© Copyright 1996 by the American Chemical Society
VOLUME 100, NUMBER 11, MARCH 14, 1996
FEATURE ARTICLE Chemistry of Multiply Charged Negative Molecular Ions and Clusters in the Gas Phase: Terrestrial and in Intense Galactic Magnetic Fields Gordon R. Freeman* Chemistry Department, UniVersity of Alberta, Edmonton, Alberta, Canada T6G 2G2
Norman H. March Inorganic Chemistry Department, UniVersity of Oxford, South Parks Road, Oxford OX1 3QR, England ReceiVed: May 30, 1995; In Final Form: October 20, 1995X
A review is first given of presently available techniques for generating and observing long-lived dianions of molecules and of clusters in the gas phase. Multiply charged anions that have been unambiguously observed are listed with the technique used to detect them. The remainder of the article is then devoted to the way quantum chemistry can contribute to the continuing search for multiply charged negative ions. This discussion is divided into two parts: (i) ions in zero magnetic fields and (ii) ions in intense magnetic fields. In (i) it is difficult to bind even two electrons to a heavy neutral atom. In (ii), however, a heavy atom with atomic number Z can bind an additional Z electrons, the binding energy of these additional electrons being on the same order as that of the first Z electrons, in the so-called “hyperstrong” field regime. Diatomic homonuclear molecules have binding energies on the order of the separated atom energies. As there should be precursor effects, it is proposed that one should attempt multiply-charged anion formation in the highest available magnetic fields in the laboratory.
1. Introduction Over some three decades, experimental and theoretical knowledge of singly charged negative atomic and molecular ions has built into an extensive area of physical chemistry. One may cite the reviews by Compton1 and Hotop and Lineberger.2 Turning to multiply charged negative ions, the existence of atomic dianions has been the subject of some controversy. Although several workers have claimed to detect doubly charged atomic ions, to date we know of no conclusive demonstration for the existence of bound or long-lived (>10-6 s) atomic dianions. As Scheller and Cederbaum3 stress, the large coulombic repulsion energy between the two excess electrons confined to the relatively small atomic regions makes the X
Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4331$12.00/0
occurrence of bound states of atomic dianions appear improbable. Theoretical arguments of Lieb and co-workers4 support this view by demonstrating, via inequalities, that at most two electrons can be bound to an initially neutral atom. In contrast to the above situation for atomic dianions, there is already a body of evidence, to be reviewed in section 2 below, for the existence in the gas phase of doubly charged anions of molecules and clusters. It is important to note here that a bound molecular dianion must be stable with respect to both electron ejection and dissociation (split into two monoanions). The latter may be direct, dissociation by quantum mechanical transition (tunneling through a barrier), or predissociation.5 From comments already made above, it is clear that to achieve these conditions, it is necessary to overcome the strong mutual Coulomb repulsion between the two excess electrons. One can © 1996 American Chemical Society
4332 J. Phys. Chem., Vol. 100, No. 11, 1996
Freeman and March
envisage achieving this latter requirement by strong binding to electronegative ligands or groups on large molecules or molecular clusters.3,6 The outline of this article is then as follows. In section 2 immediately below, the experimental techniques used to generate negative ions of molecules and clusters are briefly reviewed, and the specific negative ions thereby detected are enumerated. Section 3 is then concerned with predictions made through computational quantum chemistry about multiply charged molecular and cluster anions. We then turn, in section 4, to consider the influence of intense magnetic fields on atomic and molecular anions. Section 5 constitutes a summary, plus some proposals for future work. 2. Experimental Techniques Doubly charged negative ions in the gas phase have been observed by various mass spectrometric techniques. The common characteristics of the stable dianions are that they contain more than five atoms, and at least two of the atoms or groups have large electron affinities. The detection method measures the ratio of mass M to charge z. The problem has been to distinguish M2- from a singly charged ion of half the mass (M/2)- and in one technique (ion cyclotron resonance) from the double harmonic of M-. We list below several dianions for which the evidence is very strong, followed by others for which the evidence is somewhat weaker. They are categorized by the method of production of the dianions. 2.1. Laser Desorption of Electrophilic Species from a Metal Surface. Buckminsterfullerene, C60, in CH2Cl2 solvent exhibits two7 or three8 reversible reduction peaks. The peaks were determined by coulometry to be one-electron processes,7 so the three peaks are assumed to correspond to e-
e-
e-
C60,s y\z C60,s- y\z C60,s2- y\z C60,s3-
(1)
each species being in the solvated state, s. The fullerenes C60 and C70 have essentially the same currentvoltage (cyclic voltammetry) behavior in four different aprotic, polar solvents (o-dichlorobenzene, tetrahydrofuran, methylene dichloride, benzonitrile).8 The reduction potentials in CH2Cl2 with respect to the Ag/AgCl electrode at a scan rate of 1 V/s are E1 ) -0.4 V, E2 ) -0.8 V, and E3 ) -1.2 V.8 The fullerenes were therefore good candidates for preparation of multicharged anions in the gas phase. A dilute solution of a fullerene was placed on a stainless steel probe tip and evaporated to dryness.9 The coated tip was placed in the source chamber of an FT/ICR (Fourier transform/ion cyclotron resonance) mass spectrometer. A laser pulse of ∼10 ns duration was focused onto the tip to desorb some of the material. The gas phase ion trapping voltage was -2 V. The broad-band frequency-sweep excitation mode (200 kHz bandwidth with sweep rate 700 Hz/µs at an rf amplitude of 80 V(pp)) excited ions to a detectable ICR orbital. The mono- and dianions of both C60 and C70 were observed in this way. The dianion M2- was distinguished from (M/2)- because the natural component of 13C gave an M/z at half-integer mass, whereas in (M/2)- it would have appeared at integer mass. The signal from the dianion M2- was distinguished from the second harmonic of the monoanion M- by selectively ejecting M- from the ion trap by single-frequency resonant irradiation at the ICR orbital frequency of M-. Subsequent broad-band excitation/detection resulted in a 95% reduction of the M- signal, with virtually no reduction in the M2- signal. The latter would have been reduced by 95% if it had been the second harmonic of the M- signal.
