Spectral Solvent Shift. I. Paraffin Hydrocarbon Solvent Interactions withPolynuclear Aromatic HydrocarbonsO. E. Weigang Jr. Citation: The Journal of Chemical Physics 33, 892 (1960); doi: 10.1063/1.1731283 View online: http://dx.doi.org/10.1063/1.1731283 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/33/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Temperature Dependence of Physical–Chemical Properties of Selected Chemicals of EnvironmentalInterest. I. Mononuclear and Polynuclear Aromatic Hydrocarbons J. Phys. Chem. Ref. Data 29, 41 (2000); 10.1063/1.556055 Electronic Spectral Shifts of Some Aromatic Compounds in Nonpolar Solvents J. Chem. Phys. 39, 2309 (1963); 10.1063/1.1701435 Comprehensive Spectroscopic Investigation of Polynuclear Aromatic Hydrocarbons. I. Absorption Spectraand State Assignments for the Tetracyclic Hydrocarbons and their AlkylSubstituted Derivatives J. Chem. Phys. 38, 2144 (1963); 10.1063/1.1733946 Spectral Solvent Shift. II. Interactions of Variously Substituted Hydrocarbons with Polynuclear AromaticHydrocarbons J. Chem. Phys. 37, 1180 (1962); 10.1063/1.1733262 Some Notes on Charge Transfer Interaction between Iodine and Polynuclear Aromatic Hydrocarbons J. Chem. Phys. 30, 1367 (1959); 10.1063/1.1730202

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THE JOURNAL OF CHEMICAL PHYSICS VOLUME 33, NUMBER 3 SEPTEMBER, 1960

Spectral Solvent Shift. I. Paraffin Hydrocarbon Solvent Interactions with Polynuclear Aromatic Hydrocarbons*

O. E. WEIGANG, JR.

Chemistry Department, Texas Lutheran College, Seguin, Texas

(Received August 3, 1959)

The electronic shifts for 11 ultraviolet transitions of the chromophores naphthalene, phenanthrene and the polar aromatic hydrocarbon, azulene, have been observed in a series of 17 paraffin hydrocarbon solvents from isopentane to n-tridecane. The contribution to the shift of branching and cyclization of solvent mole­cules has been observed by including the five structural isomers of hexane, 2,2,4-trimethylpentane and 2,2,5-trimethylhexane together with the cyclo- and methy1cyclopentanes and hexanes.

The statistical approach is used to interpret the electronic shifts in terms of interbond potentials and the solvent radial distribution function and is compared to the McRae extension of the Bayliss solvent shift theory. Dispersive type potentials suffice to account for the frequency shifts of transitions, except the 1 L" transition of azulene which shifts to the blue from the vapor to hydrocarbon solutions. The behavior can be accounted for by a change in the static dipole moment of azulene on excitation, a phenomenon predicted by quantum mechanical calculations on the molecule.

INTRODUCTION

THE immersion of a light absorbing material in a liquid solvent shifts the electronic spectrum as­

sociated with the pure light absorber in the vapor state. Figure 1, for example, shows the paraffin hydrocarbon solution spectrum of azulene superimposed on its vapor spectrum. Such effects may be attributed to the difference in energy of interaction with the surrounding solvent molecules between the excited state and ground state chromophore and several theories have been proposed to account for the phenomenon.I- 5

Recent studies have been made of this phenomenon by pressurizing the solvent-chromophore solution so that continuous effects may be observed.4•6 However, for this work the spectral solvent shift is studied by varying the solvent without additional external pressure. The effect is observed for a group of nonpolar hydro­carbon solvents, including observations on the effect of branching or cyclization of the hydrocarbon chain. While the shifts from solvent to solvent are not as large as might be obtained with a polar solvent series, the effect is more amenable to interpretation since the environment of the chromo ph ore is varied quite gradually and regularly. In addition, drastic reshaping and loss of structural detail in the spectra, occurring typically with polar solvents, are held to a minimum in hydrocarbon solvents, if they occur at all.

Aromatic polynuclear hydrocarbons form a con­venient set of chromophores since each contains several

* Presented at the 137th meeting of the American Chemical Society, Division of Physical Chemistry, Cleveland, Ohio (April, 1960) .

