A STUDY OF THE FUNDAMENTAL VIBRATION-ROTATION BANDS IN THE SPECTRA OF ST I BENE AND DEUTERO-STIBENE

DISSERTATION

Presented in Partial Fulfillment of the Requirements

for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By William Howard Haynle, S.F., M*Sc« The Ohio State University 1961

Approved byi

«w-<'s i wi[//// Adviser ACKNOWLfcDGLlEHTS

It gives me pleasure to acknowledge the help and oooperation extended to me by many persons during the course of this investiga­ tion* For advice on the theory of molecular structure and sugges­ tions on the interpretation of the experimental data I am indebted to Professors K* H* Nielsen and E* E* Bell* I am very grateful to Professor J. 0* Lord of the Department of Metallurgy for help in preparing a suitable alloy, and to Professor A* B. Garrett of the Department of Chemistry for advice concerning the chemical proce­ dures involved in generating the samples. My thanks are due to Mr* William Ward for help in obtaining the data* I am particularly Indebted to Professor R* A* Oetjen for his advice and encouragement over the past five years* Finally, I wish to express my sincere gratitude to Gloria Westphal Haynle who has checked the proof and verified all of the calculations* Her help and encouragement have been invaluable*

0 2 2 1 < > 2 TABLE OF CONTENTS

Fag®

Introduction ...... 1

Summary of Theoretical Work ...... 5

Experimental W o r k ...... 18

Analysis of the Absorption Spectra of SbH and SbD_ ...... 26 3 3 Appendix...... 55

Bibliography ...... 60

Autobiography ...... * 61

ii A STUDY OF THE FUNDAMENTAL VI b RAT I ON -ROTATION BANDS

IN THE INFRARH) SPECTRA OF STIBENE AND DEUTERO-STIBENE

Part I* Introduction

The pyramidal XY moleoular model represents the simplest O nonlinear, nonplanar framework that oan he classified as a true symmetric rotator or symmetric top* For this model two of the principal moments of inertia are identioal* The rotational details of the spectra of a symmetric molecule have certain regularities which lend themselves rather readily to a determination of certain of the constants of the molecule* For this reason, the available speotra of symmetric top molecules have been studied quite thoroughly and have contributed substantially to the development of the theory of moleoular structure as it exists today*

The tri-hydrides of the fifth group of elements in the periodic table are among the most interesting examples of symmetric top moleaulea* Ammonia, phosphlne, arsine, and atibene are all pyramidal XY^ molecules with hydrogen as the Y atoms and nitrogen, phosphorus, arsenic and antimony respectively as the X atom* In order to calculate the geometry and force constants of moleoules suoh as these, It is desirable, if not entirely essential, to have data from the spectra of the molecule in several of its isotopic forma* The data involving the isotope effect are more easily interpreted if the three hydrogen atoms are replaoed by three deuterium atoms in forming the isotope*

1 Starting in 1926 with Robertson and Fox^* who obtained prism spectra of NHj# FHand A&H^, progressively more useful data have been obtained on these three molecules by several investigators^*®» 4,5,6#7# j|. haB been established in these earlier investigations tliat the pyramidal XY^ moleoule has the four normal modes of vibra­ tion indioated in Figure 1**» These normal modes are classified by group theory according to the symmetry species of the vibrations* I.'odes to and u> Involve changes of the electric dipole moment es- 1 o sentially parallel to the symmetry axis of the moleoule. They are called parallel inodes of vibration and belong to the totally symmetric species A^. Modes to ^ and to ^ involve changes of the dipole moment essentially perpendicular to the axis of the top. They are called perpendicular modes of vibration and belong to the degenerate species

E. Modes t*j and to are doubly degenerate and thus the 3N-G• » 6 normal modes are satisfaotorily aocounted for* It may be noted from Figure 1 that modes (_,j and t*> have in common that they are primarily "bond A £ stretching" vibrations and the two vibrations should involve essen­ tially the same foroe constants. One might expect that these two vibrations would have nearly the same . Modes u# ^ and

Lu ^ have in oossnon that they are both primarily "bond angle distor­ tion" vibrations and thus they might be expected to have frequencies of the same order of magnitude. The data on phosphlne and arsine

•Superscript numbers refer to the bibliography •*The figures are grouped together at the and of the text. ••*The notation used to designate the normal frequencies is that of Dennison. 2 beor this out »!/.,♦ andy 11s within Tew wave numbers of saoh X 4* a other in the 4 to B nlcror* region, andj/^ and>/^, although farther apart, both lie in the 10 to 12 mioron region* As the mass of the

X atom increases from NH^ to to Ash^, the corresponding normal frequencies of theee molecules are successively lower* Thus the normal frequencies of SbH^ would be expected to be lower than the corresponding frequencies of AsH^*

This investigation of stibene, the last chemically stable member of the family of tri-hydrides of the fifth group, was under­ taken with the purpose of determining as many of the constants of the moleoule from a study of the infrared absorption spectra as the data would permit* Previous experimental work on stibene is described in two papersi one published by D*C* Smith®j the other by Loomis and

Strandberg®* Smith obtained prism spectra of SbHg in the region from 2 to IB microns and found two regions of Intense absorption* The first, in

the 6 mioron region, which has the appearance of a parallel band with a strong Q branoh at 1690 om"^, he assumed to be a superposition of

V upon a weaker y • The second region extends from 10 to 14 microns X w with two strong absorption maxima at 761*6 and 631 oin”^. Smith interpreted this absorption region as an overlapping of the two vibrations of v j and y ^*

^Throughout this paperw^ will be used to indicate the observed corresponding to the normal frequenoywj,

3 Loomis and Strandberg have obtained absorption spectra of SbHgD along with the data on EfcjjD and AsH~D. These data were used to oaloulate the molecular geometry and the results extrapolated to SbHg on the reasonable assumptions that the force oonstants and geometry of SbH^D and Sbllg are the same* Prom their data they determined the moleoular constants listed in Table !•

TAELE I,

a * ro ** O FH3 93*5° 1.419 A o A 0 H3 92.0° 1.623 A a SbH, 91.6° 1.712 A

*** is the Y-X-Y bond angle. the X-Y bond distance.

4 Part II • Sumntry of Theoretical Work Tho modora lnterpretatien of moleoular band apootra i« baaod upon tho roaulta of a quantum—moohanioaI thoory developed and roflnod over tho paot twenty-five yoaro by many investigators* Application of group thoory prinoiploa haa aupplouantod and abottod thia interpre­ tation* It la intondod to proaont horo a briof outline of tho quantum-meohanioal treatment, and a imply to quote the group theory reaults that will be of uae in thia paper* In order to prediot the appearanoe of or to interpret a moleoular vibratlon-rotatlon band two aeta of information are required, namely, an expreaaion for the allowed energiea and a aet of aeleotion rules* The allowed energioa or eigexnraluea of energy are aimply the quantised vibration-retation energy atatea in whioh the partioular moleoule may exist* The aeleotion rulea govern the tranaitiona of the moleoule

from one energy atate to another* A* The Energy Term Value Expreaaion In eaaenoe the problem of determining the allowed energy atatea for a vibrating-rotating moleoule ia that of solving the Sohrodinger

equation

HY*EY (1) for that particular moleoule* H ia the ao—oalled "quantum-meohanioal Hamiltonian" and ia a function of the masses of the moleoule, the coordinates used to deeorlbe the moleoular oonfiguration, and the momenta, expressed in operator form, oonjugate to the coordinates*

Nielsen* 0 has aet up the Hamiltonian for the general polyatomio moleoule and has separated the extremely oomplioated expreaaion into

6 three parts, H . H , and H , whioh contribute to the energy in v X £ zero, first and saoond order of approximation respectively* He has substituted this Hamiltonian into the Sohrodinger equation and has obtained an expression for the energy term value to seoond order

of approximation* Shaffer** has solved the problem speoifioally for the pyramidal XY_ moleoular model and has given the energy expression o to second order of approximation as followst

