Doubly Tuned Exchange-Correlation Functionals for Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory

Abstract

It is demonstrated that significant accuracy improvements of MRSF-TDDFT can be achieved by introducing two different XC functionals for the reference Kohn-Sham DFT and the response part of calculations, respectively. Accordingly, two new exchange-correlation (XC) functionals of DTCAM-VEE and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set (mean absolute error (MAE) and interquartile range (IQR) of 0.218 and 0.327 eV, respectively). On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections of trans-butadiene and thymine, and the NAMD simulations on thymine. The latter functional also remarkably exhibited the exact 1/R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer, and the accurate potential energy surfaces along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). The current idea can be also applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory: Multireference Advantages with the Practicality of Linear Response Theory

“… 13 − 17 Recently, by individually tuning XC functionals for SCF and response parts of computations, we have developed a new family of XC functionals designed for MRSF-TDDFT, which would alleviate these situations. 129 In the benchmarks against Thiel’s set, 130 the conventional BH&HLYP functionals in combination with MRSF-TDDFT exhibits the MAE = 0.379 eV and IQR = 0.511 eV, while the MAE of CC2 theory is 0.32 eV. However, the MAE by the recently developed new functionals of DTCAM-VEE is reduced to 0.218 eV and IQR = 0.327 eV, demonstrating the accuracy of VEE can be significantly improved.…”

“…13−17 Recently, by individually tuning XC functionals for SCF and response parts of computations, we have developed a new family of XC functionals designed for MRSF-TDDFT, which would alleviate these situations. 129 In the benchmarks against Thiel's set, 130 As illustrated in Figure 2b, it would be interesting to explore further expansion along the multireference axis, which would allow us to study even more difficult multiconfigurational systems such as metallic complexes with highly degenerated electronic states, where the response configurations generated by the current MRSF-TDDFT may not be sufficient. Methods for systems with odd electrons should be also developed.…”

“…Regarding XC functionals, these approximate XC functionals in general do not exhibit the correct 1/ r asymptotic behavior, where r is the electron–nucleus distance, but fall off too rapidly. Consequently, TDDFT in general gives substantial errors for excited states of molecules with extended π-systems as well as for charge-transfer (CT) states. − Recently, by individually tuning XC functionals for SCF and response parts of computations, we have developed a new family of XC functionals designed for MRSF-TDDFT, which would alleviate these situations . In the benchmarks against Thiel’s set, the conventional BH&HLYP functionals in combination with MRSF-TDDFT exhibits the MAE = 0.379 eV and IQR = 0.511 eV, while the MAE of CC2 theory is 0.32 eV.…”