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Theoretical prediction of geometries and vibrational infrared spectra of ruthenium oxide molecules
JOURNAL
OF MOLECULAR
SPECTROSCOPY
150,2 18-22 1 ( 199 I)
Theoretical Prediction of Geometries and Vibrational Infrared Spectra of Ruthenium Oxide Molecules HENDRIK F. HAMEKA Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323
JAMES 0. JENSEN U.S.Army
Chemical Research, Development and Engineering Center, Aberdeen Proving Ground, Maryland 21010
JACK G. KAY’ AND CAREY M. ROSENTHAL Department of Chemistry, Drexel University, Philadelphia, Pennsylvania 19104
GEORGE L. ZIMMERMAN Department of Chemistry, Bryn Mawr College, Bryn Mawr, Pennsylvania 19010
We present computations of the optimized geometries and the corresponding vibrational frequencies of the molecules Ru02, RuOr, and Ru04. The computations utilize the Gaussian 90 Program Package, and they are based on the use of effective core potentials. In the case of RuOr , we obtain a closed shell singlet configuration with a bond angle of 150.6” and also a close and, possibly, lower lying triplet state with a bond angle of 133.7”. The trioxide is trigonal planar and the tetroxide is tetrahedral. On the whole, the calculated vibrational frequencies and geometries agree web with experimental VdUeS. 0 1991 Academic Press, Inc. 1. INTRODUCTION
Recently, some of us presented experimental infrared spectra in an argon matrix at 14 K for a group of ruthenium oxides, namely RuO, Ru02, Ru03, and Ru04 ( 1) . The vibrational assignments were made by comparing the infrared spectra for different isomer substituted species, in particular for different isotopomers with I60 and 180 and with the seven stable isotopes of ruthenium. Frequencies quoted below are for the “*Ru isotope. From the experimental results, the geometries of the dioxide Ru02 and of the trioxide RuOs were also determined. It was found that Ru02 is bent with a bond angle of 149 +- 2” and that Ru03 is trigonal planar. In another similar study (2), we confirmed and strengthened previous results showing that RuOd has a regular tetrahedral structure. Stretching force constants,f, andf,, and geometries were determined from the calculated best fit to all isotopomer frequencies; standard deviations were from 0.1 to 0.3 cm-‘. For RuO and Ru02, anharmonicities were also calculated. For Ru03 and Ru04, calculations were made including bending modes (assumed to be in the 300-400 cm-’ range) and using typical values (from similar molecules) of ’ To whom correspondence should be addressed. 218
0022-2852/P] $3.00 Copyright 0 I99
I by Academic
Pres, Inc.
All rights of reproduction in any form reserved.
COMPUTED
IR FREQUENCIES
AND SHAPES
21’)
the bending and interaction force constants; including bending modes had a negligible effect on the frequencies and geometries deduced. In addition, for Ru03 and Ru04, the sharpness of the lines corresponding to the superposition of identical isotopomer frequencies resulting from degeneracies in exact DY, and Td symmetries confirm more precisely the geometries found as described above. The forbidden vI frequencies (in parentheses) in Table I were calculated from the experimental force constants. It is possible to calculate the energies, geometries, and vibrational frequencies of ruthenium compounds by the introduction of effective core potentials. This procedure was first introduced by Kahn (4). The use of effective core potentials is now conveniently implemented because they have been incorporated in the latest version, Gaussian 90, of the Gaussian Program Package (5). We present the results of our computations on the three molecules RuOz , Ru03, and Ru04, where the computations are performed by using effective core potentials within the framework of the Gaussian 90 Program Package. II. COMPUTATIONS
We used the Gaussian 90 Program Package (5) to evaluate the energies, optimized geometries, and the vibrational frequencies of the three molecules RuOz , RuOj , and RuO,. We do not report computations on RuO because Krauss and Stevens ( 6) reported extensive ab initio MC-SCF calculations on RuO, and we do not feel that we can improve on their calculations. The Gaussian 90 Program Package offers two basis set options for computations based on the use of effective core potentials. The first option, denoted by LANL 1MB, did not lead to satisfactory results, and we decided, therefore, to use the second option, denoted by LANLlDZ, which utilizes an improved quality basis set. In the latter option, the oxygen atoms are represented by Dunning/Huzinaga valence double-zeta functions ( 7) and the ruthenium effective core potentials and basis sets are described by Hay and Wadt (8-10). The computations yield relative intensities of the IR absorption lines which are qualitatively in agreement with experiment. The computed Raman intensities are all zero, however, and this is contrary to well-known selection rules. We believe that the Raman result is due to the lack of intermediate polarizability data in the numerical frequency calculation option of the Gaussian 90 Program Package. Ill. RESULTS AND CONCLUSIONS
