J o u r n a l o f Molecu lar Liquids, 53 (1992) 6 5 - 7 4 65 E l sev ie r Sc ience P u b l i s h e r s B.V. , A m s t e r d - , ~

ON THE INFLUENCE OF ISOTOPIC COMPOSITION ON VIBRATIONAL

BANDSHAPES IN LIQUIDS *

R. SZOSTAK, J. P. HAWRANEK

Institute of Chemistry, University of Wroclaw, F. Jollot-Curie Id, 50-383 Wroc~aw, Poland

(R~celved I October 1990)

AB ~TRACT

The influence of isotopic composition of molecules on

vibrational band contours in condensed phases is demonstrated.

Simulated bandshapes and vibrational and rotational correlation

functions for selected A x modes of recently studied symmetric top

molecules of the (CHs)3XY type (X = C, Si, Ge; Y = CI0 Br, CN,

C[]CH, CuCD) are presented. The problem of ~nhomogeneous broadening

due to isotopic composition and other effects is discussed in more

detail for isotropic Raman bands. Procedures enabling the

evaluation of "true" bandshapes and related correlation functions

are discussed. Finally, methods for numerical description of the

overall band contour of such systems are given. Experimental

results are also demonstrated to show the relevance of effects

mentioned above.

INTRODUCTION

More than 60 elements occur in nature as a mixture of stable

isotopes, some of them in trace~, but other in considerable

amounts. This has an impact on a vast majority of observed

vibrational spectra. Sometimes one observes separate lines resul-

ting £rom the presence of different isotopic species in the studied

systems. More often, especially for vibrations where heavier atoms

are involved, only broadening and asymmetrisatlon of the contours

takes place.

*Dedlcm~d to Professor ParaBkeva Simovn

0167-73221921505.00 q) 1999- - - ESmvie r Sc ience P u b l i s h e r s B.V. All r igh t s r e se rved

In such a case. which belongs to a class of inhomogeneous

broadening phenomena, the vibrational band profile can be regarded

ah a sum of overlapping subbands with different centers and

intensities and of the same shape- It offers a way of analysis of

these spectra, which is particularly convenient in the time domain-

VIBRATIONAL BAND PROFILES

The intrinsic shape of the band caused by homogeneous shaping

mechanisms is considered to be close to a Lorentz function 111 -

Because of inhomogeneous processes and instrumental distorsions,

observed spectra gain partly "Gaussian character" Cl.23 and real

contours are often successfully approximated by a product, sum or

convolution of these functions 131.

TABLE 1 Abundance (%I of isotopic species for the Y_(XY) vibration in compounds of the (CH,),xY type

Y 38C1 37c1 70Br 81Br '~CB~~N+ 12C~i2C*

X (75-53) (24,471 (50-54) (49-46) (98-52) (97,791

12 C (98,891

13 C ( l-11)

2aSi (92.211

-si ( 4-70)

=Osi ( 3,391

70Ge (20.52) 15.50 5.02 10-37 10-15 20-22 20-07

73Ge (27.43) 20.72 6.71 13-86 13-57 27-03 26-82

==Ge ( 7.76) 5-86 1.90 3.92 3-84 7.65 7-59

7hGe (36-54) 27-60 8.94 18.47 18-07 36-00 35-73

76Ge ( 7,761 5-86 1.90 3-92 3.84 7-65 7.59

74-69 24-20

O-84 O-27

69-65 22.56 46-60 45-61

3-55 1.15 2.38 a-32

2-33 0.76 1.56 l-53

49-98

O-56

48-91

O-55

97-43 96-71

l-09 l-09

90,435 go-17

U-63 Q-60

3-04 3-02

<+> - only the most abundant form

67

Particularly suitable for the analysis of the influence of

isotopic composition on the infrared and Raman band profiles and

related correlation funct:ions seemed to be compounds containing

group IV elements, as silicon, germanium and tin, which have 3, 5

and 10 isotopes respectively (see e-g- [UJ). That makes 6, 10 and

20 isotopic species for Si-Cl. Ge-Cl and Sn-Cl bonds wfth the

most populated being =Si -36C1 (69,65&j, 7SGe -36C1 (27_60%) and

‘=kIh - =%I (24.81%) (Table 1).

