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The 3Πi-3Σ− transition of the SH+ radical ion: Rotational analysis of the 0, 0 band
LETTERS 8. 9. 10. lf. 12. IS.
115
TO THE EDITORS
I). S. MCCLURE, J. Chem. Phys. 19, 670 (1951). G. W. ROBINSON AND R. P. FROSCH, J. Chem. Phys. 37, 1962 (1962); 38, 1187 (1963). M. K. ORLOFF (unpublished results). J. P. BYRNE, E. F. MCCOY, AND I. G. Ross, Australian J. Chem. 18, 1589 (1965). J. L). LAPOSA, E. C. LIM, AND R. E. KELLOGG, J. Chem. Phys. 42,3025 (1965). E. C. LIM AND J. D. Laposa, J. Chem. Phys. 41, 3257 (1964).
Central Research Division, American Cyanamid Company, Stamford, Connecticut 06904 Received Febrctary 2, 1967
The 311i-3Z- Transition Analysis
J. 8. BRINEN, W. AND
of the SH+ Radical
G. HODGSON, M. K. ORLOFF
ion: Rotational
of the 0, 0 Band
Using a crossed beam technique (1,2), in which a collimated stream of H&I or D.$ vapor was excited by a controlled electron source, we previously observed, under low spectral resolution, ultraviolet emission that we attributed to the %i--Ztransition of SH+ or SD+, respectively (3). The considerable gain of emission intensity obtained with an improved excitation source using multiple beams (4) has enabled us to photograph the 0, 0 band of the SH+ spectrum in the 331&3470 A region under much higher resolution. Spectra were taken in the fifth order of a R.E.O.S.C. Hb type grating instrument with a resolution of 60 000 and reciprocal linear dispersion of 4.4 A/mm. The 2- ground state of the SH+ radical ion, isoelectronic with the PH radical, has the electronic configuration KL 3sa~3pvz3pr*; promotion of a 3pu electron to the 3p~ orbital leads to the configuration KL 3su23pu3p?r3 for the *Iii excited state. The three sub-bands observed correspond to the %O + Yz-, a, + %, and a, -+ ?ztransitions, respectively. The order of the sub-levels confirms that %I is an inverted state. Of the 27 possible branches for a *II-Z- transition, the Pnn , & , and R22 branches should have zero intensity if the *II~ state corresponds fully to Hund’s coupling case a (6). Experimentally we observed 25 branches, whose N values run up to between 15 and 20; branches NPlt and ‘& are completely absent while the first lines of the PZZ , Q22 , and R22 branches are P?,(6), &(5), and R22(5). These observations and the results of our analysis of the ~II; state show that the latter corresponds to an intermediate a-b coupling case but rather closer to case a than to case b. The rotational constants I&” and Do” of the ?z- state were determined using the azFz” values in the usual way (6). Values for the spin-splitting constants X” and y” were obtained by use of the appropriate energy equation of Schlapp (7). The results are given in Table I. For the a; state we first calculated the term values by adding the experimental rotational line transition energies on to the ?z- state term values which we previously determined from t,he energy equation of Schlapp. The following sub-band transition origins (extrapolated to J = 0 for the 3~I and ~II? levels), were obtained: 29 675.55 cm-l, 29 912.81 cm-l, and 30 141.71 cm-l, respectively, for the 3~~-2-, %-Z-, and %&ztransit,ions. Since, on this basis, the aIIl level does not lie halfway in energy, we cannot use t,his approximation in order to calculate the spin-orbit coupling constant A’. The terms values of the “IIi state can be obtained, in principle, using the exact Hamiltonian given by Hill and Van Vleck (8). An approximate solution for the energies F,;(J) (where k = 1,2,3) of the alTsub-levels was obtained by Bud6 (9). From the work of Gilbert
116
LETTERS TO THE EDITORS TABLE I CONSTANTSFOR THE X3 2- STATE OF SH+ Be” = 9.1340cm-i. ro” = 1.384~A Dab = 4.88 X 10-&m-i X0” = 5.7L,cm-1; 70” = -O.l6scm-1
TABLE II CONSTANTSFOR THE A3 I& STATE OF SH+ BO’ = 7.474rcm-1; rg’ = 1.53&A Do’ = 6.2, X 10-4cm-1 A’ = -216.4acm-1;s -216.5scm-1 b Co = -5.8scm-1 Ci = +O.lscm-l Ca = -0.26 X 10-4cm-1 To = 29 911.71cm-l
CZ = -0.45 X 10-2cm-1
