© Copyright 2001 by the American Chemical Society
VOLUME 105, NUMBER 25, JUNE 28, 2001
FEATURE ARTICLE Compressed Atoms A. L. Buchachenko* Institute of Chemical Physics, Russian Academy of Sciences, Moscow 117334 Russia ReceiVed: October 19, 2000; In Final Form: January 24, 2001
Many atomic systems exhibit indications of compressed electronic shell: atoms locked in crystals, solids at cryogenic temperatures, atoms trapped by fullerene cages, and atoms in substances under high pressure. This paper collects available experimental data on the ESR, NMR, and magnetic moments of compressed atoms and formulates some general trends in the behavior of magnetic parameters displayed by compressed atoms. The paper lays special emphasis on the electron-nuclear (hyperfine) coupling as a parameter characterizing the modification of atomic orbitals and the redistribution of spin density in atoms under compression.
1. Introduction Any electronic excitation of atoms, molecules, and ions is accompanied by dilation of electronic shell insofar as energyrich orbitals are more extended than those of ground state so that electrons are more distant from the nuclear core. The limiting case is Rydberg atoms and molecules, in which quantum numbers of outer electrons reach a few tens (even hundreds), the energy of electron-nuclear coupling being comparable with or even smaller than kT. Electronically excited atoms, ions, molecules, and clusters are extensively studied both in chemistry and physics; a great body of information on the structure and properties of excited electronic shells are now amassed. It makes intriguing an inverted problemswhat the properties and behavior of compressed electronic shells are, in contrast to those of extended shells of electronically excited molecules. This intriguing problem is even hotter because of the clearly exhibited interest in modern chemistry for the extreme and exotic conditions and regimes of chemical reactions, particularly for those in powerful shock waves, both classical and laser-stimulated.1 First of all, it is necessary to select such structural parameters which could respond to the compression and could be considered * Fax: (007)(095)938-2484. E-mail:
[email protected].
as reliable indicators of compression. It is not a simple choice since the effects of compression may be masked or imitated by those which are not a direct result of compression of electronic shells. Thus, hydrostatic pressure is known to induce a shift of absorption and luminescence bands or modify their intensity; however, it does not yet necessarily mean the compression of electronic shell. These optical effects may be due to the conformational fixation or geometrical distortion of molecule, the change of relative populations of the nearly degenerated states, the freezing out of vibronic interactions, etc. In other words, optical effects can be induced by changes in nuclear skeleton of molecule and cannot be unambiguously attributed to the direct perturbation (compression) of electronic shell. It is logical to seek symptoms of compression in the behavior of such structural parameters which characterize a total electronic shell rather than its outer part (outer orbitals) which is usually responsible for the optical effects. These are (i) isotropic chemical shifts in NMR, X-ray, photoelectron, and Mo¨ssbauer spectra and (ii) isotropic hyperfine coupling constants and g-factors in the ESR spectra. However, these parameters are also extremely sensitive to even small distortions of molecules (interatomic distances, covalent and dihedral angles, out-of-plane deviations of atoms, solvation, etc). Ultimately, it is necessary to admit that one should seek only the “pure” symptoms of compression for
10.1021/jp003852u CCC: $20.00 © 2001 American Chemical Society Published on Web 05/16/2001
5840 J. Phys. Chem. B, Vol. 105, No. 25, 2001
Buchachenko
TABLE 1: Matrix Effects φ for H and D Atoms atom
matrix
φ (%)
ref
atom
matrix
φ (%)
ref
H D H D H D H H H H H
H2 D2 Ne Ne Ar Ar Kr Ne Ar Kr Kr
-0.23a -0.32a -0.10a -0.07a -0.47a -0.53a -0.59a +0.43b +1.15b +0.47b +0.55b
2 4 4 4 4 4 3 3 3 3 5
D H D H H D H D H D
Kr Ne Ne Ar Kr Kr Xe Xe Xe Xe
+0.62b +4.0c +5.0c +10.8c +5.4c +8.2c -0.97a -1.04b -1.5c -1.8c
5 6 6 6 6 6 5 5 6 6
c
a Deposited from gas discharge. b Photolysis of HI or DI in matrix. Deposited on SiO2.
