MRD-CI studies of vertical excitation energies of unsaturated hydrocarbon molecules

Comparison of many-particle representations for selected-CI I: A tree based approach

The full configuration interaction (FCI) method is only applicable to small molecules with few electrons in moderate size basis sets. One of the main alternatives to obtain approximate FCI energies for bigger molecules and larger basis sets is selected CI. However, due to: (a) the lack of a well-defined structure in a selected CI Hamiltonian, (b) the potentially large number of electrons together with c) potentially large orbital spaces, a computationally and memory efficient algorithm is difficult to construct. In the present series of papers, we describe our attempts to address these issues by exploring tree-based approaches. At the same time, we devote special attention to the issue of obtaining eigenfunctions of the total spin squared operator since this is of particular importance in tackling magnetic properties of complex open shell systems. Dedicated algorithms are designed to tackle the CI problem in terms of determinant, configuration (CFG) and configuration state function many-particle bases by effective use of the tree representation. In this paper we describe the underlying logic of our algorithm design and discuss the advantages and disadvantages of the different many particle bases. We demonstrate by the use of small examples how the use of the tree simplifies many key algorithms required for the design of an efficient selected CI program. Our selected CI algorithm, called the iterative configuration expansion, is presented in the penultimate part. Finally, we discuss the limitations and scaling characteristics of the present approach.

Calculating Absorption Shifts for Retinal Proteins: Computational Challenges

Rhodopsins can modulate the optical properties of their chromophores over a wide range of wavelengths. The mechanism for this spectral tuning is based on the response of the retinal chromophore to external stress and the interaction with the charged, polar, and polarizable amino acids of the protein environment and is connected to its large change in dipole moment upon excitation, its large electronic polarizability, and its structural flexibility. In this work, we investigate the accuracy of computational approaches for modeling changes in absorption energies with respect to changes in geometry and applied external electric fields. We illustrate the high sensitivity of absorption energies on the ground-state structure of retinal, which varies significantly with the computational method used for geometry optimization. The response to external fields, in particular to point charges which model the protein environment in combined quantum mechanical/molecular mechanical (QM/MM) applications, is a crucial feature, which is not properly represented by previously used methods, such as time-dependent density functional theory (TDDFT), complete active space self-consistent field (CASSCF), and Hartree-Fock (HF) or semiempirical configuration interaction singles (CIS). This is discussed in detail for bacteriorhodopsin (bR), a protein which blue-shifts retinal gas-phase excitation energy by about 0.5 eV. As a result of this study, we propose a procedure which combines structure optimization or molecular dynamics simulation using DFT methods with a semiempirical or ab initio multireference configuration interaction treatment of the excitation energies. Using a conventional QM/MM point charge representation of the protein environment, we obtain an absorption energy for bR of 2.34 eV. This result is already close to the experimental value of 2.18 eV, even without considering the effects of protein polarization, differential dispersion, and conformational sampling.