Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Dr. Mark R. Hoffmann

Second Advisor

Dr. Harmon Abrahamson

Third Advisor

Dr. Kathryn Thomasson


The ground and low-lying excited electronic states of molecules of the first ( 2 Sc , 2 Cr , 2 Mn , and 2 Ni ) and second ( 2 Y , 2 Mo , and 2 Tc ) row of transition elements have been investigated for the first time with the generalized Van Vleck second order multireference perturbation theory (GVVPT2) method, a variant of MRPT. All potential energy curves (PECs) obtained in these studies were smooth and continuous; that is, they are free from wiggles or inflexion points. In order to account for relativistic effects, which become important in heavy elements, the GVVPT2 method was extended to include scalar relativistic effects through the spin-free exact two component (sf-X2C) method and used in the studies of all molecules of second row transition elements and some of those of the first row considered in this present work. GVVPT2 studies of triatomic lithium and beryllium were also done as a first step to studies of small clusters of transition metals. The spectroscopic constants (bond lengths, harmonic frequencies, bond energies, and adiabatic transition energies) obtained for all PECs at the GVVPT2 level were in good agreement with experimental data, where available, and with results from previous studies using other high level ab initio methods. Optimized geometries of the triatomics were also in good agreement with previous findings. The studies included electronic states (e.g., the   g 1 g 1 2 Σ and 3 Σ states of 2 Y as well as the  g 5 1 Σ and  g 9 1 Σ states of 2 Tc ) not previously discussed in the literature.

As a first step to applying GVVPT2 to the study of relatively larger systems, the present work includes the results of efforts on improving DFT-in-DFT embedding theory. New equations were determined which involved an additional constraint of orthogonality of the orbitals of one subsystem to those of the complementary subsystem as warranted by formal arguments based on the formulation of DFT-in-DFT embedding. A computer program was realized using the new embedding equations and test calculations performed. Analyses of electron density deformations in embedding theory, in comparison with conventional Kohn-Sham (KS)-DFT densities, were performed using the new embedding program and a computer code that was also written to compute electron densities of molecules in real space, given reduced one particle density matrices. The results revealed that whereas the current formulation of DFT-in-DFT embedding theory generally underestimates electron density, at the interface between subsystems in comparison with conventional KS-DFT calculations of the supermolecule, the new DFT-in-DFT embedding scheme with the external orthogonality constraint was found to remedy the situation. Worthy of special note in this new embedding protocol is the fact that the nonadditive kinetic potential ( T v ), thought to be a major cause of weaknesses in DFT-in-DFT embedding and to which many previous research efforts have been devoted, can be set exactly to zero. The present work therefore realized, for the first time, a new DFT-in-DFT embedding theory that neither relies on kinetic functionals nor requires a supermolecular DFT calculation. Test calculations using the new embedding theory and supermolecular basis set expansion of KS orbitals reproduced conventional KS-DFT energies to at least the 7th decimal place (and even exactly at many geometries). A new way of expanding KS orbitals was also employed in the new embedding protocol, which is intermediate between the usual supermolecular and monomer basis expansions, referred to as the “extended monomer expansion”. The monomer basis expansion scheme was inadequate for the new DFT-in-DFT embedding protocol. Test calculations found this novel, computationally cheaper, extended monomer approach to give results quite close to those from supermolecular basis expansions.

Included in

Chemistry Commons