7808
J . Phys. Chem. 1990, 94. 7808-781 1
Those of geometry c in Figure 1 are L, = 13.26 A (average diameter) and L, = 9.73 A. Substitution of these values into eq 1 gives energy increases for geometries b and c of Figure 1, 1.60 and 1.62 eV, respectively. The increment in transition energies due to variation from geometry b to c results in only 0.02 eV, while the average increment in single-electron transition energies between geometries b and c is 0.80 eV in the rigorous ab initio calculations (Table Ill). Finally, geometry c of Figure 1 was frozen, except for the central iodine atoms on the top and bottom layers (Io atoms). The z coordinates of these atoms alone were optimized (Figure Id, Table I, column d). The equilibrium geometry in this scheme corresponds to the lowest total valence energy of all Pb12 clusters studied. (The system was not fully optimized in all four degrees of freedom because of computational limitations.) The final optimum geometry is quasi-spherical. Variation from geometries c to d of Figure 1 resulted in state crossings, blue-shifted UV spectra (Table 111, column d) and the further energy spreading shown in Figure 2d. Transitions 1-3, 1-4, and 1-6 (1.95-4.36 e v ) are seen to be predominantly Pbo-PbA in-plane transitions. The transition energies increased by only 0.09-0.22 eV from cluster c to cluster d (Table 111, columns c and d), because these transitions are largely Pb-Pb inplane transitions and are unperturbed by the changed positions of the Io atoms. On the other hand, large increases in transition energies in transitions 2-5 and 2-8 (1.28-1.66 eV) are attributable to the Io locations. In these cases, Io-PbA electron transfer is predominant. The transition energies 2.82-4.67 eV in transitions 1-4, 1-6, 2-5, and 2-8 (Table 111) agree well with the experimentally observed optical peaks at 3.42,
3.95, and 4.80 eViOor 3.1, 3.6, and 4 eV.33 Conclusions Geometric and optical properties of layered Pb7II4clusters, reported here at several levels of geometry optimization, indicate an evolution of quantum confinement effects. Surface and internal geometric reconstructions are important components in understanding the nature of such effects. A carefully optimized geometry for layered Pb7II4indicated a drastic contraction in the Pb-Pb in-plane interatomic distances and blue-shifted UV spectra compared to crystalline Pb12. Bulk fragments treated by using ab initio procedures without full geometry ~ p t i m i z a t i o nor ~~.~~ a-particle-in-a-box models (with effective mass approximations)2 are not sufficiently rigorous for the unambiguous treatment of quantum size effects in semiconductor microclusters Surface and internal geometric reconstructions cause increases in transition energies resulting in blue-shifted optical absorption spectra. Complete geometry optimization is expected to result in even larger blue shifts. Acknowledgment. We thank Peter Figliozzi for assisting with the construction of Figure 1 and Maria Marino for helpful discussions. This research was supported in part by the National Science Foundation under Grant CHE-8912674 and the Air Force Office of Scientific Research. The Pittsburgh Supercomputing Center is acknowledged for a grant of Cray supercomputer time. Registry No. Pblz, 10101-63-8. (33) Nozue, Y. Private communication.
ESR Spectrum and Ground State of the ScCr Molecule M. Cheeseman, R. J. Van Zee, and W. Weltner, Jr.* Chemical Physics Center and Department of Chemistry, University of Florida, Gainesuille, Florida 3261 1-2046 (Received: January 2, 1990)
The diatomic molecule ScCr is found to have a 68 ground state (unlike its isoelectronic counterpart TiV which is 42) by ) splittings were observing its X-band ESR spectrum in a solid argon matrix at 4 K. 45Sc(1=7/2)and 5 3 C r ( f = 3 / 2hyperfine detected. gtensor and zero-field-splitting parameters were found to be g , = 2.070 ( I ) (gi’= 2.0023, assumed) and D = -0.1 31 1 (2) cm-l. Magnetic parameters are interpreted and discussed in terms of a su2d$du* d?r2dti2electronic configuration. A low-lying 611istate is indicated by the large positive value of Ag,.
