John S. Sears

Long-range corrected hybrid functionals for π-conjugated systems: Dependence of the range-separation parameter on conjugation length

Long-range corrected (range-separated hybrid) functionals represent a relatively new class of functionals for generalized Kohn-Sham theory that have proven to be very successful, for instance, when it comes to predicting ionization potentials and energy gaps for a wide range of molecules and solids. The results obtained from long-range corrected density functional theory approaches can be improved dramatically, if the range-separation parameter (ω) is optimized for each system separately. In this work, we have optimized ω for a series of π-conjugated molecular systems of increasing length by forcing the resulting functionals to obey the ionization potential-theorem, i.e., that their highest occupied eigenvalue be equal to the ΔSCF ionization potential. The optimized ω values are observed to vary substantially from their default values for the functionals. For highly conjugated chains such as oligoacenes and polyenes, we find that the characteristic length scale of the range-separation, i.e., 1/ω, grows almost linearly with the number of repeat units, for saturated alkane chains, however, 1/ω quickly saturates after 5-6 repeat units. For oligothiophenes, we find that 1/ω grows linearly for the shorter oligomers but then saturates at around 10 repeat units. Our results point to a close relation between the optimal range-separation parameter and the degree of conjugation in the system.

Effects of electronegative substitution on the optical and electronic properties of acenes and diazaacenes

Large acenes, particularly pentacenes, are important in organic electronics applications such as thin-film transistors. Derivatives where CH units are substituted by sp(2) nitrogen atoms are rare but of potential interest as charge-transport materials. In this article, we show that pyrazine units embedded in tetracenes and pentacenes allow for additional electronegative substituents to induce unexpected redshifts in the optical transitions of diazaacenes. The presence of the pyrazine group is critical for this effect. The decrease in transition energy in the halogenated diazaacenes is due to a disproportionate lack of stabilization of the HOMO on halogen substitution. The effect results from the unsymmetrical distribution of the HOMO, which shows decreased orbital coefficients on the ring bearing chlorine substituents. The more strongly electron-accepting cyano group is predicted to shift the transitions of diazaacenes even further to the red. Electronegative substitution impacts the electronic properties of diazaacenes to a much greater degree than expected.

A spin-complete version of the spin-flip approach to bond breaking: What is the impact of obtaining spin eigenfunctions?

Spin-complete versions of the spin-flip configuration-interaction-singles (SF-CIS) approach have been investigated to determine the impact of making the wave function an eigenfunction of Ŝ2. The method has been implemented within an extended restricted active space configuration interaction formalism. Spin-complete results are presented for excitation energies, equilibrium geometries, and potential energy curves for dissociation of a single bond in several small molecules. The effect of different orbital choices has also been investigated. The spin-complete results are compared both to results using the original spin-flip method and to more computationally expensive benchmarks. Using spin eigenfunctions dramatically improves upon the accuracy of the SF-CIS approach.

Evaluating the Performance of DFT Functionals in Assessing the Interaction Energy and Ground-State Charge Transfer of Donor/Acceptor Complexes: Tetrathiafulvalene−Tetracyanoquinodimethane (TTF−TCNQ) as a Model Case

We have evaluated the performance of several density functional theory (DFT) functionals for the description of the ground-state electronic structure and charge transfer in donor/acceptor complexes. The tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) complex has been considered as a model test case. Hybrid functionals have been chosen together with recently proposed long-range corrected functionals (ωB97X, ωB97X-D, LRC-ωPBEh, and LC-ωPBE) in order to assess the sensitivity of the results to the treatment and magnitude of exact exchange. The results show an approximately linear dependence of the ground-state charge transfer with the HOMOTTF-LUMOTCNQ energy gap, which in turn depends linearly on the percentage of exact exchange in the functional. The reliability of ground-state charge transfer values calculated in the framework of a monodeterminantal DFT approach was also examined.

On the relationship between bond-length alternation and many-electron self-interaction error

Predicting accurate bond-length alternations (BLAs) in long conjugated molecular chains has been a major challenge for electronic-structure theory for many decades. While Hartree-Fock (HF) overestimates BLA significantly, second-order perturbation theory and commonly used density functional theory (DFT) approaches typically underestimate it. Here, we discuss how this failure is related to the many-electron self-interaction error (MSIE), which is inherent to both HF and DFT approaches. We use tuned long-range corrected hybrids to minimize the MSIE for a series of polyenes. The key result is that the minimization of the MSIE alone does not yield accurate BLAs. On the other hand, if the range-separation parameter is tuned to yield accurate BLAs, we obtain a significant MSIE that grows with chain length. Our findings demonstrate that reducing the MSIE is one but not the only important aspect necessary to obtain accurate BLAs from density functional theory.

