Calculation of Electronic Circular Dichroism Spectra with Time-Dependent Double-Hybrid Density Functional Theory

Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/GW, and Wave Function Methods

To expand the QUEST database of highly accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly accurate excitation energies. For several singlet transitions, we have been able to determine CCSDT transition energies with a compact basis set, finding minimal deviations from the CC3 values for most states. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both G0W0 and evGW quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models among those with respective O ( N 5 ) and O ( N 6 ) scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, ωB97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-ωB88PP86 and SOS-ωPBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/evGW calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts.

How do spin-scaled double hybrids designed for excitation energies perform for noncovalent excited-state interactions? An investigation on aromatic excimer models

Time-dependent double hybrids with spin-component or spin-opposite scaling to their second-order perturbative correlation correction have demonstrated competitive robustness in the computation of electronic excitation energies. Some of the most robust are those recently published by our group (M. Casanova-Páez, L. Goerigk, J. Chem. Theory Comput. 2021, 20, 5165). So far, the implementation of these functionals has not allowed correctly calculating their ground-state total energies. Herein, we define their correct spin-scaled ground-state energy expressions which enables us to test our methods on the noncovalent excited-state interaction energies of four aromatic excimers. A range of 22 double hybrids with and without spin scaling are compared to the reasonably accurate wavefunction reference from our previous work (A. C. Hancock, L. Goerigk, RSC Adv. 2023, 13, 35964). The impact of spin scaling is highly dependent on the underlying functional expression, however, the smallest overall errors belong to spin-scaled functionals with range separation: SCS- and SOS- ω PBEPP86, and SCS-RSX-QIDH. We additionally determine parameters for DFT-D3(BJ)/D4 ground-state dispersion corrections of these functionals, which reduce errors in most cases. We highlight the necessity of dispersion corrections for even the most robust TD-DFT methods but also point out that ground-state based corrections are insufficient to completely capture dispersion effects for excited-state interaction energies.

Chiral Induction in a Self-Assembled Pd4 Coordination Cage with Chiral Guests

The dynamic interplay of coordination bonds within metal-organic cages offers a unique avenue for structural evolution in response to external stimuli, presenting a promising strategy for the construction of chiral assemblies. This adaptability is crucial for the selective synthesis of homochiral assemblies and advancement of asymmetric catalysis. In this study, we report the self-assembly of an achiral square-planar Pd(II) acceptor with a C2-symmetric tetrapyridyl donor resulted in the formation of a racemic mixture of the chiral octahedral cage Pd4L2. The existence of this racemic mixture was confirmed using circular dichroism spectroscopy as well as single crystal X-ray diffraction analysis. We encoded chiral information into the asymmetric cavity of the cage by encapsulating chiral aromatic guests through efficient π-π stacking and hydrophobic interactions in aqueous media. The inclusion of a chiral guest induces a preference for one enantiomeric conformation of the cage over the other, effectively shifting the equilibrium towards a single, enantiopure host-guest complex. While the concept of chiral guest recognition by a chiral host is well-established, this work constitutes a remarkable example of guest-mediated chirality transfer leading to the formation of a single enantiopure coordination complex from achiral building blocks.

Total absorption spectrum of benzene aggregates obtained from two different approaches

CONTEXT

The study of molecular aggregation effects on the electronic spectrum is essential for the development of optoelectronic devices. However, investigating the entire valence absorption spectrum of aggregates using quantum mechanical methods is a challenging task. In this work, we perform systematic simulations of the absorption spectrum of benzene molecular clusters up to 35 eV applying two approaches based on time-dependent density functional theory. The results show that depending on the dimer packing, different energy shifts occur for the symmetry allowed [Formula: see text] transition, in comparison to the monomer. The transition intensity increases for the band around 6 eV for larger aggregates from the monomer to dimers and tetramer, indicating the occurrence of the symmetry forbidden (in [Formula: see text] point group) [Formula: see text] [Formula: see text] transition. The benzene crystal exhibits a large redshift following the experimental spectrum. Also, the continuum regions of all spectra show a good agreement with the experiments both in gas and solid phases.