1. Introduction
This is another contribution to our continuing investigations of small transition-metal clusters, particularly the diatomics.l+ Electron spin resonance (ESR)spectroscopy in matrices has, within its limitations, been relatively successful in determining the electronic and magnetic properties of many such diatomics. There are indications of an isoelectronic, or better, isovalency principle2+’ holding among these electronically complex molecules, but it is sure to be an oversimplification, as this study reveals. ( I ) Weltner, Jr., W.; Van Zee, R. J. Annu. Reu. Phys. Chem. 1984, 35, 291-327. (2) Weltner. Jr., W.; Van Zee, R. J. In Comporison of Ab Initio Quontum Chemistry with Experiment for Small Molecules; Bartlett, R. J., Ed.; Reidel: Dordrecht, 1985; pp 1-16. (3) Van Zee. R J.; Weltner, Jr.. W. Chem. Phys. Lett. 1988. 150, 329-333. (4) Cheeseman, M.; Van Zee, R. J.; Weltner, Jr., W. High Temp. Sci. 1988, 25, 143. ( 5 ) Weltner. Jr.. W.; Van Zee, R. J. In The Challenge of d ond f Electrons, Theory and Computation; ACS Symp. Ser. 394;; Salahub, D. R., Zerner, M. C., Eds.; American Chemical Society: Washington, DC, 1989; pp 213-227. ( 6 ) Cheeseman, M.; Van Zee, R. J . ; Flanagan, H. L.: Weltner, Jr., W. J . Chem. Phys. 1990. 92, 1553.
0022-3654/90/2094-7808$02.50/0
The ESR spectrum of the ScCr molecule was found to be observable, thus adding to the meager knowledge of the first-row transition-metal diatomics. But, also, ScCr is isoelectronic with the TiV molecule, which we have previously shown to have a 42 ground state.’ In that case the deduced major electron configuration was s ~ ~ d u I d a ~implying d 6 ~ , multiple two-electron su and d r bonds and three u plus d6 unpaired spins. However, as will be shown here, ScCr has a 6 2 ground state, implying less d a bonding and a redistribution of spin. Thus, this is another case (such as CrMn and Mn2+6or CrCu and CrAg*) where the isoelectronic principle is too naive. 2. Experimental Section The X-band ESR spectrometers used for recording spectra of ScCr isolated in solid argon have been previously d e ~ c r i b e d . ~ (7) Van Zee, R. J.; Weltner, Jr., W. Chem. Phys. Leu. 1984, 107, 173. (8) Baumann, C. A,; Van Zee, R. J.; Weltner, Jr., W. J . Chem. Phys. 1983, 79, 5272. (9) Baumann, C. A.; Van Zee, R. J.: Weltner, Jr., W . J . Chem. Phys. 1983, 79, 5 2 7 2 . Van Zee, R. J.; Ferrante, R. F.; Zeringue, K. J.; Weltner, Jr., W . J . Chem. Phys. 1988, 88, 3465, and references therein.
0 1990 American Chemical Society
ESR Spectrum and Ground State of ScCr
The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 7809
XY2
XY5
6100
6200
6300
H(G) I775
1875
1975
2075
XY3
H(G)
XYI
A
I
1375
I
I
1475
1575
I
1675
H(G)
Figure 1. Observed ESR perpendicular lines (xy, and xy2) of the 45S~Cr molecule trapped in an argon matrix at 4 K (v = 9.578 88 GHz). Eight line splittings are due to the magnetic moment of the 45Sc nucleus ( I = 712).
Samples of scandium powder (99.9% pure, Aesar, Spex) and chromium powder (99.99% pure, Aldrich) were simultaneously vaporized by using two resistively heated tantalum Knudsen cells. During these depositions the cell temperatures were maintained at approximately 1600 and 1700 "C for Sc and Cr, respectively. (Temperatures were measured with an optical pyrometer and are uncorrected for emissivity.) A second procedure used the 532-nm output of a Nd:YAG laser (Spectra Physics DCR 11)9to vaporize a (fixed, nonrotating, 9-mm diameter) pellet of the two metal powders (1 :1 molar ratio) formed by pressing the powders together under a force of about 15OOO Ib. Experiments were also performed using a pellet enriched to 55% in the stable isotope 53Cr(97% pure 53Cr,Oak Ridge National Laboratory). Metal vapor was codeposited with argon (99.9995% pure, Air Products) onto either a single-crystal sapphire rod or a copper rod maintained at 4 or 12 K, respectively, by a Heli-Tran continuous flow of liquid helium or by a Air Products Displex helium refrigerator. 3. Results The five lines observed in the X-band ESR spectra of the 45S~oCr molecule in an argon matrix at 4 K are shown in Figures 1-3. (OCr indicates that the molecules containing the major Cr isotopes, having no nuclear magnetic moments, are being observed here. Substitution of chromium enriched in 53Cr(I=3/2) will be discussed below.) Each of these lines is split by 45Sc(I=7/2) hyperfine (hf) interaction. The centers of these hf patterns occur at approximately 1540, 1955,2945,4660, and 6190 G. The phases o f four of these lines and their positions indicate that they are to be assigned as perpendicular ( x y ) lines of a 6 2molecule, with the fifth line accounted for as an off-principal-axis ("extra") line.I0 They are designated as xy, (1 540 G ) , xy2 (1955 G),xy, (2945 G),xy5 (6190 G),and e, (4660 G).The observance of all of these lines except for xy4 places the zfs in a rather narrow range between 0.10 and 0.20 cm-' (see Figure 6 of ref 11 or p 270 of ref 10). (10) Weltner, Jr., W. Mogneiic Aioms and Molecules, Dover: Mineola,
NY, 1989.
