Axial-equatorial equilibrium in substituted cyclohexanes: a DFT perspective on a small but complex problem.

In Chemistry, complexity is not necessarily associated to large systems, as illustrated by the textbook example of axial-equatorial equilibrium in mono-substituted cyclohexanes. The difficulty in modelling such a simple isomerization is related to the need for reproducing the delicate balance between two forces, with opposite effects, namely the attractive London dispersion and the repulsive steric interactions. Such balance is a stimulating challenge for density-functional approximations and it is systematically explored here by considering 20 mono-substituted cyclohexanes. In comparison to highly accurate CCSD(T) reference calculations, their axial-equatorial equilibrium is studied with a large set of 48 exchange-correlation approximations, spanning from semilocal to hybrid to more recent double hybrid functionals. This dataset, called SAV20 (as Steric A-values for 20 molecules), allows to highlight the difficulties encountered by common and more original DFT approaches, including those corrected for dispersion with empirical potentials, the 6-31G*-ACP model, and our cost-effective PBE-QIDH/DH-SVPD protocol, in modeling these challenging interactions. Interestingly, the performance of the approaches considered in this contribution on the SAV20 dataset does not correlate with that obtained with other more standard datasets, such as S66, IDISP or NC15, thus indicating that SAV20 covers physicochemical features not already considered in previous noncovalent interaction benchmarks.

SOS1-RSX-QIDH: A spin-opposite-scaled range-separated-exchange quadratic-integrand double-hybrid density functional.

We develop and validate the SOS1-RSX-QIDH density functional, a one-parameter spin-opposite-scaled variant of the range-separated-exchange quadratic-integrand double-hybrid (RSX-QIDH) model. By entering into the family of spin-biased double hybrids, this new density functional benefits from an improved computational scaling that rivals with the one of hybrids, still conserving the accuracy of its RSX-QIDH version. As part of the latter family, this density functional is well-adapted to treat molecular systems that are particularly prone to self-interaction errors in their ground and excited states. In particular, we show that the SOS1-RSX-QIDH model is a good compromise to treat ground-state problems dealing with kinetics and has a real added value when applied to the evaluation of the excited-state properties of equilibrium and out-of-equilibrium molecular complexes. Even if spin-biased double hybrids are recognized to strongly underestimate noncovalent interactions, we notice and recommend coupling SOS1-RSX-QIDH with a nonlocal van der Waals potential, a combination that is here proved to compete with the best density-functional approximations currently in use.

RPA, an Accurate and Fast Method for the Computation of Static Nonlinear Optical Properties.

The accurate computation of static nonlinear optical properties (SNLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with density-fitting techniques and integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict SNLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyperpolarizabilities. We show that the RPA based on hybrid functional self-consistent field calculations yields accurate SNLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that the RPA avoids any system-specific adjustment.

Tackling an accurate description of molecular reactivity with double-hybrid density functionals.

In this Communication, we assess a panel of 18 double-hybrid density functionals for the modeling of the thermochemical and kinetic properties of an extended dataset of 449 organic chemistry reactions belonging to the BH9 database. We show that most of DHs provide a statistically robust performance to model barrier height and reaction energies in reaching the "chemical accuracy." In particular, we show that nonempirical DHs, such as PBE0-DH and PBE-QIDH, or minimally parameterized alternatives, such as ωB2PLYP and B2K-PLYP, succeed to accurately model both properties in a balanced fashion. We demonstrate, however, that parameterized approaches, such as ωB97X-2 or DSD-like DHs, are more biased to only one of both properties.

Assessing challenging intra- and inter-molecular charge-transfer excitations energies with double-hybrid density functionals.

We investigate the performance of a set of recently introduced range-separated double-hybrid functionals, namely ωB2-PLYP, ωB2GP-PLYP, RSX-0DH, and RSX-QIDH models for hard-to-calculate excitation energies. We compare with the parent (B2-PLYP, B2GP-PLYP, PBE0-DH, and PBE-QIDH) and other (DSD-PBEP86) double-hybrid models as well as with some of the most widely employed hybrid functionals (B3LYP, PBE0, M06-2X, and ωB97X). For this purpose, we select a number of medium-sized intra- and inter-molecular charge-transfer excitations, which are known to be challenging to calculate using time-dependent density-functional theory (TD-DFT) and for which accurate reference values are available. We assess whether the high accuracy shown by the newest double-hybrid models is also confirmed for those cases too. We find that asymptotically corrected double-hybrid models yield a superior performance, especially for the inter-molecular charge-transfer excitation energies, as compared to standard double-hybrid models. Overall, the PBE-QIDH and its corresponding range-separated RSX-QIDH functional are recommended for general-purpose TD-DFT applications, depending on whether long-range effects are expected to play a significant role.

Range-separated hybrid and double-hybrid density functionals: A quest for the determination of the range-separation parameter.

