decompo-

sition. The spectrum of 4FST-Ne was recorded using neon as

the expansion gas and that of 4FST-Ar using a 5% mixture

of argon in helium. The intensity ratio of the monomer spec-

trum to that of the complex was about 44:1 for 4FST-Ar, 6:1

for 4FST-²²Ne and 23:1 for 4FST-²⁰Ne.

II. EXPERIMENT

The experimental apparatus has been described in great

detail elsewhere¹³and a brief description only will be given

here. A molecular beam is formed by expanding the carrier

gas, at a pressure of 400–500 kPa, through a conical nozzle

͑50 ␮m diam͒ and skimmer ͑400 ␮m diam͒ into the detec-

tion chamber. The gas ﬂow is seeded by passing it over the

sample, contained in a heated container, before it enters the

nozzle. The nozzle assembly is stabilized to a temperature

about 10–15 °C higher than that of the sample to prevent

condensation at the nozzle throat. The laser radiation enters

and exits the detection chamber through a well bafﬂed path

and crosses the molecular beam perpendicularly. The total

undispersed laser-induced ﬂuorescence ͑LIF͒ is focused onto

a photomultiplier tube ͑EMI 9893Q/350͒ and the signal is

processed by a photon counter ͑Stanford Research 400͒.

The UV laser radiation is generated by an intracavity

doubled single-mode ring dye laser ͑Coherent Radiation 699-

21͒ operating on Rhodamine 6G dye ͑Exciton͒ and pumped

by an argon ion laser ͑Spectra-Physics mod. 2040-E͒. In this

region, the frequency stability of the system is about Ϯ2

MHz, the laser power at the crossing point with the molecu-

lar beam is 1.5–2.5 mW and the instrumental line broaden-

ing is about 15 MHz, which is mainly due to residual Dop-

pler broadening. Absolute frequency calibration to an

accuracy of within Ϯ120 MHz is provided by simulta-

neously monitoring the absorption spectrum of iodine ex-

cited by the dye laser fundamental. Relative frequency shifts

III. DESCRIPTION OF SPECTRA AND ANALYSIS

The laser excitation spectra of the S₁←S₀0⁰₀vibronic

bands of the 4FST-X vdW complexes with XϭAr and Ne

are shown in the upper traces of Figs. 1 and 2 respectively.

2

q

The corresponding spectra of 4FST consists of P and R

branches onto which are superimposed a few strong ^qQ lines.

In contrast the spectra of the complexes contain strong Q

branches, consisting of many overlapping transitions.

FIG. 2. Comparison between the experimental ͑exp͒ and simulated spectra

for a-type (a²⁰Ne and c²⁰Ne͒ and c-type (a²²Ne͒ components of the

S₁←S₀0⁰₀transition in 4FST-Ne. The simulated spectra were convoluted

with a Lorenzian function of 33 MHz line width.

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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1838

Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

TABLE I. Results from the least-squares ﬁt of the S₁←S₀0⁰₀band of

In this type of complex, the equilibrium position of the

4FST-Ar. Here the symbols ␯₀, ␪, and ␴ refer to the band origin, rotational

temperature of the expansion ͑estimated by simulation of the spectrum as-

suming a Boltzmann distribution in the ground state͒ and the standard de-

viation of the ﬁt respectively.

rare gas atom is normally about 3.5 Å above the center of the

aromatic ring.^1,3Complexation is not expected to greatly al-

ter the orientation of the transition moment and the principal

inertial axes of the complex are primarily a translation of

those of the bare molecule towards the rare-gas atom. A

re-labeling of the inertial axes occurs: The a axis of the

complex remains approximately parallel to that of the bare

molecule but the labels of the other two axes are exchanged

͑i.e., a→a, b→c, c→b). As a result, the a/b-hybrid bands

of 4FST are expected to become a/c-hybrids in the complex;

this is conﬁrmed by the spectral assignments. The greater

intensity of the Q branch in the spectra of the 4FST-X com-

plexes compared to that for the bare molecule results from

Variable

Unit

Value^a

A

BЉ

C

A

B

C

␯

␪

cm^Ϫ1

K

0.035 746͑13͒

0.027 348 7͑53͒

0.018 859 2͑53͒

0.036 186͑14͒

0.027 271 9͑54͒

0.0191842͑54͒

Љ

Ј

34 270.0892͑12͒

0

2.0͑5͒

␴

MHz

8.2

q

two effects. First, the Q transitions, produced by the com-

^aNumbers in parentheses represent one standard deviation of the parameter

in units of the last quoted decimal place.

ponent of the transition moment along the a axis, is over-

p

lapped by Q and ^rQ transitions produced by the component

along the c axis. Second, the intensity and number of observ-

able transitions is increased by a lowering of the ground state

A rotational constant upon complexation, increasing the

of 4FST-Ne: The strong Q branch is accompanied by a simi-

lar feature of about one quarter the intensity, shifted to the

red by ϳ0.1 cm^Ϫ1. These two features are assigned to the

isotopomers 4FST-²⁰Ne and 4FST-²²Ne respectively.

populations of the lowest K levels. The same effect was

_aЉ

observed in the spectra of the equivalent aniline-X

complexes.¹

Starting values for the rotational constants of the 4FST-

²⁰Ne complex were estimated by assuming that the 4FST

moiety has the same geometry as the bare molecule²and that

the neon atom sits in the same equilibrium position calcu-

lated for the rare-gas atom in 4FST-Ar.¹⁰Initial assignments

for the much weaker lines produced by the 4FST-²²Ne iso-

topomer required more accurate starting estimates of the ro-

tational constants for both states. These were calculated

from the effective inertial tensor, given in Sec. IV, using the

effective coordinates values obtained from the rotational

constants of the 4FST-²⁰Ne complex but with the appro-

priate effective mass term for the 4FST-²²Ne complex. The

ﬁnal least-squares ﬁts contained 263 and 55 rovibronic as-

signments for 4FST-²⁰Ne and 4FST-²²Ne, respectively,

with Jр14 and K_aр7 and accounted for 97% of the total

observed intensity. Again, no consistent set of assignments

to b-type transitions could be made. For the more intense

The spectra of both 4FST-X complexes are well repro-

duced by a rigid asymmetric rotor Hamiltonian; least-squares

ﬁtting and simulations were performed using a modiﬁed ver-

sion of the ASYROT Fortran code written by Sears.¹⁴

For 4FST-Ar, initial assignments were obtained by simu-

lating the spectrum using, for both states, the previous cal-

culated ground-state rotational constants.¹⁰The number of

assignments was built-up iteratively by simulation and least-

squares ﬁtting. The lines were weighted with the squared

inverse of their uncertainty, which was taken as half of the

experimental linewidth ͑33 MHz͒ for features with a single

_{assignment, or a factor of}ͱ_{n less for a feature assigned to n}

transitions of approximately equal predicted intensity. The

ﬁnal ﬁt contained 234 rovibronic assignments with Jр15

and K_aр10, accounting for 97% of the total observed inten-

sity. No consistent set of assignments to b-type transitions

ϩ4

could be made. The band was estimated to be of 62

%

4FST-²⁰Ne isotopomer, the percentages of the two compo-

Ϫ3

ϩ5

a-type and 38^Ϫ_ϩ3⁴% c-type, by averaging the value of

_obs/I_calc, where I is the intensity of a particular line, over

nents of the transition moment were estimated as 73

%

Ϫ4

I

a-type and 27^Ϫ_ϩ4⁵% c-type. For the less intense 4FST-²²Ne

isotopomer, all of the observable lines were assigned as

a-type transitions and the c-type transitions were simply too

weak to be seen.

the ten strongest unblended lines of each transition type. The

results from the least-squares ﬁt of the spectrum of 4FST-Ar

are given in Table I. The lower two traces of Fig. 1 show

simulations of the spectra produced by each component of

the transition moment, assuming a Boltzmann distribution of

rotational populations in the ground state ͑see Table I͒ and

convoluting the transitions with a Lorenzian function.

The spectrum of the 4FST-Ne complex, shown in Fig. 2,

is very similar to that expected for an asymmetric near-

prolate top, as is the case for the analogous spectrum of

aniline-Ne.¹The aniline-Ne spectrum consists of superim-

posed signals assigned to the isotopomers resulting from

complexation with ²⁰Ne and ²²Ne atoms, despite the fact that

the experimental ratio (Ϸ3.5:1͒ does not agree with the ratio

of their natural isotopic abundances ͑Ϸ9.8:1͒. It is clear from

Fig. 2 that a similar phenomenon is observed in the spectrum

The intensity ratio for the two isotopomers (Ϸ3.5:1͒ was

estimated from the relative intensities of the Q branches. For

aniline-Ne the increase in the relative intensity of transitions

for the more massive complex was attributed to an increase

in the efﬁciency of complex formation resulting from the

slightly lower zero-point energy.¹Brooks et al. reported a

similar increase in the intensity of the strongest lines in the

IR spectra of the ␯ band of jet cooled ²²Ne-SiH₄compared

3

to ²⁰Ne-SiH₄.¹⁵They explained this increase in terms of a

quasi-equilibrium, maintained by binary collisions in the ex-

pansion, which interconverts the two isotopomers. Applying

this model to 4FST-Ne, using the rotational temperature es-

timated from simulations of the band proﬁles ͑see Table II͒

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

1839

TABLE II. Results from the least-squares ﬁts of the S₁←S₀0⁰₀bands of

4FST-²⁰Ne and 4FST-²²Ne. The symbols ␯₀, ␪, and ␴ have the deﬁnitions

given in the heading to Table I.

