Modeling Multi-Step Organic Reactions: Can Density Functional Theory Deliver Misleading Chemistry?

Many organic reactions are characterized by a complex mechanism with a variety of transition states and intermediates of different chemical natures. Their correct and accurate theoretical characterization critically depends on the accuracy of the computational method used. In this work, we study a complex ambimodal cycloaddition with five transition states, two intermediates, and three products, and we ask whether density functional theory (DFT) can provide a correct description of this type of complex and multifaceted reaction. Our work fills a gap in that most systematic benchmarks of DFT for chemical reactions have considered much simpler reactions. Our results show that many density functionals not only lead to seriously large errors but also differ from one another in predicting whether the reaction is ambimodal. Only a few of the available functionals provide a balanced description of the complex and multifaceted reactions. The parameters varied in the tested functionals are the ingredients, the treatment of medium-range and nonlocal correlation energy, and the inclusion of Hartree-Fock exchange. These results show a clear need for more benchmarks on the mechanisms of large molecules in complex reactions.

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.

Comparing Density Functional Theory Metal-Ligand Bond Dissociation Enthalpies with Experimental Solution-Phase Enthalpies of Activation for Bond Dissociation.

The predictive ability of density functional theory is fundamental to its usefulness in chemical applications. Recent work has compared solution-phase enthalpies of activation for metal-ligand bond dissociation to enthalpies of reaction for bond dissociation, and the present work continues those comparisons for 43 density functional methods. The results for ligand dissociation enthalpies of 30 metal-ligand complexes tested in this work reveal significant inadequacies of some functionals as well as challenges from the dispersion corrections to some functionals. The analysis presented here demonstrates the excellent performance of a recent density functional, M11plus, which contains nonlocal rung-3.5 correlation. We also find a good agreement between theory and experiment for some functionals without empirical dispersion corrections such as M06, r2SCAN, M06-L, and revM11, as well as good performance for some functionals with added dispersion corrections such as ωB97X-D (which always has a correction) and BLYP, B3LYP, CAM-B3LYP, and PBE0 when the optional dispersion corrections are added.

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.

Double hybrids and time-dependent density functional theory: An implementation and benchmark on charge transfer excited states.

In this paper we present the implementation and benchmarking of a Time Dependent Density Functional Theory approach in conjunction with Double Hybrid (DH) functionals. We focused on the analysis of their performance for through space charge-transfer (CT) excitations which are well known to be very problematic for commonly used functionals, such as global hybrids.Two different families of functionals were compared, each of them containing pure, hybrid and double-hybrid functionals.The results obtained show that, beside the robustness of the implementation, these functionals provide results with an accuracy comparable to that of adjusted range-separated functionals, with the relevant difference that for DHs no parameter is tuned on specific compounds thus making them more appealing for a general use. Furthermore, the algorithm described and implemented is characterized by the same computational cost scaling as that of the ground state algorithm employed for MP2 and double hybrids.

Calculation of magnetic properties with density functional approximations including rung 3.5 ingredients.

Density functional theory is widely used for modeling the magnetic properties of molecules, solids, and surfaces. Rung-3.5 ingredients, based on the expectation values of nonlocal one-electron operators, are new promising tools for the construction of exchange-correlation functional approximations. We present the formal extension of rung-3.5 ingredients to the calculation of magnetic properties. We add to the underlying nonlocal operators a dependence on the gauge of the magnetic field, and we derive the working equations for rung-3.5 expectation values in basis sets of gauge-including atomic orbitals. We demonstrate that the gauge corrections are significant. We conclude with an initial study of chemical shifts, optical rotatory dispersion, and Raman optical activity spectra predicted by M11plus, a range-separated hybrid meta functional incorporating nonlocal rung-3.5 correlation. M11plus proves to be reasonably accurate, further motivating the incorporation of nonlocal rung-3.5 ingredients in new density functional approximations.

How are the charge transfer descriptors affected by the quality of the underpinning electronic density?

With the aim of investigating qualitatively and quantitatively the impact of using excited state relaxed or unrelaxed density for the estimation of nature and characteristic of electronic excited states, we analyzed the behavior of 52 exchange correlation functionals for the prediction of density-based indexes such as those recently introduced in literature to evaluate the charge transfer distance (DCT ) (Le Bahers et al. J. Chem. Theory Comput. 2011, 7, 2498) in the case of a prototype family of push-pull dyes. Our results show that while a qualitatively consistent assessment of the nature of the excited states is obtained using either the unrelaxed or the relaxed density, from a quantitative standpoint we observe large discrepancies in the charge transfer distance for electronic transitions having substantial CT character. This behavior is independent of nature of the exchange-correlation functional used. © 2018 Wiley Periodicals, Inc.

