Large‐scale RPA calculations of chiroptical properties of organic molecules: Program RPAC

Abstract

The computational considerations involved in calculating ordinary and rotatory intensities and electronic excitation energies in the random phase approximation (RPA) are examined. We employ a localized orbital formulation in order to analyze the results in terns of local and charge-transfer excitations. Occupied orbitals are localized by the Foster-Boys procedure. The virtual space is transformed into a localized "valence" set that maximizes dipole strengths with the occupied counterparts, and a delocalized remainder. The two-electron integral transformation is performed with an efficient algorithm, based on Diercksen's, that generates only the particle-hole-type integrals required in the RPA. The lowest solutions of the RPA equations a;e obtained iteratively using a modification of the Davidson-Liu simultaneous vector expansion method. This allows the inclusion of the entire set of particle-hole states supported by a basis set of up to I02 orbitals. Calculations at this level give better excitation energies and intensities than SDCI methods, at substantial savings in computational effort. Comparative timings, computed results and analysis in terms of localized orbitals are given far planar and distorted ethylene using extended atomic orbital bases including diffuse functions. The results for planar ethylene are in excellent agreement with experiment.

An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules

“…The only required modification is ͑essentially͒ the diagonalization of a small reduced non-Hermitian matrix. This approach, advocated by Bouman et al, 16 works well in practice, but has been shown to take many iteration steps to converge. 17 A much more efficient method proposed by Olsen et al 17 is based on projecting the large dimensional equation given in ͑14͒ into a subspace via paired expansion vectors.…”

“…16 Here we considered the six lowest singlet roots of formaldehyde at the 6-31GϩG*/RPA level of theory with all electrons active. The ͑distorted͒ geometry we employed for this molecule is as follows: C 2v symmetry; C-O bond length of 1.22 Å, C-H bond length of 1.08 Å, and all interior angles of 120°.…”

Theoretical CD spectrum calculations of the crown‐ether aralkyl‐ammonium salt complex

“…Diagonalization of the moderately large RPA matrix can be easily done by the direct techniques. 17 Still, the RPA scheme was reported to provide reliable results for transition properties. 18 We recorded the six lowest RPA excitation energies and the corresponding transition moments for use in Eqs.…”

Six‐Membered Heterocycles: Triazines, Tetrazines and Other Polyaza Systems

“…Several theoretical methods have been used to study 1,2,4-triazines. Thus, the H€ uckel method was used to calculate the p-electron energies [137,138], the electronic excitation energies and intensities were calculated by the RPAC molar properties program [139], the electronic state of 1,2,4-triazines were obtained [140] and the ionization energies were calculated by the outler valence Green function technique (OVGF) [141]. The CNDO/2 method has been used to calculate the sites of protonation and alkylation [142].…”