Value^a

Variable

Unit

4FST-²⁰Ne

4FST-²²Ne

A

B

C

A

B

C

cm^Ϫ1

K

0.056 539͑11͒

0.054 01͑58͒

0.027341͑16͒

0.022 860͑16͒

0.053 96͑58͒

0.027 265͑15͒

0.023 152͑15͒

34 304.0756͑32͒

1.2͑5͒

Љ

Ј

0.027 329 1͑44͒

0.023 389 6͑44͒

0.056 411 9͑94͒

0.027 259 8͑44͒

0.023 678 1͑44͒

Ј

b

␯

34 304.1211͑32͒

0

␪

1.2͑5͒

␴

MHz

8.0

7.4

^aNumbers in parentheses represent one standard deviation of the parameter

in units of the last quoted decimal place.

FIG. 3. Principal axes (a₀, b₀) and molecular geometry of 4FST in its

electronic ground state used for calculation in this paper (c₀axis is perpen-

dicular to the page͒. The atoms are represented as follows: Solid circle for

carbon, open circle for hydrogen, centered circle for ﬂuorine.

^bThe error in the band origin is dominated by the uncertainty in line posi-

tions of the iodine spectrum caused by Doppler broadening in the static

cell. The separation between the two isotopic bands is better determined:

⌬␯ϭ0.045 57͑17͒ cm^Ϫ1; the accuracy in this case is limited by the uncer-

tainty determined in the least-squares ﬁt.

structural information from the rotational constants. In the

lowest vibrational levels of the complexes these constants

depend upon the average of the instantaneous inverse inertial

tensor over the zero-point oscillations of the atoms in the

complex. The oscillations are particularly large and anhar-

monic for the vdW modes owing to the weak dispersive

interaction between the rare-gas atom and the aromatic mol-

ecule.

and zero-point energies from the vibrational eigenvalues cal-

culated in Sec. V ͑see Tables XI and XIII͒, the relative popu-

lations of the lowest rovibronic levels of the two isomeric

forms of the 4FST-Ne cluster should be about 5:1. Consid-

ering the approximate nature of this model ͑which neglects

three body collisions͒ this value is in reasonable agreement

with experiment.

The results from our least-squares ﬁt of the spectra of

4FST-²⁰Ne and 4FST-²²Ne are given in Table II. Simulations

of the spectra of both isotopomers using these constants are

shown in the lower three traces of Fig. 2.

As in our previous work on aniline-X complexes,¹we

have used the rotational constants to determine an effective

inertial tensor for each electronic state. The tensor is set up in

the body-ﬁxed reference frame ͑BF͒ with its origin at the

center of mass of the complex and with axes parallel to the

principal axes ͑a₀, b₀, c₀) of the molecule. The principal axis

system is shown in Fig. 3 for 4FST. The inertial tensor is

given by

IV. d₀STRUCTURE

The ‘‘loose’’ nature of the binding in the 4FST-X com-

plexes makes it particularly difﬁcult to extract unambiguous

k/A ϩ␮ Y²ϩZ²͒

Ϫ␮XY

Ϫ␮XZ

Ϫ␮YZ

͑

0

Ϫ␮XY

k/B ϩ␮ Z²ϩX²͒

͑

0

,

͑1͒

ͭ

ͮ

Ϫ␮XZ

Ϫ␮YZ

k/C ϩ␮ X²ϩY²͒

͑

0

where ␮ is the reduced mass of the complex, X, Y and Z are

the Cartesian coordinates of the rare-gas atom with respect to

the principal axes of 4FST, the proportionality constant k

ϭh/8␲²c and A₀, B₀, C₀are the rotational constants of the

bare 4FST molecule in the same electronic state.²The effec-

tive X, Y, and Z have been called the d₀structure by Brooks

and van Koeven.¹⁶

plexation. In aromatic-rare gas complexes, this assumption is

normally justiﬁed by the fact that the internal modes of the

aromatic molecule are much higher in frequency than the

vdW modes. The assumption is questionable for complexes

involving 4FST, particularly in the S₀state where the tor-

sional internal mode, ␯ ϭ 42 cm^Ϫ1,⁴is very close in fre-

₄₂Љ

quency to the calculated vdW vibrational modes ͑see Tables

IX and XI͒. In the S₁state, where the lowest vibrational

mode is the out-of-plane motion of the vinyl group ͓41͑1-0͔͒

The d₀approach makes the assumption that the aromatic

molecule remains a rigid body which is unchanged by com-

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Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

TABLE III. Comparison between the d₀coordinates for the argon atom in 4FST-Ar determined from experi-

mental rotational constants ͑exp͒, and those obtained from rotational constants calculated variationally ͑var͒ and

by perturbation theory ͑per͒. The calculations are numbered according to the parameter sets give in Table VII.

Calc^a

1

2

3

͑Å͒

Exp^a

per

var

per

var

S₀state

X

Y

Z

0.014͑10͒

0.542͑8͒

3.469͑2͒

0.216͑5͒

0.069͑46͒

3.476͑2͒

0.217͑7͒

0.459͑31͒

3.453͑4͒

0.050͑27͒

0.086͑55͒

3.493͑2͒

0.042͑25͒

0.537͑27͒

3.462͑4͒

0.037͑22͒

0.484͑28͒

3.491͑3͒

S₁state

X

Y

Z

0.019͑3͒

0.501͑13͒

3.423͑3͒

0.205͑6͒

0.072͑48͒

3.460͑2͒

-0.016͑4͒

0.204͑11͒

0.428͑45͒

3.441͑5͒

0.039͑23͒

0.098͑61͒

3.478͑2͒

0.039͑24͒

0.522͑32͒

3.450͑5͒

0.036͑23͒

0.452͑34͒

3.441͑5͒

b

Z -Z

Ϫ0.046͑5͒

-0.012͑9͒

Ϫ0.015(4)

Ϫ0.012(9)

Ϫ0.050(8)

Ј

Љ

^aNumbers in parentheses represent the range of solutions within the tolerance levels of the calculation in units

of the last quoted decimal place.

^bDifference in the Z coordinates determined for S₁and S₀states.

at about 79 cm^Ϫ1, an adiabatic separation of the vibrational

modes is more justiﬁable. This is further supported by the

relatively small ‘‘solvation’’ effects of attaching an argon

atom to the aromatic modes on the internal modes of ST and

trans-␤-methylstyrene ͑BMS͒ in their S₁states: The frequen-

cies of the in-plane vibrations generally change by less than

1% and the out-of-plane vibrations by only 3%–4%.³The

treatment of the 4FST molecule as a rigid body is also more

reasonable for the excited state where its inertial defect is

less negative than in the ground state.²

Tables III and IV contain the effective coordinates of the

rare-gas atom calculated from the experimental rotational

constants for the 4FST-Ar and 4FST-Ne complexes, respec-

tively. The inertial tensor is calculated using trial values for

X, Y, and Z and then diagonalized to give values for the

rotational constants. The trial coordinates are accepted if the

calculated rotational constants reproduce the experimental

ones to within certain tolerance limits. The effective param-

eters are then obtained by averaging over the set of accept-

able parameter values. In the calculations for 4FST-Ar and

4FST-²⁰Ne tolerance limits of 2ϫ10^Ϫ5and 3ϫ10^Ϫ5cm^Ϫ1

were required to produce solutions from the ground-state and

excited-state rotational constants, respectively. These limits

are of the same order of magnitude as the experimentally

determined standard deviation in the A rotational constant

but about an order greater than the standard deviations in the

Band Cconstants, reﬂecting the approximation made in de-

termining the rotational constants from the inertial tensor ͑1͒.

For 4FST-²²Ne the experimental rotational constants are not

so well determined and the tolerance limits were set equal to

their standard deviations.