Long-range-corrected Rung 3.5 density functional approximations.

Rung 3.5 functionals are a new class of approximations for density functional theory. They provide a flexible intermediate between exact (Hartree-Fock, HF) exchange and semilocal approximations for exchange. Existing Rung 3.5 functionals inherit semilocal functionals' limitations in atomic cores and density tails. Here we address those limitations using range-separated admixture of HF exchange. We present three new functionals. LRC-ωΠLDA combines long-range HF exchange with short-range Rung 3.5 ΠLDA exchange. SLC-ΠLDA combines short- and long-range HF exchange with middle-range ΠLDA exchange. LRC-ωΠLDA-AC incorporates a combination of HF, semilocal, and Rung 3.5 exchange in the short range, based on an adiabatic connection. We test these in a new Rung 3.5 implementation including up to analytic fourth derivatives. LRC-ωΠLDA and SLC-ΠLDA improve atomization energies and reaction barriers by a factor of 8 compared to the full-range ΠLDA. LRC-ωΠLDA-AC brings further improvement approaching the accuracy of standard long-range corrected schemes LC-ωPBE and SLC-PBE. The new functionals yield highest occupied orbital energies closer to experimental ionization potentials and describe correctly the weak charge-transfer complex of ethylene and dichlorine and the hole-spin distribution created by an Al defect in quartz. This study provides a framework for more flexible range-separated Rung 3.5 approximations.

Charge transfer excitations in TDDFT: A ghost-hunter index.

This work presents a new index, MAC , enabling the on-the-fly detection of ghost charge transfer (CT) states, a major problem in time-dependent density-functional theory calculations. This computationally inexpensive index, derived as a modification of the Mulliken estimation of transition energy for CT excitations, relies on two basic ingredients: an effective CT distance, computed using our density-based index (DCT ), and an orbital weighted estimation of the Ionization Potential and Electron Affinity. Some model systems, representative of both intermolecular and intramolecular CT excitations, were chosen as test cases. The robustness of our approach was verified by analyzing the behavior of functionals belonging to different classes (GGA, global hybrids and range separated hybrids). The results obtained show that ghost states are correctly spotted, also in the delicate case of intramolecular excitations displaying substantial donor-bridge-acceptor delocalization, in a regime for which the standard Mulliken formulation attends its limits. © 2017 Wiley Periodicals, Inc.

Investigating the optical properties of BOIMPY dyes using ab initio tools.

Using a computational approach combining Time-Dependent Density Functional Theory (TD-DFT) and second-order Coupled Cluster (CC2) approaches, we investigate the spectral properties of a large panel of BOIMPY dyes. BOIMPY derivatives constitute a new class of fluorophores that appeared only very recently [Angew. Chem. Int. Ed., 2016, 55, 13340-13344] and display intriguing properties. First, we show that theory is able to reproduce experimental 0-0 energies with reasonable accuracy, and more importantly excellent consistency (R = 0.99). Next, by analyzing the nature of the excited-states, we show that the first electronic transition does not imply a significant charge-transfer character and significantly differs from the one of the parent BODIPYs. Third, we unravel the vibrational modes responsible for the specific band shapes of the BOIMPY derivatives. Finally, using theory to design new compounds, we propose substitution patterns leading to redshifted absorption spectra, up to ca. 1000 nm.

Excited state gradients for a state-specific continuum solvation approach: The vertical excitation model within a Lagrangian TDDFT formulation.

The accurate modeling of the environment response is a fundamental challenge for accurately describing the photophysics and photochemistry of molecules both in solution and in more complex embeddings. When large rearrangements of the electron density occur after an electronic transition, state-specific formulations, such as the vertical excitation model, are necessary to achieve a proper modeling of the processes. Such a state-specific model is fundamental not only to obtain accurate energies, but also to follow the geometrical relaxation accompanying the evolution of the excited-states. This study presents the analytical expression of the gradients of the vertical excitation model approach by a Lagrangian formulation in the time dependent density functional theory framework. Representative organic chromophores in solution are used to test the reliability of the implementation and provide comparisons with the linear response description.

Quantifying solvated electrons' delocalization.

