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On the Electronic Structure of FeF and Its Cations
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
183, 419–420 (1997)
MS977289
NOTE On the Electronic Structure of FeF and Its Cations Recently, iron monofluoride has been investigated both theoretically (1) and experimentally (2). In a high level ab initio study, Bauschlicher (1) confirmed that the ground state of the molecule should be a 6D (rr[1d 34p 29s]10s ) electronic state (all the orbitals are essentially metallic and those in brackets arise from Fe/ 3d). He found that the 4D state of the same configuration lies 5210 cm01 above the ground state at the MCPF level of calculations. The 4F(rr[1d 34p 39s]) state is calculated to be at 11 073 cm01 . Simultaneously, Ram et al. (2) observed, by Fourier transform emission spectroscopy, the g 4D –a 4D system and, assuming a complete similarity between the FeF and FeH (3) spectra, they assigned it to a transition between the 4D states arising from the Fe/ 3d 64s( 4 D) and 3d 7 ( 4 F) configurations. However, the derivation of the 3d-halides spectra from those of the corresponding hydrides is often deceptive because the ligand charge could be either H / or H 0 . A very instructive and pedagogical case is the NiH molecule: the ligand charge zH is calculated to be /0.538 in the d 9 ( 2 D) s 2 supermultiplet and 00.442 in the d 8 ( 3 F) s 2s* 1 manifold of states (4). In this note we reinvestigate the ordering of the low-lying electronic states of FeF on the basis of combined ab initio and ligand field theory (LFT) calculations (5). The ab initio calculations are based on density functional theory as implemented in the deMon program (6, 7). They were performed on the sextet 6D (rr[1d 34p 29s]10s ), 6P(rr[1d 24p 39s]10s ), and 6S / (rr[1d 24p 29s 2 ]10s ) states since the lowest energy terms of Fe/ (a 6 D, a 4 F, and a 4 D) are expected to give rise to all the low-lying electronic states of FeF. All internal molecular orbitals are fully occupied and keep their atomic character. The valence orbitals are essentially metallic even though they exhibit some mixing with 2p(F). This causes a polarization of the electronic cloud toward fluorine which leads to a lack of negative charge on the iron atom (about 0.47 from Mulliken population analysis). Similarly to Bauschlicher’s results on the ground state, the two remaining sextet states present a nearly Fe d 6s 1 occupation. The energy ordering is consistent with a negatively charged ligand: Te ( 6P ) Å 5960 cm01 and Te ( 6S / ) Å 8232 cm01 . Note that these values deviate from Pouilly et al.’s SCF values (8) by /1460 and /1812 cm01 , respectively. The quartet states, except the 4F, have not been calculated because they could not be well described by a single Slater determinant. The calculated energy of the 4F state is found to lie at 3540 cm01 , 7533 cm01 below the Bauschlicher’s value. This probably results, in a large extent, from the usual energy lowering of the d n configuration with respect to the d n 01s one (1). The ligand field calculations were carried out in Hund’s case (a) for both d 6s( 4,6 D) and d 7 ( 4 F) configurations, separately. First, the matrix of the d 6s configuration was diagonalized and its eigenvalues fitted on the transition energies of our 6P and Bauschlicher’s a 4D states. Then the d 7 matrix was diagonalized by fitting the 4D state on the observed g 4D one (2). The LFT parameters were: d 6s (B 20 Å 15 612 cm01 , B 40 Å 4788 cm01 , G2 Å 962 cm01 , zd Å 0413 cm01 ) and d 7 (B 20 Å 15 202 cm01 , B 40 Å 4580 cm01 , zd Å 0298 cm01 ). The resulting averaged levels are depicted in Fig. 1. The lowest spin–orbit component of the 4F state is found to lie at 10 728 cm01 , in very good agreement with the Bauschlicher’s value (11 073 cm01 ). The 6S / state lies at about 10 520 cm01 , 2288 cm01 above our density functional value. This downward displacement could probably be due to a crystal-field-induced interaction (9) between the zero-order
FIG. 1. Low-lying energy levels of FeF from combined LFT and ab initio calculations. Only the 3d 64s ( 6 D), 3d 64s ( 4 D), and 3d 7 ( 4 F) configurations are considered.