Pratt and co-workers have pointed out that the d₀coor-

dinates should be regarded as root-mean-square displace-

ments averaged over the vibrational wavefunction of the

complex.¹⁷This is re-enforced by the fact that the inertial

tensor is invariant to sign changes in X, Y, or Z. These co-

ordinates will contain both static contributions, reﬂecting the

equilibrium position of the rare-gas atom with respect to the

center of mass of the 4FST molecule in the lowest vibra-

tional level, and dynamic contributions, reﬂecting the vibra-

tional excursions due to the zero-point motion. In the case of

the aniline-X vdW complexes, the rare-gas atoms have their

equilibrium positions in the symmetry plane of the complex;

the static contribution to the b₀coordinate, perpendicular to

this plane, is therefore necessarily zero and the effective

Y-coordinate contains only dynamic information.^1,14In com-

plexes of lower symmetry, such as 4FST-X, it is more difﬁ-

cult to predict a priori the exact extent to which the effective

coordinates will depend upon either of these contributions

and their interpretation is aided by comparison with calcu-

lated values.

TABLE IV. Expectation values of the argon atom coordinates, X , and

͗

͘

RMS amplitudes of zero-point motion along these coordinates, ⌬X, calcu-

lated for 4FST-Ar in the lowest vibrational levels. The calculations are

numbered according to the parameter sets give in Table VII.

V. QUANTUM CALCULATIONS ON VAN DER WAALS

STATES

1

2

3

͑Å͒

S₀

S₁

S₀

S₁

S₀

S₁

A. LCHOP method

X

Y

Ϫ0.221

Ϫ0.053

3.475

0.265

0.319

Ϫ0.212

Ϫ0.053

3.460

0.259

0.310

0.065

Ϫ0.064

3.492

0.316

0.352

0.045

Ϫ0.064

3.477

0.305

0.342

0.054

Ϫ0.071

3.515

0.276

0.314

0.019

Ϫ0.071

3.462

0.257

0.294

͗

͘

We have used the linear combination of harmonic oscil-

lator products ͑LCHOP͒ method of Brocks and van

Koeven^16,18to calculate the rotational and vibrational energy

levels of the 4FST-X complexes. This method has previously

been used successfully to interpret the 1C-R2PI spectra of

Z

͗ ͘

⌬X

⌬Y

⌬Z

0.112

0.119

0.107

0.105

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

1841

TABLE V. Comparison between the d₀coordinates for the neon atom in 4FST-Ne determined from experi-

mental rotational constants ͑exp͒, and those obtained from rotational constants calculated variationally ͑var͒.

The calculations are numbered according to the parameter sets given in Table VIII.

4FST-²⁰Ne

4FST-²²Ne

1

2

3

4

͑Å͒

Exp^a

Var^a

Exp^a

Var^a

S₀state

X

Y

Z

0.039͑26͒

0.414͑11͒

3.368͑2͒

0.223͑19͒

0.335͑15͒

3.166͑2͒

0.355͑11͒

0.416͑15͒

3.324͑2͒

0.040͑26͒

0.364͑9͒

3.168͑1͒

0.030͑20͒

0.432͑7͒

3.377͑1͒

0.139͑84͒

0.508͑47͒

3.338͑18͒

0.101͑61͒

0.497͑30͒

3.355͑10͒

S₁state

X

Y

Z

0.035͑23͒

0.374͑9͒

3.334͑1͒

0.198͑21͒

0.301͑14͒

3.152͑2͒

0.306͑19͒

0.380͑22͒

3.311͑2͒

0.037͑24͒

0.328͑7͒

3.155͑1͒

0.019͑13͒

0.377͑3͒

3.344͑1͒

0.131͑79͒

0.467͑39͒

3.301͑15͒

0.096͑57͒

0.449͑26͒

3.320͑8͒

b

Z -Z

Ϫ0.034(3) Ϫ0.014(4) Ϫ0.013(4) Ϫ0.010(2) Ϫ0.033(2) Ϫ0.037(33) Ϫ0.035(18)

Ј

Љ

^aNumbers in parentheses represent the range of solutions within the tolerance levels of the calculation in units

of the last quoted decimal place.

^bDifference in the Z coordinate determined for S₁and S₀states.

these complexes,^10–12as well as those of several related

complexes ͑styrene-Ar,^3,10ﬂuorene-Ar,¹⁶aniline-Ar,^1,19

aniline-Ne,¹benzene-Ar^18,20͒.

between this rotation and the internal motions. This Hamil-

tonian is used in full variational calculations for each given

value of J. Rotational constants are then obtained for the

ground vibrational level by ﬁtting the levels computed for a

series of J-values to a rigid asymmetric rotor Hamiltonian ͑in

the same way as one usually deduces rotational constants

from the measured frequencies of the rotational levels͒. In

addition, we calculate the vibrationally averaged rotational

constants of the complex from the vdW eigenfunctions com-

puted for Jϭ0 by means of ﬁrst and second order perturba-

tion theory, with the Coriolis coupling operator as the per-

turbation.

Apart from the validity of the adiabatic separation of

vibrational frequencies, the accuracy of these calculations is

mainly limited by the quality of the aromatic molecule–rare-

gas interaction potential. Ab initio calculations for this type

of complex have only been performed for benzene-Ar.^20,21In

the absence of such calculations, we represent the potential,

V(r), as a sum of pairwise atom–atom dispersive interaction

terms of the Lennard-Jones 6-12 form

Brieﬂy, the Hamiltonian is constructed in the BF frame,

described in Sec. IV. This choice enables the Cartesian co-

ordinates of the noble gas atom to be used to describe the

intermolecular vdW vibrations and the internal vibrations of

the aromatic species to be described by their normal coordi-

nates. The only approximation made in this derivation is the

adiabatic separation of the internal modes and the vdW

modes. The Hamiltonian for a given rovibronic state is aver-

aged over the internal modes and the vdW eigenfunctions are

then calculated by diagonalizing the matrix representation of

the purely vibrational part of the Hamiltonian in a basis set

of products of harmonic oscillator functions in x, y, and z.

These oscillators are centered at the equilibrium position of

the rare-gas atom, X_e, Y_e, Z_e, and their frequencies, ␻_x,

␻_y, ␻_z, are scaling parameters which are optimized varia-

tionally. The matrix elements of the kinetic energy operator

are obtained through the use of harmonic oscillator creation

and annihilation operators.

The rovibrational energy levels are calculated from the

rotation–vibration part of the Hamiltonian, including the

overall rotation of the complex and the Coriolis coupling

12

V r͒ϭ

͑

4␧ Ϫ ␴ /r͒⁶ϩ ␴ /r͒ ͒,

͑2͒

͑

ij

͚

ij

i, j

TABLE VI. Expectation values of the argon atom coordinates, X , and RMS amplitudes of zero-point motion

͗

͘

along these coordinates, ⌬X, calculated for 4FST-Ne in the lowest vibrational levels of the S₀and S₁states. The

calculations are numbered according to the parameter sets given in Table VIII.

4FST-²⁰Ne

4FST-²²Ne

4

͑Å͒

1

2

3

4

State:

S₀

S₁

S₀

S₁

S₀

S₁

S₀

S₁

S₀

S₁

X

Y

Ϫ0.256 Ϫ0.243 Ϫ0.372 Ϫ0.333 Ϫ0.076 Ϫ0.081

Ϫ0.051 Ϫ0.053 Ϫ0.042 Ϫ0.043 Ϫ0.070 Ϫ0.069 Ϫ0.069 Ϫ0.069 Ϫ0.069 Ϫ0.069

0.025 Ϫ0.002

0.021 Ϫ0.006

͗

͘

Z

3.177

0.351

0.387

0.155

3.160

0.342

0.377

0.156

3.338

0.386

0.423

0.166

3.322

0.379

0.411

0.166

3.178

0.368

0.391

0.159

3.163

0.358

0.381

0.159

3.391

0.385

0.408

0.158

3.354

0.361

0.385

0.155

3.388

0.377

0.403

0.154

3.351

0.354

0.381

0.151

͗ ͘

⌬X

⌬Y

⌬Z

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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1842

Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

TABLE VII. Parameter values used in the atom–atom pair potentials of

4FST-Ar.

where ␧ is the well depth and ␴ is the distance at the

ij

minimum of the interaction between atoms i and j ͑alterna-

tively, they are referred to as the ‘‘energy’’ and ‘‘geometric’’

parameters, respectively²²͒. This model excludes the dipole-

induced dipole contribution to the vdW interaction, which

has been evaluated as less than 3% of the total energy in

complexes of aniline and ﬂuorobenzene.²³Interatomic sepa-

rations are calculated using the effective molecular geom-

etries for the relevant state of 4FST determined in our recent

study.²The matrix elements of this potential are evaluated

numerically using Gauss–Hermite quadrature in x, y, and z.

One of the problems with this approach is the lack of knowl-

1^a

2^b

3^c

State:

S₀and S₁

S₀

S₁

␧

␴

͑cm^Ϫ1

)

53.63

32.34

81.0

3.37

3.03

3.52

44.71

30.85

38.49

3.37

2.98

3.03

70.87

30.85

38.49

3.382

2.98

77.45

30.85

38.49

3.349

2.98

C–Ar

H–Ar

F–Ar

͑cm^Ϫ1

͑Å͒

)

C–Ar

H–Ar

F–Ar

͑Å͒

3.03

^aReference 10 and 11.

