816
J. Phys. Chem. 1993,97, 816-830
Negative Ion Photoelectron Spectroscopy of Cr2 Sepn M.C a y and Doreen C . Leopold’J Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455
Received: July 21, 1992
The 476-5 14-nm photoelectron spectra of Crl-, recorded at 4-meV resolution, show vibrationally resolved transitions to the ground state and to one excited electronic state of neutral Cr2. The measured electron affinity of Cr2 is 0.505 f 0.005 eV. Observed vibrational energies in the I&+ ground state of Cr2 up to v = 9, 3040 cm-1 above the zero point level, fit a Morse potential with we = 480.6 f 0.5 cm-l and w& = 14.1 f 0.3 cm-I. Twenty additional Cr2 levels that are evenly spaced with a 128-cm-I average interval are observed 4880-7320 cm-1 above the 0-0 transition. Based on the measured isotope shift for 52Cr2and 50Cr52Crand other considerations, we assign these as highly excited vibrational levels of the Cr2 ground state. An RKR potential is reported for this state that fits all of the measured vibrational levels to within experimental error. The observed 128-cm-I intervals are similar to the 110-cm-I intervals predicted by Goodgame and Goddard for the 4 s 4 s bonded outer well of a double-minimum ground-state potential. However, the observed intervals occur at much lower energies above the zero-point level than are predicted, and the fitted potential obtained here differs considerably from the MGVB potential. Intensities of transitions to u 1 2 levels in the photoelectron spectrum do not follow a Franck-Condon intensity profile; in addition, they vary dramatically with laser wavelength. Peak spacings from the 0-0 transition, however, are not wavelength dependent. These results indicate that the intensities of these relatively weak spectral features are strongly affected by an indirect photodetachment process involving a resonant autodetaching state of the Crz- anion, a possible assignment for which is proposed. The spectrum also shows a transition to an excited electronic state of neutral Cr2 14 240 f 20 cm-I above the ground state. This excited state has a high vibrational frequency (AGlp) of 574 f 10 cm-I and a short 1.65 f 0.02-A bond length. It is assigned as a %,,+ state with single occupation of the 4sug orbital and the 4suu* orbital. For the ground state of the Cr2- anion, we obtain AGlp = 41 1 f 10 cm-I, ut = 440 f 20 cm-1, w d e = 14 f 6 cm-1, re = 1.705 f 0.010 A, and a bond dissociation energy 0.17 f 0.01 eV lower than that of Cr2. The anion ground state is assigned as a 2&+ state in which the extra electron occupies the 4su,* orbital.
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unchanged from itsground-statevalue (1.6788 A). Similar results have been reported for the analogous transitions of CrMo and Mo2. I Anomalous spectroscopicresults for Cr2 have also been obtained from resonance Raman matrix studies.12J3 Moskovits and co-workersl3 measured the ground-state anharmonicity constant of Cr2 in solid xenon to be 14.5cm-I, considerably higher than the 14-cm-1 values measured for other transition metal dimers.Is2 In addition, the 438.0-cm-I harmonic frequency obtainedin thisstudy’3isshifted by -3Ocm-I from theestimated6 gas-phasevalueof470cm-l,andby 1Ocm-I from the427.5-cm-I value observedl2in an argon matrix. These unusually large matrix shifts indicate that the Cr2 ground-state potential is much more sensitive to the matrix environment than is generally the case for diatomicmolecules with reasonably strong bonds.” Several other spectroscopic studies of matrix-isolated Cr2 have also been reported.16l9 In addition, the measured bond dissociation energy of Cr2 is surprisingly low for a molecule with such a high bond order. This value has recently been remeasured by Hilpert and Ruthardt using a sensitive Knudsen cell-mass spectrometer system and employing a second-law analysis that does not require information about low-lying electronic states.20 The resulting Do value of 1.44 i 0.05 eV (33.2 f 1.2 kcal/mol)20 is actually lower than that of the singly-bonded Cu2 molecule (2.03 f 0.02 eV).2 In contrast, multiply-bonded metal dimers usually have increased bond strengths as compared with the correspondingcoinage metal dimers. Indeed, this increase is considered to provide a quantitative signature of the extent of d-orbital contributions to the chemical bonding.2.21 The complex nature of the bonding in Cr2 can be understood to result, in part, from the large size disparity between the 4s and 3d valence orbitals of the Cr atom. SCF calculations22 indicate that the 4s orbital is about 2.7 times larger than the 3d orbital,
I. Introduction The bare dimers of the open d-shell transition metalslJ provide an opportunity to examine multiple bonds between metal atoms3 in the absence of ligand effects. Among the dimers of the first transition series, Cr2 potentially provides the most extreme example of multiple metal-metal bonding. Since the Cr atom has a high-spin ’S3 ground state with a (3d)5(4s)1valence electron configuration, the spin pairing of two ground-state atoms can produce a 12,+Cr2molecule with a (3d~,)~(3d~,)~(3dL,)~(4su~)~ valence electron configuration and a formal bond order of 6. Several experimental results for Cr2 appear consistent with this bonding picture. Rotationally resolved studies of the intense A X band near 460 nm have shown that the ground state of Cr2 is indeed a IZg+ state.” Its high vibrational frequency6of 452.34 cm-I ( A G , I ~is) indicative of a high bond order. The very short bond length of Crz provides additional evidence for 3d-3d bonding; at 1.6788 A,6 it is only two-thirds of the 2.5-A nearest neighbor distance in metallic chromium.5 The bond in bare Cr2 is thus even shorter than the shortest bonds of 1.8 A that have been observed3 in quadruply-bonded CrZ4+organodichromium complexes. A comparison of the bond length and vibrational frequency of Cr2 to those of the singly 4.9-4s bonded Cu2 molecule (re = 2.2197 A, we = 266.43 ~ m - l ) , in ~ .which ~ the filled (3d)IO atomic orbitals are not directly involved in the bonding,lJ underscores the importance of 3d-3d bonding in Cr2. However, other experimental results reveal that the bonding in Cr2 is considerably more complex than this simple picture would suggest. For example, the excitation of a formally bonding 4sugelectron to a formally antibonding uu*orbital in the A( IC,+) +X(’Zg+)transitionleaves thebondlength (1.6751 A)7virtua11y
