Ab initio quality one-electron properties of large molecules: development and testing of molecular tailoring approach

Constructing Potential Energy Surface with Correlated Theory for Dipeptides Using Molecular Tailoring Approach

We demonstrate a cost-effective alternative employing the fragment-based molecular tailoring approach (MTA) for building the potential energy surface (PES) for two dipeptides viz. alanine-alanine and alanine-proline employing correlated theory, with augmented Dunning basis sets. About 1369 geometries are generated for each test dipeptide by systematically varying the dihedral angles Φ ${{\rm{\Phi }}}$ and Ψ ${{{\Psi }}}$ . These conformational geometries are partially optimized by relaxing all the other Z-matrix parameters, fixing the values of Φ ${{\rm{\Phi }}}$ and Ψ ${{{\Psi }}}$ . The MP2 level PES is constructed from the MTA-energies of chemically intact geometries using minimal hardware. The fidelity of MP2/aug-cc-pVDZ level PES is brought out by comparing it with its full calculation counterpart. Further, we bring out the power of the method by reporting the MTA-based CCSD/aug-cc-pVDZ level PES for these two dipeptides containing 498 and 562 basis functions respectively.

A double exponential coupled cluster theory in the fragment molecular orbital framework

Fragmentation-based methods enable electronic structure calculations for large chemical systems through partitioning them into smaller fragments. Here, we have developed and benchmarked a dual exponential operator-based coupled cluster theory to account for high-rank electronic correlation of large chemical systems within the fragment molecular orbital (FMO) framework. Upon partitioning the molecular system into several fragments, the zeroth order reference determinants for each fragment and fragment pair are constructed in a self-consistent manner with two-body FMO expansion. The dynamical correlation is induced through a dual exponential ansatz with a set of fragment-specific rank-one and rank-two operators that act on the individual reference determinants. While the single and double excitations for each fragment are included through the conventional rank-one and rank-two cluster operators, the triple excitation space is spanned via the contraction between the cluster operators and a set of rank-two scattering operators over a few optimized fragment-specific occupied and virtual orbitals. Thus, the high-rank dynamical correlation effects within the FMO framework are computed with rank-one and rank-two parametrization of the wave operator, leading to significant reduction in the number of variables and associated computational scaling over the conventional methods. Through a series of pilot numerical applications on various covalent and non-covalently bonded systems, we have shown the quantitative accuracy of the proposed methodology compared to canonical, as well as FMO-based coupled-cluster single double triple. The accuracy of the proposed method is shown to be systematically improvable upon increasing the number of contractible occupied and virtual molecular orbitals employed to simulate triple excitations.

Guide to tuning the chalcone molecular properties based on the push-pull effect energy scale created via the molecular tailoring approach

Using the molecular tailoring approach, a total energy scale for the push-pull effect in the range from -40 to 100 kcal/mol is created for the wide series of neutral, charged and doubly charged compounds on the chalcone platform. Taking into account similar energy scale for hydrogen bonds, the strength of the push-pull effect is ranked in the seven categories, ranging from negative (anti-push-pull) to very weak and very strong push-pull effect. It is demonstrated that the molecular properties of chalcone can be tuned prior synthesis due to the created energy scale for the push-pull effect. The single bonds of the π-spacer in the chalcones are shortened, the double ones are lengthened, and the C=O bond vibrations are red shifted when the push-pull effect is enhanced along the energy scale. The HOMO and LUMO energies change systematically while the HOMO-LUMO energy gap narrows as the strength of the push-pull effect increases.

