Fragment-Based Approach for the Evaluation of NMR Chemical Shifts for Large Biomolecules Incorporating the Effects of the Solvent Environment

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing

We present a graph-theory-based reformulation of all ONIOM-based molecular fragmentation methods. We discuss applications to (a) accurate post-Hartree-Fock AIMD that can be conducted at DFT cost for medium-sized systems, (b) hybrid DFT condensed-phase studies at the cost of pure density functionals, (c) reduced cost on-the-fly large basis gas-phase AIMD and condensed-phase studies, (d) post-Hartree-Fock-level potential surfaces at DFT cost to obtain quantum nuclear effects, and (e) novel transfer machine learning protocols derived from these measures. Additionally, in previous work, the unifying strategy discussed here has been used to construct new quantum computing algorithms. Thus, we conclude that this reformulation is robust and accurate.

Accurate Computation of Aqueous pKas of Biologically Relevant Organic Acids: Overcoming the Challenges Posed by Multiple Conformers, Tautomeric Equilibria, and Disparate Functional Groups with the Fully Black-Box pK-Yay Method

The use of static electronic structure calculations to compute solution-phase pKas offers a great advantage in that a macroscopic bulk property could be computed via microscopic computations involving very few molecules. There are various sources of errors in the quantum chemical calculations though. Overcoming these errors to accurately compute pKas of a plethora of acids is an active area of research in physical chemistry pursued by both computational as well as experimental chemists. We recently developed the pK-Yay method in our attempt to accurately compute aqueous pKas of strong and weak acids. The method is fully black-box, computationally inexpensive, and is very easy for even a nonexpert to use. However, the method was thus far tested on very few molecules (only 16 in all). Herein, in order to assess the future applicability of pK-Yay, we study the effect of multiple conformers, the presence of tautomers under equilibrium, and the impact of a wide variety of functional groups (derivatives of acetic acid with substituents at various positions, dicarboxylic acids, aromatic carboxylic acids, amines and amides, phenols and thiols, and fluorine bearing organic acids). Starting with more than 1000 conformers and tautomers, this study establishes that overall errors of ∼ 1.0 pKa units are routinely obtained for a majority of the molecules. Larger errors are noted in cases where multiple charges, intramolecular hydrogen bonding, and several ionizable functional groups are simultaneously present. An important conclusion to emerge from this work is that, the computed pKas are insensitive (difference <0.5) to whether we consider multiple conformers/tautomers or only choose the most stable conformer/tautomer. Further, pK-Yay captures the stereoelectronic effects arising due to differing axial vs equatorial pattern, and is useful to predict the dominant acid-base equilibrium in a system featuring several equilibria. Overall, pK-Yay may be employed in several chemical applications featuring organic molecules and biomonomers.

Competition between Solvent···Solvent and Solvent···Solute Interactions in the Microhydration of the Tetrafluoroborate Anion, BF4-(H2O)n=1,2,3,4

This study systematically examines the interactions of the tetrafluoroborate anion (BF4-) with up to four water molecules (BF4-(H2O)n=1,2,3,4). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed using a variety of density functional theory (DFT) methods (B3LYP, B3LYP-D3BJ, and M06-2X) and the MP2 ab initio method with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for B, O, and F; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the CCSD(T) ab initio method and the haTZ basis set for the mono- and dihydrate (n = 1, 2) structures. The 2-body:Many-body (2b:Mb) technique, in which CCSD(T) computations capture the 1- and 2-body contributions to the interactions and MP2 computations recover all higher-order contributions, was used to extend these demanding computations to the tri- and tetrahydrate (n = 3, 4) systems. Four, five, and eight new stationary points have been identified for the di-, tri-, and tetrahydrate systems, respectively. The global minimum of the monohydrate adopts a symmetric double ionic hydrogen bond motif with C2v symmetry and an electronic dissociation energy of 13.17 kcal mol-1 at the CCSD(T)/haTZ level of theory. This strong solvent···solute interaction, however, competes with solute···solute interactions in the lowest-energy BF4-(H2O)n=2,3,4 minima that are not seen in the other di-, tri-, or tetrahydrate minima. The latter interactions help increase the 2b:Mb dissociation energies to more than 26, 41, and 51 kcal mol-1 for n = 2, 3, and 4, respectively. Structures that form hydrogen bonds between the solvating water molecules also exhibit the largest shifts in the harmonic OH stretching frequencies for the waters of hydration. These shifts can exceed -280 cm-1 relative to an isolated H2O molecule at the 2b:Mb/haTZ level of theory.