atoms; they are free of any effects induced by distortions of geometry. The purpose of this paper is to collect and summarize experimental data on the ESR, NMR, and magnetic moments of compressed atoms (only these data are now available) to generalize regularities in the compression effects, if any, and to discuss theoretical basis of the effects. A special emphasis is being placed on the electron-nuclear (hyperfine) coupling as a quantitative parameter characterizing modification of atomic orbitals and redistribution of spin density of unpaired electrons in atoms under compression. 2. Hydrogen and Deuterium Atoms The most “pure” compression effects are expected for H (and D) atoms possessing a single 1s electron. In fact, it has been experimentally found that the hyperfine coupling (HFC) constants a depend on the matrix which traps the H or D atom, and this matrix effect manifests itself at cryogenic temperatures (4.2 K and below).2-5 We will define its magnitude as a difference of HFC constants a and a0 in reference to a0
φ ) (a - a0)/a0
(1)
where a0 is the HFC constant for the free, unperturbed atom in the gas phase. The HFC constant is a measure of spin density of unpaired electron at the proton (or at any other nucleus); it is expressed by equation
a ) (8π/3)µeµn|ψ(0)|2
(2)
where µe and µn are the magnetic moments of the electron and nucleus and |ψ(0)|2 is the square of the electron wave function at the proton. The latter is the spin density of the unpaired electron on the spherically symmetric s-orbital since only these orbitals have a nonzero magnitude of |ψ(0)|2. It is exactly spin density on the s-orbitals which will be further discussed, and the compression effects will be treated in terms of this value. Experimentally measured φ for H and D atoms are collected in Table 1; they are of different signs in different matrixes. The negative φ indicates decreasing HFC constant of trapped atom with respect to that of free atom (a < a0); it means a leakage of spin density from the trapped atom. A positive φ (a > a0) demonstrates a pumping of the additional spin density onto the trapped atom. It is also clearly seen that the sign of φ depends on the method of generation of trapped atoms: for atoms trapped from hydrogen gas discharge, φ < 0; for atoms generated by the photolysis of HI, incorporated into the matrix in advance, φ >
TABLE 2: Matrix Effects φ for Nitrogen and Phosphorus Atoms (4.2 K) atom
matrix
φ (%)
ref
P N N N N N
Ar H2 N2 CH4 Ne KN3, crystal
+19 +9.6 +15.6 +29.5 +7.8 +48.6
7 8 8 8 9 10
0. In the first case, H atoms occupy predominantly substitutional sites and vacancies in the rare gas matrix; in the second case, they are locked in the interstitial sites. In the first case, trapped atoms are almost free and comfortably arranged in the matrix; in the second case, they are strongly compressed by van der Waals interactions with neighbor matrix atoms. From this analysis, one can derive a general conclusion: both effectssspin leakage (spin delocalization onto the matrix atoms) and spin pumpingscoexist; however, the latter dominates for strongly compressed atoms, which occupy strongly stressed interstitial sites in the crystal lattice of rare gas matrixes or locked in the stressed sites on SiO2 (see Table 1). It is a remarkable result which will be discussed in section 10. The second feature of trapped H atoms is that the effects of both signs are observed only in matrix of weakly polarizable atoms (Ne, Ar, Kr); in matrix of strongly polarizable Xe, φ is always negative, independent of the method of generation of trapped atoms. It evidences that in Xe the leakage of spin density from hydrogen atoms to matrix atoms dominates over pumping; i.e., spin delocalization on the Xe atoms via van der Waals interaction prevails in a xenon matrix. 3. Nitrogen and Phosphorus Atoms In the ESR spectrum of a phosphorus atom generated by the photolysis of PH3 in a rare gas matrix, the hyperfine splitting in doublet of 31P (I ) 1/2) is 23.8 G, while for the free atom, this splitting is 20.0 G, i.e., φ ) +19%.7 This large effect demonstrates strong compression of phosphorus atomic shell along with additional pumping of about 20% spin density on the s-orbital (Table 2). Even more large-scale effects of compression take place for the nitrogen atom (Table 2); the additional spin pumping accounts for 10-50%. These effects exceed those for H and D atoms by 2 orders of magnitude, that is the extent of compression being directly related to the size of atom; for the larger atom, the compression and spin pumping are much stronger. The other feature of N and P is that, in contrast to the H atom, unpaired electrons in N and P atoms occupy atomic p-orbitals, which have a node and, therefore, zero spin density at the nucleus. The origin of both hyperfine coupling in these atoms and its changing under compression will be discussed in section 10. 