Temperature Effect on Pyrene as a Polarity Probe for Supercritical Fluid and Liquid Solutions

S H U - H U I C H E N and V I C T O R I A L. M C G U F F I N * Department of Chemistry, Michigan State University, East Lansing, Michigan 48824

The effect of temperature on the fluorescence spectrum of pyrene in supercritical and liquid carbon dioxide and liquid organic solvents is sys temat ica l ly studied. The Py parameter (intensity ratio of vibronic bands 1 and 3) is found to increase with the density of supercritical carbon dioxide in the range from 0.54 to 0.75 g /cm 3. This observation is consistent with the fact that dispersion forces, which represent the major interaction between pyrene and carbon dioxide, depend inversely on the sixth power of distance. However, the Py parameter of both supercritical and liquid carbon dioxide is also found to decrease with temperature at constant density, which is not consistent with expecta- tions for dispersion forces. Carbon dioxide, which is generally regarded as a nonpolar solvent, shows a temperature effect comparable to that for polar liquid solvents. The origin of this temperature effect is examined in this study by computer simulation using both semiempirical molecular orbital and molecular mechanics methods. On the basis of these simu- lations, a s t rong electrostatic at t ract ion arises between pyrene and carbon dioxide which is similar in magnitude to tha t with polar solvents. The temperature dependence of the Py parameter can be qualitatively ex- plained by these simulation results. Index Headings: Fluorescence; Pyrene; Solute-solvent interactions; Temperature; Supercritical fluids.

INTRODUCTION

The use of pyrene as a fluorescence probe to classify solvent strength 1-4 or to characterize the surface microenvironment 5-12 has become a well-established and well-accepted technique. This method involves monitor- ing the solvent-influenced fluorescence spectrum of py- rene, which is introduced into the investigated system. The fluorescence spectrum ofmonomeric pyrene exhibits five major vibronic bands between 370 and 400 nm, la- beled for convenience in numerical order. Band 1 shows significant intensity enhancement with increasing solvent polarity in comparison with band 3, so that the ratio of emission intensities (Py = 11/13) serves as a quantitative measure of polarity. It is generally believed that the sol- vent dependence of the Py parameter arises from sym- metry distortion of the pyrene structure induced by dis- persion or van der Waals forces. 13 Hence, pyrene appears to be a suitable probe for characterizing systems in which dispersion forces are predominant. However, numerous problems including both instrumental and chemical ar- tifacts associated with determination of the Py parameter have been noted by Street and Acree. 14,15 Among these problems, a significant temperature dependence has been observed in both supercritical and liquid solvents. 16-19 Although the use of calibration standards has been rec- ommended to minimize this effect, 14 the application of the Py parameter to study temperature-dependent sys- tems is still limited.

Received 13 Augus t 1993; accepted 15 February 1994. * Au tho r to w h o m correspondence should be sent.

It is noteworthy that temperature effects are observed not only for the Py parameter but also for solvatochro- matic parameters. In this method, the probe molecules are introduced into the system, and the shift of their maximum absorbance or fluorescence wavelength rela- tive to that in a reference solvent (solvatochromatic shift) serves as a scale of solvent polar i tyY ° The wavelength shift with temperature (thermochromic shift) 21 is found to be negligible for nonpolar solvents, then increases and reaches a maximum for those of intermediate polarity, and decreases again for those of higher polarity. The ther- mochromic shift has been attributed to changes in dipole orientation and induction, as well as dispersion interac- tions between the solute and solvent. 21,22 On the basis of an extension of the classical Onsager model 23 that incor- porates all these interactions in a continuum reaction field, 21,22 there appears to be a reasonable correlation be- tween the observed temperature dependence of the wave- length shift and the dielectric constant and refractive in- dex of the solvent. However, no significant correlation has been found between the Py parameter and any phys- ical property of the bulk solvent. 24-26 Kalyanasundaram and Thomas 3 noted that the Py parameter is more de- pendent on the solvent dipole moment than on the bulk solvent dielectric constant, and they have proposed that local dipole-dipole interactions, rather than environ- mental effects of the solvent as a whole, are responsible for the symmetry distortion of pyrene. Because the Py parameter is related to an intensity variation, rather than a wavelength (energy) variation that may be readily pre- dicted from the solute-solvent interaction energy, there appears to be no appropriate theoretical model. There- fore, the origin of the temperature effect on the Py pa- rameter remains the subject of considerable controversy and speculation.