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’ NSF Presidential Young Investigator, 1988-1993. 0022-3654/58/2097-08 16$04.00/0
(0
1993 American Chemical Society
Negative Ion Photoelectron Spectroscopy of Cr2 as measured by the expectation values ( r 3 d ) = 0.72 A and ( r d S ) = 1.94 A. Thus, at the equilibrium Cr2 bond length of 1.6788 A, the atoms are at a reasonable distance for 3d-3d bonding but are much too close for optimum 4 s 4 s bonding. Based on these considerations and the results for the A X transitions noted above, it has been suggestedlJOJ1that Cr2 (and its group 6 congeners CrMo and Mo2) actually have a pentuply d-d bonded Mz2+ core surrounded by a nonbonding pair of electrons in a diffuse, Rydberg-like su orbital. In addition, as pointed out by McLean and Liu,22the sizes of the 3p and 3d orbitals of the Cr atom, as measured by the positions of the maxima of their outermost lobes, are virtually identical (0.5 A). Thus, the formation of 3d-3d bonds requires the filled 3p orbitals to move out oftheway toreduceelectron repulsion.IJ2 Theenergy required for this electron rearrangement, as well as the considerable loss of intraatomic exchange energy on 3d-3d bond formation, are two of the factors that contribute to the low bond dissociation energy of Cr2.1J3 Over 30 theoretical studies of Cr2 have been reported, employing ab initio,2z+ local spin density,4’-45Xa,@-46-51 and HiickeP55 techniques. Many of these studies have provided insight into the different effects of the s-s and the various d-d bonds on the ground-state potential energy curve, but perhaps the most striking prediction in this regard was made by Goodgame and Goddard in 1985.32 They used a modified generalized valence bond (MGVB) method in which the correlation error was reduced by subtracting a constant energy from the one-center self-Coulomb integrals to give the experimentally observed difference between the ionization potential and electron affinity of the Cr atom. This approach yielded reasonable values for the Cr2bond length (1.61 A) and bond dissociation energy (De = 1.86 eV),32 a substantial improvement over the results of earlierz6,27(unmodified) GVB calculations that gave re= 3.0 A, De = 0.3 eV, and oe= 110cm-1. The MGVB study also predicted ground- and excited-state potential energy curves for Crz, which have been regarded56 as among the most quantitative yet reported for this molecule. The ground state is calculated to have a double-well potential, dominated by the five 3d-3d bonds at short internuclear distance and by the single 4 s 4 s bond at long distance.32 In the “longbond form” of Cr2, each atomic 3d5 core is high-spin coupled, and the two weakly-interacting 6s cores are antiferromagnetically coupled to produce a singlet state. This outer minimum, which was the only one found in the earlier26.27GVB calculations, is predicted to occur at 3.06 A, and to have a 0.3-eV binding energy and a 0.4-eV barrier to conversion to the 3d-3d bonded form.32 Results of two-color resonance Raman experiments on matrixisolated Cr2by Moskovits and co-workers have been interpret& as possible evidence for this double-minimum ground-state potential.14 Moskovits et al. have also suggested that such a potential might provide a rationale for the unusually large matrix shifts that they observed for this molecule.’3 In contrast, local spin density calculations have yielded quite different results for the Crz ground-state potential. For example, Baykara, McMaster, and Salahub have reported several calculations using different approximations for the exchange and correlation potential^.^^ With correlated (rather than Xa) potentials, these calculations yield excellent results for the bond length (1.68 A) and harmonic frequency (-440 cm-I) and give dissociation energies of 2.0-2.8 eV, depending on the potential used. In contrast to the MGVB result, the ground-state potential is predicted to be highly anharmonic but to contain only a single minimum.@ Local spin density calculations by Delley et a1.,42 Bernholc and Holzwarth,” and Painter45 have yielded similar results. The qualitatively different predictions of the MGVB and local spin density studies of Cr2 have been discussed by several authors.1J4~22~32~42~5658 As hasoften been pointedout, thegroundstate potential energycurve of this molecule provides a particularly
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The Journal of Physical Chemistry, Vol. 97, No. 4, 1993 817 sensitive test of the abilities of different theoretical approaches to model several fundamental aspects of transition metal-metal bonding. These include the relative bonding contributions of the valence d and s orbitals, and the delicate balance between magnetism and chemical bonding, as a function of internuclear separation. Unfortunately, since the highest vibrational level that has been observed experimentally for gas phase Crz is u = 1, and the matrix results are complicatedby unusually large matrix effects, only limited experimental data have been available to test these diverse theoretical predictions of the Cr2ground-state potential. In this paper, we report a study of Cr2 by negative ion photoelectron spectr~scopy,~~ a techniquethat has profitably been used to study a number of other transition metal dimers.As described in our preliminary reports on this the photoelectron spectrum of Cr2- displays about 30 of the vibrational levels of neutral Crz within -7300 cm-’ of its zero-point level. These results, obtained at an instrumental resolution of 4 meV (- 30 cm-I), provide the first panoramic view of the controversial ground-state potential energy curve of this molecule. An RKR potential consistent with these data is compared with theoretical predictions. The unusually long vibrational progression observed in the spectrum displays a highly non-Franck-Condon intensity profile, which varies dramatically with the laser wavelength. These results indicate an indirect photodetachment process involving electronic autodetachment from a resonant autodetaching state of the negative ion about 2 eV above the electron detachment threshold. This propitious resonance enables us to probe regions of the Cr2 ground-state potential that would be inaccessible in a direct photodetachment transition due to negligible FranckCondon factors with the anion ground state. The spectrum also displays a vibrationally resolved transition to a low-lying excited electronic state of neutral Cr2and provides measurements of the ground-state vibrational frequency, bond length, and bond dissociation energy of the Cr2- anion. 11. Experimental Section