Accelerating the Convergence of Self-Consistent Field Calculations Using the Many-Body Expansion

The balance between cost-effective and sufficiently accurate methods represents the proverbial "promised land" for quantum chemistry calculations. The burden thus falls upon theoretical and computational chemists to provide such alternatives to mitigate the issues that arise from the employ of finite computing resources. In this paper, we attempt to demonstrate the importance of the quality of the initial guess for the self-consistent field (SCF) calculation when considering cost reduction techniques. We broach this challenge by using the many body expansion (MBE) to yield high quality density matrices (DMs) which, in turn, are applied as an SCF initial guess. The MBE-DM approaches combined with purification schemes and distance-based cutoff schemes can serve as initial guesses to reduce the SCF cycles necessary for convergence or derive energy directly through one Fock build. To this end, four unique types of clusters including water clusters, fluoride anion water clusters, sodium cation water clusters, and ammonium-bisulfate salt clusters have been used to test the performance of MBE-DM where its truncation at three-body expansion, MBE(3)-DM, shows vast improvement for those four clusters with reductions in the number of SCF cycles up to 40% as compared with the traditional superposition of atomic densities (SAD) guess. Other types of typical initial guesses, superposition of atomic potentials (SAP) and basis set projection (BSP), perform much worse than MBE-DM and SAD. In addition, the MBE-DM shows consistency across an array of fragment types irrespective of charges, size, level of theory, and basis set selection. Through MBE(3)-DM with the distance cutoff and the average purification scheme, the energy can be obtained directly with a mere 3.2 mH of the mean absolute deviation (MAD) for (H₂O)_N=6-55 which is at least 73 times better than the energy prediction using the typical initial guesses (SAD, SAP, and BSP). The corresponding MAD per monomer is only 0.14 mH which reaches the threshold of the "dynamical accuracy". The promising results of the methods outlined in this paper not only indicate two direct routes for computational cost reduction but also lay the possible foundation for composite techniques (i.e., ab initio sampling) that make best use of near converged values as their starting point.

Density-Based Many-Body Expansion as an Efficient and Accurate Quantum-Chemical Fragmentation Method: Application to Water Clusters

Fragmentation methods based on the many-body expansion offer an attractive approach for the quantum-chemical treatment of large molecular systems, such as molecular clusters and crystals. Conventionally, the many-body expansion is performed for the total energy, but such an energy-based many-body expansion often suffers from a slow convergence with respect to the expansion order. For systems that show strong polarization effects such as water clusters, this can render the energy-based many-body expansion infeasible. Here, we establish a density-based many-body expansion as a promising alternative approach. By performing the many-body expansion for the electron density instead of the total energy and inserting the resulting total electron density into the total energy functional of density functional theory, one can derive a density-based energy correction, which in principle accounts for all higher-order polarization effects. Here, we systematically assess the accuracy of such a density-based many-body expansion for test sets of water clusters. We show that already a density-based two-body expansion is able to reproduce interaction energies per fragment within chemical accuracy and is able to accurately predict the energetic ordering as well as the relative interaction energies of different isomers of water clusters.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

Machine Learning for Chemical Reactions

Machine learning (ML) techniques applied to chemical reactions have a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to computational platforms for reaction planning. ML-based techniques can be particularly relevant for problems involving both computation and experiments. For one, Bayesian inference is a powerful approach to develop models consistent with knowledge from experiments. Second, ML-based methods can also be used to handle problems that are formally intractable using conventional approaches, such as exhaustive characterization of state-to-state information in reactive collisions. Finally, the explicit simulation of reactive networks as they occur in combustion has become possible using machine-learned neural network potentials. This review provides an overview of the questions that can and have been addressed using machine learning techniques, and an outlook discusses challenges in this diverse and stimulating field. It is concluded that ML applied to chemistry problems as practiced and conceived today has the potential to transform the way with which the field approaches problems involving chemical reactions, in both research and academic teaching.