I
I
2775
2875
I
I
2975 3075 H(G) Figure 2. Observed ESR perpendicular lines (xy, and xys) of the "ScCr molecule trapped in an argon matrix at 4 K ( v = 9.578 88 GHz). Line splittings are due to hyperfine interaction with the 45Sc(I=7/2) nucleus (see text). "
8.65"
Extra " Line
L
I
4550
I
4650
I
I
I
4750
H (GI
Figure 3. Observed ESR line attributed to an off-principal-axis ("extra") transition of the 45ScCrmolecule trapped in an argon matrix at 4 K ( v = 9.57888 GHz).
The positions of the observed lines are listed in Table I. The weaker parallel lines were not observed. 4. Analysis The axially symmetric spin Hamiltonian applied here is
7f = gl,PffzS,+ g,P(H$, .A\(S;Pi
+ S;li,)+
+ H $ y ) + z.Ap;r; +
D[Sz - I/JS(S+ I ) ]
I
+ Q?< - Y J ( I + I ) ] (1)
where D is the zfs parameter and Q' is the electric quadrupole coupling constant with the 45Sc(I=7/2) nucleus. Higher terms in the zfs (involving b: and the nuclear Zeeman terms) have been ( 1 1 ) De Vore, T. C.; Van Zee, R. J.; Weltner, Jr., W. J . Chem. Phys. 19%. 68, 3522.
7810 The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 TABLE I: Observed ESR Spectral Line Positions (in G ) of the 'ScCr Molecule in an Argon Matrix at 4 K ( v = 9.57888 GHz); ComDarison with the Calculated Line Positions" MI exptl calc Mi exptl calc XYI
+7/2 +5/2 +3/2 +1/2
1425.8 (2) 1456.1 1488.8 1521.7
1426.2 1457.8 1489.9 1522.2
+7/2 +5/2 +3/2 +l/2
1839.2 (2) 1871.6 1903.8 1936.2
1839.7 1871.4 1903.6 1936.3
+7/2 +5/2 +3/2 +1/2
2830.0 (5) 2862.7 2895.0 2927.0
2831.9 2863.7 2896.0 2928.3
-112 -312 -512 -712
1555.2 1588.8 1622.2 1655.8
1554.9 1588.0 1621.5 1655.2
-112 -312 -512
-712
1969.2 2002.8 2036.8 2070.8
1969.2 2002.6 2037.3 2071.7
-112 -312 -512 -712
2960.0 2993.7 3027.0 3060.0
2961.1 2993.9 3026.9 3010.0
XY2
Cheeseman et al. TABLE 11: Magnetic Parameters of the '%cS%3 Molecule in an Argon Matrix" 2.070 ( I ) 2.0023c -0.1311 (2) cm-' 94.5 (10) MHz 28 (15) MHz 72 (6) MHzb -22 (5) MHZ' I 3b 1.2 (2) MHz 46 (6) MHz
"Obtained via the Hamiltonian in eq I . bAssuming A11(45S~) and AL(45S~) have the same positive signs. CAssumed.
XY 3
M~ (
5 3 ~
3/2
1/2 I
-1/2 I
-31'2
,
MY53Cr)
h, 3/2
112 I
-3/2
-112
1
I
XY 5
+7/2 +5/2 +3/2 +1/2
6078.4 ( I O ) 6107.0 6140.0 6170.0
6075.0 61 10.4 6142.6 6174.8
-112 -312 -512 -712
6205.0 6237.0 6270.0 6305.0
6207.4 6240.0 6272.8 6305.8
4680.0 4706.0 4730.0 4762.0
4677.7 4705.2 4732.6 4759.8
el = "extra" line, 0 = 65O 4566.0 ( 5 ) 4602.0 4632.0 4654.0
4566.3 4594.3 4622.2 4650.1
'Parameters used in calculation: g, = 2.070, g,l = g, = 2.0023 = 0.40 G, = 94.5 (assumed), D = -0.131 1 cm-', MHz, AII(4'Sc)= 28 MHz. 5c
w'
0
20
40
20
40
60
80
80
2975
3025
H (GI
Figure 5. Observed ESR spectrum of a portion of the xy3 line of the 45S~53Cr molecule in an argon matrix at 4 K ( u = 9.578 88 GHz). The chromium was enriched to 55 atomic % with S3Cr(I=3/2).