METHODS

Geometry optimization of the monomer was carried out with Gaussian 09 software using the PBE0/def2-TZVP level of theory. We used dimers and tetramer molecular geometries extracted from the experimental crystal structure. The absorption spectra were directly obtained by the Liouville-Lanczos TDDFT approach with plane waves basis set or indirectly by TDDFT pseudo-spectra calculated in a [Formula: see text] basis followed by analytic continuation procedure to obtain complex polarizability. The former is available at Quantum ESPRESSO, and the latter was calculated using Gaussian 09 with the post-processing performed with a code previously developed in our group.

Noncovalently bound excited-state dimers: a perspective on current time-dependent density functional theory approaches applied to aromatic excimer models

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for time-dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

Theoretical-Computational Modeling of CD Spectra of Aqueous Monosaccharides by Means of Molecular Dynamics Simulations and Perturbed Matrix Method

The electronic circular dichroism (ECD) spectra of aqueous d-glucose and d-galactose were modeled using a theoretical-computational approach combining molecular dynamics (MD) simulations and perturbed matrix method (PMM) calculations, hereafter termed MD-PMM. The experimental spectra were reproduced with a satisfactory accuracy, confirming the good performances of MD-PMM in modeling different spectral features in complex atomic-molecular systems, as already reported in previous studies. The underlying strategy of the method was to perform a preliminary long timescale MD simulation of the chromophore followed by the extraction of the relevant conformations through essential dynamics analysis. On this (limited) number of relevant conformations, the ECD spectrum was calculated via the PMM approach. This study showed that MD-PMM was able to reproduce the essential features of the ECD spectrum (i.e., the position, the intensity, and the shape of the bands) of d-glucose and d-galactose while avoiding the rather computationally expensive aspects, which were demonstrated to be important for the final outcome, such as (i) the use of a large number of chromophore conformations; (ii) the inclusion of quantum vibronic coupling; and (iii) the inclusion of explicit solvent molecules interacting with the chromophore atoms within the chromophore itself (e.g., via hydrogen bonds).

Double-Hybrid Density Functional Theory for Core Excitations: Theory and Benchmark Calculations

The double-hybrid (DH) time-dependent density functional theory is extended to core excitations. Two different DH formalisms are presented utilizing the core-valence separation (CVS) approximation. First, a CVS-DH variant is introduced relying on the genuine perturbative second-order correction, while an iterative analogue is also presented using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH ansatz. The performance of the new approaches is tested for the most popular DH functionals using the recently proposed XABOOM [J. Chem. Theory Comput.2021, 17, 1618] benchmark set. In order to make a careful comparison, the accuracy and precision of the methods are also inspected. Our results show that the genuine approaches are highly competitive with the more advanced CVS-ADC(2)-based methods if only excitation energies are required. In contrast, as expected, significant differences are observed in oscillator strengths; however, the precision is acceptable for the genuine functionals as well. Concerning the performance of the CVS-DH approaches, the PBE0-2/CVS-ADC(2) functional is superior, while its spin-opposite-scaled variant is also recommended as a cost-effective alternative. For these approaches, significant improvements are realized in the error measures compared with the popular CVS-ADC(2) method.

Role of Exact Exchange in Difference Projected Double-Hybrid Density Functional Theory for Treatment of Local, Charge Transfer, and Rydberg Excitations

Difference approaches to the study of excited states have undergone a renaissance in recent years, with the development of a plethora of algorithms for locating self-consistent field approximations to excited states. Density functional theory is likely to offer the best balance of cost and accuracy for difference approaches, and yet there has been little investigation of how the parametrization of density functional approximations affects performance. In this work, we aim to explore the role of the global Hartree-Fock exchange parameter in tuning accuracy of different excitation types within the framework of the recently introduced difference projected double-hybrid density functional theory approach and contrast the performance with conventional time-dependent double-hybrid density functional theory. Difference projected double-hybrid density functional theory was demonstrated to give vertical excitation energies with average error and standard deviation with respect to multireference perturbation theory comparable to more expensive linear-response coupled cluster approaches ( J. Chem. Phys.2020, 153, 074103). However, despite benchmarking of local excitations, there has been no investigation of the methods performance for charge transfer or Rydberg excitations. In this work we report a new benchmark of charge transfer, Rydberg, and local excited state vertical excitation energies and examine how the exact Hartree-Fock exchange affects the benchmark performance to provide a deeper understanding of how projection and nonlocal correlation balance differing sources of error in the ground and excited states.