4. Metal Atoms The HFC constants in alkaline metal atoms exhibit the behavior similar to that in the hydrogen atom. ESR spectra of 23Na, 39K, 87Rb, and 133Cs trapped in matrixes of Ne, H , and 2 N2 display the sites with atoms differing in the sign of φ.11,12 The sites with φ > 0 are specific in that they disappear very fast at the annealing while those with φ < 0 survive long time. These observations imply that atoms with φ > 0 occupy unstable, strongly compressed, and distorted positions (such as interstitials) while atoms with φ < 0 are placed in comfortable
Feature Article
J. Phys. Chem. B, Vol. 105, No. 25, 2001 5841
TABLE 3: Matrix Effects φ for Metal Atoms atom 7
Li 63Cu
matrix
φ (%)
ref
atom
Ar Ne Ar Kr Xe
+4.2 +2.0 +4.8 +3.0 +0.5
12 16 16 16 16
107
Ag
197Au
matrix
φ (%)
ref
Ne Ar Kr Xe Ne Ar Kr Xe
+1.3 +5.7 +3.8 +1.0 +1.3 +2.8 +1.4 -0.9
16 16 16 16 16 16 16 16
stable sites of matrix crystals and for these atoms the leakage of spin density on the matrix atoms dominates. Similar behavior of HFC constants has been observed in the gas phase: the shifts of ESR lines, induced by the pressure of inert gases and measured in molecular beams, were of different signs. Thus, the HFC constant in 23Na increases as the pressure of neon grows (positive shift of +80 Hz/Torr), while in argon (more polarizable atom), the pressure-induced shift is negligibly small.13 It is logically to suppose that the rigid collisions of Na atom with neon induces compression of Na atom and spin density pumping while in argon both effects, spin pumping and spin leakage, are comparable and compensate each other. Hydrogen, deuterium, and helium induce in 87Rb a positive shift in HFC constant (+10 Hz/Torr); the shifts of the same sign are produced by Ne (+2.6 Hz/Torr) and N2 (+6 Hz/Torr). However, atoms and molecules with high polarizability (Ar, Kr, CH4) stimulate small but negative shifts in the HFC constants (-3, -5, and -6 Hz/Torr, respectively). It is in accordance with general idea that “rigid” collisions of H2, He, Ne, and N2 with alkali metal atoms result in the pumping of spin density on the s-orbitals of metal atoms, while in the more “soft” collisions with Ar, Kr, and CH4, spin leakage dominates.14 The 133Cs atom behaves similarly: the positive shifts in HFC constant is observed in He, Ne, H2, and N2 (+1600, +650, +1900, and +930 Hz/Torr, respectively); however, collisions with “heavy”, highly polarizable atoms of argon, krypton, and xenon induce negative shifts in a sequence (-250, -1300, -2400 Hz/Torr, respectively)15 which parallels to the polarizability of these atoms. In the first series, spin pumping dominates; in the second one, spin leakage via delocalization prevails. Table 3 shows parameter φ for the HFC constants in atoms Li, Cu, Ag, and Au trapped in inert matrixes of Ne, Ar, Kr, and Xe at 4.2 K. Needless to say, these large atoms are strongly compressed in the crystal lattice of matrix even if they occupy nodal positions. Secondary to this condition, these atoms experience spin pumping. Only in the lattice of strongly polarizable Xe atoms are the positive φ not large because a compressioninduced positive shift is presumably compensated by spin leakage; for the Au atom, the latter contribution even becomes dominating and inverts the sign of φ (Table 3). 5. Endofullerenes of Metals Endofullerenes are the most exotic substances, the product of the art of chemistry. The basic motif of their structure is the capture of atoms (and even molecules) and their incapsulating inside of fullerene cage. Among the great number of synthesized endofullerenes with trapped metal atoms, only La@C82, Y@C82, Sc@C82, and Sc3@C82 demonstrate ESR spectra with hyperfine structure; i.e., only these species are available to derive conclusions on the status of electronic shells of trapped atoms and compression effects. Table 4 summarizes HFC constants for the metal atoms trapped in fullerene C82.