These studies employed a new negative ion photoelectron spectrometer that has been described in detail elsewhere.68 Ions are prepared in a flowing afterglow ion-molecule reactor@ equipped with a 2.45-GHz microwave discharge ion source. Although the ions may initially be produced in highly excited states, they are relaxed by lo4-lo5 collisionswith a helium buffer gas and other species in the flow tube. At the end of the tube, a small fraction of the ions passes through a n m n e sampling aperture and into a seriesof three differentiallydiffusion-pumped chambers. In these chambers, electrostatic lenses focus the ions into a beam and accelerate them from the ground potential of the flow tube to 1200 V for mass analysis. Ions are mass-selected by a 90° sector magnet at a resolving power of up to m/Am = 400 (where Am is the full width at half-maximum intensity of a peak at mass m). This capability represents a 10-fold improvement over the mass resolution typically obtained in previous instruments of this type,S997s73which have employed Wien velocity filters for mass selection. The mass-selected ion beam then enters the photoelectron spectroscopy chamber, where it is decelerated to 20 V to increase the interactiontime with the laser and to reduce kinematicspectral broadening. The ion beam is then focused to a tight spot at the intersection with a focused cw argon ion laser beam, which detaches the -extra” electron from the negative ion in a onephoton process. The laser is operated as a four-mirror folded cavity resonator that encloses the photoelectron spectrometer to provide a high circulating power of -100 W at the laser-ion crossing. The laser is usually operated at 488 nm and is tilted at the “magic angle”74to provide a polarization yielding signal intensitiesproportional to average photodetachment cross sections. To obtain a photoelectron spectrum, photoelectrons collected from a small solid angle are energy analyzed by an electrostatic
818 The Journal of Physical Chemistry, Vol. 97, No. 4, 1993
hemisphericalanalyzer typically operated at a constant pass energy of 1.5 V. The spatially dispersed output of the analyzer is detected by a position sensitive microchannel plate array detector, whose output is digitized and signal averaged by a computer. The computer also controls the voltages on the hemispheres and on six additional electron optical elements in the analyzer so as to scan repeatedly through the electron kinetic energy range of interest. The electron energy resolution in the present study, as measured from Lorentzian fits to W- atomic lines, was 4 meV (-30 cm-I). Absolute electron kinetic energies were calibrated with respect to 0-,whose electron detachment energy is accurately known.75 To improve the precision with which vibrational and electronic splittings observed in the spectrum could be measured, special care was taken to reduce errors in the relative electron kinetic enery scale. A very low energy scale compression factor76( 7 ) of 1.001 was routinely achieved by carefully centering the laser over the hemisphere gap (as indicated by the absence of a translation of the image on the electron detector when the analyzer input lenses are defocused), and by focusing the ion beam at the ion-laser crossing to a spot comparable in size to that of the -0.2-mm-diameter laser beam. This tight focus could be achieved for the low (20%) change in the relative intensities of the peaks in the 128-cm-1 progression with respect to each other, or to the 0-0 or 1 0 transitions. While this result does not prove that these features arise from the Cr2- ground state (since collisional relaxation of excited electronic states in the flowing afterglow ion source could be inefficient), it is certainly consistent with that conclusion.
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To determine whether these transitions access highly excited vibrational levels of the Cr2 ground electronic state, or lower vibrational levels of an excited electronic state, we recorded a spectrum of~50Cr52Cr-. In" the mass spectrum shown in Figure " ' " ' ~ ~ ' ' ~ 1, the 5oCr52Cr-peak appears with about 10%the intensity of the main W r 2 - peak, and the two peaks are completely resolved. Figure 6 comparesa portion of the 488-nm photoelectronspectrum of 52Cr2(dashed line) with that of 50Cr52Cr(solid line), both plotted as a function of energy (cm-I) from their respective 0-0 transitions. The 50Cr52Crspectrum was obtained with a 0.1-pA mass selected ion beam,giving 14 000 counts on the 0-0peak after 7 h of signal averaging. All of the peaks in the 5000-6500-cm-1region are observably shifted to higher energy in the 50Cr52Crspectrum. For the seven most intense peaks, whose positions can be measured most accurately, least-squares Lorentzian fits indicate an average isotope shift of 24 cm-I. As noted in Section 11,specialcare was taken during these experiments to reduce errors in the relative electron kinetic energy scale. As a result, we estimate a small experimental uncertainty of f 8 cm-I for the average isotope shift of these seven peaks. As is further discussed in Section IVA3, this relatively large isotope shift of 24 f 8 cm-1 supports an assignment of the 128-cm-l progression to highly excited vibrational levels of the Cr2 ground state. Since no features are observed in the spectrum between the 9 + 0 transition at 3040 cm-l and the 4290-cm-I peak, quantum numbers for the higher energy transitions are uncertain and are given simply as n 0 through n + 12 0 in Table I. As described in Section IVBl, an RKR fit to the spectrum gives the best results for the assignment n = 25. 3. Lon eKE Transition to the Cr2 Excited State. At lower electron kinetic energy, Figure 2 shows a relatively intense transition to an excited electronicstate of neutral Cr2. This region of the spectrum is expanded in Figure 7,which was obtained at 476.5 nm to shift the peaks to higher eKE where our instrumental sensitivity is improved. Peak positions measured from this
