Perspective on Simplified Quantum Chemistry Methods for Excited States and Response Properties

Abstract

We review recent developments in the framework of simplified quantum chemistry for excited state and optical response properties (sTD-DFT) and present future challenges for new method developments to improve accuracy and extend the range of application. In recent years, the scope of sTD-DFT was extended to molecular response calculations of the polarizability, optical rotation, first hyperpolarizability, two-photon absorption (2PA), and excited-state absorption for large systems with hundreds to thousands of atoms. The recently introduced spin-flip simplified time-dependent density functional theory (SF-sTD-DFT) variant enables an ultrafast treatment for diradicals and related strongly correlated systems. A few drawbacks were also identified, specifically for the computation of 2PA cross sections. We propose solutions to this problem and how to generally improve the accuracy of simplified schemes. New possible simplified schemes are also introduced for strongly correlated systems, e.g., with a second-order perturbative correlation correction. Interpretation tools that can extract chemical structure–property relationships from excited state or response calculations are also discussed. In particular, the recently introduced method-agnostic RespA approach based on natural response orbitals (NROs) as the key concept is employed.

Simplified GW/BSE Approach for Charged and Neutral Excitation Energies of Large Molecules and Nanomaterials

“…44 These affordable, semiempirical methods have had significant impact in the field of chemical simulations, enabling ground-state and excited-state calculations of large molecules with more than 1000 atoms; for more details and specific examples, we refer the reader to a recent Perspective article. 45 Inspired, in particular, by Grimmeʼs sTDA, here we present a simplified GW/BSE approach that we call sGW/sBSE. At the heart of both approaches is an approximation to the electron repulsion integrals, which we show leads to an sGW/sBSE implementation with storage requirements that are quadratic in system size and execution times that are cubic in system size.…”

“…The same observations about computational costs of ab initio density functional theory (DFT) and time-dependent DFT (TDDFT) have led to a number of more affordable semiempirical approximations, including density functional tight-binding (DFTB), , extended tight-binding (xTB), − the simplified Tamm–Dancoff approximation/TDDFT (sTDA/sTDDFT), , and combinations thereof, such as TD-DFTB, , sTDA-xTB, and TDDFT + TB . These affordable, semiempirical methods have had significant impact in the field of chemical simulations, enabling ground-state and excited-state calculations of large molecules with more than 1000 atoms; for more details and specific examples, we refer the reader to a recent Perspective article . Inspired, in particular, by Grimmeʼs sTDA, here we present a simplified GW/BSE approach that we call sGW/sBSE.…”

Effects of Size and Morphology on the Excited-State Properties of Nanoscale WO3 Materials from First-Principles Calculations: Implications for Optoelectronic Devices

“…In this regard, Grimme and co-workers developed an effective approach to decrease the computational cost of the linear optical response calculations by applying a series of approximations to solve the two-electron repulsion integrals, representing the major computational bottleneck for this type of calculations, meanwhile maintaining the essential physics of TD-DFT. This method, known as simplified TD-DFT (sTD-DFT or sTDA), , provided results of comparable level of accuracy of TD-DFT, but within a much lower computational burden …”

All-Atom Quantum Mechanical Calculation of the Second-Harmonic Generation of Fluorescent Proteins

“… a a x is the Hartree–Fock exchange percentage, i and j refer to occupied molecular orbitals (MOs) while a and b to unoccupied ones, C α i is the LCAO coefficient considering atomic orbital (AO) α and MO i , and A ia , jb is an element of the linear response matrix A . P- and S-CSFs stand for primary and secondary configuration state functions, respectively …”

“…This QM protocol retains most of the quality expected from higher levels of theory as it was demonstrated for the dynamical structural effects on β of tryptophan-rich amino peptides. 34 The reader interested in simplified quantum chemistry methods for evaluating response properties and excited states can consult our recent perspective articles 35,36 on the subject. Briefly, three approximations are introduced in the simplified scheme: (a) two-electron integrals are approximated by damped short-range Coulomb interactions with two globally fitted y J and y K parameters, (b) the configuration state function (CSF) space is truncated to cover a spectral range up to E thresh , and (c) the response of the exchange-correlation potential is neglected.…”