Pig_ l- Simulated band profiles for JJ (GeCl) vibration; some intense isotopic subbands are-shown

Figure 1 shows simulated band profiles for u_(Ge-Cl) vibral%on

obtained assuming a symmetrical individual band, given by a

-1 Lorentz-Gauss product function, with a half-width Au%= 4 cm and

Au = %

12 cIr& the shape parameter A";/(bu= %

+ {m A+ %

equals to

O.-r- The band maxima positions were estimated

approximation on the basis of data for (CH,),GeCl.

dramatically different band contours reault-

from diatomic

As can be seen,

RKORIENTATION&L CORREZATION FUNCTIONS

It is not surprising that except for very small molecules and

these having the hydrogen atom replaced by deuterium (in both cases

changes of moment of inertia tensor can be remarkable), rotational

parts of infrared and aniaotropic Raman profiles in condensed

phases differ relatively little for variolls isotopfc species,

In Figure 2 first and second or<er rotational correlation

functions for ensembles of freely rotating (CH,);*SiCCH and

(CHI,), '*SiCCD obtarLned for temperature 303 K are shown C5.61,

------- ( CH~IYJSICCD

LO t Ipsl

Fig, a_ Free rotor first and second order correlation functions

69

In Figure 3 related second order rotational correlation

functions G3p(t), obtained from J-diffusion model 171# calculated

for three angular momentum correlation times rJ are depicted_

The dIfferencea in Gic (t1 are of the same magnitude-

These functions obtained for various isotopic species listed in

Table 1 differ much lees than the functions mentioned above; notice

Gz,(t

8-

B-

A-

Z-

A-

---------- (CH3)3SiCCD 1

I

1.0

I

2.0 1

30 I

LO I [PSI

Fig. 3, Second order J-diffusion rotational correlation functions

TABLE 2 Prfncipal components of the moment of inertia tensor for (cH,),sICCA molecules (A = H, D)

Molecule I=1 I

I -I x f

x Y P I

Cl0 -cogcm=] Cl0 -Cogcm~] z

(CH, I3 "SICCH 432-o 262-O O-649

(CH,), '*SiCCH 432-2 262.0 0.650

(CHSJB 30SiCCH 432.4 262-O 0.651

(CH_& =*SiCCD 455-5 262-O o-739

(CH91s 39SiCCD 455-a 262-O 0,740

(CHB)s S"SiCCD 456-O 262-O 0,741

70

extren.&ly similar values of principal components of the momonts of

inertia for isotopically substituted (CH,),SiCCH molecules

(Table 2).

VIBRATIONAL CORRELATION FUNCTIONS

The offsct of isotopic compositon

vibrational correlation functions in

on isotropic band profiles and

liquids is far more pronounced

than on the rotational ones (Fig, 1) _ This problem was studied by

several authors, Van Ronynenburg and Steele [S] applied a numerical

procedure which enabled them to recover correlation functions

the Raman spectra of ordinary chloroform, under the assumption

subbands are symmetrical: see also Cl]_ Rothschild studied

isotopically pure 36 C1,CH Cl.91 using Raman spectroscopy- At

Laubereau and coworkers investigated liquid mixtures

isctogically different molecules with the use of picosecond

resolved spectroscopy [lO,llJ.

from

that

the

last

of

time

Assuming that the experimental band profile is a sum of N

subbands originating from the isotopic species Cl21

(1)

where denotes th

aJ contribution of the j isotopic species,

J m b-P--Y j m m

is the difference between the position of the maximum of

the mch and jfh isotopic species, and I(u) is a shape function

identical for all species, one can easily show, thzt the

unnormalized correlation function corresponding to I(v) is given

by I121

71

- QdV G(t) ‘=Re a

II

c ad J-1

expW!=cb,t)

(2)

In order to apply this formula to the spectra of real systems it

is necessary to know not only the relative populations of the iso-

topic forma, but also positions of their maxima in respect to P",.