Assessing Recent Time-Dependent Double-Hybrid Density Functionals on Doublet-Doublet Excitations

This work is the first thorough investigation of time-dependent double-hybrid density functionals (DHDFs) for the calculation of doublet-doublet excitation energies. It sheds light on the current state-of-the-art techniques in the field and clarifies if there is still room for future improvements. Overall, 29 hybrid functionals and DHDFs are investigated. We separately analyze the individual impacts of the Tamm-Dancoff approximation (TDA), range separation, and spin-component/opposite scaling (SCS/SOS) on 45 doublet-doublet excitations in 23 radicals before concluding with an overarching analysis that includes and excludes challenging excitations with double-excitation or multireference character. Our results show again that so-called "nonempirical" DHDFs are outperformed by semiempirical ones. While the best assessed functionals are DHDFs, some of the worst are also DHDFs and outperformed by all assessed hybrids. SCS/SOS is particularly beneficial for range-separated DHDFs. Spin-scaled, range-separated DHDFs paired with the TDA belong to the best tested methods here, and we particularly highlight SCS-ωB2GP-PLYP, SOS-ωB2PLYP, SOS-ωB2GP-PLYP, SOS-ωB88PP86, SOS-RSX-QIDH, and SOS-ωPBEPP86. When comparing our functional rankings with previous studies on singlet-singlet and singlet-triplet excitations, we recommend TDA-SOS-ωB88PP86 and TDA-SOS-ωPBEPP86 as robust methods for excitation energies in general until further improvements have been achieved that surpass the chemical accuracy threshold for challenging open-shell excitations without increasing the computational effort.

Noncovalently bound excited-state dimers: a perspective on current time-dependent density functional theory approaches applied to aromatic excimer models

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for Time-Dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

Do Double-Hybrid Functionals Benefit from Regularization in the PT2 Term? Observations from an Extensive Benchmark

We put to the test a recent suggestion [Shee, J., et al. J. Phys. Chem. Lett. 2021, 12 (50), 12084-12097] that MP2 regularization might improve the performance of double-hybrid density functionals. Using the very large and chemically diverse GMTKN55 benchmark, we find that κ-regularization is indeed beneficial at lower percentages of Hartree-Fock exchange, especially if spin-component scaling is not applied [such as in B2GP-PLYP or ωB97M(2)]. This benefit dwindles for DSD and DOD functionals and vanishes entirely in the ∼70% HF exchange region optimal for them.

Origin invariant electronic circular dichroism in the length dipole gauge without London atomic orbitals

We present a method for obtaining origin-independent electronic circular dichroism (ECD) in the length-gauge representation LG(OI) without the usage of London atomic orbitals. This approach builds upon the work by Caricato [J. Chem. Phys. 153, 151101 (2020)] and is applied to rotatory strengths and ECD spectra from damped response theory. Numerical results are presented for time-dependent Hartree-Fock and density-functional theory, the second-order algebraic diagrammatic construction method, and linear-response coupled-cluster theory with singles and approximate doubles. We can support the finding that the common choice of placing the gauge origin in the center of mass of a molecule in conventional length-gauge calculations involving chiroptical properties might not be optimal and show that LG(OI) is a valuable alternative for the origin-independent calculation of ECD spectra. We show that, for a limited test set, the convergence of the rotatory strengths calculated with the LG(OI) approach toward the basis-set limit tends to be faster than for the established velocity gauge representation. Relationships between the sum-over-states expression of the optical rotation in the LG(OI) framework and its representation in terms of response functions are analyzed.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange-correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach

Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz (J. Chem. Theory Comput. 2019, 15, 4440. DOI: 10.1021/acs.jctc.9b00391) is combined with range-separation techniques. In the present scheme, both the exchange and the correlation contributions are range-separated, while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range separation for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range corrected DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addition, the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.

Surprisingly Good Performance of XYG3 Family Functionals Using a Scaled KS-MP3 Correlation

By adding a GLPT3 (third-order Görling-Levy perturbation theory, or KS-MP3) term E₃ to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wave function ab initio approaches. Intriguingly, (a) the introduction of E₃ makes an empirical dispersion correction redundant; (b) generalized gradient approximation (GGA) or meta-GGA semilocal correlation functionals offer no advantage over the local density approximation (LDA) in this framework; (c) if a dispersion correction is retained, then simple Slater exchange leads to no significant loss in accuracy. It is possible to create a six-parameter functional with WTMAD2 = 1.42 that has no post-LDA density functional theory components and no dispersion correction in the final energy.

Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet-Singlet and Singlet-Triplet Excitation Energies

Following the work on spin-component and spin-opposite scaled (SCS/SOS) global double hybrids for singlet-singlet excitations by Schwabe and Goerigk [ J. Chem. Theory Comput. 2017, 13, 4307-4323] and our own works on new long-range corrected (LC) double hybrids for singlet-singlet and singlet-triplet excitations [ J. Chem. Theory Comput. 2019, 15, 4735-4744 and J. Chem. Phys. 2020, 153, 064106], we present new LC double hybrids with SCS/SOS that demonstrate further improvement over previously published results and methods. We introduce new unscaled and scaled versions of different global and LC double hybrids based on Becke88 or PBE exchange combined with LYP, PBE, or P86 correlation. For singlet-singlet excitations, we cross-validate them on six benchmark sets that cover small to medium-sized chromophores with different excitation types (local-valence, Rydberg, and charge transfer). For singlet-triplet excitations, we perform the cross-validation on three different benchmark sets following the same analysis as in our previous work in 2020. In total, 203 excitations are analyzed. Our results confirm and extend those of Schwabe and Goerigk regarding the superior performance of SCS and SOS variants compared to their unscaled parents by decreasing mean absolute deviations, root-mean-square deviations, or error spans by more than half and bringing absolute mean deviations closer to zero. Our SCS/SOS variants are shown to be highly efficient and robust for the computation of vertical excitation energies, which even outperform specialized double hybrids that also contain an LC in their perturbative part. In particular, our new SCS/SOS-ωPBEPP86 and SCS/SOS-ωB88PP86 functionals are four of the most accurate and robust methods tested in this work, and we fully recommend them for future applications. However, if the relevant SCS and SOS algorithms are not available to the user, we suggest ωPBEPP86 as the best unscaled method in this work.

Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States

Our recently presented range-separated (RS) double-hybrid (DH) time-dependent density functional approach [J. Chem. Theory Comput. 17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calculations confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm-Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

Global double hybrids do not work for charge transfer: A comment on "Double hybrids and time-dependent density functional theory: An implementation and benchmark on charge transfer excited states"

We comment on the results published by Ottochian et al. in J. Comput Chem. 2020, 41, 1242. Therein, the authors claim that the second-order, perturbative correlation correction applied to the time-dependent version of the PBE-QIDH global double-hybrid functional approximation (DHDFA) enables the description of charge-transfer (CT) excitations. Herein, we point out some inadvertent oversights related to what had already been previously known and achieved in the field of time-dependent DHDFAs. Exemplified for the same four systems that Ottochian et al. have used to analyze intermolecular CT excitations, we show how a systematic and unacceptably large redshift in global DHDFAs is rectified when using the latest long-range corrected DHDFAs published earlier in J. Chem. Theory Comput. 2019, 15, 4735.

The Trip to the Density Functional Theory Zoo Continues: Making a Case for Time-Dependent Double Hybrids for Excited-State Problems

This account is written for general users of time-dependent density functional theory (TD-DFT) methods as well as chemists who are unfamiliar with the field. It includes a brief overview of conventional TD-DFT approaches and recommendations for applications to organic molecules based on our own experience. The main emphasis of this work, however, lies in providing the first in-depth review of time-dependent double-hybrid density functionals. They were first established in 2007 with very promising follow-up studies in the subsequent four years before developments or applications became scarce. The topic has regained more interest since 2017, and this account reviews those latest developments led by our group. These developments have shown unprecedented robustness for a variety of different types of electronic excitations when compared to more conventional TD-DFT methods. In particular, time-dependent double hybrids do not suffer from artificial ghost states and are able to reproduce exciton-coupled absorption spectra. Our latest methods include range separation and belong to the currently best TD-DFT methods for singlet-singlet excitations in organic molecules. While there is still room for improvement and further development in this space, we hope that this account encourages users to adjust their computational protocols to such new methods to provide more real-life testing and scenarios.

