In this study, divide-and-conquer (DC) based density-functional tight-binding (DFTB) and time-dependent density-functional tight-binding (TD-DFTB) methods were developed using long-range correction (LC), which resolved the underestimation of energy gaps between the highest occupied molecular orbital and lowest unoccupied molecular orbital. We implemented the LC term by the entrywise product for the effective utilization of the math kernel library. Test calculations of formaldehyde in explicit water molecules demonstrate the efficiency of the developed method. Furthermore, the DC-TD-LCDFTB method was applied to 2,2′-bipyridine-3,3′-diol (BP­(OH)2), which exhibits excited-state intramolecular proton transfer in polar solvents.

In this study, the divide-and-conquer (DC) method was extended to time-dependent density functional tight-binding (TDDFTB) theory to enable excited-state calculations of large systems and is denoted by DC-TDDFTB. The efficient diagonalization algorithms of TDDFTB and DC-TDDFTB methods were implemented into our in-house program. Test calculations of polyethylene aldehyde and p-coumaric acid, a pigment in photoactive yellow protein, in water demonstrate the high accuracy and efficiency of the developed DC-TDDFTB method. Furthermore, the (TD)-DFTB metadynamics simulations of acridinium in the ground and excited states give reasonable pK a values compared with the corresponding experimental values.

The present study implemented the divide-and-conquer timedependent density-functional tight-binding (DC-TDDFTB) code on a graphical processing unit (GPU). The DC method, which is a linear-scaling scheme, divides a total system into several fragments. By separately solving local equations in individual fragments, the DC method could reduce slow central processing unit (CPU)-GPU memory access, as well as computational cost, and avoid shortfalls of GPU memory. Numerical applications confirmed that the present code on GPU significantly accelerated the TDDFTB calculations, while maintaining accuracy. Furthermore, the DC-TDDFTB simulation of 2-acetylindan-1,3-dione displays excitedstate intramolecular proton transfer and provides reasonable absorption and fluorescence energies with the corresponding experimental values.

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