6277
J. Phys. Chem. 1995,99, 6277-6285
FEATURE ARTICLE Magnetic Molecules in Matrices W. Weltner, Jr.,* R. J. Van Zee, and S. Li Department of Chemistry and Center for Chemical Physics, University of Florida, Gainesville, Florida 3261 1 Received: November 15, 1994; In Final Form: February 2, 1995@
Molecules and ions with one or more unpaired electrons have been investigated in matrices, usually the solid rare gases, via electron spin resonance and magneto-infrared spectroscopies. Discussed here are (1) matrix perturbations and quenching mechanisms, (2) structural and wave function information from hyperfine interaction, (3) contributions of spin-spin (dipolar) and the usual dominance of spin-orbit interactions in zero-field splittings, (4) large zero-field splittings requiring measurements in the far-infrared and in high magnetic fields, (5) relativistic effects upon the ordering of low-lying electronic states, ( 6 ) application of the superposition model to calculate zero-field splittings from inorganic solid-state data, ( 7 ) inner-shell exchange coupling in homonuclear transition-metal and rare-earth-metal diatomics, and (8) solid hydrogen as a matrix.
Introduction Unpaired electrons in molecules are usually the origin of their reactivity and the source of hyperfine interactions, zero-field splittings, exchange couplings, and Zeeman effects. Understanding the magnetic interactions of spins within molecules, and with an extemal field, is one of the challenges of molecular spectroscopy. A direct way of investigating the magnetism is via electron spin resonance (ESR), as illustrated in Figure 1 for a molecule containing four unpaired electrons (total S = 2). The Zeeman pattem shQwn is for one orientation of a linear molecule in the magnetic field. Indicated there are the fineand hyperfine-structure transitions and zero-field splittings (parameter D ) typical of such a quintet molecule. In Figure 1, D is positive in sign; if negative, the entire Zeeman pattem would be inverted. The sign may be determined by comparing the relative strengths of the fine-structure transitions as a function of temperature. Table 1 gives the parameters of the S = 2 molecule SCZin a solid neon matrix at 4 K determined from an analogous ESR spectrum.' The hyperfine parameters /A111and lAll may be obtained from the spectrum since the 45Sc atom has a nuclear spin I = '12. SCZin its ground 52 state exhibits zero-field splitting (zfs) given by D = b*O, and a higherorder b4O parameter is also determinable. The sign of D could not be established because a large enough temperature variation is not possible while still retaining a rigid neon matrix. For future reference note that the dominant configuration of Sc#Z,,-) is 4~a,23da~'4su,'3dn,'3dn,~' involving what Walch and Bauschlicher2 term three one-electron d bonds. These molecular parameters (plus others, such as spinrotation constants) can often be obtained from the analysis of rotational transitions in high-resolution gas-phase spectra, particularly when cooled i n supersonic beams. Matrix work is more direct but less accurate; in general, matrices simply remove a few significant figures from the constants for the free molecules. Matrix Perturbations Diatomic molecules isolated in rare-gas matrices are not significantly perturbed by the environment, and this is usually @Abstractpublished in Advance ACS Abstrucrs, April 1, 1995.
I
! $ t ~ ~ ~
Fine Structure, AMs=fl
Hyperfine Structure, AM,=O (for 1=1/2 nucleus)
Magnetic Field
Figure 1. Zeeman effect of a linear quintet (S = 2) molecule at a particular orientation in a magnetic field. Zero-field splittings (for positive D)are indicated. Fine- and hyperfine-structure transitions are illustrated as they might occur in the electron spin resonance spectrum: however, these will vary with the orientation of the molecule in the field.