Theory and algorithms for chiroptical properties and spectroscopies of aqueous systems

Chiroptical properties and spectroscopies are valuable tools to study chiral molecules and assign absolute configurations. The spectra that result from chiroptical measurements may be very rich and complex, and hide much of their information content. For this reason, the interplay between experiments and calculations is especially useful, provided that all relevant physico-chemical interactions that are present in the experimental sample are accurately modelled. The inherent difficulty associated to the calculation of chiral signals of systems in aqueous solutions requires the development of specific tools, able to account for the peculiarities of water-solute interactions, and especially its ability to form hydrogen bonds. In this perspective we discuss a multiscale approach, which we have developed and challenged to model the most used chiroptical techniques.

Vibrationally resolved electronic circular dichroism and circularly polarized luminescence spectra of a boron-fused double helicene: A theoretical study

In this work, we present the theoretical study of the vibrationally resolved absorption (ABS), electronic circular dichroism (ECD), emission (EMI), and circularly polarized luminescence (CPL) spectra of a boron-fused double helicene, with a detailed and complete discussion of the alternative possible approximate methods. Given the fact that few examples of CPL calculations exist, the potential energy surfaces (PESs) have been constructed and compared with Adiabatic (AH) and Vertical Hessian (VH) models. All the vibronic calculations have accounted for Duschinsky mixings, Franck-Condon (FC) effect and Herzberg-Teller (HT) contribution. Moreover, different HT expansions have been checked and compared, by computing the derivatives of the electric and magnetic dipole transition moments around the equilibrium geometries of the initial and final states. Our results show that both AH and VH models have well reproduced the experimental vibronic structures and VH model shows a better performance in the simulation of spectral lineshapes. They also show that HT effects dominate the shapes of EMI and CPL, tuning the relative heights of the different vibronic peaks, improving the agreement with the experiment for EMI. Moreover, HT effects are the main reason for the mirror-symmetry breaking between ECD and CPL spectra. Furthermore, interesting interference effects between FC and HT contributions have also been addressed.

The one-electron self-interaction error in 74 density functional approximations: a case study on hydrogenic mono- and dinuclear systems

The self-interaction error (SIE), i.e. unphysical interactions of electrons with themselves, has plagued developers and users of Density Functional Approximations (DFAs) since the inception of Density Functional Theory (DFT). Formally, it can be separated into the one-electron and many-electron SIE; herein we present one of the most comprehensive studies of the first. While we focus mostly on the total SIE, we also make use of two different decompositions. The first is a separation into functional and density-driven errors as championed by Sim, Burke and co-workers [J. Phys. Chem. Lett., 2018, 9, 6385-6392]; the second separates the error into exchange, correlation, and one-electron components, with the latter being a density error that has not been discussed in this form before. After investigating the familiar hydrogen atom and dihydrogen cation, we establish a relationship between the SIE and the nuclear charge with the help of a series of heavier hydrogenic analogues. For the mononuclear systems and the diatomics at the dissociation limit, this relationship is linear in nature with prominent exceptions, mostly belonging to the Minnesota and range-separated (double-)hybrid DFAs. For the first time, we also show how the magnitude of the SIE depends on the underlying atomic-orbital basis set and how DFAs that rely on a popular van-der-Waals DFT type London-dispersion term exhibit "self-dispersion". We find that range separation is not a panacea for solving the one-electron SIE. DFAs that have been developed to be one-electron SIE free for one system, such as the hydrogen atom, show larger errors for heavier hydrogenic systems. Often, one-electron SIE-free DFAs rely on fortuitous error cancellation between their exchange and correlation components. An analysis of the most robust methods for general applications to date reveals that they suffer moderately from the one-electron SIE, while DFAs that are nearly SIE-free do not perform well in applications. Implicit in the continued existence of the one-electron SIE is that well-performing DFAs continue to suffer insufficiencies at their fundamental levels that are being compensated for by the SIE. Our analysis includes more than 250 000 datapoints, resulting in multiple insights that may drive future developments of new DFAs or SIE corrections.

Absolute Configuration of Alkaloids from Uncaria longiflora through Experimental and Computational Approaches

The structure elucidation of three new alkaloids named isoformosaninol (1), formosaninol (2), and longiflorine (3), isolated from the leaves of Uncaria longiflora var. pteropoda (Miq.) Ridsdale, along with their biosynthetic pathways are discussed. Their absolute structures were determined through a combination of physical data interpretation and quantum chemical calculations using the time-dependent density functional theory (TDDFT) method.