Automated Fragmentation Quantum Mechanical Calculation of 15N and 13C Chemical Shifts in a Membrane Protein

In this work, we developed an accurate and cost-effective automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method to calculate the chemical shifts of 15N and 13C of membrane proteins. The convergence of the AF-QM/MM method was tested using Krokinobacter eikastus rhodopsin 2 as a test case. When the distance threshold of the QM region is equal to or larger than 4.0 Å, the results of the AF-QM/MM calculations are close to convergence. In addition, the effects of selected density functionals, basis sets, and local chemical environment of target atoms on the chemical shift calculations were systematically investigated. Our results demonstrate that the predicted chemical shifts are more accurate when important environmental factors including cross-protomer interactions, lipid molecules, and solvent molecules are taken into consideration, especially for the 15N chemical shift prediction. Furthermore, with the presence of sodium ions in the environment, the chemical shift of residues, retinal, and retinal Schiff base are affected, which is consistent with the results of the solid-state nuclear magnetic resonance (NMR) experiment. Upon comparing the performance of various density functionals (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB95, and OPBE), the results show that mPW1PW91 is a suitable functional for the 15N and 13C chemical shift prediction of the membrane proteins. Meanwhile, we find that the improved accuracy of the 13Cβ chemical shift calculations can be achieved by the employment of the triple-ζ basis set. However, the employment of the triple-ζ basis set does not improve the accuracy of the 15N and 13Cα chemical shift calculations nor does the addition of a diffuse function improve the overall prediction accuracy of the chemical shifts. Our study also underscores that the AF-QM/MM method has significant advantages in predicting the chemical shifts of key ligands and nonstandard residues in membrane proteins than most widely used empirical models; therefore, it could be an accurate computational tool for chemical shift calculations on various types of biological systems.

MIM-ML: A Novel Quantum Chemical Fragment-Based Random Forest Model for Accurate Prediction of NMR Chemical Shifts of Nucleic Acids

We developed a random forest machine learning (ML) model for the prediction of 1H and 13C NMR chemical shifts of nucleic acids. Our ML model is trained entirely on reproducing computed chemical shifts obtained previously on 10 nucleic acids using a Molecules-in-Molecules (MIM) fragment-based density functional theory (DFT) protocol including microsolvation effects. Our ML model includes structural descriptors as well as electronic descriptors from an inexpensive low-level semiempirical calculation (GFN2-xTB) and trained on a relatively small number of DFT chemical shifts (2080 1H chemical shifts and 1780 13C chemical shifts on the 10 nucleic acids). The ML model is then used to make chemical shift predictions on 8 new nucleic acids ranging in size from 600 to 900 atoms and compared directly to experimental data. Though no experimental data was used in the training, the performance of our model is excellent (mean absolute deviation of 0.34 ppm for 1H chemical shifts and 2.52 ppm for 13C chemical shifts for the test set), despite having some nonstandard structures. A simple analysis suggests that both structural and electronic descriptors are critical for achieving reliable predictions. This is the first attempt to combine ML from fragment-based DFT calculations to predict experimental chemical shifts accurately, making the MIM-ML model a valuable tool for NMR predictions of nucleic acids.