They also selectively excited and detected only the M2- signal, with only a small signal from M- (possibly arising from some collision-induced loss of an electron from M2- during the excitation period), from a sample containing M- as the most abundant anion.9 This observation would have been unlikely if the attributed M2- signal had been actually the second harmonic of the unexcited signal from M-. Furthermore, the ICR frequency shift caused by reducing the trapping potential to -1 V was virtually the same for M2- (86 Hz/V) as for M(84 Hz/V), whereas the former should have been 168 Hz/V if it had been the second harmonic of the M- signal.9 The gas phase C602- and C702- have been definitely observed, and they endure long enough to give ICR signals, J1 ms. The mono- and dianions of C60 and C70, laser desorbed from stainless steel plates, have also been observed by FTMS (Fourier transform mass spectrometry).10 The electron affinity of C60 is 2.65 eV,11 whereas pseudopotential calculations indicate the electron affinity of C60- to be 0.1-0.4 eV.10 The observed abundance ratios of M2-/M- in these laser desorption experiments10 were in the range 0.02-0.20. The lifetimes of C602and C702-, observed by trapping at a base pressure of 10-5 Pa, are J10-2 s.10 An attempt was made to attach two successive electrons to fullerenes in the gas phase by thermally desorbing C60 or C70 and interacting the vapor with a low-energy electron beam.10 Only M- was obtained, so attachment of a second electron to M- was negligible. Thus, the laser desorption technique ejects M- and M2- directly from the metal surface.10 The observed abundance ratios of M2-/M-, combined with the ∼2.2 eV difference in the electron affinities of C60 and C60-, might indicate that the laser-heated surface of the metal at the desorption site reaches a temperature of several thousands of degrees.10 However, an alternative is that electrons are photoassisted from the metal onto the carbon molecules. We prefer a shock desorption model rather than a high-temperature evaporation model. 2.2. Sputtering. By hitting a graphite surface with highenergy Cs+ ions (14.5 keV) or Ar+ (17 keV), segments of carbon Cn can be blasted off the surface.12 This violent process is called sputtering. Some of the fragments are charged. By holding the graphite at a potential of -4.5 kV, the observed ions sputtered with Cs+ are Cm-, with m ) 1-27, and Cn2-, with n ) 7-28. Sputtering with Ar+ produced Cm-, with m ) 1-19, but no Cn2-. The intensity ratio Cn2-/Cm- from Cs+ sputtering oscillated for odd-even-odd values of m and n, being 10-5 for m ) n ) 7, 10-3 for m ) n ) 8, 10-4 for m ) n ) 9, 10-2 for m ) n ) 10, ..., 1 for m ) n ) 26, and 0.1 for m ) n ) 27.12 The detection method requires that the ions live for at least 10 µs.12 The M2- doubly charged ions were distinguished from (M/2)- by the 13C component appearing at half-integer values of M/z, as described in the previous section. Singly charged fragments Cm- sputtered with Ar+ followed trends reported by Honig:13 even-m ions were more abundant than odd-m neighbors up to m ) 8, and then abundances decreased monotonically up to m ) 19. Pitzer and Clementi,14 using molecular orbital theory, predicted linear chain structures for these anions and found that the oscillations in stability should decrease with increasing chain length. The smaller ions sputtered by Cs+ showed similar oscillations up to m ) 8, but above m ) 14 the odd-m ions had the larger abundances. This agreed with carbon ion intensities observed from a graphite spark source.15 On the basis of theory,16,17 the change in periodicity was taken to indicate monocyclic rings for the larger anions.15 Photoelectron spectroscopic determination of the vertical
Feature Article
J. Phys. Chem., Vol. 100, No. 11, 1996 4333
electron affinities of Cm- showed odd-even alternations with electron affinities being larger for even-m up to m ) 10, and larger for odd-m at m > 10.18 C11- evidently had both linear (EA ) 4.0 eV) and cyclic (EA ) 2.9 eV) structures.18 The relative abundances of Cn2- remain strongly alternate with even-n larger than neighboring odd-n all the way up to n ) 28.12 The opposite even-odd relative stability of the 1and 2- ions for m ) n > 10 is an important clue to their structures, but has not been clearly interpreted. The shock-mechanism fragmentation of the graphite surface could produce ions of diverse structures that relax to different structures before, for example, their electron affinities are measured by photoelectron spectroscopy. 2.3. Neutral Clusters of Electrophilic Molecules Capture Electrons. Expansion of O2 gas from 0.65 MPa pressure at T ) 133 K into vacuum through a 10 µm diameter nozzle produces (O2)x clusters by adiabatic cooling. The clusters were drifted through a low-energy (∼0 eV) electron beam, from which electrons could be scattered and captured.19 Anions were extracted from the gas by a very weak extraction field and analyzed in a double-focusing sector field mass spectrometer. Both mono- and dianions were detected and in particular (O2)x2with x ) 3, 5, 7, and 9.19 Dianions with even-x values were presumably not distinguishable from monoanions of half the mass. The dianions were presumably formed by successive capture of two electrons. 2.4. Electron Capture by a Large Organic Anion That Contains Two Electrophilic Groups. Some molecules upon electron impact have a significant probability of forming a monoanion. If the molecule also contains two or more electrophilic groups which can capture low-energy electrons, one has the possibility of forming a monoanion by electron impact and then a dianion by subsequent electron capture.20
