Transition state-finding strategies for use with the growing string method

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

Scaled and Dynamic Optimizations of Nudged Elastic Bands

We present a modified nudged elastic band routine that can reduce the number of force calls by more than 50% for bands with nonuniform convergence. The method, which we call "dyNEB", dynamically and selectively optimizes images on the basis of the perpendicular PES-derived forces and parallel spring forces acting on that region of the band. The convergence criteria are scaled to focus on the region of interest, i.e., the saddle point, while maintaining continuity of the band and avoiding truncation. We show that this method works well for solid state reaction barriers-nonelectrochemical in general and electrochemical in particular-and that the number of force calls can be significantly reduced without loss of resolution at the saddle point.

Machine Learning in Computational Chemistry: An Evaluation of Method Performance for Nudged Elastic Band Calculations

The localization of transition states and the calculation of reaction pathways are routine tasks of computational chemists but often very CPU-intense problems, in particular for large systems. The standard algorithm for this purpose is the nudged elastic band method, but it has become obvious that an "intelligent" selection of points to be evaluated on the potential energy surface can improve its convergence significantly. This article summarizes, compares, and extends known strategies that have been heavily inspired by the machine learning developments of recent years. It presents advantages and disadvantages and provides an unbiased comparison of neural network based approaches, Gaussian process regression in Cartesian coordinates, and Gaussian approximation potentials. We test their performance on two example reactions, the ethane rotation and the activation of carbon dioxide on a metal catalyst, and provide a clear ranking in terms of usability for future implementations.

Fast exploration of an optimal path on the multidimensional free energy surface

In a reaction, determination of an optimal path with a high reaction rate (or a low free energy barrier) is important for the study of the reaction mechanism. This is a complicated problem that involves lots of degrees of freedom. For simple models, one can build an initial path in the collective variable space by the interpolation method first and then update the whole path constantly in the optimization. However, such interpolation method could be risky in the high dimensional space for large molecules. On the path, steric clashes between neighboring atoms could cause extremely high energy barriers and thus fail the optimization. Moreover, performing simulations for all the snapshots on the path is also time-consuming. In this paper, we build and optimize the path by a growing method on the free energy surface. The method grows a path from the reactant and extends its length in the collective variable space step by step. The growing direction is determined by both the free energy gradient at the end of the path and the direction vector pointing at the product. With fewer snapshots on the path, this strategy can let the path avoid the high energy states in the growing process and save the precious simulation time at each iteration step. Applications show that the presented method is efficient enough to produce optimal paths on either the two-dimensional or the twelve-dimensional free energy surfaces of different small molecules.

Quantum chemical approaches to [NiFe] hydrogenase

The mechanism by which [NiFe] hydrogenase catalyses the oxidation of molecular hydrogen is a significant yet challenging topic in bioinorganic chemistry. With far-reaching applications in renewable energy and carbon mitigation, significant effort has been invested in the study of these complexes. In particular, computational approaches offer a unique perspective on how this enzyme functions at an electronic and atomistic level. In this article, we discuss state-of-the art quantum chemical methods and how they have helped deepen our comprehension of [NiFe] hydrogenase. We outline the key strategies that can be used to compute the (i) geometry, (ii) electronic structure, (iii) thermodynamics and (iv) kinetic properties associated with the enzymatic activity of [NiFe] hydrogenase and other bioinorganic complexes.