The quantities •nd Fro^ ore, respectively, the vibrational and rotational term values in wave numbers* These term values are given by the following expressionss

Grw b -G.+ (3)

= B v3(3 + l) -t(C< -B,)K"-DJ3*(3 + 0*-DJRJ(3+l)K.*-D1(KH. (4)

In the expression for GTit, the coefficients Gq , ®22* *to* are oonstants depending essentially upon the normal frequencies,^^,

and the foroe oonstants in the potential energy expression! d^ is a

weight faotor which denotes the degree of degeneraoy of the 1 th normal

mode of vibratlonj (d^s 1 when the oscillation is nondegensrate,

d^» 2 when the osoillation is twofold degenerate, etc*) v^ ia the

vibrational quantum number associated with the 1 th normal mode, and

ig and 5 ^ are quantum numbers associated with vibrational or internal

6 angular momentum in the two doubly degenerate m o d e s and w ^* v^ is a positive integer ( v j - O* 1, 2 , — -) and is sere except in the oase or the degenerate frequencies* Here it may have values v^* v^-2, v^—4* —---- * 1, or 0* The quantities in the rotational term Fro^_ are defined as follows t J is the quantum number associated with the total angular momentum of the molecule} K is the quantum number associated with the component of angular momentum directed along the top (z) axis; and Dg are known as the oentrifugal dis­ tortion oonstants and depend upon the atomic masses* the normal frequencies* and the force oonstants of the moleoule} B and C are proportional to the reciprocals of the moments of Inertia and are

defined asi

= “ m V i I *= r & T ? (6 )

in terms of an xyz coordinate system with its origin at the oenter of mass of the moleoule and its z axis along the axis of the top* The subscripts and superscripts e and v indicate that the quantity refers to the equilibrium state or to the vth vibrational state

respectively*

In the two perpendicular modes of vibration* w ^ and w 4 * the motion of the X atom is isotropic in two mutually perpendioular directions* both of whioh induce electric moments perpendicular to

the axis of the top* In other words* the X atom behaves as a two dimensional isotroplo oscillator and thus during vibration it 7 desorlbea a circular path whoaa plana la parpandloular to tha axis ol* tha top* Teller^* has shown that tha angular momentum arising from thia circular motion has magnitude where -l— Tha 'S the so—called Taller parameters,may be thought of qualitatively as measures of tha amounts by which tha dipole moment vector leads or lags the component of tha angular momentum vector of tha moleoular framework: parallel to axis of tha top* A Corlolia interaction exists moreover between this vibrational or internal angular momentum and the parallel component of framework angular momentum which gives rise to a first order correction to the energy* This contribution to the energy is represented by the last quantity in the energy expression*

- -Vf $1 )£• The 5 ^ may also be considered as measures of the magnitudes of the Corlolls couplings*

In the expression for the rotational term the quantities

D j J 2 ( J ♦ 1)2, DJKJ (J+ 1)k2* and *r# sin* H corrections to the energy whioh arise because rotation of the moleoular framework tends to alter the effective moments of inertia* These centrifugal distor­ tion terms contribute to the energy in an order higher than was experi­ mentally detectable in this investigation and therefore they shall be omitted from the rotational term* The energy term value expression* to the approximation that will apply to the data* is then

& . aB t <6 )

B* The Selection Rules Selection rules are obtained by considering the following type

of integrals Involving components of the dipole momenta 8 JV'rW'dt ^ (?) whereY" •BdY* ar# 'th* eigenfunctions aesooiated with tha lowar and tha uppar energy atatas respectivelyj ia a oomponant of tha dipola momarrt; and dx ia tha volume element of tha configuration apaoa uaad

to daaoriha tha moleoule. A tranaition from tha lowar (doubla prima) anargy atata to tha uppar (aingla prima) anargy atata is allowad only whan tho intagral doaa not vanish* Thaaa integrals or matrix alamanta

have baan thoroughly investigated and the results are summarised below. Vibrational transitions are governed by tha rule

AVi. - . (8 )

Rotational transitions are governed by two sets of aeleotion

rules, depending upon the nature of tha normal mode of vibration.

Dennison^"® has derived the rotational selaotion rules and states that for modes of vibration in whioh the dipole moment is oscillating

essentially parallel to tho top axis tha rules are

A. K = O, A l = i l ; J J ^ i C = 0

A K = o , A 3 - o, i l j .

An anargy transition from tha ground state to an exoited state

of one of tho parallel modes of vibration ooupled with a simultaneous

ohange of tha rotational anargy aooording to the above rules gives

rise to a parallel vibration-rotation band. 9 for modas of vibration in whioh tho dipolo moment io oscillat­ ing essentially perpendicular to the axis of tho top tho selection rules are

j As-Ojti do)

T«ll«r ^ h*a shown that tho solootlon rulo for tho lntornal angular momentum quantum number £. depends upon the K aeleotion rule as follows

AS--M *, Jf»vAV<=tt \

> (ii) AS=~\ \ . J

Bands arising from this type of transition are oalled perpendicular bands•

The energy term value expression together with the aeleotion rules and a qualitative idea of the relative intensities are suffi­ cient to allow us to predict the appearanoe of the vibratlon-rota- tion bands of a pyramidal XY_ molecule* The dlsoussion will be

confined to the fundamental bands ( v 0 to t^I), and the two types of bands will be considered separately* Quantities identified by a double prime are associated with the lower state and those with a

single prime refer to the upper state of the particular transition being considered*

C* The Parallel Bands The final energy term value expression for a pyramidal XYj

10 molecule was found to bo

For tho parallel modtiw and cj value is zoroi i.e., tho intornal angular momentum Is sera* Lot us consider y^ as tho example of a parallel band* In the lower state the term value has the form

(12) and in the upper state it is

(13) where G« VJ represents the vibrational term value for v — 1* For the transition a v « + l and A K = 0, A«J=- 0, we obtain

(14)

This transition gives rise to tho Q branoh of tho band* It should bo noted that If tho rotational oonstants have tho same values in tho ground state and in the first exalted state, i.e., if B’VB* and C s C 1, then the Q branoh should consist of a group of lines having tho same frequency y^» In phosphino, arsine, and, as will be shown, in stibene, B” is slightly greater than B* and also tho quantity

[(C1 —C")-(B*-BH)3 is very nearly coro. Thus tho Q branoh oonaista of a sot of lines very closely spaced with respeot to oaoh other 11 (usually spsotrosooploally unresolvable)•

For tha transition* A v »-■*■ 1 a nd A K- 0 rAJ*11, tha frequencies are given by

V « X ± 3"(B + B"i + 3*V6'-B"»+{(C,-C») K*s . (16)

Ths transitions AJ - ^ 1 and A J- - 1 give rise to ths P and R branohss

respectively, and these branohss 1 1 s on ths low and ths sidss of ths Q branoh* Eaoh branoh consists of a sst of

lints, on« for saah value of Jn and saoh 11ns has J components corresponding to all ths possible values of K. Slnoe BH is usually

greater than B 1, the term oauses tha P branoh lines to diverge and tha R branoh lines to oonvsrge as J Increases. If tho

difference B'-B” is negligibly small the K components will coincide

for eaoh line and ths P and R branohss will oonslst eaoh of a set of

single, equally spaoed lines* Another mors oommon way of looking

at the fine structure of a parallel band la to say that the band con­

sists of a superposed set of sub-bands, one sub-band for eaoh of the

possible values of K* Bach sub-band is comprised of a P, Q, and R

branoh exoept for the sub-band where K«0, in whioh the Q branoh is

missing. In the previous paragraph it is pointed out that lines in tho

R branoh arise from a transition A vl or J” to J’S 1 and in the P

branoh the lines arise from t ransition A J* - 1 or J* to JB—1* If we

subtract the term value for the P branoh line P(JMvl) from the term

value for the R branoh line R(JM-l) the resulting expression oontalns

18 only tho rotational constant Tor the lower state* To simplify the notation let us denote J” simply by J and let F"(J) and F*(J) denote ths rotational term values for the lower and the upper state respectively* Then the frequenoies of the P(J+1) and the R(J-l)

lines may be expressed as

R ( 3 - 0 = V, t F '(3) - F"( 3 -O (16)

Taking the differenoe we obtain

- PC3 to = F " ( . 3 to - F"C3-i') * A l F"Ci) y (17) where

F"(3-»») = B" C 3 + 0 ( 3 +2.1

(18) F"f3-l) t LCc'-c")-CB -

and thus

A t F " ( 3 ) . (19)

If instead, we take the differenoe between R(J) and P(J) the

result involves the rotational oonstant of the upper state only

and Is

(20)

13 R C3) - P(.3) - f 'C3 i-n - F fC3 - o = A t F * (3^ , (21)

(22) A t F'(cO - aB ' U l i .