8 Using Bud6 formula. b Using Gilbert formula. (IO) one can also obtain the relation zFb(J) = B(3J(J + 1) - 1) - D(3J2(J + 1)2 + 6J(J + 1) + 31. The expressions of Gilbert and of Bud6 (adding certain terms neglected by the latter) were used to determine the constants Bo’, DO’, A’ and the transition origin 2’0 (Table II). Formulas derived from the work of Bud6 and of Gilbert were found to be not entirely satisfactory for expressing the %I term values. We were therefore led, in determining A’ and the term values, to consider the possible intervention of spin splitting terms in Y’ and of perturbations due to neighboring Z, II, and A states (11). A study of the &type doubling has also been made on the basis of the theory developed by Hebb (18) for Q states. Hebb showed that it is possible to express the A-type splittings in each sub-level in terms of three constants CO, Cl , and CZ and appropriate matrix elements. We have determined the constants (Table II) CO, Ci , and Cz as well as CS , a fourth constant that we found necessary to add, as did Dixon in his work on NH (IS). The detailed results and discussion will be published elsewhere (11). High resolution studies of the 0, 1 band of SH+ and of the corresponding transition for SD+ are in progress. REFERENCES 1. M. HORANIANDS. LEACH,Corn@. Rend. 248, 2196 (1959). 8. M. HORANIANDS. LEACH,J. Chim. Phys. 68, 825 (1961). 8. M. HORANI,S. LEACH,ANDJ. ROSTAS, “Vie Confbrence Inbrnationale aur les phbnombnes d’ionisation duns les gaz S.E.R.M.A. Paris, 1963,” Vol. I, pp. 45-47. 4. M. HORANI,J. Chim. Phys. 84,331 (1967). 6. P. NOLANANDF. A. JENKINS,Phys. Rev. 60, 943 (1936). 6. G. HERZBERQ, “Molecular Spectra and Molecular Structure,” 2nd ed., Vol. I. Van Nostrand, Princeton, New Jersey, 1950. 7. R. SCHLAPP,Phys. Rev. 39, 806 (1932).
117
LETTERS TO THE EDITORS 8. E. L. HILL AND J. H. VAN VLECK,Phys. Rev. 32, 250 (1923). 9. A. BUD& 2. Physik 06, 219 (1935). 10. C. GILBERT,Phys. Rev. 49, 619 (1936). 11. M. HORANI,S. LEACH,ANDJ. ROSTAS(to be published). 18. M. H. HEBB, Phys. Rev. 49. 610 (1936). 13. R. N. DIXON, Gun. J. Phys. 37, 1171 (1959). Luboratoire de Chimie-Physique, Facultt? des Sciences,
MARCELHORANI, SYDNEYLEACH, AND JO~LLEROSTAS
&say, France Received February
7, 1967
Rotational
Constants
of Quasi-linear
Molecules
The infrared spectrum of isocyanic acid, HNCO was first investigated by Reid (1). One of the interesting features of the spectrum of quasi-linear molecules is that most often the change in the rotational constant A with vibrational state is rather large. Thus, in HNCO, while in the ground state A” = 30.6 cm-l, in the first excited state of the r1 = 777 cm-1 fundamental it increases by fifty percent to A’ = 45.7 cm-i. These values are quoted from the more recent work by Ashby and Werner (2). These authors attribute the large increase in A to Coriolis interaction between the upper state and some other, lying at lower frequencies. Although this may have an effect on the values of A for some states, the main reason for the large changes is not hard to find. In these molecules the least moment of inertia is very small indeed and its relative change on vibrational excitation can be very large, particularly for those vibrations whose excitation causes the molecule to assume an average configuration closer to the linear one. According to these arguments one should also expect some of the centrifugal distortion coefficients to behave differently than for other types of molecules. In fact, the values for Dgn and Hg” reported in these investigations are DK” = 0.17 cm-l and Hg” = 0.6636 cm-l. These values are several orders of magnitude larger than those usually encountered. Similar “anomalies” in other centrifugal distortion coefficients have been reported in the investigations of the microwave spectra of HNCO, HNCS, HNa and their deuterated compounds (3). The coupling between vibrational and rotational motions in quasi-linear molecules can be expected to be very pronounced when one considers that in the transition from a nonlinear to a linear configuration a rotational degree of freedom goes into a vibrational degree of freedom. This clearly suggests that the rotation about the axis of least inertia may be so strongly coupled to the bending vibrations in particuIar, that the separation of these motions effected by the usual methods developed for nonlinear polyatomic molecules may not be the most convenient way to handle these extreme cases. Rather, the effect of the rotation may be treated as creating an effective potential for the vibrational motions, in the same form that the simpler case of diatomic molecules is treated. A first rough approximation is obtained if the HNC bending vibration PPand the rotation about the axis of least inertia are treated in this fashion, neglecting all other degrees of freedom. This affords estimates of the molecular constants a~(, y,, Ad’ - A”, DKn, and HK”. In the harmonic approximation these can be calculated from a knowledge of A and Weonly.