H plot from which that spectrum was derived.I0 The three strong
I00
FIELD (KGI
I
00
6 0
2925
100
I20
FIELD ( K G )
Figure 4. (a, top) Calculated 8 versus H curves and (b, bottom) firstderivative simulated ESR spectrum of a % molecule with the parameters ID1 = 0.131 1 cm-I, g, = 2.070, and gll = 2.002.
neglected. From the assigned xy lines for a molecule, assuming g,, = 2.0023, approximate values of ID1 = 0.131 cm-' and g, = 2.070 were obtained and used to calculate the simulated firstderivative spectrum in Figure 4b. Figure 4a shows the 0 versus
low-field perpendicular lines are evident in Figure 4b, although the shape and intensity of xy3 are anomalous. Note that in the plot in Figure 4a that line also has some "extran character on its low field side. The degree of overlap of these perpendicular and off-principal-axis lines at this field is sensitive to the magnetic parameters chosen, and therefore it has an effect upon the xy3 line shape. As noted earlier, none of the parallel lines were observed which is not surprising since they have a very low intensity, hardly detectable in Figure 4b. The xy5 line in Figure 2 shows broader peaks than the other observed transitions. This may be due to the existence of matrix sites with slightly different D values which broaden the lines and is exacerbated at the higher fields. This simulation also predicts three "extra" lines of which only the strongest one at -4700 G, 0 r 6 5 O , was observed. This is not unexpected since these lines are usually broadened because of their mixed hf splittings at intermediate angles of 0. (Hyperfine effects are, of course, not included in Figure 4.) This anomalous hf character is evident in the extra line shown in Figure 3 and in Table I . The intensities of the high-field perpendicular lines appear to decrease relative to the low-field lines as the temperature is raised above 4 or 12 K. Since when D is positive these lines arise from transitions between higher lying Zeeman levels which would be more populated at the higher temperature, their observed decrease in intensity indicates that the levels are inverted and the sign of the zfs is negative. Fitting of the lines in Table I yielded firm values for D,g,, and JAL(45S~)I, with g,,assumed equal tog,. The value of Q'(45S~) is small but less certain, while A11(45S~) is not well established at all except that it appears to be less than A,. These magnetic parameters are listed in Table 11. Figure 5 shows a portion of the xy3 line observed by using a vaporization target enriched to 55% in s3Cr(I=3/2). The S3Cr hfs appears to be 16 G, whereas the 45Scsplitting is about 32 G. Also, there are always other lines present due to diatomic 4sSc2,12
The Journal of Physical Chemistry, Vol. 94, No. 20, I990 7811
ESR Spectrum and Ground State of ScCr particularly in the range of the two lower xy lines.
5. Discussion Accepting the evidence that ScCr has a S = 5/2 ground state, what (dominant) electronic configuration would one expect from the binding of a 4s23d1and a 4si3d5 atom? Note the following: 1. Among the first-row transition metals those on the left of the periodic table having relatively low nuclear charges will tend to more readily form 3d bonds. Both Sc212313 and Cr2I4involve d a and d r bonding. 2. To allow 4sa bonding, only the Sc atom must be promoted (4s23d1 4s13d2, 1.43 eVi5). At the shorter bond distances necessary to achieve dcr-da and d d r bonding, this s-s interaction may actually be repulsive (as appears to be the case in Cr2 and Mo2I4). Reasonable ground-state electronic configurations are
-
4sa23da23da*13da~3dr~3d62
(2a)
4sa23da24sa*13da~3dr~3d62
(2b)
and
where the 3d6 orbital might be largely localized on Cr. Hybridization of the sa and d a orbitals is expected so that the dominant configuration would then be a combination of these two. The amount of sa character among the unpaired spins can be approximately obtained by comparing the isotropic hyperfine constants with the atomic values in the usual way.i0si6 A maximum percentage at Sc that can be obtained from the A,, and A , parameters given in Table 11, assuming their signs are the same, would be 100(72/565) = 13%, indicating that indeed configuration (2b) contributes. With less certainty, at Cr 100(46/150) = 31%, probably a maximum which could be too high by a factor of 2 or 3. (IAiSo(Cr)lhas been obtained assuming All.