Development of robust ab initio methods for description of excited states and autoionizing resonances

High level ab initio methods are indispensable tools for theoretical studies of molecular systems. By using quantum‐mechanical principles, these methods enable solution of complex chemical problems by using the power of computers. Knowing only the positions and types of the atoms, one can calculate virtually all the properties of the molecules such as charge distributions, dipole moments, reaction and excitation energies. Among ab initio techniques coupled cluster (CC) and equation‐of‐motion EOM family of methods plays a special role. These methods enable accurate and systematic treatment of electron correlation for both the ground and excited states. Accurate recovery of electron correlation is essential for achieving chemical accuracy in calculations (1 kCal/mol). ❧ In Chapter 2 we present high level ab initio calculations of the electronic structure of the two isomers of the photoactive yellow protein (PYP) model chromophores. We found that the phenolate and carboxylate isomers of the model chromophore (para‐coumaric acid, pCA) have distinctly different pattern of ionization and excitation energies, which contradicts published experimental results. Their excitation energies differ by more than 1 eV and the first excited states in both isomers are autoionizing resonances. The phenolate form of pCA exhibits shape resonance, whereas for carboxylate we predicted Feshbach‐type resonance. Next, in Chapter 3, we investigate how microhydration affects the electronic structure of the PYP and GFP model chromophores. We found that microhydration leads to a larger blue shift in ionization than in excitation energy, thus converting resonances into bound states. ❧ Following our findings of resonance states in gas‐phase chromophores we began the development of new methods for proper description of resonance positions and lifetimes. In Chapter 4 we extend EOM methods to atomic resonances by applying complex scaled formalism in which all coordinates are rotated by a complex angle θ. By computing θ‐trajectories and finding an optimal angle, we are able to find positions and lifetimes of the resonances in He, H-, and Be. For the description of molecular resonances, we use another approach in which we introduce complex absorbing potential (CAP) into the original Hamiltonian. CAP is devised to absorb the divergent tail of the resonance wave function. By using the CAP‐augmented Hamiltonian with EOM methods we study electronically attached shape resonances in various medium‐size molecules. We find that an artificial perturbation induced by the CAP can be diminished by introducing a first‐order correction to the energy. We also observe that the corrected energies are much less sensitive to the onset of the CAP (e.g., box size) and that accurate results can be obtained using standard basis sets augmented by diffuse functions. ❧ In Chapter 6 improvement of the memory requirements in CC and EOM methods is presented. By performing Cholesky decomposition of the two‐electron integrals tensor we significantly reduce its storage requirements from O(N⁴) to O(N³), which extends the applicability of the method to larger systems that may not be accessible by canonical EOM‐CCSD. The errors introduced by the decomposition are small and can be controlled by a single threshold specified by the user. ❧ Finally, in Chapter 7 we present a new version of Davidson's algorithm for solving the eigenvalue problems in quantum chemical calculations. These new algorithms facilitate finding the roots either around the user‐specified energy shift or by user‐defined guess orbitals. These modifications will enable obtaining highly lying states that are not accessible using standard methods that find only the lowest eigenstates. Such enhancements will be useful for many applications, for example, in studies of core ionization processes where the ionization potential can be as high as hundreds of electron‐volts. We also present an implementation of a new method for non‐Hermitian eigenvalue problems within EOM family of methods, generalized preconditioned locally residual method (GPLMR), which also has the capabilities of finding interior eigenvalues around a specified shift. We present benchmarks for aforecited methods comparing their robustness and computational cost.