Simplified Time-dependent Density Functional Theory Research Articles

The eXact integral simplified time-dependent density functional theory (XsTD-DFT).

In the framework of simplified quantum chemistry methods, we introduce the eXact integral simplified time-dependent density functional theory (XsTD-DFT). This method is based on the simplified time-dependent density functional theory (sTD-DFT), where all semi-empirical two-electron integrals are replaced by exact one- and two-center two-electron integrals, while other approximations from sTD-DFT are kept. The performance of this new parameter-free XsTD-DFT method was benchmarked on excited state and (non)linear response properties, including ultra-violet/visible absorption, first hyperpolarizability, and two-photon absorption (2PA). For a set of 77 molecules, the results from the XsTDA approach were compared to the TDA data. XsTDA/B3LYP excitation energies only deviate on average by 0.14eV from TDA while drastically cutting computational costs by a factor of 20 or more depending on the energy threshold chosen. The absolute deviations of excitation energies with respect to the full scheme are decreasing with increasing system size, showing the suitability of XsTDA/XsTD-DFT to treat large systems. Comparing XsTDA and its predecessor sTDA, the new scheme generally improves excitation energies and oscillator strengths, in particular, for charge transfer states. TD-DFT first hyperpolarizability frequency dispersions for a set of push-pull π-conjugated molecules are faithfully reproduced by XsTD-DFT, while the previous sTD-DFT method provides redshifted resonance energy positions. Excellent performance with respect to the experiment is observed for the 2PA spectrum of the enhanced green fluorescent protein. The obtained robust accuracy similar to TD-DFT at a fraction of the computational cost opens the way for a plethora of applications for large systems and in high throughput screening studies.

Iron(II) Complexes with Porphyrin and Tetrabenzoporphyrin: CASSCF/MCQDPT2 Study of the Electronic Structures and UV-Vis Spectra by sTD-DFT.

The geometry and electronic structures of iron(II) complexes with porphyrin (FeP) and tetrabenzoporphyrin (FeTBP) in ground and low-lying excited electronic states are determined by DFT (PBE0/def2-TZVP) calculations and the complete active space self-consistent field (CASSCF) method, followed by the multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2) approach to determine the dynamic electron correlation. The minima on the potential energy surfaces (PESs) of the ground (3A2g) and low-lying, high-spin (5A1g) electronic states correspond to the planar structures of FeP and FeTBP with D4h symmetry. According to the results of the MCQDPT2 calculations, the wave functions of the 3A2g and 5A1g electronic states are single determinant. The electronic absorption (UV-Vis) spectra of FeP and FeTBP are simulated within the framework of the simplified time-dependent density functional theory (sTDDFT) approach with the use of the long-range corrected CAM-B3LYP function. The most intensive bands of the UV-Vis spectra of FeP and FeTBP occur in the Soret near-UV region of 370-390 nm.

Ultrafast Evaluation of Two-Photon Absorption with Simplified Time-Dependent Density Functional Theory.

This work presents the theoretical background to evaluate two-photon absorption (2PA) cross-sections in the framework of simplified time-dependent density functional theory (sTD-DFT). Our new implementation allows the ultrafast evaluation of 2PA cross-sections for large molecules based on a regular DFT ground-state determinant as well as a variant employing our tight-binding sTD-DFT-xTX flavor for very large systems. The method is benchmarked against higher-level calculations for trans-stilbene and typical fluorescent protein chromophores. For eGFP, a quadrupolar chromophore and its branched version, the flavine mono-nucleotide, and the iLOV protein, we compare sTD-DFT 2PA spectra to experimental ones. This includes extension and testing of our all-atom quantum chemistry methodology for the evaluation of 2PA for a system of ∼2000 atoms, providing striking agreement with the experimental spectrum.

Exchange Spin Coupling in Optically Excited States.