Communication: Orbital instabilities and triplet states from time-dependent density functional theory and long-range corrected functionals

Long-range corrected hybrids represent an increasingly popular class of functionals for density functional theory (DFT) that have proven to be very successful for a wide range of chemical applications. In this Communication, we examine the performance of these functionals for time-dependent (TD)DFT descriptions of triplet excited states. Our results reveal that the triplet energies are particularly sensitive to the range-separation parameter; this sensitivity can be traced back to triplet instabilities in the ground state coming from the large effective amounts of Hartree-Fock exchange included in these functionals. As such, the use of standard long-range corrected functionals for the description of triplet states at the TDDFT level is not recommended.

Lowest excited states and optical absorption spectra of donor-acceptor copolymers for organic photovoltaics: a new picture emerging from tuned long-range corrected density functionals.

Polymers with low optical gaps are of importance to the organic photovoltaics community due to their potential for harnessing a large portion of the solar energy spectrum. The combination along their backbones of electron-rich and electron-deficient fragments contributes to the presence of low-lying excited states that are expected to display significant charge-transfer character. While conventional hybrid functionals are known to provide unsatisfactory results for charge-transfer excitations at the time-dependent DFT level, long-range corrected (LRC) functionals have been reported to give improved descriptions in a number of systems. Here, we use such LRC functionals, considering both tuned and default range-separation parameters, to characterize the absorption spectra of low-optical-gap systems of interest. Our results indicate that tuned LRC functionals lead to simulated optical-absorption properties in good agreement with experimental data. Importantly, the lowest-lying excited states (excitons) are shown to present a much more localized nature than initially anticipated.

Understanding the Density Functional Dependence of DFT-Calculated Electronic Couplings in Organic Semiconductors.

We present an analysis of the magnitude of density functional theory (DFT)-calculated intermolecular electronic couplings (transfer integrals) in organic semiconductors to give insight into the impact that the choice of functional has on the value of this parameter, which is particularly important in the context of charge transport. The major factor determining the magnitude of the calculated transfer integrals is the amount of nonlocal Hartree-Fock (HF) exchange within a given functional, with the transfer integrals increasing by up to a factor of 2 when going from 0 to 100% HF exchange for a series of conventional functionals. We underline that these variations in the transfer integrals are in fact to be expected, with the computed transfer integrals evolving linearly with the amount of HF exchange. We also use a long-range corrected functional to tune the contributions of (semi)local and nonlocal HF exchanges and highlight their respective roles as a function of intermolecular separation.

Theoretical Study of the Local and Charge-Transfer Excitations in Model Complexes of Pentacene-C60 Using Tuned Range-Separated Hybrid Functionals

The characteristics of the electronic excited states and the charge-transfer processes at organic-organic interfaces play an important role in organic electronic devices. However, charge-transfer excitations have proven challenging to describe with conventional density functional theory (DFT) methodologies due to the local nature of the exchange-correlation potentials often employed. Here, we examine the excited states of model pentacene-C60 complexes using time-dependent DFT with, on one hand, one of the most popular standard hybrid functionals (B3LYP) and, on the other hand, several long-range corrected hybrid functionals for which we consider both default and nonempirically tuned range-separation parameters. The DFT results based on the tuned functionals are found to agree well with the available experimental data. The results also underline that the interface geometry of the complex has a strong effect on the energies and ordering of the singlet and triplet charge-transfer states.

Assessing the Performance of Density Functional Theory for the Electronic Structure of Metal-Salens: The M06 Suite of Functionals and the d4-Metals

We have systematically investigated the electronic structure of the d⁴ metal-salen complexes including the Cr(II)-, Mn(III)-, Fe(IV)-, Mo(II)-, Tc(III)-, and Ru(IV)-salen complexes. Density functional theory (DFT) has been employed, using the BP86 and B3LYP functionals, and the entire M05 and M06 suites of meta-generalized gradient functionals. These results are compared to robust complete active-space self-consistent field (CASSCF) optimized geometries and complete active-space third-order perturbation theory (CASPT3) energies for the lowest singlet, triplet, and quintet states. Although the M06 and M06-L DFT functionals have been generally recommended for computations on complexes that contain main group and transition metals, none of the M0-functionals appear statistically better than the B3LYP functional for the computation of spin-state energy gaps. DFT- and CASSCF-optimized geometries normally agree to within 0.3 Å least root mean squared deviation (LRMSD) for the singlet and triplet structures and less than 0.1 Å LRMSD for the quintet structures. It can be concluded that no DFT functional tested here can be considered reliable over all metal-salen complexes and it is highly recommended that the accuracy of any given DFT functional should be assessed on a case-by-case basis.