Our computations for the Ru04 molecule predict a tetrahedral structure with a bond length Ru-0 of 1.6083 A. We predict nine vibrational frequencies, a two-fold degenerate mode at 398.1 cm-’ with relative IR intensity of 22, another three-fold degenerate mode at 923.1 cm-’ with relative IR intensity of 297, and a non-degenerate mode at 1065.9 cm-’ with zero IR intensity. In summary, the computations predict one strong IR line at 923.1 cm-‘. This agrees exceptionally well with our recent experimental result ( 1, 2) of 9 16.9 cm-’ and the gas phase value (3) of 92 1 cm-’ . Our experimental measurements did not cover the range of the other theoretical frequency at 4 13.2 cm-’ , but the literature value (3) for the u4 bending mode is 336 cm-’ . Our computed A, frequency of 1066 cm-’ is around 20% higher than the reported A, Raman frequency of 885 cm-’ (3). We are unable to offer an explanation for this
220
HAMEKA
ET AL.
discrepancy. A survey of other tetrahedral oxides ( 11) with known frequencies fails to give additional insight. In the case of RuOJ, our computations predict a planar symmetric structure with an Ru-0 bond length of 1.6098 A, almost identical to the Ru04 bond length. We find six vibrational modes, two two-fold degenerate modes at 329.8 cm-’ (IR intensity 13) and at 758.6 cm-’ (IR intensity 146), and two non-degenerate modes at 185.0 cm-’ (IR intensity 27) and at 1054.9 cm-’ (IR intensity zero). Our experimental IR spectrum of Ru03 in the argon matrix (1) shows an absorption line at 893.5 cm-‘, and this corresponds to the theoretical line at 758.6 cm-‘. The difference between the two frequencies is 15.5%, which is a bit larger than we would have expected. Our measurements did not extend below 600 cm-‘, so we have no experimental verification for the other theoretical frequencies. In the case of RuO*, our experiments (I) showed a symmetric structure with a bond angle of 149 + 2”. We also found two IR lines at 926 and at 902 cm-’ , respectively. In our computations for RuOz , we first obtained a closed shell singlet state with an energy E = -165.93659 a.u, a bond angle of 150.6”, and a bond length of 1.5953 A. There are three vibrational modes located at 306.8 cm-’ (IR intensity = 55), 817.2 cm-’ (IR intensity = 8 16), and 1098.2 cm-’ (IR intensity = 2 1). Subsequently, we computed a number of possible triplet configurations by performing single-configuration unrestricted HF computations. We found that one of the triplet states, with the unpaired electrons in (B,) and (Al) orbitals, has a molecular energy E = -165.95276 a.u at an optimized geometry with a bond angle of 122.7” and a bond length of 1.80 A. This energy is 10.14 kcalfmole lower than the closed shell singlet state. We were unable to derive the corresponding vibrational frequencies for this state. It appears that our theoretical results leave a certain degree of uncertainty in assigning them to the experimentally observed configuration of RuOz in the argon matrix ( 1). The computed energies seem to favor the triplet state, but the computed singlet geometry parameters and frequencies are in good agreement with the observations. We do not believe that matrix effects are strong enough in the case of RuOz to affect the relative energies of electronic states of different multiplicities. In view of the fact that the theoretical results for the singlet designated calculation appear to be more complete than for the triplet, we attribute greater credence to the former than to the latter. Table I compares the computed vibrational frequencies and relative infrared intensities, as reported in this paper, with the experimental values as given by McDowell, Asprey, and Haskins (3) for ruthenium tetroxide and by some of us for matrix isolation (I, 2) studies of all the simple oxides of ruthenium. In summary, we have shown that, using effective core potentials within the framework of the Gaussian 90 Program Package, the molecular structures of the ruthenium oxides, Ru02, Ru03, and RuO,, are correctly predicted and that the vibrational frequencies and relative IR intensities, as predicted in the calculations, are generally in reasonable agreement with experiment. ACKNOWLEDGMENT We express our appreciation to CRDEC, U.S. Army, for their support of the work as part of the Laser Standoff Detection Project, Project Number lC162622A553C, Reconnaissance, Detection and Identification. RECEIVED:
April
29, 1991
COMPUTED
IR FREQUENCIES
221
AND SHAPES
TABLE I Comparison of Theoretical and Experimental Values of Vibrational Frequencies and Relative
IR Intensities for the Simple Ruthenium
Theore(itaf IA mtensity
Y
(from Ref. 1 md2) IR. matrix
Oxides
(ff0rn Ref. 3j
gas
Raman
C’CRI, I1q.
