The MSINDO-sCIS and MSINDO-UCIS methods. Procedures for the calculation of properties of excited states in molecules and periodic systems by a semiempirical approach

Theoretical background, parameterization and performance of the newly developed semiempirical configuration interaction singles (CIS) method MSINDO-sCIS (scaled configuration interaction singles) are presented. The CIS Hamiltonian is modified by scaling of the Coulomb and exchange integrals and a semiempirical correction of the diagonal elements. For a recently proposed benchmark set of 28 medium-sized organic molecules, vertical excitation energies for singlet and triplet states have been calculated and statistically evaluated. A full reparameterization of the MSINDO method for both ground and excited state properties was performed. The results of the reparameterized MSINDO-sCIS method are compared to the currently best semiempirical method for excited states, OM3-CISDTQ by Thiel et al., and to other standard methods, such as time-dependent density- functional theory. The mean absolute deviation with respect to the theoretical best estimates (TBEs) for MSINDO-sCIS is 0.44 eV, comparable to the OM3 method but significantly smaller than for Zerner's INDO/S. The computational effort is strongly reduced compared to OM3-CISDTQ and OM3-MRCISD, since only single excitations are taken into account. Higher excitations are implicitly included by parameterization and the empirical correction term. By application of the Davidson-Liu block diagonalization method high computational efficiency is achieved. Furthermore it is demonstrated, that the MSINDO-sCIS method correctly describes charge-transfer (CT) states, that represent a crucial problem for time-dependent density functional theory (TD-DFT) methods. Additionally this method is extended to open-shell systems by the UCIS (unrestricted CIS) approach. MSINDO allows the calculation of periodic systems via the cyclic cluster model (CCM) which is a direct-space approach and therefore can be in principle combined with all molecular quantum-chemical techniques. The sCIS/UCIS equations are solved for a cluster with periodic boundary conditions using the Davidson-Liu iterative block diagonalization approach. The present approximate approach is one of the first examples of a quantum-chemical methodology for solids where excited states are correctly described as n-electron state functions. As excited-state properties oscillator strengths, densities (and difference densities) and left angle S2 right angle for open-shell systems are available in MSINDO-sCIS and -UCIS. Analytical expressions for the sCIS and UCIS energy gradients are taken from the literature and adjusted to the new equations. The theoretical background of the derivation of the analytical gradients is presented and the implementation into the MSINDO program package is described. The computational efficiency of the underlying Z-vector method by Handy and Schaeffer is greatly enhanced by making use of the transpose-free quasiminimal residual (TFQMR) algorithm. Benchmark timing tests are compared to the widely used TD-B3LYP approach. For a statistical evaluation of the accuracy of MSINDO-sCIS, geometry optimizations have been performed for a small set of organic molecules in selected excited states. The obtained results are compared to literature values. As first chemical applications two systems are considered. In the molecular case the vibronically coupled excitation spectrum of naphthodithiophene has been calculated under consideration of the Franck-Condon-factors (FCFs). As an example of solid-state photo-physics the F-center in NaCl has been calculated using the MSINDO-CCM-UCIS approach. Here the main attention is given to the difference densities and flourescence spectra of the excited state. For both systems reasonable agreement with the experimental spectra is observed.