A multireference density functional approach to the calculation of the excited states of uranium ions

An accurate and efficient hybrid Density Functional Theory (DFT) and Multireference Configuration Interaction (MRCI) model for computing electronic excitation energies in atoms and molecules was developed. The utility of a hybrid method becomes apparent when ground and excited states of large molecules, clusters of molecules, or even moderately sized molecules containing heavy element atoms are desired. In the case of large systems of lighter elements, the hybrid method brings to bear the numerical efficiency of the DFT method in computing the electron-electron dynamic correlation, while including non-dynamical electronic correlation via the Configuration Interaction (CI) calculation. Substantial reductions in the size of the CI expansion necessary to obtain accurate spectroscopic results are possible in the hybrid method. Where heavy element compounds are of interest, fully relativistic calculations based upon the Dirac Hamiltonian rapidly become computationally prohibitive, as the basis set requirements in four-component calculations increase by a factor of two or more in order to satisfy kinetic balance between the large electronic components and small positronic components, while the size of the MRCI Hamiltonian quadruples with respect to a non-relativistic calculation. In this hybrid method, applications to heavy element compounds such as bromine and uranium were accomplished through the use of relativistic effective core potentials, allowing for the first time both scalar relativistic and spin-orbit effect treatment necessary for the accurate calculation of electronic excitation energies in heavy elements in a Density Functional Theory Multireference Configuration Interaction Hybrid Model (DFT/MRCI) method. This implementation of the original hybrid method, developed by Grimme and Waletzke, was modified to remove inherent spin-multiplicity limitations, as well as reduce the number of free parameters used in the method from five to three.; The DFT portion of the hybrid method used 100% Hartree-Fock (HF) exchange and an electron correlation-only density functional as the basis for a modified Graphical Unitary Group Approach (GUGA) based CI calculation. The CI algorithm was modified to exponentially scale the off-diagonal matrix elements of the CI Hamiltonian in order to reduce the double counting of electronic correlation computed by both the DFT correlation functional and the CI calculation. The scaling applied to the interaction between states in the CI calculation exponentially decreased to zero as the energy difference between states grew. This algorithm left interactions between degenerate or nearly degenerate states unsealed, while rapidly scaling to zero interactions between states widely separated in energy.; The two empirical parameters which controlled this off diagonal matrix element scaling were determined through the use of a training set of light atoms and molecules consisting of H2, He, Li, Be, B, C, N, O, F, Ne, and Be2. The average DFT/MRCI errors with respect to exact Full Configuration Interaction (FCI) results on this training set was 9.0559 milli Hartrees (mH) over 11 atomic and molecular systems. CI expansion length tailoring through virtual orbital freezing. Consistently favorable results were obtained when virtual orbitals 30-40 electron Volts (eV) above the highest occupied molecular orbital were frozen, providing the best trade off between method accuracy and reduction in CI expansion length. Using this approach to paring the CI expansion length, reductions in the size of the CI expansions of a factor of 25-64 were achieved.; The values of the two off diagonal scaling parameters were determined by minimizing the average absolute error between the DFT/MRCI and exact FCI calculations for all test atoms and molecules combined. The values of the parameters obtained for the 100% HF exchange and Perdew Burke and Ernzerhof (PBE) 1996 Generalized Gradient Approximation (GGA) correlation functional combina...