1 N. S. Bayliss, J. Chern. Phys. 18, 292 (1950). 2 Y. J. Ooshika, Phys. Soc. (Japan) 9, 594 (1954). 3 H. C. Longuet-Higgins and J. A. Pople, J. Chern. Phys. 27,

192 (1957). 4 W. W. Robertson, O. E. Weigang, Jr., and F. A. Matsen,

J. Mol. Spectroscopy 1, 1 (1957). 6 E. G. McRae, J. Phys. Chern. 61, 562 (1957). 6 W. W. Robertson, S. E. Babb, Jr., and F. A. Matsen, J. Chern.

Phys. 26, 367 (1957).

electronic transitions in the near ultraviolet with widely varying oscillator strengths, and the nature of their transitions is fairly well understood with regard to polarization and other details.7- 9 For these reasons they have been used in several other investigations of solvent effects.4,10

THEORETICAL

Statistical Theory

The statistical theory interprets a spectral shift as due to the unequal perturbation of a light absorber in its ground and its excited state when surrounded by a particular configuration of solvent molecules. The intensity at each frequency is taken to be proportional to the probability of occurrence of a given configura­tion, and different configurations generally produce various degrees of interaction that lead to solvent broadening. 11

Within the approximation of additivity of inter­molecular potentials, the interaction with the solvent or solvation energy per mole of chromophore in a given state may be expressed as

where no is the mean number density in the system (for dilute solutions the density of the solvent), R is the chromophore to solvent intermolecular distance, VAB(R) is the intermolecular potential between chromophore (A) and solvent (B), gAB(R) is the radial distribution (rd) function for the solvent about the chromophore.

7 H. B. Klevens and J. R. Platt, J. Chern. Phys. 17,470 (1949). 8 D. E. Mann, J. R. Platt, and H. B. Klevens, J. Chern. Phys.

17,264 (1949). 9 R. Pariser, J. Chern. Phys. 25, 1112 (1956). 10 N. D. Coggeshall and A. Pozefsky, J. Chern. Phys. 19, 980

(1951). 11 S. Ch'en and M. Takeo, Revs. Modern Phys. 29, 20 (1957).

892

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SPECTRAL SOLVENT SHIFT. I 893

The shift arises from the difference between an excited state term and a ground state term, a change occurring in the potential term VAB(R). According to the Franck-Condon principle, the rd function gAB (R) , or more precisely, anyone of the momentary configura­tions which go into the average, will remain constant during the brief light absorption process. Accordingly, the shift from the vapor may be written

hcflll= EABX - EABG

where VABX and VABG represent the potentials between solvent and excited and ground state chromophores, respectively. In Eqs. (1) and (2) the variety of solvent configurations have been replaced by a single most probable or average distribution, as might be deter­mined from x-ray diffraction, and thus the shift may be measured from the band maximum. Solvent broaden­ing of single vibration bands in ultraviolet spectra are observed to be quite symmetrical,12 indicating that the most probable is very nearly identical to the mean solvent distribution.

Dispersive Interactions Between Hydrocarbons

For dispersive type interactions, the intermolecular potentials, VAB(R) , may be developed on the basis of bond-bond interactions according to Haugh and Hirschfelder's extension of London's treatment by transition multipoles in extended molecules.13 •14 The perturbation treatment involves the interaction of these transition multipoles in a fashion formally identical to the interactions of electrostatic distribu­tions. The transition moments of carbon-hydrogen and carbon-carbon sigma bond electrons are adequately treated by the point dipole approximation, while for pi electron transition moments, the multipoles are treated as distributions of monopoles each of which is a point transition polarization, all the same sign in a given region j of the molecule, of magnitude

gOkA(j) = jifioA,flkAdVa, 1

(3)

where ifioA and ifikA are the wave functions of the chro­mophore in the 0 and k states, the monopoles being centered at

ROk A (j) = 1 r aifiOAifik Adv,,/ gOk A (j) . ( 4) 1

For transitions between pi electron states of the

12 O. E. Weigang, Jr. and W. W. Robertson, J. Chern. Phys. 30, 1413 (1959).

13 E. F. Haugh and J. O. Hirschfelder, J. Chern. Phys. 23, 1778 (1955) .

14 See also, J. N. Murrell and H. C. Longuet-Higgins, J. Chern. Soc. 1955,2552; Proc. Phys. Soc. (London) A68,601 (1955).

