The Interpretation of the Spectra of Diatomic Molecules

Considerable effort has been expended by experimentalists in the last two decades in trying to understand the electronic structure of the simplest transition metal compounds, those containing a metal atom bound to one other atom. Yet in spite of the very detailed information available from the study of the electronic spectra of diatomic molecules, the basic principles of the bonding of these molecules are still largely unknown. This thesis illustrates the important role that molecular orbital calculations can play in helping to elucidate the electronic structure of both the ground and excited states of molecules of chemical, rather than purely physical, interest.
Chapter 1
The theoretical methods to be adopted are outlined. Eartree-Fock theory for closed- and open-shell systems is described, and the errors inherent in the theory are discussed. Several methods of treating the correlation energy problem are outlined, and the computer programmes used in the work are described. A brief survey of the field of diatomic molecules containing one transition metal atom is given, indicating the types of experimental methods that have been used, and the nature of the information which is available.
Chapter 2
Hund's rules for atoms have often been extended in a rather arbitrary way to molecules, without explicit justification, and the validity of this extension is investigated. The model used is an invariant orbital approximation; the limitations of this model are discussed, and it is shown that the model will give the same results as the best possible orbital model. Expressions are derived for the relative energies of the electronic states of linear molecules derived from the same electron configuration. General inequalities relating to coulomb and exchange integrals often permit definite conclusions to be drawn concerning the ordering of the states. The predictions sometimes agree with Hund's rules, sometimes disagree, and also predict the ordering of Σ+ and Σ- states, which is not considered by Hund's rules. It is shown that in cases where sufficient experimental data exist, they are in agreement with the theoretical predictions.
Chapter 3
A theoretical investigation of the excited states of the molecule ScF is described. Single configuration wave functions are calculated for the low-lying and excited states of the molecule; the agreement between the calculated and observed spectroscopic constants for the low-lying states, whose electronic structures are well understood, is very good. It is shown that the lowest 3Π state is well described by the electron configuration 4sσ3dπ, but that the lowest 3Φ state corresponds to the configuration 3dδ4pπ, and not 3dδ3dπ as previously thought, and that differences in electron repulsion therefore play an important role in determining the ordering of electronic states in transition metal diatomic molecules. It is further concluded that the observed 3Δ state corresponds to the configuration 3dδ4pσ, and not 3dδ3dσ as previously supposed. These reassignments are shown to resolve a discrepancy which previously existed between the relative energies of the 3d and 4p electrons in ScF and ScO.
Limited configuration interaction studies show that there is no appreciable mixing between the 3Φ states, but that the excited 3Π states are not well described by single configuration wave functions. The difference between the Φ and Π states is explained by the difference in magnitudes of off-diagonal matrix elements representing one- and two-electron excitations. The configuration mixing in the Π states allows a rationalisation of the intensity distribution among the 1Π-X1Σ+ transitions, which is not possible using a single configuration model.
Chapter 4
Ab initio molecular orbital calculations on a number of monohydrides of first row transition metals are described. Although the monohydrides are the simplest transition metal compounds, very little experimental information on them is available, and the calculations attempt to predict and rationalise the orderings of their ground and low-lying electronic states.
Hartree-Fock calculations are performed on the molecule ScH, and the correlation energies of the low-lying states are estimated semi-empirically from atomic data. Two states are found to be very low-lying, 1
Σ+ and 3Δ. The suggestion that the transition observed in absorption at 5500 Å is between states of multiplicity greater than three is not supported; it is suggested that this transition could be 3Φ-3Δ. The splitting of the d orbitals by the hydrogen atom is shown to be δ>π>σ, with the δ orbital most stable, although the splitting is rather smaller than in the corresponding fluoride.
Calculations and semi-empirical estimates of correlation energies on TiH suggestthat the low-lying states of the molecule are derived from configurations essentially of the type 4s3d2; similar calculations on VH show that in this molecule the low-lying states are derived from configurations which are well described as 4s3d2. It is shown that near-degeneracy effects must be taken into account for the Σ- and Π states of TiH and VH, and 2×2 configuration interaction calculations are described. It is shown that in each molecule the states may be regarded as the four spatial components of the 4F and 5F states of the ions Ti+ and V+, and the two components of the 4P and 5P states, and that the H atom therefore acts only as a small perturbation on the metal atom. A hole formalism is used to explain why the perturbation in VH has the opposite sign to that in TiH, and it is shown that this perturbation is compatible with the stabilisation of the d orbitals being δ>π>σ, as in ScH.
A single centre perturbation treatment of the molecule FeH has suggested that the ground state is 6Σ+, with the d orbitals stabilised in the order δ<π<σ. Calculations are described which predict the ground state of FeH to be 6Δ, with the dδ orbital more stable than dπ and dσ. Comparison of other spectroscopic constants calculated by the Hartree-Fock and single-centre techniques show wide discrepancies, and even trends between different states are often not reproduced. It is concluded that the single-centre method is not an appropriate tool for studying transition metal hydrides, as the convergence characteristics are much slower than had previously been thought.
Calculations on NiH and PdH predict the ground states of these molecules, which have isoelectronic valence shells, to be 2Δ and 2Σ+ respectively, in agreement with experimental results. The bonding in PdH is interpreted as covalent bonding between the 4dσ and 1sσ orbitals, giving a 6Σ+ ground state with two near-degenerate excited states, 2Δ and 2Π. In NiH it is shown that the greater stability of the 4s orbital relative to the 3d stabilises the anti-bonding combination of the 3dσ and 1sσ orbitals, and the 2Σ+ state lies above the 2Δ and 2Π states. It is further shown that the difference in energies between the 2Δ and 2Π states is 5000 cm-1, larger than has previously been supposed, and it is shown that two hypotheses explaining why the orbital is more stable than the dδ do not account for a splitting of this magnitude. The splitting is explained by the difference in repulsion energies between a dδ and dσ electron, and a dπ and dσ electron. A population analysis shows that this effect is sufficiently large to explain the calculated splitting, and that it is the same factor, the greater stability of the s orbital relative to the d, which causes the change in ground state and the increase in 2Π-2Δ splitting from PdH to NiH.