TABLE 1: Magnetic Parameters for Sc2(X5Z)in Neon at 4 K= bz0 (cm-]) b4O (cm-I glI
f O . 11 12(2) F0.00157(3) 2.002
JAlI (MHz) ( 4 5 S ~ ) lA,sol (MHz) (45Sc) IAdlpl (MHz) (45Sc) lV(O)(* (au) (45Sc) ((3 cos2 e - I)/+) (au) (45Sc)
2.000 IAill (MHz) ( 4 5 S ~ ) 291(28)
+ +
+ +
233(3) 252( 11) 20(11) 0.23(1) 0.3i(ii)
+
The spin Hamiltonian is 9T=gl@H:Sz gl(H,S, H,S,) bZ0(S:2 (1/60)bd0(35S,4 - 155S> 72) Al1SJz Al(SJX SJ,), where the fine-structure parameters are b2' = D = 382O and b4' = 6OB4O. a
- 2)
+
+
+
attributed to the large dominant axial electric field in the molecule. [This is not true of atoms, such as those of the alkali metals, aluminum, and boron, where unsymmetrical sites in these matrices can produce crystal field or possibly Jahn-Teller effects, thoroughly studied via ~ p t i c a l ,magnetic ~ circular dichroism: and ESR ~pectra.~]Generally, spectral lines are inhomogeneouslybroadened in matrices, principally by slightly differing interactions of the molecules in more than one site. Jacox has made thorough comparison of vibrational6 and electronic7 data obtained in the matrix versus gas phase. Shifts
0022-3654/95/2099-6277$09.00/0 0 1995 American Chemical Society
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6278 . I Phys. . Chem., Vol. 99, No. 17, 1995
are no more than a few percent depending upon the matrix. Magnetic parameters vary similarly.8 Knight and co-workers have successfully measured the ESR spectra of small ionic species in neon mat rice^.^ Where gas-matrix comparisons can be made (Nz+, H20+, CO*) shifts of only 1-3% from gasphase measurements are observed. An example of the reliability of zero-field splittings (to be discussed in detail below) is provided by GdO, a high-spin molecule recently observed in gas-phase high-resolution laser spectroscopy.I0 Those spectra yield D = bzO= -0.207 06(10) cm-' and b4O = -6.20(25) x cm-' as compared to D = bzo = &0.2078(3) and b4O = f 4.0(5) x cm-' determined via ESR spectroscopy in an argon matrix." ESR had established that its ground state is 9C,confirmed by the gas-phase study. Because molecules are usually randomly oriented in the solid matrices, orbitally degenerate molecules with S I '12 are unobservable in matrix ESR due to their large g tensor anisotropy. For example, for a molecule in a 2n3/2state, gl = 0 and gll= 4, causing the absorptions to be broadened beyond detection.I2 A strong perturbation, such as an adjacent cation, which removes the cylindrical symmetry of the molecule can quench this orbital angular momentum, reduce the g anisotropy, and cause a narrowing and strengthening of the s p e ~ t r u m . ' ~ What is interesting, and unprecedented, is recent evidence that the (proposed) ground 2A states of VC, NbC, VSi, and NbSi molecules are partially quenched in neon, argon, and krypton mat rice^.'^ This is attributed to strong unsymmetrical interaction of these ionic molecules with the matrix such that each is situated in an orthorhombic crystal field. [Their dipole moments are estimated to lie between 3.5 and 4.5 D.] The derived crystal field splitting parameter is both molecule and matrix dependent, varying from approximately 1400 to 7800 cm-'. The proposal of 2A, ground states for these molecules has recently been supported by local density functional computations on VC by Mattar.I5 Assuming the general validity of proposed 2A, ground states, a relevant question is whether this quenching is unique. Are electrons in d6 orbitals on the metal more vulnerable to environmental interaction, which is sufficiently enhanced by the high ionic character of the diatomic? Matrix isolation, as it is called, makes possible the application of experimental techniques such as ESR, which are difficult, or even impossible, to apply in the gas phase. However, since molecules are nonrotating (or in a few cases, undergo hindered rotation) in these solids, rotational transition information providing molecular structure parameters is lost. Hyperfine Interaction. The anisotropy of hyperfine splittings (hfs) provides evidence of the character of the wave function of the unpaired electrons (e.g., proportions of su, pn, dd, etc.). From the pattem of lines the hf structure may also establish the number of equivalent nuclei and determine the symmetry of the molecular structure. Usually the hyperfine splittings at each nucleus are compared with the known atomic valuesI6 to obtain approximate indications of percent s, d, etc., character in the unpaired electron wave function.'* This procedure is based on the LCAO approximation and is understandably rather suspect. Knight, Ligon, Woodward, Feller, and Davidson9have made an analysis of this approximation in the case of the SiO+(2Z) radical by comparison with detailed ab initio calculations. There are significant differences in the spin populations. This is of most concern for molecules containing heavier elements with many inner shells and relativistic effects.I7 An interesting case is the B3 molecule, where the hyperfine splitting pattems in ESR spectra in neon, argon, and krypton matrices at 4 K prove that the trimer contains three equivalent
MI
9
I
i
-
A13:Ar
3 2
50 G
5 -
mrm
fi
I
2
9 2
7 2
! 1I 1I/
Figure 2. Hyperfine structure in the ESR spectra of "B? (i = 3/2) and ,413 ( i = 5 / 2 ) in an argon matrix at 4 K.
boron nuclei, Le., has D3h equilateral triangle ~ymmetry.'~.'~ The I'B (i = 3/2) hf structure is quite extensive, consisting of 30 lines corresponding to one fine-structure line centered at essentially g = 2. (The fact that only one fine-structure line was detected constitutes proof that the ground state is S = ' / I , in accord with 2 A ~from ' theory.'O) These 30 lines are divided into 10 groups with relative intensities 1:3:6:10:12:12:10:6:3:1 corresponding to MI values equal to 9/2, ..., -9/2. For three equivalent "B nuclei with il = i2 = i3 = 3/2, the total nuclei spin I takes the values 9/2, ..., lM11, resulting in the observed spectra. For example, the pattems for MI = 5/2, 3/2, are shown in Figure 2. This illustrates the establishment of molecular structure through hf interaction, but further analysis unexpectedly indicates that the A tensor is isotropic, requiring the molecules to be rapidly rotating in these matrices. There are also variations in line widths in the spectra which support that conclusion. 27A13(i = 5 / 2 ) has an analogous ESR spectrum to B3; a comparison is shown in Figure 2. The conclusion that A13 also has a *AI' ground state is in agreement with StemGerlach experiments of Cox et aL2' Zero-Field Splitting. If a molecule contains more than one unpaired electron, then the energy levels exhibit zero-field splittings (zfs). This name implies that the splittings are produced by intrinsic (magnetic) interactions between the electrons even in the absence of a magnetic field. In the axial case, as illustrated in Figure 1, only one parameter, D, characterizes the zfs. Note that zfs is also directional but its tensor is traceless (as is the dipolar hyperfine tensor), implying that its three principal values are not independent and in general can be replaced by two, D and E. Also, it implies that rapid rotation will average the zfs to zero." As expected, the magnitude of D increases the closer on the average that the unpaired electrons are to each other in the
J. Phys. Chem., Vol. 99, No. 17, 1995 6219
Feature Article molecule, in fact, as ( l h 3 ) . Also of importance is the enhancement of D through the spin-orbit coupling associated with large nuclear charge; Le., the magnitude of the zfs is enhanced in molecules containing heavier atoms and, as we shall see, even rather light atoms. For nonlinear molecules two zfs parameters are necessary, D and E, but we will focus attention almost exclusively on the larger D parameter here. Then D can be separated into two parts
+
D = D,, D,,
(1)
where “ss” signifies spin-spin (or dipole-dipole) interaction between the unpaired electrons and “so” indicates the contributions from spin-orbit coupling. Let us consider these two contributions in tum. Electrons as Magnetic Dipoles; the Dipolar Contribution. For two electrons disposed largely in orbitals on atoms lying along the z axis and interacting as magnetic dipoles, the zfs parameters D,, and E,, resulting from the dipolar interaction are given by
s, =(SA + q
2
(Cm-1)
g,, an average of the atomic spin-orbit coupling constants in the diatomic molecules. (Data are taken from ref 31.) The line is D = at> and fits the homonuclear diatomics rather well. It is understandable that the heteronuclear species all lie to the left of the line since the g, for the heavier atoms should be weighted more. Figure 3. A plot of the zero-field splittings versus
TABLE 2: Second-Order Spin-Orbit Contributions to D,, for the X3C.- State of Of state
‘Z,+ 3x,+
(3)
+
+
where x 1 2 ~ y 1 2 ~ 2 1 2 ~= r 1 2 ~g, zz 2.0, and p = Bohr magneton. If cylindrically symmetrical, then E,, = 0 since y12 = x 1 2 . For this case one sees that if both electrons are on the same atom (say in n or n-n orbitals perpendicular to each other) in a disc-shaped electron distribution, then 212 = 0 and D varies approximately as (llr123)and is positive in sign. On the other hand, if there is a rod-shaped electron distribution 112 = 212, then D will be negative in sign. This kind of rudimentary reasoning has been applied to rationalizing the zfs in small triplet molecules22and quintet molecules containing carbenes separated by unsaturated chains23and most recently in judging the most probable conformations of nonet planar molecules containing five benzene rings separated by four carbenes in the meta positions.24 D,, in any S 1 1 molecule can be derived exactly if one knows the wave function of the unpaired spins. Then the equivalent of eqs 2 and 3 can be calculated more a c c ~ r a t e l y . ~For ~.~~ example, consider the He2 molecule in its excited 3Z,,u$.excited state; it qualifies as a molecule where spin-orbit effects would be at a minimum. The experimental value of D = -0.0367 cm-’ determined by Lichten et aL2’ is then attributable entirely to spin-spin interaction. Using only this first-order contribution, Beck et a1.28with a wave function computed by Pahusta and M a t ~ e ncalculated ~~ a value of -0.040 89 cm-’, in good agreement in both sign and magnitude with experiment. Beck et a1.28also considered the contributions of second-order spinorbit coupling (see below) and spin-rotation coupling and found them to be negligible. The dominant MO configuration in the 3Z,,u+state of He2 is 10g210,120g1, not as in the 32,- state of 0 2 where the configuration is mainly ...nvlnxl. Further discussion of the spin-orbit contributions in the two molecules will be deferred to the next section. Aromatic diradicals also qualify as cases where spin-orbit effects are small or negligible, as long as a heavier atom such as sulfur is not attached. In general, ID1 is found to be less than 0.1 cm-’, and /El is an order of magnitude smaller. It has been shown by McClure that spin-orbit contributions can be exactly zero when the symmetry is suitable.30
5z,+
3n, In, 5n% 3ns In, 3ns In,
net D,, net D,, Dso + Dss
excitation
-----
30,nu 3a,n, 30,n, 3a,n, 30, n, 3Ug n, n” 30, iz” 30” nu 30, n,X, 3u,n, n“Xg 3uuTc,
DC’
(cm-1)
2.400
-2.8 x 10-4 2.4 10-5 0.110 -0.096 -0.034 0.046 -0.024 3.6 x 10-4 -4.8 10-5 2.402 1.453 3.855
Experimental value is 3.965 cm-’.