TABLE 4: HFC Constants for Metal Atoms and Cluster Trapped in Fullerene C82 atom/cluster 139
La 89Y 45 Sc 45Sc 3
a (G)
ref
1.15 0.48 3.83 6.25
17, 18, 19 17, 19 17, 18, 19 20
La and Y in the cage of C82 are known to be in ionic states La3+ and Y3+, but Sc and three-atomic cluster Sc3 are in oxidative states Sc2+ and (Sc2+)3; i.e., each scandium atom carries positive charge +2. It was independently proven by synchrotron spectroscopy.21 Unfortunately, the lack of HFC constants for “free” ions fails to compare these constants with those for ions trapped in fullerenes and to extract the conceivable compression effects produced by the incapsulating of ions in fullerene cage. However, the only such possibility follows from the comparing HFC constants in Sc@C82 and Sc3@C82. The radius of Sc2+ ion is unknown, but it is obviously less than 1 Å (for Sc3+, it is 0.732 Å) and less than the characteristic size of C82 cage so that Sc2+ in C82 can be considered as a free, not compressed ion. Atomic cluster Sc3 is a triangle of D3h symmetry with interatomic pairwise distance 2.875 Å.22 Ionic cluster (Sc2+)3 is identical to atomic cluster with the exception of the interatomic distance, which increases to 3.54-3.57 Å owing to the Coulomb repulsion. This cluster may appear to be subjected to compression by the fullerene cage. The ESR spectrum of Sc3@C82 consists of 22 lines with splitting 6.25 G; it complies exactly with that of three magnetically (and, therefore, energetically and spatially) equivalent nuclei 45Sc. (The nuclear spin of 45Sc is 7/2, and the number of ESR lines is 2I + 1 ) 2‚3(7/2) + 1 ) 22.) It means that each of the three unpaired electrons of the trapped cluster (Sc2+)3 is delocalized on the three nuclei and results in hyperfine splitting 6.25 G. If every unpaired electron would “sit” on the one nucleus, the HFC constant would be 3 times larger; i.e., it would be equal to 18.75 G. It is a true magnitude of HFC constant normalized to the unit spin density of unpaired electron localized on the ion Sc2+. One needs to compare only this magnitude with the HFC constant in “free” ion Sc2+ of Sc@C82, which equals 3.83 G (Table 4). This situation is perfectly identical to that in nitroxyl monoand polyradicals. ESR spectra of biradicals consist of five lines split by a/2, where a is the HFC constant in monoradical with unit electron spin. In the biradical, every unpaired electron serves two nitrogen nuclei and shares spin density between them equally; it results in twice decreasing the HFC constant. For the same reason in triradicals, in which every unpaired electron serves three nitrogen nuclei, the HFC splitting decreases three times and equals a/3; in tetraradicals, it equals a/4, etc. In Sc3@C82 and Sc@C82, it is necessary to compare HFC constants normalized to unit spin density on the every Sc2+ ion because ESR detects one-spin transitions between Zeeman levels. In other words, one needs to compare normalized HFC constants: 18.75 G in Sc3@C82 and 3.83 G in Sc@C82. It is just evident that the HFC constant at the 45Sc nucleus in compressed cluster (Sc2+)3 is much larger than that in “free” ion Sc2+. An alternative to the compression would be partial covalent bonding between Sc2+ ions in Sc3@C82; however, it should be accompanied by decreasing HFC constant, so this alternative is hardly acceptable.
5842 J. Phys. Chem. B, Vol. 105, No. 25, 2001
Buchachenko
TABLE 5: Effective Magnetic Moments µeff, Effective Spins Seff, and Effective Number of Unpaired Electrons neff in Free and Imprisoned Lanthanide Ions ions Gd3+ Gd@C82 Gd@C82 Gd@C82 Tb3+ Tb@C82 Dy3+ Dy@C82 Ho3+ Ho@C82 Ho@C82 Er3+ Er@C82
ground state 8
S7/2
7F
6
L
µeff
Seff
neff
0
7.94 6.66 6.95 6.9 9.72 6.80 10.64 8.48 10.60 6.30 5.55 9.58 6.37
3.5 2.9 3.0 3.0 4.4 2.9 4.8 3.8 4.8 2.7 2.3 4.3 2.7
7.0 5.8 6.0 6.0 8.8 5.8 9.6 7.6 9,6 5.4 4.6 8.6 5.4
3
6
5
5I 8
6
H15/2
4
I15/2
6
∆µ(%) 16 13 13 30 20 41 47 33
The effect of compression computed according to eq 1
φ ) (18.73 - 3.83)/3.83 ) 3.9 reaches almost 400%. This effect strongly exceeds those which were observed for the compressed H, N, P, and metal atoms in cryogenic matrixes (see Tables 1-3). Noteu that in Sc3@C82, the HFC constant was shown to depend on the temperature: it increases from 6.22 G at 333 K to 6.80 G at 103 K20 (in contrast to Sc@C82, in which HFC constant does not depend on temperature). It certifies that the magnitude of φ increases from 390% to 530% as the temperature decreases. This enormously large growth is universal for all tested solvents. It is worth mentioning that Sc2@C82 is silent in ESR although each of two Sc2+ ions carries unpaired electron. This fact is easily tractable if we take into account for the compression of ions, which impels ions to unite in a diamagnetic “molecule” Sc2; the ESR spectra are not expected to appear for this molecule. Note that this contradicts what is observed in Sc3@C82 (see above); possibly a covalent bonding is induced by low compression (in Sc2@C82), and at high compression (in Sc3@C82), the spin pumping effect dominates. 