^bReference 7.

edge of the potential parameters, ␧ and ␴_ij. Furthermore,

ij

^cThis work.

the simpliﬁcation is made that these parameters are identical

for interactions between atoms of the same type regardless of

their position in the molecule.

7,24,25

the Scheraga model ͑set 2͒

and empirically optimized

Previous attempts to model the vibrational energy levels

of 4FST-Ar in this way made use of parameter values col-

lected from various sources in the literature.^10,11In following

section we test the ability of these parameter sets to repro-

duce the rotational constants of the 4FST-Ar and 4FST-Ne.

We also test a parameter set calculated using the Scheraga

model.^7,24,25The geometric parameter is calculated from the

equilibrium distance, r_ii⁰, for interactions between atoms of

the same type

͑set 3͒ for the S₀and S₁states of 4FST-Ar, respectively. The

vdW modes in which the rare gas moves approximately par-

allel to the aromatic plane are referred to as ‘‘bending’’

modes, b_x, b_y, and that involving motion of the argon

mostly perpendicular to this plane as a ‘‘stretching’’ mode,

s_z. The characters of the calculated vibrational eigenstates

were deﬁned by the highest contributing functions of the

harmonic basis set, labeled (n_x, n_y, n_z) where n_xis the

harmonic quantum number in the x axis, etc. The frequencies

of b_x, b_y, and s_zare then the eigenvalues of the states which

contain the highest percentages of the ͑100͒, ͑010͒, and ͑001͒

basis functions, respectively. The rotational constants, A, B,

C, given in the tables refer to the values obtained from a full

variational treatment of the rotation vibration Hamiltonian

for the lowest vibrational level. Both tables contain the equi-

librium coordinates and well depth, V_min. Table X also con-

tains the dissociation energy from the lowest vibrational

1/7

0

␴ ϭ 1/2͒

r

͑

ii

⁰ϩr_jj͒,

͑3͒

͑

ij

and the energy parameter is then determined from a modiﬁed

version of the Slater and Kirkwood formula²⁴for the vdW

attraction between a generic group of atoms

Z_c␣_i␣_j

4␧ ␴ ⁶ϭ

.

͑4͒

ij ij

␣ /N ͒^1/2ϩ ␣ /N ͒

1/2

͑

j

i

j

Here ␣_iis the polarizability and N_iis an ‘‘effective’’ number

of electrons for atom i, and the Z_cis a constant. The values

of r_ii⁰, ␣_i, and N_irequired for the calculation of the two

parameters have been optimized by Scheraga to reproduce

the molecular crystal structure of a large number of organic

compounds. Finally, empirical parameterizations of the po-

tentials for these complexes are obtained by ﬁtting the cal-

culations to the experimentally determined rotational con-

stants and vdW vibrational intervals.

level of the excited state, D , and the ‘‘solvent’’ shift,

₀Ј

⌬␯

.

solv

1. Parameter sets 1 and 2

Parameter set 1 was recommended by Consalvo et al. on

the basis of a good agreement between the separations of the

main bands in the S₁←S₀1C-R2PI spectrum and the vdW

eigenvalues calculated for the S₀state.¹⁰The potential was

subsequently used to extend the set of assignments to com-

The parameter sets discussed in these sections are listed

in Table VII for 4FST-Ar and Table VIII for 4FST-Ne. For

the calculations on 4FST-Ar, the optimum scaling of the ba-

TABLE VIII. Parameter values used in the atom–atom pair potentials of

4FST-Ne.

sis functions was achieved using ␻_xϭ5 cm^Ϫ1, ␻_yϭ6 cm^Ϫ1

and ␻_zϭ35 cm^Ϫ1and for 4FST-Ne using ␻_xϭ6 cm^Ϫ1

,

1^a

2^b

3^c

4^d

␻_yϭ5 cm^Ϫ1, and ␻_zϭ30 cm^Ϫ1. In both cases the calcula-

tions were converged with 10 harmonic oscillator functions

in the xand y coordinates and 8 functions in the z coordinate.

The interaction potential matrix elements were calculated

over a grid of 24ϫ24ϫ24 integration points in the Gauss–

Hermite quadrature.

State:

S₀and S₁S₀and S₁S₀and S₁

S₀

S₁

␧e_C–Ne(cm¹)

21.48

25.39

43.00

3.109

2.887

3.204

20.01

16.03

44.02

3.22

2.79

3.18

25.28

15.65

26.16

3.06

2.68

2.72

28.91

15.65

26.16

3.239

2.68

31.06

15.65

26.16

3.220

2.68

␧

␴

_H–Ne(cm¹)

_F–Ne(cm^Ϫ1

)

_C–Ne(Å)

_H–Ne(Å)

_F–Ne(Å)

2.72

^aReference 12.

^bReference 28.

^cReference 7.

^dThis work.

B. 4FST-Ar

Tables IX and X compare the results of calculations us-

ing parameter sets taken from the literature ͑set 1͒,^10,11from

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

1843

TABLE IX. Comparison between experimental data and the results of calculations for 4FST-Ar in its S₀state. The calculations are numbered according to

the parameter sets given in Table VII. The rotational constants were obtained in a full variational calculation.

Exp^a

Calc^b

2

1

3

X_e͑Å͒

Y_e͑Å͒

Ϫ0.255

Ϫ0.060

3.433

502.2

0.036 457͓1.99͔

0.027 091 0͓Ϫ0.94͔

0.018 950 5͓0.49͔

13.47

25.33

25.26

Ϫ0.041

Ϫ0.075

3.445

387.0

0.035 892͓0.41͔

0.027 324 2͓Ϫ0.09͔

0.018 874 3͓0.08͔

9.32

17.00

20.63

34.93

Ϫ0.022

Ϫ0.078

3.477

566.9

0.035 559͓Ϫ0.52͔

0.027 298 6͓Ϫ0.18͔

0.018 799 0͓Ϫ0.32͔

12.40

23.20

26.44

44.56

Z_e͑Å͒

V_min͑cm^Ϫ1

)

A͑cm^Ϫ1

B͑cm^Ϫ1

C͑cm^Ϫ1

)

0.035 746͑13͒

0.027 348 7͑53͒

0.018 859 2͑53͒

11.5^c

b¹_x͑cm^Ϫ1

b²_x͑cm^Ϫ1

b¹_y͑cm^Ϫ1

19.0^d

s¹_z͑cm^Ϫ1

)

41.46

^aThis work. Numbers given in round parentheses are one standard deviation of the ﬁtted constant in units of the last quoted decimal place.

^bNumbers given in square parentheses are the percentage deviation from the experimentally determined value of the rotational constant.

^cReference 11.

^dReference 7.

bination vdW bands by Piccirillo et al.¹¹The expected

Franck–Condon factors for these transitions were also used

as a guide, so that two features at 28.2 and 31.1 cm^Ϫ1to the

provement on the results of Consalvo et al.: The b_xand s_z

eigenvalues agree with the assigned intervals to within Ϯ1

cm^Ϫ1and b_yis about 5 cm^Ϫ1too low. Only the value of b_x

changes appreciably in the ground-state calculation but the

decrease of about 0.7 cm^Ϫ1is much less than that expected

from the hot band assignment.

The well depths obtained for these states can be judged

by comparing the experimental solvent shift and dissociation

energy for the S₁state with the calculated values. To a ﬁrst

approximation

blue of the 0⁰₀band were assigned as b_xand b_y, respec-

2

1

0

tively, contrary to their calculated energy order. A weak fea-

ture at 0⁰₀ϩ3.5 cm^Ϫ1was assigned as the hot band b_x,

1

giving a ﬁrst vibrational interval of about 11.5 cm^Ϫ1for this

mode in the ground state.

In our calculations we ﬁrst used parameter set 1 to rep-

resent the potential in both ground and excited states; the

calculations differ only in the geometries of the 4FST moiety

in these states. The agreement of the calculated vdW eigen-

states for the excited state with experiment, obtained using a

more accurate geometry for 4FST in this state, is an im-

D

ϷϪV

S ͒,

͑5͒

͑6͒

͑

₀Ј

vϭ0

1

⌬␯_solvϷV_vϭ0S ͒ϪV

S ͒,

͑

0

͑

1

vϭ0

TABLE X. Comparison between experimental data and the results of calculations for 4FST-Ar in its S₁state. The calculations are numbered according to the

parameter sets given in Table VII. The rotational constants were obtained in full variational calculation.