AZlLENE

2000 A 3200 3600

FIG. 1. The near-ultraviolet electronic transitions of azulene in the vapor state and.in 2, 2,4-trimethylpentane solution. One may note the transition dependence of the spectral shift. The 1Bb

transition moves at such a rate as to partially cover a much less solvent sensitive and weaker transition to the red side of it on going from vapor to solution.

chromophore in paraffin solvents, the potential differ­ence (V ABX - VABG) reduces to interactions between the solvent sigma bond transition dipoles and the excited and ground state transition monopoles of the chromophore, other terms cancelling in the difference. Then the interaction with each solvent bond is

=aB{L: I:[gOkA(j)]2/2[41+EkA/IB] kr'O i Ri B

_ L: I:[gikA(j)]2/2[1+:EkA-EiA)/IB]}

k."i i Ri B

The summations are over the j monopoles of each kth chromophore state. aB is the polarizability of the solvent sigma bond, IB the ionization energy of the solvent sigma bond, g ikA (j) is the jth monopole of the chromophore i-k transition, EkA the energy of the chromophore k state relative to its ground state, and RiB is the monopole to solvent bond distance. Haugh and Hirschfelder's equation has been partially reduced here by the approximations used in the more common polarizability dispersion expression.15

•4

The transition dependence is virtually separated from the solvent dependence since the solvent bond ionization energy is nearly constant and since the solvent sigma bond to chromophore monopole distance RiB should not vary greatly for the various transition polarizations with a given solvent configuration. Here KA G and KAx are terms which correspond to energy terms and the ground state and excited state polariza­bilities of the chromophore in the usual point dipole development of dispersion forces, the greater polariza­bility of the excited state leading to red (negative) frequency shifts.

15 S. E. Babb, Jr., J. M. Robinson, and W. W. Robertson, J. Chern. Phys. 30, 427 (1959).

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Solvent

Isopentane

2,2-Dimethyl­butane

n-Pentane

2,3-Dimethyl­butane

Mole bond

density· nb

(cm-3)

0.1374

0.1433

0.1389

0.1459

2-Methylpentane 0.1440

3-Methylpentane 0.1463

2,2,4-Trimethyl­pentane

n-Hexane

2,2,5-Trimethyl­hexane

n-Heptane

Methylcyclo­pentane

Cyclopentane

n-Nonane

Cyclohexane

Methylcyclo­hexane

n-Undecane

n-Tridecane

0.1515

0.1455

0.1543

0.1503

0.1604

0.1593

0.1568

0.1661

0.1646

0.1612

0.1644

t:.W/N2

0.0800

0.1944

0.1667

0.0833

0.1111

0.2812

0.2716

Bayliss parameter

n2-1 2n2+1

0.1785

0.1840

0.1796

0.1863

0.1851

0.1869

0.1923

0.1863

0.1947

0.1909

0.1985

0.1972

0.1970

0.2041

0.2022

0.2005

0.2030

Surface tension&

(dyne'/4 'cm-'/4)

1.951

1.994

1.984

2.027

2.027

2.048

2.069

2.056

2.104

2.105

2.16b

2.19b

2.175

2.222

2.194

2.218

2.248

TABLE I. Solvent parameters and spectral shifts.

Relative spectral frequency shifts. Average deviation about ±5 cm-'

Naphthalene

'£0

o

-3

o

-17

-11

-17

-19

-30

-37

-29

-27

-38

-64

-38

-44

'La

+5

+1

o

-16

-17

-28

-22

-42

-36

'Bb

+37

+16

o

-39

-58

-54

-68

-47 -124

-65

-80 -220

-81 -201

-84 -238

-86 -234

-59 -125

-71 -134

'£0

+10

+2

o

+5

+2

-4

-20

-9

-15

-26

Phenanthrene

'La

-10

+20

o

-19

-18

-35

-48

-51

'Bb

+14

+9

o

-50

-61

-60

-88

-63 -103

-81 -133

-30 -112 -165

'Gb

+17

+23

o

-20

-27

-55

-88

-40 -127 -193 -138

-35 -135 -203 -117

-38 -139 -233 -148

-37 -148 -272 -164

-57 -160

-52 -196

'£0 .