NH and 0 2 are “light” molecules where spin-orbit contributions to the zfs are beginning to appear. In triplet N-H both electrons are localized on N, and the nitrogen atom has about 3 times the spin-orbit coupling constants of the carbon atom. This leads to a spin-orbit contribution of about 13% of the zfs. However, this contribution rises to 62% and dominates D for 0 2 . If we examine the series of isovalent diatomics formed in group VIA, 0 2 , SO, S2, Se2, etc., the D values rise rapidly from 4 cm-’ for 0 2 to 1975 cm-’ for Te2. This trend in D as a function of the average atomic spin-orbit coupling constant in the molecule is plotted in Figure 3.3’ Spin-Orbit Interaction. This interaction can be separated into one-electron and two-electron terms, the so-called spinsame-orbit and spin-other-orbit terms, reflecting the magnetic interaction of an electron with its own orbital angular momentum and with the orbital angular momentum of another e l e ~ t r o n . ~ ~ . ~ ~ Each is dependent upon the spin-orbit coupling constant of the molecule. The size and sign of D,, depend upon the coupling of the ground state with excited electronic states through second-order perturbation which therefore implies, in general, a complex source of contributions to the z ~ s . ~ ~ 0 2 , which cannot be classified as a “heavy” molecule, nevertheless has a large contribution of D,, to its zfs. This is because the low-lying ICg+state (at 13 000 cm-I), derived from the same configuration as the ground state, couples strongly to X3Zg- to give D = f 2 . 4 cm-’ within the total D = +3.9 cm-’. The calculated contributions from other excited states are shown in Table 2, taken from the review by Langhoff and D,, rapidly completely dominates the zfs in the isovalent series in
6280 J. Phys. Chem., Vol. 99, No. 17, 1995
Weltner et al.
1-
1-
I
7 1 16
Number of x electrons
Figure 4. Zero-field splitting parameters, D,in a series of linear C, and C,O molecules in their ground 3X states (adapted from ref 37).
Figure 3, constituting 95% of D even in the SO(X3Xg-) molecule. In He2 the l u 2 l ~ ~ l n , ~ 3 ~states & , - lie too high in energy to contribute significantly to D,,, and the states arise from configurations such as la~lu,nd.z whose contributions can be expected to be very small. The point to be made is that although a 32state is being considered in both He2 and 0 2 , the second-order D,, is quite different in the two cases, not only because of the magnitudes of the spin-orbit parameters but also because of the configurational origin of these states and the consequent differing arrays of excited states. N2 in its excited A3& state also does not have this large D,, contribution because its configuration is ...nU3ng*', and D,, accounts for essentially the entire D = -2.66 cm-'. 0 2 is an example that emphasizes the possible important contributions that may occur in C, N, and 0 containing molecules, even though the spinorbit coupling constants are relatively small. The contributions of D,, become apparent in a study of the series of polycarbon molecules, C4, c6, and c8, all having triplet ground states.34 The electrons can be considered as in the configuration, similar to the 0 2 molecule. On the basis of dipolar electron interactions, one expects rapidly diminishing ID1 values in this series because of its ll? dependence, but in fact, the values rise from 0.224 cm-' in C4, to 0.331 cm-I in c6, to 0.624 cm-' in Cs. One must attribute this to spin-orbit coupling, and if again one excited state may be assumed the major contributor, that state is expected to be the state low lying with respect to the ground 32g-state. Then in this homologous series it is apparent that coupling to this state is larger for the longer molecules, implying that the state is progressively lower lying. Theoretical calculations by Ewing indicated indeed that this is the case.34 An analogous variation of JDI has been found among the triplet C,O molecules where n = 2, 4, 6, and 8. Neon matrix ESR studies yielded ID1 = 0.74, 0.76, and 1.10 cm-I for the n = 2, 4, and 6 molecules, respectively. (I3C and I7O hyperfine structure was also o b ~ e r v e d . ~ ?Recently, ~ ~ , ~ ~ ) Oshima et al.37 have produced these molecules, and CsO, by discharge of carbon suboxide in argon with subsequent supersonic cooling and observed them in a Fabry-Perot type Fourier-transform microwave spectrometer. Their observed D values are 0.7668,0.7792, 1.1577, and 2.275, cm-'. (Here we have deleted many of the significant figures determined in those precise measurements.) As expected, the matrix values are lower than those in the gas phase by about 0.03-0.05 cm-1.836 A plot of D (cm-l) versus number of n electrons (adapted from Figure 3 in the OhshimaEndo-Ogata paper3') is shown in Figure 4. The parallel behavior in the two series is clear. C2S with D = 6.484 cm-' 1 9 3 1 1 u