The goal of this work is to gain a greater understanding of temperature effects on the Py parameter through the direct comparison of data from supercritical and liquid carbon dioxide, as well as several liquid organic solvents of varying polarity. In view of the lack of a suitable the- oretical model, the interactions between pyrene and the investigated solvents are simulated by using of semiem- pirical quantum mechanics and classical molecular me- chanics methods for correlation with the experimental results.

EXPERIMENTAL

Fluorescence Measurements. Sample Preparation. Py- rene (Matheson Coleman & Bell) is purified by vacuum sublimation at 25°C before use. Solutions are prepared in high-purity, spectroscopic-grade organic solvents (Bur- dick & Jackson Division, Baxter Healthcare) with a final

596 Volume 48, Number 5, 1994 0003,702s/94/4805-059652.00/0 APPLIED SPECTROSCOPY © 1994 Society for Applied Spectroscopy

: • - - VALVE

WATER OUTLET

___H._____~-~ QUARTZ TUBE

i i ..M._f / / WINDOWS

0 / e ~ WATER INLET

X-Y POSITIONER

FIG. 1. The assembly of the static cell.

z_~ L d " O ¢,.9o Z . N _

~E O ~

* ~ = 3 1 0 n m *

* A = 325nm

350 400 450 500 WAVELENGTH (nm)

FIG. 2. Fluorescence spectrum of pyrene in supercfitical carbon di- oxide (0.660 g/cm 3, 33°C), together with background spectra from the static cell.

concentration ranging from 10 -5 to 10 -4 M pyrene. For the preparation of carbon dioxide solutions, a known amount of pyrene in acetone is transferred to a static cell (vide infra). After evacuation of the solvent and air, the cell is filled with carbon dioxide (> 99.99% purity, Mathe- son Gas Products Inc.) by means of a syringe pump (Mod- el 140, Applied Biosystems Inc.) to produce a final con- centration of approximately 7 x 10 -6 M pyrene. The temperature is maintained at 33°C during delivery of the supercritical fluid and at 25°C for delivery of the liquid, with an accuracy of ±0.5°C. The pressure is measured by an electronic transducer at the pump outlet with an ac- curacy of ± 5 psi. On the basis of the temperature and pressure at which the carbon dioxide is delivered, the density of the fluid can be calculated from an empirical relationship. 27 In this manner of preparation, the fluid density remains constant and the temperature may be independently varied during the experiments.

Instrumentation. The temperature-controlled static cell, which is designed to fit a commercial fluorometer, is de- picted in Fig. 1. The optical cell is constructed by sealing a small quartz tube (0.5 mm i.d., 6 mm o.d., 2 cm length; Heraeus Amersil) to a thick-walled, bottom-sealed quartz tube (2 mm i.d., 8 mm o.d., 8 cm length; Heraeus Amersil). The cell is treated with trimethylchlorosilane (Petrarch Systems Inc.) for about two hours at room temperature in order to deactivate silanol groups on the quartz surface, which may cause adsorption of pyrene. 28 The cell is then connected to a stainless steel shut-off valve (Model SS- 3NTRF2, Whitey) by means o f a graphite-vespel ferrule. The cell holder, which is constructed of anodized alu- minum, is thermostatically controlled by means of water circulation from an external bath (Model RTE-9B, Nes- lab). The windows for excitation and emission are on adjacent faces of the cell holder, and an X-Y positioner is attached to the base for sensitive adjustment of the focal point. The complete assembly is placed in the sam- ple compartment of the fluorometer (Model IFL-66, Per- kin-Elmer), which is equipped with a microcomputer (Model ? 300, Perkin-Elmer) for data acquisition and ma- nipulation.