Electrostatic Potential Topology for Probing Molecular Structure, Bonding and Reactivity

Following the pioneering investigations of Bader on the topology of molecular electron density, the topology analysis of its sister field viz. molecular electrostatic potential (MESP) was taken up by the authors’ groups. Through these studies, MESP topology emerged as a powerful tool for exploring molecular bonding and reactivity patterns. The MESP topology features are mapped in terms of its critical points (CPs), such as bond critical points (BCPs), while the minima identify electron-rich locations, such as lone pairs and π-bonds. The gradient paths of MESP vividly bring out the atoms-in-molecule picture of neutral molecules and anions. The MESP-based characterization of a molecule in terms of electron-rich and -deficient regions provides a robust prediction about its interaction with other molecules. This leads to a clear picture of molecular aggregation, hydrogen bonding, lone pair–π interactions, π-conjugation, aromaticity and reaction mechanisms. This review summarizes the contributions of the authors’ groups over the last three decades and those of the other active groups towards understanding chemical bonding, molecular recognition, and reactivity through topology analysis of MESP.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.

Forecasting System of Computational Time of DFT/TDDFT Calculations under the Multiverse Ansatz via Machine Learning and Cheminformatics

With the view of achieving a better performance in task assignment and load-balancing, a top-level designed forecasting system for predicting computational times of density-functional theory (DFT)/time-dependent DFT (TDDFT) calculations is presented. The computational time is assumed as the intrinsic property for the molecule. Based on this assumption, the forecasting system is established using the "reinforced concrete", which combines the cheminformatics, several machine-learning (ML) models, and the framework of many-world interpretation (MWI) in multiverse ansatz. Herein, the cheminformatics is used to recognize the topological structure of molecules, the ML models are used to build the relationships between topology and computational cost, and the MWI framework is used to hold various combinations of DFT functionals and basis sets in DFT/TDDFT calculations. Calculated results of molecules from the DrugBank dataset show that (1) it can give quantitative predictions of computational costs, typical mean relative errors can be less than 0.2 for DFT/TDDFT calculations with derivations of ±25% using the exactly pretrained ML models and (2) it can also be employed to various combinations of DFT functional and basis set cases without exactly pretrained ML models, while only slightly enlarge predicting errors.

Effective Fragment Potentials for Flexible Molecules: Transferability of Parameters and Amino Acid Database

An accurate but efficient description of noncovalent interactions is a key to predictive modeling of biological and materials systems. The effective fragment potential (EFP) is an ab initio-based force field that provides a physically meaningful decomposition of noncovalent interactions of a molecular system into Coulomb, polarization, dispersion, and exchange-repulsion components. An EFP simulation protocol consists of two steps, preparing parameters for molecular fragments by a series of ab initio calculations on each individual fragment, and calculation of interaction energy and properties of a total molecular system based on the prepared parameters. As the fragment parameters (distributed multipoles, polarizabilities, localized wave function, etc.) depend on a fragment geometry, straightforward application of the EFP method requires recomputing parameters of each fragment if its geometry changes, for example, during thermal fluctuations of a molecular system. Thus, recomputing fragment parameters can easily become both computational and human bottlenecks and lead to a loss of efficiency of a simulation protocol. An alternative approach, in which fragment parameters are adjusted to different fragment geometries, referred to as "flexible EFP", is explored here. The parameter adjustment is based on translations and rotations of local coordinate frames associated with fragment atoms. The protocol is validated on extensive benchmark of amino acid dimers extracted from molecular dynamics snapshots of a cryptochrome protein. A parameter database for standard amino acids is developed to automate flexible EFP simulations in proteins. To demonstrate applicability of flexible EFP in large-scale protein simulations, binding energies and vertical electron ionization and electron attachment energies of a lumiflavin chromophore of the cryptochrome protein are computed. The results obtained with flexible EFP are in a close agreement with the standard EFP procedure but provide a significant reduction in computational cost.