has been observed by Saito et al.,38 and C S with D = 7.579 cm-' by Hirahara et al.,39 illustrating the large effect the heavier sulfur atom has on the zfs in these series. Large Zfs. As seen above, spin-orbit coupling is the dominant factor determining the zfs. Thus, in cases of molecules containing metal atoms, one can expect the zfs to be comparable to or larger than the Zeeman splitting (see Figure 1). (In the usual treatments of the spin Hamiltonian, the Zeeman term is considered to be much larger than the zfs term.) This has important ramifications when considering the effects of paramagnetic metal ions in solution on the nuclear spin relaxation rates. These are strongly dependent on electron spin relaxation which is, for large zfs, detem-hed by the precession about molecule-fixed axes rather than external field axes. This difference in quantization profoundly affects the NMR paramagnetic relaxation enhancements.40 The zfs is conveniently derived from ESR spectra, but only if D is not too large. As illustrated in Figure 1, if D is large, at low temperatures where only the lowest Zeeman level is populated, no ESR transition can be observed with the usual fixed hv of microwave radiation. Conventional microwave sources are X-band (9.3 GHz = 0.31 cm-I) and Q-band (36 GHz = 1.2 cm-I), and appropriate cavities are used with each to increase the sensitivity. Ideally, one wishes to have a source providing a continuously variable frequency and a correspondingly variable Fabry-Perot cavity. The latter may not be available, but if the zfs is large enough to lie in the far-infrared, spectrometers are available to cover the range 5-400 cm-' and higher. Brackett, Richards, and Caughey (BRQ4' have used such an arrangement to measure the absorption spectra of polycrystalline compounds where transition-metal ions experience large crystal-field distortions and therefore large ID\values, in the range 3-100 cm-I. Absorptions over this range could be measured in magnetic fields from 0 to 5 T. Two difficulties enter into these measurements: (1) the absorptions are weak since they are (largely) magnetic dipole in character and thousands of times weaker than electric dipole transitions; (2) the source of infrared is the tail end of the mercury arc radiation which provides very low intensity. Nevertheless, with rather large samples (-1 g powders) BRC could map out the entire Zeeman level scheme (as in Figure 1) and thus measure D (and E). We have adapted BRC's methods to the study of isolated molecules in matrices, with magnetic fields up to 5 T. The two difficulties named above are now magnified by the necessity of low concentrations of molecules in the matrices. The apparatus is shown in Figure 5. The matrix is made in the usual way on a flat polished gold surface kept at low temperature by a constant flow of liquid helium. This gold surface can then be raised into a split-coil superconducting magnet (highly homogeneous field) and rotated to face an IR beam projected by mirrors from the Bruker IFS 113V spectrometer. The spectrum is measured by reflection using the appropriate range of beam splitters and detectors and in magnetic fields varying from 0 to 5 T. An example of the results that can be obtained is shown in Figure 6 for the nickelocene molecule in a krypton matrix.42 The two unpaired electrons in this axial sandwich compound are located largely on the Ni (see Figure 7) so that the D value is quite large, 32.4(2) cm-' in neon (and argon) matrices. [From solid-state magnetic susceptibility measurements, Baltzer et a!3l had previously found D = 33.6(3) cm-l. In order to eliminate exchange coupling between the nickelocene molecules in the pure solid, measurements were made on increasingly dilute samples of nickelocene in the diamagnetic solids ruthenocene and ferrocene, and the values of D were
Feature Article
J. Phys. Chem., Vol. 99, No. 17, 1995 6281
Liq. He Cryostat
-
Supercon.
I R Beam
- -UF - -/I-
-/IMagnet
Matrix Prep. Liq. He Cooled Gold Surface
To Vacuum
Figure 5. Apparatus used for measurement of the infrared spectra of matrix-isolated molecules in magnetic fields. The matrix is prepared on the gold surface at 4 K in the usual way and then raised into the split-coil superconducting magnet where the IR beam from an FTIR vacuum spectrometer measures absorption by reflection. The magnetic field can reach 5 T with a homogeneity of 1 part in lo4.
1
% 26
28
30
32
w A v ENUMBER
34
36
36
40
'
( c m- )
Figure 6. Far-infrared absorption spectra of nickelocene in a krypton matrix at 4 K in various magnetic fields, B = 0, 1, 2, and 4 T.
extrapolated to zero concentration.] Further tests of the magnetic field effects were made on matrix-isolated triplet Se2, TeSe, and Te2 molecules where the zfs values are greater than 1000 cm-' (see Figure 3).44 It has been recognized that much of the difficulty of working in the far-infrared can be assuaged by using a stronger source, Le., an optically pumped laser. Such lasers can provide emission lines between -5 cm-' (-2 mm) and -20 cm-' (-600 pm) detected with a bolometer operating at 1.5 K. Also, magnetic fields can be attained to about 30 T (CW) and higher fields in a pulsed mode. Thus, even without a resonant cavity ESR can be extended over a large frequency range4s,46with magnetic fields available at facilities such as the National High Magnetic Field Laboratory in Florida. There are still disadvantages to these constant-light-frequency, swept-magnetic-field experiments in that there are a limited number of laser lines, and absorptions extending beyond narrow lines, or weakly dependent on the magnetic field, may not be observable. It is still preferable, of
Figure 7. Triplet ground state nickelocene molecule and the energy splitting of 3d orbitals in a ligand field of symmetry D5d. Orbital occupation in the
3A2,
ground state is shown.