Reliable and efficient reaction path and transition state finding for surface reactions with the growing string method

The computational challenge of fast and reliable transition state and reaction path optimization requires new methodological strategies to maintain low cost, high accuracy, and systematic searching capabilities. The growing string method using internal coordinates has proven to be highly effective for the study of molecular, gas phase reactions, but difficulties in choosing a suitable coordinate system for periodic systems has prevented its use for surface chemistry. New developments are therefore needed, and presented herein, to handle surface reactions which include atoms with large coordination numbers that cannot be treated using standard internal coordinates. The double-ended and single-ended growing string methods are implemented using a hybrid coordinate system, then benchmarked for a test set of 43 elementary reactions occurring on surfaces. These results show that the growing string method is at least 45% faster than the widely used climbing image-nudged elastic band method, which also fails to converge in several of the test cases. Additionally, the surface growing string method has a unique single-ended search method which can move outward from an initial structure to find the intermediates, transition states, and reaction paths simultaneously. This powerful explorative feature of single ended-growing string method is demonstrated to uncover, for the first time, the mechanism for atomic layer deposition of TiN on Cu(111) surface. This reaction is found to proceed through multiple hydrogen-transfer and ligand-exchange events, while formation of H-bonds stabilizes intermediates of the reaction. Purging gaseous products out of the reaction environment is the driving force for these reactions. © 2017 Wiley Periodicals, Inc.

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

A stochastic roadmap method to model protein structural transitions

Evidence is emerging that the role of protein structure in disease needs to be rethought. Sequence mutations in proteins are often found to affect the rate at which a protein switches between structures. Modeling structural transitions in wildtype and variant proteins is central to understanding the molecular basis of disease. This paper investigates an efficient algorithmic realization of the stochastic roadmap simulation framework to model structural transitions in wildtype and variants of proteins implicated in human disorders. Our results indicate that the algorithm is able to extract useful information on the impact of mutations on protein structure and function.

Efficiently computing pathway free energies: New approaches based on chain-of-replica and Non-Boltzmann Bennett reweighting schemes

BACKGROUND

Accurately modeling condensed phase processes is one of computation's most difficult challenges. Include the possibility that conformational dynamics may be coupled to chemical reactions, where multiscale (i.e., QM/MM) methods are needed, and this task becomes even more daunting.

METHODS

Free energy simulations (i.e., molecular dynamics), multiscale modeling, and reweighting schemes.

RESULTS

Herein, we present two new approaches for mitigating the aforementioned challenges. The first is a new chain-of-replica method (off-path simulations, OPS) for computing potentials of mean force (PMFs) along an easily defined reaction coordinate. This development is coupled with a new distributed, highly-parallel replica framework (REPDstr) within the CHARMM package. Validation of these new schemes is carried out on two processes that undergo conformational changes. First is the simple torsional rotation of butane, while a much more challenging glycosidic rotation (in vacuo and solvated) is the second. Additionally, a new approach that greatly improves (i.e., possibly an order of magnitude) the efficiency of computing QM/MM PMFs is introduced and compared to standard schemes. Our efforts are grounded in the recently developed method for efficiently computing QM-based free energies (i.e., QM-Non-Boltzmann Bennett, QM-NBB). Again, we validate this new technique by computing the QM/MM PMF of butane's torsional rotation.

CONCLUSIONS

The OPS-REPDstr method is a promising new approach that overcomes many limitations of standard pathway simulations in CHARMM. The combination of QM-NBB with pathway techniques is very promising as it offers significant advantages over current procedures.

GENERAL SIGNIFICANCE

Efficiently computing potentials of mean force is a major, unresolved, area of interest. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Automated Transition State Searches without Evaluating the Hessian

Accurate and speedy determination of transition structures (TSs) is essential for computational studies on reaction pathways, particularly when the process involves expensive electronic structure calculations. Many search algorithms require a good initial guess of the TS geometry, as well as a Hessian input that possesses a structure consistent with the desired saddle point. Among the double-ended interpolation methods for generation of the guess for the TS, the freezing string method (FSM) is proven to be far less expensive compared to its predecessor, the growing string method (GSM). In this paper, it is demonstrated that the efficiency of this technique can be improved further by replacing the conjugate gradient optimization step (FSM-CG) with a quasi-Newton line search coupled with a BFGS Hessian update (FSM-BFGS). A second crucial factor that affects the speed with which convergence to the TS is achieved is the quality and cost of the Hessian of the energy for the guessed TS. For electronic structure calculations, the cost of calculating an exact Hessian increases more rapidly with system size than the energy and gradient. Therefore, to sidestep calculation of the exact Hessian, an approximate Hessian is constructed, using the tangent direction and local curvature at the TS guess. It is demonstrated that the partitioned-rational function optimization algorithm for locating TSs with this approximate Hessian input performs at least as well as with an exact Hessian input in most test cases. The two techniques, FSM and approximate Hessian construction, therefore can significantly reduce costs associated with finding TSs.