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822 The Journal of Physical Chemistry, Vol. 97, No. 4, 1993
TABLE II: Peaks Observed 4000-7500 cm-1 above the CrZ(1&+) = eWavelength height IIof04I
cm-1 from04
width (meVI
5240
0.3
7
5485 5620 5745 5870 5995 6130 6270 6395 6525 6660 6790 6920 7060 7190 7320
0.5 0.7 0.8 1.o 1.2 1.2 1.o 1 .o 0.5 0.4 0.4 0.4 0.3 0.1 0.1
9 8 8 9 8 8 8 9 9 9 7 9 7 7 7
cm-I
from04
4990 5120 5240 5360 5490 5620 5745 5875 6000 6140 6265 6400 6530
height (%of04)
0.2 0.3 0.6 0.8 0.9 1.1 0.8 0.8 0.9 0.5 0.3 0.3 0.3
CrZ-('%+) 0-0 Transition at Different Lurer
496.5 nm (2.496 eV)
488.0 nm (2.540 eV)
476.5 nm (2.601 eV)
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Casey and Leopold
width (meV)
8 10 7 8 9 10 10
IO IO 8 7 8 8
cm-l from04
height (%of04)
514.5 nm (2.409 eV)
width (meV)
4880 5000 5115 5245 5360 5490 5610 5740 5855 6000
0.6 0.7 0.9 1.o 1.1 0.6 0.8 0.8 0.3 0.2
5 9 8 9 8 9 8 9
6265
0.2
9
cm-I from04
height ('KDof0-0)
width (meV)
4290 4570
0.2 0.9
7 10
51 10
0.2
8
5 9
E l e c t r o n K i n e t i c E n e r g y (eV) 0.200 0.300 0.400
0.100
t " ' " " ' ' " ' " " " ' i
0.500
1
I I . , . I , . . , I . I I . I I
JV 0
5500 5000 E n e r g y A b o v e 0-0 T r a n s i t i o n
6500
6000
km-1)
1000 500 0 -500 -1000 E n e r g y Above 0 - 0 T r a n s i t i o n ( c m - 1 )
1500
Figure 7. Expansion of the low electron kinetic energy region of the
Figured Photoelectron spectra of W r 2 (dashed line) and 5oCrS2Cr(solid line) obtained at 488 nm, plotted as a function of cm-I above the 04 transition. For the w e n most intense peaks in the 128-cm-I progression, whose positions can be measured most accurately, the average isotope shift is 24 i 8 cm-I. This large isotope shift provides support for our assignment of these transitions to highly excited vibrational levels of the Cr2 ground state (Section IVA3).
476-nm photoelectron spectrum, showing a transition to an excited electronic state of Cr2 14 240 20 cm-l above the ground state. This excited state has a high vibrational fr uency (AG1/2) of 574 110 cm-I We assign this as a QU+ state and a short bond length of 1.65 i 0.0% in which the 4su, and 4suu* orbitals are each singly occupied (Section IVA2). Hot bands to the right of the 04 transition give we = 440 i 20 cm-l and w g , = 14 i 6 cm-I for the ground state of the Cr2- anion.
spectrum are given in Table I, which also lists the corresponding electron kinetic energies for 488-nm excitation. The intense peak at 0.331-eV eKE in Figure 7 is assigned as the origin of the transition from the ground electronic state of Cr2- to the Crz excited state. Its position gives an excited state energy of 14 240 f 20 cm-' relative to the zero point level of the Crz ground state. A rotational analysis of this transition, using theCr2-bondlengthobtainedinSectionIIIBl and theCr2excitedstate bond length obtained below, indicates an insignificant ( 1 5 cm-I) shift of the origin band due to unresolved rotational structure. The peak to the left of the 0-0 is assigned as the 1 0 transition and indicates an excited state vibrational frequency (AG1/2) of 574 f 10 cm-I. A weaker 2 0 peak is also observed 1125 f 20 cm-l from the origin. Spectra obtained at 488 and 476 nm show no evidence for wavelength-dependent relative intensities in this region. The relative intensities of the two 0-0 transitions in the Cr2- spectrum also did not vary significantly with laser wavelength or intensity, or with the flow tube temperature.
Hot bands to the right of the 0-0 peak give energies of 41 1 f 10,797 f 10, and 1148 f 15 cm-' for the u = 1 through u = 3 levels of the anion. These values yield oc= 440 f 20 cm-I and up, = 14 f 6 cm-I for the Cr2- ground state. A 1 2 sequence band is also observed about 220 cm-' to the right of the 0-0 transition, consistent with the measured values for u = 2 of Crl(797 cm-1) and u = 1 of Cr2 (574 cm-1). To check that the measured relative intensities of these peaks are sufficiently accurate for use in a Franck-Condon analysis, despite the expected reduction in our instrumental sensitivity at very low electron kinetic energies, we recorded spectra of the phenoxide anion at 476 and 488 nm. Accurate relative peak heights for the 364-nm photoelectron spectrum of CbHsO- have recently been reported by Gunion et a1.85 This anion provides an excellent calibrant for relative intensities in this region of the Cr2- spectrum, since the positions of the three main peaks in the spectra of the two anions differ in electron kinetic energy by only 20-30 meV. In addition, recording the phenoxide spectrum at 488 and 476 nm provides intensity calibrations on either side of
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Negative Ion Photoelectron Spectroscopy of Cr2
The Journal of Physical Chemistry, Vol. 97, No.4, 1993 823
each Cr2- peak. At both wavelengths, our measured relative intensities for phenoxide agreed with the previously reported valuesss to within 2096, indicating a similar experimental uncertainty for Cr2- intensity ratios in this region.86 A Franck-Condon fit to the relative intensities of the 0-0 through 2 0 peaks indicates that the bond length in the Cr2 excited state differs from that in Cr2- by 0.052 f 0.010 A. This experimental uncertainty includes contributions from a &40% uncertainty in relative peak heights and from uncertainties in the vibrational constants of the anion and the Cr2 excited state. The higher vibrational frequency in the Cr2 excited state (AGl12 = 574 f 10 cm-I) than in the anion (AG1/2 = 411 f 10 cm-I) suggests that the bond is longer in the anion. This direction for the bond length change also gives a better Franck-Condon fit to the oberved intensity profile. The anion bond length of 1.705 f 0.010 A obtained in Section IIIBl then implies a Cr2 excitedstate bond length of 1.65 f 0.02 A. An anion vibrational temperature of 160 f 20 K is indicated by the intensity ratio of the 0-0 and 0 1 peaks, when the Franck-Condon factors for these transitions are taken into account. This temperature is substantially lower than that of the flow tube, which was heated to 350 K when this spectrum was recorded, consistent with the vibrational cooling expected in the mild supersonic expansion at the nosecone (Section IIIA). However, a Franck-Condon analysis of the relatively intense hot bands from higher levels indicatesthat the anion vibrational levels are not thermally equilibrated.