course, to have available both continuously variable frequencies and high magnetic fields. As in the nickelocene experiments, Hausenblas, Wittlin, and W ~ d e i have ' ~ adapted a far-IR Fourier transform spectrometer (with mercury arc source) to make measurements (10-700 cm-I) on magnetic semiconductors up to fields of 20 T. Low-Lying States. As noted, relativistic effects, expressed through spin-orbit interaction, produce large zero-field splittings in systems with large nuclear charges, and such splittings can be as large as the energetic separation between low-lying electronic states. This can have major effects upon the ordering of the lowest states, the mixing of spin-orbit components from different states, and vibronic perturbation^.^^ It is clear that relativistic effects must be included in ab initio calculations on heavy atom systems, and experimental verification is generally advisable. NiH is an example where spin-orbit contributions are vital in the interactions between the lowest 2A3~2,~/2, 22~~2, and 2n1/2,3/levels, 2 as calculated by M a ~ i a n . ~ ~Recently, .~* we have been concemed with the zfs and energies of low-lying electronic states in the series Si2, Ge2, and Sn2, where there is a shift from case a to case c down the series because of increasing spin-orbit coupling.50 ESR had earlier established the zfs in the ground 3$- state of Si2 as ID1 = 2.6 cm-' and probably positive in sign;s' Le., this is the energy spacing, 3Zg*1-3Zg0.With increasing spinorbit coupling in Ge2, it is estimated that D = f l O O cm-', but now the zfs in the ground 32g-state is more properly indicated as a splitting into 1, and O,+ states [Q is now the good quantum number]. This magnetic dipole transition 1, Og+ was not observed for Ge2, although it was detected for Sn2 at 770.5 cm-I (in an argon matrix at 4 K). The weak Sn2 transition exhibited strong Zeeman splitting, indicative of a magnetic dipole transition; however, this measured value differs from the relativistically calculated value of 342 cm-' .52 Besides these zfs transitions, there is a low-lying 311ustate in Si2, split widely by spin-orbit coupling in Ge2 and Sn2 into 2,, l,, Ou-,0,- energy levels [case c coupling]. Transitions to this state(s) all lie in the infrared, 300-1900 cm-I. The 311u X3C,- transition in Si2 occurs at 313 cm-I with the upper state split into 52 = 0, 1, 2 triplets with spacings of S2 0-2 of
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-
Weltner et al.
6282 J. Phys. Chem., Vol. 99, No. 17,1995 Ar
1 I
3000
2500
zoo0
Wawnumbers (cm-1)
1500
-
Figure 8. Infrared absorption spectra of the 1, XO,+ electronic transition of the Snz molecule in argon and neon matrices at 4 K. Because of the large change in interatomic distance in the two states, a long progression of bands separated by the vibrational frequency in the upper state is observed. The shapes of the bands are due to phonon
interactions in the solids; the sharp features are the zero-phonon transitions.
-
145.5 cm-I. In Ge2 the allowed transition is 1, XO,+, occumng at 71 1 cm-’, and in Snz at 1807 cm-I. In all of these cases, the vibrational frequency in the upper (3111,) state could be detennined. Because there is a large change in the interatomic distance, re, from this ground to the excited state, long progressions of vibrational bands (Franck-Condon envelopes) appear in the absorption spectra. This is shown for Snz in Figure 8. Zfs in Inorganic Molecules; the Superposition Model. There is a vast literature on the zero-field splittings in inorganic solids.s3 In general, the sign and magnitude of the zfs in solids containing metal ions with S 1 1 are determined by crystal fields and spin-orbit couplings. In higher approximation, overlap, covalency, distortion, exchange, and relativistic effects must be considered. Measurements of magnetic susceptibility or heat capacity at low temperatures are analyzed to derive the zfs in the solid, but other effects, such as exchange coupling, may prevent this. However, there are cases, such as octahedral Ni(11) in a 3Az ground state, where the D value can be obtained from the form of the low-temperature heat capacity of the solid. The theoretical attack on this problem in a given solid requires the selection of an appropriate cluster about a central metal ion, usually containing only nearest-neighbor counterions, and characteristic of its structure. For example, Ribbing et al.54have recently made nonempirical calculations on complexes of Ni2+(HzO), (n = 1-6) and N ~ F Gwhere ~ - distortions from octahedral symmetry produce zfs. Small distortions can cause significant changes in the zfs values. [Those authors’ interest has its origin in the dynamics of nuclear spin relaxation and its relation to the modulation of the zfs by random molecular motion^.^] In such calculations involving only spin-orbit contributions, the spin-other-orbit terms may be incorporated into the one-electron terms (spin-same-orbit) by scaling the charge of the metal to reproduce atomic optical data. Thus, the calculation of zfs is reduced to a one-center, one-electron approximation. Such calculations can undoubtedly be applied to inorganic molecules, such as GdF3, MnC12, etc., but perhaps more interesting is the question as to whether the results of the many crystal field methods commonly applied to ionic solids can be used in estimating the zfs parameters in molecules. Basically, these methods appear in three simplified forms: the electrostatic model (EM), the angular overlap model (AOM), and the superposition model (SM). The electrostatic assumes