6. Magnetic Moments of Compressed Atoms A detailed study on the magnetic properties of rare-earth metal ions imprisoned by fullerene C82 cage has been carried out last years.23-25 Magnetic moments µeff as well as effective spins Seff and effective number of unpaired electrons neff are summarized in Table 5. The ground state of free ions and their orbital angular momentum L are also presented. The values of µeff have been derived from the experimental data on the temperature and magnetic field dependences of magnetization by fitting to Brillouin function; these values are not too different from those estimated by fitting to Curie-Weiss function.23 In all these endohedral metallofullerenes the oxidative state of metal ions is identical to that of free ions; i.e., the metal atom trapped inside the cage donates three electrons to the cage. It is demonstrated by photoelectron and optical spectroscopy as well as by monitoring of synchrotron X-ray diffraction. Comparing magnetic parameters of imprisoned and free metal ions, one can reveal a general trend of decreasing magnetic moments and effective spins of trapped ions with respect to those of free ions. The percentage of decreasing ∆µ ranges from 10% to 50% and indicates no correlation with orbital momentum L (Table 5).23-25 The reduction of magnetic moment and effective spin of ions in the endohedral fullerenes is unambiguously a result of
TABLE 6: Compression Effects φ for Atoms N and P Incapsulated by Fullerene Cages atom
φ (%)
size of cage (Å)
ref
N@C70 N@C66(COOC2H5)12 N@C61(COOC2H5)2 N@C60 P@C60
+49.1 +53.4 +54.1 +54.1 +250
7.80 (6.99, equator) 7.31
28 28 28 27, 28 29b
6.96 6.96
imprisoning the atoms, which generates a negative exchange interaction between electrons on the ion and electrons transferred from atom to the cage, which, in turn, partly aligns the electron spins of Me3+ and C823- into antiferromagnetic order and reduces the magnitudes of µeff, Seff, and neff in metallofulerenes. This effect originates from the fact that, in contrast to free ions, which are formed from atoms by the loss of three electrons, in metallofullerenes these three electrons are not completely lost, they are located in the nearest vicinity of the ion on the C82 cage and strongly interact with electrons of donating ion. The exchange interaction in the system M3+-C823- strongly imitates pure electronic effects of atom compression, so it is impossible to derive some certain conclusions concerning compression of central atom. But it is hardly reliable to believe that the effect is significant since the radii of ions (not more that 1 Å) are much less than the size of C82 cage (g7 Å). The ions are known not to be centered in the cage; they are usually closer to one of the five- or six-membered rings of the cage, so that they have enough freedom to move in the cage. 7. Endofullerenes of Nitrogen and Phosphorus In contrast to metal-encapsulated fullerenes, in which electrons of metal atoms are transferred to the fullerene cage, in atomic endofullerenes, the electron configuration of trapped atoms is conserved. Discrete-variational local density functional calculations have shown that the nitrogen atom inside C60 is not covalently bonded; its bonding energy with the cage is not larger than 0.9 kcal/mol. The elevation of electronic levels of C60 under influence of N atom is also small and does not exceed 0.2 eV.26a The electron structure of N atom is also retained: each of the three atomic p-orbitals carries one unpaired electron (as in free atom). The HFC on the 13C of fullerene cage C60 is also negligibly small; it was measured by ENDOR and constitutes only 0.01 G.26b It confirms noncovalent character of the interaction between electronic clouds of N and C60 and reflects the absence of strong host-guest interaction. The other symptom of compression is significant increasing of the HFC constant for the N atom: in N@C60, it reaches more that 50%27 (Table 6). Moreover, HFC constants are sensitive to any chemical modification of fullerene cage which changes its size. A general regularity is clearly seen from Table 6: the less the size of cage, the larger the compression and φ values. The contraction of the nitrogen charge cloud in N@C60 was confirmed by theoretical analysis.30 Two sets of calculations have been performed: in terms of the density functional theory with the B3-LYP exchange-correlation functional with spinunrestricted orbitals and in the Hartree-Fock approximation with Kohn-Sham eigenvalues and spin-restricted orbitals. The difference charge density, F(N@C60) - F(C60) - F(N), has been calculated as a function of the distance from the center. Analysis of the charge distribution within N@C60 convincingly demonstrates that the nitrogen atom retains its atomic nature but reveals contraction of the charge cloud.30 It is also worthy to note that these reliable calculations have not confirmed an unexplainably