o

+3

-16

+6

+7

+1

+27

+31

-3

+33

+6

Azuleneo

'La 3000 'Bb

o o o

-29 -5 -33

-31 o -36

-46 +6 -44

-34 -14 -44

-69 -5 -79

-76 -31 -109

-49 -33 -136

-82 -13 -127

-90 -25 -157

-62 -29 -157

-81 -44

-87 -51 -197

Average propor­tionate

shiftd

+9

+7

o

-18

-19

-29

-33

-40

-48

-65

-78

-95

-100

-108

-109

-125

-138

& Taken or calculated from A.P.1. Project 44, Selected Values of Properties of Hydrocarbons and Related Compounds. Petroleum Research Laboratory, Carnegie Institute of Technology, Pittsburgh, Pennsylvania. b Surface tension determined in this laboratory by the ring method with correction factor. o The lCb azulene band is too broad for accurate wavelength determination. d n-Pentane to n-Nonane shifts taken to be 100. Azulene '4 and 3000 A not inclUded in the average.

00

~

o

trJ

~ trJ ..... C"l ;... Z C"l

'-< ~

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SPECTRAL SOLVENT SHIFT. I 895

Thus, for a given chromophore transition observed in a series of paraffin solvents, Eq. (2) together with Eq. (5) would predict that the solvent shift would depend on: (1) the density of solvent bonds, con­veniently measured in moles of bonds per cc, nb, the mole density times the number of bonds per molecule; (2) the rd of solvent bonds about a chromophore; and (3) the solvent bond ionization energy and bond polarizability. The linear density dependence has been observed previously with the pressurization of n-pen­tene solutions of the same chromophores.4

Chromophore-Dipole Solvent-I nduced-Dipole Interactions

If a chromophore dipole moment should change on excitation, additional contributions to the potential difference must be considered. For qualitative con­siderations one may use the point-dipole induced-dipole potentiaP6 which leads to the potential difference term

(V AB"' - V ABG)dip_ind

=aB[(/-LAG)L (/-LAX) 2]/ R6, (6)

where /-LAG and /-LAX are the magnitudes of the chromo­phore dipole moments in the ground and excited state, respectively. Red (negative) or blue (positive) con­tributions may arise depending on whether the excited dipole is larger or smaller in magnitude, respectively. It should be noted that the actual direction of dipole moment is immaterial for nonpolar solvents since the induced dipole presumably follows the direction of the inducing static dipole.

McRae Solvent Shift Theory

McRae has applied second-order perturbation theory to the solvent-chromophore interaction and expresses the potential fields of the solvents in terms of their macroscopic properties.- The complete theory includes the effect of polarity of the solvent as well as the chromophore and has received considerable attention in the literature.11 ,l8 Considering only dispersive con­tributions and chromophore-dipole solvent-induced­dipole interactions, the McRae theory reduces to

The solvent refractive index parameter was first proposed by Bayliss. l A and B are constants of the chromophore, Lo is the "weighted mean wavelength" of the solvent.

EXPERIMENTAL

Measurements were made with a Beckman DK-1 recording spectrophotometer. Various techniques were

18 J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory oj Gases and Liquids (John Wiley & Sons, Inc., New York, 1954) p. 29.

17 O. Popovych and L. B. Rogers, J. Am. Chern. Soc. 81;'4469 (1959) .

18 E. G, McRae, Spectrochim. Acta 12, 192 (1958).

o

-100

~-200 !J f-

Ul > 0 o. i t § -100

8 a: ....

o

-100

o.

co

FIG. 2. Spectral frequency shifts of the transitions 'Bb, 1 L4

and '4 of naphthalene. The circles approximate the average devi­ation from experimental error. See Fig. 3 for the solvents.

devised for maintaining maximum wavelength ac­curacy, the most recent and successful consisting of superimposing on the spectrogram a mercury emission line of known wavelength near the region under in­vestigation. This is accomplished without interrupting the synchronized movements of the wavelength and recorder drives. Thus errors which involve failure to match the wavelength scroll to the strip recorder calibrations and errors from temperature change are minimized or eliminated. The data do not show any significant variations in relative wavelength shifts for the different correction methods used. The data are the average of at least two and usually three deter­minations. Usually the first reasonably intense vibra­tion band maximum of a transition was measured. The relative precision is estimated to be about one-half A, ranging possibly to one A in some instances, band broadness most often being the limiting factor.

Most of the hydrocarbon solvents were Phillips "Pure Grade," 99 mole % minimum purity. Cyclo­hexane, methylcyclohexane, and 2,2,4-trimethylpen­tane were spectrograde solvents obtained from Dis­tillation Products Industries. The solvents were used as received except for Phillips cyclopentane which was distilled over sulfuric acid and collected in a narrow temperature range near 49°C. This treatment de­creased the cutoff wavelength from 2850 to 2200 A. Also, 2,3-dimethylbutane was distilled immediately before use to remove an antioxidant (du Pont No.6 inhibitor) .