A- + e- f A2-
(2)
Suitable compounds are p-NO2C6H4(CH2)nCO2R, with R ) H or CH3, and n ) 0-9. The most abundant dianions were found for n ) 4,20 with an abundance ratio M2-/M- ) 0.01. In the n ) 4 dianion the two negative charges are ∼1.1 nm apart, with the chain at maximum extension due to electrostatic repulsion between the two negative end groups. The formation mechanism is probably as follows (1 aJ ) 1000 zJ ) 6.24 eV):
O | O2N-C6H4-(CH2)4-COCH3 + e-(few aJ) f O2N-C6H4-(CH2)4-CO2- + CH3 O2N-C6H4-(CH2)4-CO2- + e-(few zJ) f -
O2N-C6H4-(CH2)4-CO2-
2.5. Electrospray of a Dilute Solution of a Dianionic Salt into a Vacuum, with Subsequent Evaporation of Solvent from the Anion. A liquid can be transformed into fine droplets by passing it through a nebulizer or alternatively through a fine capillary to which a high voltage is applied to produce a strong, nonhomogeneous electric field. One such nebulizer21 is made of a 50 µm i.d. fused-silica capillary inside a 200 µm i.d. stainless steel capillary inside an 800 µm i.d. Teflon tube. Liquid is fed into the silica capillary and N2 gas is blown through the Teflon tube so that a highspeed jet of N2 envelopes the end of the silica capillary. Strong turbulence is generated at the end of the capillary when the annulus of gas in the Teflon tube collapses at the exit. Liquid
that extends from the end of the silica capillary is broken into fine droplets by the turbulent gas and carried away. If the average diameter of the droplets is ∼1 µm and the solution contains electrolyte at a concentration < 0.1 µmol/m3, then each droplet contains on average less than one ion. By placing a potential of -3 kV on the steel capillary that surrounds the liquid and to which it is joined by a meniscus, the ions in the droplets are usually anions.21 The neutral droplets are carried away in a stream of N2 gas, and the anionic droplets are focused by an electrostatic lens toward a 100 µm i.d. hole that leads to vacuum (10-3 Pa). Solvent evaporates from the droplets in vacuum, leaving little or no solvent on the ion. In some cases remaining solvent molecules are removed by accelerating the ions to 120 eV and then colliding them with argon atoms (collision-induced dissociation). In this way organic disulfate ions, in which two -OSO3- groups are separated by seven carbons, have been observed.21 A simpler electrospray source, in which a capillary of methanol solvent is held at -4 kV and the annular flow of N2 is not required, led to the observation of S2O62- and S2O82-.22 Methanol sprays more easily than water, due to the lower surface tension of the former. The final solvent molecules were removed from the ions by colliding the accelerated ions with Ar atoms. Collision-induced dissociation of SO42-‚H2O produced HOSO3- and OH-.22 The observed dianions would have the negative charges distributed over several oxygen atoms at opposite ends of the structures:
2.6. Electron Capture by Large Organic Molecules To Form Monoanions, Followed by Dimerization To Form Dianions. Capture of slow electrons by the fused-ring aromatic benzpyreneone, C19H10O, in a mass spectrometer source at relatively high pressures (∼10-3 Pa) and ion currents (not stated) led to the observation of C19H10O- (M/z ) 254) and [C19H10O-]2.23 The latter was identified by the 13C component, which gave M/z ) 254.5. The half-integer value of M/z disappeared at a lower source pressure (∼10-4 Pa) or when the ion current was reduced 10-fold. 2.7. Collision-Induced Dissociation of a High-Energy Monoanion To Form a Dianion and a Cation. The mass spectrometer source temperature was 553 K, the pressure was ∼4 × 10-4 Pa, the electron beam energy was 100-250 eV.24 Dicarboxylic esters under these conditions produced monoanions [M - alkyl]- and [M - H]-, along with other anions, cations, and radicals. Anions were accelerated through 8 kV, mass selected, and passed into a field-free collision cell containing He gas to induce dissociation. In this way dianions -O2C(CH2)nCO2-, with n ) 2-7, and -O2CCH2C(CH3)2CO2- were observed. The favored mechanism for production of the dianions was24
(RO2C(CH2)nCO2-)* + He f R+ + -O2C(CH2)nCO2- + He*, n ) 2-7 (3) This ionic dissociation would require ∼10 eV of energy to separate the charges. Dissociation to neutral radicals would require only 3-4 eV, but subsequent capture of an electron by the monoanion radical under these conditions was considered to be negligible. 2.8. Summary. The dianions that have been observed are listed in Table 1.