A quantum biochemistry investigation of the protein-protein interactions for the description of allosteric modulation on biomass-degrading chimera

The worldwide dependence of population on fossil fuels continues to have several harmful implications for the environment. Bioethanol is an excellent option for renewable fuel to replace the current greenhouse gas emitters. In addition, its production by enzymatic route has gained space among the industrial processes because it replaces the traditional acid treatment. Due to its high versatility, the xylanase family is used in this process as an accessory enzyme for degrading the lignocellulosic substrate of biomass. A chimera built by a xylanolytic domain (Xyl) and a xylose-binding protein (XBP) showed an experimentally improved catalytic efficiency and interdomain allosteric modulation after xylose binding. In this context, we performed a quantum biochemistry characterization of the interactions between these domains and dynamic cross-correlation (DCC) analysis after performing molecular dynamics (DM) simulations of the systems in the presence and absence of xylose in the XBP active site. We used the density functional theory (DFT) within the molecular fractionation with the conjugated caps (MFCC) approach to describe the pair energies, and the corresponding energy difference between the chimera domains responsible for the allosteric effect and amino acid DCC to evaluate the interdomain coupling differences between the energy states. The detailed energetic investigation together with the related structural and dynamics counterparts revealed the molecular mechanisms of chimeric improvement of the xylanase activity observed experimentally. This mechanism was correlated with greater stability and high connectivity at the interdomain interface in the xylose bound relative to the free chimera. We identify the contributions of hydrogen bonds, hydrophobic interactions and water-mediated interactions in the interdomain region responsible for stability together with the structural and dynamical elements related to the allosteric effect. Taken together, these observations led to a comprehensive understanding of the chimera's modulatory action that occurs through the formation of a highly connected interface that makes the essential movements related to xylanolytic activity in xylanase correlated to those of the xylose-binding protein.

Combining the Fragmentation Approach and Neural Network Potential Energy Surfaces of Fragments for Accurate Calculation of Protein Energy

Accurate and efficient all-atom quantum mechanical (QM) calculations for biomolecules still present a challenge to computational physicists and chemists. In this study, an extensible generalized molecular fractionation with a conjugate caps method combined with neural networks (NN-GMFCC) is developed for efficient QM calculation of protein energy. In the NN-GMFCC scheme, the total energy of a given protein is calculated by taking a proper combination of the high-precision neural network potential energies of all capped residues and overlapping conjugate caps. In addition, the two-body interaction energies of residue pairs are calculated by molecular mechanics (MM). With reference to the GMFCC/MM calculation at the ωB97XD/6-31G* level, the overall mean unsigned errors of the energy deviations and atomic force root-mean-squared errors calculated by NN-GMFCC are only 2.01 kcal/mol and 0.68 kcal/mol/Å, respectively, for 14 proteins (containing up to 13,728 atoms). Meanwhile, the NN-GMFCC approach is about 4 orders of magnitude faster than the GMFCC/MM method. The NN-GMFCC method could be systematically improved by inclusion of two-body QM interaction and multibody electronic polarization effect. Moreover, the NN-GMFCC approach can also be applied to other macromolecular systems such as DNA/RNA, and it is capable of providing a powerful and efficient approach for exploration of structures and functions of proteins with QM accuracy.

Fragmentation method reveals a wide spectrum of intramolecular hydrogen bond energies in antioxidant natural products

Very strong and weak IHBs in curcumin.

Quantum Mechanics/Extremely Localized Molecular Orbital Method: A Fully Quantum Mechanical Embedding Approach for Macromolecules

The development of methods for the quantum mechanical study of macromolecules has always been an important challenge in theoretical chemistry. Nowadays, the techniques proposed in this context can be used to investigate very large systems and can be subdivided into two main categories: fragmentation and embedding strategies. In this paper, by modifying and improving the local self-consistent field approach originally proposed for quantum mechanics/molecular mechanics techniques, we introduce the new multiscale embedding quantum mechanics/extremely localized molecular orbital (QM/ELMO) method. The new strategy enables treatment of chemically relevant regions of large biological molecules through usual methods of quantum chemistry while describing the remaining parts of the systems by means of frozen extremely localized molecular orbitals transferred from properly constructed libraries. Test calculations have shown the correct functioning and the high reliability of the new approach, thus anticipating its possible applications to different fields of physical chemistry, such as rational drug design and structural refinements of proteins.