115
TO THE EDITORS
I). S. MCCLURE, J. Chem. Phys. 19, 670 (1951). G. W. ROBINSON AND R. P. FROSCH, J. Chem. Phys. 37, 1962 (1962); 38, 1187 (1963). M. K. ORLOFF (unpublished results). J. P. BYRNE, E. F. MCCOY, AND I. G. Ross, Australian J. Chem. 18, 1589 (1965). J. L). LAPOSA, E. C. LIM, AND R. E. KELLOGG, J. Chem. Phys. 42,3025 (1965). E. C. LIM AND J. D. Laposa, J. Chem. Phys. 41, 3257 (1964).
Central Research Division, American Cyanamid Company, Stamford, Connecticut 06904 Received Febrctary 2, 1967
The 311i-3Z- Transition Analysis
J. 8. BRINEN, W. AND
of the SH+ Radical
G. HODGSON, M. K. ORLOFF
ion: Rotational
of the 0, 0 Band
Using a crossed beam technique (1,2), in which a collimated stream of H&I or D.$ vapor was excited by a controlled electron source, we previously observed, under low spectral resolution, ultraviolet emission that we attributed to the %i--Ztransition of SH+ or SD+, respectively (3). The considerable gain of emission intensity obtained with an improved excitation source using multiple beams (4) has enabled us to photograph the 0, 0 band of the SH+ spectrum in the 331&3470 A region under much higher resolution. Spectra were taken in the fifth order of a R.E.O.S.C. Hb type grating instrument with a resolution of 60 000 and reciprocal linear dispersion of 4.4 A/mm. The 2- ground state of the SH+ radical ion, isoelectronic with the PH radical, has the electronic configuration KL 3sa~3pvz3pr*; promotion of a 3pu electron to the 3p~ orbital leads to the configuration KL 3su23pu3p?r3 for the *Iii excited state. The three sub-bands observed correspond to the %O + Yz-, a, + %, and a, -+ ?ztransitions, respectively. The order of the sub-levels confirms that %I is an inverted state. Of the 27 possible branches for a *II-Z- transition, the Pnn , & , and R22 branches should have zero intensity if the *II~ state corresponds fully to Hund’s coupling case a (6). Experimentally we observed 25 branches, whose N values run up to between 15 and 20; branches NPlt and ‘& are completely absent while the first lines of the PZZ , Q22 , and R22 branches are P?,(6), &(5), and R22(5). These observations and the results of our analysis of the ~II; state show that the latter corresponds to an intermediate a-b coupling case but rather closer to case a than to case b. The rotational constants I&” and Do” of the ?z- state were determined using the azFz” values in the usual way (6). Values for the spin-splitting constants X” and y” were obtained by use of the appropriate energy equation of Schlapp (7). The results are given in Table I. For the a; state we first calculated the term values by adding the experimental rotational line transition energies on to the ?z- state term values which we previously determined from t,he energy equation of Schlapp. The following sub-band transition origins (extrapolated to J = 0 for the 3~I and ~II? levels), were obtained: 29 675.55 cm-l, 29 912.81 cm-l, and 30 141.71 cm-l, respectively, for the 3~~-2-, %-Z-, and %&ztransit,ions. Since, on this basis, the aIIl level does not lie halfway in energy, we cannot use t,his approximation in order to calculate the spin-orbit coupling constant A’. The terms values of the “IIi state can be obtained, in principle, using the exact Hamiltonian given by Hill and Van Vleck (8). An approximate solution for the energies F,;(J) (where k = 1,2,3) of the alTsub-levels was obtained by Bud6 (9). From the work of Gilbert
116
LETTERS TO THE EDITORS TABLE I CONSTANTSFOR THE X3 2- STATE OF SH+ Be” = 9.1340cm-i. ro” = 1.384~A Dab = 4.88 X 10-&m-i X0” = 5.7L,cm-1; 70” = -O.l6scm-1
TABLE II CONSTANTSFOR THE A3 I& STATE OF SH+ BO’ = 7.474rcm-1; rg’ = 1.53&A Do’ = 6.2, X 10-4cm-1 A’ = -216.4acm-1;s -216.5scm-1 b Co = -5.8scm-1 Ci = +O.lscm-l Ca = -0.26 X 10-4cm-1 To = 29 911.71cm-l
CZ = -0.45 X 10-2cm-1
