An official website of the United States government
Understanding photoluminescent mechanisms has become essential for photocatalytic, biological, and electronic applications. Unfortunately, analyzing excited state potential energy surfaces (PESs) in large systems is computationally expensive, and hence limited with electronic structure methods such as time-dependent density functional theory (TDDFT). Inspired by the sTDDFT and sTDA methods, time-dependent density functional theory plus tight binding (TDDFT + TB) has been shown to reproduce linear response TDDFT results much faster than TDDFT, particularly in large nanoparticles. For photochemical processes, however, methods must go beyond the calculation of excitation energies. Herein, this work outlines an analytical approach to obtain the derivative of the vertical excitation energy in TDDFT + TB for more efficient excited state PES exploration. The gradient derivation is based on the Z vector method, which utilizes an auxiliary Lagrangian to characterize the excitation energy. The gradient is obtained when the derivatives of the Fock matrix, the coupling matrix, and the overlap matrix are all plugged into the auxiliary Lagrangian, and the Lagrange multipliers are solved. This article outlines the derivation of the analytical gradient, discusses the implementation in Amsterdam Modeling Suite, and provides proof of concept by analyzing the emission energy and optimized excited state geometry calculated by TDDFT and TDDFT + TB for small organic molecules and noble metal nanoclusters.
more »
« less
Implementation of energy and gradient for the TDDFT-approximate auxiliary function (aas) method
In this work, we have implemented the time-dependent density functional theory approximate auxiliary s function (TDDFT-aas) method, which is an approximate TDDFT method. Instead of calculating the exact two-center electron integrals in the K coupling matrix when solving the Casida equation, we approximate the integrals, thereby reducing the computational cost. In contrast to the related TDDFT plus tight-binding (TDDFT+TB) method, a new type of gamma function is used in the coupling matrix that does not depend on the tight-binding parameters. The calculated absorption spectra of silver and gold nanoparticles using TDDFT-aas show good agreement with TDDFT and TDDFT+TB results. In addition, we have implemented the analytical excited-state gradients for the TDDFT-aas method, which makes it possible to calculate the emission energy of molecular systems.
more »
« less
- Award ID(s):
- 1955823
- PAR ID:
- 10545200
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 161
- Issue:
- 2
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We introduce an individually fitted screened-exchange interaction for the time-dependent Hartree–Fock (TDHF) method and show that it resolves the missing binding energies in polymethine organic dye molecules compared to time-dependent density functional theory (TDDFT). The interaction kernel, which can be thought of as a dielectric function, is generated by stochastic fitting to the screened-Coulomb interaction of many-body perturbation theory (MBPT), specific to each system. We test our method on the flavylium and indocyanine green dye families with a modifiable length of the polymethine bridge, leading to excitations ranging from visible to short-wave infrared. Our approach validates earlier observations on the importance of inclusion of medium range exchange for the exciton binding energy. Our resulting method, TDHF@vW, also achieves a mean absolute error on a par with MBPT at a computational cost on a par with local-functional TDDFT.more » « less
-
A new reference state for density functional theory (DFT), termed the independent atom ansatz, is introduced in this work. This ansatz allows for the formally exact representation of electron density in terms of atom-localized orbitals. Self-consistent equations for such states are derived in general and asymptotic forms. The resultant total energy functional is found to closely resemble tight-binding theory. The independent atom ansatz facilitates partial cancellation of inter-atomic electron–electron and nucleus–electron interactions, which allows for the derivation of analytical tight-binding Hamiltonian matrix elements in a weak interaction limit. The formalism provides energy decomposition and charge analyses at no additional cost and links tight-binding, localized orbital, and electronegativity concepts. Numerical accuracy of the total energy functional has been previously reported for hydrogenic systems [Mironenko, J. Phys. Chem. A 127, 7836 (2023)] and is demonstrated here for He2, Li2, Be2, B2, N2, O2, F2, and Ne2. The method accurately reproduces the shapes of potential energy curves, capturing large-basis CCSD(T)-level bond lengths and bond dissociation energies for N2, O2, and F2 using only a minimal basis set. It outperforms both CCSD(T) and some mainstream approximate restricted Kohn–Sham DFT functionals in describing bond dissociation behavior away from equilibrium geometries.more » « less
-
Abstract The acoustic response of defect‐based acoustic interferometer‐like designs, known as Coupled Resonator Acoustic Waveguides (CRAWs), in 2D phononic crystals (PnCs) is reported. The PnC is composed of steel cylinders arranged in a square lattice within a water matrix with defects induced by selectively removing cylinders to create Mach‐Zehnder‐like (MZ) defect‐based interferometers. Two defect‐based acoustic interferometers of MZ‐type are fabricated, one with arms oriented horizontally and another one with arms oriented diagonally, and their transmission features are experimentally characterized using ultrasonic spectroscopy. The experimental data are compared with finite element method (FEM) simulations and with tight‐binding (TB) calculations in which each defect is treated as a resonator coupled to its neighboring ones. Significantly, the results exhibit excellent agreement indicating the reliability of the proposed approach. This comprehensive match is of paramount importance for accurately predicting and optimizing resonant modes supported by defect arrays, thus enabling the tailoring of phononic structures and defect‐based waveguides to meet specific requirements. This successful implementation of FEM and TB calculations in investigating CRAWs systems within PnCs paves the way for designing advanced acoustic devices with desired functionalities for various practical applications, demonstrating the application of solid‐state electronics principles to underwater acoustic devices description.more » « less
-
Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin–orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm–Dancoff approximation to TDDFT, spin–flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine–Ag 20 complex), we emphasize that caution is needed to properly account for system–environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0213587