Figure 2 shows a typical fluorescence spectrum of py- rene in supercritical carbon dioxide, together with the

background spectra at excitation wavelengths of 310 and 325 nm. Because of the cylindrical cross section of the optical cell, a substantial amount of scattered light is ob- served. There are two major bands (denoted by an asterisk in Fig. 2) that show constant displacement from the ex- citation wavelength and, hence, may be attributed to in- elastic scattering processes. On the basis of near-IR ab- sorbance measurements, the scattering band with 53-nm (5500-cm -1) shift at 310-nm excitation wavelength may be tentatively identified as the second overtone of the combination band arising from Si-O and O - H stretch vibrations from unreacted silanol groups remaining on the quartz surface. Although the origin of the second band with 157-nm (16,300-cm-0 shift is not known, it may correspond to the sixth overtone of the same combination band. In order to avoid the interference of this scattered light with the fluorescence emission of pyrene, an exci- tation wavelength of 310 nm is used throughout this study. The spectral bandpass for both excitation and emission is 2 nm, and the spectra are acquired as the average of three to five scans.

To avoid experimental artifacts associated with mea- surement of the Py parameter, Street and Acree ~5 have recommended a series of specifications. First, a small spectral bandpass (1 nm) is recommended to provide sufficient resolution of the overlapped bands. Second, the concentration of pyrene should be sufficiently low (10 -6

TABLE I. Py parameter for liquid solvents.

Py Solvent py2 py~5 (this study)

Vapor 0.41 Hexane 0.58 Cyclohexane 0.58 0.58 n-Butyl ether 0.84 p-Xylene 0.95 Benzene 1.05 Ethanol 1.18 Chloroform 1.25 1.18 Methanol 1.35 1.23 Tetrahydrofuran 1.35 1.22 Acetone 1.64 Acetonitrile 1.79 1.59

0.60 0.58

1.17 1.24 1.21 1.38 1.48 1.85

APPLIED SPECTROSCOPY 597

TABLE II. Electronic charge distribution of the pyrene molecule in ground 0Ag) and excited (JB2., ~B~.) states. The atom number assignment is shown in Fig. 3.

Atom no. ~Ag *B2. ~B~.

1 -0.077 -0.036 -0.068 2 -0.048 -0.080 -0.058 3 -0.007 -0.054 -0.003 4 -0.007 -0.054 -0.003 5 -0.048 -0.080 -0.058 6 -0.077 -0.036 -0.068 7 -0.048 -0.080 -0.058 8 -0.077 -0.036 -0.068 9 -0.077 -0.036 -0.068

10 -0.048 -0.080 -0.058 11 -0.067 +0.000 -0.069 12 -0 .100 -0.185 -0.098 13 -0.067 +0.000 -0.069 14 -0 .067 +0.000 -0.069 15 -0 .100 -0.185 -0.098 16 -0.067 +0.000 -0.069 17 +0.098 +0.095 +0.098 18 +0.098 +0.095 +0.098 19 +0.099 +0.091 +0.098 20 +0.099 +0.098 +0.098 21 +0.099 +0.091 +0.098 22 +0.098 +0.095 +0.098 23 +0.098 +0.095 +0.098 24 +0.099 +0.091 +0.098 25 +0.099 +0.098 +0.098 26 +0.099 +0.091 +0.098

M) to prevent primary and secondary absorption effects. In this study, the spectral bandpass and pyrene concen- tration are slightly larger than the recommended values. However, because the optical pathlength (2 mm) is much smaller than that of a conventional cell (1 cm), absorbance effects are greatly diminished. In addition, the concen- tration of pyrene is sufficiently dilute, so that dimer and excimer formation is not observed in either supercritical or liquid solutions. Several Py values measured with this system are summarized in Table I and compare favorably to previously published values. 2,~5

Computer Simulations. Molecular Orbital Calculations. Semiempirical MNDO (modified neglect of differential overlap) 29 calculations are performed by using unrestrict-

25

FIG. 3.

17 18

2 9

20

25 22 Molecular structure and atom number assignment of pyrene.

