The relative thermodynamic stabilities of certain transition metal complexes is such that, by tuning the choice of ligand, the complexes may be switched between high- and low-spin states by a simple change in temperature. The ability to predict this transition temperature requires a very precise understanding of the inter and intramolecular energy and entropy contributions to the high-spin/low-spin free energy difference. It is already an excited-state problem. The situation becomes even more interesting, from the point of view of fabricating optical devices, for those complexes which also show a significant kinetic barrier between the ground low-spin state and the metastable high-spin state. It then becomes possible to create a molecular optical switch by laser-induced switching between the two states which have different magnetic properties, effective volumes, and colors. A correct modeling of the phenomenon requires the ability to calculate the relative energies of the two low-energy states and ultimately of the manifold of excited states, including numerous open-shell states. As such it is a great challenge for any first principles method, DFT or otherwise. As shown in Fig. 1, our work ranks highly when compared to citation statistics for other articles applying DFT to the spin-crossover problem.

Since NMR is one of the most important spectroscopies for chemists, it would be nice to have an efficient way to calculate chemical shifts within DFT. Our now classic 1994 paper [MMCS94] proposes the Sum-Over-States Density-Functional Perturbation Theory (SOS-DFPT) method for doing just this. One unsatisfying aspect of that work was the somewhat ad hoc nature of the correction to the uncoupled approximation. More recently, we have shown how a precise form of this correction term (which we call "Loc.3") can be derived from time-dependent density-functional theory and performs as well as or better than the previous Loc.1 and Loc.2 approximations in SOS-DFPT [FCS03a,FCS03b].

Electron momentum spectroscopy (EMS) is an (e,2e) scattering method which uses energy conservation to obtain ionization potentials and momentum conservation to measure, to a good approximation, the spherically-averaged momentum distribution of the Dyson orbital from which the electron was ionized. As the experimental resolution of EMS has improved, the spectroscopists have become eager to apply EMS to larger molecules. However, accurate calculations are required for interpreting the measured spectra. The cost of calculations using traditional ab initio methods mounts rapidly with the size of the molecule, especially since extended basis sets are required for calculating EMS cross-sections. Although the idea of using density-functional theory (DFT) for this purpose, by taking Kohn-Sham orbitals to approximate Dyson amplitudes, was heretical, my work on the optimized effective potential model showed that this idea has a rigorous meaning and is well-founded. I used a Klein-Luttinger-Ward-like energy expresssion, which is a functional of the Green function, to generalize the optimized effective potential model of the exact exchange potential in DFT to include correlation [C95a]. This made a contribution to the fundamental problem of interpreting the exchange-correlation potential, v_xc, in DFT by showing that v_xc is the best (in a certain variational sense) local approximation to the exchange-correlation self-energy in Dyson's quasiparticle equation. This suggested that, at least for outer valence orbitals, the Kohn-Sham orbitals might be used to approximate Dyson amplitudes. This laid the foundations for our highly successful pioneering application of DFT to calculate EMS triple differential cross-sections [DCCS94]. The ability to use DFT for this purpose has proven to be of considerable practical value for experimental EMS [see e.g. Y. Zheng, J.J. Neville, and C.E. Brion, Science 270, 786 (1995).]

The one-electron Green function method provides a rigorous description of ionization, electron attachment, and electron scattering processes via Dyson's quasiparticle equation. Many-body effects are included in this equation via the self-energy operator. Although sophisticated, accurate approaches to the self-energy are known, these are quite computationally demanding. Physically-motivated, simpler approximations to the self-energy are useful, both for treating larger systems and for interpretation. Little had been done to develop simple self-energy approximations that are appropriate for molecules. Hedin's GW approximation (and variants thereon) has long been used in conjunction with density-functional theory (DFT) as a state-of-the-art method for solid-state band-structure calculations but it had never been tested in the realm of quantum chemistry. Its application to chemical problems was potentially attractive since molecular Green function (GF) methods, are significantly more computationally demanding. As a first step toward the adaptation of the GW method to molecular calculations, (which were usually based on a Hartree--Fock reference state) I implemented a second-order post-Hartree-Fock treatment, and reported the first GW-type calculations on molecules [CC89c CC91b]. These were second-order (i.e. GW2) calculations because the polarization propagator was only treated at the level of the independent particle approximation, but showed that the GW2 approximation gives ionization potentials comparable in quality to the usual second-order Green function (GF2) approximation, as long as care is taken to remove unphysical self-polarization effects in the GW2 calculation. (Although negligible in solids, these effects can result in a significant error in molecules.) This indicates that the nature of the approximations used by no means restricts the GW approximation to solids, but that it is a viable approach in the molecular realm. Although it is well-known that GF results are not particularly good at second order, my comparison of GW2 with GF2 suggests that a (self-polarization corrected) full GW calculation (i.e. using a time-dependent DFT or Hartree-Fock polarization propagator), would offer dramatically improved results while yielding significant computational advantages. In publication [HCC97] we have used the fact that the GW2 approximation already gives qualitatively correct results in order to introduce a semi-empirical scale factor leading to a GF method which is simultaneously quantitative and simple.

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