A STUDY OF THE FUNDAMENTAL VIBRATION-ROTATION BANDS IN THE INFRARED 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 frequencies. 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 frequency corresponding to the normal frequenoywj, 3 Loomis and Strandberg have obtained microwave 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 ^