A Fragment Quantum Mechanical Method for Metalloproteins

An accurate energy calculation of metalloprotein is of crucial importance and also a theoretical challenge. In this work, a metal molecular fractionation with conjugate caps (metal-MFCC) approach is developed for efficient linear-scaling quantum calculation of potential energy and atomic forces of metalloprotein. In this approach, the potential energy of a given protein is calculated by a linear combination of potential energies of the neighboring residues, two-body interaction energy between non-neighboring residues that are spatially in close contact and the potential energy of the metal binding group. The calculation of each fragment is embedded in a field of point charges representing the remaining protein environment. Numerical studies were carried out to check the performance of this method, and the calculated potential energies and atomic forces all show excellent agreement with the full system calculations at the M06-2X/6-31G(d) level. By combining the energy calculation with molecular dynamic simulation, we performed an ab initio structural optimization for a zinc finger protein with high efficiency. The present metal-MFCC approach is linear-scaling with a low prefactor and trivially parallelizable. The individual fragment typically contains about 50 atoms, and it is thus possible to be calculated at higher levels of the quantum chemistry method. This fragment method can be routinely applied to perform structural optimization and ab initio molecular dynamic simulation for metalloproteins of any size.

Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.

Harmonizing accuracy and efficiency: A pragmatic approach to fragmentation of large molecules

Fragmentation methods offer an attractive alternative for ab initio treatment of large molecules and molecular clusters. However, balancing the accuracy and efficiency of these methods is a tight-rope-act. With this in view, we present an algorithm for automatic molecular fragmentation within Molecular Tailoring Approach (MTA) achieving this delicate balance. The automated code is tested out on a variety of molecules and clusters at the Hartree-Fock (HF)- and Møller-Plesset second order perturbation theory as well as density functional theory employing augmented Dunning basis sets. The results show remarkable accuracy and efficiency vis-à-vis the respective full calculations. Thus the present work forms an important step toward the development of an MTA-based black box code for implementation of HF as well as correlated quantum chemical calculations on large molecular systems.

Full QM Calculation of RNA Energy Using Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps Method

In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree-Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol.

Molecular energies from an incremental fragmentation method

The systematic molecular fragmentation method by Collins and Deev [J. Chem. Phys. 125, 104104 (2006)] has been used to calculate total energies and relative conformational energies for a number of small and extended molecular systems. In contrast to the original approach by Collins, we have tested the accuracy of the fragmentation method by utilising an incremental scheme in which the energies at the lowest level of the fragmentation are calculated on an accurate quantum chemistry level while lower-cost methods are used to correct the low-level energies through a high-level fragmentation. In this work, the fragment energies at the lowest level of fragmentation were calculated using the random-phase approximation (RPA) and two recently developed extensions to the RPA while the incremental corrections at higher levels of the fragmentation were calculated using standard density functional theory (DFT) methods. The complete incremental fragmentation method has been shown to reproduce the supermolecule results with a very good accuracy, almost independent on the molecular type, size, or type of decomposition. The fragmentation method has also been used in conjunction with the DFT-SAPT (symmetry-adapted perturbation theory) method which enables a breakdown of the total nonbonding energy contributions into individual interaction energy terms. Finally, the potential problems of the method connected with the use of capping hydrogen atoms are analysed and two possible solutions are supplied.

The MOD-QM/MM Method: Applications to Studies of Photosystem II and DNA G-Quadruplexes

Quantum mechanics/molecular mechanics (QM/MM) hybrid methods are currently the most powerful computational tools for studies of structure/function relations and catalytic sites embedded in macrobiomolecules (eg, proteins and nucleic acids). QM/MM methodologies are highly efficient since they implement quantum chemistry methods for modeling only the portion of the system involving bond-breaking/forming processes (QM layer), as influenced by the surrounding molecular environment described in terms of molecular mechanics force fields (MM layer). Some of the limitations of QM/MM methods when polarization effects are not explicitly considered include the approximate treatment of electrostatic interactions between QM and MM layers. Here, we review recent advances in the development of computational protocols that allow for rigorous modeling of electrostatic interactions in biomacromolecules and structural refinement, beyond the common limitations of QM/MM hybrid methods. We focus on photosystem II (PSII) with emphasis on the description of the oxygen-evolving complex (OEC) and its high-resolution extended X-ray absorption fine structure spectra (EXAFS) in conjunction with Monte Carlo structural refinement. Furthermore, we review QM/MM structural refinement studies of DNA G4 quadruplexes with embedded monovalent cations and direct comparisons to NMR data.