62

58- -5 E

_~ 54- >- o

5 5o- .J

0 ~ 46- •1• ' 44 "~ '~ : : : i : E~

i

42 0.00 2.00 4 .O0' 6.00 8.60 10.00' 12100 14.00

DISTANCE (.~)

FiG. 4. Total interaction energy (kcal/mol) between pyrene and carbon dioxide as a function of their intermolecular distance (A).

ed open-shell wavefunctions with an STO-3G basis set (Gaussian 86, Gaussian, Inc.). Pyrene is assumed to have DEh symmetry in both the ground state (lAg) and the ex- cited states (IB2u and IBm,) without further geometric op- timization. From these calculations, the distribution of excess valence electronic charge on each atorh is deter- mined, as summarized for pyrene in Table II and Fig. 3. Similar calculations are performed for the solvents ace- tonitrile, tetrahydrofuran, acetone, methanol, and hex- ane.

Molecular Mechanics Calculations. Simulations of the interaction between pyrene and the selected solvents are per formed by using classical molecular mechanics methods 3° (BioGraf, BioDesign, Inc.). A generic force field, DREIDING, 31 is employed for energy calculations. The total energy of the molecule is the sum of the bonding and nonbonding interactions. The bonding interactions include contributions from stretching (Es), bending (Eb), and torsional (E~) energy between atoms that are cova- lently bonded. These bonding interactions remain rela- tively constant while molecules interact and, thus, can be neglected during the simulations. The nonbonded inter- actions consist of contributions from dispersion or van der Waals (Evdw), electrostatic (EeL and explicit hydrogen bond (Ehb) energy between atoms that are not covalently bonded. The van der Waals energy (Evdw) is expressed by a standard Lennard-Jones equation

Evd w = ARab -12 - BRab -6 (1)

where Rab is the distance between atoms a and b, and A and B are empirically derived constants. The electrostatic energy (Ee) is calculated by using Coulomb's law

E e = 332.0637 QaQb/~Rab (2)

where Q, and Qb are the net charge on atoms a and b, respectively, which are input parameters obtained from the molecular orbital calculations. The dielectric constant is assumed to be that of a vacuum environment (~ = 1). The vectorial summation of electrostatic forces between all atoms within the same molecule represents the net dipole moment of that molecule. Likewise, the electro- static forces between two molecules are representative of the dipole--dipole component of their interaction.

598 Volume 48, Number 5, 1994

0.95 1.12

0.90- 33 ~C

. 0.85-

0.80-

50 ~C

0.75 0.25 0.~0 0_% 0.~0 0.~5 0.;0 oA5 0.60

SQUARE OF DENSITY (g/cm+) +

FIG. 5. Py parameter of carbon dioxide as a function of the square of density (g/cm3).

v

1.02-

0.92-

0.82-

0.72 0 1 ~0 2~0 3~0 4~0 5~0 60

TEMPERATURE (°C)

FIG. 6. Py parameter of carbon dioxide as a function of temperature CC). (@) Liquid phase 0.860 g/cm~; (xT) 0.745 g/cm3; ( 0 ) 0.700 g/cm3; (A) 0.660 g/cm~; (D) 0.600 g/cm3; (O) 0.565 gfcm 3.

During the simulation, one pyrene and one solvent molecule are allowed to systematically approach each other until an optimum configuration in three-dimensional space is attained. As shown in Fig. 4, the total energy reaches a minimum value at the optimum separation distance. The total interaction energy (Ex) is calculated by subtracting the energy when the solute and solvent molecules are at the optimum separation distance from that at infinite distance.

E T = E~ - EOPT- (3)

The van der Waals (ET,vdw) and electrostatic (ET,Q) com- ponents of the total energy are calculated in an analogous manner.

ET,vdw = E~.vdw - Eovr,vdw (4)

ET.Q = E~,e - EOPT,Q. (5 )

When defined in this manner, the most stable solute- solvent pair will have the greatest positive interaction energy. For solute-solvent pairs that have more than one optimum configuration, a statistical weighting factor (Zi) is calculated from the total energy (ET,+) corresponding to each configuration (i).

Z , = exp(-ET,i/kT) (6) Z exp(-ET,i/kT)"

On the basis of the calculated weighting factor, the total energy (ET), van der Waals energy (ET,v~+), and electro- static energy (ET,e) are then computed.