4334 J. Phys. Chem., Vol. 100, No. 11, 1996
Freeman and March
TABLE 1: Gaseous Dianions Observed Mass Spectrometrically dianion
method of preparation
C602-, C702Cn2-, n ) 7-28 (O2)x2-, x ) 3, 5, 7, 9 -O NC H (CH ) CO -, n ) 3, 4 2 6 4 2 n 2 O3SO-CnHm-OSO3-, n > 7 -O S-SO -, -O S-O-SO 3 3 3 3 [C19H10O-]2 O2C(CH2)nCO2-, n ) 2-7
electron capture and dimerization electron impact on a diester followed by collision-induced dissociation of the monoanion
3. Theoretical Treatments The preceding experimental discoveries may be usefully supplemented by computational quantum chemical techniques. 3.1. Theoretical Work on Negative Ions of Carbon Radicals and Molecules. As summarized in the previous section, anions of carbon radicals and molecules Cn have been generated and detected in several chemical and physical environments. In particular, there is a wealth of data on the smallest of these molecules, C2-, which could also exist in the interstellar medium and carbon stars (which contain high concentrations of carbon and have relatively low temperatures). This anion appears first to have been observed by Honig,13a who also presented evidence for the existence of several larger Cn anions, including C3- and C4-. Subsequently, many other Cn anions have been detected, and photoelectron spectra of a considerable number have been measured. Specifically, Yang and co-workers18 have obtained photoelectron spectra of anions from C2- to C84-. Subsequently, Arnold and co-workers25 also measured at high resolution the photoelectron spectra for C2- through C11-. The spectra measured as above have yielded much important information about both nuclear geometry and electronic structure of these anionic carbon species. For the smaller systems, up to and including those containing nine atoms, linear anions (and neutral molecules) are generated and detected in these experiments. Arnold and co-workers have argued that, in addition to the small linear species, their spectra exhibit evidence attributable to cyclic species. For C10- through C20-, the spectra of Yang and coworkers18 indicate the presence of cyclic (presumably monocyclic) isomers. For C11-, evidence of both linear and cyclic isomers is observed. For larger species, there are many possible structures, including fullerenes. The structure of neutral C4 in graphite vapor has received much attention from theorists.26-28 It was concluded that the most stable structure is cyclic, for example C C
refs
laser desorption from steel sputtering with 14.5 keV Cs+ electron capture by clusters electron impact on an ester to form a carboxyl ion, followed by electron capture electrospray, followed by solvent evaporation, and collision-induced dissociation
C C
A cyclic structure has been confirmed by the Coulomb explosion imaging method.29 In these interesting measurements graphite was sputtered with high-energy Cs+ ions. From the resulting gaseous anions C4- was mass selected and then accelerated through 12 MV. When the ions reached the field-free region in the middle of the accelerator, they interacted with laser light (535 nm, 25 mJ/cm2, 20 ns pulse) to detach the electrons. The neutral C4 molecules were drifted 30 m (4 µs) to hit a 3.0 nm thick Formvar foil. On average 12 electrons were stripped from the C4 species on passing through the foil, and the four C3+ ions separated “explosively” from each other due to their mutual Coulombic repulsion. Their positions and times of arrival at a microchannel plate detector were recorded. The “exploded” structure indicated that the neutral C4 entered the foil as a ring.