The chromophores naphthalene, azulene, and phen­anthrene were the best grades from J. T. Baker Chemi­cal Co., Terra Chemicals, Inc., and Distillation Pro­ducts Industries, respectively. No further purifications were carried out since the spectrograms obtained with them compared favorably in every detail without

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896 O. E. WEIGANG, JR.

0 ~pb22

~4 I-... I V'J -40 e.H• \ 225 w \ 0 !( fi"\ z 0 \ OMc. f= -80 a:

~C\CM 0 Q.

~ Q.

\ u \ -120

~T OJ4 OJ5 0.16 0.17

MOLE BOND DENSITY (MOI.ES/C,,3)

FIG. 3. Proportionate spectral shift (n-pentane 0, n-nonane 100) averaged over transitions vs the mole bond density of the solvent. Reference lines are drawn through the normal hydro­carbon solvent points (filled circles) and through the most highly branched solvents. The circles approximate the average devia­tion from experimental error. The solvents are: P-n-pentane, Hx--n-hexane, Hp-n-heptane, N--n-nonane, U--n-undecane, T --n-tridecane, I -isopentane, 2-2-methylpentane, 3-3-methyl­pentane, 22-2,2-dimethylbutane, 23-2,3-dimethylbutane, 224 -2,2,4-trimethylpentane, 225-2,2, 5-trimethylhexane, Cp­cyclopentane, M cp-methyIcyclopentane, C h-cyclohexane, M ch -methylcyclohexane.

spurious bands to those given in API Ultraviolet Spectrograms,19 KIevens and Platt/ or Mann, Platt, and Klevens.8

Stock solutions appropriate for the weakest transi­tion (concentrations 0.004 molar or less) were freshly mixed, diluted for the stronger transitions and com­pared to the solvent as reference. One centimeter matched silica cells were used. Isopentane solutions were cooled to prevent excessive evaporation and the density was probably somewhat greater than indicated in Table I and Figs. (2) and (3). Vapor spectra were obtained by heating the cell compartment and using a ten-centimeter cell with quartz windows compared to air as reference.

RESULTS AND DISCUSSION

General

Table I shows that the frequency shift of maxima relative to their position in n-pentane solution varies with the transition for given solvents, and for a given transition varies from solvent to solvent well outside of experimental error. Figure 1 shows the vapor to 2,2,4-trimethylpentane solvent spectral shift for four of the five transitions of azulene observed in this investigation. Here the transition dependence is particularly apparent as the IBb transition shifts at a rate to partially cover the less sensitive 3000 A transition in solution.

19 A.P.I. Project 44, Ulfraviolet Spectral D3Jta, Petroleum Re­search Laboratory, Carnegie Institute of Technology, Pitts­burgh, Pennsylvania.

Tables II and III show that while the relative shift observed for two solvents is some measure of vapor to n-pentane shift, the behavior is not regular enough to give vapor frequency predictions of any great accuracy. The rather capricious agreement between extrapolations and experimental vapor values has been observed before.l,4,6 While some cases may be due to incorrect assignments of corresponding vapor and solution bands, most discrepencies are undoubtedly real and quite marked.

Red (negative) shifts from vapor to hydrocarbon solutions are observed in every case with the exception of 1 Lb transition of azulene which displays a relatively small, but distinct shift to the blue.

Nonpolar Chromophores-Naphthalene and Phenanthrene

Table II shows that the n-pentane to n-nonane red shift increases with the oscillator strength of the transition. A similar behavior has been observed for the same chromophores in pressurized n-pentane solutions where the rate of frequency shift with density was found to have a high correlation with the oscillator strength of transitions of a large number of catacon­densed hydrocarbon chromophores.4 While Eq. (5) (or consideration of charge-transfer complexing be­tween solute and solvent) might suggest a dependence on transition energies, it apparently plays a minor role on consideration of the 1Gb transition of phenanthrene, where the lower shift goes with the reduced intensity of the higher energy transition. Furthermore, the rates of frequency shift with density of two pyrene transi­tions of similar intensity have been observed to be nearly equal even though they were quite widely separated in frequency.4

