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Abstract
The complete active space self-consistent-field (CASSCF) linear response method for the simulation of ultraviolet-visible (UV/Vis) absorption and electronic circular dichroism (ECD) spectra of large open-shell molecules is presented. By using a one-index transformed Hamiltonian, the computation of the most time-consuming intermediates can be pursued in an integral-direct fashion, which allows us to employ the efficient resolution-of-the-identity and overlap-fitted chain-of-spheres approximation. For the iterative diagonalization, pairs of Hermitian and anti-Hermitian trial vectors are used which facilitate, on the one hand, an efficient solution of the pair-structured generalized eigenvalue problem in the reduced space, and on the other hand, make the full multiconfigurational random phase approximation as efficient as the corresponding Tamm-Dancoff approximation. Electronic transitions are analyzed and characterized in the particle-hole picture by natural transition orbitals that are introduced for CASSCF linear response theory. For a small organic radical, we can show that the accuracy of simulated UV/Vis absorption spectra with the CASSCF linear response approach is significantly improved compared to the popular state-averaged CASSCF method. To demonstrate the efficiency of the implementation, the 50 lowest roots of a large Ni triazole complex with 231 atoms are computed for the simulated UV/Vis and ECD spectra.
Highlights
Nowadays, computational spectroscopy of open-shell molecules is still one of the major challenges in molecular electronic-structure theory
Some of the most problematic features of (TD-)DFT are the following: (i) There is currently no way to converge the Kohn-Sham DFT2 energy systematically toward the energy of the exact N-electron wavefunction (WF). (ii) Excitation energies of charge-transfer (CT) transitions are systematically underestimated3 and can only be described by special classes of functionals that compute the long-range interaction with the exact Hartree–Fock (HF) exchange.4–6 (iii) Open-shell systems are usually described within the unrestricted Kohn-Sham formalism, which may be severely affected by spin contamination
An algorithm for the solution of the random-phase approximation31 (RPA)-type general eigenvalue problem (GEP) was presented in Sec
Summary
Computational spectroscopy of open-shell molecules is still one of the major challenges in molecular electronic-structure theory. Some of the most problematic features of (TD-)DFT are the following: (i) There is currently no way to converge the Kohn-Sham DFT2 energy systematically toward the energy of the exact N-electron wavefunction (WF). (ii) Excitation energies of charge-transfer (CT) transitions are systematically underestimated and can only be described by special classes of functionals that compute the long-range interaction with the exact Hartree–Fock (HF) exchange. (iii) Open-shell systems are usually described within the unrestricted Kohn-Sham formalism, which may be severely affected by spin contamination. The inherent singlereference nature of DFT is not appropriate for describing open-shell low-spin states. The latter two points become crucial when simulating electronic spectra of organometallic compounds like transition-metal complexes or metalloproteins
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