9, 10 12 19 20 21 22 23 24
A variety of experiments and theoretical calculations have shown that linear neutral Cn species exhibit two different electronic ground states.30 Apart from C2, the even-n linear structures have πg2 or πu2 configurations and 3Σg- cumulenic ground electronic states. The ground states of the odd-n neutral species on the other hand are also cumulenic, but are closed shell 1Σg+ states. Due to their partially occupied π orbitals, one would expect the linear even-n species to have higher electron affinities than the odd-n species. This expectation has been confirmed by both experiment and theory. Furthermore, due to the presence of partially occupied π orbitals, one would expect the ground state of the anions to be 2Πu or 2Πg. Likewise, since the lowest unoccupied orbitals of odd-n neutral molecules are π orbitals, one would anticipate that the ground states would also be 2Πu or 2Πg. While the ground states of odd- and even-n linear anions are expected to be the same, one must remember that the configurations are different: either π3 (even) or π1 (odd). Thus, they will be expected to have quite different properties. Such predictions of ground electronic states of the linear anions have been supported by theoretical calculations of C3-, C5-, and C6- (for references, see ref 30). For the case of C8-, however, some calculations31 have indicated that the ground electronic state is 4Σ rather than 2Π. Turning to our major focus in this present article, Cn dianions are less common than Cn monoanions. Watts and Bartlett30 have considered the theory of linear Cn- and Cn2- with n ) 2-10. They estimated the geometries of neutrals, monoanions, and dianions. Also, attention was given to the detailed electronic structure. Vertical and adiabatic electron affinities and electron detachment energies were thereby obtained. 3.2. Additional Electrons Bound to C60. We shall consider below results, from both experiment and theory, on C60 with an added electron. The electron affinity of C60 has been measured as 2.65 ( 0.02 eV.18 We shall be concerned below with a brief discussion of the way such a result can be represented by a pseudopotential constructed by Hettich and co-workers.10 Electron Density Calculation for Added Electron in C60Pseudopotential. The binding of an additional electron to C60 has been explored numerically using the central field pseudopotential description:10
V(r) )
-e2R [c + 21/2(r - rc)2]2
(4)
Here R is the polarizability, rc is approximately the radius of the soccer ball representing C60, and c is an adjustable constant. Hettich and co-workers fit c to reproduce the known binding energy of 2.65 eV.10 Here an approximate calculation of some properties associated with the pseudopotential (4) will be obtained analytically from electron density theory. The starting point is to model the electron density of the ground state generated by V(r) in eq 4 as the Gaussian
Feature Article
J. Phys. Chem., Vol. 100, No. 11, 1996 4335
F(r) ) Fmax exp(-A{r - rc}2)
(5)
Next we shall invoke the approximate result of March and Wind,32 which can be described as a spatial generalization of Kato’s theorem:
∂F(r) -2r2 ∂V ) 2 Fs(r) ∂r e a ∂r
(6)
eq 13 is of Gaussian form,
F(r) ) N exp[-B(r - rc)2]
where B < A in eq 5. Again we use the relation of March and Wind.32 Differentiating eq 14 with respect to r, we find, again near r ) rc,
∂F ) -2B(r - rc)F(rc) ∂r
0
where Fs(r) is the s-state contribution to the total density F(r). Equation 6 is exact for closed shells in a bare Coulomb field33 but otherwise approximate. For the ground state generated by V(r) in eq 4, F ) Fs. We now differentiate eqs 4 and 5 and substitute the results into eq 6. Working near the “surface” of C60, where r = rc, we find the approximate result
A ) 2 R rc /c a0 2
5/2
3
(8)
is plainly an upper bound to the binding energy. It requires correcting by the zero-point energy associated with the curvature of the potential energy (4) around r ) rc. Evidently, the expansion of eq 4 for r = rc is
[
2 (r - rc) V(r) ) V(rc) 1 c
]
/2k ) 23/2e2R/c3
1
(9)
(10)
Hence, the zero-point energy 1/2pω referred to above corresponds to the electron phase angular speed
ω ) (k/m)1/2
(11)
with m the electron mass. Finally, therefore, the binding energy, Eb, say, of the added electron to the neutral C60 molecule is given by
)-
]
(16)
Hence r2∂Ve(r)/∂r can be written in terms of the total amount of charge Q(r) inside a sphere of radius r, namely,
Q(r) ) ∫r4πr2F(r) dr
(17)
r2∂Ve(r) ) Q(r) ∂r
(18)
e2R pω + 2 c2 1/2 e2R (a0R) e2 + 2 c3/2 c2
(12)
In summary, eq 7 shows how the (model) ground-state density (5) is to be expected to vary with the pseudopotential parameters in eq 4. Equation 12 is the corresponding result for the binding energy. Generalization to C602-. Here we sketch the generalization of the approximate density functional theory given above for C60- to the dianion C602-. We construct a new effective potential energy, Veff(r), say, as
F(r′) Veff(r) ) V(r) + e2∫ dr′ (r - r′)
From eqs 6 and 15 one then finds
-2B(r - rc) )
2
with force constant k given by
Eb ) -
[
1 ∂ 2∂Ve(r) r ) 4πF(r)e2 2 ∂r ∂r r
