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.

Comparison of Variational and Perturbative Spin-Orbit Coupling within Two-Component CASSCF.

The modeling of spin-orbit coupling (SOC) remains a challenge in computational chemistry due to the high computational cost. With the rising popularity of spin-driven processes and f-block metals in chemistry and materials science, it is incumbent on the community to develop accurate multiconfigurational SOC methods that scale to large systems and understand the limits of different treatments of SOC. Herein, we introduce an implementation of perturbative SOC in scalar-relativistic two-component CASSCF (srX2C-CASSCF-SO). Perspectives on the limitations and accuracy of srX2C-CASSCF-SO are presented via benchmark calculations.

Multiple-time scale integration method based on an interpolated potential energy surface for ab initio path integral molecular dynamics.

A new multiple-time scale integration method is presented that propagates ab initio path integral molecular dynamics (PIMD). This method uses a large time step to generate an approximate geometrical configuration whose energy and gradient are evaluated at the level of an ab initio method, and then, a more precise integration scheme, e.g., the Bulirsch-Stoer method or velocity Verlet integration with a smaller time step, is used to integrate from the previous step using the computationally efficient interpolated potential energy surface constructed from two consecutive points. This method makes the integration of PIMD more efficient and accurate compared with the velocity Verlet integration. A Nosé-Hoover chain thermostat combined with this new multiple-time scale method has good energy conservation even with a large time step, which is usually challenging in velocity Verlet integration for PIMD due to the very small chain mass when a large number of beads are used. The new method is used to calculate infrared spectra and free energy profiles to demonstrate its accuracy and capabilities.

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.

Improved Geometries and Frequencies with the PFD-3B DFT Method.

Bond lengths have been calculated for a test set of 120 diatomic species, including all homonuclear diatomics, hydrides, fluorides, and oxides for elements H through Kr for which experimental data is available for comparison. The performance of the PFD-3B functional is significantly better than competitive DFT methods. The rms error in bond lengths is reduced to 0.01 Å using a moderate size 3Za1Pa + f triple-ζ basis set, with the rms error in harmonic vibrational constants, ωe, equal to 38 cm-1. A very small 2ZP0H basis set is sufficient to calculate anharmonic constants, ωeXe, within ±4 cm-1. The rotational constants, Be, agree with experiment to within ±2%, and the vibration-rotation coupling constants, αe, agree within 10%. The calculated vibrational zero-point energy, ZPE, agrees with experiment to within ±0.06 kcal mol-1 for the diatomic test set, and the error increases to just ±0.11 kcal mol-1 for a set of 12 small polyatomic species. Comparison of a detailed anharmonic analysis of the twisted ethylene cation to the PFI-ZEKE experimental data illustrates the reliability of the PFD-3B for atypical structures.

Simultaneous Optimization of Nuclear-Electronic Orbitals.

Accurate modeling of important nuclear quantum effects, such as nuclear delocalization, zero-point energy, and tunneling, as well as non-Born-Oppenheimer effects, requires treatment of both nuclei and electrons quantum mechanically. The nuclear-electronic orbital (NEO) method provides an elegant framework to treat specified nuclei, typically protons, on the same level as the electrons. In conventional electronic structure theory, finding a converged ground state can be a computationally demanding task; converging NEO wavefunctions, due to their coupled electronic and nuclear nature, is even more demanding. Herein, we present an efficient simultaneous optimization method that uses the direct inversion in the iterative subspace method to simultaneously converge wavefunctions for both the electrons and quantum nuclei. Benchmark studies show that the simultaneous optimization method can significantly reduce the computational cost compared to the conventional stepwise method for optimizing NEO wavefunctions for multicomponent systems.

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.

Re-integration with anchor points algorithm for ab initio molecular dynamics.

A new integration scheme for ab initio molecular dynamics (MD) is proposed in this work for efficient propagation using large time steps (e.g., 2.0 fs or a larger time step with one ab initio evaluation of gradients for the dynamics point and one additional evaluation for the anchor point per dynamics step). This algorithm is called re-integration with anchor points (REAP) integrator. The REAP integrator starts from a quadratic potential energy surface based on the updated Hessian to propagate the system to the halfway of the MD step that is called the anchor point. Then, an approximate dynamics position for this step is obtained by the propagation based on an interpolated surface using the anchor point and the previous MD point. The approximate dynamics step can be further improved by the re-integration steps, i.e., integration based on the interpolated surface using the calculated energies, gradients, and updated Hessians of the previous step, the anchor point, and the approximate current step. A trajectory only needs one analytical Hessian calculation at the initial geometry, and thereafter, only calculations of gradients are required. This integrator can be considered either as a generalization of Hessian-based predictor-corrector integration with substantial improvement of accuracy and efficiency or as a dynamics on interpolated surfaces that are built on the fly. An automatic correction scheme is implemented by comparing the interpolated energies and gradients to the actual ones to ensure the quality of the interpolations at a certain level. The tests in this work show that the REAP method can increase computational efficiency by more than one order of magnitude than that of the velocity Verlet integrator and more than twice that of Hessian-based predictor-corrector integration.

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.

Three-Body Dispersion Corrections to the Spherical Atom Model: The PFD-3B Density Functional.

