Occupied-Orbital Fast Multipole Method for Efficient Exact Exchange Evaluation

Analytic gradients for local density fitting Hartree-Fock and Kohn-Sham methods

We present analytic gradients for local density fitting Hartree-Fock (HF) and hybrid Kohn-Sham (KS) density functional methods. Due to the non-variational nature of the local fitting algorithm, the method of Lagrange multipliers is used to avoid the solution of the coupled perturbed HF and KS equations. We propose efficient algorithms for the solution of the arising Z-vector equations and the gradient calculation that preserve the third-order scaling and low memory requirement of the original local fitting algorithm. In order to demonstrate the speed and accuracy of our implementation, gradient calculations and geometry optimizations are presented for various molecular systems. Our results show that significant speedups can be achieved compared to conventional density fitting calculations without sacrificing accuracy.

Speeding up Hartree-Fock and Kohn-Sham calculations with first-order corrections

Several approaches are presented to improve the efficiency of Hartree-Fock and Kohn-Sham self-consistent field (SCF) calculations relying on a simple first-order energy correction reminiscent of the scheme used in dual-basis SCF methods. The basic idea is to perform an initial SCF calculation computing approximate Fock-matrices and, in the final iteration step, to use a more complete Fock-matrix builder together with the energy correction to diminish the error. The approximation is tested for conventional and local density fitting (DF) SCF approaches combining various auxiliary basis sets, fitting metrics, and Fock-matrix construction algorithms in the initial and final iterations as well as for seminumerical SCF methods combining integration grids of different qualities. We also report the implementation of the occupied orbital resolution of identity exchange construction algorithm with local DF approximations. Benchmark calculations are presented for total energies, reaction energies, and molecular geometries. Our results show that speedups of up to 80% can be expected utilizing the new approaches without significant loss of accuracy.

CASSCF linear response calculations for large open-shell molecules

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.