gas
liq.
forbidden
885
882
RuO, (T,j)
v,(A,)
1066
0
(682)
v3Cr2)
923
297
917
v2E)
398
0
-
v4V2)
413
22
noi measured
(950) not measured
IR 921
916
913
IR fohidden
322
336
333
330
R’Jos (Dsh) v,(A,‘)
1055
0
va(A2”)
185
v#‘)
759 330
27 146
v4(E’) RuO,
13
893 not measured
IRforbidden
______
(C,,)
v,(A,)
1098
21
vz(A,)
307
55
v3P1
a17
816
I
(927)928’ not measured 902
WJ (C,,) 804’ IW*=B14 w,x,=s.o]
-
834 [We=839 o&=1
B]
Note. RuO is included for purposes of comparison. All wavenumbers are in cm-‘. Intensities are relative intensities. Frequencies in () are not measured, but calculated from force constants derived from the Wilson FG matrix treatment of experimental data in the matrix-isolation experiments described in Refs. ( I ) and (2). * Theoretical values calculated in Ref. (6). ’ This IR line in the matrix was weak and partly obscured.
REFERENCES I. 2. 3. 4. 5.
6. 7.
8. 9. 10.
Il.
J. G. KAY, D. W. GREEN, K. DUCA, AND G. L. ZIMMERMAN, J. Mol. Spectrosc. 138,49-61 (1989). D. W. GREEN, J. G. KAY, G. L. ZIMMERMAN, AND B. A. BALKO, J. Mol. Specfrosc. 138,62-68 ( 1989). R. S. MCDOWELL, L. B. ASPREY, AND L. C. HASKINS,J. Chem. P&s. 56, 5712-5721 (1972). L. R. KAHN, P. BAYBUTT,AND D. G. TRUHLAR,J. Chem. Phys. 65,3826-3853 (1976). H. M. J. FRISCH,M. HEAD-GORDON,G. W. TRUCKS, J. B. FORESMAN,H. B. SCHLEGEL,K. RAGHAVACHARI,M. ROBB,J. S. BINKLEY,C. GONZALEZ,D. J. DEFREES,D. J. Fox, R. A. WHITESIDE, R. SEEGER,C. F. MELIUS,J. BAKER,R. L. MARTIN,L. R. KAHN, J. J. P. STEWART.S. TOPIOL,AND J. A. POPLE,“Gaussian 90, Revision,” Gaussian, Inc., Pittsburgh. PA, 1990. M. KRAUSS AND W. J. STEVENS,J. Chem. Phys. 82,5584-5596 (1985). T. H. DUNNINGAND P. J. HAY, in “Modem Theoretical Chemistry” (H. F. Schaefer, III. Ed.), Vol. 3. p. 1, Plenum Press, New York, NY, 1977. P. J. HAY AND W. R. WADT, J. Chem. Phyx 82,270-283 (1985). W. R. WADT AND P. J. HAY, J. Chem. Phys. 82,284-298 (1985). P. J. HAY ANDW. R. WADT, J. Chem. Phyx 82.299-3 10 ( 1985). K. NAKAMOTO,“infrared and Raman Spectra of Inorganic and Coordination Compounds.” 4th ed., Table B-6, John Wiley & Sons, Inc., New York. 1986.