Accurate vibrational spectra via molecular tailoring approach: a case study of water clusters at MP2 level

In spite of the recent advents in parallel algorithms and computer hardware, high-level calculation of vibrational spectra of large molecules is still an uphill task. To overcome this, significant effort has been devoted to the development of new algorithms based on fragmentation methods. The present work provides the details of an efficient and accurate procedure for computing the vibrational spectra of large clusters employing molecular tailoring approach (MTA). The errors in the Hessian matrix elements and dipole derivatives arising due to the approximation nature of MTA are reduced by grafting the corrections from a smaller basis set. The algorithm has been tested out for obtaining vibrational spectra of neutral and charged water clusters at Møller-Plesset second order level of theory, and benchmarking them against the respective full calculation (FC) and/or experimental results. For (H2O)16 clusters, the estimated vibrational frequencies are found to differ by a maximum of 2 cm(-1) with reference to the corresponding FC values. Unlike the FC, the MTA-based calculations including grafting procedure can be performed on a limited hardware, yet take a fraction of the FC time. The present methodology, thus, opens a possibility of the accurate estimation of the vibrational spectra of large molecular systems, which is otherwise impossible or formidable.

Libraries of Extremely Localized Molecular Orbitals. 1. Model Molecules Approximation and Molecular Orbitals Transferability

Despite more and more remarkable computational ab initio results are nowadays continuously obtained for large macromolecular systems, the development of new linear-scaling techniques is still an open and stimulating field of research in theoretical chemistry. In this family of methods, an important role is occupied by those strategies based on the observation that molecules are generally constituted by recurrent functional units with well-defined intrinsic features. In this context, we propose to exploit the notion of extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, or functional groups), are in principle transferable from one molecule to another. Accordingly, the construction of orbital libraries to almost instantaneously build up approximate wave functions and electron densities of very large systems becomes conceivable. In this work, the ELMOs transferability is further investigated in detail and, furthermore, suitable rules to construct model molecules for the computation of ELMOs to be stored in future databanks are also defined. The obtained results confirm the reliable transferability of the ELMOs and show that electron densities obtained from the transfer of extremely localized molecular orbitals are very close to the corresponding Hartree-Fock ones. These observations prompt us to construct new ELMOs databases that could represent an alternative/complement to the already popular pseudoatoms databanks both for determining electron densities and for refining crystallographic structures of very large molecules.

Fragment quantum chemical approach to geometry optimization and vibrational spectrum calculation of proteins

Geometry optimization and vibrational spectra (infrared and Raman spectra) calculations of proteins are carried out by a quantum chemical approach using the EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) method (J. Phys. Chem. A, 2013, 117, 7149).

Low energy isomers of (H2O)25 from a hierarchical method based on Monte Carlo temperature basin paving and molecular tailoring approaches benchmarked by MP2 calculations

We report new global minimum candidate structures for the (H2O)25 cluster that are lower in energy than the ones reported previously and correspond to hydrogen bonded networks with 42 hydrogen bonds and an interior, fully coordinated water molecule. These were obtained as a result of a hierarchical approach based on initial Monte Carlo Temperature Basin Paving sampling of the cluster's Potential Energy Surface with the Effective Fragment Potential, subsequent geometry optimization using the Molecular Tailoring Approach with the fragments treated at the second order Møller-Plesset (MP2) perturbation (MTA-MP2) and final refinement of the entire cluster at the MP2 level of theory. The MTA-MP2 optimized cluster geometries, constructed from the fragments, were found to be within <0.5 kcal/mol from the minimum geometries obtained from the MP2 optimization of the entire (H2O)25 cluster. In addition, the grafting of the MTA-MP2 energies yields electronic energies that are within <0.3 kcal/mol from the MP2 energies of the entire cluster while preserving their energy rank order. Finally, the MTA-MP2 approach was found to reproduce the MP2 harmonic vibrational frequencies, constructed from the fragments, quite accurately when compared to the MP2 ones of the entire cluster in both the HOH bending and the OH stretching regions of the spectra.