While the extent of spectral frequency shift pro­duced by a hydrocarbon solvent clearly depends on the chromophore transition, the same proportionate fre­quency shift, independent of the transition, is obtained for a given solvent nearly within experimental error, in agreement with the separation of solvent and chromo­phore contributions proposed for Eq. (5). This enables the construction of a relative proportionate shift scale, arbitrarily taking n-pentane and n-nonane to produce 0 and 100 relative units of shift respectively for each transition, other solvents being assigned proportionate values accordingly. The proportionate shift produced by each of the solvents averaged over the transitions is given in Table I. The general features of plots using proportionate shifts are the same as those of plots of shifts of individual transitions as shown by Fig. 2 compared to Fig. 3.

Averages taken only over transitions with small shifts (due to solvent cutoff) show larger deviations from the average proportionate shift due to the experi­mental error of wavelength determinations becoming quite large on the proportionate scale. However, the cyclics, especially methylcyclohexane, cyclopentane,

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SPECTRAL SOLVENT SHIFT. I 897

TABLE II. Nonpolar ehromophores and spectral shifts.

Transition Oscillator strengths' Experimental vapor Vapor to n-Pentane n-Pentane to n-Nonane

frequency shifts (em-I) frequency shifts (em-I) frequencies (em-I)

:\faphthalene ILb 0.002 ILa 0.18 IBb 1. 70

Phenanthrene

ILb 0.003 ILa 0.18 IBb 1.09 ICb 0.60

a Taken from footnote reference 7. b W. E. Deal, Jr., Doctoral Dissertation, The University of Texas (1951). (' Determined in this laboratory.

32456b -258 -64 35919b -870 -81 47481- -2068 -201

29163b -214 -35 35260b -986 -135 41314- -1328 -203

-117

T ABLE III. Polar ehromophore and spectral shifts.

Oscillator strengths' (/lAG)2- (/lAXh" Experimental vapor

Vapor to n-Pentane frequency

shifts (em-I)

n-Pentane to n-Nonane frequency

shifts (em-I) Transition (lJ2) frequencies (em-I)

Azulene ILb

ILa

3000 'Bb

0.009 0.08 0.1 1.10

1.68 -3.76

1.95 0.22

14270-29760d

34164d

37382-

+53 -366 -368

-1607

-3 -82 -13

-127

~ Experimental values from footnote reference 8, except 3000 A, calculated by Pariser, footnote reference 9. Calculated from theoretical values, footnote reference 9.

C Determined in this laboratory. dE. Heilbrenner and K. Wieland, Relv. Chim. Acta 30,947 (1947).

and cyclohexane in that order, show average deviations nearly twice as large as comparable solvents even though their spectral purity allowed observation of all the transitions.

Figure 3 shows a plot of the relative proportionate shift versus the mole bond density nb of the solvents used. One may note that (1) the normal hydrocarbon solvents (filled circles) give a remarkably linear shift with solvent bond density, (2) the noncyclic hydro­carbons isomers with one, two and three methyl branches, in that order, produce less shift than would normal hydrocarbon solvents of equal bond density, and (3) the cyclic hydrocarbons also produce less shift than would normal hydrocarbons solvents of equal bond density.

Such dependence on structure appears in the physical properties of the hydrocarbons and has been correlated with a remarkable degree of accuracy to Platt's j, p, W

structural parameters, where j is the sum of first C-C bond neighbors of every C-C bond in the molecule p is the number of carbon atoms three bonds apart; and w, the Wiener number, is the sum of the number of bonds between all pairs of carbon atoms in the mole­cule.20 Attempts to fit the shift data to correlations of the type used by Platt were not as successful however

20 J. R. PJatt, J. Chem. Phys.17, 484 (1949).

as the following, suggested by the large coefficients that were obtained for the w parameter. The relative proportionate shift for normal and branched hydro­carbons (except isopentane for the reason mentioned) may be given by

reI prop shift= 776- S.S9X l()3nb

+131~w/N2±2 (6 ma..-.;: dev) , (8)

where ~w is the change in the Wiener number from branched to normal isomer, and N is the number of carbon atoms in the skeleton.

Platt interpreted the w/l'v'2 term as a measure of the mean external contact area of the molecule (except for steric hindrance). Greenshields and Rossini observed that the similar (for correlations) term,2w/N(N-1) was the average distance between pairs of carbon atoms measured in bond lengths,21 i.e., a measure of the linear extension of the molecule and a qualitative index of the solvent radial distribution function arising from intra­molecular distribution.