The two relatione

A dF"0) - R(3-U - PCs ii) - ^ " U s - n ) , (IS)

A^F'C3)= K(3) - PCJ) =20'(Z3ti) , (22)

are the 1 0 -oalled combination relations* If* A g F(J) is plotted against 2Jvl the slope of the resulting line gives the value of* ths

rota1 ional constant B. There is one more relation that is useful*

It is obtained by adding the term value of P(J) to the term value of*

R(J-l) and the result is

ft('s-i) i p (3) =awt -» ale' -b ")t * . (23)

A plot of ^ [r(J-1)v P(J)] against J 2 yields the band oenter ^ as the Intercept* and the differenoe B*— Bn as the slope*

D • The Perpendicular Bands In order to discuss the perpendioular bands of a pyramidal

XYj moleoule we need to reoall the energy term value (6 ) and the rotational selection rules associated with an oscillation of the

dipole moment perpendioular to the top axis (1 0 )# and (1 1 )•

14 A K - — I , A 3 - 0 , 1 1 (1 0 )

A S m i ■, a kK - -t > (11) A S - -I > A We shall oonsider Vg as an example of the perpendioular bands.

In the ground state (vg-jfg-O) the energy term value is

F “ = 0ro te.Vc5''-H> ^ cc"-b *)k "* , <24)

and in the first exoited state (vg»l, Jfg* - 1 ) the term value is

E ' - Gr„ +1/ tB'3'f3'+»> -+(c'-B')K'*-aCe C^ S J k '. (25)

For the transit ions A J-0 # A K- t 1 *Ajwe obtain the following

expressions for the frequencies of the lines in the ^Q(AK*tl) and

PQ(AK- -1) branohes of the Kth sub-band

+ (B"-C*) K ( V t ' " £ , C € -G*J 1 3C3VIXI3'- B") (26)

+ K ’Lfc'-C*) -f B ' - B " ) ] .

For the transitions AJ — v 1# A K 1 il and A J - - 1, A K - ± 1 D p we obtain the following expression for the lines in the R, R, and

®P, PP branohes of the Kth sub-bandi

v -- * Cb“-c") t aK L

15 In order to simplify these expressions somanhat, tha assumption is usually made that 0^*3: C". Than tha coefficient of

K, £

Tha parpandioular band is oompoaad of a suparpoaition of several sub-bands, one for aaoh value of K* Eaoh sub—band has tha general appaaranoa of a parallal band with a strong Q branoh and P and R branohss with approximately squally spaced lines* However, even whan it is assumed that tha rotational constants have the same values in the upper and lowar states, tha Q branoh lines

PQ and Rq will not fall oloss together unlees the quantity

^ (1— 3 saro or negligibly small* Thus, in general* tha parpandioular bands will present a much more oomplax appearance than tha parallal bands of tha same molecule*

E* Resonance Interactions

Whenever two vibrational frequencies lie close together there exists the possibility that the two may perturb eaoh other and oause a shift in the frequencies predicted by the energy term value

expression (6 )* Nielsen^® states that in seoond order of approxima­ tion only two types of resonanoes need be considered* These are of the Fermi—Dennison type and of the Coriolis type* The Fermi—Dennison type is a resonance interaction between a fundamental frequency Ui ^ and a combination frequencyWj -t co Thia type of resonanoe results in a shift of the vibration band centers without seriously disturbing

-che rotational line spaolng* The Coriolis type is a resonanoe inter­ action between two fundamental frequencies and alters the effective

16 momenta of Inertia thus giving rls« to anomalous rotational llna spacings*

In stibene tha oomiblnatlon fraquanoy of tha band oantara and also tha first ovartonas of thasa band oantars dlffsr

from tha fraquanolas of tha shortwave band oantars by mora than 2 0 0 wave numbers* Tha "resonance denominators" +

(cOj-OJ j -*■ («-** j—2 » sto* are large and, therefore, tho Fermi— Dennison resonanoe Interactione should be small*

Nielsen? has shown that there is a strong Coriolis interaction between the longwave vibrations to ^ and to ^ in FH^ and in AsIIg*

Anomalies in the rotational struoture of the longwave bands of stibene

indioate that a similar interaotion exists between 3 and to ^ in this moleoule* The nature of the shortwave vibrations to j and co ^ suoh that the eleotrla dipole moment vectors and the framework angular momentum vectors should be very nearly In phase) for this reason it may be assumed that £ ^ z * aiu* ^ 12 ara Prao^^c*^^y aero* Thus, the

Coriolis coupling between oj ^ and co g should be negligibly small*

17 Part III* Experimental Work

A* Sample Preparation Stibene (SbHg) le formed by the combination of nasoent hydrogen with antimony* Mellar^ describee several methods of generating the gas* The method used in this investigation is essentially the same O Q as that used by Smith0 and by Loomis and Strandberg , and consists of the addition of a dilute mineral aoid to an alloy of antimony and one

of the "hydrogen generating metals" such as zlno, magnesium, eto*

None of these antimony alloys were commercially availablet so

the first step in preparing the sample was to make a suitable alloy*

It was decided to use an alloy composed of 80^ zinc and 2Qfo antimony*

The alloy was prepared by melting the zinc in a clay—graphite orucible*

Then the antimony was added to the molten zinc and the mixture was

stirred with a quartz rod* Finally, the molten alloy was poured into

a rod-shaped mold, in order that it could be ohuoked in a lathe and

turned to produce small shavings* Figure 9 shows the glass apparatus used to generate the samples*

Lathe turnings of the zlno—antimony alloy were placed in the bottom of the generating flask (F), and the drying tube (D) was charged with

fresh oalolum ohloride* The system was then pumped down to a pressure

of about 5 miorons of mercury before the reaction was started* This pressure was originally measured with a MoLeod gauge, not shown in the figure* In order to reduce the volume of the system, the MoLeod

gauge was removed after the first few experiments* After closing

stopoook (Sg) the reaotion was oarried out by allowing dilute aoid

from the funnel (a ) to drop into the flask* The reaotion was

18 continued until the manometer (m) indicated a pressure or approximately

740 ran of meroury in the system* At this point atopoooke (S^) and (Sg) were oloeed, and the absorption oell (C) was removed from the system*

This reaotion yields only 2 to 3% stibene mixed with hydrogen* There­ for*, in order to obtain the strongest possible stibene sample, the oell was filled as oloso to atmospheric pressure as possible*