as
V(rc) ) -e2R/c2
3/2
(15)
Turning to construct r2∂Veff/∂r from eq 13, the first term from the pseudopotential V(r) has already been dealt with above. The second, screening contribution to Veff(r), say Ve(r) in eq 13 can be handled using Poisson’s equation of electrostatics in the form
(7)
which demonstrates the parametric dependence of the model electron density (5) on the pseudopotential (4). For C60, Hettich and co-workers10 take the polarizability R = 80 Å3. The depth V(rc) of the pseudopotential, namely,
(14)
(13)
Again, the assumption is made that the electron density F(r) in
(
)
r2 ∂V Q(r) - Q(rc) + a0 e a0 ∂r 2
(19) r=rc
Using the explicit form (14) in eq 17, one can obtain Q(r) in terms of B and rc. Equation 19 can then be used iteratively to determine B, for given parameters R, rc, and c in the Hettich and co-workers pseudopotential V(r) starting with a zero-order approximation B ) γA, γ = 1. Although this numerical iteration has not been performed at the time of writing, we have estimated B ∼ 0.15 Å-2 from the different numerical study reported by Hettich and co-workers.10 3.3. Heteronuclear Multiply Charged Negative Ions. Scheller and Cederbaum6 have presented a “construction principle” which they argue should allow the design of stable multiply charged molecular anions in the gas phase. They then construct a sequence of anionic potassium fluorides KaFa+bbwith b ) 2-7, on the basis of their proposed principle. Then, at the ab initio and ionic level of theory, these workers studied the stability of such systems to electron detachment and to Fdetachment. It is clear that a bound or at least long-lived (>10-6 s) doubly charged molecular anion can exist only if stable with respect to these two processes. To achieve the second condition, one must overcome the mutual Coulomb repulsion between the F- ions. Considering the example of small molecular dianions, highly symmetric systems consisting of a positively charged central species and surrounding electronegative ligands (atoms or groups) have emerged as especially favorable candidates. Major ingredients with respect to the stability of such compounds are strong binding and delocalization of the excess electrons on the symmetry-equivalent ligands as well as a nonbonding center-ligand interaction.3,9,10,12,19,34-38 The knowledge of the existence of dianionic species (see section 2) motivates the question as to whether the stabilizing effects fundamental to a specific atomic constitution can be transferred to triply or even more highly charged negative ions.
4336 J. Phys. Chem., Vol. 100, No. 11, 1996
Figure 1. Schematic depiction of the gas phase molecules (A) KF32-, (B) K2F42-, and (C) K2F53-. HF-SCF optimized values for the bond distances (Å) and bond angles (deg) at the ground-state structure of these systems are given. From ref 6, with permission. Copyright 1993 (Elsevier).
Scheller and Cederbaum34 argue that preserving a basic structural unit, as for example an MX32- type of alkali halide ion, such a configuration can be taken as a starting point for a “construction principle” which then permits the prediction of stable highly charged negative ions. Below, we summarize their main results for the sequence of anionic potassium fluorides, based on the particular structural unit KF32-. They employed, as the ab initio methods involved in their study, the Hartree-Fock self-consistent-field (HF-SCF) approximation and the outer-valence Green function (OVGF) approach. The latter technique was used to compute the binding energies of the excess electrons. This approach includes both electron correlation and relaxation effects.39 Scheller and Cederbaum34 stress that for small molecular dianions the stability against dissociation and against electron autodetachment depends crucially on the type of constituent atoms or groups of atoms that one chooses to arrange. Any construction principle, they note, should therefore retain the atomic arrangement of the structural unit used as the starting point, for the systematic extension to higher negatively charged species. In their particular example, this means that, starting from the KF32- unit (see Figure 1, part A), one has to preserve the triple coordination of the metal center. This requirement implies that the systematic extension of the KF32- structural unit has to proceed via fluorine cross-linking of the metal atoms by addition of one or more KF or KF2- subunits. They note that their construction principle excludes the addition of F- to the basic unit KF32-. Their ab initio results40 confirm this prediction and demonstrate that KF43- with a quadruply coordinated metal center is indeed unstable to (a) electron autodetachment and (b) detachment of an F- ion. To illustrate their principle, it is to be noted that the smallest member of this series of molecules is K2F42-. This can evidently be derived from the addition of a KF unit to KF32-. Their theoretical studies at the ab initio HF-SCF level have shown that K2F42- has the D2h symmetrical ground-state configuration (Figure 1B) with triply coordinated metal atoms only.