We recently derived a new and simple route to the determination of the range-separation parameter in range-separated exchange hybrid and double-hybrid density functionals by imposing an additional constraint to the exchange-correlation energy to recover the total energy of the hydrogen atom [Brémond et al., J. Chem. Phys. 15, 201102 (2019)]. Here, we thoroughly assess this choice by statistically comparing the derived values of the range-separation parameters to the ones obtained using the optimal tuning (OT) approach. We show that both approaches closely agree, thus, confirming the reliability of ours. We demonstrate that it provides very close performances in the computation of properties particularly prone to the one- and many-electron self-interaction errors (i.e., ionization potentials). Our approach arises as an alternative to the OT procedure, conserving the accuracy and efficiency of a standard Kohn-Sham approach to density-functional theory computation.

sp-hybridized carbon allotrope molecular structures: An ongoing challenge for density-functional approximations.

The recent synthesis of a C18 monocyclic ring constitutes a major breakthrough as a new all-carbon disclosed form. However, modern density functional theory approaches do not lead to the correct experimental polyynic structure and favor the cumulenic one instead. We demonstrate here that this serious drawback can be solved by recently developed range-separated nonempirical schemes, independently of which kind of functional is being applied (i.e., semilocal, hybrid, or double-hybrid).

Range-separated hybrid density functionals made simple.

In this communication, we present a new and simple route to derive range-separated exchange (RSX) hybrid and double hybrid density functionals in a nonempirical fashion. In line with our previous developments [Brémond et al., J. Chem. Theory Comput. 14, 4052 (2018)], we show that by imposing an additional physical constraint to the exchange-correlation energy, i.e., by enforcing to reproduce the total energy of the hydrogen atom, we are able to generalize the nonempirical determination of the range-separation parameter to a family of RSX hybrid density functionals. The success of the resulting models is illustrated by an accurate modeling of several molecular systems and properties, like ionization potentials, particularly prone to the one- and many-electron self-interaction errors.

Charge transport parameters for carbon based nanohoops and donor-acceptor derivatives.

The effect of donor-acceptor (D-A) moieties on magnitudes such as reorganization energies and electronic couplings in cycloparaphenylene (CPP) carbon based nanohoops (i.e. conjugated organic molecules with cyclic topology) is highlighted via model computations and analysis of the available crystalline structure of N,N-dimethylaza[8]CPP. For the sake of comparison, intra-molecular and inter-molecular charge transport parameters are concomitantly modelled for the recently determined herringbone polymorph of [6]CPP, along with [8]CPP and [12]CPP. The peculiar contribution of low frequency vibrations to intramolecular reorganization energies is also disclosed by computing the Huang-Rhys factors for the investigated [n]CPPs and the N,N-dimethylaza derivative. In contrast with most planar organic semiconductors where the layer in which molecules are herringbone arranged identifies the high-mobility plane, nanohoops disclose inter-layer electronic couplings larger than the intra-layer counterparts. Charge transfer rate constants modelled with three different approaches (Marcus, Marcus-Levich-Jortner and spectral overlap) suggest that D-A nanohoops, owing to orbital localization, may be more efficient for charge transport than [n]CPPs for suitable solid phase arrangements.

Range-Separated Double-Hybrid Functional from Nonempirical Constraints.

On the basis of our previous developments in the field of nonempirical double hybrids, we present here a new exchange-correlation functional based on a range-separated model for the exchange part and integrating a nonlocal perturbative correction to the electron correlation contribution. Named RSX-QIDH, the functional is free from any kind of empirical parametrization. Its range-separation parameter is set to recover the total energy of the hydrogen atom, thus eliminating the self-interaction error for this one-electron system. Subsequent tests on some relevant benchmark data sets confirm that the self-interaction error is particularly low for RSX-QIDH. This new functional provides also correct dissociation profiles for charged rare-gas dimers and very accurate ionization potentials directly from Kohn-Sham orbital energies. Above all, these good results are not obtained at the expense of other properties. Indeed, further tests on standard benchmarks show that RSX-QIDH is competitive with the more empirical ωB97X-2 double hybrid and outperforms the parent LC-PBE long-range corrected hybrid, thus underlining the important role of the nonlocal perturbative correlation.

Speed-Up of the Excited-State Benchmarking: Double-Hybrid Density Functionals as Test Cases.

The EX6-0, EX7-0, and EX7-1 representative benchmark sets are developed for the fast evaluation of the performance of a density functional, or more generally of a computational protocol, in modeling low-lying valence singlet-singlet excitation energies of organic dyes within the range of 1.5 to 4.5 eV. All sets share the advantage of being small (a maximum of 7 molecules) but providing statistical errors representative of larger and extended databases. To that extent, the EX7-1 benchmark set goes a step further and is composed of systems as small as possible in order to alleviate the associated computational cost. The reliability of all the sets is assessed through the benchmarking of 15 modern double-hybrid density functionals. The investigation shows not only that the 3 benchmark sets provide close error metrics for each density functional but also that when taking advantage of the Resolution-of-the-Identity and a balanced triple-ζ basis set (e.g., def2-TZVP), double hybrids overperform the "popular" hybrids in modeling vertical absorption, emission, and adiabatic energies.

Determining the role of the underlying orbital-dependence of PBE0-DH and PBE-QIDH double-hybrid density functionals.

We study the orbital-dependence of three (parameter-free) double-hybrid density functionals, namely the PBE0-DH, the PBE-QIDH models, and the SOS1-PBE-QIDH spin-opposite-scaled variant of the latter. To do it, we feed all their energy terms with different sets of orbitals obtained previously from self-consistent density functional theory calculations using several exchange-correlation functionals (e.g., PBE, PBE0, PBEH&H), or directly with HF-PBE orbitals, to see their effect on selected datasets for atomization and reaction energies, the latter proned to marked self-interaction errors. We find that the PBE-QIDH double-hybrid model shows a great consistency, as the best results are always obtained for the set of orbitals corresponding to its hybrid scheme, which prompts us to recommend this model without any other fitting or reparameterization. © 2017 Wiley Periodicals, Inc.

Benchmarking Density Functionals on Structural Parameters of Small-/Medium-Sized Organic Molecules.

In this Letter we report the error analysis of 59 exchange-correlation functionals in evaluating the structural parameters of small- and medium-sized organic molecules. From this analysis, recently developed double hybrids, such as xDH-PBE0, emerge as the most reliable methods, while global hybrids confirm their robustness in reproducing molecular structures. Notably the M06-L density functional is the only semilocal method reaching an accuracy comparable to hybrids'. A comparison with errors obtained on energetic databases (including thermochemistry, reaction barriers, and interaction energies) indicate that most of the functionals have a coherent behavior, showing low (or high) deviations on both energy and structure data sets. Only a few of them are more prone toward one of these two properties.

Intra- and intermolecular dispersion interactions in [N]cycloparaphenylenes: do they influence their structural and electronic properties?

Cycloparaphenylenes (CPPs) are nanosized structures with unique isolated and bulk properties, and are synthetic targets for the template-driven bottom-up synthesis of carbon nanotubes. Thus, a systematic understanding of the supramolecular order at the nanoscale is of utmost relevance for molecular engineering. In this study, it is found that intramolecular noncovalent (dispersion) interactions must be taken into account for obtaining accurate estimates of the structural and optoelectronic properties of [n]CPP compounds, and their influence as the number of repeat units increases from n=4 to n=12 is also analyzed, both in the gas phase and in solution. The supramolecular self-assembly, for which both intra- and intermolecular noncovalent interactions are relevant, of [6]CPP is also investigated by calculating the binding energies of dimers taken along several crystal directions. These are also used to estimate the cohesive energy of the crystal, which is compared to the value obtained by means of dispersion-corrected DFT calculations using periodic boundary conditions. The reasonable agreement between both computational strategies points towards a first estimate of the [6]CPP cohesive energy of around 50 kcal mol(-1) .

Systematic Improvement of Density Functionals through Parameter-Free Hybridization Schemes.

It is suggested here that the ultimate accuracy of DFT methods arises from the type of hybridization scheme followed. This idea can be cast into a mathematical formulation utilizing an integrand connecting the noninteracting and the interacting particle system. We consider two previously developed models for it, dubbed as HYB0 and QIDH, and assess a large number of exchange-correlation functionals against the AE6, G2/148, and S22 reference data sets. An interesting consequence of these hybridization schemes is that the error bars, including the standard deviation, are found to markedly decrease with respect to the density-based (nonhybrid) case. This improvement is substantially better than variations due to the underlying density functional used. We thus finally hypothesize about the universal character of the HYB0 and QIDH models.

Communication: double-hybrid functionals from adiabatic-connection: the QIDH model.

A new approach stemming from the adiabatic-connection (AC) formalism is proposed to derive parameter-free double-hybrid (DH) exchange-correlation functionals. It is based on a quadratic form that models the integrand of the coupling parameter, whose components are chosen to satisfy several well-known limiting conditions. Its integration leads to DHs containing a single parameter controlling the amount of exact exchange, which is determined by requiring it to depend on the weight of the MP2 correlation contribution. Two new parameter-free DHs functionals are derived in this way, by incorporating the non-empirical PBE and TPSS functionals in the underlying expression. Their extensive testing using the GMTKN30 benchmark indicates that they are in competition with state-of-the-art DHs, yet providing much better self-interaction errors and opening a new avenue towards the design of accurate double-hybrid exchange-correlation functionals departing from the AC integrand.