Delocalized, solvated electrons are a topic of much recent interest. We apply the electron delocalization range EDR(r;u) (J. Chem. Phys., 2014, 141, 144104) to quantify the extent to which a solvated electron at point r in a calculated wavefunction delocalizes over distance u. Calculations on electrons in one-dimensional model cavities illustrate fundamental properties of the EDR. Mean-field calculations on hydrated electrons (H2O)n(-) show that the density-matrix-based EDR reproduces existing molecular-orbital-based measures of delocalization. Correlated calculations on hydrated electrons and electrons in lithium-ammonia clusters illustrates how electron correlation tends to move surface- and cavity-bound electrons onto the cluster or cavity surface. Applications to multiple solvated electrons in lithium-ammonia clusters provide a novel perspective on the interplay of delocalization and strong correlation central to lithium-ammonia solutions' concentration-dependent insulator-to-metal transition. The results motivate continued application of the EDR to simulations of delocalized electrons.

Structure and Stereochemical Determination of Hypogeamicins from a Cave-Derived Actinomycete.

Culture extracts from the cave-derived actinomycete Nonomuraea specus were investigated, resulting in the discovery of a new S-bridged pyronaphthoquinone dimer and its monomeric progenitors designated hypogeamicins A-D (1-4). The structures were elucidated using NMR spectroscopy, and the relative stereochemistries of the pyrans were inferred using NOE and comparison to previously reported compounds. Absolute stereochemistry was determined using quantum chemical calculations of specific rotation and vibrational and electronic circular dichroism spectra, after an extensive conformational search and including solute-solvent polarization effects, and comparing with the corresponding experimental data for the monomeric congeners. Interestingly, the dimeric hypogeamicin A (1) was found to be cytotoxic to the colon cancer derived cell line TCT-1 at low micromolar ranges, but not bacteria, whereas the monomeric precursors possessed antibiotic activity but no significant TCT-1 cytotoxicity.

How far do electrons delocalize?

Electron delocalization is central to chemical bonding, but it is also a fundamentally nonclassical and nonintuitive quantum mechanical phenomenon. Tools to quantify and visualize electron delocalization help to understand, teach, and predict chemical reactivity. We develop a new approach to quantify and visualize electron delocalization in real space. Our electron delocalization range function EDR (r⃗;u) quantifies the degree to which electrons at point r⃗ in a calculated wavefunction delocalize over length scale u. Its predictions are physically reasonable. For example, EDR (r⃗;u=0.25 bohr ) is close to one at points r⃗ in the cores of first-row atoms, consistent with the localization of core electrons to ~0.25 bohr. EDR (r⃗;u=1 bohr ) is close to one at points r⃗ in typical covalent bonds, consistent with electrons delocalizing over the length of the bond. Our approach provides a rich representation of atomic shell structure; covalent and ionic bonding; the delocalization of excited states, defects, and solvated electrons; metallic and insulating systems; and bond stretching and strong correlation.

Practical auxiliary basis implementation of Rung 3.5 functionals.

Approximate exchange-correlation functionals for Kohn-Sham density functional theory often benefit from incorporating exact exchange. Exact exchange is constructed from the noninteracting reference system's nonlocal one-particle density matrix γ(r(->), r(->)'). Rung 3.5 functionals attempt to balance the strengths and limitations of exact exchange using a new ingredient, a projection of γ(r(->), r(->)') onto a semilocal model density matrix γ(SL)(ρ(r(->)), ∇ρ(r(->)), r(->) - r(->)'). γSL depends on the electron density ρ(r(->) at reference point r(->), and is closely related to semilocal model exchange holes. We present a practical implementation of Rung 3.5 functionals, expanding the r(->) - r(->)' dependence of γSL in an auxiliary basis set. Energies and energy derivatives are obtained from 3D numerical integration as in standard semilocal functionals. We also present numerical tests of a range of properties, including molecular thermochemistry and kinetics, geometries and vibrational frequencies, and bandgaps and excitation energies. Rung 3.5 functionals typically provide accuracy intermediate between semilocal and hybrid approximations. Nonlocal potential contributions from γSL yield interesting successes and failures for band structures and excitation energies. The results enable and motivate continued exploration of Rung 3.5 functional forms.

Quantum, classical, and hybrid QM/MM calculations in solution: general implementation of the ddCOSMO linear scaling strategy.

We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.

M11pz: A Nonlocal Meta Functional with Zero Hartree-Fock Exchange and with Broad Accuracy for Chemical Energies and Structures.