In optically excited states in molecules and materials, coupling between local electron spins plays an important role for their photoemission properties and is interesting for potential applications in quantum information processing. Recently, it was experimentally demonstrated that the photogenerated local spins in donor-acceptor metal complexes can interact with the spin of an attached radical, resulting in a spin-coupling-dependent mixing of excited doublet states, which controls the local spin density distributions on donor, acceptor, and radical subunits in optically excited states. In this work, we propose an energy-difference scheme to evaluate spin coupling in optically excited states, using unrestricted and spin-flip simplified time-dependent density functional theory. We apply it to three platinum complexes which have been studied experimentally to validate our methodology. We find that all computed coupling constants are in excellent agreement with the experimental data. In addition, we show that the spin coupling between donor and acceptor in the optically excited state can be fine-tuned by replacing platinum with palladium and zinc in the structure. Besides the two previously discussed excited doublet states (one bright and one dark), our calculations reveal a third, bright excited doublet state which was not considered previously. This third state possesses the inverse spin polarization on donor and acceptor with respect to the previously studied bright doublet state and is by an order of magnitude brighter, which might be interesting for optically controlling local spin polarizations with potential applications in spin-only information transfer and manipulation of connected qubits.

Organic Photovoltaic Efficiency Predictor: Data-Driven Models for Non-Fullerene Acceptor Organic Solar Cells.

In the design of organic solar cells, there has been a need for materials with high power conversion efficiencies. Scharber's model is commonly used to predict efficiency; however, it exhibits poor performance with new non-fullerene acceptor (NFA) devices, since it was designed for fullerene-based devices. In this work, an empirical model is proposed that can be a more accurate alternative for NFA organic solar cells. Additionally, many screening studies use computationally expensive methods. A model based on using semiempirical simplified time-dependent density functional theory (sTD-DFT) as an alternative method can accelerate the calculations and yield a similar accuracy. The models presented in this paper, termed organic photovoltaic efficiency predictor (OPEP) models, have shown significantly lower errors than previous models, with OPEP/B3LYP yielding errors of 1.53% and OPEP/sTD-DFT of 1.55%. The proposed computational models can be used for the fast and accurate screening of new high-efficiency NFAs/donor pairs.

Energy-based fragmentation contribution approach for calculating the fluorescence spectrum of biomacromolecules

It remains challenging to calculate the fluorescence spectra of biomacromolecules due to the large number of atoms involved. Here, we propose an efficient computation method, named the energy-based fragmentation contribution (EBFC) approach, to calculate the fluorescence spectra of super-large proteins. Specifically, an optimized molecular tailoring rule is provided to divide a super-large protein into smaller fragments, then the extended tight binding method and the simplified time-dependent density functional theory approach are employed to calculate the fluorescence spectrum of each fragment in parallel, and finally, the fluorescence spectrum of the target protein is obtained by superimposing the contributions of all fragments. Utilizing the EBFC approach, we calculated fluorescence spectra of three different super-large proteins and the calculated spectra show excellent agreement with experimental data with the difference of less than 1.5%. This work provides an efficient and reliable approach to enhance the modeling capability of the excited states in biomacromolecules.

Accelerating molecular property calculations with semiempirical preconditioning.

Computing ab initio molecular linear response properties, e.g., electronic excitation energies and transition dipole moments, requires the solution of large eigenvalue problems or large systems of equations. These large eigenvalue problems or large systems of equations are commonly solved iteratively using Krylov space algorithms, such as the Davidson algorithm for eigenvalue problems. A critical ingredient in Krylov space algorithms is the preconditioner, which is used to generate optimal update vectors in each iteration. We propose to use semiempirical approximations as preconditioners to accelerate the calculation of ab initio properties. The crucial advantage to improving the preconditioner is that the converged result is unchanged, so there is no trade-off between accuracy and speedup. We demonstrate our approach by accelerating the calculation of electronic excitation energies and electric polarizabilities from linear response time-dependent density functional theory using the simplified time-dependent density functional theory semiempirical model. For excitation energies, the semiempirical preconditioner reduces the number of iterations on average by 37% and up to 70%. The semiempirical preconditioner reduces the number of iterations for computing the polarizability by 15% on average and up to 33%. Moreover, we show that the preconditioner can be further improved by tuning the empirical parameters that define the semiempirical model, leading to an additional reduction in the number of iterations by about 20%. Our approach bridges the gap between semiempirical models and ab initio methods and charts a path toward combining the speed of semiempirical models with the accuracy of ab initio methods.