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Iv. Mscussion A. Electronic-State Assignments. 1. Anion Ground-State Assignment. As noted in the Introduction, the IZg+ ground state of neutral Cr2 has a valence electron configuration that can be denoted concisely as (3d)"3(4s)2andcorrelates with two Cr atoms in their (3d)5(4s)l 7S3ground states. To determine the ground state of the 0 2 - anion, it is useful first to establish whether its valence electron configuration is best described as (3d)Io(4s)3, (3d)ll(4s)2, or (3d)IO(Ss)2(4p)l. Since the atomic Cr- anion has a (3d)s(4s)26S5/2ground state, the combination of a ground-state C r anion with a ground-state Cr atom will give a (3d)lO(4s)3 Cr2- anion. On the other hand, the combination of an excited C r (3d)6(4s)l anion with a ground-state Cr atom, or an excited (3d)6 Cr atom with a ground-state C r ion, could give rise to a (3d)11(4s)2configuration for Crz-. For this to be the groundstate configuration, the additional bonding or exchange stabilization in this configuration must exceed the energy required to promote C r or Cr to its excited state. Although the s to d promotion energy of C r is not known, this value can be estimated from that of theisoelectronicMn atom, which also has a (3d)'(49)2 6Ss/2 ground state. The lowest (3d)6(4s)1excited state of Mn, which is a 6D9/2state, is about 2.1 eV above the ground state.77 The value in Cr- is probably even greater, in view of the increased stability760fthe (n + 1)s orbital relative to the nd orbital in going from the neutrals to the isoelectronic negative ions. For the Cr atom, the promotion energy to the lowest (3d)6 state is 4.4 eV.77 Since the bond energy of Crz is only 1.44 eV and its strongly bonding 3du and 3dr orbitals are already filled, it does not seem possible that the addition of a 3d electron to form the anion could provide sufficiently greater stabilization over the addition of a 4s electron to compensatefor these high 4s to 3d promotion energies. Occupation of the extra electron in a Cr2-orbital of 4s (or perhaps 4p) rather than 3d atomic parentage is also suggested by the similar relative photodetachment cross sectionsobserved in these experiments for the Cr2+ e- 0 2 - ground-state transition and for the atomic Cr(7S3) + eCr-(6Ss/z) or Cr(%2) + eCr(6S5/2)transitions. In contrast, the intensities of these Crs-electron detachments are about 5 times greater than the combined intensities of the fine structure components of the W D J ) + e- Cr(6S5/2)d-electron detachment. In view of
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thesc considerations, we reject the possibility of a (3d)11(4s)2 groundstate for Cr2-. A (3d)10(4~)*(4p)l ground statealsoappears unlikely, in view of the high energetic cost of promoting the Cr atom toits lowest (3d)s(4p)1state (2.9 eV),77or of promoting Mn (isoelectronic with C r ) to its lowest (3d)5(4s)l(4p)l state (2.3 eV).77 Thus, we conclude that the ground-state configuration of Cr2is (3d)lO(4s)3, arising from the Cr[(3d)s(4s)2] Cr[(3d)s(4s)1] ground state asymptote. Since the extent of sd hybridization in the molecule will be limited by the dissilimar spatial extents and energies of these orbitals, it is meaningful to retain the 3d and 4s designationsto indicate the atomic parentage of the u orbitals, whose mixing is symmetry allowed. If a closed-shell (3dug)2(3d..y)4(3d6g)4(4sug)2configuration is assumed for the IZg+ground state of Crz, and if it is also assumed that the addition of the extra electron is not accompanied by substantial electronic rearrangement, then the Cr2- anion can be deduced to have a 2Zu+ground state with a ( 3 d ~ ~3dru)4( ) ~ ( 3d6,)4(4su,)2(4suu*)I valence electron configuration. The slightly reduced vibrational frequency in the anion (w, = 440 20 cm-I) as comparedwith the neutral molecule (we = 480.6 f 0.5 cm-I), the small difference between their bond lengths (1.705 f 0.010 Cr2-, 1.6788A Cr2,assuming this direction for the bond length change based on the frequency shift), and the slightly reduced ion bond strength (1-27 f 0.06 eV Cr2-, 1.44 f 0.05 eV Cr2),all appear reasonable for the addition of the extra electron to the 4suu*orbital. This assignment is also consistent with the electron affinity trend observed among the three group 6 homonuclear transition metal dimers, whose similar photoelectron spectra suggest that the extra electron occupiesthe same type of orbital in all three ions. The measured electron affinities of Cr2 (0.505 eV), Mo2 (0.74 eV),84 and W2 (1.12 eV)n7 are similar to the s-electron affinities68of Cr (0.675 eV), Mo (0.747 eV), and W (1.183 eV), consistent with the occupation of the extra electron in a molecular orbital of s atomic parentage. 2. Cr2 Exdted-StateAssignment. The photoelectron spectrum reveals an excited state of neutral Cr2 at 14 240 f 20 cm-I. Accordingto the propensityrules for photoelectronspectrogcopy,88 this intense transition can be attributed to a one-electron process involving electron detachment without extensive electron rearrangement. Thus, our assignment of a (3dug)2(3dr,)4(3d6,)4(4sug)2(4suu*)~ configuration for Cr2- considerably limits the possible configurations of this excited Cr2 state. Since detachment of the 4su,* electron produces the ground state of Cr2, the excited state must be associated with electron detachment froma 4sug,3dSg,3dr,, or 3du,orbital. Thevibrational frequency is consderably higher in this state ( A G I = ~ 574 f 10 cm-I) than in the anion ( A G I = ~ 41 1 f 10 cm-I), and the Franck-Condon fit to the spectrum (in which both states were modeled as Morse oscillators) suggests that the bond in this excited state is also shorter (1.65 f 0.02 A) than that of Crz- (1.705 f 0.010 A). Thus, this tightly bonded