The correlation between Raman spectroscopy and bond lengths in high-valent actinide complexes

The correlation of vibrational energies to bond strength and molecular structure has a long tradition in inorganic chemistry. For example, Badger's rules allow the metal-metal bond length for second- and third-row transition dimetallic complexes to be predicted based on the bond vibrational energy. In the course of our studies of structure and bonding in actinide complexes in high-oxidation states, we have examined a variety of axial dioxo systems in which the linear O=An=O moiety is both highly sensitive to the electronic configuration of the complex and also yields a characteristic Raman band, identified as the symmetric stretch n1.

While a handful of crystallographic studies of actinyl complexes has been published, until recently there has been a relative paucity of the structural data needed for the development of structure/vibrational band correlations. Now, however, x-ray beam-line studies, especially EXFAS spectroscopy, are used to characterize the structural properties of solution and polycrystalline actinide samples, creating a much more expansive structural data base for actinide complexes. As a result, we can now correlate the energy of the n1 Raman band, either from the literature or our own data, with structural data derived from both crystallographic and solution EXAFS studies to seek the common relations between the vibrational energies and An–O bond lengths.

The correlation of actinyl bond distance to vibrational energy for a variety of actinide metals and oxidation states.

Plots comparing the structural and vibrational data for representative U, Np, and Pu dioxo species are shown in the figure above, where the An–O bond length (y-axis) is maintained between the different actinides to facilitate comparisons. The units on the x-axis reflect the fact that the mathematics of relations like Badger's rule are such that the bond distance is a linear function of the vibrational energy to the –2/3 power. Clear trends can be seen within a particular oxidation state of an actinide, for example U(VI) and Np(V); however, unlike dimetallic transition metal complexes, no universal trend between the actinides or even between oxidation states of the same actinide is observed.

The sensitivity of Raman band energy to the bond distance (slope) is much greater for Np(V) than for U(VI), which in turn is more sensitive than that observed for Np(VI). Pu(VI) manifests shifts in n1 > 40 cm^-1 even though the changes in the "-yl" bond length are very limited. Thus, for Np(V), bond distance is a more sensitive indicator of changes in the equatorial bonding structure than are the vibrational data, while for Pu(VI) the opposite is true.

Given the successful application of Badger's rule for entire rows of transition metal dimer stretches, the lack of a consistent trend for the symmetric "-yl" stretches, which is also a two-atom motion, is perhaps surprising. Thus, the identity of the actinide itself, its oxidation state, and the equatorial ligand content must all be considered to be of potential influence in determining the combined distance and bond-energy properties of the actinyl structural element.

For example, encompassing dioxo Np(V) into a rather large crown ether minimizes the equatorial (ether) interactions and causes the axial "-yl" bond to be considerably shorter than that for the tris carbonato species, where carbonate interacts very strongly in the equatorial position and engages bonding electrons that might otherwise interact with the axial oxygens. Another means of comparison can be made in terms of f-orbital occupancy. Thus, we can find consistency in the structural and vibrational properties of the f1 configuration complexes of [UO₂⁺] and [NpO₂²⁺]. However, such comparisons must be carefully made. As an example, the structural and vibrational properties of f0 dioxo U(VI) complexes cannot be compared with Np(VII) complexes because the latter adopt a tetraoxo core structure.

Comparing the structural and vibrational data from similar complexes of different actinides provides an interesting perspective. Across the actinide series, for a given oxidation state, the metal atomic radius decreases as the atomic mass increases. This actinide contraction, similar to the well-studied lanthanide contraction, results in the prediction that the "-yl" bond length should get shorter as one proceeds along the actinide row of the periodic table.

Such a result is indeed observed in the structural data but yields a surprising correlation with the vibrational energies. Generally, shorter bond lengths yield higher energies for the corresponding stretching mode; however, the opposite relation is found here. A comparison of the Np(V) → Pu(V) and Np(VI) → Pu(VI) aquo complexes, as well as the U(VI) → Np(VI) → Pu(VI) tris carbonato complexes and Np(VI) → Pu(VI) tetrachloro complexes all show decreasing stretching frequencies accompanying the shorter bonds.

This result can be interpreted as follows. The bonds to the "-yl" oxygens include contributions from the 5f orbitals. The primary physical cause of the actinide (and lanthanide) contraction is decreased shielding of the core positive charge across the series: as electrons are added to the outermost frontier orbitals they do a poorer job of screening the charge from the additional protons crowded at the atomic core.

Decreased shielding, in turn, causes the 5f orbitals to shrink toward the core, and their directionality decreases as they become more diffuse. Therefore, although the axial oxygens "chase" these orbitals inward across the actinide series (the vibrational potential energy curve minimum moves to a smaller equilibrium distance), their overlap with the increasingly buried 5f orbitals still decreases, and the bond order is reduced (the potential energy surface becomes less curved).

Badger's rule

Fundamental manifestations of chemical bonding include the strength of the bonds that are formed as well as their length. Intuitively, there should be a link between the bond strength and the subsequent length of that bond, and this link is provided by Badger-type rules. However, with the vibration viewed as a potential energy curve, the position of the potential energy minimum (bond length) does not necessarily have a unique link to the width/steepness of the potential energy curve (bond strength).

In fact, an example is mentioned in the main article for the tris carbonato species where weaker dioxo bonds are accompanied by shorter bond lengths. Therefore, care must be taken to tune the Badger-type relationships and to test how wide their application is. Many of the Badger-type relationships involve stretches that are described as being due to the vibration of two atoms, as in the case of metal-metal bonding. The linear dioxo moiety involving the early actinides in high-valence states is an uncommon structural motif in chemistry and requires its own Badger-type relationships.

Badger's rule is named for the late Richard McLean Badger, whose career as a student, teacher, and researcher at the California Institute of Technology spanned more than 50 years. His "rule," which relates a change in stretching frequency with a change in bond lengths, was the result of his extensive study the force constant and internuclear distance in a large number of diatomic molecules.

Badger-type relations provide a link between bond strength and bond length, which in turn, provides important constraints to check the theoretical calculations (with their associated approximation methods) performed to inform us of the orbitals used in constructing the molecule. Alternatively, bond lengths of unknown or new molecules can be estimated from vibrational information on the bond strengths. Because growing single crystals for x-ray diffraction studies is difficult and sometimes not possible, this is a valuable tool to have.

This research was supported by a Laboratory Directed Research and Development (LDRD) CD Thrust administered by the Glenn T. Seaborg Institute of Transactinium Science at Los Alamos National Laboratory. EXAFS experiments were performed at the Stanford Synchrotron Radiation Laboratory, which is supported by the DOE Office of Basic Energy Sciences.

This article was contributed by Los Alamos researchers C. Drew Tait, D. Webster Keogh, Mary P. Neu, Sean R. Reilly, Wolfgang Runde, and Brian L. Scott of the Chemistry Division; Robert J. Donohoe of the Biosciences Division; David L. Clark of the Nuclear Materials and Technology Division; Steven D. Conradson of the Materials Science and Technology Division; and Scott A. Ekberg, formerly of the Chemistry Division.

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