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

Fluorescent proteins (FPs) are biotags of choice for second-harmonic imaging microscopy (SHIM). Because of their large size, computing their second-harmonic generation (SHG) response represents a great challenge for quantum chemistry. In this contribution, we propose a new all-atom quantum mechanics methodology to compute SHG of large systems. This is now possible because of two recent implementations: the tight-binding GFN2-xTB method to optimize geometries and a related version of the simplified time-dependent density functional theory (sTD-DFT-xTB) to evaluate quadratic response functions. In addition, a new dual-threshold configuration selection scheme is introduced to reduce the computational costs while retaining overall similar accuracy. This methodology was tested to evaluate the SHG of the proteins iLOV and bacteriorhodopsin (bR). In the case of bR, quantitative agreement with respect to experiment was reached for the out-of-resonance low-energy part of the βHRS frequency dispersion. This work paves the way toward an accurate prediction of the SHG of large structures-a requirement for the design of new and improved SHIM biotags.

A Unified Strategy for the Chemically Intuitive Interpretation of Molecular Optical Response Properties.

Interpreting response properties such as the polarizability, optical rotation (OR), or hyperpolarizabilities is a complex task for which a uniform strategy would be desirable. We propose a response analysis procedure called the RespA approach with two interrelated schemes to describe molecular optical response properties in terms of natural response orbitals (NROs) and chemical fragment response for convenient elucidation of structure-(optical)property relationships. These quantities can be easily extracted from the frequency-dependent perturbed one-electron transition/current density matrix obtained from any quantum mechanical response function calculation. NROs provide the most compact representation of the virtual excitations occurring in the (hyper)scattering process. It is decomposed in hole and electron NRO pairs providing a simple exciton picture. For a chemist, it is natural to interpret a property by decomposing it into functional groups or fragment contributions. In this spirit, the response is partitioned into on-site and between-site fragment responses, allowing a property mapping into real space. The new RespA procedure was implemented and tested at the simplified time-dependent density functional theory (sTD-DFT) level enabling calculations for large systems. The RespA strategy is a method-independent route for the understanding of a wide variety of response properties. We showcase how the chemically intuitive RespA approach extracts easily structure-property relationships for the particularly difficult case of OR. As examples, we demonstrate how to enhance the OR of [5]helicene and norbornenone, provide an analysis of the change of the OR observed for camphor and fenchone, and finally investigate the case of a (P,P)-bis-helicenic 2,2'-bipyridine chiroptical switch.

Simplified time-dependent density functional theory (sTD-DFT) for molecular optical rotation.

Theoretical methods able to screen large sets (e.g., conformers) of possibly large compounds are needed in many typical quantum chemistry applications. For this purpose, we here extend the well-established simplified time-dependent density functional theory (sTD-DFT) method for the calculation of optical rotation. This new scheme is benchmarked against 42 compounds of the OR45 set as well as thirteen helicene derivatives and one bio-molecular system. The sTD-DFT method yields optical rotations in good quantitative agreement with experiment for compounds with a valence-dominated response, e.g., conjugated π-systems, at a small fraction of the computational cost compared to TD-DFT (1-3 orders of magnitude speed-up). For smaller molecules with a Rydberg state dominated response, the agreement between TD-DFT and the simplified version using standard hybrid functionals is somewhat worse but still reasonable for typical applications. Our new implementation in the stda code enables computations for systems with up to 1000 atoms, e.g., for studying flexible bio-molecules.

Systematic Computational Design and Optimization of Light Absorbing Dyes.

We present a workflow to aid the discovery of new dyes for the role of a photosensitive unit in the dye-sensitized photo-electrochemical cells (DS-PECs). New structures are generated in a fully automated way using the Compound Attachment Tool (CAT) introduced in this work. These structures are characterized with efficient approximate density functional theory (DFT) methods, and molecules with favorable optical properties are suggested for possible further use in DS-PECs. As around 2500 structures are generated in this work, and as we aim for still larger volumes of compounds to screen in subsequent applications, we have assessed the reliability of low-cost screening methods and show that simplified time-dependent density functional theory (sTDDFT) provides a satisfying accuracy/cost ratio. From the dyes considered, we propose a set that can be suitable for panchromatic sensitization of the photoelectrode in DS-PECs to further increase DS-PEC efficiency.

Combining Graphics Processing Units, Simplified Time-Dependent Density Functional Theory, and Finite-Difference Couplings to Accelerate Nonadiabatic Molecular Dynamics.