419 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
AID
JMS 7289
/
6t1b$$$141
05-03-97 02:55:12
mspas
420
NOTE
d 6s( 6 D) and d 5s 2 ( 6 S) 6S / states. This interaction yields the B 6S / state and the 2 6S / state calculated by Pouilly et al. at 17 530 cm01 (8). It is clear that the d 7 configuration in FeF is destabilized enough to locate the center of gravity of the quartet states above that of the quartets given by d 6s( 4 D) ( DB 00 (d 6s, d 7 ) Å 7124 cm01 ). All the calculated states are inverted, except the B 6S / state that exhibits the ordering V Å 3/2, 1/2, 5/ 2 because of the spin–orbit interaction with the close lying 4P state (see Fig. 1). Further high level ab initio calculations and high resolution experiments are needed to confirm or refute this energy ordering between the B 6S / spin–orbit components. It should be noted that the estimated spin– orbit constants of the observed 4D states (2) cannot be reproduced with the full ionic model. The second part of this note is devoted to the cation and dication of FeF. The ground state of FeF / is calculated to be a 5D state arising from a 6 s 01 s ionization of the FeF X D state. This is in full agreement with Bauschlicher’s work (1). Furthermore, the ionization energy IP Å 8.21 eV compares very well with the published value, 8.29 eV ( 1). As the Fe–F bond is essentially ionic and the removed electron is mainly metallic, the (Fe– F) / bond can also be viewed as Fe2/ F 0 . However, an analysis of orbital populations shows that this ionic bond presents only 32% of the actual structure. The difference between these LFT and ab initio viewpoints is that the LFT assigns each orbital to one center even if it engulfs the other (5). An extreme case is TiCl / : the 3F ground state (10) and all the lowlying excited states contain an important contribution of the covalent structure (the charge distribution is almost Ti /1.1Cl 00.1 ) even though the overall energy level diagram of this ion turns out to be well described by considering the ionic structure alone (9, 11). Mandich et al. (12) used an energetical criterion to evaluate the importance of the ionic character in the cations. Using this criterion, FeF / and TiCl / can be reasonably described as Fe2/ F 0 and Ti 2/ Cl 0 , respectively (see Table IV and Eq. [3] of Ref. 12). The two quintet states, 5P and 5S / , arising from the same ionization process ( s 01 S ) of the two excited sextets of FeF were also calculated and found to lie at 6110 and 10 337 cm01 , respectively. Finally, the ground state of FeF // is calculated to be 6S / and arises from a d 01 ionization of the X 5D state of FeF / with an ionization energy of 19.47 eV. As for the neutral and the monocation ground states, the X 6S / state of FeF // has an Fe 3d occupation number of roughly 6. The gross Mulliken population gives almost Fe2/ F 0 . This can be rationalized by the fact that, during the dication formation, it is easier to extract two electrons from Fe than one electron from F since IP(Fe/ ) Å 16.18 eV while IP(F) Å 17.42 eV (13). Mandich et al.’s criterion (12) shows in this case the inadequacy of the Fe3/ F 0 ionic picture. In conclusion, the ionic structure of the neutral radical has been used to locate its low-lying electronic states. The ligand field model seems also to be useful to calculate the low energy spectrum of FeF / by using the 3d 6 and 3d 54s configurations of Fe/ .
ACKNOWLEDGMENTS I thank Lars G. M. Pettersson and Olli Launila of Stockholm University for allowing me to use the deMon program and Leonid A. Kaledin from Emory University for sending me his TiCl / results prior to publication. The Centre d’Etudes et de Recherches Laser et Applications is supported by the Ministe`re charge´ de la Recherche, the Re´gion Nord/Pas de Calais, and the Fonds Europe´ens de De´veloppement Economique des Re´gions.