In some of the earlier experiments attempts were made to inoreas* the sample oonoentration by condensing the stibene in a liquid air trap (T)* The hydrogen was removed and the trap was then warmed to distill the stibene over into the oell* The several samples obtained in this manner proved to be weaker than those obtained without the oold trap and so the trap was discarded* Thorneyoroftstates that stibene deoomposes more rapidly in the liquid than in the gaseous state* A blaok deposit, noted in the bottom of the trap, was assumed to be metallic antimony* Decomposition in the trap seems to be the only plausible explanation for the weaker samples obtained by this method• Both Mellor^* and Thorneyoroft^-^ state that the mineral aoid used in this reaotion should be "dilute* but neither specifies a oonoentration* The experiments were first performed using sulphurlo aoid of various ooncentrations* It was found that if the oonoentration exoeeded 0*2N a blaok deposit formed in the reaotion flask and the stibene yield decreased. To attain a pressure of 740 mm of meroury in the system required the addition of about a liter of 0*2N H^SO^ to the antimony alloy* It was thought that the HgSO^ might be

19 oxydizing the stibene in the reaction flask, and so sxpsrimsnts were performed using both phosphorio aoid and hydroohlorlo aoid*

Ths rasulta wars similar to those obtained when HgSO^ was used* It was found that the best stibene yields were obtained when the aoid

oonoentration was less than 0*2N* 0.2N HC1 produced slightly better

yields than either H^SO^ or h 3f o 4*

Deutero—stibene, SbDg, was generated in the same manner as

ordinary stibene, SbHg* "Heavy* sulphurio aoid, D^SO^, obtained

from Traoerlab, Incorporated, was diluted to 0*2N with DgO anc*

dropped on lathe turnings of the same zino—antimony alloy* In order

to reduoe the hydrogen contamination to a minimum, the apparatus was

evacuated for 48 hours and flamed several times before starting the

reaction* The available supply of DgO, necessary to dilute tho

D2S0^, was limited to 76 grams* To obtain maximum sample pressure with the resultant small quantity of dilute aoid the volume of the

generating system was made as small as possible* After most of the

0*2N aoid had been added to the alloy, the aoid oonoentration was

gradually increased until the blaok deposit, metallio antimony,

began to appear in the reaotion flask* It was possible in this way

to obtain a pressure of from 600 to 700 run of meroury in the system

with probably about the same percentage of deutero—stibene as was

previously obtained for ordinary stibene*

It ie stated*-® that stibene is readily decomposed into its

elements, antimony and hydrogen or deuterium, but when kept at room

temperature in a thoroughly olean glass vessel with no rough surfaces

the gae remains "fairly" stable* In thia investigation it was found

20 that in a olean pyrex oell fitted with w«ll polished salt windows a sample oould bo used for from two to three days before the absorp­ tion bands became too weak to measure* Upon removal from the speotro- graph after about two days, the inside of the oell was coated with a shiny antimony mirror* In running the speotrum of SbHg traoes of water vapor were found indicating that the CaClg drying tube was not completely efficient in drying the sample* In generating the SbDg* since the drying tube had been shortened to decrease the volume of the system* the reaction flask was immersed in an ice bath to reduce the water vapor pressure in the system* As a further precaution to eliminate water vapor an

aluminum "boat" containing ^3 ^ 6 was plsosd in the absorption cell* The effectiveness of the drying the gas was never determined since the SbDg in this oell decomposed in two hours time to a point where even the strongest absorptions were no longer measurable* A second and a third sample of SbD^ contained in cells without the PgOg were used for 48 and 24 hours respectively* The life of the third sample was shortened beoause the gas was kept in the same oell that had previously contained the sample referred to above as the second sample* An antimony mirror whioh had been deposited on the inside of the oell before the third sample was introduced had not been removed* It is oonoluded that the presence of the antimony catalyses the decomposition*

8* Speotrographlo Work As noted in the previous section* the stibene samples were oontained in cells which oould be introduced into the optioal path

21 of tha spectrograph* Eaoh oall consisted of a 5 om diamatar pyrax cylinder with a stopoook to admit tha gas sample* Tha anda of tha oall wara fittad with windows tranaparant to tha raglon of tha apaotrum In whioh tha abaorption band a of tha aampla lay* For study­ ing SbHj sodium ohlorida windows wara adaquata ainoa all four fund a - manta 1 bands ara in tha raglon short of 15 miorona* For SbD^ potassium ohlorida windows wara naoasaary baoauaa tha j and ^ bands 11a batwaan 16 and 20 miorona* Sinoe tha oalls wara usad In on evacuated speotrograph* tha prassura Insida tha oalls axoaadad that outaida* In ordar to obtain a tight saal naoprana gaskets ware sandwlohad batwaan tha salt windows and tha ands of tha cylinder* and tha insida of all tha joints was paintsd with Glyptal* Rubber gaskets and brass and plates wara plaoed oxer tha two windows and the plates ware pulled together by means of threaded rods and nuts*

In the work on SbH aaoh time a new sample was generated * two oalls* one 6 om long *nd tha other either IS or 26 om long* ware filled* Th« 5 om oall was usad in tha Beokman Uodel IR—3 prism spaotrophotometer to reoord tha strength of the sample* A tracing of one of these reoorda is reproduced in Figure 10* where only the two regions embraoing the fundamental bands are shown* Tha record olearly indicates the weakness of tha two longwave bands at 12 to 13 miorona relative to tha shortwave bands at 5*3 miorona* Several runs oompletely covering the region from 2 to 15 miorona showed only tha fundamental banda* indicating that tha samples wara too weak to show overtone and combination banda* No prism reoords wara run on SbD^ baoauaa of tha amall quantity of gas generated*

22 To obtain raoords of the fins structure of th« fundamental bands the gas samples were run on a vacuum grating spsotrograph*

This instrument is essentially ths ons dssoribsd by Ball, Noble, and Nielsen'*’0Tfi with ths sxoeption of ths dstsotor and amplifisr systems* For this invsstigation a Golay pnaumatio dstsotor and assooiatsd amplifisr wsrs ussd to fssd a Spssdomax strip chart rsoordsr in obtaining ths spsotra* Bsoauss ths Golay osll has a widsr reoelver than ths thsrmooouplss previously ussd in this in­ strument, ths dstsotion systsm was mors efficient in ths 10 to 15 mioron rsgion whsrs widsr slits ars required* In ths shortwave re— gion from 3 to 10 microns ths maximum ssnsltivity of ths Golay osll was found to bs oomparabls to that of a good thermocouple* Ths Golay osll dssoribsd hsrs was ths first modsl built by Epplsy Labora- torlss to bs ussd in a vacuum spsotrograph, and at first oonsidsrabls troubls was snoountsrsd in maintaining maximum ssnsltivity whsn ths spsotrograph was evacuated* It was found that if ths dstsotor was allowsd to stand for about two days in ths svaouatsd tank and was thsn readjusted to maximum ssnsltivity, ths ssnsltivity would rsmaln fairly oonstant providsd that subssqusnt sxposurss to atmosphsrlo prsssurs wsrs of short duration ^leas than half an hour)*

Ths fundamental bands, y ^ and mi or ons shown in Figurs 2 wsrs rim with ths 15 om sample osll using a 3600 lins psr inoh rsplloa sohslstts grating blazed at about 7 miorona in ths first ordsr* Ths avsrags spsotral slit width was 0*45 om"^•

Bsoauss ths longwavs fundamental bands, i/g and of SbH^ shown in Figurs 8 wsrs found to bs rslativsly muoh wsaksr than ths 23 shortwavs bands* th« 25 on osll was ussd to rsoord thsas bands*

Ths two bands ovsrlap and togsthsr covsr ths spsotral rangs from

about 10*5 to 14 mlorons* Thsss bands wsrs run with both ths 5500

lins grating and an 1800 lins rsplloa sohslstts grating whloh Is

blassd In ths first ordsr at about 14 mlorons * Ths 3600 lins grat­ ing gavs bsttsr rssults from 10*5 to about 12*5 ml orons* Prom 12*5 out to 14 ml orons ths 1800 lins grating was found to bs mors sffiol-

ont although widsr spsotral slit widths wsrs rsqulrsd* From 10*6

to 12*5 ml orons ths avsrags spsotral slit width was 0*36 on“^ and

from 12*5 to 14 mlorons ths avsrags spsotral slit width was 0*50 om"^»