Starting from our recently published implementation of nonadiabatic molecular dynamics (NAMD) on graphics processing units (GPUs), we explore further approaches to accelerate ab initio NAMD calculations at the time-dependent density functional theory (TDDFT) level of theory. We employ (1) the simplified TDDFT schemes of Grimme et al. and (2) the Hammes-Schiffer–Tully approach to obtain nonadiabatic couplings from finite-difference calculations. The resulting scheme delivers an accurate physical picture while virtually eliminating the two computationally most demanding steps of the algorithm. Combined with our GPU-based integral routines for SCF, TDDFT, and TDDFT derivative calculations, NAMD simulations of systems of a few hundreds of atoms at a reasonable time scale become accessible on a single compute node. To demonstrate this and to present a first, illustrative example, we perform TDDFT/MM-NAMD simulations of the rhodopsin protein.

Optical limiting properties, structure and simplified TD-DFT calculations of scandium tetra-15-crown-5 phthalocyaninates

The optical limiting properties of crown-ether-substituted scandium(III) phthalocyaninate complexes, bis-tetra-15-crown-5-phthalocyaninates Sc[(15C5)4Pc][Formula: see text] (I) and Sc[(15C5)4Pc][Formula: see text] (Ia), together with monophthalocyaninate [(15C5)4Pc]Sc(OAc) (II) were measured by using the Z-scan technique (532 nm laser and pulse rate of 10 ns). It was revealed that expansion of the [Formula: see text]-system on moving from the monomeric Sc complex II to sandwich compound I and changing the electronic state of the sandwich compound from the anionic Ia species to the neutral radical I improves the optical limiting properties. The Im[[Formula: see text]] values obtained lie in the 10[Formula: see text]–10[Formula: see text] esu range that is consistent with those reported previously for other organic chromophores. The crystal structure of sandwich Sc(III) complex I was elucidated by means of single-crystal X-ray diffraction analysis and was used to guide a series of theoretical calculations. It was demonstrated that the application of simplified time-dependent density functional theory (sTD-DFT) calculations can provide reasonably accurate predictions for compounds of this type when the geometries of the complexes are clearly defined.

Dynamic Structural Effects on the Second-Harmonic Generation of Tryptophane-Rich Peptides and Gramicidin A.

Peptide chains can model endogenous biotags for applications in second-harmonic imaging microscopy. Such structures are flexible which may strongly affect their structure-property relationship. Here, we explore quantum-mechanically the conformational space of a set of tryptophan-rich model peptides. This has become feasible because of the recently proposed meta-dynamics method based on efficient tight-binding (TB) calculations. The TB version of the simplified time-dependent density functional theory (sTD-DFT-xTB) method is used to evaluate the first hyperpolarizability (β). These new tools enable us to calculate nonlinear optical properties for systems with several thousand atoms and/or to screen large structure ensembles. First, we show that the indole chromophore in tryptophan residues dominates the β response of these systems. Their relative orientation mostly determines the global β tensor and affects the static β response. The results underline the importance of finding low-energy conformers for modeling β of flexible molecules. Additionally, we compare calculated and extrapolated experimental static β. The sTD-DFT-xTB method is capable of providing reliable second-harmonic generation values for tryptophan-rich systems at a fraction of the computational cost of the commonly used TD-DFT/TD-HF levels of theory.

Nonlinear-response properties in a simplified time-dependent density functional theory (sTD-DFT) framework: Evaluation of excited-state absorption spectra.

The energy conversion efficiency of organic solar cells seems crucial for a clean future. The design of new light-harvesting devices needs an in-depth understanding of their optical properties, including the excited-state absorption (ESA). In biology, the optical characterization of photochemical/physical processes happening in photosynthetic pigments and proteins can be difficult to interpret due to their structural complexities. Experimentally, an ultrafast transient absorption experiment can probe the excited state interaction with light. Quantum chemistry could play an important role to model the transient absorption spectrum of excited states. However, systems that need to be investigated can be way too large for existent software implementations. In this contribution, we present the first sTDA/sTD-DFT (simplified time-dependent density functional theory with and without Tamm Dancoff approximation) implementation to evaluate the ESA of molecules. The ultrafast ESA evaluation presents a negligible extra cost with respect to sTDA/sTD-DFT original schemes for standard ground state absorption. The sTD-DFT method shows ability to assign ESA spectra to the correct excited state. We showed that in the literature, wrong assignments were proposed as for the L34/L44 mixture and N-methylfulleropyrrolidine. In addition, sTDA/sTD-DFT-xTB tight-binding variants are also available, allowing the evaluation of ESA for systems of a few thousands of atoms, e.g., the spectrum of the photoactive yellow protein composed of 1931 atoms.