REFERENCES 1. C. W. Bauschlicher, Jr., Chem. Phys. 211, 163–169 (1996). 2. R. S. Ram, P. F. Bernath, and S. P. Davis, J. Mol. Spectrosc. 179, 282– 298 (1996). 3. S. R. Langhoff and C. W. Bauschlicher, Jr., J. Mol. Spectrosc. 141, 243–257 (1990). 4. E. M. Spain and M. D. Morse, J. Chem. Phys. 97, 4641–4660 (1992). 5. J. Schamps, M. Bencheikh, J. C. Barthelat, and R. W. Field, J. Chem. Phys. 103, 8004–8013 (1995). 6. A. St-Amant and D. R. Salahub, Chem. Phys. Lett. 169, 387–392 (1990). 7. A. St-Amant, Ph.D. thesis, University of Montreal, 1991. 8. B. Pouilly, J. Schamps, D. J. W. Lumley, and R. F. Barrow, J. Phys. B 11, 2289–2299 (1978). 9. L. A. Kaledin, J. E. McCord, and M. C. Heaven, J. Mol. Spectrosc. 173, 499–509 (1995). 10. L. A. Kaledin, J. P. Parrish, and M. C. Heaven, ‘‘Abstract ME08, presented at the 51st International Symposium on Molecular Spectroscopy,’’ The Ohio State University, Columbus, OH 1996. 11. L. A. Kaledin and M. C. Heaven, to be submitted for publication. 12. M. L. Mandich, M. L. Steigerwald and W. D. Reents, Jr., J. Am. Chem. Soc. 108, 6197–6202 (1986). 13. C. E. Moore, ‘‘Atomic Energy Levels,’’ Vols. I. and II. National Bureau of Standards, 1949, 1952. M. Bencheikh Laboratoire de Dynamique Mole´culaire et Photonique URA CNRS No. 779 Centre d’Etudes et de Recherches Laser et Applications Universite´ de Lille I UFR de Physique, Baˆt. P5 59655 Villeneuve d’Ascq Cedex, France Received December 23, 1996
Copyright q 1997 by Academic Press
AID
JMS 7289
/
6t1b$$$141
05-03-97 02:55:12
mspas
183, 419–420 (1997)
MS977289
NOTE On the Electronic Structure of FeF and Its Cations Recently, iron monofluoride has been investigated both theoretically (1) and experimentally (2). In a high level ab initio study, Bauschlicher (1) confirmed that the ground state of the molecule should be a 6D (rr[1d 34p 29s]10s ) electronic state (all the orbitals are essentially metallic and those in brackets arise from Fe/ 3d). He found that the 4D state of the same configuration lies 5210 cm01 above the ground state at the MCPF level of calculations. The 4F(rr[1d 34p 39s]) state is calculated to be at 11 073 cm01 . Simultaneously, Ram et al. (2) observed, by Fourier transform emission spectroscopy, the g 4D –a 4D system and, assuming a complete similarity between the FeF and FeH (3) spectra, they assigned it to a transition between the 4D states arising from the Fe/ 3d 64s( 4 D) and 3d 7 ( 4 F) configurations. However, the derivation of the 3d-halides spectra from those of the corresponding hydrides is often deceptive because the ligand charge could be either H / or H 0 . A very instructive and pedagogical case is the NiH molecule: the ligand charge zH is calculated to be /0.538 in the d 9 ( 2 D) s 2 supermultiplet and 00.442 in the d 8 ( 3 F) s 2s* 1 manifold of states (4). In this note we reinvestigate the ordering of the low-lying electronic states of FeF on the basis of combined ab initio and ligand field theory (LFT) calculations (5). The ab initio calculations are based on density functional theory as implemented in the deMon program (6, 7). They were performed on the sextet 6D (rr[1d 34p 29s]10s ), 6P(rr[1d 24p 39s]10s ), and 6S / (rr[1d 24p 29s 2 ]10s ) states since the lowest energy terms of Fe/ (a 6 D, a 4 F, and a 4 D) are expected to give rise to all the low-lying electronic states of FeF. All internal molecular orbitals are fully occupied and keep their atomic character. The valence orbitals are essentially metallic even though they exhibit some mixing with 2p(F). This causes a polarization of the electronic cloud toward fluorine which leads to a lack of negative charge on the iron atom (about 0.47 from Mulliken population analysis). Similarly to Bauschlicher’s results on the ground state, the two remaining sextet states present a nearly Fe d 6s 1 occupation. The energy ordering is consistent with a negatively charged ligand: Te ( 6P ) Å 5960 cm01 and Te ( 6S / ) Å 8232 cm01 . Note that these values deviate from Pouilly et al.’s SCF values (8) by /1460 and /1812 cm01 , respectively. The quartet states, except the 4F, have not been calculated because they could not be well described by a single Slater determinant. The calculated energy of the 4F state is found to lie at 3540 cm01 , 7533 cm01 below the Bauschlicher’s value. This probably results, in a large extent, from the usual energy lowering of the d n configuration with respect to the d n 01s one (1). The ligand field calculations were carried out in Hund’s case (a) for both d 6s( 4,6 D) and d 7 ( 4 F) configurations, separately. First, the matrix of the d 6s configuration was diagonalized and its eigenvalues fitted on the transition energies of our 6P and Bauschlicher’s a 4D states. Then the d 7 matrix was diagonalized by fitting the 4D state on the observed g 4D one (2). The LFT parameters were: d 6s (B 20 Å 15 612 cm01 , B 40 Å 4788 cm01 , G2 Å 962 cm01 , zd Å 0413 cm01 ) and d 7 (B 20 Å 15 202 cm01 , B 40 Å 4580 cm01 , zd Å 0298 cm01 ). The resulting averaged levels are depicted in Fig. 1. The lowest spin–orbit component of the 4F state is found to lie at 10 728 cm01 , in very good agreement with the Bauschlicher’s value (11 073 cm01 ). The 6S / state lies at about 10 520 cm01 , 2288 cm01 above our density functional value. This downward displacement could probably be due to a crystal-field-induced interaction (9) between the zero-order
FIG. 1. Low-lying energy levels of FeF from combined LFT and ab initio calculations. Only the 3d 64s ( 6 D), 3d 64s ( 4 D), and 3d 7 ( 4 F) configurations are considered.
419 0022-2852/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.
AID
JMS 7289
/
6t1b$$$141
05-03-97 02:55:12
mspas
420
NOTE
d 6s( 6 D) and d 5s 2 ( 6 S) 6S / states. This interaction yields the B 6S / state and the 2 6S / state calculated by Pouilly et al. at 17 530 cm01 (8). It is clear that the d 7 configuration in FeF is destabilized enough to locate the center of gravity of the quartet states above that of the quartets given by d 6s( 4 D) ( DB 00 (d 6s, d 7 ) Å 7124 cm01 ). All the calculated states are inverted, except the B 6S / state that exhibits the ordering V Å 3/2, 1/2, 5/ 2 because of the spin–orbit interaction with the close lying 4P state (see Fig. 1). Further high level ab initio calculations and high resolution experiments are needed to confirm or refute this energy ordering between the B 6S / spin–orbit components. It should be noted that the estimated spin– orbit constants of the observed 4D states (2) cannot be reproduced with the full ionic model. The second part of this note is devoted to the cation and dication of FeF. The ground state of FeF / is calculated to be a 5D state arising from a 6 s 01 s ionization of the FeF X D state. This is in full agreement with Bauschlicher’s work (1). Furthermore, the ionization energy IP Å 8.21 eV compares very well with the published value, 8.29 eV ( 1). As the Fe–F bond is essentially ionic and the removed electron is mainly metallic, the (Fe– F) / bond can also be viewed as Fe2/ F 0 . However, an analysis of orbital populations shows that this ionic bond presents only 32% of the actual structure. The difference between these LFT and ab initio viewpoints is that the LFT assigns each orbital to one center even if it engulfs the other (5). An extreme case is