Direct measurements of the rd of constituent atoms of solvents may be made by observing x-ray scattering by the liquids. By graphically integrating the Zernicke­Prins scattering equation, Warren has shown that the

21 J. B. Greenshields and F. D. Rossini, J. Phys. Chern. 62, 271 (1958).

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898 o. E. WEIGANG, JR.

0 ~O22

I- ~o224 ... I -40 ~. 225 If) \J? w !;{ Z

~ 0 -80 i= 0: c. 0 N n.

" 0 0: n.

U -120 ~\ T

~ -160

J8 .19 .20

m2 _ n 1(202 .11

FIG. 4. Proportionate spectral shift versus the Bayliss-McRae spectral shift parameter. See Fig. 3 for the solvents.

single intense scattering peak in long chain hydro­carbons is due to a main concentration of scattering matter at a distance determinable from the corre­sponding scattering angle.22 Stewart's measurements of the positions of these peaks shows that this concentra­tion of matter (maximum of the rd function) is at the same radial distance in all the normal hydrocarbons from n-pentane to n-pentadecane.23 Further measure­ments on branched hydrocarbons show that this dis­tance increases with branching24 and also with cycliza­tion,2. although the interpretation of the scattering may be somewhat different in the latter case. If gAB(R) of Eq. (2) at least follows the rd of the pure solvents, an attractive potential gives qualitative agreement be­tween these simple rd analyses and the relative position of the data points in Fig. 3, and furthermore, supports the interpretations of the Wiener parameter.

No meaningful method of assigning Wiener numbers to the cyclic hydrocarbons by summing over neighbors, etc., has been proposed and extensive scattering measurements of the substituted cyclics seem not to have been made. However recent conformational studies of the cyclohexanes, cyclopentanes and their derivatives draws speculation as to whether the shifts follow their conformations. Cyclic shapes certainly reduce the external contact area of the molecule and would lead to less interaction than normals of the same nb as is observed. Furthermore, the preferred equatorial position of the methyl group in the methyl­cyclohexane changes very little the over-all planar shape of the molecule,26 while one of the preferred configura­tions of methylcyclopentane thrusts the methyl group

22 B. E. Warren, Phys. Rev. 44, 969 (1933). 23 G. W. Stewart, Phys. Rev. 31,174 (1928). 24 G. W. Stewart, Phys. Rev. 32, 153 (1928). 25 S. Katzoff, J. Phys. Chern. 2, 841 (1934). 26 C. W. Beckett, K. S. Pitzer, and R. Spitzer, J. Am. Chern.

Soc. 69,2488 (1947).

back toward the ring to resemble a highly branched noncyclic, as opposed to the nearly planar cyclopentane molecule.27

Figure 4 shows the average proportionate shift ver­sus the Bayliss-McRae parameter, giving a plot which is indistinguishable from the bond density plot. If the refractive index dispersion constant is a good measure of the variation of weighted mean wavelength Lc, as suggested by McRae, then the variation in Lo for hydrocarbons does not satisfactorily account for the smaller shift of both branched-chain and cyclic hydro­carbons. The work of Lauer shows that the former has a dispersion constant higher and the latter a dispersion constant lower than the straight chain hydrocarbons.28

The use of solvent refractive indices at 250 mu, calculated from Lauer, which should measure bond polarizabilities at frequenCies near the absorptions of the chromophores, gives a plot which differs by little more than 0.01 units in the relative positions of branched and cyclics to the normal solvent line, effecting no significant change in the plot. Ko regular variation can be detected in the ratio of branched to straight chain solvent shift on going from short wave­length to long wavelength transitions. It would seem from these tests of the data that solvent bond energies or polarizabilities do not vary to an extent that produce observable effects in the paraffin solvents.

Since the McRae derivation of the reaction field from which the refractive index term arises makes the assumption of a continuous homogeneous dielectric about the spherical chromophore cavity, it is plausible to assume that here also the modified shifts arise from neglect of short range order in the liquid state, i.e., is due to solvent molecular conformation.

0 O\t \ 23

I- 2~~224 .... I -40

H 0 225 If)

w ~H. tt Z "fMC. 0 -80 i= (( c. 0

:~cf· n. ~ n. \u -120

G\ T ~

\

FIG. 5. Proportionate spectral shift versus the fourth root of the solvent surface tension. See Fig. 3 for the solvents.