Comparison of Three Chain-of-States Methods: Nudged Elastic Band and Replica Path with Restraints or Constraints

Chain-of-state methods are becoming important tools in studying the chemical reaction mechanisms, especially for biomacromolecules. In this article, three chain-of-state methods, nudged elastic band (NEB) method and the replica path method with restraints or constraints, were tested and compared using three model systems with various sizes and at different levels of theory: alanine dipeptide isomerization, β-alanine intramolecular condensation, and the matrix metalloproteinase 2 inhibition mechanism. The levels of theory used to describe the three model systems include molecular mechanics (MM), quantum mechanics (QM), and combined quantum mechanics and molecular mechanics (QM/MM). All three methods could correctly determine a reaction path with reasonable estimation of reaction barriers in most cases. The RMSD measurement with additional weighting schemes provides practically infinite choices of reaction coordinates to describe the reaction progress. These findings demonstrate that the chain-of-state methods are powerful tools when being used carefully to generate a plausible reaction mechanism with full pathway for complex systems at an affordable computational cost.

The Activation-Relaxation Technique: ART Nouveau and Kinetic ART

The evolution of many systems is dominated by rare activated events that occur on timescale ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the full thermal description to focus specifically on mechanisms that generate a configurational change. We present here the activation relaxation technique (ART), an open-ended saddle point search algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based on-the-fly off-lattice self-learning kinetic Monte Carlo method.

An enhanced splined saddle method

We present modifications for the method recently developed by Granot and Baer [J. Chem. Phys. 128, 184111 (2008)]. These modifications significantly enhance the efficiency and reliability of the method. In addition, we discuss some specific features of this method. These features provide important flexibilities which are crucial for a double-ended saddle point search method in order to be applicable to complex reaction mechanisms. Furthermore, it is discussed under what circumstances this methods might fail to find the transition state and remedies to avoid such situations are provided. We demonstrate the performance of the enhanced splined saddle method on several examples with increasing complexity, isomerization of ammonia, ethane and cyclopropane molecules, tautomerization of cytosine, the ring opening of cyclobutene, the Stone-Wales transformation of the C(60) fullerene, and finally rolling a small NaCl cube on NaCl(001) surface. All of these calculations are based on density functional theory. The efficiency of the method is remarkable in regard to the reduction of the total computational time.

The need for enzymatic steering in abietic acid biosynthesis: gas-phase chemical dynamics simulations of carbocation rearrangements on a bifurcating potential energy surface

Abietic acid, a constituent of pine resin, is naturally derived from abietadiene --a process that requires four enzymes: one (abietadiene synthase) for conversion of the acyclic, achiral geranylgeranyl diphosphate to the polycyclic, chiral abietadiene (a complex process involving the copalyl diphosphate intermediate) and then three to oxidize a single methyl group of abietadiene to the corresponding carboxylic acid. In previous work (Nature Chem.2009, 1, 384), electronic structure calculations on carbocation rearrangements leading to abietadienyl cation revealed an interesting potential energy surface with a bifurcating reaction pathway (two transition-state structures connected directly with no intervening minimum), which links two products--one natural and one not yet isolated from Nature. Herein we describe direct dynamics simulations of the key step in the formation of abietadiene (in the gas phase and in the absence of the enzyme). The simulations reveal that abietadiene synthase must intervene in order to produce abietadiene selectively, in essence steering this reaction to avoid the generation of byproducts with different molecular architectures.