RELATIVISTIC EFFECTS IN ATOMS AND IN URANIUM COMPOUNDS VRIJE UNIVERSITEIT RELATIVISTIC EFFECTS IN ATOMS AND IN URANIUM COMPOUNDS ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Vrije Universiteit te Amsterdam, op gezag van de rector magnificus dr. C. Datema, hoogleraar aan de faculteit der letteren, in het openbaar te verdedigen ten overstaan van de promotiecommissie van de faculteit der scheikunde op donderdag 20 februari 1992 te 15.30 uur in het hoofdgebouw van de universiteit, De Boelelaan 1105 door Engelbertus Maria van Wezenbeek geboren te Noordoostpolder FEBODRUK Enschede 1992 Promotor: prof.dr. E.J. Baerends Copromotor: prof.dr. J.G. Snijders Referent: prof.dr. P. Pyykkö voor mijn vader† en moeder voor Saskia Contents Summary 9 Chapter 1 General Introduction 13 Chapter 2 The Origin of Relativistic Effects of Atomic Orbitals 45 W.H.E. Schwarz, E.M. van Wezenbeek, E.J. Baerends and J.G. Snijders, J. Phys. B 22 (1989) 1515 2+ Chapter 3 The Relativistic Bond Lengthening of UO2 and UO2 63 E.M. van Wezenbeek, E.J. Baerends and J.G. Snijders, Theor. Chim. Acta 81 (1991) 139 2+ Chapter 4a An explanation for the short U-O bond length in UO2 83 in E.M. van Wezenbeek, E.J. Baerends, J.G. Snijders and R.L. DeKock, to be submitted to J. Phys. Chem. Chapter 4b A qualitative study of the relativistic effects on the bond between HfCl3, ThCl3 and H 101 E.M. van Wezenbeek, T. Ziegler and E.J. Baerends, to be submitted 6 Contents Chapter 4c The Central Bond in the three CN• Dimers NC-CN, CN-CN and CN-NC: Electron Pair Bonding and Pauli Repulsion Effects. 123 F.M. Bickelhaupt, N.N. Nibbering, E.M. van Wezenbeek and E.J. Baerends, Submitted to J. Phys. Chem. Chapter 5 Spectroscopy of Uranyl Compounds 149 in E.M. van Wezenbeek, E.J. Baerends, J.G. Snijders and R.L. DeKock, to be submitted to J. Phys. Chem. Chapter 6 Organoactinide Chemistry: The ground electronic structure of UCp3 and interaction with the ligands CO, NO and H 167 E.M. van Wezenbeek, R.L. DeKock and E.J. Baerends, to be submitted Samenvatting 199 Nawoord 203 Curriculum Vitae 204 7 Summary Relativistic effects are important in the study of molecules containing heavy atoms, because in those systems the electrons move very fast near the nucleus. Before investigating relativity in molecules one must understand the relativistic effects on atomic orbitals. Therefore this thesis starts with a chapter on atomic relativistic effects, after a general introduction about relativity and the method of calculation in Chapter 1. The other work concerns molecular calculations, where relativistic effects on bonding, bond-lengths and spectroscopy of molecules containing heavy elements are studied. Also bonds are investigated in a relativistic scheme, without explicit reference to changes due to relativity. Some of the molecules that were studied are built up of open shell fragments. The method that was developed to analyze the bond energies also in these systems, is described extensively in Chapter 1. Using this method we are now able to study the formation of electron pair bonds, which is a very important process in Chemistry. Chapter 4b consists of applications of the electron pair bond method. For atoms the situation concerning relativistic effects on orbitals is clear: s1/2 and p1/2 are stabilized and contract, d and f are destabilized and expand, while the behaviour of p3/2 orbitals is intermediate. The investigation in Chapter 2 does therefore not concentrate on this, but on the question of the (spatial) origin of the relativistic effects on AOs. The incentive for this work was the result that relativistic corrections on valence AO properties of many-electron atoms depend on the total nuclear charge, instead of the effective charge as was expected. The explanation for this surprising dependence can be found by dividing the integral in the expectation value of an AO property into spatial shells, starting from the nucleus. These shells correspond to the usual K, L, M etc. notation of energy levels. It appears that the direct relativistic first order mass-velocity, Darwin and spin- orbit corrections build up entirely in the neighbourhood of the nucleus, and therefore feel the total nuclear charge. The indirect relativistic effect was investigated too. Usually this is associated with destabilization, due to contraction of inner orbitals. The present work shows some new interesting viewpoints. One should realize that while relativistically contracted s and p orbitals cause indirect destabilization, expanding d and f orbitals can cause indirect stabilization. This is especially important in the case of a filled d or f shell just below