Fragment-based models for dissociation of strong acids in water: Electrostatic embedding minimizes the dependence on the fragmentation schemes

Fragmentation methods such as MIM (Molecules-in-Molecules) provide a route to accurately model large systems and have been successful in predicting their structures, energies, and spectroscopic properties. However, their use is often limited to systems at equilibrium due to the inherent complications in the choice of fragments in systems away from equilibrium. Furthermore, the presence of charges resulting from any heterolytic bond breaking may increase the fragmentation error. We have previously suggested EE-MIM (Electrostatically Embedded Molecules-In-Molecules) as a method to mitigate the errors resulting from the missing long-range interactions in molecular clusters in equilibrium. Here, we show that the same method can be applied to improve the performance of MIM to solve the longstanding problem of dependency of the fragmentation energy error on the choice of the fragmentation scheme. We chose four widely used acid dissociation reactions (HCl, HClO4, HNO3, and H2SO4) as test cases due to their importance in chemical processes and complex reaction potential energy surfaces. Electrostatic embedding improves the performance at both one and two-layer MIM as shown by lower EE-MIM1 and EE-MIM2 errors. The EE-MIM errors are also demonstrated to be less dependent on the choice of the fragmentation scheme by analyzing the variation in fragmentation energy at the points with more than one possible fragmentation scheme (points where the fragmentation scheme changes). EE-MIM2 with M06-2X as the low-level resulted in a variation of less than 1 kcal/mol for all the cases and 1 kJ/mol for all but three cases, rendering our method fragmentation scheme-independent for acid dissociation processes.

Atomic-level structure determination of amorphous molecular solids by NMR

Structure determination of amorphous materials remains challenging, owing to the disorder inherent to these materials. Nuclear magnetic resonance (NMR) powder crystallography is a powerful method to determine the structure of molecular solids, but disorder leads to a high degree of overlap between measured signals, and prevents the unambiguous identification of a single modeled periodic structure as representative of the whole material. Here, we determine the atomic-level ensemble structure of the amorphous form of the drug AZD4625 by combining solid-state NMR experiments with molecular dynamics (MD) simulations and machine-learned chemical shifts. By considering the combined shifts of all 1H and 13C atomic sites in the molecule, we determine the structure of the amorphous form by identifying an ensemble of local molecular environments that are in agreement with experiment. We then extract and analyze preferred conformations and intermolecular interactions in the amorphous sample in terms of the stabilization of the amorphous form of the drug.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

Accurate and Cost-Effective NMR Chemical Shift Predictions for Nucleic Acids Using a Molecules-in-Molecules Fragmentation-Based Method

We have developed, implemented, and assessed an efficient protocol for the prediction of NMR chemical shifts of large nucleic acids using our molecules-in-molecules (MIM) fragment-based quantum chemical approach. To assess the performance of our approach, MIM-NMR calculations are calibrated on a test set of three nucleic acids, where the structure is derived from solution-phase NMR studies. For DNA systems with multiple conformers, the one-layer MIM method with trimer fragments (MIM1trimer) is benchmarked to get the lowest energy structure, with an average error of only 0.80 kcal/mol with respect to unfragmented full molecule calculations. The MIMI-NMRdimer calibration with respect to unfragmented full molecule calculations shows a mean absolute deviation (MAD) of 0.06 and 0.11 ppm, respectively, for 1H and 13C nuclei, but the performance with respect to experimental NMR chemical shifts is comparable to the more expensive MIM1-NMR and MIM2-NMR methods with trimer subsystems. To compare with the experimental chemical shifts, a standard protocol is derived using DNA systems with Protein Data Bank (PDB) IDs 1SY8, 1K2K, and 1KR8. The effect of structural minimizations is employed using a hybrid mechanics/semiempirical approach and used for computations in solution with implicit and explicit-implicit solvation models in our MIM1-NMRdimer methodology. To demonstrate the applicability of our protocol, we tested it on seven nucleic acids, including structures with nonstandard residues, heteroatom substitutions (F and B atoms), and side chain mutations with a size ranging from ∼300 to 1100 atoms. The major improvement for predicted MIM1-NMRdimer calculations is obtained from structural minimizations and implicit solvation effects. A significant improvement with the explicit-implicit solvation model is observed only for two smaller nucleic acid systems (1KR8 and 7NBK), where the expensive first solvation shell is replaced by the microsolvation model, in which a single water molecule is added for each solvent-exposed amino and imino protons, along with the implicit solvation. Overall, our target accuracy of ∼0.2-0.3 ppm for 1H and ∼2-3 ppm for 13C has been achieved for large nucleic acids. The proposed MIM-NMR approach is accurate and cost-effective (linear scaling with system size), and it can aid in the structural assignments of a wide range of complex biomolecules.

Nuclear Magnetic Shielding Constants with the Polarizable Density Embedding Model

We extend the polarizable density embedding (PDE) model to support the calculation of nuclear magnetic resonance (NMR) shielding constants using gauge-including atomic orbitals (GIAOs) within a density functional theory (DFT) framework. The PDE model divides the total system into fragments, describing some by quantum mechanics (QM) and the others through an embedding model. The PDE model uses anisotropic polarizabilities, inter-fragment two-electron Coulomb integrals, and a non-local repulsion operator to emulate the QM effects. The terms involving Coulomb integrals are straightforwardly extended with GIAOs. In contrast, we consider two approaches to handle the gauge dependency of the non-local operator, employing either simple symmetrization or a gauge transformation. We find the latter approach to be most stable with respect to increasing the basis set size of the QM region. We examine the accuracy of the PDE model for calculating NMR shielding constants on several solutes in a water solution. The performance is compared with the classical polarizable embedding (PE) model in addition to supermolecular reference calculations. Based on these systems, we address the basis set convergence characteristics and the QM region size requirements. Furthermore, we investigate the performance of the PDE model for a system with significant electron spill-out. In many cases, we find that the PDE model outperforms the PE model, especially regarding the accuracy of nuclear shielding constants when using small QM region sizes and in systems with significant electron spill-out.

Reference interaction site model self-consistent field with constrained spatial electron density approach for nuclear magnetic shielding in solution

We propose a new hybrid approach combining quantum chemistry and statistical mechanics of liquids for calculating the nuclear magnetic resonance (NMR) chemical shifts of solvated molecules. Based on the reference interaction site model self-consistent field with constrained spatial electron density distribution (RISM–SCF–cSED) method, the electronic structure of molecules in solution is obtained, and the expression for the nuclear magnetic shielding tensor is derived as the second-order derivative of the Helmholtz energy of the solution system. We implemented a method for calculating chemical shifts and applied it to an adenine molecule in water, where hydrogen bonding plays a crucial role in electronic and solvation structures. We also performed the calculations of 17O chemical shifts, which showed remarkable solvent dependence. While converged results could not be sometimes obtained using the conventional method, in the present framework with RISM–SCF–cSED, an adequate representation of electron density is guaranteed, making it possible to obtain an NMR shielding constant stably. This introduction of cSED is key to extending the method’s applicability to obtain the chemical shift of various chemical species. The present demonstration illustrates our approach’s superiority in terms of numerical robustness and accuracy.

Improving IDP theoretical chemical shift accuracy and efficiency through a combined MD/ADMA/DFT and machine learning approach

This work extends the multi-scale computational scheme for the quantum mechanics (QM) calculations of Nuclear Magnetic Resonance (NMR) chemical shifts (CSs) in proteins that lack a well-defined 3D structure. The scheme couples the sampling of an intrinsically disordered protein (IDP) by classical molecular dynamics (MD) with protein fragmentation using the adjustable density matrix assembler (ADMA) and density functional theory (DFT) calculations. In contrast to our early investigation on IDPs (Pavlíková Přecechtělová et al., J. Chem. Theory Comput., 2019, 15, 5642-5658) and the state-of-the art NMR calculations for structured proteins, a partial re-optimization was implemented on the raw MD geometries in vibrational normal mode coordinates to enhance the accuracy of the MD/ADMA/DFT computational scheme. In addition, machine-learning based cluster analysis was performed on the scheme to explore its potential in producing protein structure ensembles (CLUSTER ensembles) that yield accurate CSs at a reduced computational cost. The performance of the cluster-based calculations is validated against results obtained with conventional structural ensembles consisting of MD snapshots extracted from the MD trajectory at regular time intervals (REGULAR ensembles). CS calculations performed with the refined MD/ADMA/DFT framework employed the 6-311++G(d,p) basis set that outperformed IGLO-III calculations with the same density functional approximation (B3LYP) and both explicit and implicit solvation. The partial geometry optimization did not universally improve the agreement of computed CSs with the experiment but substantially decreased errors associated with the ensemble averaging. A CLUSTER ensemble with 50 structures yielded ensemble averages close to those obtained with a REGULAR ensemble consisting of 500 MD frames. The cluster based calculations thus required only a fraction of the computational time.