Molecular forces, geometries, and frequencies by systematic molecular fragmentation including embedded charges

The accuracy of energies, energy gradients, and hessians evaluated by systematic molecular fragmentation is examined for a wide range of neutral molecules, zwitterions, and ions. A protocol is established that may employ embedded charges in conjunction with fragmentation to provide accurate evaluation of minimum energy geometries and vibrational frequencies in an automated procedure.

Stability of conformationally locked free fructose: theoretical and computational insights

Total stabilization is governed by three predominant factors viz. the sum of energy of all H-bonds, ring strain and anomeric stabilization.

MoD-QM/MM Structural Refinement Method: Characterization of Hydrogen Bonding in the Oxytricha nova G-Quadruplex

A generalization of the Moving-Domain Quantum Mechanics/Molecular Mechanics (MoD-QM/MM) hybrid method [Gascon, J. A.; Leung, S. S. F.; Batista, E. R.; Batista, V. S. J. Chem. Theory Comput. 2006, 2, 175-186] is introduced to provide a self-consistent computational protocol for structural refinement of extended systems. The method partitions the system into molecular domains that are iteratively optimized as quantum mechanical (QM) layers embedded in their surrounding molecular environment to obtain an ab initio quality description of the geometry and the molecular electrostatic potential of the extended system composed of those constituent fragments. The resulting methodology is benchmarked as applied to model systems that allow for full QM optimization as well as through refinement of the hydrogen bonding geometry in Oxytricha nova guanine quadruplex for which several studies have been reported, including the X-ray structure and NMR data. Calculations of (1)H NMR chemical shifts based on the gauge independent atomic orbital (GIAO) method and direct comparisons with experiments show that solvated MoD-QM/MM structures, sampled from explicit solvent molecular dynamics simulations, allow for NMR simulations in much improved agreement with experimental data than models based on the X-ray structure or those optimized using classical molecular mechanics force fields.

The combined fragmentation and systematic molecular fragmentation methods

Conspectus Chemistry, particularly organic chemistry, is mostly concerned with functional groups: amines, amides, alcohols, ketones, and so forth. This is because the reactivity of molecules can be categorized in terms of the reactions of these functional groups, and by the influence of other adjacent groups in the molecule. These simple truths ought to be reflected in the electronic structure and electronic energy of molecules, as reactivity is determined by electronic structure. However, sophisticated ab initio quantum calculations of the molecular electronic energy usually do not make these truths apparent. In recent years, several computational chemistry groups have discovered methods for estimating the electronic energy as a sum of the energies of small molecular fragments, or small sets of groups. By decomposing molecules into such fragments of adjacent functional groups, researchers can estimate the electronic energy to chemical accuracy; not just qualitative trends, but accurate enough to understand reactivity. In addition, this has the benefit of cutting down on both computational time and cost, as the necessary calculation time increases rapidly with an increasing number of electrons. Even with steady advances in computer technology, progress in the study of large molecules is slow. In this Account, we describe two related "fragmentation" methods for treating molecules, the combined fragmentation method (CFM) and systematic molecular fragmentation (SMF). In addition, we show how we can use the SMF approach to estimate the energy and properties of nonconducting crystals, by fragmenting the periodic crystal structure into relatively small pieces. A large part of this Account is devoted to simple overviews of how the methods work. We also discuss the application of these approaches to calculating reactivity and other useful properties, such as the NMR and vibrational spectra of molecules and crystals. These applications rely on the ability of these fragmentation methods to accurately estimate derivatives of the molecular and crystal energies. Finally, to provide some common applications of CFM and SMF, we present some specific examples of energy calculations for moderately large molecules. For computational chemists, this fragmentation approach represents an important practical advance. It reduces the computer time required to estimate the energies of molecules so dramatically, that accurate calculations of the energies and reactivity of very large organic and biological molecules become feasible.