ET = ~ ZiET,i (7)

ET,vd w = ~ ZiET,vdw, ̀ (8)

ET, a = ~ ZiET,Q, i (9)

RESULTS AND DISCUSSION

The solvent polarity of supercritical carbon dioxide is measured as a function of density by using of the Py parameter. As shown in Fig. 5, the Py value is found to increase with the square of the density (p) in the range from 0.54 to 0.75 g/cm 3. This observation is consistent

with the expectation that dispersion forces are propor- tional to p2 o r R -6, as expressed in the second term of Eq. 1. However, the Py value is significantly larger at 33°C than at 50°C, which is not consistent with the ex- pectation that dispersion forces are independent of tem- perature at constant density. This phenomenon has been observed previously by Brennecke et a1.16,32 and has been attributed to clustering of solvent molecules around py- rene near the critical point. Clustering, which causes an increase in the local density and a decrease in the local compressibility, appears to rationalize satisfactorily the higher Py value and the decreased slope (APy/AT) shown in Fig. 5 near the critical temperature (31°C). Simulations performed by molecular dynamics support the occurrence of clustering as the critical density of carbon dioxide is approached at constant temperature, 33-35 but provide no insight into the behavior at constant density with varying temperature. Moreover, these simulations suggest that solute-solvent clustering between pyrene and carbon di- oxide is no more extensive than solvent-solvent cluster- ing? 4 It is noteworthy that solvatochromic parameters,

2.00 1.90- 1.80- 1.70- 1.60- 1.50- 1.40- 1.30-

.~ 1.20-

1.I0- 1.00- 0,90- 0.80- 0.70- 0.60- 0.50

0 1 ~0 2~0 3~0 410 510

TEMPERATURE (*C) 60

FIG. 7. Py parameter as a function of temperature for liquid solvents. ( I ) Acetonitfile; (v) acetone; ( , ) methanol; (A) tetrahydrofuran; (~) liquid carbon dioxide; (0) hexane.

APPLIED SPECTROSCOPY 599

A B

i { 1 Fie. 8. Frontal (A) and lateral (B) view of pyrene and carbon dioxide at the position of minimum energy.

in contrast to the Py parameter, do not exhibit variation with temperature for supercritical fluids at constant den- sity.36. 37

Further insight into this problem can be gained by ex- amining the temperature effect in liquid carbon dioxide, where solute-solvent clustering is not expected to occur. As shown in Fig. 6, the Py value decreases linearly with temperature within the liquid phase. The regression line describing the data for the liquid phase appears to have the same slope (APy/AT) as those in the supercritical region at high density. These results suggest that, while clustering may or may not occur in the supercritical re- gion, it cannot be wholly responsible for the variation of the Py parameter with temperature.

The effect of temperature on the Py parameter has also been measured in polar liquid solvents. 17-19 As shown in Fig. 7, the Py value appears to decrease with temperature in polar solvents such as acetonitrile, tetrahydrofuran, acetone, and methanol, but remains quite constant in nonpolar solvents such as hexane. Carbon dioxide, which is generally regarded as a nonpolar solvent, exhibits a change in the Py parameter with temperature as great as acetonitrile and tetrahydrofuran. Since there is presently no theoretical basis for the Py parameter, the cause of this temperature effect is not fully understood. However, it may arise from the intrinsic photophysical and pho-

44'75 1

44.55 0 2'0 4'0 6'0 dO 160 120 1'40 160 180

ANGLE (DEGREE) FIG. 9. Total interaction energy (kcal/mol) as a function of the angle between pyrene and carbon dioxide.

FIG. 10. Lateral view of two stable configurations of pyrene and ace- tonitrile at the minimum energy.

tochemical properties of pyrene, particularly those of the excited state, since fluorescence spectroscopy reflects an excited-state phenomenon.