ωB2PLYP and ωB2GPPLYP: The First Two Double-Hybrid Density Functionals with Long-Range Correction Optimized for Excitation Energies

Double-hybrid density functionals are currently the most accurate density functionals for ground-state properties and electronic excitations. Nevertheless, the lack of a long-range correction scheme makes them unreliable when it comes to long-range excitations. For this reason, we propose the first two time-dependent double-hybrid functionals with correct asymptotic long-range behavior named ωB2PLYP and ωB2GPPLYP. Herein, we demonstrate their excellent performance and show that they are the most accurate and robust time-dependent density functional theory methods for electronic excitation energies. They provide a balanced description of local-valence, Rydberg, and charge-transfer states. They are also able to tackle the difficult first two transitions in polycyclic aromatic hydrocarbons and show very promising results in a preliminary study on transition-metal compounds, exemplified for titanium dioxide clusters. This work shows that double hybrids can be systematically improved also for excitation energies, and further work in this field is warranted.

Combined Density Functional and Algebraic-Diagrammatic Construction Approach for Accurate Excitation Energies and Transition Moments

A composite of time-dependent density functional theory (TDDFT) and the second-order algebraic-diagrammatic construction [ADC(2)] approach is presented for efficient calculation of spectral properties of molecules. Our method can be regarded as a new excited-state double-hybrid (DH) approach or a dressed TDDFT scheme, but it can also be interpreted as an empirically tuned ADC(2) model. Several combinations of exchange-correlation functionals and spin-scaling schemes are explored. Our best-performing method includes the Perdew, Burke, and Ernzerhof exchange and Perdew's 1986 correlation functional and employs the scaled-opposite-spin approximation for the higher-order terms. The computation time of the new method scales as the fourth power of the system size, and an efficient cost-reduction approach is also presented, which further speeds up the calculations. Our benchmark calculations show that the proposed model outperforms not only the existing DH approaches and ADC(2) variants but also the considerably more expensive coupled-cluster methods.

Chiroptical Properties of Twisted Acenes: Experimental and Computational Study

Acenes that are twisted out of planarity are expected to display chiroptical properties. However, the effect of twisting on the chiroptical properties of acenes has not been investigated computationally or experimentally. Herein, we present a computational investigation of the chiroptical properties of anthracenes to pentacenes, combined with an experimental study using a series of helically locked acenes, twisted to different torsional angles in their enantiopure form. The lowest energy transition, which is relatively weak in acenes, becomes dominant in their circular dichroism spectra upon twisting. We find that the rotational strength of acenes consistently increases with increasing twist. The experimental data obtained from enantiopure tethered twistacenes show the same trend as the calculated result, with a strong Cotton effect and anisotropy factor, rendering twisted acenes as excellent chiroptical materials.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

Accuracy of Td-DFT in the Ultraviolet and Circular Dichroism Spectra of Deoxyguanosine and Uridine

Accuracy of the time-dependent density functional theory (Td-DFT) was examined for the ultraviolet (UV) and circular dichroism (CD) spectra of deoxyguanosine (dG) and uridine, using 11 different DFT functionals and two different basis sets. The Td-DFT results of the UV and CD spectra were strongly dependent on the functionals used. The basis-set dependence was observed only for the CD spectral calculations. For the UV spectra, the B3LYP and PBE0 functionals gave relatively good results. For the CD spectra, the B3LYP and PBE0 with 6-311G(d,p) basis gave relatively permissible result only for dG. The results of other functionals were difficult to be used for the studies of the UV and CD spectra, though the symmetry adapted cluster-configuration interaction (SAC-CI) method reproduced well the experimental spectra of these molecules. To obtain valuable information from the theoretical calculations of the UV and CD spectra, the theoretical tool must be able to reproduce correctly both of the intensities and peak positions of the UV and CD spectra. Then, we can analyze the reasons of the changes of the intensity and/or the peak position to clarify the chemistry involved. It is difficult to recommend Td-DFT as such tools of science, at least from the examinations using dG and uridine.

Central substitution of azacalixphyrins: a strategy towards acidochromic NIR dyes

A new substitution pattern of azacalixphyrins is proposed and assessed with theoretical tools.

