Calculation of excitation energies from the CC2 linear response theory using Cholesky decomposition

Stochastic Resolution of Identity to CC2 for Large Systems: Excited State Properties

We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for the excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O(N3), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O(N5) to O(N3). We test the sRI-CC2 for different molecular systems and basis sets, and we show that our sRI-CC2 method can accurately reproduce the results of the deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O(N2.59) for a series of olefin chains, allowing us to calculate systems with nearly thousands of electrons.

An effective sub-quadratic scaling atomic-orbital reformulation of the scaled opposite-spin RI-CC2 ground-state model using Cholesky-decomposed densities and an attenuated Coulomb metric

An atomic-orbital reformulation of the Laplace-transformed scaled opposite-spin (SOS) coupled cluster singles and doubles (CC2) model within the resolution of the identity (RI) approximation (SOS-RI-CC2) is presented that extends its applicability to molecules with several hundreds of atoms and triple-zeta basis sets. We exploit sparse linear algebra and an attenuated Coulomb metric to decrease the disk space demands and the computational efforts. In this way, an effective sub-quadratic computational scaling is achieved with our ω-SOS-CDD-RI-CC2 model. Moreover, Cholesky decomposition of the ground-state one-electron density matrix reduces the prefactor, allowing for an early crossover with the molecular orbital formulation. The accuracy and performance of the presented method are investigated for various molecular systems.

Photoprotection: extending lessons learned from studying natural sunscreens to the design of artificial sunscreen constituents

Evolution has ensured that plants and animals have developed effective protection mechanisms against the potentially harmful effects of incident ultraviolet radiation (UVR). Tanning is one such mechanism in humans, but tanning only occurs post-exposure to UVR. Hence, there is ever growing use of commercial sunscreens to pre-empt overexposure to UVR. Key requirements for any chemical filter molecule used in such a photoprotective capacity include a large absorption cross-section in the UV-A and UV-B spectral regions and the availability of one or more mechanisms whereby the absorbed photon energy can be dissipated without loss of the molecular integrity of the chemical filter. Here we summarise recent experimental (mostly ultrafast pump-probe spectroscopy studies) and computational progress towards unravelling various excited state decay mechanisms that afford the necessary photostability in chemical filters found in nature and those used in commercial sunscreens. We also outline ways in which a better understanding of the photophysics and photochemistry of sunscreen molecules selected by nature could aid the design of new and improved commercial sunscreen formulations.

Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions

A reduced-cost density fitting (DF) linear-response second-order coupled-cluster (CC2) method has been developed for the evaluation of excitation energies. The method is based on the simultaneous truncation of the molecular orbital (MO) basis and the auxiliary basis set used for the DF approximation. For the reduction of the size of the MO basis, state-specific natural orbitals (NOs) are constructed for each excited state using the average of the second-order Møller-Plesset (MP2) and the corresponding configuration interaction singles with perturbative doubles [CIS(D)] density matrices. After removing the NOs of low occupation number, natural auxiliary functions (NAFs) are constructed [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], and the NAF basis is also truncated. Our results show that, for a triple-zeta basis set, about 60% of the virtual MOs can be dropped, while the size of the fitting basis can be reduced by a factor of five. This results in a dramatic reduction of the computational costs of the solution of the CC2 equations, which are in our approach about as expensive as the evaluation of the MP2 and CIS(D) density matrices. All in all, an average speedup of more than an order of magnitude can be achieved at the expense of a mean absolute error of 0.02 eV in the calculated excitation energies compared to the canonical CC2 results. Our benchmark calculations demonstrate that the new approach enables the efficient computation of CC2 excitation energies for excited states of all types of medium-sized molecules composed of up to 100 atoms with triple-zeta quality basis sets.

Tensor numerical methods in quantum chemistry: from Hartree–Fock to excitation energies

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations.