NMR Solvent Shifts of Acetonitrile from Frozen Density Embedding Calculations

Multiscale Frozen Density Embedding/Molecular Mechanics Approach for Simulating Magnetic Response Properties of Solvated Systems

We present a three-layer hybrid quantum mechanical/quantum embedding/molecular mechanics approach for calculating nuclear magnetic resonance (NMR) shieldings and J-couplings of molecular systems in solution. The model is based on the frozen density embedding (FDE) and polarizable fluctuating charges (FQ) and fluctuating dipoles (FQFμ) force fields and permits the accurate ab initio description of short-range nonelectrostatic interactions by means of the FDE shell and cost-effective treatment of long-range electrostatic interactions through the polarizable force field FQ(Fμ). Our approach's accuracy and potential are demonstrated by studying NMR spectra of Brooker's merocyanine in aqueous and nonaqueous solutions.

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Subsystem Density Functional Theory Augmented by a Delta Learning Approach to Achieve Kohn-Sham Accuracy

Simulations based on electronic structure theory naturally include polarization and have no transferability problems. In particular, Kohn-Sham density functional theory (KS-DFT) has become the method of reference for ab initio molecular dynamics simulations of condensed matter systems. However, the high computational cost often poses strict limits on the affordable system size as well as on the extension of sampling (number of configurations). In this work, we propose an improvement to the subsystem density functional theory approach, known as the Kim-Gordon (KG) scheme, thus enabling the sampling of configurations for condensed molecular systems keeping the KS-DFT level accuracy at a fraction of computer time. Our scheme compensates the known KG shortcomings of the electronic kinetic energy term by adding a simple correction and can match KS-DFT accuracy in energies and forces. The computationally cheap correction is determined by means of a machine learning procedure. The proposed KG scheme is applied within a linear scaling self-consistent field formalism and is assessed by a series of molecular dynamics simulations of liquid water under different conditions. Although system-dependent, the correction is transferable between system sizes and temperatures.

Environmental Effects with Frozen-Density Embedding in Real-Time Time-Dependent Density Functional Theory Using Localized Basis Functions

Frozen-density embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane waves and periodic boundary conditions [Pavanello, M.; J. Chem. Phys. 2015, 142, 154116]. In the current paper, we extend our recent formulation of the real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We employed this new implementation to investigate the stability of the time-propagation procedure, which is based on an efficient predictor/corrector second-order midpoint Magnus propagator employing an exact diagonalization, in combination with the FDE scheme. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem, and in the limit of the weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear-response TDDFT. The method is found to give stable numerical results also in the presence of a strong external field inducing nonlinear effects. Preliminary results are reported for high harmonic generation (HHG) of a water molecule embedded in a small water cluster. The effect of the embedding potential is evident in the HHG spectrum reducing the number of the well-resolved high harmonics at high energy with respect to the free water. This is consistent with a shift toward lower ionization energy passing from an isolated water molecule to a small water cluster. The computational burden for the propagation step increases approximately linearly with the size of the surrounding frozen environment. Furthermore, we have also shown that the updating frequency of the embedding potential may be significantly reduced, much less than one per time step, without jeopardizing the accuracy of the transition energies.

Nonlocal Subsystem Density Functional Theory

By invoking a divide-and-conquer strategy, subsystem DFT dramatically reduces the computational cost of large-scale, ab initio electronic structure simulations of molecules and materials. The central ingredient setting subsystem DFT apart from Kohn-Sham DFT is the nonadditive kinetic energy functional (NAKE). Currently employed NAKEs are at most semilocal (i.e., they only depend on the electron density and its gradient), and as a result of this approximation, so far large-scale simulations only included systems composed of weakly interacting subsystems. In this work, we advance the state-of-the-art by introducing fully nonlocal NAKEs in subsystem DFT simulations for the first time. A benchmark analysis based on the S22-5 test set shows that nonlocal NAKEs considerably improve the computed interaction energies and electron densities compared to commonly employed GGA NAKEs, especially when increasing intersubsystem electron density overlap is considered. Most importantly, we resolve the long-standing problem of too attractive interaction energy curves typically resulting from the use of GGA NAKEs.

On the calculation of second-order magnetic properties using subsystem approaches in a relativistic framework

The implementation of second-order magnetic properties in a frozen density embedding scheme in a four component relativistic framework is outlined and applied to model H₂X–H₂O systems (X = Se, Te, Po).

Extending the density functional embedding theory to finite temperature and an efficient iterative method for solving for embedding potentials

A key element in the density functional embedding theory (DFET) is the embedding potential. We discuss two major issues related to the embedding potential: (1) its non-uniqueness and (2) the numerical difficulty for solving for it, especially for the spin-polarized systems. To resolve the first issue, we extend DFET to finite temperature: all quantities, such as the subsystem densities and the total system's density, are calculated at a finite temperature. This is a physical extension since materials work at finite temperatures. We show that the embedding potential is strictly unique at T > 0. To resolve the second issue, we introduce an efficient iterative embedding potential solver. We discuss how to relax the magnetic moments in subsystems and how to equilibrate the chemical potentials across subsystems. The solver is robust and efficient for several non-trivial examples, in all of which good quality spin-polarized embedding potentials were obtained. We also demonstrate the solver on an extended periodic system: iron body-centered cubic (110) surface, which is related to the modeling of the heterogeneous catalysis involving iron, such as the Fischer-Tropsch and the Haber processes. This work would make it efficient and accurate to perform embedding simulations of some challenging material problems, such as the heterogeneous catalysis and the defects of complicated spin configurations in electronic materials.

Constrained subsystem density functional theory

Constrained Subsystem Density Fucntional Theory (CSDFT) allows to compute diabatic states for charge transfer reactions using the machinery of the constrained DFT method, and at the same time is able to embed such diabatic states in a molecular environment via a subsystem DFT scheme.

(1)H NMR spectra of alcohols in hydrogen bonding solvents: DFT/GIAO calculations of chemical shifts

Proton nuclear magnetic resonance (NMR) shifts of aliphatic alcohols in hydrogen bonding solvents have been computed on the basis of density functional theory by applying the gauge-including atomic orbital method to geometry-optimized alcohol/solvent complexes. The OH proton shifts and hydrogen bond distances for methanol or ethanol complexed with pyridine depend very much on the functional employed and very little on the basis set, provided it is sufficiently large to give the correct quasi-linear hydrogen bond geometry. The CH proton shifts are insensitive to both the functional and the basis set. NMR shifts for all protons in several alcohol/pyridine complexes are calculated at the Perdew, Burke and Ernzerhof PBE0/cc-pVTZ//PBE0/6-311 + G(d,p) level in the gas phase. The results correlate with the shifts for the pyridine-complexed alcohols, determined by analysing data from the NMR titration of alcohols against pyridine. More pragmatically, computed shifts for a wider range of alcohols correlate with experimental shifts in neat pyridine. Shifts for alcohols in dimethylsulfoxide, based on the corresponding complexes in the gas phase, correlate well with the experimental values, but the overall root mean square difference is high (0.23 ppm), shifts for the OH, CHOH and other CH protons being systematically overestimated, by averages of 0.42, 0.21 and 0.06 ppm, respectively. If the computed shifts are corrected accordingly, a very good correlation is obtained with a gradient of 1.00 ± 0.01, an intercept of 0.00 ± 0.02 ppm and a root mean square difference of 0.09 ppm. This is a modest improvement on the result of applying the CHARGE programme to a slightly different set of alcohols. Some alcohol complexes with acetone and acetonitrile were investigated both in the gas phase and in a continuum of the relevant solvent.

Solvent Dependence of (14)N Nuclear Magnetic Resonance Chemical Shielding Constants as a Test of the Accuracy of the Computed Polarization of Solute Electron Densities by the Solvent

Although continuum solvation models have now been shown to provide good quantitative accuracy for calculating free energies of solvation, questions remain about the accuracy of the perturbed solute electron densities and properties computed from them. Here we examine those questions by applying the SM8, SM8AD, SMD, and IEF-PCM continuum solvation models in combination with the M06-L density functional to compute the (14)N magnetic resonance nuclear shieldings of CH3CN, CH3NO2, CH3NCS, and CH3ONO2 in multiple solvents, and we analyze the dependence of the chemical shifts on solvent dielectric constant. We examine the dependence of the computed chemical shifts on the definition of the molecular cavity (both united-atom models and models based on superposed individual atomic spheres) and three kinds of treatments of the electrostatics, namely the generalized Born approximation with the Coulomb field approximation, the generalized Born model with asymmetric descreening, and models based on approximate numerical solution schemes for the nonhomogeneous Poisson equation. Our most systematic analyses are based on the computation of relative (14)N chemical shifts in a series of solvents, and we compare calculated shielding constants relative to those in CCl4 for various solvation models and density functionals. While differences in the overall results are found to be reasonably small for different solvation models and functionals, the SMx models SM8, and SM8AD, using the same cavity definitions (which for these models means the same atomic radii) as those employed for the calculation of free energies of solvation, exhibit the best agreement with experiment for every functional tested. This suggests that in addition to predicting accurate free energies of solvation, the SM8 and SM8AD generalized Born models also describe the solute polarization in a manner reasonably consistent with experimental (14)N nuclear magnetic resonance spectroscopy. Models based on the nonhomogeneous Poisson equation show slightly reduced accuracy. Scaling the intrinsic Coulomb radii to larger values (as has sometimes been suggested in the past) does not uniformly improve the results for any kind of solvent model; furthermore it uniformly degrades the results for generalized Born models. Use of a basis set that increases the outlying charge diminishes the accuracy of continuum models that solve the nonhomogeneous Poisson equation, which we ascribe to the inability of the numerical schemes for approximately solving the nonhomogeneous Poisson equation to fully account for the effects of electronic charge outside the solute cavity.

Investigation of solute-solvent interactions in phenol compounds: accurate ab initio calculations of solvent effects on 1H NMR chemical shifts

Accurate (1)H chemical shifts of the -OH groups of polyphenol compounds can be calculated, compared to experimental values, using a combination of DFT, polarizable continuum model (PCM) and discrete solute-solvent hydrogen bond interactions. The study focuses on three molecular solutes: phenol, 4-methylcatechol and the natural product genkwanin in DMSO, acetone, acetonitrile, and chloroform. Excellent linear correlation between experimental and computed chemical shifts (with the GIAO method at the DFT/B3LYP/6-311++G(2d,p) level) was obtained with minimization of the solvation complexes at the DFT/B3LYP/6-31+G(d) and DFT/B3LYP/6-311++G(d,p) level of theory with a correlation coefficient of 0.991. The use of the DFT/B3LYP/6-31+G(d) level of theory for minimization could provide an excellent means for the accurate prediction of the experimental OH chemical shift range of over 8 ppm due to: (i) strong intramolecular and solute-solvent intermolecular hydrogen bonds, (ii) flip-flop intramolecular hydrogen bonds, and (iii) conformational effects of substituents of genkwanin. The combined use of ab initio calculations and experimental (1)H chemical shifts of phenol -OH groups provides a method of primary interest in order to obtain detailed structural, conformation and electronic description of solute-solvent interactions at a molecular level.

Multiscale Modeling of Chemistry in Water: Are We There Yet?

This paper critically evaluates the state of the art in combined quantum mechanical/molecular mechanical (QM/MM) approaches to the computational description of chemistry in water and supplies guidelines for the setup of customized multiscale simulations of aqueous processes. We differentiate between structural and dynamic performance, since some tasks, e.g., the reproduction of NMR or UV-vis spectra, require only structural accuracy, while others, i.e., reaction mechanisms, require accurate dynamic data as well. As a model system for aqueous solutions in general, the approaches were tested on a QM water cluster in an environment of MM water molecules. The key difficulty is the description of the possible diffusion of QM molecules into the MM region and vice versa. The flexible inner region ensemble separator (FIRES) approach constrains QM solvent molecules within an active (QM) region. Sorted adaptive partitioning (SAP), difference-based adaptive solvation (DAS), and buffered-force (BF) are all adaptive approaches that use a buffer zone in which solvent molecules gradually adapt from QM to MM (or vice versa). The costs of SAP and DAS are relatively high, while BF is fast but sacrifices conservation of both energy and momentum. Simulations in the limit of an infinitely small buffer zone, where DAS and SAP become equivalent, are discussed as well and referred to as ABRUPT. The best structural accuracy is obtained with DAS, BF, and ABRUPT, all three of similar quality. FIRES performs very well for dynamic properties localized deep within the QM region. By means of elimination DAS emerges as the best overall compromise between structural and dynamic performance. Eliminating the buffer zone (ABRUPT) improves efficiency and still leads to surprisingly good results. While none of the many new flavors are perfect, all together this new field already allows accurate description of a wide range of structural and dynamic properties of aqueous solutions.

Computing the 7Li NMR chemical shielding of hydrated Li+ using cluster calculations and time-averaged configurations from ab initio molecular dynamics simulations

Ab initio molecular dynamics (AIMD) simulations have been used to predict the time-averaged Li NMR chemical shielding for a Li(+) solution. These results are compared to NMR shielding calculations on smaller Li(+)(H(2)O)(n) clusters optimized in either the gas phase or with a polarizable continuum model (PCM) solvent. The trends introduced by the PCM solvent are described and compared to the time-averaged chemical shielding observed in the AIMD simulations where large explicit water clusters hydrating the Li(+) are employed. Different inner- and outer-coordination sphere contributions to the Li NMR shielding are evaluated and discussed. It is demonstrated an implicit PCM solvent is not sufficient to correctly model the Li shielding, and that explicit inner hydration sphere waters are required during the NMR calculations. It is also shown that for hydrated Li(+), the time averaged chemical shielding cannot be simply described by the population-weighted average of coordination environments containing different number of waters.

PyADF--a scripting framework for multiscale quantum chemistry

Applications of quantum chemistry have evolved from single or a few calculations to more complicated workflows, in which a series of interrelated computational tasks is performed. In particular multiscale simulations, which combine different levels of accuracy, typically require a large number of individual calculations that depend on each other. Consequently, there is a need to automate such workflows. For this purpose we have developed PYADF, a scripting framework for quantum chemistry. PYADF handles all steps necessary in a typical workflow in quantum chemistry and is easily extensible due to its object-oriented implementation in the Python programming language. We give an overview of the capabilities of PYADF and illustrate its usefulness in quantum-chemical multiscale simulations with a number of examples taken from recent applications.

Electron density fingerprints (EDprints): virtual screening using assembled information of electron density

We have designed a method to encode properties related to the electron densities of molecules (calculated (1)H and (13)C NMR shifts and atomic partial charges) in molecular fingerprints (EDprints). EDprints was evaluated in terms of their retrospective virtual screening accuracy against the Directory of Useful Decoys (DUD) and compared to the established ligand-based similarity search methods MOLPRINT 2D and FCFP-4. Although there are no significant differences in the overall virtual screening accuracies of the three methods, specific examples highlight interesting differences between the new EDprints fingerprint method and the atom-centered circular fingerprint methods of MOLPRINT 2D and FCFP-4. On one hand, EDprints similarity searches can be biased by the molecular protonation state, especially when reference ligands contain multiple ionizable groups. On the other hand, EDprints models are more robust toward subtle rearrangements of chemical groups and more suitable for screening against reference molecules with fused ring systems than MOLPRINT 2D and FCFP-4. EDprints is furthermore the fastest method under investigation in comparing fingerprints (average 56-233-fold increase in speed), which makes it highly suitable for all-against-all similarity searches and for repetitive virtual screening against large chemical databases of millions of compounds.