Time-Dependent Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling

For the first time, we combine time-dependent double-hybrid density functional approximations (TD-DHDFAs) for the calculation of electronic excitation energies with the concepts of spin-component and spin-opposite scaling (SCS/SOS) of electron-pair contributions to their nonlocal correlation components. Different flavors of this idea, ranging from standard SCS parameters to fully fitted parameter sets, are presented and tested on six different parent DHDFAs. For cross-validation, we assess those methods on three benchmark sets that cover small- to medium-sized chromophores (up to 78 atoms) and different excitation types. For this purpose, we also introduce new CC3 reference values for the popular Gordon benchmark set that we recommend using in future studies. Our results confirm that already the (unscaled) parent TD-DHDFAs are accurate and outperform some wave function methods. Further introduction of SCS/SOS eliminates extreme outliers, reduces deviation spans from reference values by up to 0.5 eV, aligns the performance of the Tamm-Dancoff approximation (TDA) to that of full TD calculations, and also enables a more balanced description of different excitation types. The best-performing TD-based methods in our cross validation have mean absolute deviations as low as 0.14 eV compared to the time- and resource-intensive CC3 approach. A very important finding is that we also obtained SOS variants with excellent performance, contrary to wave function based methods. This opens a future pathway to highly efficient methods for the optimization of excited-state geometries, particularly when paired with computing strategies such as the Laplace transform. We recommend our SCS- and SOS-based variants for further testing and subsequent applications.

Dissecting the accountability of parameterized and parameter-free single-hybrid and double-hybrid functionals for photophysical properties of TADF-based OLEDs

Organic light emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) emitters are an attractive category of materials that have witnessed a booming development in recent years. In the present contribution, we scrutinize the accountability of parameterized and parameter-free single-hybrid (SH) and double-hybrid (DH) functionals through the two formalisms, full time-dependent density functional theory (TD-DFT) and Tamm-Dancoff approximation (TDA), for the estimation of photophysical properties like absorption energy, emission energy, zero-zero transition energy, and singlet-triplet energy splitting of TADF molecules. According to our detailed analyses on the performance of SHs based on TD-DFT and TDA, the TDA-based parameter-free SH functionals, PBE0 and TPSS0, with one-third of exact-like exchange turned out to be the best performers in comparison to other functionals from various rungs to reproduce the experimental data of the benchmarked set. Such affordable SH approximations can thus be employed to predict and design the TADF molecules with low singlet-triplet energy gaps for OLED applications. From another perspective, considering this point that both the nonlocal exchange and correlation are essential for a more reliable description of large charge-transfer excited states, applicability of the functionals incorporating these terms, namely, parameterized and parameter-free DHs, has also been evaluated. Perusing the role of exact-like exchange, perturbative-like correlation, solvent effects, and other related factors, we find that the parameterized functionals B2π-PLYP and B2GP-PLYP and the parameter-free models PBE-CIDH and PBE-QIDH have respectable performance with respect to others. Lastly, besides the recommendation of reliable computational protocols for the purpose, hopefully this study can pave the way toward further developments of other SHs and DHs for theoretical explorations in the field of OLEDs technology.

α-Aminoxy Oligopeptides: Synthesis, Secondary Structure, and Cytotoxicity of a New Class of Anticancer Foldamers

α-Aminoxy peptides are peptidomimetic foldamers with high proteolytic and conformational stability. To gain an improved synthetic access to α-aminoxy oligopeptides we used a straightforward combination of solution- and solid-phase-supported methods and obtained oligomers that showed a remarkable anticancer activity against a panel of cancer cell lines. We solved the first X-ray crystal structure of an α-aminoxy peptide with multiple turns around the helical axis. The crystal structure revealed a right-handed 2₈ -helical conformation with precisely two residues per turn and a helical pitch of 5.8 Å. By 2D ROESY experiments, molecular dynamics simulations, and CD spectroscopy we were able to identify the 2₈ -helix as the predominant conformation in organic solvents. In aqueous solution, the α-aminoxy peptides exist in the 2₈ -helical conformation at acidic pH, but exhibit remarkable changes in the secondary structure with increasing pH. The most cytotoxic α-aminoxy peptides have an increased propensity to take up a 2₈ -helical conformation in the presence of a model membrane. This indicates a correlation between the 2₈ -helical conformation and the membranolytic activity observed in mode of action studies, thereby providing novel insights in the folding properties and the biological activity of α-aminoxy peptides.