Calc^b

exp^a

1

2

3

X_e͑Å͒

Y_e͑Å͒

Z_e͑Å͒

Ϫ0.243

Ϫ0.060

3.417

505.2

460.4

Ϫ2.5

0.036 286͓0.28͔

0.027 036 6͓0.86͔

0.019 109 3͓Ϫ0.13͔

14.14

26.59

25.48

53.01

38.23

41.69

Ϫ0.049

Ϫ0.073

3.429

388.9

350.7

Ϫ1.5

0.035 731͓-1.25͔

0.027 256 1͓Ϫ0.05͔

0.019 029 6͓Ϫ0.81͔

10.05

18.37

20.98

46.33

34.72

35.43

Ϫ0.044

Ϫ0.076

3.424

616.8

567.2

V

_min(cm^Ϫ1

)

350–581^c

Ϫ42.017(5)

0.036 186͑14͒

D₀Ј ͑cm^Ϫ1

)

⌬␯ ͑cm^Ϫ1

)

Ϫ46.8

solv

A͑cm^Ϫ1

B͑cm^Ϫ1

C͑cm^Ϫ1

)

0.036 023͓-0.45͔

0.027 225 3͓0.17͔

0.019 132 6͓Ϫ0.27͔

14.21

26.70

28.42

57.96

40.77

47.18

0.027 271 9͑54͒

0.019 184 2͑54͒

b¹_x͑cm^Ϫ1

)

15.0^d

28.2

31.1

56.0

40.5

41.0

b²_x͑cm^Ϫ1

b¹_y͑cm^Ϫ1

b²_y͑cm^Ϫ1

b¹_xb¹_y͑cm^Ϫ1

)

s¹_z͑cm^Ϫ1

)

^aThis work. Numbers given in round parentheses are one standard deviation of the ﬁtted constant in units of the last quoted decimal place.

^bNumbers given in square parentheses are the percentage deviation from the experimentally determined value of the rotational constant.

^cReference 7.

^dvdW vibrational intervals obtained from Ref. 11.

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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1844

Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

where V_vϭ0is the value of the potential function for the

were identical to those used for the corresponding experi-

mental values.

lowest vibrational level. The calculated value of ⌬␯

solv

ϭϪ2.5 cm^Ϫ1using parameter set 1 compares poorly with

the experimental shift of Ϫ42.017͑5͒ cm^Ϫ1, indicating that

different parameter values are needed to model the two

states. It is difﬁcult to judge the accuracy of the calculation

for the dissociation energy in either state because of the large

uncertainty in experimental measurements of this quantity

͑see Ref. 26 for a review of the experimental difﬁculties͒.

Comparison of the 1C-R2PI spectra of 4FST and 4FST-Ar,

reveals that the intensities of analogous vibronic bands are

similar up until 0⁰₀ϩ350 cm^Ϫ1after which the intensity of

the bands of the complexes drop off until there is no sign of

a band corresponding to that of the bare molecule at 0₀⁰

ϩ581 cm^Ϫ1.⁷This reduction in intensity is attributed to the

onset of predissociation and the dissociation energy of the

complex in the excited state may then be put within the

It is immediately apparent that, for both parameter sets,

the variationally determined coordinates are much closer to

the experimental values. This is reﬂected best in the effective

Y coordinate, for which a value close to 0.5 Å is determined

experimentally for both states. For both parameter sets the

variational calculations yield YϷ 0.4–0.5 Å, whilst pertur-

bation theory gives YϷ0 for both states of the complex. In

addition, the Z coordinates obtained variationally were also

closer to the experiment in all of the calculations than those

obtained by perturbation theory. From this point on we shall

concentrate solely on the results of the variational calcula-

tions.

The main difference in the effective coordinates ob-

tained with the two parameter sets occurs in the values ob-

tained for X. This coordinate is close to 0.2 Å for the set 1

calculations, while the negligibly small experimental values

are well reproduced by the set 2 calculations. Parameter sets

limits 360ϽD Ͻ 581 cm^Ϫ1. Haas and Kedler warn that

₀Ј

one-color photo-ionization schemes may lead to excitation

from levels above the dissociation limit of the complex and

that the true dissociation energy will be lower than those

determined here.²⁶This is supported by recent LIF and life-

time measurements for ST-Ar by the same authors.²²The

values of 460 cm^Ϫ1for the dissociation energy in S₁calcu-

lated using parameter set 1 is therefore probably on the high

side. In the following sections we demonstrate that the well

depth is the quantity most sensitive to the choice of param-

eters used in the atom–atom pair potentials.

1 and 2 differ most signiﬁcantly in the value of the ␧

Ar–F

parameter used ͑81.0 cm^Ϫ1in set 1 compared to 38.89 cm^-1

in set 2͒. Table IV contains the calculated values of the root-

mean-square ͑RMS͒ amplitudes of the zero-point motion,

⌬X, and average value of the coordinates, X , for the argon

͗ ͘

atom in the lowest vibrational level of each state. The RMS

amplitudes are similar for both states and both parameteriza-

tions; ⌬X and ⌬Y are about 0.3 Å, indicating large freedom

of motion parallel to the molecular plane, and ⌬Z is about

0.1 Å, since the potential well is narrower in this coordinate.

The vibrationally averaged coordinates are only slightly dis-

placed from the equilibrium coordinates of the potential

͑given in Tables IX and X͒ but differ signiﬁcantly in the two

Calculations using the same parameter set 2, obtained

from the Scheraga model, were performed for both ground-

and excited-state geometries. The calculated vdW eigenstates

consistently under-estimate the experimental values for both

states. However, their energy order for the S₁state repro-

duces that of the assignments in 1C-R2PI spectrum. The

parameterizations. The larger value of ␧

in set 1 pro-

F–Ar

duces a stronger dispersive interaction between this atom-

pair which shifts the potential towards the ﬂuorine atom,

2

1

eigenstates labeled b_xand b_yare the third and fourth, re-

X Ϸ X ϷϪ0.2 Å. While using set 2 gives a potential mini-

͗ ͘

e

1

spectively. Moreover, the eigenstates labeled b_x, b_yand,

mum much closer to the center of mass of the 4FST mol-

s_zare the sixth and eighth, separated by about 0.7 cm^Ϫ1

,

1

ecule, X Ϸ X Ϸ0.0 Å. The effective coordinate, X, ob-

͗ ͘

e

which is in good agreement with the experimental separation

of about 0.5 cm^Ϫ1. A smaller dissociation energy for the S₁

state ͑350.7 cm¹) is obtained using this parameterization but,

the use of the same parameters to represent the potential in

tained with the two parameter sets reﬂects the difference in

the position of the potential minimum. The effective Z coor-

dinate reﬂects mainly the vibrationally average value of this

coordinate, since Z ӷ⌬Z. Neither parameter set reproduces

͗ ͘

both states, results in a calculated solvent shift ͑Ϫ1.5 cm^Ϫ1

)

the reduction in the value of this coordinate upon excitation,

which results from the strengthening of the dispersive inter-

action. The interpretation of the effective coordinates will be

discussed in more detail in Sec. VI.

which is again far too small.

Using parameter set 1, the rotational constants obtained

in the full variational calculation agree with the experimental

values to within about 2% for both states. Using parameter

set 2, the level of agreement is about 0.5% for the ground

state and 1% for the excited state. The rotational constants

determined by treating the Coriolis term as a perturbation are

ϳ0.5% worse in all of the calculations. It was found that the

effective d₀coordinates for the argon atom, obtained from

the calculated rotational constants, are of much greater use in

judging the two parameter sets than the constants them-

selves. Table III compares the effective coordinates obtained

from both the perturbative ͑per͒ and variational ͑var͒ calcu-

lations with those determined from experiment. The toler-

ance limits applied to the calculated rotational constants

It was concluded that parameter set 2 produces the more

realistic description of 4FST-Ar in these states. Although set

1 produces a better approximation to the observed vdW fre-

quencies in S₁, this is achieved by using an artiﬁcially high

parameter for the Ar–F atom-pair potential which shifts the

potential towards the ﬂuorine to an extent not suggested by

the experimental d₀coordinates. This highlights the danger

of collecting parameter values from different literature

sources. The parameters contained in set 2, while underesti-

mating the vdW frequencies, were calculated in a consistent

manner and more correctly reﬂect the balance of the disper-

sive interactions which determined the position of the argon

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

1845

1

FIG. 5. Dependence of the ͑i͒ well depth, V_min, and ͑ii͒ s_zvdW vibrational

eigenvalue calculated for the S₁state of 4FST-Ar on the C–Ar atom pair

parameters. These quantities are plotted against the geometric parameter,

␴

_C–Ar, using different symbols for calculations using different values of the

FIG. 4. Dependence of the ͑i͒ A, ͑ii͒ B, and ͑iii͒ C rotational constants

calculated for the S₁state of 4FST-Ar on the C–Ar atom pair parameters.

energy parameter, ␧

͓30͑ᮀ͒, 40͑᭺͒, 50͑⌬͒, 60ٌ͑͒, 70͑छ͒, 80͑ϩ͒ cm^Ϫ1].

C–Ar

The constants obtained are plotted against the geometric parameter, ␴

,

C–Ar

using a different symbols for calculations using different values of the en-

ergy parameter, ␧

͓30͑ᮀ͒, 40͑᭺͒, 50͑⌬͒, 60ٌ͑͒, 70͑छ͒, 80͑ϩ͒ cm^Ϫ1].