excited state is not likely to result from detachment of an electron from the 3dugor 3dru orbitals, which are the most strongly bonding at these short internuclear separations.22.23 The detachment of a weakly bonding 3dbg electron, producing a (3du,)2(3dru)4(3d6,)~(4sug),2(4suu*)~ excited-state configuration, also does not appear consistent with the observed changes in bond length and frequency on electron detachment. In addition, as noted above, the detachment of an electron from an orbital of 3d atomic parentage is expected to produce a substantially weaker photodetachment transition than a 4s electron d ~ t a c h m e n t .However, ~~ the integrated intensity of the low eKE excited-state transition actually exceeds that of the high eKE ground-state transition, which we have assigned to a 4s electron detachment, when allowance is made for the linear dependenceof the photodetachment c r m sections* on theelectron velocity. Thus, we also reject the possibility that the Cr2excited state is associated with the detachment of a 3db, electron.
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*
824 The Journal of Physical Chemistry, Vol. 97, No. 4, 1993
Casey and Leopold
Therefore, we conclude that the 14 240-cm-l excited Cr2 state 3. 1%-cm-1 Progressh The photoelectron spectra show a observed here is associated with the detachment of a 4sugelectron series of 20 closely spaced peaks between 4880 and 7320 cm-1 from the negative ion. The Cr2-electron configuration proposed abovethe04transition totheCr2groundstate. Resultsdescribed above would then imply a (3d~~)~(3dr,)~(3d6,)~(4sa,)~(4su,*)~ in Section IIIBZ confirm that these transitions, which are each only 51% as intense as the 04 transition, arise from the zeroconfiguration for this excited state, again assuming a one-electron picture for the photodetachment process. Transitions to the IZ,+ point level of the ground state of the Cr2- anion. Although the and 3Zu+ states arising from this configuration are both allowed intensities of these peaks vary dramatically with the wavelength of the photodetachment laser, an unusual phenomenon that is in this experiment, although evidently only one of these is (barely) discussed further in Section IVC, their spacings from the 04 within our spectral range at 476 nm. Since high-spin coupling of the unpaired electronsis expected to be energeticallyfavorable, transition are, as expected, wavelength independent. Thesepeaks, we assign the observed state as 3Zu+. whose average spacing is 128 cm-I, appear to be evenly spaced at our resolution, suggesting that they are vibrational levels of These results can be compared with those previously reported a single electronic state. There are then two reasonable possifor other low-lying excited states of Cr2. Andrews and OzinI7 bilities for the identity of these levels: they may be vibrational report weak absorptions at 719 nm (13 910 cm-I) and 688 nm levels of a low-lying excited electronic state of Cr2 with a (14 540 cm-I) for matrix-isolated Cr2,energies close to the 14240 vibrational frequency of about 128 cm-1, or they may be very cm-l (04)and 14815 cm-l (1 0) gas-phase values obtained highly excited vibrational levels of the !Eg+ ground state. here. However, in analogy with results for V2, the Cr2 matrix absorptions are assignedi7as spin-allowed transitions from the We consider first the possible assignment of these levels to a ground state to a (3d~,)2(3dr,)~(3d6,)~(4su,)2(3d6,*)~ low-lying (54880 cm-I) excited electronic state of Cr2 with a state, which would then also be a singlet state. In contrast, the 128-cm-l vibrationalfrequency. Although no excited electronic considerations discussed above suggest that the state observed states have been predicted17-26~32~51 below 12 000 cm-l to our here isa (3d~~)2(3dr,)~(3d6,)4(4su~)~(4su~*)~tripletstate. Thus, knowledge, this result does not preclude this assignment since it would appear that the state observed in the present experiment most theoretical studies have focwed on theground-state potential. differs from the one accessed in the matrix absorption study. Based on a recently published Badger's rule correlation between we and re for the first transition series dimers,93 which includes The next lowest lying state of Crz that has previously been both ground- and excited-state data, a Cr2state with a frequency observed in the gas phase is at 19 335 c ~ - I . I , * ~ This state has of 128cm-1 would havea bond length of about 2.9 A. Although been assigned as IC,+ on the basis of the rotational structure in resonant two-photon ionization spectra of 52Cr2and s2Cr50Cr,1+*9 we could ordinarily reject the possibility of accessing such a state based on the negligible Franck-Condon factors expected for a but its molecular orbital configuration has not been determined. direct photodetachment transition from the 1.705 A ion, this The vibrational frequency (AGlj2 = 575.2 f 2 cm-I) and bond argument does not apply in this case in view of the indirect nature length (1.635 f 0.010 A) measured for this 'Xu+state are the of this photodetachment transition, which is discussed in Section same, to within the experimental uncertainties, as those of the IVC. excited state observed here (574 f 10 cm-I, 1.65 f 0.02 A). This result suggests that this I&+ state may have the same electron There are, however, at least two strong arguments against this configuration with the 4sug and 4su,* electrons singlet coupled. assignment. First, the 128cm-I progressionobserved here starts In contrast, have suggested this ( 4 s u , , ) ~ ( 4 s ~ ~ * ) ~only 4880 cm-I (0.61 eV) above the zero-point level of the I&+ configuration for the A(IZ,+) state at 21 750 cm-l, which has a ground state. Since the ground state dissociates