Solvent effects on the NMR shieldings of stacked DNA base pairs

Stacking effects are among the most important effects in DNA. We have recently studied their influence in fragments of DNA through the analysis of NMR magnetic shieldings, firstly in vacuo. As a continuation of this line of research we show here the influence of solvent effects on the shieldings through the application of both explicit and implicit models. We found that the explicit solvent model is more appropriate for consideration due to the results matching better in general with experiments, as well as providing clear knowledge of the electronic origin of the value of the shieldings. Our study is grounded on a recently developed theoretical model of our own, by which we are able to learn about the magnetic effects of given fragments of DNA molecules on selected base pairs. We use the shieldings of the atoms of a central base pair (guanine-cytosine) of a selected fragment of DNA molecules as descriptors of physical effects, like π-stacking and solvent effects. They can be taken separately and altogether. The effect of π-stacking is introduced through the addition of some pairs above and below of the central base pair, and now, the solvent effect is considered including a network of water molecules that consist of two solvation layers, which were fixed in the calculations performed in all fragments. We show that the solvent effects enhance the stacking effects on the magnetic shieldings of atoms that belong to the external N-H bonds. The net effect is of deshielding on both atoms. There is also a deshielding effect on the carbon atoms that belong to CO bonds, for which the oxygen atom has an explicit hydrogen bond (HB) with a solvent water molecule. Solvent effects are found to be no higher than a few percent of the total value of the shieldings (between 1% and 5%) for most atoms, although there are few for which such an effect can be higher. There is one nitrogen atom, the acceptor of the HB between guanine and cytosine, that is more highly shielded (around 15 ppm or 10%) when the explicit solvent is considered. In a similar manner, the most external nitrogen atom of cytosine and the hydrogen atom that is bonded to it are highly deshielded (around 10 ppm for nitrogen and around 3 ppm for hydrogen).

Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for ¹³C, ¹⁵N, ¹⁷O, ¹⁹F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for ¹H and ¹³C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental ¹³C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.

Accurate and cost-effective NMR chemical shift predictions for proteins using a molecules-in-molecules fragmentation-based method

We have developed an efficient protocol using our two-layer Molecules-in-Molecules (MIM2) fragmentation-based quantum chemical method for the prediction of NMR chemical shifts of large biomolecules. To investigate the performance of our fragmentation approach and demonstrate its applicability, MIM-NMR calculations are first calibrated on a test set of six proteins. The MIM2-NMR method yields a mean absolute deviation (MAD) from unfragmented full molecule calculations of 0.01 ppm for 1H and 0.06 ppm for 13C chemical shifts. Thus, the errors from fragmentation are only about 3% of our target accuracy of ∼0.3 ppm for 1H and 2-3 ppm for 13C chemical shifts. To compare with experimental chemical shifts, a standard protocol is first derived using two smaller proteins 2LHY (176 atoms) and 2LI1 (146 atoms) for obtaining an appropriate protein structure for NMR chemical shift calculations. The effect of the solvent environment on the calculated NMR chemical shifts is incorporated through implicit, explicit, or explicit-implicit solvation models. The expensive first solvation shell calculations are replaced by a micro-solvation model in which only the immediate interaction between the protein and the explicit solvation environment is considered. A single explicit water molecule for each amine and amide proton is found to be sufficient to yield accurate results for 1H chemical shifts. The 1H and 13C NMR chemical shifts calculated using our protocol give excellent agreement with experiments for two larger proteins, 2MC5 (the helical part with 265 atoms) and 3UMK (33 residue slice with 547 atoms). Overall, our target accuracy of ∼0.3 ppm for 1H and ∼2-3 ppm for 13C has been achieved for the larger proteins. The proposed MIM-NMR method is accurate and computationally cost-effective and should be applicable to study a wide range of large proteins.