C–Ar

The calculations treated the Coriolis term as a perturbative correction to the

rotation–vibration Hamiltonian.

for the same change in ␴_C–Ar). The calculated B rotational

constant is always an underestimate of the experimental

value. It is a much weaker function of ␴

than the other

C–Ar

above the aromatic plane. There was, however, a need to

produce a new set of parameters which better reproduce the

vdW frequencies without adversely inﬂuencing the d₀struc-

ture.

two constants and may also be considered approximately in-

dependent of ␧_C–Ar. The calculated vdW eigenstates are

strongly dependent upon both parameters ͑the frequencies

change by about 10% and 40% for 20% changes in ␧_C–Arand

␴

_C–Ar, respectively͒ and the well depth is more sensitive to

2. Parameter set 3

changes in ␧

4%͒.

͑the corresponding changes are 18% and

C–Ar

Ab initio calculations indicate that the S₁←S₀transition

in ST is dominated by two conﬁgurational changes, both

involving promotion of one electron to an antibonding or-

bital located primarily on the aromatic ring.²⁷Consequently,

it might be expected that the potential parameters which

change most signiﬁcantly between the ground and excited

states will be those which model the interaction of the argon

atom with the carbon atoms of the aromatic ring. Clearly, a

deﬁciency in the present model of the potential is that it does

not differentiate between the carbon atoms of the aromatic

ring and those of the vinylic group.

The simple, near-linear dependence of these quantities

upon the two parameters enabled estimates of each parameter

to be determined by least-squares ﬁtting to the experimen-

tally determined rotational constants and vibrational inter-

vals. The derivatives were determined analytically and the

data were weighted as the inverse of their experimental un-

certainties, taken as twice the standard deviation of the ﬁtted

rotational constants ͑see Table I͒ and Ϯ0.5 cm^Ϫ1for the

vibrational intervals measured by 1C-R2PI.¹¹The parameter

values at convergence were ␧

ϭ 77.5Ϯ1.2 cm^Ϫ1and

C–Ar

To quantify their effect, the LCHOP calculation was re-

␴_C–Arϭ 3.349 Ϯ 0.001 Å ͑parameter set 3 in Table VII͒. The

peated over a grid of values for ␧

and ␴_C–Ar, with the

results of the calculation using parameter set 3 for the excited

state are given in Table IX. The calculation reproduces the

rotational constants to within about 0.5% and effective coor-

dinates, determined from these constants ͑see Table III͒, are

in agreement with the experimental values. The vdW vibra-

tional eigenvalues for the levels involving only the bending

C–Ar

other parameters constrained to those of the ground state in

set 2. The graphs given in Fig. 4 show the rotational con-

stants calculated by perturbation theory and those in Fig. 5

1

the potential well depth ͑i͒ and the s_zvdW vibrational in-

tervals ͑ii͒ as functions of ␧

and ␴_C–Ar. The other vdW

C–Ar

1

2

1

3

vibrational eigenstates showed a dependence upon the pa-

rameters similar to that of s_z¹. These calculations were per-

formed with the S₁geometry of 4FST-Ar since the vdW

vibrational intervals are known for this state. The A and C

rotational constants are largely independent of the energy

parameter, ␧_C–Ar, but are strongly dependent upon the geo-

vibrations ͑b_x, b_x, b_y, b_x, b_y, and b_y) reproduce the

0 0 0 0 0 0

intervals obtained in the 1C-R2PI spectrum to within 0.2–2.7

cm^Ϫ1. The calculated vdW stretching eigenvalue is, how-

ever, about 6 cm^Ϫ1greater than the experimental value and

the energy order of the eigenstates does not reproduce that

deduced experimentally. In addition, the calculation gives a

high value for the dissociation energy ͑567.2 cm^Ϫ1) for this

state.

metric parameter, ␴

͑the calculated values change by

C–Ar

less than 0.2% for a 20% change in ␧

but by about 20%

C–Ar

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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1846

Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

TABLE XI. Comparison between experimental data and the results of calculations for 4FST-²⁰Ne in its S₀state. The calculations are numbered according to

the parameter sets given in Table VIII. The rotational constants were obtained in a full variational calculation.

Calc^b

Exp^a

1

2

3

4

X_e͑Å͒

Y_e͑Å͒

Ϫ0.308

Ϫ0.063

3.088

233.7

0.061 514 6͓9.05͔

0.027 247 0͓Ϫ0.05͔

0.024 156 5͓2.02͔

10.43

17.67

42.69

Ϫ0.384

Ϫ0.056

3.246

187.7

0.057 764 9͓1.21͔

0.027 179 3͓Ϫ0.55͔

0.023 466 8͓0.33͔

8.94

15.71

36.68

Ϫ0.181

Ϫ0.079

3.085

203.8

0.061 305 5͓8.67͔

0.027 329 3͓0.25͔

0.024 165 3͓2.06͔

9.23

23.33

41.04

Ϫ0.103

Ϫ0.080

3.309

224.1

0.056 287 6͓Ϫ0.22͔

0.027 344 1͓0.31͔

0.023 343 5͓Ϫ1.41͔

8.85

17.20

41.97

Z_e͑Å͒

149–251^c

)

V_min͑cm^Ϫ1

A͑cm^Ϫ1

B͑cm^Ϫ1

)

0.056 411 9͑94͒

0.027 259 8͑44͒

0.023 678 1͑44͒

C͑cm^Ϫ1

1

b_x͑cm^Ϫ1

)

1

b_y͑cm^Ϫ1

)

1

s_z͑cm^Ϫ1

)

^aThis work. Numbers given in round parentheses are one standard deviation of the ﬁtted constant in units of the last quoted decimal place.

^bNumbers given in square parentheses are the percentage deviation from the experimentally determined value of the rotational constant.

^cReference 7.

this complex.¹²Set

´

2 was kindly provided by Ph.

For the ground state, ﬁtting to the experimentally deter-

mined rotational constants and a single vdW interval ͑which

is determined from the position of the b_xhot band^7,11͒ gives

Brechignac;²⁸they were obtained for the aniline-Ne complex

by empirical optimization of the parameters of Ondrechen

et al.²⁹Set 3 contains values calculated using the Scheraga

model⁷and set 4 was obtained from this set by ﬁtting the

parameters for the C–Ne atom pairs, as was done in the

previous section for 4FST-Ar. The results of these calcula-

tions are given in Tables XI and XII for the ground and

excited states of the complex, respectively. The results of

calculations for both states of 4FST-²²Ne using parameter set

4 are given in Table XIII.

␧

_C–Arϭ 70.9Ϯ4.6 cm^Ϫ1and ␴_C–Arϭ 3.382 Ϯ 0.001 Å. Pa-

2

rameter set 3 predicts that the b_xlevel should occur about

23 cm^Ϫ1above the 0⁰level, this supports the assignment of

a weak feature at 0⁰₀ϩ9 cm^Ϫ1in 1C-R2PI spectrum to the

2

b_xhot band.⁷The solvent shift of Ϫ46.8 cm^Ϫ1calculated

using this parameterization compares well with the experi-

mental one of Ϫ42.017͑5͒ cm^Ϫ1. The effective coordinates

obtained for the ground state agree well with experiment

and, in addition, the reduction in the Z coordinate upon ex-

citation is reproduced reasonably by this parameterization.

The high values calculated for the dissociation energy

1. Parameter sets 1–3

Only the vdW bending fundamentals, b_x0(0⁰₀ϩ11.2

cm^Ϫ1) and b_y0(0₀⁰ϩ20.0 cm^Ϫ1), have been assigned with

certainty in the 1C-R2PI spectra of the S₁←S₀transition of

4FST-Ne. A band of similar intensity (0⁰₀ϩ31.0 cm^Ϫ1) was

tentatively assigned as sz¹₀and a much weaker feature (0₀⁰

ϩ43.3 cm^Ϫ1) was unassigned.^7,12The ﬁrst vibronic band

observed for 4FST but absent in the corresponding spectrum

of 4FST-Ne occurs at 0₀⁰ϩ222 cm^Ϫ1, providing the upper

1

and s_zeigenvalue in the S₁state suggest that ﬁtting the

␧

parameter to the anharmonicity of the bending vdW

C–Ar

vibrations probably overestimates the interaction energy of

the argon atom with the aromatic molecule. The good agree-

ment in the solvent shift and reduction in the effective Z

coordinate suggest, however, that the difference in this inter-

action energy is well reproduced. The calculations using pa-

rameter sets 1 and 2 show that the vdW vibrational eigenval-

ues were also affected by the parameterization of the F–Ar

atom pair. Attempts were therefore made to simultaneously

limit for D . The band at 0⁰ϩ120 cm^Ϫ1is observed at

₀Ј

0

comparable intensities in both spectra but it is more cau-

tiously used as the lower limit on D since bands resulting

from 4FST-H₂0, present as an impurity, are expected in this

region.