a penetrating orbital (s or p). Reasoning along this line it is now understood why the relativistic effects are so large in the central columns of the periodic table, especially the large relativistic effects on Au and its compounds. The remaining part of this thesis concerns relativistic calculations on molecules, including the investigation of the changes due to relativity on bond length, bonding and 9 Summary 2+ spectroscopy. The uranyl molecule UO2 makes up a substantial part of these investigations. It has a number of special characteristics, that are all related to the special character of the semi-core U 6p orbital. This orbital has both core and valence character. It is spatially even more extended than the valence U 5f, which results in large overlaps in uranyl with its short U-O bond length (see Chapter 4a for an explanation for this). Also in UCp3L (Chapter 6) the U 6p plays a role, although less important than in uranyl, as the distances between the atoms are larger there. Relativistic calculations show a bond length expansion for uranyl, in contrast to the usually found contraction for molecules. In Chapter 3 we show that this expansion is not related to the atomic relativistic destabilization of the U 5f orbitals, which is important for the bond in uranyl. The U 6p orbital is the cause of the expansion. The valence character of U 6p causes large overlaps and consequently large interaction with O, in which the short U-O distance also plays a role. The strong interaction with O 2p makes the antibonding U 6p-O 2p combination end up high in the virtual spectrum, above U 5f. The interaction between U 5f and O 2p (in the antibonding U 6p-O 2p) leads to a HOMO with much 5f character. The strong participation of U 6p to the bond in uranyl leads to a depopulation, there is only 1.5 electron left in U 6p: a '6p hole' is present. This hole increases with shorter U-O distance, leading to an increasing loss of stabilizing mass- velocity correction. This effect is important due to the large mass-velocity correction from the core character of U 6p. This effect is clearly expanding. More directly the core character contributes to the expansion also through the off-diagonal mass-velocity element with U 5p. The lowest virtual orbitals in uranyl are the non-bonding U 5fd and 5ff orbitals. From the previous it follows that the excitation spectrum is determined by excitation from the mainly 5f HOMO to fd, ff . In Chapter 5 we give an assignment of the excitation spectrum 2- of Cs2UO2Cl4, for which UO2F4 was used as model. Due to the F ligand field the ff is above fd. Using a spin-orbit model our assignment of the spectrum is: s udu < s uf u , s udu < s uf u. This differs from the s udu (2x) < s uf u (2x) found in the literature. However the differences are only in the second and third origins, and our calculations show extensive mixing between the diagonal spin-orbit split ff 5/2 and fd5/2 orbitals, which result in these origins. The assignment can therefore not be done to individual du or f u orbitals. Also in Chapter 5 we present results of calculations on the Xray PES spectrum of uranyl. Like the strong interaction with O 2p, the U 6p interaction with O 2s is very large, with bonding and antibonding orbitals split by 14 eV. In experiments the peaks were assigned to individual atomic orbitals. We show that this is not correct: the strong U 6p-O 2s interaction precludes this sort of assignment. The U 6p-O 2s interaction can best be viewed as the result of an interaction where first the spin-orbit splitting acts. 10 Summary The final study on uranyl in Chapter 4a concerns the short U-O bond length, that is much shorter than for secondary ligands. In this work uranyl was built up from open 3+ 2 - 2 4 2 shell fragments U (5fsa 5fpa ) and O2(2ss u 2ps ub 2ppg 2ppub ). For performing an energy analysis from such open shell fragments a method was developed, which is described in Chapter 1. Using this method one can study the formation of pair bonds. The first application was the investigation of uranyl as given above, with 5fs -O 2ps u and 5fp-O 2ppu pair bonds. The short distance U-O distance in uranyl is surprising, because much repulsion is expected from the spatially extended U 6p orbital. Indeed the U 6p orbital leads to large repulsive effects. The dominant contribution to the steric interaction in uranyl comes from the closed shell U 6ps -O 2ss u Pauli repulsion. The U 6ps -O 2ps u steric effect is surprisingly small, the explanation for which is the cancelling of Pauli repulsion and electrostatic effects. For the same reason the U 5fs -O 2ps u steric interaction is small.