Often it is possible to determine them experimentally; when not,

normal coordinate analysis or product rule can help. Eventually

these frequencies can be estimated from diatomic approximation.

"Raw" and corrected correlation functions (Fig. 4) obtained from

spectra presented in Fig. 1 show striking differences, tisr>i-ially

for narrow bands (see also Tables 3 and 4).

TABLE 3 Vibrational correlation times for simulated o_(GeCl) band

Half-widths (in cm-') Correlation times (in ps) t PO"

&V CoCal OCPF

% Av; Raw Corrected t

4.5 2.0 2.67

6.5 4.0 1.90

9.8 6.0 1.53

11.8 8.0 1.29

13.6 10.0 1.11

15.3 12.0 0.97

17.0 14.0 0.86

18.8 16.0 0.77

20.6 18.0 0.70

6.93

3.44

2.30

1.72

1.38

1.15

0.99

0.86

0.77

0.385

0.552

0.665

0.750

0.804

0.843

0.869

0.895

0.909

-1 A&=4 cm

G(t)

0.8

0.6

0-L

0.2

---_ ----_ //--

----_c ----_ I -. L’

1.0 -. NN 3-o .c

L.0 ___--

-----_-- /4-

Fig, 4. "Raw" (- - -I and corrected ( 1 correlation functions

TABLE 4 Experimental vibrational correlation ti.mes for selected modes of liquid (CH3),GsC1 Cl23 and (CH,),SiCl 1151

Mode Correlation times Iin pa)

CQY t

Raw Corrected t 03oFP

u.(GeCl) 0.71 0.88 0.808

u_(G~(CH,),) 1.35 1.62 0,833

v_(siCl) O-84 0.91 o-923

YI(Si(CHS)S) 2-21 2.44 0.906

CONTOUR OF OVERLAPPING BANDS

A variety of functions can be used to describe

nonsymmetric vibrational bands 13,131. unfortunately

the shape of

most of them

account for asymmetry in a purely formal way. Application of eg_(l)

offers a simple and well justified procedure for approximation of a

contour composed of overlapping subbands of the same shape-

Assuming that the individual band can be described by a Lorentz

function the resulting bandshape is given by 1141

a IO(D) -5(:

*J ,

J-1 1 + 8: (D-a,J)' (3)

where 2/a, is the half-width of the component band centered at

a3j- a3 - b. J

Expanding each constituent of the above sum into

a Taylor series about v - a,, and collecting terms with like powers

of V - a9, one obtains Cl41

IO(V) = Bo

1 + a5 (u-a,la

k

+c Bl + C, (v-a,)

1-i 1 + at (v-a,j2 i+1 -

(4)

This formula with k = 1 or k = 2 can serve as a useful 5-7

parameter approximation of a real vibrational bands in condensed

phases [14.163_

If the elementary band is described by a Gauss function, the

final result is 1141

I"(V) 3 i-0

A,W-a,)‘. (5)

with the half-width of the subband

A i' 9,. =, can be expressed through

equal to 2/iEF/a,. Parameters

al. a,. a iJ and b J C163-

74

CONCLUSIONS

1, Isotopic substitution in the discussed molecules has negligible

influence on rotational correlation functions except for H/D

exchange,

2_ Vibrational contours and related correlation functions may be

predominated by isotopic composition.

3, The tntrinsic correlation functions can be d9r-l red from the

overall profile basing on the shift theorem, The related shape

of the component band can be recovered subsequently by inverse

Fourier transformation.

4. The vibrational profile of inhomogeneously broadened bands can

be successfully described by means of u derived family of shape

functions_

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1

a

3

4

5

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9

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