OF MOLECULAR
SPECTROSCOPY
150,2 18-22 1 ( 199 I)
Theoretical Prediction of Geometries and Vibrational Infrared Spectra of Ruthenium Oxide Molecules HENDRIK F. HAMEKA Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323
JAMES 0. JENSEN U.S.Army
Chemical Research, Development and Engineering Center, Aberdeen Proving Ground, Maryland 21010
JACK G. KAY’ AND CAREY M. ROSENTHAL Department of Chemistry, Drexel University, Philadelphia, Pennsylvania 19104
GEORGE L. ZIMMERMAN Department of Chemistry, Bryn Mawr College, Bryn Mawr, Pennsylvania 19010
We present computations of the optimized geometries and the corresponding vibrational frequencies of the molecules Ru02, RuOr, and Ru04. The computations utilize the Gaussian 90 Program Package, and they are based on the use of effective core potentials. In the case of RuOr , we obtain a closed shell singlet configuration with a bond angle of 150.6” and also a close and, possibly, lower lying triplet state with a bond angle of 133.7”. The trioxide is trigonal planar and the tetroxide is tetrahedral. On the whole, the calculated vibrational frequencies and geometries agree web with experimental VdUeS. 0 1991 Academic Press, Inc. 1. INTRODUCTION
Recently, some of us presented experimental infrared spectra in an argon matrix at 14 K for a group of ruthenium oxides, namely RuO, Ru02, Ru03, and Ru04 ( 1) . The vibrational assignments were made by comparing the infrared spectra for different isomer substituted species, in particular for different isotopomers with I60 and 180 and with the seven stable isotopes of ruthenium. Frequencies quoted below are for the “*Ru isotope. From the experimental results, the geometries of the dioxide Ru02 and of the trioxide RuOs were also determined. It was found that Ru02 is bent with a bond angle of 149 +- 2” and that Ru03 is trigonal planar. In another similar study (2), we confirmed and strengthened previous results showing that RuOd has a regular tetrahedral structure. Stretching force constants,f, andf,, and geometries were determined from the calculated best fit to all isotopomer frequencies; standard deviations were from 0.1 to 0.3 cm-‘. For RuO and Ru02, anharmonicities were also calculated. For Ru03 and Ru04, calculations were made including bending modes (assumed to be in the 300-400 cm-’ range) and using typical values (from similar molecules) of ’ To whom correspondence should be addressed. 218
0022-2852/P] $3.00 Copyright 0 I99
I by Academic
Pres, Inc.
All rights of reproduction in any form reserved.
COMPUTED
IR FREQUENCIES
AND SHAPES
21’)
the bending and interaction force constants; including bending modes had a negligible effect on the frequencies and geometries deduced. In addition, for Ru03 and Ru04, the sharpness of the lines corresponding to the superposition of identical isotopomer frequencies resulting from degeneracies in exact DY, and Td symmetries confirm more precisely the geometries found as described above. The forbidden vI frequencies (in parentheses) in Table I were calculated from the experimental force constants. It is possible to calculate the energies, geometries, and vibrational frequencies of ruthenium compounds by the introduction of effective core potentials. This procedure was first introduced by Kahn (4). The use of effective core potentials is now conveniently implemented because they have been incorporated in the latest version, Gaussian 90, of the Gaussian Program Package (5). We present the results of our computations on the three molecules RuOz , Ru03, and Ru04, where the computations are performed by using effective core potentials within the framework of the Gaussian 90 Program Package. II. COMPUTATIONS
We used the Gaussian 90 Program Package (5) to evaluate the energies, optimized geometries, and the vibrational frequencies of the three molecules RuOz , RuOj , and RuO,. We do not report computations on RuO because Krauss and Stevens ( 6) reported extensive ab initio MC-SCF calculations on RuO, and we do not feel that we can improve on their calculations. The Gaussian 90 Program Package offers two basis set options for computations based on the use of effective core potentials. The first option, denoted by LANL 1MB, did not lead to satisfactory results, and we decided, therefore, to use the second option, denoted by LANLlDZ, which utilizes an improved quality basis set. In the latter option, the oxygen atoms are represented by Dunning/Huzinaga valence double-zeta functions ( 7) and the ruthenium effective core potentials and basis sets are described by Hay and Wadt (8-10). The computations yield relative intensities of the IR absorption lines which are qualitatively in agreement with experiment. The computed Raman intensities are all zero, however, and this is contrary to well-known selection rules. We believe that the Raman result is due to the lack of intermediate polarizability data in the numerical frequency calculation option of the Gaussian 90 Program Package. Ill. RESULTS AND CONCLUSIONS