Polarizable continuum models provide an effective electrostatic embedding model for fragment-based chemical shift prediction in challenging systems

Ab initio nuclear magnetic resonance chemical shift prediction provides an important tool for interpreting and assigning experimental spectra, but it becomes computationally prohibitive in large systems. The computational costs can be reduced considerably by fragmentation of the large system into a series of contributions from many smaller subsystems. However, the presence of charged functional groups and the need to partition the system across covalent bonds create complications in biomolecules that typically require the use of large fragments and careful descriptions of the electrostatic environment. The present work shows how a model that combines chemical shielding contributions from non-overlapping monomer and dimer fragments embedded in a polarizable continuum model provides a simple, easy-to-implement, and computationally inexpensive approach for predicting chemical shifts in complex systems. The model's performance proves rather insensitive to the continuum dielectric constant, making the selection of the optimal embedding dielectric less critical. The PCM-embedded fragment model is demonstrated to perform well across systems ranging from molecular crystals to proteins.

Accurate Backbone 13 C and 15 N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate 13 C and 15 N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for 15 N atoms. Here we compare experimentally determined backbone 13 Cα and 15 NH chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed 15 NH chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.

Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry

We introduce an implementation of the truncated many-body expansion, MBE(n), in which the n-body corrections are screened using the effective fragment potential force field, and only those that exceed a specified energy threshold are computed at a quantum-mechanical level of theory. This energy-screened MBE(n) approach is tested at the n = 3 level for a sequence of water clusters, (H₂O)_N=6-34. A threshold of 0.25 kJ/mol eliminates more than 80% of the subsystem electronic structure calculations and is even more efficacious in that respect than is distance-based screening. Even so, the energy-screened MBE(3) method is faithful to a full-system quantum chemistry calculation to within 1-2 kJ/mol/monomer, even in good quality basis sets such as aug-cc-pVTZ. These errors can be reduced by means of a two-layer approach that involves a Hartree-Fock calculation for the entire cluster. Such a correction proves to be necessary in order to obtain accurate relative energies for conformational isomers of (H₂O)₂₀, but the cost of a full-system Hartree-Fock calculation remains smaller than the cost of three-body subsystem calculations at correlated levels of theory. At the level of second-order Møller-Plesset perturbation theory (MP2), a screened MBE(3) calculation plus a full-system Hartree-Fock calculation is less expensive than a full-system MP2 calculation starting at N = 12 water molecules. This is true even if all MBE(3) subsystem calculations are performed on a single 40-core compute node, i.e., without significant parallelization. Energy-screened MBE(n) thus provides a fragment-based method that is accurate, stable in large basis sets, and low in cost, even when the latter is measured in aggregate computer time.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Variational Formulation of the Generalized Many-Body Expansion with Self-Consistent Charge Embedding: Simple and Correct Analytic Energy Gradient for Fragment-Based ab Initio Molecular Dynamics

The many-body expansion (MBE) and its extension to overlapping fragments, the generalized (G)MBE, constitute the theoretical basis for most fragment-based approaches for large-scale quantum chemistry. We reformulate the GMBE for use with embedding charges determined self-consistently from the fragment wave functions, in a manner that preserves the variational nature of the underlying self-consistent field method. As a result, the analytic gradient retains the simple "sum of fragment gradients" form that is often assumed in practice, sometimes incorrectly. This obviates (without approximation) the need to solve coupled-perturbed equations, and we demonstrate stable, fragment-based ab initio molecular dynamics simulations using this technique. Energy conservation fails when charge-response contributions to the Fock matrix are neglected, even while geometry optimizations and vibrational frequency calculations may yet be accurate. Stable simulations can be recovered by means of straightforward modifications introduced here, providing a general paradigm for fragment-based ab initio molecular dynamics.