8 Using Bud6 formula. b Using Gilbert formula. (IO) one can also obtain the relation zFb(J) = B(3J(J + 1) - 1) - D(3J2(J + 1)2 + 6J(J + 1) + 31. The expressions of Gilbert and of Bud6 (adding certain terms neglected by the latter) were used to determine the constants Bo’, DO’, A’ and the transition origin 2’0 (Table II). Formulas derived from the work of Bud6 and of Gilbert were found to be not entirely satisfactory for expressing the %I term values. We were therefore led, in determining A’ and the term values, to consider the possible intervention of spin splitting terms in Y’ and of perturbations due to neighboring Z, II, and A states (11). A study of the &type doubling has also been made on the basis of the theory developed by Hebb (18) for Q states. Hebb showed that it is possible to express the A-type splittings in each sub-level in terms of three constants CO, Cl , and CZ and appropriate matrix elements. We have determined the constants (Table II) CO, Ci , and Cz as well as CS , a fourth constant that we found necessary to add, as did Dixon in his work on NH (IS). The detailed results and discussion will be published elsewhere (11). High resolution studies of the 0, 1 band of SH+ and of the corresponding transition for SD+ are in progress. REFERENCES 1. M. HORANIANDS. LEACH,Corn@. Rend. 248, 2196 (1959). 8. M. HORANIANDS. LEACH,J. Chim. Phys. 68, 825 (1961). 8. M. HORANI,S. LEACH,ANDJ. ROSTAS, “Vie Confbrence Inbrnationale aur les phbnombnes d’ionisation duns les gaz S.E.R.M.A. Paris, 1963,” Vol. I, pp. 45-47. 4. M. HORANI,J. Chim. Phys. 84,331 (1967). 6. P. NOLANANDF. A. JENKINS,Phys. Rev. 60, 943 (1936). 6. G. HERZBERQ, “Molecular Spectra and Molecular Structure,” 2nd ed., Vol. I. Van Nostrand, Princeton, New Jersey, 1950. 7. R. SCHLAPP,Phys. Rev. 39, 806 (1932).
117
LETTERS TO THE EDITORS 8. E. L. HILL AND J. H. VAN VLECK,Phys. Rev. 32, 250 (1923). 9. A. BUD& 2. Physik 06, 219 (1935). 10. C. GILBERT,Phys. Rev. 49, 619 (1936). 11. M. HORANI,S. LEACH,ANDJ. ROSTAS(to be published). 18. M. H. HEBB, Phys. Rev. 49. 610 (1936). 13. R. N. DIXON, Gun. J. Phys. 37, 1171 (1959). Luboratoire de Chimie-Physique, Facultt? des Sciences,
MARCELHORANI, SYDNEYLEACH, AND JO~LLEROSTAS
&say, France Received February
7, 1967
Rotational
Constants
of Quasi-linear
Molecules
The infrared spectrum of isocyanic acid, HNCO was first investigated by Reid (1). One of the interesting features of the spectrum of quasi-linear molecules is that most often the change in the rotational constant A with vibrational state is rather large. Thus, in HNCO, while in the ground state A” = 30.6 cm-l, in the first excited state of the r1 = 777 cm-1 fundamental it increases by fifty percent to A’ = 45.7 cm-i. These values are quoted from the more recent work by Ashby and Werner (2). These authors attribute the large increase in A to Coriolis interaction between the upper state and some other, lying at lower frequencies. Although this may have an effect on the values of A for some states, the main reason for the large changes is not hard to find. In these molecules the least moment of inertia is very small indeed and its relative change on vibrational excitation can be very large, particularly for those vibrations whose excitation causes the molecule to assume an average configuration closer to the linear one. According to these arguments one should also expect some of the centrifugal distortion coefficients to behave differently than for other types of molecules. In fact, the values for Dgn and Hg” reported in these investigations are DK” = 0.17 cm-l and Hg” = 0.6636 cm-l. These values are several orders of magnitude larger than those usually encountered. Similar “anomalies” in other centrifugal distortion coefficients have been reported in the investigations of the microwave spectra of HNCO, HNCS, HNa and their deuterated compounds (3). The coupling between vibrational and rotational motions in quasi-linear molecules can be expected to be very pronounced when one considers that in the transition from a nonlinear to a linear configuration a rotational degree of freedom goes into a vibrational degree of freedom. This clearly suggests that the rotation about the axis of least inertia may be so strongly coupled to the bending vibrations in particuIar, that the separation of these motions effected by the usual methods developed for nonlinear polyatomic molecules may not be the most convenient way to handle these extreme cases. Rather, the effect of the rotation may be treated as creating an effective potential for the vibrational motions, in the same form that the simpler case of diatomic molecules is treated. A first rough approximation is obtained if the HNC bending vibration PPand the rotation about the axis of least inertia are treated in this fashion, neglecting all other degrees of freedom. This affords estimates of the molecular constants a~(, y,, Ad’ - A”, DKn, and HK”. In the harmonic approximation these can be calculated from a knowledge of A and Weonly.