₀Ј

determine the ␧

and ␴

parameters but the ﬁts were

C–Ar

ill-conditioned and did not converge despite damping. Con-

straining the C–Ar parameters for the vinylic carbon atoms

to the values calculated using the Scheraga model, while

ﬁtting the parameters for the aromatic ring, led to further

increases in the calculated well depth. The parameter values

of set 3 are therefore recommended for calculations of the

vdW eigenstates and molecular geometries in clusters of this

type.

The vdW vibrational eigenvalues calculated for the S₁

state, given in Table XII, are very similar for all three pa-

rameter sets and are consistently about 2 to 3 cm^Ϫ1less than

the experimental separations of the b_x0and b_y0bands from

the 0⁰₀band. The s¹_zeigenvalue is calculated at 37–43 cm^Ϫ1

,

suggesting that the correct assignment of sz¹₀is the feature at

0⁰₀ϩ43.3 cm^Ϫ1. This is also in agreement with the values

assigned for the s_zvdW stretching frequencies in the other

4FST-X complexes ͓41͑1͒ cm^Ϫ1for XϭAr, 37͑1͒ cm^Ϫ1for

XϭKr, 38͑1͒ cm^Ϫ1for XϭXe⁷͔. The assignment of the band

at 0⁰₀ϩ31.0 cm^Ϫ1is less clear cut since a large number of

levels are calculated with energies in this region. The bend-

ing eigenvalues are underestimated by about 20% in these

C. 4FST-Ne

The parameter values used to represent the potential in

4FST-²⁰Ne are listed in Table VIII. Set 1 is a collection of

values taken from the literature and used in a previous

LCHOP calculation of the vdW vibrational eigenvalues of

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

1847

TABLE XII. Comparison between experimental data and the results of calculations for 4FST-²⁰Ne in its S₁state. The calculations are numbered according

to the parameter sets given in Table VIII. The rotational constants were obtained in a full variational calculation.

Calc^b

Exp^a

1

2

3

4

X_e͑Å͒

Y_e͑Å͒

Z_e͑Å͒

V_min͑cm^Ϫ1

Ϫ0.292

Ϫ0.063

3.069

235.0

196.1

Ϫ1.0

0.060 780 5͓7.74͔

0.027 176 7͓Ϫ0.30͔

0.024 367 5͓2.91͔

11.00

Ϫ0.354

Ϫ0.055

3.228

189.6

155.5

Ϫ1.6

0.057 079 0͓1.18͔

0.027 136 3͓Ϫ0.45͔

0.023 678 7͓0.003͔

Ϫ0.178

Ϫ0.076

3.067

204.8

167.3

Ϫ0.8

0.060 581 1͓7.39͔

0.027 248 5͓Ϫ0.04͔

0.024 370 2͓2.92͔

Ϫ0.111

Ϫ0.077

3.270

240.8

201.8

)

D

͑cm^Ϫ1

120–222 ^c

Ϫ7.895͑7͒

)

₀Ј

⌬␯ ͑cm^Ϫ1

Ϫ14.6

solv

A͑cm^Ϫ1

B͑cm^Ϫ1

)

0.056 411 9͑94͒

0.027 259 8͑44͒

0.023 678 1͑44͒

11.2

20.0

43.3

0.056 188 1͓Ϫ0.40͔

0.027 257 8͓Ϫ0.007͔

0.023 634 2͓Ϫ0.19͔

10.07

18.48

43.32

C͑cm^Ϫ1

1

b_x͑cm^Ϫ1

)

9.28

16.00

37.01

9.82

17.41

41.45

1

b_y͑cm^Ϫ1

)

17.87

42.99

1

s_z͑cm^Ϫ1

)

^aThis work. Numbers given in round parentheses are one standard deviation of the ﬁtted constant in units of the last quoted decimal place.

^bNumbers given in square parentheses are the percentage deviation from the experimentally determined value of the rotational constant.

^cReference 7.

calculations, indicating that the correct eigenstate should be

obtained at about 25 cm^Ϫ1. The strongest candidates are the

b_xand b_xb_ylevels, which are close to this value in all

three parameterizations. Both might be expected to have

good Franck–Condon factors for excitation from the lowest

with set 2. By analogy with 4FST-Ar, these constants are

expected to be most sensitive to the choice of the geometric

parameter, ␴_C–Ne. The larger value of this parameter in set 2

produces a better agreement with experiment than the similar

values used in the other sets. The effective d₀coordinates for

the neon atom, derived from these calculated rotational con-

stants, are given in Table V. The poor reproduction of the

experimental rotational constants using sets 1 and 3 results

because the effective Z coordinates obtained using these sets

are about 0.1 Å less than the experimental values for both

states. The values of this coordinate obtained with set 2 are

much closer to the experimental ones. Table VI contains the

RMS vibrational amplitudes and average coordinate values

for the lowest vibrational level calculated using these param-

eter sets. The Z coordinates are dominated by the contribu-

3

1

vdW level of the ground state, but the lack of observation of

2

a band assignable to b_xin the spectrum favors the assign-

0

1

0

1

0

ment to the b_xb_ycombination band.

The dissociation energies for the S₁state are acceptable

in all three calculations but little more can be said because of

the lack of precise knowledge of this quantity. The use of the

same parameters in the ground state calculation gives a sol-

vent shift of about Ϫ1 cm^Ϫ1in all three cases, which con-

siderably underestimates the experimental value of

Ϫ7.895͑7͒cm^Ϫ1

.

tion from Z , which is reduced by the use of a smaller value

The rotational constants obtained in a full variational

calculation again provide the most signiﬁcant test of the

three parameterizations. The values of these constants calcu-

lated using parameter sets 1 and 3 are very similar and in

much poorer agreement with experiment than those obtained

͗ ͘

for ␴_C–Ne. Although the effective Y coordinates are in rea-

sonable agreement with the experimental values in all three

calculations, the effective X coordinates again demonstrate

the differences in the parameterizations. The negligibly small

TABLE XIII. Comparison between experimental data and the results of calculations for 4FST-²²Ne in its S₀and

S₁states using the atom–atom pair potential represented by parameter set 4 in Table VIII. The rotational

constants were obtained in a full variational calculation.

S₀

S₁

͑cm^Ϫ1

)

Exp^a

Calc^b

0.053 342 Ϫ1.54

0.027 346 7͓0.02͔

0.022 817 5͓Ϫ0.18͔ 0.023 152͑15͒

188.3

8.69

17.07

40.26

Exp^a

Calc^b

A

B

C

D

b_x

b_y

0.054 01͑58͒

0.027 341͑16͒

0.022 860͑16͒

0.053 96͑58͒

0.027 265͑15͒

0.053 308͓Ϫ1.21͔

0.027 263 9͓Ϫ0.004͔

0.023 105 3͓Ϫ0.20͔

͓

͔

͑cm^Ϫ1

)

203.0

₀Ј

1

9.88

18.30

42.44

1

s_z

^aNumbers given in round parentheses are one standard deviation of the ﬁtted constant in units of the last quoted

decimal place.

^bNumbers in square parentheses represent the percentage deviation from the experimentally determined value of

the constant given in Table II.

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1848

Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

TABLE XIV. Comparison between the d₀coordinates for the argon atom in

FB-Ar, 4FST-Ar and 2FN-Ar in their S₀states.

values obtained from the experimental rotational constants

are reproduced using parameter set 3 only. Similar to the

4FST-Ar calculations, parameter sets 1 and 2 differ from set

3 in the use of much larger values for the energy parameter,

in this case ␧_F–Ne. The minima of the potentials calculated

using sets 1 and 2 are shifted towards the ﬂuorine atom com-

pared to that obtained with set 3 by the larger interaction

energy for the F–Ne atom pair. Since the a₀axis is inclined

at only about 6° to the C–F bond in both states of 4FST, this

difference in the position of the minimum is mostly reﬂected

͑Å͒

FB-Ar^a,b

4FST-Ar^a,c

2FN-Ar^a,d

X

Y

Z

0.420͑5͒

0.372͑19͒

3.540͑3͒

0.014͑10͒

0.542͑8͒

3.469͑2͒

0.232͑11͒

0.513͑15͒

3.456͑4͒

^aNumbers in parentheses represent estimated errors in coordinate values.

^bDetermined using rotational constants from Ref. 30.

^cThis work.

^dReference 17.

in the values of X , given in Table VI, and in the effective

͗ ͘

values for the X coordinate of the neon atom. The effective Y

coordinates of the neon are in reasonably good agreement

with experiment for calculations with all three parameter

sets.

It was concluded that the most realistic description of the

4FST-²⁰Ne complex in the S₀and S₁states using a potential

constructed from an atom–atom summation was again pro-

vided by the Scheraga model ͑set 3͒, but that the parameters

were in need of reﬁnement in order to produce more accurate

predictions of the vdW vibrational eigenstates and the mo-

lecular geometries in these states.

ergy parameters for ground- and excited-state calculations.