27 K. S. Pitzer and W. E. Donath, J. Am. Chern. Soc. 81, 3213 (1959) .

28 J. L. Lauer, J. Chern. Phys. 16, 612 (1948).

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SPECTRAL SOLVENT SHIFT. I 899

Attempts to find solvent properties which implicitly include the structural effects and give high correlations with the shift have led to examination of solvent boiling point, heat of vaporization, surface tension and others. None is as successful as Eq. (8) and most show gross inversions of the shift versus the parameter. The most successful is found to be the fourth root of the surface tension, shown in Fig. 5 which can be derived from Eqs. (2) and (5) by assigning a constant parachor contribution per hydrocarbon bond.29 The average deviation is about ±4 proportionate shift units.

Polar Chromophore-Azulene

Table III gives the transition oscillator strengths of azul ene, which should be some measure of the red shift contribution from dispersive potentials, and the difference of the squares of static dipole moments in ground and excited states, which gives a qualitative estimate of the sign and magnitude of induced dipole contributions according to Eq. (6). The dipole moments were calculated by Pariser using Huckel MO's with configuration interaction.9

Accordingly, static dipoles should lead to a red (negative) shift contribution for the 1 La and nearly zero contribution for the IBb transition from the ground state in addition to the dispersive red shift, agreeing with the behavior observed.

The 1 Lb transition should have a rather large blue induced dipole contribution with the weakest red dispersive contribution. Experimentally, a small blue shift is observed from the vapor that can also be detected in pressurized hydrocarbon solutions.30 The 3000 A band should have a slightly larger blue con­tribution, but the greater dispersive red shift to be expected from the oscillator strength of the transition seems to predominate to give the smallest red shift observed, much smaller than shifts of comparable intensity transitions in nonpolar chromophores of this type.

The two latter solvent shifts were omitted from the average of the proportionate shift scale since they are barely outside of experimental error. However the other transitions of azulene followed and were included in the scale since the discussion of solvent dependence for

29 J. O. Hirschfelder, C. F. Curtis, and R. B. Bird, see footnote 16, pp. 352, 354.

30 W. W. Robertson, O. E. Weigang, Jr., and A. D. King, Jr., Ohio State Symposium on Molecule Structure and Spectroscopy, Ohio State University (1959).

nonpolar chromophores should apply equally well to polar azulene.

SUMMARY

It would seem that the statistical approach to the problem of spectral solvent shifts may be applied with some success to liquid systems of this type, and there is no distinguishable difference between a simple bond density interpretation and the McRae extension of the Bayliss solvent shift theory for these systems. Solvent structural variations give rise to modified shifts which might be laid to varying solvent bond polarizabilities or energy levels with branching. However no relation between such variables and the modified shift can be observed. Rather there is evidence that the modified shifts arise from the change in physical conformation of the molecules and the resultant opportunity for close contact or interaction with the chromophore, i.e., from varying short range order in the liquid state as disclosed by the radial distribution function. This is in keeping with other evidence that "anomolous" proper­ties of other than straight chain hydrocarbons can be accounted for in the main by considering conformations and nearest neighbor interactions without recourse to different potentials for different bond types.27.31-34

However, discrepancies from the average in the individual behavior of transitions, in the influence of certain solvents, and the absence of at least a regular behavior in vapor to hydrocarbon solution shifts point up to the complexities of the phenomenon. Quite possibly only complete quantum mechanical treat­ments of the interactions, both attractive and repulsive together with detailed knowledge about liquid state solutions can fully explain these details.

ACKNOWLEDGMENTS

This research was supported in part by a grant from the Petroleum Research Fund administered by the American Chemical Society. Grateful acknowledgment is hereby made to the donors of said fund.

This research was also supported by a grant from the National Science Foundation, whose support is grate­fully acknowledged.

Many helpful discussions with Professors F. A. Matsen and W. W. Robertson are gratefully ac­knowledged together with the capable help of research assistants A. J. Dahl and H. K. Loeffier.

31 T. L. Allen, J. Chern. Phys. 29, 951 (1958). 32 William Weltner, Jr., J. Chern. Phys. 31. 264 (1959). 33 Linus Pauling, Proc. Nat!. Acad. Sci. U. S. 44, 211 (1958). 34 L. S. Bartell, J. Chern. Phys. 32. 827 (1960).

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