In an effort to gain more understanding of the ground and excited states of pyrene, molecular orbital calcula- tions have been employed. The ground state of pyrene (D2h point group) is the totally symmetric lAg state, where- as the first and second excited states are generally assigned as IB2u and IB1,, respectively. 13,3s The charge distribution of the ground and excited states, determined by semiem- pirical MNDO calculations, is shown in Table II with the atom number assignment given in Fig. 3. In the lAg ground state, the charge density on the two central carbon atoms (3, 4) is less negative than that of the surrounding atoms (2, 5, 7, 10), and substantially less negative than that of the perimeter atoms (1, 6, 8, 9, 11-16). The charge dis- tribution of the ~B1, excited state is very similar to that of the ground state, but the central atoms are nearly neu- tral and the surrounding and perimeter atoms are of com- parable negative charge. However, the 'B2, state is dis- tinctly different; the central atoms are more negatively charged than the perimeter atoms along the short axis (1, 6, 8, 9), but much less charged than those along the long axis (1 2, 1 5). The first singlet absorption (nB2u ~ lag) is very weak and the transition moment is polarized along the short axis of the molecule; the second singlet absorp- tion (IB1, ~-- lAg) is much stronger and is polarized along the long axis.13,38 The fluorescence spectrum exhibits mixed polarization, which indicates that vibronic coupling can

A

N

O

B

FIG. 11. Lateral view of two stable configurations ofpyrene and tetra- hydrofuran at the minimum energy.

600 Volume 48, Number 5, 1994

A

I I ! I

e k FIG. 12. Lateral view of two stable configurations of pyrene and ace- tone at the m in im u m energy.

occur between the closely spaced IBlu and lB2u states through c o m m o n b3g vibrational modes. 3s,39 Although as- signment of the vibronic bands of pyrene in supercritical and liquid solvents is complicated due to spectral overlap, fluorescence measurements in a supersonic jet and in the solid state suggest that band 1 is predominantly ag in character, bands 3 and 4 are predominantly b3g , while bands 2 and 5 contain significant contributions from both ag and b3g vibrations. 3,3s,4°m The forbidden, totally sym- metric ag vibrations show significant intensity enhance- ment through vibronic coupling of the ~B2u and ~B~, states, whereas this enhancement is minimal for the allowed b3g vibrations. 3 Therefore, specific solute-solvent interac- tions that influence this vibronic coupling may be an important factor contributing to the mechanism of the Py parameter. This hypothesis can be examined by means of computer simulation using classical molecular me- chanics.

In this simulation, the relative positions of the solute and solvent are systematically adjusted in three-dimen- sional space until the most stable configuration is iden- tified. The optimum position of ground-state pyrene and carbon dioxide is illustrated in Fig. 8. Carbon dioxide resides preferentially in the central region parallel to the ah plane of pyrene at a distance approximately equal to the sum of their van der Waals radii (Fig. 4). By rotation of carbon dioxide about the principal C2 axis of pyrene, orientation appears to be favored along the short axis, although the depth of the energy well is small (Fig. 9).

9.00-

r~q

A

1 FIG. 13. Lateral view of two stable configurations ofpyrene and meth- anol at the min imum energy.

FIG. 14. Lateral view ofpyrene and hexane at the position of min imum energy.

This orientation is intuitively reasonable since the carbon atom bears a net positive charge (+0.58), with attraction to the central atoms, and the oxygen atoms bear a net negative charge (-0.29), with least repulsion from the perimeter atoms along the short axis. The optimum con- figuration of carbon dioxide with excited-state pyrene is found to be similar to that with the ground state, differing only in the magnitude of the interaction energy. Hence, the interaction is greatest for the 1Bzu state because of increased attractive forces at the central atoms (which are more negatively charged) and reduced repulsive forces at the perimeter atoms along the short axis (which are less negatively charged). It is noteworthy that this optimum position is inherently well suited to influence the first b3g vibration, where the central and surrounding atoms (2, 5, 7, 10) are perturbed to a much greater extent than those at the perimeter? 8

Acetonitrile, tetrahydrofuran, acetone, and methanol have two preferential positions with ground-state pyrene, as depicted in Figs. 10 to 13 and characterized in Table III. Highly electronegative atoms, such as nitrogen and oxygen, are closer to the ah plane ofpyrene in position A than in position B. Both acetonitrile and acetone have a greater total interaction energy but less electrostatic en- ergy at position A than at position B. Methanol shows both greater total interaction energy and electrostatic en- ergy at position A. There is a significant electrostatic re- pulsion between tetrahydrofuran and pyrene at position

. . . .11 - - - - - - - -

8.50-

o ~ 8.00-

,5 _J

£, 7.50-

7.00

NUMBER OF THE METHANOL MOLECULE

FiG. 15. Total interaction energy (kcal/mol) as a function of the num- ber of methanol molecules in a cyclic hydrogen-bonded structure.