For rsasons prsviously disousssd* only ths 15 om osll was ussd

to run all four of ths fundamsntal bands of SbDg* Ths data obtainsd

on ths shortwavs bands* i / ^ and y 2* shown in Figurs 5 ars slightly

bsttsr than ths oorrsspondlng data on SbH^ by "irtus of ths faot

that ths first ordsr blass of ths 3600 lins grating Is at 7 mlorons*

just abovs ths osntsr of ths shortwavs SbD^ bands* Ths avsrags

spsotral slit width for thsss two bands was 0*36 om“^• Ths SbD^

samplss* whloh wsrs adsquatsly strong for ths shortwavs bands* wsrs

found to bs too wsak to rsvsal muoh of ths struoturs of ths longwavs bands whloh lis in ths rsglon bstwssn 15 and 20 mlorons* Ths band osntsrs and a fsw llnss in ths rsglon of ovsrlap bstwssn ths two

bands wsrs all of ths data that oould bs rsproduosd* It may bs notsd

that in using ths 1600 lins grating bsyond about 17 miorons thsrs is

a ssrlous snsrgy limitation* about half soals dsflsotion oould bs

obtainsd at 17 mlorons with ths slits at thslr maximum width of

1*50 m * and at 19 microns ths dsflsotion was about 15/C of full soals*

24 In obtaining the data presented here the grating was rotated continuously at one of four possible speeds. Angular positions of the grating were determined by ■viewing a divided oirole through a mloroBoope, and marks were plaoed on the reaorder chart by shorting the input to the reaorder eaoh time a five minute index on the oirole passed under the crosshair. The angular position of the cental image was measured to the nearest 128th of an inch between two five minute marks and then computed to the nearest one hundredth of a minute* The angular position of the cental image was subtracted from eaoh of the mark angles to give the grating angle*^. The frequencies of the marks were then calculated from the grating formula _g~* x where K^, * the grating oonstant* was determined experimentally for eaoh grating by using higher orders of some of the strong meroury arc lines* The oenter of each absorption line was estimated and its frequency was calculated by linear interpolation between the two adjacent mark frequencies* On most of the records obtained in this investigation it is felt that the greatest error in the frequencies of the absorption lines was introduced in locating the centers of the lines properly* This error is estimated to be ± 0.1 om"^ since in most eases the variation in frequency of a given line, determined from several different records* was within these limits. The line frequencies tabulated in this paper represent weighted averages of at least two* and in many oases five or six* independent measurements from as many separate records*

25 Fart IV* Analysis of the Absorption Spectra of SbHg and SbDj

Figure 2 shows the 6 micron region in the absorption spectrum of SbH^* and Figure 3 shows the corresponding region In the spectrum of SbDg near 7 microns* In appearance they are strikingly similar and hence they will be discussed together* The double sets of lines near the centers of the two regions represent two sets of data run with different sample pressures*

Qualitatively each of the two spectra shows two strong absorption maxima within 4 om"^ of eaoh other and essentially two strong over­ lapping sets of sharp lines on both sides of these maxima* These spec­ tra are interpreted as representing an overlapping of the two funda­ mental bands* y ^ and V with \/ the parallel band* lying at a slightly lower frequency than the perpendicular band* y g* The in­ tense maxima near the oenters of the bands represent the overlapping Q branches (Aj« o) and the two sets of sharp lines are the rotational fine structure comprising the F and R branches ( A J * - 1 #A J = + 1). It is apparent from the appearance of the two opeotra that the sub-bands

(one for eaoh value of K — J) in both y ^ and y ^ must be very nearly superposed* No apparent anomaly is disoernable in the rotational structure which indicates that very little interaction exists between the two vibrations* y ^ and y g* as was indeed painted out in Fart II.

For this reason (15) and (27) should represent the fine struoture frequencies for the two bande*

We will first confine our attention to the parallel bands* y ^* With the absorption maximum having the lower frequency assigned as the i band center for both SbH and SbD_* a series of nearly \s 1 o o 26 •quid 1st ant lines nay b« a«l«ot«d In the P and E branches of saoh

spectrum. In eaoh oass th« sot of linos chosen Is suoh that ths

interval between ths first 11ns Identified In the P branch and th« first line Identified in the R branoh Is an Integral multiple of the average spaolng between successive lines ef the set. J values

(J3 J") are assigned to eaoh line by considering the positions of the first identified P and R lines relative to the band center. All of the reasonable ohoioes of sets of lines and J assignments were tried.

The two sets of lines and the J assignments finally selected are the

only ones for which the combination relations (18) and (22) plot properly and yield a reasonable value for the apex angle of the XYg pyramid. Seme of the ohoioes were disoarded because the combination relation plots did not go through the coordinate origini for ethers the oemhination relation plots had two infleotions whloh oould not be

justified by centrifugal distortlenj and A r soae of the ohoioes an entirely unreasonable value of the pyramid apex angle was obtained.

The rotational lines associated with 1/ ^ are marked in Figures 2 and

3, and the frequencies (t/TKQ) these lines are listed in Table II for SbHg and in Table III for SbDg. It is somewhat disturbing that the

R branoh lines selected for \s ^ 8bHg are predominantly the weaker

lines while the oerrexpending lines for SbDg are the stronger lines.

However, since these are two different molecules, the parallel and ths

perpendioular bands do not overlap in exactly the same manner in the

two oases and it is difficult to prediot hew the intensities of the

superposed lines ef V 1 and y ^ will add. Moreover, it may be pointed

out that in the oase of arsine a similar situation prevails.

2T TABLE II

Obssrvo Frsquanoiaa of the Linas of \ s ^ for SbH^

J R(J) (vao om"1) P(j) (vao om“^)

1 1902.4

2 1908.2

3 1913*4 1873.4

4 1919.0 1867.0

6 1924*9 1860.9

6 1930.2 1864.6

7 1936.7 1848.6

8 1941.0 1842.3

9 1946.2 1836.0

10 1951.2 1829.6

11 1966*6 1823.1

12 1961.9 1816.6

13 1966*7 1809.9

14 1971.5 1603.3

16 1976.3 1796.6 16 1981.2 1789.8

17 1986.2 1782.8

18 1776.2

19 1768.8

28 TABLE III

Observed Frequencies of the Lines of \/ ^ for SbD^

J R(J) (t o o om“^) P(J) (t s o < 1 1365*3

2 1368.0 3 1370.5 1349.9

4 1373.4 1347.0 5 1376.2 1343.7

6 1379.0 1340.6 7 1361.8 1337.3

8 1384.7 1334.3 9 1387.6 1331.1

io 1390.2 1326.0 11 1392.9 1324.9

12 1395.6 1321.7 13 1396.2 1318.4

14 1400.9 1315.5 15 1403.5 1312.0

16 1405.9 1308.7 17 1408.6 1306.3 18 1411.2 1302.0 19 1413.5 1298.6

20 1415.8 1296.3 29 Having ohosen the fin® struotur® lin«a and havingassigned tha

J valuta, w® ncm proo®«d to apply th® oombinatlon relations, (19),

( Z 2) 0 and (25), d®riv«d in Part II. In order to magnify th® aoala

of th® plot and tharaby obtain a nor® aoourat® valu® of tha alop® of

tha lin®, a oonatant ia aubtraotad from both aid«a of th® first two

aquations giving for SbH3

A 4 F"(3) - 5(2-3^^ = (*&*-5)0.3 (28)

A z F'C 3 ) - 50 ^ t O (29)

and for SbD^

A lF ”C3l -2.Ca3-*0 =(aB''-2Xaj4i) , (so)

A^F'fJ) -e.Cs.3 -n' = (2.6-2X23 + 0 . (31)