Nonlinear-response properties in a simplified time-dependent density functional theory (sTD-DFT) framework: Evaluation of the first hyperpolarizability.

Recent developments in nonlinear imaging microscopy show the need to implement new theoretical tools, which are able to characterize nonlinear optical properties in an efficient way. For second-harmonic imaging microscopy (SHIM), quantum chemistry could play an important role to design new exogenous dyes with enhanced first hyperpolarizabilities or to characterize the response origin in large endogenous biological systems. Such methods should be able to screen a large number of compounds while reproducing their trends and to treat large systems in reasonable computation times. To fulfill these requirements, we present a new simplified time-dependent density functional theory (sTD-DFT) implementation to evaluate the first hyperpolarizability where the Coulomb and exchange integrals are approximated by short-range damped Coulomb interactions of transition density monopoles. For an ultra-fast computation of the first hyperpolarizability, a tight-binding version (sTD-DFT-xTB) is also proposed. In our implementation, a sTD-DFT calculation is more than 600 time faster with respect to a regular TD-DFT treatment, while the xTB version speeds up the entire calculation further by at least two orders of magnitude. We challenge our implementation on three test cases: typical push-pull π-conjugated compounds, fluorescent proteins, and a collagen model, which were selected to model requirements for SHIM applications.

Electronic Circular Dichroism of [16]Helicene With Simplified TD-DFT: Beyond the Single Structure Approach.

The electronic circular dichroism (ECD) spectrum of the recently synthesized [16]helicene and a derivative comprising two triisopropylsilyloxy protection groups was computed by means of the very efficient simplified time-dependent density functional theory (sTD-DFT) approach. Different from many previous ECD studies of helicenes, nonequilibrium structure effects were accounted for by computing ECD spectra on "snapshots" obtained from a molecular dynamics (MD) simulation including solvent molecules. The trajectories are based on a molecule specific classical potential as obtained from the recently developed quantum chemically derived force field (QMDFF) scheme. The reduced computational cost in the MD simulation due to the use of the QMDFF (compared to ab-initio MD) as well as the sTD-DFT approach make realistic spectral simulations feasible for these compounds that comprise more than 100 atoms. While the ECD spectra of [16]helicene and its derivative computed vertically on the respective gas phase, equilibrium geometries show noticeable differences, these are "washed" out when nonequilibrium structures are taken into account. The computed spectra with two recommended density functionals (ωB97X and BHLYP) and extended basis sets compare very well with the experimental one. In addition we provide an estimate for the missing absolute intensities of the latter. The approach presented here could also be used in future studies to capture nonequilibrium effects, but also to systematically average ECD spectra over different conformations in more flexible molecules. Chirality 28:365-369, 2016. © 2016 Wiley Periodicals, Inc.

A simplified time-dependent density functional theory approach for electronic ultraviolet and circular dichroism spectra of very large molecules

We present a simplified time-dependent density functional theory approach (sTD-DFT) that allows fast computation of electronic ultraviolet (UV) or circular dichroism (CD) spectra of molecules with 500–1000 atoms. The matrix elements are treated in the same way as in the recently proposed simplified Tamm-Dancoff approach (sTDA, S. Grimme, J. Chem. Phys., 138 (2013), 244104) but instead of applying the Tamm-Dancoff approximation, the standard linear-response density functional theory problem is solved. Compared to sTDA, the method leads to an increase in computation time (typically a factor of 2–5 compared to the corresponding sTDA) which is justified since the resulting transition dipole moments are in general of higher quality. This becomes important if spectral intensities (e.g. single-photon oscillator and rotatory transition strengths) are of interest. Comparison of UV and CD spectra obtained from sTD-DFT and sTDA for some typical systems employing standard hybrid functionals shows that both yield very similar excitation energies but the advantage of using the former approach for transition moments. In order to show the applicability of sTD-DFT to systems which are far beyond the scope of conventional TD-DFT, we present the CD spectrum of a substituted, chiral fullerene over a range of almost 1200 excited states. We propose this method as a more reliable alternative for the prediction especially of the more challenging CD spectra.