Freeman and March In the electronic closed shell ground state, the excess electrons of K2F42- are bound by 4.8 and 3.8 eV at the HF-SCF and OVGF level of theory, respectively. Scheller and Cederbaum34 demonstrate that the D2h symmetrical K2F42- is much more stable than the basic structural unit KF32- by itself (see shortening of K-F bonds in K2F42- compared with KF32- in Figure 1). Scheller and Cederbaum define a ratio, R, of the excess squared charge per F atom. In general they observe that the smaller the value of this ratio R, the more pronounced the stability of an anionic molecule both to the ejection of an excess electron and to split-off of F-. The intuitive idea underlying this is that a lower value of R reflects a smaller mutual Coulomb repulsion between the excess charges. Thus, the excess squared charge per atom, R, is 1.33 for KF32- and decreases to a value of unity for the more stable K2F42-. Next consider the addition of a single KF2- subgroup to the basic structural unit KF32-. For the resulting K2F53- trianion, the D2d structure shown in Figure 1C was predicted from the ab initio HF-SCF study of Scheller and Cederbaum for the ground-state geometry of the resulting K2F53- trianion. They note that this configuration preserves the triple coordination of the metal centers present in the basic structural unit KF32-. Their ab initio results indicate that the trianion is stable. The overall stability of K2F53-, however, falls off appreciably with respect to that of KF32- or K2F42-. This is consistent with the lengthening of the K-F bonds in K2F53- (see Figure 1). The ratio R is also increased to 1.8. We shall not press further detail of the work of Scheller and Cederbaum, but to conclude this account, they systematically construct a sequence of anion potassium fluorides with up to seven excess electrons. They present weighty evidence that such highly charged negative molecular systems should exist as longlived compounds in the gas phase. It is relevant in the present context to refer here to the earlier work of Boldyrev and Simons.38 These authors studied the electronic stabilities of some small linear doubly charged anions. The linear diatomics included BN2-, BP2-, BeO2-, BeS2-, MgO2-, MgS2-, O22-, SO2-, and S22-. However, all these diatomic dianions were found, when studied at the HF level with Gaussian basis sets including diffuse and polarization functions, as well as at the second-order Moller-Plesset level, to be unstable to electron loss. A similar conclusion was reached for sets of triatomic and tetratomic dianions. However, a study of the pentatomic Be2O32-, Be2S32-, Mg2O32-, and Mg2S32- dianions led to the prediction that Mg2S32- was stable to electron loss with an electron detachment energy of 0.2 eV. Boldyrev and Simons conjecture that this is likely to be the smallest electronically stable linear dianion. They note that Scheller and Cederbaum3 predicted the stability of the very small nonlinear dianion LiF32-, evidently closely related to the anionic potassium fluoride discussed above. 4. Heavy Ions in Intense Magnetic Fields Following early work by Kadomtsev,41 there has been much progress in treating heavy ions in intense magnetic fields. This has come, until very recently, largely through the simplest form of density functional theory, namely, the Thomas-Fermi (semiclassical) method, which uses electron gas theory locally (see, for example, Lundqvist and March,42 and Gordon and Kim43). Briefly, this method writes an equation for the chemical potential µ of the inhomogeneous electronic cloud in a molecule (neutral or charged) as
Feature Article
J. Phys. Chem., Vol. 100, No. 11, 1996 4337
µ ) KE(r) + V(r)
(20)
In zero magnetic field, and in nonrelativistic theory, the kinetic energy contribution KE(r) is simply pmax2(r)/2m, where pmax(r) is the maximum (Fermi) momentum at position r and m is the electron mass. Using the electron gas relation between density F and pmax locally, namely,
(21)
µ ) constant{F(r)}2/3 + V(r)
(22)
one finds
In an atomic ion, or a multicenter molecular ion, eq 22 can be solved self-consistently by combining it with Poisson’s equation of electrostatics, which relates the (electrostatic) potential V(r) to the electron density F(r). While the generalization of eq 22 to an arbitrary magnetic field H has been made,44 applications to date have come from the extremely high field limit (to be made more precise below). Thus, Hill and co-workers45 (see also ref 46) have solved selfconsistently the Thomas-Fermi problem in the intense field limit, for positive atomic ions. We draw attention here to some basic consequences that follow from eq 22 applied to (a) atomic ions and (b) neutral homonuclear diatomic molecules. First of all, for a heavy neutral atom to which eq 22 applies, the chemical potential µ is identically zero. This means that an extra electron added will not be bound to the neutral atom. In other words, in zero magnetic field for which eq 22 is valid, negative atomic ions are not stable. Turning to (b) above, eq 22 predicts that very heavy neutral homonuclear diatomic molecules, such as Pb2 or Po2, are nonbonding in the gas phase. This is the essence of Teller’s theorem,47 which asserts that no fully local density approximation (even including local exchange and correlation) in the oneelectron potential V(r) in eq 22 can produce a stable bond in such neutral molecules. We turn, therefore, from eq 22, and its generalization to intense magnetic fields, to consider the recent work of Lieb and co-workers,48 which has been also developed by Lehmann and March.49 Hyperstrong Fields. Lieb and co-workers48 have generalized the above treatment on the basis of the analog of eq 22 in an intense magnetic flux density B. In “reduced units” (p ) c ) m ) e ) 1) they delineated, for very heavy atoms (large atomic number Z), five regions. Three of these are embraced by the inequality B , Z3, and these are covered by the Thomas-Fermi theory summarized above. However, regime 4, of major interest below, is that in which B ≈ Z3, while regime 5 is evidently B . Z 3. Lieb and co-workers48 stress that in the hyperstrong field regime 5 an initially spherical atom will have degenerated into a needle, elongated along the field direction.50 Introducing η ) B/Z3, the regime is evidently one of large η. The groundstate energy of an atomic ion with atomic number Z and N electrons then has the scaling property