The rotational constants obtained using these parameters,

given in Table XI, and the effective coordinates determined

from them, given in Table V, are both in good agreement

with the experimental values. Furthermore the reduction in

the effective Z coordinate on excitation of the complex is

very well reproduced by the calculation. Good agreement

with experiment was also obtained for the rotational con-

stants ͑Table VIII͒ and effective coordinates for the neon

atom in the 4FST-²²Ne complex ͑Table V͒ calculated using

parameter set 4.

2. Parameter set 4

Following the same procedure as described in Sec.

V A 2. for the 4FST-Ar complex, the geometric and energy

parameters for the C–Ne atom pairs in the S₁states were

least-squares ﬁtted to the vdW vibrational intervals deter-

mined from the 1C-R2PI spectrum^7,12and the rotational con-

stants obtained in this study. The values of the other param-

eters were constrained to those calculated by the Scheraga

model for the S₀state. Uncertainties of Ϯ1 cm^Ϫ1were used

to weight the vdW intervals because of the lower signal-to-

noise in the 1C-R2PI spectra of 4FST-Ne compared to that

for 4FST-Ar. The ﬁt converged to give ␴_C–Neϭ3.220Ϯ0.001

VI. DISCUSSION

The orientation of the S₁← S₀transition moment for the

4FST-X complexes with respect to their a inertial axes, ␪,

may be calculated using

tan²␪ϭI c͒/I a͒,

͑7͒

͑

where I(a) and I(c) are the percentages of a- and c-type

character in a band, respectively. The resulting values of

Ϯ͑38Ϯ2͒° for 4FST-Ar and Ϯ͑31Ϯ3͒° for 4FST²⁰Ne are

both within the experimental error of the value of Ϯ(35^ϩ_Ϫ5⁴)°

for the angle between the S₁←S₀transition moment and a

inertial axes in 4FST.²The principal axes of the complexes

are mainly a translation of those of the 4FST molecule, sug-

gesting that the S₁←S₀transition moment in 4FST is not

greatly affected by the complexation.

In the previous section the effective coordinates of the

rare-gas atom in the 4FST-X complexes were used as an

indirect guide to the position of the potential minima. The

accuracy of the calculated average coordinate values and

RMS amplitudes in the lowest vibronic levels was assessed

by the ability of the calculation to reproduce the experimen-

tal values of the effective coordinates. This represents a dif-

ferent approach from that adopted in previous publica-

tions,^1,17where the values of the effective coordinates were

used to estimate the expectation values and RMS amplitudes

in complexes of this type. A simple correspondence of this

type can be made in complexes involving mono-substituted

benzene derivatives but they do not apply in lower symmetry

complexes such as 4FST-X. This is demonstrated in Table

XIV which compares the effective coordinates for the argon

atom in the ground state of 4FST-Ar with those derived from

Å and ␧

ϭ31.1Ϯ1.5 cm^Ϫ1. The calculation using these

C–Ne

parameter values ͑set 4 in Table VIII͒ is given in Table XI.

The vdW vibrational intervals are reproduced to within 1.5

cm^Ϫ1for all three modes and the b_xb_yeigenstate is calcu-

lated at 30.99 cm^Ϫ1, further supporting the assignment of 0₀⁰

ϩ31.0 cm^Ϫ1as the combination band. The calculated rota-

tional constants differ from the experimental ones by less

than 0.4% and all three of the effective coordinates for the

neon atom, given in Table V, are now in good agreement

with those determined from experiment.

1

No vdW vibrational intervals have been measured for

4FST-²⁰Ne in its ground state. To enable a determination of

the energy parameter for the C–Ne atom pairs we ﬁtted to

V_vϭ0͑S₀), which was determined from the corresponding

value calculated for the excited state and the experimental

solvent shift using Eq. ͑6͒. This gave D ϷV_vϭ0(S₀)

₀Ј

ϭ194Ϯ10 cm^Ϫ1, where the error bar is inherited from the

uncertainty in the ␧_C–Neparameter value for the excited state

calculation. The parameter ﬁt converged to give ␴

C–Ne

ϭ3.239Ϯ0.001 Å and ␧_C–Neϭ28.9Ϯ1.6 cm^Ϫ1. The calcu-

lated solvent shift of Ϫ14.6 cm^Ϫ1is subject to an error of

about Ϯ10 cm^Ϫ1, due to the uncertainties of the C–Ne en-

J. Chem. Phys., Vol. 108, No. 5, 1 February 1998

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Lakin et al.: Spectroscopy of 4-ﬂuorostyrene van der Waals

1849

VII. CONCLUSION

the rotational constants of the corresponding vdW complexes

30

with ﬂuorobenzene ͑FB͒

͑1/2FN͒.¹⁷

and 1/2-ﬂuoronapthalene

In conclusion, the S₁← S₀0⁰₀bands of 4FST-X ͑XϭAr

and Ne͒ have been recorded at rotational resolution for the

ﬁrst time. Rotational constants obtained from the analysis of

the spectra were used to obtain effective coordinates for the

rare gas atoms in the complex. The rare gas-aromatic poten-

tials were represented as a pairwise sum of atom–atom

terms. These potentials were judged by their ability to repro-

duce the effective coordinates, vibrational intervals, dissocia-

tion energies, and solvent shifts of the complexes. The po-

tentials were optimized by least-squares ﬁtting the

parameters of the C–X atom pair to the experimental data.

The ﬁtted parameters produce good agreement with the rota-

tional constants and in-plane bending vdW frequencies, but

overestimate the dissociation energies and vdW stretching

frequency. We believe that a better description of the poten-

tial surface can only be achieved with a more sophisticated

model than simple atom–atom pair interaction. Future work

includes the use of these parameters to predict the structure

and vibrational frequencies in the clusters of ST with one or

more attached rare-gas atoms.

The signs of the effective coordinates are not obvious in

vdW complexes ͑as they are when the Kraitchmann equa-

tions are applied to covalently bound molecules͒ and eight

possible sets of solutions are possible. The four pairs corre-

sponding to opposite signs of Z correspond to stereo-

isomers, which cannot be distinguished experimentally. As

previously mentioned, the effective Z coordinate is generally

in good agreement with the calculated vibrational average,

Z , since the RMS amplitude is a much smaller quantity

͗ ͘

(⌬ZϷ 0.1 Å͒. The reduction in the value of Z in the ground

state in going from FB to 4FST to 2FN reﬂects the increase

in ␲-electron density in the complexed aromatic. In FB-Ar,

the C_2vsymmetry of the aromatic molecule leads to the re-

quirement that Y ϭ 0 and the effective Y coordinate re-

͗ ͘

ﬂects only the contribution to the inertial tensor from the

zero-point vibrational oscillation with respect to the b₀axis.

The value of Yϭ0.37 Å for the ground state of FB-Ar is

reasonable as a measure of the vibrational amplitude by com-

parison with the values calculated for the corresponding

complexes of benzene¹⁸and aniline.¹Calculations indicate a

displacement of the argon atom towards the ﬂuorine in

ACKNOWLEDGMENTS

It is a pleasure to acknowledge Professor Y. Haas for his

interest in the work and for many helpful discussions. The

FB-Ar giving X Ϸ 0.18 Å.³⁰Therefore both the average

͗ ͘

value and the RMS vibrational amplitude with respect to this

coordinate are of the same magnitude and the effective X

coordinate is not directly related to one or the other.

The replacement of a hydrogen by a vinylic group to

give 4FST produces a rotation of the principal axes of about

7° about the c axis and translates the center of mass towards

the new group. The calculations of the previous section in-

dicate that the potential minima in both S₀and S₁states of

4FST-Ar are located almost directly above the center of mass

´

authors are also indebted to Professor Ph. Brechignac for

supplying parameter values used in the 4FST-Ne calcula-

tions. This work was supported by the European Union un-

der contract number CHRX-CT-94-0561 and by the Con-

siglio Nazionale delle Ricerche under contract number

CNR-EC 205.13.13/1. N.M.L. wishes to thank the EC for a

Marie Curie research fellowship ͑Ref. no. ERBFM-

BICT961046͒ and M.C. wishes to thank the CNR for a fel-

lowship.

of the 4FST moiety. Therefore both

X and Y are ex-

͗ ͘ ͗ ͘

1

pected to be small. Nevertheless no simple correspondence

can be made between the effective values of these coordi-

nate, XϷ0.0 Å, YϷ0.5 Å, and their RMS vibrational ampli-

tudes, calculated to be ⌬XϷ0.26 Å, ⌬YϷ0.30 Å. This sug-

gests that the effective coordinates of the rare-gas atom

should be interpreted with caution in systems where symme-

try does not impose a zero value for one or more of the

equilibrium coordinates.

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Article Doi

High-resolution spectroscopy of 4-fluorostyrene-rare gas van der Waals complexes: Results and comparison with theoretical calculations

DOI: 10.1063/1.475561

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