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Rotational distortion constants for axially symmetric ZX3Y (Z = Si or Ge; X, Y = H, D, or T) molecules; Sign of the constants in some molecules
JOURNAL OF MOLECULARSPECTROSCOPY8, 73-76 (1962)
Rotational Distortion Constants for Axially Symmetric ZX,Y (Z = Si or Ge; X, Y = H, D, or T) Molecules; Sign of the Constants in Some Molecules G. THYAGARAJ~N Spectroscopy
Laboratory,*
Department
of Physics, Illinois 16, Illinois
Znstitde
of Technology,
Chicago
The rotational distortion constant,s L)J and D.,R have been evaluated for the partially deuteriated and tritiated silane and germane of the axially symmetric ZY,Y type. The procedure used is that of Dowling et al. which is based on Kivelson and Wilson’s method and which makes use of the potential energy constants (F’s) obtained for the symmetry coordinates. It has been found that the sign of D.,K is positive when rp~r (mass of the Y atom) > ,nx (mass of the S atom) and negative when my < )tzx For the pyramidal SE-Z2 (Y and Z are isotopes) molecules, the distortion constants R, and 6~ are positive and R, is negative when wey > n&z ; hut Rg and 6J are negative and Rs is positive when niy < ~LZ I. IXTRODUCTION
Kivelson and Wilson (1) have given a m&hod for calculating the rotational distortion constants from the potential energy constants of molecules. Using symmetry coordinates, Dowling et al. (2) applied this method to some axially symmetric ZX,Y molecules and calculated t,heir rotational distortion constants. Such a procedure calls for a unique det,erminat,ion of t#hepotent’ial energy constants (F’s) corresponding to t,he symmetry roordinat,es. In an earlier invest,igat,ion by Thyagarajan et al. (Y), unique values for the F’s were obt,ained for silane ( SiH4) and germane ( GeH4), using Coriolis coupling constants. In the present investigation, those constants have been transferred to the partially deuteriated and tritiated molecules of t>heaxially symmetric ZX,Y type and rot,ational distortion constants for these molecules have been evaluated by the procedure of Dowling et al. (2). Such an investigation, besides testing t,he feasibility of using symmetry coordinates for these calculations, yields certain informat,ion regarding the changes in the sign of the distortion constant DJKwhen different atomic masses are substituted. II.
POTENTIAL
ENERGY
CONSTANTS
The expressions for t#heelements of the potential energy matrix (F) have been given for molecules of this type by Jones and McDowell (4). The numerical * Publication
No. 157. 73
71
THYAGARAJAN
vales of these for the isotopically substituted silancs and gcrmant~s, from the cwnst,ants listed ill (J ), are given in Tahlc I.
ohtaitwtl
whcrc~~, 6, y, or 6 = J, !I, or z; ( J&),, is the partial derivative, clvaluatrdat cb(lulitwiam, of the a-p caomponent of the moment of inertia tensor with respect to the it#h symmetry coordinat)c; and (:k’P’),k is an element of the matrix in\-vrw to t,he potential energy matrix \vrittcn ill terms of the symmetry coordinatc~s. The (J& lo clcment,s arc give11 in (2). The FP’ matrix is obtained from thr> F’s listed in Table I. The cwstants D,, and I).,, thus ohtaincd for the purtinlt> deut,eriat~d and tritiatcd silanw and germanes are given in Table II. In cwlumll 4 of this table is given the sign of 1 which refers to the displawmcnt~ of the cellter-of-mass of the molcculc from the % atom. This displawmcnt is dcfi11c~1 t)> th(b relation (RI
xherc 91 is t,ht mass of the molwnle, ~1F is the mass of the I7 atom, w.~- is thv mass of the X atom, TVis the Z-I7 bond distance, r2 is t,he Z-----X holid distant, :uld 6 is the X-Y-2 angle. If 0 is tetrahedral or nearly tckahcdral, :i WH B z
