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Multiple ERI (Electron Repulsion Integral) tensor contractions (METC) with several matrices are ubiquitous in quantum chemistry. In response theories, the contraction operation, rather than ERI computations, can be the major bottleneck, as its computational demands are proportional to the multiplicatively combined contributions of the number of excited states and the kernel pre-factors. This paper presents several high-performance strategies for METC. Optimal approaches involve either the data layout reformations of interim density and Fock matrices, the introduction of intermediate ERI quartet buffer, and loop-reordering optimization for a higher cache hit rate. The combined strategies remarkably improve the performance of the MRSF (mixed reference spin flip)-TDDFT (time-dependent density functional theory) by nearly 300%. The results of this study are not limited to the MRSF-TDDFT method and can be applied to other METC scenarios. [ABSTRACT FROM AUTHOR]

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The formulations and performances of spin‐restricted ensemble‐referenced KS and mixed‐reference spin‐flip time‐dependent density functional theory incorporating strong correlations into density functional theories are documented. As a result of balanced dynamic and nondynamic correlation, they are capable of describing strongly correlated challenging systems including diradicals, bond dissociation, conical intersections, doubly excited states, and so on, overcoming the limitations of current density functional theories. [ABSTRACT FROM AUTHOR]

Cyanobacteriochromes (CBCRs) are promising optogenetic tools for their diverse absorption properties with a single compact cofactor-binding domain. We previously uncovered the ultrafast reversible photoswitching dynamics of a red/green photoreceptor AnPixJg2, which binds phycocyanobilin (PCB) that is unavailable in mammalian cells. Biliverdin (BV) is a mammalian cofactor with a similar structure to PCB but exhibits redder absorption. To improve the AnPixJg2 feasibility in mammalian applications, AnPixJg2_BV4 with only four mutations has been engineered to incorporate BV. Herein, we implemented femtosecond transient absorption (fs-TA) and ground state femtosecond stimulated Raman spectroscopy (GS-FSRS) to uncover transient electronic dynamics on molecular time scales and key structural motions responsible for the photoconversion of AnPixJg2_BV4 with PCB (Bpcb) and BV (Bbv) cofactors in comparison with the parent AnPixJg2 (Apcb). Bpcb adopts the same photoconversion scheme as Apcb, while BV4 mutations create a less bulky environment around the cofactor D ring that promotes a faster twist. The engineered Bbv employs a reversible clockwise/counterclockwise photoswitching that requires a two-step twist on ~5 and 35 picosecond (ps) time scales. The primary forward Pfr → Po transition displays equal amplitude weights between the two processes before reaching a conical intersection. In contrast, the primary reverse Po → Pfr transition shows a 2:1 weight ratio of the ~35 ps over 5 ps component, implying notable changes to the D-ring-twisting pathway. Moreover, we performed pre-resonance GS-FSRS and quantum calculations to identify the Bbv vibrational marker bands at ~659,797, and 1225 cm−1. These modes reveal a stronger H-bonding network around the BV cofactor A ring with BV4 mutations, corroborating the D-ring-dominant reversible photoswitching pathway in the excited state. Implementation of BV4 mutations in other PCB-binding GAF domains like AnPixJg4, AM1_1870g3, and NpF2164g5 could promote similar efficient reversible photoswitching for more directional bioimaging and optogenetic applications, and inspire other bioengineering advances. [ABSTRACT FROM AUTHOR]