Bquationa 28 and 50 ara plottad in Flguraa 4 and 5. Tha alopsa of tha two llnaa yiald tha following ground stat® (v^*. 0) rotational

constants* for SbH^, B" - 2*955 om“^ and for SbD^, B*"» 1.486 om“^•

In tha diaouaaion to follow tha atarrad quantities will be associated with SbDj and th® unatarrad quantities will refer to SbHg* Tha third

oombination relation (25) ia plottad in Figures 6 and 7 for SbH^ and

SbDg respectively* Tha intaroapts of these plots give th® values of tha band oantara as 1890.9 om“^ and ^ ~ 1556.8 om"^. From the

slopes of the two plots th® differences in th® rotational constants

in tha ground state and th® first axoitad state are found to be

SO B*-Bn ~ —0*031 on”^ and B**— = —0*011 om“^* Using thsss diffsrsnos* and ths BN values determined abovs, ths rotational aonstanta in ths first exolted stats ars obtainsd as B*& 2*904 om-^ and B*1 = 1*475 on^« Ths moment of inertia, — about an axis psrpsnd ioular to ths axis of ths top is rslatsd to ths rotational constant B by ths sxprsssion

Using t s Iusb of ths physioal oonstants given by Du Mond and Cohen^, ths proportionality constant is oaloulatsd to bs

— HO / \ *UlC ~ £7. * IO <^w\ Ovm ^ (33^ and ths momsnta of insrtia ars

I * »* V S 3*# * IO **° c w l ^

> (54)

_*>» —*40 1 1 “■ IVfc35 * IO cjvw _

Ths momsnts of insrtia sxprsassd in tsrms of ths atondo masses, ths pyramid height, h, and / 3 , ths angle bstwssn ons of ths XY bonds and ths axis of ths top, ars

1 * - 3 rw, V (i U ^ " / 3 + ) , (35)

i c = 3 r m -l\ £a/w*/3 j (36) whsrs it is assumed that ths differences bstwssn ths values of ths

31 moment■ of inertia in the ground state* I"* and the equilibrium values* * are small so that I" may be used for I# * M is the mass of the X atom (antimony) and m represents the mass of the Y atom

(hydrogen or deuterium)* and IQ is the moment of inertia about the axis of the top* If the expression for 1 B is divided by the oorres* ponding expression for Ig** the resulting equation is

° . (37)

where it Is assumed that h » h * and BsB*» Let us simplify the expressionby making the following substitution!

M M m B* «H* » R* where the oonstants have the following values for stibenei H» 0*97576* 0 * 0.95271* and R* 0*60037.

Then (37) beoomes

— ~l - 5 (se) L'xi^.^/3 -t- D J

If this equation is solved for & tan^/3* the result la

t ^ / 3 _ K H - SP (39) Z ~ S ~ R

The quantities H* D* and R are all positive with H > D and* therefore*

in order that the angle/ 3 be a real angle* the quantity S must lie DU within the limits R <■ 8 < — Substituting numerioal values for the

32 constants it is found that ths ratio of tha rsolprooals of insrtia must 11s within ths rathsr narrow limits 0*50037* -5 “ * 0.61247• This is equivalent to stating that in ths oass of stibsns ths pyramid apex angle,/3, is sxtrsmsly sensitive to ths ratio of ths B's* Soms lati— tuds exists in choosing ths bsst straight lins through ths points plottad from the combination relations and therefore the values of B and B* are somewhat indeterminate in the third decimal* This in­ determinacy introduces an error in the angle / 3 whloh is estimated to be t 1 °.

When the value of the ratio is substituted in (39) the angle / 3 is found to be / 3 — 64° 40*• This value agrees satisfactorily with the value 56° 48* calculated from ths microwave data of Loomis and Strandberg9* The value of /3 may be substituted into (36) and this equation may then be solved for the pyramid height, h* If the value of h is used in (36), the moment of inertia Iq may bs determined*

Beoause of the uncertainty of the exact value of / 3 these calculations

will be performed for three assumed values of/ 3 , hereafter designated as / 3^ , *nd the results will be used later to determine the most proba­ ble value ofand, therefore, of h and C* When the values of the oonstants ars substituted in (35) we obtain for

I c is oalculated from (36) and is related to C by the equation 33 c _ S 7 J U L ? . ( 4 1 )

Tha rasults or tha calculation* for thraa valuas /3 ^ » uaing both

B and B*# ara aunsnarlcad in Tabla IV*

34 TAB LB IV

B - 2.935 o 64° IO IO 56° h2 (i) 0.968 0.962 0.916 h d ) 0.994 0.976 0.967

IqCIO- 4 0 gm om2) 9.393 9.744 1 0 . 1 0 0

C(oa"^) 2.979 2.672 2.770

I*(1 0 ~*° gm om2) 18.701 19.473 20.186

C*(om"^) 1.491 1.437 1.386

B*= 1.486

54° 65° 6 6 ° h2( i 2) 0.988 0.952 0.916 h(A) 0.994 0.976 0.967

Ic (1 0 “*° gm om2) 9.396 9.745 10.094

C ( on“ ^ ) 2.978 2.872 2.772 iVlCT 4 0 gm om2) c 18.777 19.471 20.174 C*(om“^) 1.490 1.437 1.307

35 Let us now turn our attention to the perpendioular bands )y g and

V Ths shortwave bands, *'2 * *r€ •kown Figures 2 and 5* Figurs 8 shows ths 12 raloron rsgion in ths infrared spsot rum of SbHg* Ths absorption pattsrn rspressnts an overlapping of ths psrpsndioular band*

V 4 * ths parallsl band, V 3 * Ths intsnss absorption maximum at

831 om“^ has bssn assignsd as ths V/ ^ band osntsr and ths intsnss maxi­ mum at 781 om"^ as ths %/ 3 band osntsr* Ths distortsd and oomplsx appsaranos of thsss bands is dus to a strong Coriolis intsraotion be — tween these two fundamentals* Beonuss of this Coriolis interaction, and ths rssulting oomplexity of the spectrum, a detailed analysis of these bands has not been attempted here* It may be mentioned, however, that Nielsen has reoently analyzed the corresponding bands in the spsotrum of arains*

In ths spsotrum of SbDg ths longwave bands were looated in ths

16 to 2 0 mioron rsgion, but ths bands were too weak to permit measur­ ing any struoturs other than the two band oenters and a few lines in the region of overlap between the two bands*

Nielsen7 has indioatsd that for the perpendioular vibration V ^ ths rotational component levels for which J" are nearly unper­ turbed by ths Coriolis intsraotion, and, therefore, these lines should appear in ths apeotrum at their "proper" positions, according to ths frsqusnoy expression (27)

I'tJ,*) * V* - K B - o 1 £*[(» * l3(B't0w) t

t K't&C-C*) -Cfc-B*)] (27)

36 Lst us oonsidsr ths high frequency aids of ths hand 1/ ^ whsrs ths linss arise from transitions A J»tllA K m l|, and whsrs only the

A J a l l , A K = + 1 ast of transitions ars of importanoo bsoauss ths

1 ,AK * - 1 transitions ars wsak relative to ths forsisr ast*

Ths frsqusnoy of tha oomponsnt lins (K** * J" * J) is

W JjJ,) • V , - K e *-c *> + a 3 [(i - S ^ c * - B* ] -» sfe't B ’) ♦ 3 lfc'-c" ) ) («) and ths frsqusnoy of an adjacent oomponsnt lins for whioh

KH « J"(JH - J-l - K") is

M(3-I,T-|) - V , -t-CB'-C.'1) - t a ( 3 - 0 [ ( t - S , ) C “- B * ] + C 3 - l X B ' » B * )

■+C3 ~lf (c'-C*). (4 3 )