ROTATIONAL
J)ISTORTION
CONSTANTS
75
TABLE II ROTATIONAL DISTORTION CONSTANTS FOR THE 8iS1Y AND MOLECULES IS MC/see Molecule __~ .._.. -._ ..~._
GeX3Y (3, I'= H, D, OR T)
DJ
DJK
1
SiHJ) SiH,T SiD,H
0.478 0.311 0.484:’
1.547 1.459
-0.350;‘
+ +
SiD,T SiT,H SiTsD
0.164 0.293 0.167
0.332 -0.322 -0.043
+ _ -
GeHaD GeH3T Gel13H GelIBT GeTsH GeTID
0.425 0.271 0.440 0.148 0 _263 0.157
1.439 1.436 -0.286 0.338 -0.284 -0.045
+ + _ + _
-
* Boyd (see Ref. 11) has obtained 0.500 and -0.378 & 0.06 MC/XC, respectively, D, and DJK from an infrared vibrational-rotational analysis. - 1; and if 1”1= rq = r, 1 can he written
by t’he approximat,e
for
formula
. . . It may be noted The sign of 1 is positive if ~2.y > mx and negative if 1)~~< ~FL_~ from Table II that the sign of D JR is the same as t’he sign of 1. In other words, when TILE> VL~, DJK is positive; and when I)L~ < ~)z.~, D,, is negat’ive. A survey of the earlier 1iterat)ure (2, S-16) shows that this is the case for all the axially symmetric ZX,Y molecules invest,igated so far. The case of CC&H has been the only except#ion where theoret,ical calculations yield a negat,ive value for D,, (2) while the microwave investigat.ion (12) yields a positjive value for this constant. Probably, a reinvestigation of the microwave spectrum of t’his molecule would decide whether or not t,his is truly an exceptional case. In t.his comiection, mention may be made of our previous results (17) for t,he pyramidal XYZz molecules (Y and 2 are isotopes). For these molecules, the const,ant,s Rs and & are positive and t’he constant Rg is negat,ive, when the mass of the Y atom is greater than that of the Z atom; but RE,and 6, are negative and I& is positive when the mass of the Y atom is less than that, of t’he 2 at,om. In ot,her words, the sign of these constanm depends on the location (towards the Y atom or t,he 2 atoms) of t,he cent’er-of-mass wit,h respect t,o t,he perpendicular from the apex to the base of the pyramid. ACKNOWLEDGMENT This work was part of a research program which has been aided by grant,s from the National Science Foundation. The author is thankful for this assistance. The author also wishes to express his grateful thanks to Dr. Forrest F. Cleveland for his kind help. RECEIVED:
April 21, 1961
THTAGARAJAN
76
REFERENCES I. 11. KI~EI,~ON ANI) E. B. WILSON, JR., J. Churl. t’hys. 20, 1575 (1952); 21, 1229 (1953~. %. J. M. I~OWLING, R. Gor,u, ANI) A. G. MEISTER,J. Mol. SpectroscopJJ 1,265 (1957). d. c+. TH~AOARAJAN, J. HERRANZ, AND F. F. CLEVEI,AND. J. &!ol. ~pectroscop!~ 7, 151 (1961).
4. L. H. JONES AND R. S. MVDOWELL,
d. 12Zol. Spedoscopy 3, 632 (1959). 5. W. GORDY, hf. V. SAUTH, END R. F. TRAMB.4RITII0, “Microwave spectroscopy,” pp. 349-56. Wiley, Sew York, 1953. Spedroscopy,” p. 79. McGra~~=Ilill, h’. (‘. H. TOWNES AKD A. L. $VHAWI>Ow, “Microwave New York, 1955. 7. T. A. WIGGINS, E. R. SHL.I,I,, J. M. BENNETT, .~ND I). H. RANK, J. ('him. Ph!/s. 21, 19Kl (1953). 8. I). R. d. BOYD IONS)H. W. THOMPSON, Trarzs.Fnrnrlay Sot. 49, 1281 (1953). 9. I,. F. H. BOGEY, b. Chem. Phys. 21, 830 (1953). 10. W. J. ORVILLE-THOMAS, J. T. Cox, AND W. (+ORI)T,J. ('hen!.Phys. 22, 1718 (19%). II. I). R. J. BOYD, .I. Chem. Ph,ys. 23, 922 (1955). 12. P. pi. WOLFE, J. Chern. Phys. 26, 976 (195ti). IS. C!. A. BARRI-S AND W. %jRI)y, J. Chew&. Phys. 26, 391 (1957). 14. &I. W. LONG, Q. WILLIAMS, AND T. 1,.WEATHERLY, J. Chem. Phys. 33, 508 (1960). 16. 11. W. ROBINSON AND L).A. MCQUTARRIE, .I. C’hem. Phys. 32,556 (1960). ih’. E:. F. DITZEL, 1961 (privat,e communication). 17. G. THYAGARAJAN, S. SI-NDARAM, ANI) F. F. CLEVELAND, J. Mol. Spectroscopy 5, 305 (1960).