APPLIED SPECTROSCOPY 601

TABLE IlL Total energy (ET,~) and electrostatic energy (ET.Qa) between the solvent and pyrene in the ground (~As) and excited (JB2., JB,u) states for each configuration shown in Figs. 10 to 13. The weighting factor (Z~) and total energies are calculated from Eqs. 6 to 9.

JAg 'B2, IBlu

ETj EV,Q., ET., ET,Q,, Er,, Er,Q,, Solvent (kcal/mol) (kcal/mol) Z, (kcal/mol) (kcal/mol) Z~ (kcal/mol) (kcal/mol) Z,

Acetonitfile A 4.09 0.25 0.69 4.20 0.36 0.66 4.12 0.35 0.69 B 3.62 0.83 0.31 3.81 1.00 0.34 3.66 0.84 0.31

Total 3.95 0.43 4.07 0.58 3.98 0.51

Tetrahydrofuran A 5.89 -0 .35 0.49 5.97 -0 .23 0.48 5.90 -0 .39 0.48 B 5.90 0.47 0.51 6.00 0.60 0.52 5.94 0.51 0.52

Total 5.90 0.41 a 6.00 0.42 a 5.92 0.45 ~

Acetone A 5.48 0.08 0.62 5.66 0.22 0.64 5.51 0.09 0.64 B 5.18 0.72 0.38 5.31 0.79 0.36 5.18 0.70 0.36

Total 5.36 0.32 5.54 0.42 5.39 0.31

Methanol A 3.66 0.78 0.75 3.80 1.00 0.74 3.69 0.81 0.76 B 3.02 0.45 0.25 3.17 0.58 0.26 3.01 0.46 0.24

Total 3.49 0.70 3.64 0.89 3.52 0.72

a Calculated on the basis of the absolute values of the electrostatic energy.

A, due to the large negative charge on the s p 3 hybridized oxygen atom (-0.37). In a manner similar to carbon dioxide, all of these solvents are significantly more stable in the central region than the perimeter region of pyrene. In contrast, hexane (Fig. 14) can be stabilized in many locations across the pyrene plane because of the nondi- rectional nature of dispersion forces.

The total interaction energy as well as the van der Waals and electrostatic components are summarized for all sol- vents in Table IV. It is apparent that the stability of the solute-solvent complex is controlled predominantly by dispersion forces, which is consistent with previous re- p o r t s . 13 However, a surprisingly strong electrostatic at- traction arises between pyrene and carbon dioxide that is similar in magnitude to that with polar solvents such as acetonitrile, tetrahydrofuran, acetone, and methanol. As discussed previously, the electrostatic energy is related to dipole--dipole interactions, which are known to be in- versely dependent on temperature. 41 Because both at- tractive and repulsive energies are sensitive to tempera- ture variation, the absolute values are used to calculate the total electrostatic energy. As shown in Table IV, the electrostatic energy between the solvent and either the 1B2u or IB~u excited states of pyrene appears to be directly and quantitatively correlated to the temperature depen- dence of the Py parameter (APy/AT). These results suggest

that the temperature effect arises as a consequence of strong local dipole orientation forces between the solvent and pyrene.