that the lattice interacts with the electrons on the metal solely in terms of an electrostatic potential function. The angular overlap model (Schtiffer and Jprrgensens6) attempts to separate the geometrical and chemical information in d-electron crystal field splittings. Its origin is the Wolfsberg-Helmholtz model, which may be more familiar to the reader. Here the open-shell electrons are considered as significantly bonding with the ligands. The superposition model (Bradbury and Newmans7) is closely related to the angular overlap model. Each of the latter two models has been comprehensively r e v i e ~ e d . ~ * * ~ ~ Molecules such as GdF3, MnC12, etc., are highly ionic and therefore susceptible to crystal field treatments. However, besides differing in the coordination numbers (CN), the degree of covalency in the bonding is greater in the molecule than in the corresponding solid. This is indicated by the shorter bond distances in the molecules, by the observed hyperfine splittings at the ligand nuclei, and by the deviations of the molecular structures from those expected of pure ionic molecules (e.g., GdF3 is pyramidal rather than planar,@TiF2 is bent rather than lined’). One expects then, in general, that information obtained from the solid will have to be appropriately altered to take care of additional covalency and change of coordination number in the molecule. The superposition model, increasingly useful in solids, offers a possible transitional approach. The superposition model (SM)59assumes that the crystal field acting on the unpaired electrons of the metal is a summation of the effects of each of the surrounding ions (or ligands) and acts axially along the metal-ligand directions. Then the zfs parameter D (=bz0)in its simplest form is given by
where the &(Ri) are the “intrinsic” crystal field parameters (i.e., geometry independent) for ligand i at distance Ri from the paramagnetic ion, and 4zis the angle of the ligand with respect to an axis in the local coordinate system. The value of D then rests upon knowing the Ri and @i in the molecule and deducing the 6 2 parameters of the metal-ligand pairs from solid-state data. The b2 (Ri)are, in general, very sensitive functions of Ri. If bz(R0) is deduced from the solid zfs at a reference distance Ro, then the multiplicative factor (RdRi)‘2,where t2 is typical of the metal-ligand pair, is usually used to obtain b2 (R,). t2 may be of the order of 7 so that accurate interatomic distances are needed to yield good predictions of zfs. We have applied the SM to the pyramidal GdF3 and linear MnXz (X = F, C1, Br) molecules62where solid-state data for Gd+3in rare-earth trifluoridesG3and for Mn+2in halide lattices@ are available. The bond distances in the MnXz molecules have been measured by gas-phase electron d i f f r a c t i ~ n . ~ The ~ D values for all molecules calculated from the SM are positive in sign and agree with ESR values& within 20%, except for MnF2. The measured ID1 = 0.34 cm-l for the difluoride, which is considerably higher than the calculated -0.19 cm-I SM value. The crystal data are suspect but the negative sign appears to be valid, which in this case is a significant result of the application of theory. Not surprisingly, it is also clear from this study and others that the coordination number about the metal ion can have a marked effect, which is of concern in deriving parameters from solids where CN = 4 or 6 to apply to molecules where CN = 2 or 3. Exchange Coupling between Inner Shells in Diatomics. Exchange interactions have been found to occur between the half-filled 3dS shells in Mnz68369and Mn2+ 70 and between the corresponding 4f7 shells in Gd2.7’ These interactions are
J. Phys. Chem., Vol. 99, No. 17, I995 6283
Feature Article antiferromagnetic (low spin in lowest state) for Mn2 but ferromagnetic for Mn2+ and Gd2. Mn2 is a van der Waalsbonded molecule whereas Mn2+ and Gd2 are chemically bonded. These are unusual interactions among transition-metal or rareearth-metal diatomics. It is interesting that CrMn, isoelectronic with Mn2+, does not exhibit this inner-shell interaction but has a 42,multiply bonded ground state, p o r e or less expected of the molecule lying between Mn2 and strongly bound Cr2.69 Mnz has a binding energy of only about 0.3 eV, but it is easily formed and trapped in rare-gas matrices at 4 K.68,69As the temperature is raised above that temperature, 11-line hyperfine patterns appear, indicating two equivalent Mn ( I = 5 / 2 ) nuclei. Thus, as predicted by Nesbet,’2 the lowest state is a singlet (S = 0, IZg+) and the two atoms are exchange-coupled antiferromagnetically. As the temperature is raised, the higher levels S = 1, 2, 3, ... are occupied and ESR spectra become visible. By measuring the intensity variation of the 11-line patterns, one can establish that the exchange coupling constant J = -9 f 3 cm-I. Here D can be measured in individual spin states and the axial anisotropic exchange interaction De = -g2p2/ 6 for the pair derived. From this one calculates the interatomic distance to be about 3.4 A, which is reasonable for a van der Waals bond. An interesting facet of the Mn2 study is the possible discovery of exchange striction in the molecule, i.e., a variation of the interatomic distance in the S = 0-5 spin states.73 The ESR spectra in the higher spin states were observed up to -1 10 K by trapping in solid cyclopropane. We are not aware of any previous detection of this phenomenon in a magnetic molecule. The removal of one electron from Mn2 to produce Mnz+ causes a surprising change in its electronic proper tie^.