Finite-Temperature Thermally-Assisted-Occupation Density Functional Theory, Ab Initio Molecular Dynamics, and Quantum Mechanics/Molecular Mechanics Methods

TL;DR

This work introduces FT-TAO-DFT and its dynamical extensions FT-TAO-AIMD and FT-TAO-QM/MM to efficiently study finite-temperature properties of large multi-reference systems. By employing a fictitious temperature θ and a locally approximate xc free-energy functional (LDA), the authors address static correlation without the prohibitive cost of conventional MR methods. Applications to n-acenes in vacuum and in an Ar matrix reveal that electronic-temperature effects on radical character and IR spectra are modest up to 1000 K, while nuclear motion and matrix environment can significantly modify these properties; in particular, 6-acene shows measurable di-radical character at elevated temperatures. The FT-TAO-QM/MM framework further enables cost-effective treatment of MR-subsystems embedded in MM surroundings, with matrix effects on IR spectra shown to be deposition-position dependent. Overall, the work provides a practical, scalable toolkit for exploring thermal equilibrium properties and spectra of MR systems in complex environments.

Abstract

Recently, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] has been demonstrated to be an efficient and accurate electronic structure method for studying the ground-state properties of large multi-reference (MR) systems at absolute zero. To explore the thermal equilibrium properties of large MR systems at finite electronic temperatures, in the present work, we propose the finite-temperature (FT) extension of TAO-DFT, denoted as FT-TAO-DFT. Besides, to unlock the dynamical information of large MR systems at finite temperatures, FT-TAO-DFT is combined with ab initio molecular dynamics, leading to FT-TAO-AIMD. In addition, we also develop FT-TAO-DFT-based quantum mechanics/molecular mechanics (QM/MM), denoted as FT-TAO-QM/MM, to provide a cost-effective description of the thermal equilibrium properties of a QM subsystem with MR character embedded in an MM environment at finite temperatures. Moreover, the FT-TAO-DFT, FT-TAO-AIMD, and FT-TAO-QM/MM methods are employed to explore the radical nature and infrared (IR) spectra of n-acenes (n = 2--6), consisting of n linearly fused benzene rings, in vacuum and in an argon (Ar) matrix at finite temperatures. According to our calculations, for n-acenes at 1000 K or below, the electronic temperature effects on the radical nature and IR spectra are very minor, while the nuclear temperature effects on these properties are noticeable. For n-acene in an Ar matrx at absolute zero, the Ar matrix has minimal impact on the radical nature of n-acene, while the co-deposition procedure of n-acene and Ar atoms may affect the IR spectrum of n-acene.

Figures (18)

• Figure 1: FT-TAO-DFT optimized geometry (in Å) of 6-acene in vacuum at the electronic temperature $T_{el}$ = 1000 K.
• Figure 2: Scratch of $n$-acene inserted into an Ar matrix. The green or purple rectangle in each subfigure represents the surface where $n$-acene is placed, including (1) 1a (green) and 1b (purple) on the (111) plane, (2) 2a (green) and 2b (purple) on the (100) plane, and (3) 3a (green) on the (110) plane. The grey dots and yellow dots represent Ar atoms. The inserted $n$-acene and the Ar box are centered at the same geometric point.
• Figure 3: Symmetrized von Neumann entropy ($S_{\text{vN}}$) of $n$-acene in vacuum at the electronic temperature $T_{el}$ = 0 K, 300 K, and 1000 K, computed using FT-TAO-DFT. For comparison, the corresponding FT-TAO-AIMD average values ($\overline{S_{\text{vN}}}$ at 1000 K) are also shown.
• Figure 4: Active orbital occupation numbers ($f_{\text{H-1}}$, $f_{\text{H}}$, $f_{\text{L}}$, and $f_{\text{L+1}}$) of $n$-acene in vacuum at the electronic temperature $T_{el}$ = 0 K, 300 K, and 1000 K, computed using FT-TAO-DFT. The HOMO/LUMO is denoted as the H/L for brevity. For comparison, the corresponding FT-TAO-AIMD average values ($\overline{f_{\text{H-1}}}$, $\overline{f_{\text{H}}}$, $\overline{f_{\text{L}}}$, and $\overline{f_{\text{L+1}}}$ at 1000 K) are also shown.
• Figure 5: Instantaneous symmetrized von Neumann entropy ($S_{\text{vN}}(t)$) of 6-acene in vacuum, obtained from four different FT-TAO-AIMD equilibrated trajectories (No.1 to No.4) at 1000 K. For comparison, the FT-TAO-AIMD average value ($\overline{S_{\text{vN}}}$ at 1000 K) and FT-TAO-DFT value ($S_{\text{vN}}$ at the electronic temperature $T_{el}$ = 1000 K) are also shown.