The accuracy of Kohn-Sham density functional theory depends strongly on the approximation to the exchange-correlation functional. In this work, we present a new exchange-correlation functional called M11pz (M11 plus rung-3.5 terms with zero Hartree-Fock exchange) that is built on the M11plus functional with the goal of using its rung-3.5 terms without a Hartree-Fock exchange term, especially to improve the accuracy for strongly correlated systems. The M11pz functional is optimized with the same local and rung-3.5 ingredients that are used in M11plus but without any percentage of Hartree-Fock exchange. The performance of M11pz is compared with eight local functionals, and M11pz is found to be in top three when the errors or ranks are averaged over eight grouped and partially overlapping databases: AME418/22, atomic and molecular energies; MGBE172, main-group bond energies; TMBE40, transition-metal bond energies; SR309, single-reference systems; MR54, multireference systems; BH192, barrier heights; NC579, noncovalent interaction energies; and MS20, molecular structures. For calculations of band gaps of solids, M11pz is the second best of the nine tested functionals that have zero Hartree-Fock exchange.

Barrier Heights for Diels-Alder Transition States Leading to Pentacyclic Adducts: A Benchmark Study of Crowded, Strained Transition States of Large Molecules.

Theoretical characterization of reactions of complex molecules depends on providing consistent accuracy for the relative energies of intermediates and transition states. Here we employ the DLPNO-CCSD(T) method with core-valence correlation, large basis sets, and extrapolation to the CBS limit to provide benchmark values for Diels-Alder transition states leading to competitive strained pentacyclic adducts. We then used those benchmarks to test a diverse set of wave function and density functional methods for the absolute and relative barrier heights of these transition states. Our results show that only a few of the tested density functionals can predict the absolute barrier heights satisfactorily, although relative barrier heights are more accurate. The most accurate functionals tested are ωB97M-V, M11plus, ωB97X-V, PBE-D3(0), M11, and MN15 with MUDs from best estimates less than 3.0 kcal. These findings can guide selection of density functionals for future studies of crowded, strained transition states of large molecules.

Molecular Dynamics Simulations Enforcing Nonperiodic Boundary Conditions: New Developments and Application to the Solvent Shifts of Nitroxide Magnetic Parameters.

Multiscale methods combining quantum mechanics and molecular mechanics (QM/MM) have become the most suitable and effective strategies for the investigation of the spectroscopic properties of medium-to-large size chromophores in condensed phases. In this context, we are developing a novel workflow aimed at improving the generality, reliability, and ease of use of the available computational tools. In this paper, we report our latest developments with specific reference to a general protocol based on atomistic simulations, carried out under nonperiodic boundary conditions (NPBC). In particular, we add to our in house MD engine a new efficient treatment of mean field electrostatic contributions to energy and forces, together with the capability of performing the simulations either in the canonical (NVT) or in the isothermal-isobaric (NPT) ensemble. Next, we provide convincing evidence that the NBPC approach enhanced by specific tweaks for rigid body propagation, allows for the simulation of solute-solvent systems with a minimum number of degrees of freedom and large integration time step. After its validation, this new approach is applied to the challenging case of solvatochromic effects on the electron paramagnetic resonance (EPR) spectrum of a prototypical nitroxide radical. To this end, we propose and validate also an automated protocol to extract and weight simulation snapshots, making use of a continuous description of the strength of solute-solvent hydrogen bridges. While further developments are being worked on, the effectiveness of our approach, even in its present form, is demonstrated by the accuracy of the results obtained through an unsupervised approach characterized by a strongly reduced computational cost as compared to that of conventional QM/MM models, without any appreciable deterioration of accuracy.

Exact-Two-Component Multiconfiguration Pair-Density Functional Theory.

Molecules containing late-row elements exhibit large relativistic effects. To account for both relativistic effects and electron correlation in a computationally inexpensive way, we derived a formulation of multiconfiguration pair-density functional theory with the relativistic exact-two-component Hamiltonian (X2C-MC-PDFT). In this new method, relativistic effects are included during variational optimization of a reference wave function by exact-two-component complete active-space self-consistent-field (X2C-CASSCF) theory, followed by an energy evaluation using pair-density functional theory. Benchmark studies of excited-state and ground-state fine-structure splitting of atomic species show that X2C-MC-PDFT can significantly improve the X2C-CASSCF results by introducing additional state-specific electron correlation.