Rotational Distortion Constants for Axially Symmetric ZX,Y (Z = Si or Ge; X, Y = H, D, or T) Molecules; Sign of the Constants in Some Molecules G. THYAGARAJ~N Spectroscopy
Laboratory,*
Department
of Physics, Illinois 16, Illinois
Znstitde
of Technology,
Chicago
The rotational distortion constant,s L)J and D.,R have been evaluated for the partially deuteriated and tritiated silane and germane of the axially symmetric ZY,Y type. The procedure used is that of Dowling et al. which is based on Kivelson and Wilson’s method and which makes use of the potential energy constants (F’s) obtained for the symmetry coordinates. It has been found that the sign of D.,K is positive when rp~r (mass of the Y atom) > ,nx (mass of the S atom) and negative when my < )tzx For the pyramidal SE-Z2 (Y and Z are isotopes) molecules, the distortion constants R, and 6~ are positive and R, is negative when wey > n&z ; hut Rg and 6J are negative and Rs is positive when niy < ~LZ I. IXTRODUCTION
Kivelson and Wilson (1) have given a m&hod for calculating the rotational distortion constants from the potential energy constants of molecules. Using symmetry coordinates, Dowling et al. (2) applied this method to some axially symmetric ZX,Y molecules and calculated t,heir rotational distortion constants. Such a procedure calls for a unique det,erminat,ion of t#hepotent’ial energy constants (F’s) corresponding to t,he symmetry roordinat,es. In an earlier invest,igat,ion by Thyagarajan et al. (Y), unique values for the F’s were obt,ained for silane ( SiH4) and germane ( GeH4), using Coriolis coupling constants. In the present investigation, those constants have been transferred to the partially deuteriated and tritiated molecules of t>heaxially symmetric ZX,Y type and rot,ational distortion constants for these molecules have been evaluated by the procedure of Dowling et al. (2). Such an investigation, besides testing t,he feasibility of using symmetry coordinates for these calculations, yields certain informat,ion regarding the changes in the sign of the distortion constant DJKwhen different atomic masses are substituted. II.
POTENTIAL
ENERGY
CONSTANTS
The expressions for t#heelements of the potential energy matrix (F) have been given for molecules of this type by Jones and McDowell (4). The numerical * Publication
No. 157. 73
71
THYAGARAJAN
vales of these for the isotopically substituted silancs and gcrmant~s, from the cwnst,ants listed ill (J ), are given in Tahlc I.
ohtaitwtl
whcrc~~, 6, y, or 6 = J, !I, or z; ( J&),, is the partial derivative, clvaluatrdat cb(lulitwiam, of the a-p caomponent of the moment of inertia tensor with respect to the it#h symmetry coordinat)c; and (:k’P’),k is an element of the matrix in\-vrw to t,he potential energy matrix \vrittcn ill terms of the symmetry coordinatc~s. The (J& lo clcment,s arc give11 in (2). The FP’ matrix is obtained from thr> F’s listed in Table I. The cwstants D,, and I).,, thus ohtaincd for the purtinlt> deut,eriat~d and tritiatcd silanw and germanes are given in Table II. In cwlumll 4 of this table is given the sign of 1 which refers to the displawmcnt~ of the cellter-of-mass of the molcculc from the % atom. This displawmcnt is dcfi11c~1 t)> th(b relation (RI
xherc 91 is t,ht mass of the molwnle, ~1F is the mass of the I7 atom, w.~- is thv mass of the X atom, TVis the Z-I7 bond distance, r2 is t,he Z-----X holid distant, :uld 6 is the X-Y-2 angle. If 0 is tetrahedral or nearly tckahcdral, :i WH B z
ROTATIONAL
J)ISTORTION
CONSTANTS
75