Nonoxido V(IV) Complexes: Prediction of the EPR Spectrum and Electronic Structure of Simple Coordination Compounds and Amavadin

Density functional theory (DFT) calculations of the (51)V hyperfine coupling (HFC) tensor A have been completed for 20 "bare" V(IV) complexes with different donor sets, electric charges, and coordination geometries. Calculations were performed with ORCA and Gaussian software, using functionals BP86, TPSS0, B1LYP, PBE0, B3LYP, B3P, B3PW, O3LYP, BHandHLYP, BHandH, and B2PLYP. Among the basis sets, 6-311g(d,p), 6-311++g(d,p), VTZ, cc-pVTZ, def2-TZVPP, and the "core properties" CP(PPP) were tested. The experimental Aiso and Ai (where i = x or z, depending on the geometry and electronic structure of V(IV) complex) were compared with the values calculated by DFT methods. The results indicated that, based on the mean absolute percentage deviation (MAPD), the best functional to predict Aiso or Ai is the double hybrid B2PLYP. With this functional and the basis set VTZ, it is possible to predict the Aiso and Az of the EPR spectrum of amavadin with deviations of -1.1% and -2.0% from the experimental values. The results allowed us to divide the spectra of nonoxido V(IV) compounds in three types-called "type 1", "type 2", and "type 3", characterized by different composition of the singly occupied molecular orbital (SOMO) and relationship between the values of Ax, Ay, and Az. For "type 1" spectra, Az ≫ Ax ≈ Ay and Az is in the range of (135-155) × 10(-4) cm(-1); for "type 2" spectra, Ax ≈ Ay ≫ Az and Ax ≈ Ay are in the range of (90-120) × 10(-4) cm(-1); and for the intermediate spectra of "type 3", Az > Ay > Ax or Ax > Ay > Az, with Az or Ax values in the range of (120-135) × 10(-4) cm(-1). The electronic structure of the V(IV) species was also discussed, and the results showed that the values of Ax or Az are correlated with the percent contribution of V-dxy orbital in the SOMO. Similarly to V(IV)O species, for amavadin the SOMO is based mainly on the V-dxy orbital, and this accounts for the large experimental value of Az (153 × 10(-4) cm(-1)).

Systematic study on the TD-DFT calculated electronic circular dichroism spectra of chiral aromatic nitro compounds: A comparison of B3LYP and CAM-B3LYP

B3LYP is one of the most widely used functional for the prediction of electronic circular dichroism spectra, however if the studied molecule contains aromatic nitro group computations may fail to produce reliable results. A test set of molecules of known stereochemistry were synthesized to study this phenomenon in detail. Spectra were computed by B3LYP and CAM-B3LYP functionals with 6-311++G(2d,2p) basis set. It was found that the range separated CAM-B3LYP gives better predictions than B3LYP for all test molecules. Fragment population analysis revealed that the nitro groups form highly localized molecule orbitals but the exact composition depends on the functional. CAM-B3LYP allows sufficient spatial overlap between the nitro group and distant parts of the molecule, which is necessary for the accurate description of excited states especially for charge transfer states. This phenomenon and the synthesized test molecules can be used to benchmark theoretical methods as well as to help the development of new functionals intended for spectroscopical studies.

Fine tuning of molecular and supramolecular properties of simple trianglimines – the role of the functional group

Readily available chiral, triangular poly-azamacrocycles can act as receptors, low molecular weight supergelators and ligands in asymmetric synthesis.

Photoisomerization action spectroscopy: flicking the protonated merocyanine–spiropyran switch in the gas phase

Molecular ions drifting through buffer gas are exposed to tunable laser light causing a detectable change in their collision cross section and arrival time at the ion detector. The effect can be exploited to obtain action electronic spectra for selected molecular isomers in the gas phase.

Miniolins A–C, novel isomeric furanones induced by epigenetic manipulation of Penicillium minioluteum

Cultivation of Penicillium minioluteum with a DNA methyltransferase inhibitor led to the isolation of a novel type of aspertetronin dimer, miniolins A–C, along with their precursor. The dimeric absolute configurations were assigned by chiral HPLC and ECD calculations.

Double helicity induction in chiral bis(triphenylacetamides)

Helicity induction in a highly flexible trityl chromophore is not only due to the presence of the neighboring stereogenic center(s).