Our computations for the Ru04 molecule predict a tetrahedral structure with a bond length Ru-0 of 1.6083 A. We predict nine vibrational frequencies, a two-fold degenerate mode at 398.1 cm-’ with relative IR intensity of 22, another three-fold degenerate mode at 923.1 cm-’ with relative IR intensity of 297, and a non-degenerate mode at 1065.9 cm-’ with zero IR intensity. In summary, the computations predict one strong IR line at 923.1 cm-‘. This agrees exceptionally well with our recent experimental result ( 1, 2) of 9 16.9 cm-’ and the gas phase value (3) of 92 1 cm-’ . Our experimental measurements did not cover the range of the other theoretical frequency at 4 13.2 cm-’ , but the literature value (3) for the u4 bending mode is 336 cm-’ . Our computed A, frequency of 1066 cm-’ is around 20% higher than the reported A, Raman frequency of 885 cm-’ (3). We are unable to offer an explanation for this
220
HAMEKA
ET AL.
discrepancy. A survey of other tetrahedral oxides ( 11) with known frequencies fails to give additional insight. In the case of RuOJ, our computations predict a planar symmetric structure with an Ru-0 bond length of 1.6098 A, almost identical to the Ru04 bond length. We find six vibrational modes, two two-fold degenerate modes at 329.8 cm-’ (IR intensity 13) and at 758.6 cm-’ (IR intensity 146), and two non-degenerate modes at 185.0 cm-’ (IR intensity 27) and at 1054.9 cm-’ (IR intensity zero). Our experimental IR spectrum of Ru03 in the argon matrix (1) shows an absorption line at 893.5 cm-‘, and this corresponds to the theoretical line at 758.6 cm-‘. The difference between the two frequencies is 15.5%, which is a bit larger than we would have expected. Our measurements did not extend below 600 cm-‘, so we have no experimental verification for the other theoretical frequencies. In the case of RuO*, our experiments (I) showed a symmetric structure with a bond angle of 149 + 2”. We also found two IR lines at 926 and at 902 cm-’ , respectively. In our computations for RuOz , we first obtained a closed shell singlet state with an energy E = -165.93659 a.u, a bond angle of 150.6”, and a bond length of 1.5953 A. There are three vibrational modes located at 306.8 cm-’ (IR intensity = 55), 817.2 cm-’ (IR intensity = 8 16), and 1098.2 cm-’ (IR intensity = 2 1). Subsequently, we computed a number of possible triplet configurations by performing single-configuration unrestricted HF computations. We found that one of the triplet states, with the unpaired electrons in (B,) and (Al) orbitals, has a molecular energy E = -165.95276 a.u at an optimized geometry with a bond angle of 122.7” and a bond length of 1.80 A. This energy is 10.14 kcalfmole lower than the closed shell singlet state. We were unable to derive the corresponding vibrational frequencies for this state. It appears that our theoretical results leave a certain degree of uncertainty in assigning them to the experimentally observed configuration of RuOz in the argon matrix ( 1). The computed energies seem to favor the triplet state, but the computed singlet geometry parameters and frequencies are in good agreement with the observations. We do not believe that matrix effects are strong enough in the case of RuOz to affect the relative energies of electronic states of different multiplicities. In view of the fact that the theoretical results for the singlet designated calculation appear to be more complete than for the triplet, we attribute greater credence to the former than to the latter. Table I compares the computed vibrational frequencies and relative infrared intensities, as reported in this paper, with the experimental values as given by McDowell, Asprey, and Haskins (3) for ruthenium tetroxide and by some of us for matrix isolation (I, 2) studies of all the simple oxides of ruthenium. In summary, we have shown that, using effective core potentials within the framework of the Gaussian 90 Program Package, the molecular structures of the ruthenium oxides, Ru02, Ru03, and RuO,, are correctly predicted and that the vibrational frequencies and relative IR intensities, as predicted in the calculations, are generally in reasonable agreement with experiment. ACKNOWLEDGMENT We express our appreciation to CRDEC, U.S. Army, for their support of the work as part of the Laser Standoff Detection Project, Project Number lC162622A553C, Reconnaissance, Detection and Identification. RECEIVED:
April
29, 1991
COMPUTED
IR FREQUENCIES
221
AND SHAPES
TABLE I Comparison of Theoretical and Experimental Values of Vibrational Frequencies and Relative
IR Intensities for the Simple Ruthenium
Theore(itaf IA mtensity
Y
(from Ref. 1 md2) IR. matrix
Oxides
(ff0rn Ref. 3j
gas
Raman
C’CRI, I1q.