Fragment quantum mechanical calculation of proteins and its applications

Conspectus The desire to study molecular systems that are much larger than what the current state-of-the-art ab initio or density functional theory methods could handle has naturally led to the development of novel approximate methods, including semiempirical approaches, reduced-scaling methods, and fragmentation methods. The major computational limitation of ab initio methods is the scaling problem, because the cost of ab initio calculation scales nth power or worse with system size. In the past decade, the fragmentation approach based on chemical locality has opened a new door for developing linear-scaling quantum mechanical (QM) methods for large systems and for applications to large molecular systems such as biomolecules. The fragmentation approach is highly attractive from a computational standpoint. First, the ab initio calculation of individual fragments can be conducted almost independently, which makes it suitable for massively parallel computations. Second, the electron properties, such as density and energy, are typically combined in a linear fashion to reproduce those for the entire molecular system, which makes the overall computation scale linearly with the size of the system. In this Account, two fragmentation methods and their applications to macromolecules are described. They are the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method and the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. The EE-GMFCC method is developed from the MFCC approach, which was initially used to obtain accurate protein-ligand QM interaction energies. The main idea of the MFCC approach is that a pair of conjugate caps (concaps) is inserted at the location where the subsystem is divided by cutting the chemical bond. In addition, the pair of concaps is fused to form molecular species such that the overcounted effect from added concaps can be properly removed. By introducing the electrostatic embedding field in each fragment calculation and two-body interaction energy correction on top of the MFCC approach, the EE-GMFCC method is capable of accurately reproducing the QM molecular properties (such as the dipole moment, electron density, and electrostatic potential), the total energy, and the electrostatic solvation energy from full system calculations for proteins. On the other hand, the AF-QM/MM method was used for the efficient QM calculation of protein nuclear magnetic resonance (NMR) parameters, including the chemical shift, chemical shift anisotropy tensor, and spin-spin coupling constant. In the AF-QM/MM approach, each amino acid and all the residues in its vicinity are automatically assigned as the QM region through a distance cutoff for each residue-centric QM/MM calculation. Local chemical properties of the central residue can be obtained from individual QM/MM calculations. The AF-QM/MM approach precisely reproduces the NMR chemical shifts of proteins in the gas phase from full system QM calculations. Furthermore, via the incorporation of implicit and explicit solvent models, the protein NMR chemical shifts calculated by the AF-QM/MM method are in excellent agreement with experimental values. The applications of the AF-QM/MM method may also be extended to more general biological systems such as DNA/RNA and protein-ligand complexes.

An Angular Overlap Model for Cu(II) Ion in the AMOEBA Polarizable Force Field

An extensible polarizable force field for transition metal ion was developed based on AMOEBA and the angular overlap model (AOM) with consistent treatment of electrostatics for all atoms. Parameters were obtained by fitting molecular mechanics (MM) energies to various ab initio gas-phase calculations. The results of parameterization were presented for copper (II) ion ligated to water and model fragments of amino acid residues involved in the copper binding sites of type 1 copper proteins. Molecular dynamics (MD) simulations were performed on aqueous copper (II) ion at various temperatures, as well as plastocyanin (1AG6) and azurin (1DYZ). Results demonstrated that the AMOEBA-AOM significantly improves the accuracy of classical MM in a number of test cases when compared to ab initio calculations. The Jahn-Teller distortion for hexa-aqua copper (II) complex was handled automatically without specifically designating axial and in-plane ligands. Analyses of MD trajectories resulted in a 6-coordination first solvation shell for aqueous copper (II) ion and a 1.8ns average residence time of water molecules. The ensemble average geometries of 1AG6 and 1DYZ copper binding sites were in general agreement with X-ray and previous computational studies.