Ths diffsrsnos in frsqusnoy, or ths spacing bstwssn successive

linss is given by

a[Ti-S,)c*-B“3 4 (e'tB")tfe. 3 -i)(c'-c"). (4 4 )

If ths diffsrsnoss B'-B** a n d ars small, the spacing is

A V - 2 (| (46)

In othsr words, to a first approximation, ths avsrags spacing

bstwssn suocsssivs oomponsnt linos for whioh J”* Kn is squal to

2(1-? )C* Ths linss on ths high frsausnoy aids of V-* • ■ 4 4

illustratsd in Figurs 6 , that ars farthest from ths band osntsr ars

singls and quits sharp* For thsss linss it is assumed that ths K

87 components all coincide and thus the components for which Kn*=■ J" will lie very near the center of the line* For lines with lower J values lying nearer the band center* the K”» JM oomponsnt is the highest frequency line in eaoh group of K components* From the frequency expression (27) one would expeot the K splitting to increase with Increasing values of J* That the opposite is true in the band

^ is probably due to the faot that the coefficients of K and have finite values and on this side of the band they have opposite signs so that when K becomes large they tend to nullify each other*

This was found to be the oase in the 1/ band of arsine by Nielsen 2 and lloConaghie®* The frequenoies (V* ) of the set of lines ohosen as those for whioh K” =■ J" are listed in Table V*

TABLK V

V (vaoom " ^ ) ■^^(vao <

949*8

941*6 8 .2 o CD 933*6 •

926.7 7.9

917.8 7 .9

909.9 7 .9 00 M 901.8 •

893.9 7.9

665.8 8*1 H 00 877.7 •

869.7 8 .0

38 The average spacing of* this set of lines is found to b« A V " 8*01 o m “ ^.

Substituting this figure in (46) we solve for ^ and obtain

(46)

From the sum rule we may then determine ^ ^ for the short wave

perpendioular band \ / 0 as

(47)

Let us now return to Figures 2 and 3 and consider the shortwave Th ese bands both have the genera l appearperpendioular bands* V These bands both have the general appearperpendioular

anoe of a parallel band in that their P and R branohes eaoh oonsist

essentially of single sets of sharp lines* Because of the way they overlap the lines of the parallel bands* the P branoh lines of these

two perpendioular bands are nearly indistinct except near the band

centers* The apparent absenoe of any K splitting indicates that the coefficients of K and in the term value are quite small* and

the faot that the lines appear sharper in the R branohes than in the A P branches probably indicates that the K and K terms effectively

oanoel on the R side of the bands and add on the P side* In the SbHg

spectrum the R branch lines associated with V g converge less rapidly than the linos associated with 1/^* From the magnitude of the differ-

enoe in convergence the quantity is estimated to be 0 * 0 4 om“^« In the SbD. spectrum the two sets of lines maintain their

relative positions throughout the R branoh* and therefore it is oon -

eluded that the quantity is zero* These two relations

39 provide us with an independent estimate of 5 X and 5^**". If we use the ■values of C listed in Table IV we obtain, for the three values of the angle , the results shown in Table VI*

TABLE VI S 2*<46b) A.

64° —0 • 344 -0.163 4 0.001 -0.003 -0.504 56° -0*394 -0*096 -0.036 -0.034 -0*449 56° -0*466 -0.024 -0.074 -0.071 -0.393

These results suggest that for a value of/3 slightly over 55° ths J g values oaloulated from 1/^ should agree with those oaloulated from 1^ 2 * 1* actually the case* however, it must be remembered that in order to make these calculations the term value expression was simplified s om err/hat and that for this reason the values of $ and Y * are only estimates* Leohner^®, assuming a valence force field, has developed a relation between the normal frequencies, the valence force constants, the atomic masses and the cosine of the pyramid apex angle,/3 * This expression is given in the form 3m v M 1 whar« p » —Id — * H—, f and d art the valence force constants, and X i le related to the normal frequency C«J by the equat ion ~A^TTXC^‘ •

If Equation 49, involving the constants for SbH^, is divided by the corresponding expression for SbD , and the assumption is made that o both molecules have the same geometry and force constants, we obtain

_t o fg-p>o.ug.n (60) VT \* j* vo» ' L-p’-fCa- J .

This expression may be simplified by the following substitutions

(£T) --R' , -P = H T * " D ttnd lr th* p resulting equation is solved for cos g®t

f 0 - / 0 2 * 8 , , C ~ o / 3 - aV5/-0»7T.-^1 - (61)

Onoe the values of the normal frequencies have been determined. Equation 61 may be used to oompute the value of the pyramid apex angle,/3 •

Dennison^® has suggested a method for correcting the observed band oerrters, V to obtain the normal frequencies, Co In molecules where all of the fundamental frequencies transform with about the same factor in going from one lsotopio form to another, the normal frequen­ cies are related to the observed band centers to a good approximation by the following equations* (62)

to J* - y^*o *■ )

In stibene all four of tha fundament a la transform with a factor of approximately 1*40; thus, (62) should represent a good approximation to the normal frequencies, Dennison has derived an expression in­ volving the normal frequencies as followsi

(63)*

^ i C -

A second equation relating the cu ^ is to be had in the Teller-

Red lioh product rule.

(54)

Using (62) to express the j in terms of the V ^ and the

Equations 53 and 54 may be solved simultaneously to obtain the anharmonlo correction factors, ol g and

used in (52) to determine the normal frequencies. This series of calculations has been performed using values of C listed in Table IV

for both sets of '$ values from Table VI* A corresponding series

*This expression is verified independently in Appendix 1

42 of calculations were mad* using valuta derived from th* isotopio form of ths moleouls. Ths results of these oalculotions are sumxnaris in Table VII.

TABLE VII CO Co * 2 *4 2 4 ^2* C04* /3

SbEj- £ 2 (48.)

54° .04690 .01984 1983.0 847.4 1407.9 600*7 53°26* 55° *4809 .01908 1986.2 846.6 1409.1 600.4 o IO

ShHj- 1 2(47)

64° .0606 • 0167 1990.0 644.8 1411.6 699.3 62°46» 66° •0468 • 018C 1986.6 846.4 1409.8 600.2 52°69'

56° •0483 • 0193 1985.7 846.4 1409.3 600.6 52c59*

SM>S-*2*(48b) 64° .04731 •01946 1963.8 847.1 1408.3 600.6 53°50»

55° .04796 .01923 1985.3 646.9 1409.1 600.4 52°321 56° .04911 .01849 1987.2 846.3 1410.1 600.1 62°18 *

In performing these oaloulations it eras found that the enhar­ monic constants, tX 2 and ot4 # *ri sensitive to the fourth significant figure* This introduces some doubt concerning the exaot values of the normal frequencies and the oaloulated angles* Coupled with this

is an estimated error of ± O.lam"*^ in determining the band centers*

It is concluded, therefore, that the normal frequencies are accurate to approximately one wave number and that the angle (3 is oorreot to within — 1*6°. An inspection of Table VII indioates that quantities calculated using J g determined from the shortwave band agree more closely with the corresponding quantities computed from the isotope than do the quantities oaleulatedusing 'S g determined from the long­ wave band- For this reason it ie felt that the Xi. determined from

Vg ***e more nearly correct*

It ia concluded that the most probable value of the pyramid apex angle is/5 - 64.5°. On the basis of this angle and the measured reciprooals of inertia, the probable constants of the molecule are

•uamarized below*

f 3 - 64.B° Qf ^ 89°40'

h = 0.961 ^ - l*6 sl -1 B' 2.936om B*" - 1.486cm"1

LB ^ 9.634xlO"4°gm cm2 I*"=r 18.eSlxlO"40gm om2 -1 C ■= 2.9060m1 C* = 1.463cm"1

O.eSBxlO-40^ om2 1 19.266xlO“40gm om2 C = G* * B* -t" - O.OSlom*1 E*•-£*" = 0.01lem"1