TABLE II ROTATIONAL DISTORTION CONSTANTS FOR THE 8iS1Y AND MOLECULES IS MC/see Molecule __~ .._.. -._ ..~._
GeX3Y (3, I'= H, D, OR T)
DJ
DJK
1
SiHJ) SiH,T SiD,H
0.478 0.311 0.484:’
1.547 1.459
-0.350;‘
+ +
SiD,T SiT,H SiTsD
0.164 0.293 0.167
0.332 -0.322 -0.043
+ _ -
GeHaD GeH3T Gel13H GelIBT GeTsH GeTID
0.425 0.271 0.440 0.148 0 _263 0.157
1.439 1.436 -0.286 0.338 -0.284 -0.045
+ + _ + _
-
* Boyd (see Ref. 11) has obtained 0.500 and -0.378 & 0.06 MC/XC, respectively, D, and DJK from an infrared vibrational-rotational analysis. - 1; and if 1”1= rq = r, 1 can he written
by t’he approximat,e
for
formula
. . . It may be noted The sign of 1 is positive if ~2.y > mx and negative if 1)~~< ~FL_~ from Table II that the sign of D JR is the same as t’he sign of 1. In other words, when TILE> VL~, DJK is positive; and when I)L~ < ~)z.~, D,, is negat’ive. A survey of the earlier 1iterat)ure (2, S-16) shows that this is the case for all the axially symmetric ZX,Y molecules invest,igated so far. The case of CC&H has been the only except#ion where theoret,ical calculations yield a negat,ive value for D,, (2) while the microwave investigat.ion (12) yields a positjive value for this constant. Probably, a reinvestigation of the microwave spectrum of t’his molecule would decide whether or not t,his is truly an exceptional case. In t.his comiection, mention may be made of our previous results (17) for t,he pyramidal XYZz molecules (Y and 2 are isotopes). For these molecules, the const,ant,s Rs and & are positive and t’he constant Rg is negat,ive, when the mass of the Y atom is greater than that of the Z atom; but RE,and 6, are negative and I& is positive when the mass of the Y atom is less than that, of t’he 2 at,om. In ot,her words, the sign of these constanm depends on the location (towards the Y atom or t,he 2 atoms) of t,he cent’er-of-mass wit,h respect t,o t,he perpendicular from the apex to the base of the pyramid. ACKNOWLEDGMENT This work was part of a research program which has been aided by grant,s from the National Science Foundation. The author is thankful for this assistance. The author also wishes to express his grateful thanks to Dr. Forrest F. Cleveland for his kind help. RECEIVED:
April 21, 1961
THTAGARAJAN
76
REFERENCES I. 11. KI~EI,~ON ANI) E. B. WILSON, JR., J. Churl. t’hys. 20, 1575 (1952); 21, 1229 (1953~. %. J. M. I~OWLING, R. Gor,u, ANI) A. G. MEISTER,J. Mol. SpectroscopJJ 1,265 (1957). d. c+. TH~AOARAJAN, J. HERRANZ, AND F. F. CLEVEI,AND. J. &!ol. ~pectroscop!~ 7, 151 (1961).
4. L. H. JONES AND R. S. MVDOWELL,
d. 12Zol. Spedoscopy 3, 632 (1959). 5. W. GORDY, hf. V. SAUTH, END R. F. TRAMB.4RITII0, “Microwave spectroscopy,” pp. 349-56. Wiley, Sew York, 1953. Spedroscopy,” p. 79. McGra~~=Ilill, h’. (‘. H. TOWNES AKD A. L. $VHAWI>Ow, “Microwave New York, 1955. 7. T. A. WIGGINS, E. R. SHL.I,I,, J. M. BENNETT, .~ND I). H. RANK, J. ('him. Ph!/s. 21, 19Kl (1953). 8. I). R. d. BOYD IONS)H. W. THOMPSON, Trarzs.Fnrnrlay Sot. 49, 1281 (1953). 9. I,. F. H. BOGEY, b. Chem. Phys. 21, 830 (1953). 10. W. J. ORVILLE-THOMAS, J. T. Cox, AND W. (+ORI)T,J. ('hen!.Phys. 22, 1718 (19%). II. I). R. J. BOYD, .I. Chem. Ph,ys. 23, 922 (1955). 12. P. pi. WOLFE, J. Chern. Phys. 26, 976 (195ti). IS. C!. A. BARRI-S AND W. %jRI)y, J. Chew&. Phys. 26, 391 (1957). 14. &I. W. LONG, Q. WILLIAMS, AND T. 1,.WEATHERLY, J. Chem. Phys. 33, 508 (1960). 16. 11. W. ROBINSON AND L).A. MCQUTARRIE, .I. C’hem. Phys. 32,556 (1960). ih’. E:. F. DITZEL, 1961 (privat,e communication). 17. G. THYAGARAJAN, S. SI-NDARAM, ANI) F. F. CLEVELAND, J. Mol. Spectroscopy 5, 305 (1960).