(23)
where EHS ≡ Ehyperstrong depends, as indicated, only on the parameter N/Z. This result (23) is to be contrasted with the zero-field (B ) 0) result of the Thomas-Fermi (T-F) theory based on eq 22, namely,
(24)
Whereas, as already argued above, heavy negative ions are not stable according to the T-F theory at B ) 0, and therefore one has N/Z E 1 in eq 24, Lieb and co-workers calculate EHS (N/Z) in eq 23 to be explicitly
EHS(N/Z) ) -
8π F(r) ) 3 pmax3(r) 3h
E(B,Z,N) ) Z3[ln η]2EHS(N/Z)
E(B)0,Z,N) ) Z7/3f(N/Z)
1N 1N2 1 N3 + 4Z 8Z 48 Z
() ()
()
(25)
They establish the result that, for large Z, N/Z E 2, a truly major change from the zero-field T-F result N/Z E 1. Thus, whereas in zero field, for large Z, negative atomic ions do not exist, in hyperstrong fields such as exist at the surface of a neutron star, one can attach a number of electrons N ) 2Z to a heavy nucleus. Not only can one find that number of electrons but the binding energy of the last Z electrons is on the same order of magnitude as the first Z electrons. When one goes over to, say, a neutral diatomic molecule, with two identical nuclei of charge Z, then in complete contrast to Teller’s theorem based on the zero-field T-F eq 22 that very heavy neutral homonuclear diatomic molecules do not bind (see also Mucci and March51), in the hyperstrong magnetic field regime B . Z3 the molecular binding energy is large and similar to the energy of the two individual atoms. While, to our knowledge, a detailed analysis of multiply charged negative molecular ions has not yet been made in the hyperstrong magnetic field regime, it is abundantly clear that terrestrial chemistry will be totally transformed when molecular ions are placed in hyperstrong magnetic fields such as exist at the surface of a neutron star. It should be noted that Tomishima and March52 proposed the scaling based on T-F theory in intense magnetic fields (regimes 1-3 above),
E(B,Z,N) ) Z9/5L2/5
(NZ) [ - NZ + ... + (NZ) ] 3/5
n
0
1
n
(26)
where n is independent of N for large N, with L ) eB/m2 ) B/Bc, with Bc ≈ 4 GT. 5. Summary and Future Directions A number of well-established techniques are now available for generating and detecting anions with multiple charges. These are reviewed, and the relatively few presently detected dianions are listed. One must expect, however, with large molecules or clusters, that it may be possible to bind more electrons. Theoretical progress in the area of multiply charged anions has been very considerable. Here, the work of Cederbaum and his colleagues has been given some prominence, as they have proposed a construction principle which allows the prediction of a sequence of negative ions. They have especially focused on the potassium fluoride sequence and have considered cases where the negative ion has a multiple charge of -7|e|. Other theoretical work, especially in the group of Bartlett, has focused on carbon dianions, Cn2-. Each of these groups has considered the stability of anions, of either molecules or clusters, against electron loss. Cederbaum and co-workers have also considered stability against fragmentation to monoanions, in some detail. The final part of the article has compared and contrasted the known facts of terrestrial chemistry for heavy homonuclear molecules with the predictions for atoms and molecules in intense magnetic fields. The magnetic field problem, in “reduced units”, can be characterized by a number of regimes. Lieb and co-workers,48 in considering the regime B . Z3, with
4338 J. Phys. Chem., Vol. 100, No. 11, 1996 Z the atomic number, have shown that atoms become needles elongated in the magnetic field direction.50 Heavy neutral atoms are then able, in principle, from nonrelativistic Schro¨dinger theory, to bind n E Z additional electrons. This leads to a situation in which, for large Z, the binding energy of the homonuclear diatomic molecule is on the order of the separated atom energies. This, of course, is in marked contrast to terrestrial chemistry. Here also one has the semiempirical analysis of Mucci and March, who compare and contrast the binding of heavy homonuclear diatomics with that of heteronuclear binding and with the theorem of Teller which states that heavy homonuclear diatomics do not bind in the ThomasFermi approximation embodied in eq 22. Although observations are presently difficult, it would be of considerable interest if present techniques for generating multiply charged anions proved still to be possible in a strong magnetic field in the laboratory. Although the detailed predictions of Lieb and co-workers have contemplated magnetic flux densities up to 1 GT, such as exist at the surface of neutron stars, it would be of interest to see if effects which are precursors of the Lieb and co-workers predictions could be observed in magnetic fields attainable in the laboratory. Photons are neutral and could readily penetrate into presently attainable fields of 102 T. If C60 were deposited on a thin film (∼100 nm) of aluminum and oriented such that some of the laser-desorbed C60 anions would be ejected from the metal in the direction of the magnetic field, the number of charges on the anions could be detected by optical spectroscopy. The magnetic field would presumably be pulsed, with a pulse duration of, say, ∼1 ms. If the eddy currents in the aluminum thin film decayed in 107 T); discrete states are obliterated by very strong fields. (51) Mucci, J. F.; March, N. H. J. Chem. Phys. 1985, 82, 5099. (52) March, N. H.; Tomishima, Y. Phys. ReV. D 1979, 19, 449.
JP951483+