'Z g ' -0.016 ^ . -0.017

$ = -0*480 « -0.472 'S 4 * 0.0476f 0.0193 -1 ~ 1890.9cm V * 1 1368.6cm"1 -1 -1 -1 Vg - 1894.2cm ^ 2 - 1984.2om IS* *■ 1362.00m"1

44 Y

FIGURE I S b H 3 - U , ond l»2 , U, lines indicoted by orrows Slit Wkffh 0.45cm-1

1800 1820 660640

Q

H3)

cm*1 1900 6 2 0680 1940

FIGURE 2 1280 A b s o r p tio n -U adi2, ,ln* niae by indicated V,line* arrows , i»2 U, and j- D b S lt WidthSlit 0,35cm'1 301320 (300 1340 IUE 3 FIGURE Q i cm 1400 u u 1440 j S b H 3or

10 2 0 30

FIGURE 4 SbD. 30

4 N N 20 k I ■> *

10

X 10 20 30

FIGURE 5 INTERCEPT - 1890.9

1890 -

Sb Hj

i

'HWA m

too 200 300

FIGURE 6 INTERCEPT = 1358.8 cm

1358

S b D

1357

1356 h e

1355

100 200

FIGURE 7 Slit Widths 0.55cmH «“t-* 0.35cmH

SbH,- y,an

! < I I I CM ' I I I I 720 740 7 60 780 800 820 840

] w HIL u a .XU-AJ-XAX j i 6 I I I I I CM*1 I I I 820 840 860 880 900 920 940

FIGURE 8 4k TO PUMP

FI6URE 9 100%

8 0 - S - 8 0

6 0 - ^ - 6 0

4 0 - - 4 0

SbH s

20- “ 20

4 .8 5 0 MICRONS ||7 5

FIGURE 10 Appendix 1* Verification of Equation 53* 1 Q Dennison has derived the following expression Involving the perpendicular normal frequencies of two isotopio forms of a pyramidal

XY_ moleculet 3

[ w* k ^ k * (-; % uj* ") J

(53)

>W ( * J f r- V I- r^f J-*- 1 S? + L S' ^ + s« ^ J ,

X A > ^ r J m + Al ) ~ -*_?* *1

J ^ ^ and • If the values of these constants are substituted into (53) the result may be written in the formt

m -r. x ; :us - « * z, z ; (% , ,■ • (55)

x i , * 1 9l

Shaffer^ has obtained expressions for the perpendicular normal frequencies of a pyramidal XY^ molecule as followsi

■ ■ i {(j.'Srla-’sr-ri* F f M > where K,» >i-* and are generalized foroe constants associated with 1 2 5 i i. the perpendicular modes of vibration* Uj ^ and and ^JLA - J J %

55 The 'transformation oosfflolants from the intermediate symmetry coordinates to the normal coordinates are expressed in terms of the force constants as

f f l (57) J 3 ,

2 c 2 where and a are related to the 3 ^ as follows*

(68)

From Equation 56 we obtain

* £ (B9> and

v j £ ] \ co) and from Equation 57 we get

= / (si) and

* - * = ~T—^ ^ <62>

56 Substituting (60) into (62) yislds

H , _ > V * 5 X " = !=. . (63)

Equations 68 and 61 may b« solvsd simultansously to giT*

I + lu X* . (64) and

L * * - J = — 1 (65) S I # X?. - '

Using (64) and (66) Equation 63 bsoomss

✓ ^ i _ b* j J \ =_ jf ( .tin t ( ,f ^ J 1 *■ JI ■» T a . -I (6 6 )

r - (* * w ^ - (jx* - £.) ^ i

* 1 — 2 ^ 1 - Lot us now writs Equation 69 for two isotopio forms of ths

XYj molsouls*

>». >■» A- (67) > < -

(68) >*1 >*>*

67 In general the force constants, will b« different from

th« force oonstarrts for tha i sot ops, however, ths poten—

tial energy of the molecule is expressed in valence coordinates,

then to a good approximation, the resulting valence force constants will be the same for both isotopio forms of the molecule* A compari­

son of the two potential energy expressions shows that the generalised

force constants are related as followsi

> / x * V *. = (i^ i„; *■ j = n> •

Equation 68 may then be expressed in terms of >i_ and /*_ as t X 3

£ - = 1 1 > * ^ > (69)

.tar. X- - ( § f § ; y

Equation 67 and 69 are solved simultaneously for and y% and gives 1 3

(70) »■ I*" < ~ ;

>** V*1 1 Y k * •>•,) - X ( *1 * . (7i)

Substituting these values into (66) yields

[ M I * ( *..» *■'•»*>]

j ^ (72) where ^

(73)

- [ ^ - o ^ o - o r +>*) ] .

A snail amount of algebraic manipulation shows that R is

Identically zero and therefore Equation 72 is equivalent to ths original expression derived by Dennison 19 •

69 BIBLIOGRAPHY

1. Robertson, R., and Fox, J.J., Proo. Roy. Soo. A120, (1928), p. 128.

2. Barker, K.F., Phys. Rev., 33_, (1929), p. 684*

3* Dennison, D.M., and Hardy, J.D., Phys. Rev., 39, (1932), p. 938.

4* Lee, B. and Yfu, O.K., Trans. Faraday Soo., 36, (1939), p. 1366*

5. MoConaghle, V.M., and Nielsen, H.H., Proo. Nat. Aoad. Sol., 34, (1948), p. 456.

6. MoConaghle, V.M., and Nielsen, H.H., Phys. Rev., 76, (1949), p. 633*

7. Nielsen, H.H., Diso. Faraday Soo., 9, (1950), p. 85.

8. Smith, D.C., J. Chem. Phys., 18, (1951), p. 384.

9. Loomis, C.C., and Strandberg, M.W.P., Phys. Rev., 61, (1951), p. 798*

10. Nielsen, H.H., Phys. Rev., 60, (1941), p. 794.

11. Shaffer, W.H., J. Chem. Phys., JJ, (1941), p. 607.

12. Teller, E., Hand-und Jahrb* d. Chem. Phys., vol. 9, II, (1934), p. 43.

13. Dennison, D.M., Phys. Rev., 28, (1926), p. 318*

14. lisllor, J.W., A Comprehensive Treatise on Inorganlo and Theoretioal

Chemistry, Vol. VIII, Longmans, and Co., Nevr York (1928).

15. Thorneyoroft, W.E., Textbook of Inorganlo Chemistry. Vol. VI,

Part 5, J.B. Lippinoott, Philadelphia (1936).

16. Bell, E.E., Noble, R.H., and Nielsen, H.H., Rev. Soi. Inst., 18.

(1947), p. 48.

17. DuMond, J.W.M., and Cohen, E.R., Rev. Mod. Phys., 20, (1948), p. 62.

18. Leohner, F., Site, ber Akad. Wiss. Wien, 141. (1932), p. 633. 19. Dennison, D.M., Phys. Rev., 12. (1940), p. 175.

60 AUTOBIOGRAPHY

I* William Howard Haynie* was born in Royal Oak* Michigan,

July 24* 1923* I obtained my sooondary education at Savannah High Sohool* Savannah* New York* and received a Baohslor of Soienoe degree with a major in physios from the Univarsity of Chioago, Chicago* Illinois* in Juna* 1944* From Juna* 1944* to

Ootobar* 1946* I ha Id a position as physicist with the National

Advisory Committee for Aeronaut!os in the instrument resaaroh seotion of their Cleveland* Ohio* laboratory* From Ootobar* 1946* to Juna* 1951* I was a resaaroh fallow on an Air Material Command projaot under the supervision of Professor R* A* Oatjan* In

June* 1948* I reoeived a degree of Master of Soienoe with a major

in physioa from the Ohio State University. Slnoe Ootobar* 1951*

I have held a graduate assistantship in the Department of Physios*

61