gas
liq.
forbidden
885
882
RuO, (T,j)
v,(A,)
1066
0
(682)
v3Cr2)
923
297
917
v2E)
398
0
-
v4V2)
413
22
noi measured
(950) not measured
IR 921
916
913
IR fohidden
322
336
333
330
R’Jos (Dsh) v,(A,‘)
1055
0
va(A2”)
185
v#‘)
759 330
27 146
v4(E’) RuO,
13
893 not measured
IRforbidden
______
(C,,)
v,(A,)
1098
21
vz(A,)
307
55
v3P1
a17
816
I
(927)928’ not measured 902
WJ (C,,) 804’ IW*=B14 w,x,=s.o]
-
834 [We=839 o&=1
B]
Note. RuO is included for purposes of comparison. All wavenumbers are in cm-‘. Intensities are relative intensities. Frequencies in () are not measured, but calculated from force constants derived from the Wilson FG matrix treatment of experimental data in the matrix-isolation experiments described in Refs. ( I ) and (2). * Theoretical values calculated in Ref. (6). ’ This IR line in the matrix was weak and partly obscured.
REFERENCES I. 2. 3. 4. 5.
6. 7.
8. 9. 10.
Il.
J. G. KAY, D. W. GREEN, K. DUCA, AND G. L. ZIMMERMAN, J. Mol. Spectrosc. 138,49-61 (1989). D. W. GREEN, J. G. KAY, G. L. ZIMMERMAN, AND B. A. BALKO, J. Mol. Specfrosc. 138,62-68 ( 1989). R. S. MCDOWELL, L. B. ASPREY, AND L. C. HASKINS,J. Chem. P&s. 56, 5712-5721 (1972). L. R. KAHN, P. BAYBUTT,AND D. G. TRUHLAR,J. Chem. Phys. 65,3826-3853 (1976). H. M. J. FRISCH,M. HEAD-GORDON,G. W. TRUCKS, J. B. FORESMAN,H. B. SCHLEGEL,K. RAGHAVACHARI,M. ROBB,J. S. BINKLEY,C. GONZALEZ,D. J. DEFREES,D. J. Fox, R. A. WHITESIDE, R. SEEGER,C. F. MELIUS,J. BAKER,R. L. MARTIN,L. R. KAHN, J. J. P. STEWART.S. TOPIOL,AND J. A. POPLE,“Gaussian 90, Revision,” Gaussian, Inc., Pittsburgh. PA, 1990. M. KRAUSS AND W. J. STEVENS,J. Chem. Phys. 82,5584-5596 (1985). T. H. DUNNINGAND P. J. HAY, in “Modem Theoretical Chemistry” (H. F. Schaefer, III. Ed.), Vol. 3. p. 1, Plenum Press, New York, NY, 1977. P. J. HAY AND W. R. WADT, J. Chem. Phyx 82,270-283 (1985). W. R. WADT AND P. J. HAY, J. Chem. Phys. 82,284-298 (1985). P. J. HAY ANDW. R. WADT, J. Chem. Phyx 82.299-3 10 ( 1985). K. NAKAMOTO,“infrared and Raman Spectra of Inorganic and Coordination Compounds.” 4th ed., Table B-6, John Wiley & Sons, Inc., New York. 1986.