^^ A chemical bond is formed and at the shorter interatomic distance ferromagnetic coupling of the unpaired spins occurs, leading to a high multiplicity I2Zgfmolecule. Thus, the two inner shells of 3d5 electrons are interacting with each other via the unpaired 4s electron to produce 11 electrons with the same spin with a zfs = -0.046 cm-’. Bauschlicher has calculated74 that the opposite condition with all 3d electrons coupled, Le., the 2Zu+ state, lies about 0.44 eV higher and the J = 700 cm-’. The rare-earth atom Gd has a 4f75d6s2configuration. Except for the half-filled 4f7 shell, it is analogous to Sc with 4s23d’. So it is not surprising that the ab initio calculation of Dolg et al.75found a 5Zuground state for Gd2, the same as observed for Sc2 (see earlier). However, ESR spectra of Gd in argon and krypton matrices at -2-20 K yielded a spectrum attributed to Gd2 containing 18 unpaired spins in the lowest state, implying exchange coupling between the 4f7 inner shell^.^' This ferromagnetism presumably arises by coupling via the unpaired 5d and 6s electrons forming the bridging and bonding molecular orbitals. This is analogous to the role of the odd s electron in Mn2+ or to the bulk metal where “indirect” exchange occurs through the itinerant electrons. As in Sc2, where Walch and Bauschlicher2propose three one-electron bonds, Gd2 is strongly bonded with a dissociation energy of 41 & 8 kcal/mol. Solid Hydrogen as a Matrix. Hydrogen forms an unusual ~ o l i d . ~ ~Molecules ,~’ in the solid are held together by weak, slightly anisotropic interactions so that the molecules largely retain their identities in the condensed phase. The small mass, small size (H2 internuclear distance 0.741 A), weak intermolecular forces, and large compressibility distinguish it from other molecular or rare-gas crystals. These properties lead to unusually large amplitudes of zero-point lattice vibration and nearly free molecular rotation. Quantum effects are important so that there are large differences in the physical properties of the isotopic solids H2, HD, and D2. Furthermore, paramagnetic
51V+D2AT2K
1.56
1.68
1.a0
1.92
2.04
B(KG)
Figure 9. ESR of a matrix formed by laser vaporization of vanadium metal into pure deuterium gas and condensed on a copper rod at -2 K. Fine-structure lines assigned to the linear VD2(4X) molecule are centered at about 1800,5800, and 6500 G (Y = 9.5849 GHz) and ID1 = 0.315 cm-l. (The line centered at 5800 G is an off-principal-axis line.12) The hyperfine structure (hfs) in these lines is due to interaction with the 5 1 V( I = ’ / 2 ) nucleus; D (and H) hfs was not observed. The more-than-eight line structure in the two high-field fine-structure lines is attributed to different matrix sites, which produce only overlapping hfs in the 1800 G lines. The resolution observed in these two highfield lines is completely lost in the spectra of VH2 and VD;! in argon and krypton matrices.
species induce the 0- to p-H2 (or p- to o-Dg) conversion, with heat release. In spite of these matrix properties, atoms including H,’8 Li,79Cu, Ag, and Au80 have been readily trapped in solid hydrogen at 1-5 K. On the other hand, because of the weak interactions and open structure, one might expect solid hydrogen to provide the most gaslike environment, surpassing solid neon, for matrix-isolated molecules. This may be the case if chemical reaction does not occur. There is evidence of reaction of dopants with the matrix in some cases; in others it is not apparent. For example, the polycarbon triplet molecules c4, c6, and c8 are trapped and observed via ESR in solid hydrogen.8‘ Vaporization of boron into solid deuterium yields B2 signals in the ESR,80but diborane, B2D6, is also detected in the IR. As one might expect, metal hydrides are readily formed, and in at least one recent case, VH2, a more highly resolved spectrum with analyzable hyperfine structure was observed than was obtained in solid argon or solid krypton (see Figure 9).82
Acknowledgment. Research cited here was generally performed under NSF grant support, the most recent being CHE-9114387. Also, acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. We thank Professor Yasuhiro Ohshima for permission to reproduce the figure in his paper on the C,O molecules (see Figure 4 and ref 37).
6284 J. Phys. Chem., Vol. 99, No. 17, I995
Weltner et al.
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J. Phys. C h m . , Vol. 99, No. 17, 1995 6285 (78) There are many references here, beginning with the studies of: Jen, C. K.; Foner, S . N.; Cochran, E. L.; Bowers, J. A. Phys. Rev. 1956, 104, 856; 1958, 112, 1169. See: Miyazaki, T.; Iwata, N.; Fueki, K.; Hase, H. J . Phys. Chem. 1990, 94, 1072 and references therein. (79) Fajardo, M. E. J . Chem. Phys. 1993, 98, 110. (80) Unpublished results. (81) Van Zee, R. J.; Li, S.; Weltner, W., Jr. J . Phys. Chem. 1993, 97, 9087. (82) Van Zee, R. J.; Li, S.; Weltner, W., Jr. J . Chem. Phys. 1995, 102, 4367. JP943045T