Exploring Reaction Energy Profiles Using the Molecules-in-Molecules Fragmentation-Based Approach

The Molecules-in-Molecules (MIM) fragmentation-based approach has been successfully used in previous studies to obtain the energies, optimized geometries, and spectroscopic properties of large molecular systems. The present work delineates a protocol to study the potential energy profiles for multistep chemical reactions using the MIM methodology. In a complex multistep chemical reaction, the fragmentation scheme needs to be changed as the reacting species transition into a new reaction step, resulting in a discontinuity in the potential energy curve of the reaction. In our approach, the fragmentation scheme for a particular step in a reaction is chosen on the basis of the nature of the bonding changes associated with that step. Thus, the reactant, transition state, and product are treated consistently throughout the reaction step, leading to an accurate energy barrier for that step. The discontinuity now occurs in describing the energies of reaction intermediates at the transition point between two reaction steps that are treated by two different fragmentation schemes. To address this issue, we propose a systematic procedure for obtaining continuous potential energy curves that are least shifted from their initial positions. The corrected MIM potential energy curves are continuous with activation energies preserved. Following this approach, energy profiles of complex reactions involving large molecular species can be obtained at high levels of theory with a reasonable computational cost.

A fast approximate algorithm for determining bond orders in large polycyclic structures

Novel logarithmic time algorithm is proposed for determining the order of chemical bonds from known valences of the atoms. The algorithm has the order of complexity N · log(N) and is applicable to polycyclic compounds containing a combination of the cycles of any size and the atoms with the valences ≤4 in cycle nodes. The algorithm is applicable to structures containing triple and cumulene bonds in the cycles. It was tested for graphene, C[12,12] nanotubes, graphyne-GY1, graphyne-GY7, graphyne-like nanotube, fullerenes C20, C60, C70, C80, C82 and their aza-analogs, polypentadienes, as well as for porphine. Determining the order of bonds in graphene, graphynes or nanotubes, containing >10⁷ atoms, took less than 2 min on a personal computer. For the compounds containing aromatic cycles with an odd number of atoms, this algorithm becomes probabilistic and successful determination of bond orders is not guaranteed. However, the probability of successful determination of bond order is significant, and Kekulé structures, if they existed, were generated for all studied fullerenes and their aza-analogs.

Computational study to understand the energy transfer pathways within amicyanin

Vibrational energy diffusivities between the residues present in Amicyanin copper protein are calculated and presented in form of communication map. From those results energy flow pathways from the copper metal ion to the inter protein residue Glu31 are identified. Our finding suggests many different pathways are possible and copper metal ion in oxidized and reduced state switches the pathways. Our finding also suggests the cooperative nature of surrounding residues and water molecules towards selecting the pathways. The major transport channels in the oxidised state are, Cu²⁺---> MET28---> LYS29---> TYR30---> GLU31 and Cu²⁺---> MET98---> TYR30--- > GLU31. And in the reduced state Cu⁺---> CYS9---> TYR30---> GLU31 and Cu⁺---> MET28---> LYS2---> TYR30---> GLU31. We studied further the interaction energies between the copper ion and neighbouring residues using B3LYP/QZVP method. Both the methods complement each other in predicting the energy flow pathways and the cooperative nature of residues.

Probing the communication of deoxythymidine triphosphate in HIV-1 reverse transcriptase by communication maps and interaction energy studies

We calculate communication maps for HIV-1 Reverse Transcriptase (RT) to elucidate energy transfer pathways between deoxythymidine triphosphate (dTTP) and other parts of the protein.