to ground-state vibrational frequency7(AG1/2)of 396.8 cm-1and a bond length7 atoms and its binding energy is 1.44 eV, such an excited state of 1.6751 A. would have a well depth of at least 0.8 eV. If the true zero-point level of this excited state were lower than the first observed level, The proposed configuration for the excited state observed here or if it dissociated to a higher energy asymptote, then its well correspondsto the promotion of one of the formally bonding 4sug depth would be even greater. However, the low vibrational electrons in the ground state of Cr2 to a formally antibonding frequency of -128 cm-l in this state, corresponding to a long 4suu*orbital. This assignment does not at first appear consistent bond length of -2.9 A, suggests a very weak Cr-Cr interaction with the much higher vibrational frequency in this state (AGI/2 with no 3d-3d bonding. Since the frequency in the ground state = 574 f 10 cm-I) than in the ground state (AGllz = 452.34 is much higher (452 cm-I) and its equilibrium bond length is cm-I). However, it is useful in this context to recall that the much shorter (1.6788 A), it seems highly unlikely that such an vibrational frequency and bond length in the Cr2ground state are excited state would have a well depth as large as 0.8 eV, or 60% themselves anomalous. The ground-state frequency of Cr2 is of the ground-statevalue. For comparison, the 3Z,+ excited state substantially lower than that of V2 (AG1/2 = 528.7 cm-I)?O of matrix-isolated CUI,which also has a low vibrational frequency although the bond in V2 is longer (1.77 A)90,91 and its of 125 f 25 cm-l and a long bond length of 2.48 i 0.03 A, has (3d~a)2(3dx,)4(3d6,)*(4~~,)23Zg- ground state has two fewer an estimated well depth of only 0.14.2 eV.94 The 4 s - 4 ~bonded formally bonding 3d6, electron^.^^,^ These results have been form of Cr2 calculated by Goodgame and Goddard,26J7 which rationalizedg0in terms of the smaller 3d orbitals, and the larger has a similar frequency (1 10 cm-I) and bond length (3.0 A) as ratio of the 4s and 3d orbital sizes, in Cr than in V. According our hypothetical excited state, is predicted to be bound by only to this argument, increased repulsive interactions at the very short 0.3 eV with respect to the ground-state atoms. internuclear distance required for 3d-3d bonding in Cr2 flattens the potential and lowers the frequency. As noted above, the diffuse A second argument against this assignment concernsthe isotope ((~4~) = 1.94 A)2*4su, orbital of Cr2 is not expected to be bonding shift observed in this region of the 52Cr2and 50Cr52Crspectra. at its short equilibrium bond length and may even be somewhat If the first observed member of this "harmonic" progression at repulsive.30 On the other hand, calculations on Cu2- by Baus4880 cm-I were assigned as the transition to the zero point level chlicher and co-workers92 indicate that its diffuse 4suy* orbital of an excited Cr2 electronic state, then the average vibrational has appreciable4pu character, resulting in an extensively polarized energy of the seven strongest members of this progression, whose orbital with relatively little electron density in the internuclear isotope shifts can be most accurately measured, would be 740 region. If a similar picture can be invoked for the diffuse 4suu* cm-I. In the harmonic oscillator approximation, peaks in the orbital in neutral Crz, then it is conceivable that a 4sug to 4su,* Wr52Cr spectrum will be shifted up from those in the 52Crz excitation would shift 4s electron density out of the 3d-3d bonding spectrum by 1% of the vibrational energy, or by an average of region, reducing these repulsive interactions and resulting in a 7 cm-I for these seven peaks. This isotope shift is much smaller higher excited state vibrational frequency. than the 24 f 8-cm-I value that we measure, on average, for these
-
-
-
-
The Journal of Physical Chemistry, Vol. 97, No. 4, 1993 8 s
Negative Ion Photoelectron Spectroscopy of Crl
TABLE Ilk Modifled RKR Potential Obtained for tbe lZg+ 0
2
Ground State
0 452.34d 875 f 10 1280 i 10 1645 f 10 1985 f 15 2300 f 15 2580 f 20 2830 20 3040 f 20
*
4290 i 2W 4570
* 2W
4880 f 20 5000i 15 5115 f 15 5240 15 5360 f 15 5490 f 15 5615 i 15 5745 f 15 5870 f 15 6000f 15 6135 f 15 6265 f 15 6400f 15 6530 f 15 6660 f 20 6790 f 20 6920 f 20 7060 i 20 7190 20 7320 20
*
**
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
0.106 0.187 0.247 0.301 0.353 0.404 0.456 0.510 0.567 0.626 0.689 0.755 0.825 0.897 0.970 1.045 1.117 1.187 1.252 1.310 1.361 1.404 1.438 1.466 1.486 1 SO6 1.523 1.541 1.560 1.579 1.598 1.618 1.638 1.658 1.678 1.697 1.717 1.736 1.755 1.774 1.793 1.812 1.833 1.855
0 452 819 1278 1647 1985 2294 2573 2824 3049 3250 3429 3589 3732 3862 3980 4089 4192 429 1 4387 4484 458 1 468 1 4784 4892 5004 5121 5240 5363 5487 5613 5741 5869 5998 6129 6259 6391 6523 6655 6788 6921 7054 7187 7320
0 0 -4
2 -2 0 6 7 6 -9
-1 -1 1 -12
4 -6
0 -3 3 2 4 1 2 6 6 9 7 5 2 -1 6 3 0
a Average vohrvcdvalues are listed for levels 25000 cm-1detected with goodsignal-to-noise in spectra obtained a t different wavelengths. Among these, different measurements of the same peak differed by < l o cm-I. The inner wall (rmin) was set equal to that of a Morse potential with we and w g x ,as given by the first two terms in the sixth-order polynomial in Section IVBl. These vcplCulat~ values were obtained from a finite differences calculation of the modified RKR potential. Reference 6. * This RKR fit predicted vibrational levels near these two peaks, which were observed only in the 514-nm spectrum. Since the arguments in Section IVA3 do not apply, we consider the assignment of these transitions to the Cr2 groud state to be less certain than those of the others.