The performance of the isotropic spherical atom model can be significantly enhanced through combination with anisotropic three-body dispersion interactions to give the new PFD-3B density functional, which reduces the mean absolute deviation (MAD) relative to CCSD(T)/CBS benchmark energies from 0.78 to 0.19 kcal/mol for the S22 test set. Comparison with the extended S22 × 5 test set in the figure indicates that this accuracy is maintained through large variations in geometry. The performance of the PFD-3B functional over the S22 × 5 test set is superior to any of the functionals previously applied to this set. Over the S22 set of examples, the MADs from the CCSD(T)/CBS values for Re, De, and ωe, are 0.032 Å, 0.21 kcal/mol, and 6 cm-1, respectively. Over a comparable set of 26 examples containing second and third row atoms, the MADs from the CCSD(T)/CBS values for Re, De, and ωe, are 0.033 Å, 0.19 kcal/mol, and 5 cm-1, respectively. If used to optimize the geometry of the 48 examples, on average the PFD-3B functional introduces an error of only 0.042 kcal/mol in CCSD(T) single-point energies. This small error combines with the reported analytical first and second derivatives to makes the PFD-3B functional an attractive model for geometry optimization and zero-point energy calculations.

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.

Implementation, feasibility, and acceptability of quality of life therapy to improve positive emotions among patients with implantable cardioverter defibrillators.

Implantable cardioverter defibrillators (ICDs) save lives, but often induce significant psychological distress among patients. Positive psychological constructs are associated with improved outcomes among cardiac patients. In this NHLBI-funded randomized controlled trial, one aim was to evaluate the feasibility and acceptability of a positive psychology intervention (Quality of Life Therapy; QOLT, n = 11), compared to a Heart Healthy Education (HHE) control (n = 10), among ICD patients. A majority of participants across groups attended all 12 sessions (71%) and completed homework assignments (80%). Agreement on participant engagement and interventionist protocol adherence were high, with no differences between groups (ps > 0.20). A greater proportion of QOLT participants rated their sessions was "very" helpful compared to HHE participants (63% vs. 10%, p = 0.19). These initial data support the feasibility and acceptability of QOLT. A larger-scale trial using positive psychology interventions among ICD patients is indicated to determine potential mechanisms underlying the relationship between positive psychological constructs and cardiovascular health.

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.

The Female Genital Tract Microbiome Is Associated With Vaginal Antiretroviral Drug Concentrations in Human Immunodeficiency Virus-Infected Women on Antiretroviral Therapy.

Background: The female genital tract (FGT) microbiome may affect vaginal pH and other factors that influence drug movement into the vagina. We examined the relationship between the microbiome and antiretroviral concentrations in the FGT. Methods: Over one menstrual cycle, 20 human immunodeficiency virus (HIV)-infected women virologically suppressed on tenofovir (TFV) disoproxil fumarate/emtricitabine and ritonavir-boosted atazanavir (ATV) underwent serial paired cervicovaginal and plasma sampling for antiretroviral concentrations using high-performance liquid chromatography-tandem mass spectrometry. Analysis of 16S ribosomal RNA gene sequencing of cervicovaginal lavage clustered each participant visit into a unique microbiome community type (mCT). Results: Participants were predominantly African American (95%), with a median age of 38 years. Cervicovaginal lavage sequencing (n = 109) resulted in a low-diversity mCT dominated by Lactobacillus (n = 40), and intermediate-diversity (n = 28) and high-diversity (n = 41) mCTs with abundance of anaerobic taxa. In multivariable models, geometric mean FGT:plasma ratios varied significantly by mCT for all 3 drugs. For both ATV and TFV, FGT:plasma was significantly lower in participant visits with high- and low-diversity mCT groups (all P < .02). For emtricitabine, FGT:plasma was significantly lower in participant visits with low- vs intermediate-diversity mCT groups (P = .002). Conclusions: Certain FGT mCTs are associated with decreased FGT antiretroviral concentrations. These findings are relevant for optimizing antiretrovirals used for biomedical HIV prevention in women.

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.

Vibrational self-consistent field theory using optimized curvilinear coordinates.

A vibrational SCF model is presented in which the functions forming the single-mode functions in the product wavefunction are expressed in terms of internal coordinates and the coordinates used for each mode are optimized variationally. This model involves no approximations to the kinetic energy operator and does not require a Taylor-series expansion of the potential. The non-linear optimization of coordinates is found to give much better product wavefunctions than the limited variations considered in most previous applications of SCF methods to vibrational problems. The approach is tested using published potential energy surfaces for water, ammonia, and formaldehyde. Variational flexibility allowed in the current ansätze results in excellent zero-point energies expressed through single-product states and accurate fundamental transition frequencies realized by short configuration-interaction expansions. Fully variational optimization of single-product states for excited vibrational levels also is discussed. The highlighted methodology constitutes an excellent starting point for more sophisticated treatments, as the bulk characteristics of many-mode coupling are accounted for efficiently in terms of compact wavefunctions (as evident from the accurate prediction of transition frequencies).

Modeling emission features of salicylidene aniline molecular crystals: A QM/QM' approach.

A new computational protocol relying on the use of electrostatic embedding, derived from QM/QM' ONIOM calculations, to simulate the effect of the crystalline environment on the emission spectra of molecular crystals is here applied to the ß-form of salicylidene aniline (SA). The first singlet excited states (S1 ) of the SA cis-keto and trans-keto conformers, surrounded by a cluster of other molecules representing the crystalline structure, were optimized by using a QM/QM' ONIOM approach with and without electronic embedding. The model system consisting of the central salicylidene aniline molecule was treated at the DFT level by using either the B3LYP, PBE0, or the CAM-B3LYP functional, whereas the real system was treated at the HF level. The CAM-B3LYP/HF level of theory provides emission energies in good agreement with experiment with differences of -20/-32 nm (cis-keto form) and -8/-14 nm (trans-keto form), respectively, whereas notably larger differences are obtained using global hybrids. Though such differences on the optical properties arise from the density functional choice, the contribution of the electronic embedding is rather independent of the functional used. This plays in favor of a more general applicability of the present protocol to other crystalline molecular systems.