The only exception to the correlation between APy/AT and the electrostatic energy shown in Table IV arises for methanol. However, the molecular mechanics simula- tions were performed under vacuum conditions with one molecule of pyrene and solvent. Because there is strong hydrogen bonding between methanol molecules in the liquid state, solvent-solvent interactions may alter the interaction with pyrene. In order to examine this possi- bility by molecular mechanics, several methanol mole- cules were first followed to interact to determine the most stable configurations. As depicted in Fig. 15, the stabi- lization energy increases substantially with the number of methanol molecules and becomes relatively constant when four or more molecules are arranged in a cyclic hydrogen-bonded structure. This conclusion is consistent with experimental vapor pressure measurements for al- cohols by Anderson et al. 42,43 When this methanol cluster is allowed to interact with one pyrene molecule, the total interaction energy is higher and the electrostatic energy is lower than that determined for one methanol and one pyrene molecule, as shown in Table V. The electrostatic energy for the methanol cluster shows good correlation with the observed APy/AT value.

TABLE IV. Total energy (ET), van der Waals energy (ET,,d.), and electrostatic energy (Er,e) between the solvent and pyrene in the ground ('A s) and excited (1B2u , ~B~u) states. The change in the Py parameter with temperature (APy/AT) is determined from Fig. 7.

ET Solvent (kcal/mol)

*Ag ~B2, IBi,

ET.v~w ET.Q ET ET,vdw ET,Q Er ET,v~w ET,Q APy/AT (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (o C t)

Acetonitfile 3.95 3.47 Tetrahydrofuran 5.90 5.73 Acetone 5.36 5.03 Methanol 3.49 2.76 Hexane 6.40 6.36 Carbon dioxide 3.41 3.11

0.43 4.07 3.45 0.58 3.98 3.42 0.51 -0 .00623 0.41 5.99 5.73 0.42 5.92 5.78 0.45 -0 .00426 0.32 5.54 5.11 0.42 5.39 5.05 0.31 -0 .00290 0.70 3.64 2.71 0.89 3.52 2.77 0.72 -0 .00287 0.00 6.75 6.58 0.08 6.58 6.43 0.04 -0 .00045 0.33 3.61 3.04 0.53 3.43 3.04 0.35 -0 .00535

602 Volume 48, Number 5, 1994

TABLE V. Total energy (Er), van der Waals energy (ET,vdw) , and electrostatic energy (ET,e) between methanol and pyrene in the ground ('Az) and excited (IB2., ~Bt.) states.

'Ag 'B2. ~B,.

ET ET.vdw Er,Q Ex ET,vdw ET.e ET ET.vdw ET.Q Solvent (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol)

1 Methanol 3.50 2.76 0.70 3.64 2.71 0.89 3.52 2.77 0.72 4 Methanol 6.20 5.76 0.32 5.92 5.60 0.36 6.12 5.84 0.24

As a final observation, it is apparent that carbon di- oxide and acetone have significantly higher polarities when evaluated by the Py parameter than by other parame- ters. 2,2°,36,44,45 Carbon dioxide appears to be of comparable polarity to xylene, whereas acetone is of greater polarity than methanol according to the Py parameter scale (Table I). It is likely that the carbonyl group, which possesses a strong dipole moment, is responsible for the anomalously high Py values for these solvents.

C O N C L U S I O N S

As a resul t o f this s tudy, the Py p a r a m e t e r scale is be l i eved to be r e spons ive to specific s o l u t e - s o l v e n t in- t e rac t ions on the mo lecu l a r scale, ra ther t han to colliga- r ive proper t ies o f the bu lk solvent . A l though the s tabi l i ty of the s o l u t e - s o l v e n t comp lex is con t ro l led p r im a r i l y by d i spe r s ion forces, the m a g n i t u d e as well as the t emper - a ture d e p e n d e n c e o f the Py p a r a m e t e r appears to be a direct consequence o f e lectrostat ic forces. Therefore , the use o f the Py p a r a m e t e r for c a r b o n d ioxide or o ther sol- ven t s wi th s t rong local d ipole or q u a d r u p o l e m o m e n t s is no t r e c o m m e n d e d .

ACKNOWLEDGMENTS

The authors are grateful to Dr. Jay A. Siegel for the use of his fluo- rometer, to Dr. James F. Harrison for helpful guidance and discussion of molecular orbital calculations, and to Dr. Rawle I. Hollingsworth for detailed instruction of molecular mechanics calculations. This research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, under Contract Number DE- FG02-89ER 14056.

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