= 4. = 16 G since parallel lines were not observed, and the hfs in Figure 5 did not yield a “second-order shift” reliable enough to allow estimation of A,,:) Then this overall sa character implies that the majority of spin is in the da, da, and d6 molecular orbitals affecting the anisotropic hf parameters. d a and d a electrons contribute positively to the Adip parameters whereas d6 electrons contribute negatively (here we take the signs of nuclear moments as all positive); thus, it is difficult to estimate their various contributions. Even with the high uncertainty in the magnitude of IA,,(Sc)l (see Table 11), the parallel component is smaller than IA,(Sc)l so that if A,(Sc) has the customary positive sign, then Adip(SC) = ( A , ,- A,)/3 is negative. To account for this, one requires unpaired spin dominantly in d6 (or possibly pn) orbitals on Sc, (12) Knight, Jr., L.B.;Van &e. R. J.; Wekner, Jr., w. Chem. P ~ Y SLeu. . 1983. 94. 296. (13) Walch, S. P.; Bauschlicher, Jr., C. W. J . Chem. PhYs. 1983,79,3590. (1 4) For discussions of the experimental data and bonding in Cr2 and Mo,, see: ref 1 an Morse, M. D. Chem. Rev. 1986, 86, 1049. ( I S ) Brewer, L.; Winn, J. S.Faraday Symp. Chem. SOC.1980, 14, 126. (16) Morton, J. R.;Preston, K. F. Maan. Reson. 1978, 30, 577. (17) Brewer, L. Science 1968,161, 1 lS.-Gingerich, K. A. Faraday Symp. Chem. Soc. 1980,14,109. Shim. I.;Gingerich, K. A. Chem. Phys. Lerr. 1983, 101, 528. and discussion in refs 4 and 5.
which is interesting since it requires a shift of d electrons from Cr to Sc, in accord with Brewer’s suggested analogy to binary alloys.” However, A,(Sc) is small enough that there may be uncertainty about its sign. If it were negative, then Adip(Sc)would be positive and could be accounted for by unpaired spins in d a and d a orbitals on Sc. In any case evidence here is that there is considerable spin density on Sc in d molecular orbitals. Again, when considering the 53Crhfs, A,, is in doubt and, in fact, completely unknown. IA,(S3Cr)l is well determined as 46 MHz, and a maximum IAdip(Cr)l is obtained by letting All = 0. Assuming A , is positive, Adi~(’~Cr) = -15 MHz = [a2 X 2/5 X 1/7 X 2/5 X (-2/7)](103.0)]. Then a2 = 0.54 is an estimated maximum da(Cr) contribution to the 3da orbital. The observed positive shift in g,(g, - ge = Ag, = +0.070) implies that there is an inverted 611ilow-lying excited-state coupling with the X6Z state through spin-orbit interaction. (This, of course, assumes that one II state is dominating, whereas it could be the overall effect of several such states, both regular and invertedi0) To arrive at such an excited state through an electron excitation of the configurations in (2a) or (2b), and one affecting g,, requires placing a 3da electron in a 3dr orbital. Then the usual expression yieldsI0 Ag, = +0.070 =
f (d41xlda)(dul1,ldr)
-
S
AE
where some average of the spin-orbit coupling constants of Sc and Cr can be used, the denominator S = 5/2, and AE is the 611i-X68 energy difference. Here the coefficients of d r and d a have been assumed unity, so that (dall,lda) = 3i/2iand an approximate maximum value of AE is obtained. Assuming t 2 145 cm-I, an average of Sc and Cr,I8 the 611i state is calculated to lie at only 2500 cm-’ above the ground state. 6. Conclusion The overall view of ScCr is then of a strongly bonded molecule probably involving a a bond and two one-electron r bonds, with an approximate electron configuration s2a2a*ir262.This is consistent with Miedema’s predicted dissociation energy of 207 kJ/mol.19 The rather large Ag. indicates that there is probably a very low-lying 611istate above the ground 6 2 state. However, Miedema predicts a lower De of 183 kJ/mol for the isoelectronic TiV molecule which has a lower spin 48ground state. The likely electron configuration of that state ( ~ ~ a l r suggests ~ 6 ~ ) that TiV is more strongly bonded than ScCr, which in turn suggests that the relative magnitudes of their predicted dissociation energies should be reversed.
Acknowledgment. This research was supported by the NSF under Grant 8814297. Thanks are also to be given to Robert F. Curl for sueaestine this small demonstration of our esteem for Kenneth S.xtzer.-We also thank H. L. Flanagan for assistance with the computations. Registry No. ScCr, 37299-78-8. (18) Dunn, T. M. Trans. Faraday SOC.1961, 57, 1441. (19) Miedema, A. R. Faraday Symp. Chem. SOC.1980, 14, 136.