Feature Article large shift in the energy (by 6.2 eV) of atomic nitrogen orbitals, induced by encapsulation, which was calculated in ref 26a. Confinement of nitrogen atom in a cage of less than spherical symmetry (in C70, see Table 6) leads to anisotropic deformation of atomic charge and spin distribution, which is probed by magnetic electron-nuclear double resonance (ENDOR) technique.29a The first sign of anisotropic deformation is significant line broadening of 14N ENDOR transitions in N@C70, in contrast to very narrow lines observed in N@C60. A ratio of axial components Azz and Qzz of electron-nuclear dipolar hyperfine and quadrupol tensors, which characterizes anisotropy of spin distribution for encapsulated in C70 nitrogen atom, was shown to be strongly different from that for the free atom. This fact strongly supports idea that the dominant effect of the interaction between atomic charge distribution in nitrogen atom and cage is the deformation of atomic orbitals rather than their repopulation.29a This deformation looks like a prolate spheroid compatible with geometry of C70 cage. Phosphorus atom in P@C60 demonstrates a giant compression effect: the HFC constant in 31P increases by 250% with respect to that in free atom (Table 6).29b The lectronic structure of P atom is similar to that of N atom; the only difference is that three unpaired electrons in P atom occupy 3p atomic orbitals. Undoubtedly, the large effect in magnitude of φ is directly related to the larger size of P atom and more strong compression. 8. Compressed Radioactive Atoms Endofullerenes provide also new opportunities in radiochemistry. By studying neutron activation of solid C60 samples in the presence of Ar, it was found residual radioactivity of 41Ar unseparable from C60. It was concluded that 41Ar is trapped in cage and its capture is accomplished by penetration of 41Ar atom into the cage owing to the energy of γ recoil of its precursor.31 Neutron activation of Gd@C82 is accompanied by an escape of Gd out of the cage as a result of recoil; only 10% of radionuclide 159Gd remains within the cage.32 The similar phenomenon has been observed for La@C8233 and
[email protected],34 These results sertificate that the loss of encapsulated atoms is accomplished by a recoil mechanism via the radioactive decay of captured and neutron activated atom. There is no doubt that the opposite process, a capture of radioactive atom by fullerene cage, may be also accomplished via mechanism of recoil of its exohedral precursor. This idea was brilliantly embedded for Xe in the C60 lattice.35 Neutron activation of Xe solutions in C60 (Xe is outside of the cage) results in the formation of 125 gXe@C60 and 133 gXe@C60; these molecules are supposed to be formed via the γ- recoil of Xe atoms in nuclear reaction (n, γ). The γ- recoil energy of this nuclei (165 and 256 eV respectively) is enough to penetrate the C60 cage and to remain trapped inside. The production of encapsulated Xe radionuclides was proved by chromatography and nuclear γ-spectroscopy.35,36 A particular interest concerns the fate of compressed radionuclides. Thus, isotope 125 gXe in C60 suffers positronic decay and transformation into 125I. Two intriguing questions remain unanswered: (i) whether the recoil energy of the β+ decay of 125 gXe is enough for the decay product, the nucleus 125I, to break away from the C60 cage; (ii) whether the rate constant of the β+ decay of compressed-atom 125 gXe is changed with respect to that of free atom.37a The latter is especially interesting; it can be formulated another waysis it feasible to influence on the nuclear reactions via electronic shells? At first sight, the answer is evidently negative, since the energetics of the electronic shells and nuclear
J. Phys. Chem. B, Vol. 105, No. 25, 2001 5843 “drops” are of too different and uncommensurable scales. Moreover, nuclear reactions are not spin-selective (in contrast to chemical reactions which are spin selective). However, for some types of nuclear processes (such as β+ and β- decay, K-capture, etc.), such influence is not excluded. (The wellknown and documented relation between electron and nuclear spin systems via magnetic interactions underlying spin chemistry is not discussed here.37b) 9. NMR of Compressed Atoms There is only one example of the NMR of a compressed atom, helium incapsulated in C70. NMR line of 3He in He@C70 is shifted in high field by -29 ppm with respect to free atom.38 It is impossible to decide what part of the shift is related to magnetic screening by curcular current of π-electrons of the fullerene cage and what part may be attributed to compression. One can only suppose that the former in such a roomy cage should dominate. The NMR line of 3He in He2@C70 is shifted to low field by 0.014 ppm with respect to that of
[email protected] It is clear that the encapsulating of two atoms produces more compression; however, in this case, it is also impossible to decide whether this effect is due to compression or it is induced by displacement of He atoms from the central position of fullerene cage, which is accompanied by the change of magnetic screening in the shifted position. 10. Compression by High Pressure In high-pressure experimental physics (particularly at the dynamic compression in shock waves), one can attain a 3-fold increase of the density of compressed metals. For the majority of metals (alkaline, alkaline-earth, rare-earth, and transition metals), the shock adiabats (the volume as a function of pressure) consist of two parts: the starting one, until 1.5-2.5 times the original density, and the following one, at even higher densities. The first part is characterized by high compressibility, and it is usually related to the low density and high compressibility of outer s-electrons following migration of these s-electrons into the deeply located unfilled or partly filled d- and f-layers. The second part (at high pressure, up to 10 Mbar) corresponds to the weakly compressible state of metal, when all inner electron layers are filled and the atom becomes an electron-compacted and almost noncompressible system.40 A great body of information on the compressibility of metals (more than 50 metals are investigated) has received a general and physically reasonable phenomenological understanding in terms modification of electronic shells under compression. Unfortunately, compressibility is not a direct probing of atomic orbitals; it gives no information on the hyperfine coupling and spin density distribution on the different orbitals. 