Linear-Scaling Implementation of Multilevel Hartree-Fock Theory.

We introduce a new algorithm for the construction of the two-electron contributions to the Fock matrix in multilevel Hartree-Fock (MLHF) theory. In MLHF, the density of an active molecular region is optimized, while the density of an inactive region is fixed. The MLHF equations are solved in a reduced molecular orbital (MO) basis localized to the active region. The locality of the MOs can be exploited to reduce the computational cost of the Fock matrix: the cost related to the inactive density becomes linear scaling, while the iterative cost related to the active density is independent of the system size. We demonstrate the performance of this new algorithm on a variety of systems, including amino acid chains, water clusters, and solvated systems.

Predictions of Pre-edge Features in Time-Resolved Near-Edge X-ray Absorption Fine Structure Spectroscopy from Hole-Hole Tamm-Dancoff-Approximated Density Functional Theory.

Time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy is a powerful technique for studying photochemical reaction dynamics with femtosecond time resolution. In order to avoid ambiguity in TR-NEXAFS spectra from nonadiabatic dynamics simulations, core- and valence-excited states must be evaluated on equal footing and those valence states must also define the potential energy surfaces used in the nonadiabatic dynamics simulation. In this work, we demonstrate that hole-hole Tamm-Dancoff-approximated density functional theory (hh-TDA) is capable of directly simulating TR-NEXAFS spectroscopies. We apply hh-TDA to the excited-state dynamics of acrolein. We identify two pre-edge features in the oxygen K-edge TR-NEXAFS spectrum associated with the S2 (ππ*) and S1 (nπ*) excited states. We show that these features can be used to follow the internal conversion dynamics between the lowest three electronic states of acrolein. Due to the low, O(N2) apparent computational complexity of hh-TDA and our GPU-accelerated implementation, this method is promising for the simulation of pre-edge features in TR-NEXAFS spectra of large molecules and molecules in the condensed phase.

Transient resonant Auger-Meitner spectra of photoexcited thymine.

We present the first investigation of excited state dynamics by resonant Auger-Meitner spectroscopy (also known as resonant Auger spectroscopy) using the nucleobase thymine as an example. Thymine is photoexcited in the UV and probed with X-ray photon energies at and below the oxygen K-edge. After initial photoexcitation to a ππ* excited state, thymine is known to undergo internal conversion to an nπ* excited state with a strong resonance at the oxygen K-edge, red-shifted from the ground state π* resonances of thymine (see our previous study Wolf, et al., Nat. Commun., 2017, 8, 29). We resolve and compare the Auger-Meitner electron spectra associated both with the excited state and ground state resonances, and distinguish participator and spectator decay contributions. Furthermore, we observe simultaneously with the decay of the nπ* state signatures the appearance of additional resonant Auger-Meitner contributions at photon energies between the nπ* state and the ground state resonances. We assign these contributions to population transfer from the nπ* state to a ππ* triplet state via intersystem crossing on the picosecond timescale based on simulations of the X-ray absorption spectra in the vibrationally hot triplet state. Moreover, we identify signatures from the initially excited ππ* singlet state which we have not observed in our previous study.

Combining multilevel Hartree-Fock and multilevel coupled cluster approaches with molecular mechanics: a study of electronic excitations in solutions.

We investigate the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable. In particular, such a coupling is discussed for the multilevel families of methods, in which the system is divided into an active and an inactive orbital space. The computational cost of the resulting three-layer approaches is reduced by treating the long-range interactions at the classical level. The developed methods are tested by the calculation of excitation energies of molecular systems in aqueous solution, for which an atomistic description of the environment is crucial to correctly reproduce the specific solute-solvent interactions, such as hydrogen bonding. In particular, we present the results obtained for three different moieties - acrolein, pyridine and para-nitroaniline - showing that an almost perfect agreement with experimental data can be achieved when the relevant physico-chemical interactions are included in the modeling of the condensed phase.

Accelerated multimodel Newton-type algorithms for faster convergence of ground and excited state coupled cluster equations.

We introduce a multimodel approach to solve coupled cluster equations, employing a quasi-Newton algorithm for the ground state and an Olsen algorithm for the excited states. In these algorithms, both of which can be viewed as Newton algorithms, the Jacobian matrix of a lower level coupled cluster model is used in Newton equations associated with the target model. Improvements in convergence then imply savings for sufficiently large molecular systems, since the computational cost of macroiterations scales more steeply with system size than the cost of microiterations. The multimodel approach is suitable when there is a lower level Jacobian matrix that is much more accurate than the zeroth order approximation. Applying the approach to the CC3 equations, using the CCSD approximation of the Jacobian, we show that the time spent to determine the ground and valence excited states can be significantly reduced. We also find improved convergence for core excited states, indicating that similar savings will be obtained with an explicit implementation of the core-valence separated CCSD Jacobian transformation.

eT 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods.

The eT program is an open source electronic structure package with emphasis on coupled cluster and multilevel methods. It includes efficient spin adapted implementations of ground and excited singlet states, as well as equation of motion oscillator strengths, for CCS, CC2, CCSD, and CC3. Furthermore, eT provides unique capabilities such as multilevel Hartree-Fock and multilevel CC2, real-time propagation for CCS and CCSD, and efficient CC3 oscillator strengths. With a coupled cluster code based on an efficient Cholesky decomposition algorithm for the electronic repulsion integrals, eT has similar advantages as codes using density fitting, but with strict error control. Here, we present the main features of the program and demonstrate its performance through example calculations. Because of its availability, performance, and unique capabilities, we expect eT to become a valuable resource to the electronic structure community.

An efficient algorithm for Cholesky decomposition of electron repulsion integrals.

Approximating the electron repulsion integrals using inner projections is a well-established approach to reduce the computational demands of electronic structure calculations. Here, we present a two-step Cholesky decomposition algorithm where only the elements of the Cholesky basis (the pivots) are determined in the pivoting procedure. This allows for improved screening, significantly reducing memory usage and computational cost. After the pivots have been determined, the Cholesky vectors are constructed using the inner projection formulation. We also propose a partitioned decomposition approach where the Cholesky basis is chosen from a reduced set generated by decomposing diagonal blocks of the matrix. The algorithm extends the application range of the methodology and is well suited for multilevel methods. We apply the algorithm to systems with up to 80 000 atomic orbitals. The accuracy of the integral approximations is demonstrated for a formaldehyde-water system using a new Cholesky-based CCSD implementation.