transitions. An increased isotope shift can be obtained by assigning the observed levels as higher vibrational levels in the hypothetical Crz excited state, but this would also imply an increased excited state well depth and further strengthen our first argument against this assignment. Based on these arguments, we assign the 128-cm-I progression instead to highly excited vibrational levels of the ground electronic state of Crz. This conclusion is also suggested by the Morse potential fit described in Section IIIBl to the lower vibrational levels in the Cr2ground state, which gave we 480.6 f 0.5 cm-l and upe= 14.1 & 0.3 cm-I. This Morse potential provides an excellent fit to levels up to u = 9,3040 cm-1 above the zero point level. However, these vibrational constants correspond to a bond dissociationenergy of only0.5 eV (4000 cm-I), considerably lower than the experimentally determined value of 1.44 eV (1 1 600 cm-I). This result suggests that the ground-state potential energy
-
curve may exhibit a "shelf" near the Morse-like asymptote at 0.5 eV, but then continue to rise. In its higher energy region, such a potential could conceivably support the series of closely spaced vibrational levels observed here between 4880 and 7320 cm-1 (0.61-0.91 eV). B. Cr2 Grolllld-State Potential. 1. RKR Fitting Procedure. The photoelectron spectra display transitions to at least 29 vibrational levels in the IZg+ ground state of Cr2. These include all of the levels up to u = 9 at 3040 cm-I, and the 20 levels spaced by 128 cm-I between 4880 and 7320 cm-I, which we have also assigned in the last section to the Cr2 ground state. Since the arguments given there do not pertain to the two additional levels observed at 4290 and 4570 cm-I in the 514-nm photoelectron spectrum, which are not spaced from others by this interval, the assignment of these levels to the ground state is less certain. The measured vibrational energies are summarized in column 1 of Table 111, where the average value from Table I1 is given for levels 25000 cm-1 observed with good signal-to-noise in spectra obtained at more than one wavelength.82 To obtain a potential energy curve for the ground state of Cr2 that is consistent with these data, we fit these 29 vibrational levels using the Rydberg-Klein-Rces (RKR) method. The observed vibrational energies were first fit in a least-squares fashion to a sixth-order polynomial in the vibrational quantum number. Since the spectrum does not contain a continuous progressionbetween u = 9 and the first member of the 128-cm-' progression at 4880 cm-I, we initially guessed a quantum number for the 4880-cm-l level and numbered the higher ones sequentially. The six coefficientsobtained from this fit (00, OGO, OGO, *-) were then converteds0 to we, up,, ocyc, etc. These six vibrational constants, the two rotational constants reported previously for Cr2 (Be= 0.2303 cm-1, ac= 0.0038 cm-'),6and theatomic masses were then input to RKRPOT,9S an RKR program purchased from the CPC Program Library. By trying various sequential vibrational assignments for the 20 levels starting at 4880 cm-I, we determined that u = 22-41 was the lowest vibrational numbering that yields an RKR potential whose vibrational levels match all 29 observed levels to within their experimental uncertainties. Assigning this series as u = 2 4 4 3 instead also gave good agreement with the two additional levels observed at 4290 and 4570 cm-1. Increasing thevibrational numbering much beyond this increased the difference between the calculated and observed isotope shifts (see below). Therefore, we chose the 2 4 43 assignment and included all 31 observed levels in the final fit. These assignments, listed in Table 111,gave the following equation for the vibrational energy (in cm-1) above the potential minimum:
-
-
G,(u) = 474.3(u
+
(8.076 X lO-')(u (1.2217 X
- 9.968(u + '/J2
-
+ '/J3 + (5.595 X 10-2)(u + '/2)4 + + (9.184 X 104)(u +
'/2)6
It is unusual to obtain such detailed vibrational information from photoelectron spectroscopy, which is inherently a relatively low resolution technique. However, fitting the exceptionally large number of vibrational levels accessed in the present experiment to within their experimental uncertainties requires that the vibrational constants be specified to the indicated degree of precision. The resulting RKR potential had a double-valued inner wall, a nonphysical result of the limited rotational data. To remedy this situation, we followed a prescription in the and replaced the RKR inner wall by a Morse potential (using values for oCand opeas given by the above quation). The outer wall was then shifted to set the width of the potential at each energy q u a l to that of the RKR potential. Since the vibrational energy levels are sensitive to the width of the potential but not to the details of the inner walI?7 this procedure is expected to yield a
826 The Journal of Physical Chemistry, Vol. 97, No. 4, 1993
.i
7000
5000
5
n G
>' zz
4000
2oool ti 3000
1000
0
I
,
1.5
,
.
I
2.0
.
.
.
.
l
.
2.5 Angstroms
,
I ,
I
3.0
.
,
3.5
F i w 8. Modified RKR potential energy curve for the IZg+ground stateof neutralCr2,obtainedfromafittothe39vibrationallevelsmcasured here, and the value for u = 1 reported in ref 6. Solid lines indicate observed levels, and dashed lines indicate calculated levels that were not observed. The vibrational levels of this potential, calculated using a finite differences method (ref 98), agree with all of the observed values to within their experimental uncertainties (Table 111).
potential whose vibrational levels are very close to those of the original RKR potential. We also adjusted the potential slightly (