11. Compressed Atoms: Theoretical Inspection Hyperfine coupling appears to be a very sensitive indicator of the modification of the electron wave function by compression. It varies in great extent depending on the level of compression. In contrast to quantification of HFC, the latter cannot be characterized quantitatively, but even qualitatively, it is clear that the HFC and, therefore, wave function modification directly related to the compression, although physical mechanisms of modification are expected to be different for different atoms. Adrian41 was the first who suggested an idea to clarify matrix effect for the hydrogen atom. He considered two sources of
5844 J. Phys. Chem. B, Vol. 105, No. 25, 2001
Figure 1. Scheme of electron interactions at the overlapping of electronic clouds of hydrogen and helium atoms in terms of the McConnell-Adrian model. Its essence is that the unpaired electron of hydrogen atom extracts partly an electron with identical spin from the He atom and repels an electron with opposite spin. This results in additional positive spin density on the H atom and negative spin density on the He atom unperturbed configuration. (b) Interpenetrating charge clouds. Arrows indicate electron spins of H and He atoms.
perturbation of 1s-orbital-van der Waals interaction and Pauli forces, which occur at the overlapping electronic clouds of hydrogen and matrix atoms. The former results in delocalization of the unpaired electron; it produces a leakage of spin density on the matrix atoms and decreasing HFC constant. The latter results in increasing HFC constant via spin polarization mechanism presented schematically in Figure 1. Exchange interaction in the atomic system H + He induces additional positive spin density on the hydrogen atom leaving negative spin density of the same magnitude on the He atom. This mechanism is completely identical to that of arising HFC on the protons of CH3 radical, where exchange interaction of unpaired π-electron induces spin polarization of C-H bond and generates additional positive spin density on the carbon atom and negative spin density on the proton; it is the well-known McConnell’s mechanism. The only distinction of Adrian’s mechanism is that it deals with unpaired s-electron rather than with π-electron, as in McConnell’s model. Theoretical predictions of Adrian’s model are in excellent quantitative agreement with experiment in description of both HFC constants and g-factors. Moreover, Adrian has also predicted HFC on the matrix atoms, in qualitative accordance with experiment. With high confidence, one can suppose that Adrian’s model is also adequate for describing the compression effects on the alkaline metal atoms with filled inner electron shells and outer unpaired s-electrons (Li, Na). Unlike hydrogen atom with a single unpaired s-electron, in N and P atoms in the electronic state 4S3/2, unpaired electrons occupy p-orbitals. In these atoms, the pressing of outer p-electrons into the inner s-orbitals and p-s spin polarization of inner s-electron lone pairs (2s2 in N and 3s2 in P) may be accomplished. This effect is accompanied by the spin pumping of s-orbitals and provokes additional increasing HFC constant. Evidently, it is again McConnell’s intra-atomic mechanism: p-s spin polarization is expected to produce negative spin density on the inner s-orbitals. The sign of HFC constant is a test parameter to identify the mechanism of compression effects. It can be determined by analysis of the ESR line broadening under conditions of hindered molecular rotation, when the anisotropy of HFC and g-factor contribute markedly in the ESR line width. For instance, if the difference g - 2.0023 (2.0023 is a g-factor of free electron) is positive and a > 0, in the ESR spectrum of nitrogen atom, the high field lines should be broader than that the low field lines; if a < 0, the low field line should broaden. Unfortunately, experimental ESR spectra of N and P atoms have been detected under such conditions when anisotropy of g-factor and HFC do not contribute significantly into the line broadening in order to determine the sign of HFC constant. The