TiCl / : the 3F ground state (10) and all the lowlying excited states contain an important contribution of the covalent structure (the charge distribution is almost Ti /1.1Cl 00.1 ) even though the overall energy level diagram of this ion turns out to be well described by considering the ionic structure alone (9, 11). Mandich et al. (12) used an energetical criterion to evaluate the importance of the ionic character in the cations. Using this criterion, FeF / and TiCl / can be reasonably described as Fe2/ F 0 and Ti 2/ Cl 0 , respectively (see Table IV and Eq. [3] of Ref. 12). The two quintet states, 5P and 5S / , arising from the same ionization process ( s 01 S ) of the two excited sextets of FeF were also calculated and found to lie at 6110 and 10 337 cm01 , respectively. Finally, the ground state of FeF // is calculated to be 6S / and arises from a d 01 ionization of the X 5D state of FeF / with an ionization energy of 19.47 eV. As for the neutral and the monocation ground states, the X 6S / state of FeF // has an Fe 3d occupation number of roughly 6. The gross Mulliken population gives almost Fe2/ F 0 . This can be rationalized by the fact that, during the dication formation, it is easier to extract two electrons from Fe than one electron from F since IP(Fe/ ) Å 16.18 eV while IP(F) Å 17.42 eV (13). Mandich et al.’s criterion (12) shows in this case the inadequacy of the Fe3/ F 0 ionic picture. In conclusion, the ionic structure of the neutral radical has been used to locate its low-lying electronic states. The ligand field model seems also to be useful to calculate the low energy spectrum of FeF / by using the 3d 6 and 3d 54s configurations of Fe/ .
ACKNOWLEDGMENTS I thank Lars G. M. Pettersson and Olli Launila of Stockholm University for allowing me to use the deMon program and Leonid A. Kaledin from Emory University for sending me his TiCl / results prior to publication. The Centre d’Etudes et de Recherches Laser et Applications is supported by the Ministe`re charge´ de la Recherche, the Re´gion Nord/Pas de Calais, and the Fonds Europe´ens de De´veloppement Economique des Re´gions.
REFERENCES 1. C. W. Bauschlicher, Jr., Chem. Phys. 211, 163–169 (1996). 2. R. S. Ram, P. F. Bernath, and S. P. Davis, J. Mol. Spectrosc. 179, 282– 298 (1996). 3. S. R. Langhoff and C. W. Bauschlicher, Jr., J. Mol. Spectrosc. 141, 243–257 (1990). 4. E. M. Spain and M. D. Morse, J. Chem. Phys. 97, 4641–4660 (1992). 5. J. Schamps, M. Bencheikh, J. C. Barthelat, and R. W. Field, J. Chem. Phys. 103, 8004–8013 (1995). 6. A. St-Amant and D. R. Salahub, Chem. Phys. Lett. 169, 387–392 (1990). 7. A. St-Amant, Ph.D. thesis, University of Montreal, 1991. 8. B. Pouilly, J. Schamps, D. J. W. Lumley, and R. F. Barrow, J. Phys. B 11, 2289–2299 (1978). 9. L. A. Kaledin, J. E. McCord, and M. C. Heaven, J. Mol. Spectrosc. 173, 499–509 (1995). 10. L. A. Kaledin, J. P. Parrish, and M. C. Heaven, ‘‘Abstract ME08, presented at the 51st International Symposium on Molecular Spectroscopy,’’ The Ohio State University, Columbus, OH 1996. 11. L. A. Kaledin and M. C. Heaven, to be submitted for publication. 12. M. L. Mandich, M. L. Steigerwald and W. D. Reents, Jr., J. Am. Chem. Soc. 108, 6197–6202 (1986). 13. C. E. Moore, ‘‘Atomic Energy Levels,’’ Vols. I. and II. National Bureau of Standards, 1949, 1952. M. Bencheikh Laboratoire de Dynamique Mole´culaire et Photonique URA CNRS No. 779 Centre d’Etudes et de Recherches Laser et Applications Universite´ de Lille I UFR de Physique, Baˆt. P5 59655 Villeneuve d’Ascq Cedex, France Received December 23, 1996
Copyright q 1997 by Academic Press
AID
JMS 7289
/
6t1b$$$141
05-03-97 02:55:12
mspas