Buchachenko lack of this information invalidates any speculations on the mechanism of compression effects for nitrogen and phosphorus atoms. In contrast to H, N, P, Li, Na, and Cu atoms, in which inner electronic layers are completely filled, the majority of multielectron atoms possess inner unfilled or partly filled orbitals. Their existence is due to the fact that in these atoms the electron energy depends not only on the main quantum number n but also on the orbital quantum number l. The more selfconsistent field of multielectron atom differs from the Coulomb field of hydrogen atom, the more the energy depends on l. That is why (n+1)s and (n+1)p states may appear to be energetically more favorable than the nd and nf states. For the same reason electrons of nd and nf layers are placed more deeply, closer to atomic nucleus, than those of (n+1)s and (n+1)p layers. At the compression, the peripheric electrons appear first, suffering Coulomb repulsion of compressing matrix atoms; their energy increases, and when it reaches that of the (n+1)s or (n+1)p layers, it happens that electrons from outer (n+1)s and (n+1)p layers migrate into inner, spatially deep nd and nf layers (Fermi named this effect as an electronic transition under pressure). It is clear that the energy level inversion at the compression is accompanied by decreasing atomic volumes of compressed metals. Theoretical description of the effects of atomic compression in terms of this idea and statistical model of atom nicely agrees with experimental data. Thus, electronic transition with migration of 6s electron into 5d layer occurs in cesium at pressure 40-50 kbar; the density increases from 1.99 g/cm3 (at 1 bar) to 4.1 g/cm3, aand the tomic radius decreases from 2.68 to 2.34 Å.42 Similar transition in Rb (with migration of 5s electron into 4d orbital) happens at 190 kbar; density increases from 1.53 to 5.6 g/cm3, and atomic radius decreases from 2.48 to 1.83 Å.42 Theory describes satisfactorily the experiment and predicts quantitatively a pressure of electronic transition, changes of density, and Grunauser coefficient for electrons (the latter is the ratio of expansion coefficient to the heat capacity of electrons; the negative sign of Grunauser coefficient predicted by theory corresponds to the compression of the electronic shell and agrees with experimental findings).43 Theory predicts also an inversion of electronic levels even for hydrogen atom confined in rigid spherical potential.44 In this electrically compressed atom, the 2s level approaches the 3d+2 level, the 3s to the 4d+2, the 3p+1 to the 4f+3, etc. Generally, the states |n,l〉 move to the |n+1,l+2〉 states; Figure 2 shows that the rise of energy of all levels is accompanied by inversion of 3d and 4d orbitals with respect to 2s and 3s orbitals, respectively; it happens at R e 1.1 Å, where R is the radius of the compressing potential.45 Other examples of calculations of energy levels of compressed hydrogen atom are given in;46 they apply to the region of low compressions where inversion of the energy levels is not reached. It is important to note that under pressure-induced electronic transitions the outer s-electrons migrate onto the inner vacant orbitals: 3d (in K), 4d (in Rb), 4f (in Ag and Cs), and 5f (in Au). However, these orbitals are not spherically symmetrical; they have a node at the nuclei, so spin density on these orbitals should not produce HFC. In other words, the compression of these atoms should diminish HFC constants, contrary to the experimental observations: in all these atoms with unfilled inner shells (K, Rb, Ag, Cs, Au), the compression increases the HFC constants; i.e., it increases spin density on the s-orbitals.
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Figure 2. Energy levels E in hydrogen atom compressed by spherical potential as a function of the radius R of the potential. Stars mark the points of energy level inversion; E and R are given in atomic units.
12. Conclusion In this paper, a complete collection of compressed atoms, their properties, and behavior are presented. This information is amply covered in order to estimate up-to-date status of the science and formulate prospects. First, compression is convincingly shown to modify electronic shells of atoms. This effect manifests itself in the hyperfine, electron-nuclear coupling and in the magnetic properties of atoms; it exhibits itself the more strongly the higher the extent of compression. Second, there is a universal generality: hyperfine coupling always increases as the compression increases; i.e., any compression produces a pumping of spin density on the spherically symmetric s-orbitals in all atoms and ions under study, independently of whether the inner electronic orbitals are filled or vacant. This regularity has no general and unambiguous explanation. For atoms and ions with filled inner orbitals (as N, P, Cu, Li, Na, Sc2+), the mechanism of spin polarization of inner orbitals by outer unpaired electrons may operate. As a test of its importance and efficiency, one can consider the sign of HFC constant; however, the lack of the experimental results, which could help to identify the sign, strongly limits understanding of the compression effects. For the compressed hydrogen atom the simplest mechanism of spin polarization of “foreign”, compressing matrix atoms may be dominant (Adrian’s model), but even this case needs more rigorous and careful theoretical inspection (particularly for multielectron atoms). In atoms with unfilled inner electron layers, the compression urges outer electrons to migrate into the inner, partly vacant orbitals (in Ag, K, Rb, Cs, Au); it clearly follows from the behavior of shock wave adiabats and atomic volumes at the compression (section 10). However, the paradox is that the population of these d- or f-orbitals should decrease the HFC constants because they are not spherically symmetrical. It is not in agreement with experimental findings (section 4). Now one should admit that there is no reliable and correct general theory which could estimate different mechanisms and
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