Analytic Gradient for Density Functional Theory Based on the Fragment Molecular Orbital Method

Ab initio calculations of electric field gradients in H-bond rich molecular crystals with nearly experimental accuracy

Ab initio calculations of electric field gradients (EFGs) in molecular crystals have advanced significantly due to the gauge including projector augmented wave (GIPAW) formalism, which accounts for the infinite periodicity in crystals. However, theoretical accuracies still lag behind experimental ones, making it challenging to distinguish experimentally distinguishable similar structures, a deficiency largely attributed to the limitation of GIPAW codes to generalized gradient approximation (GGA) density functional theory (DFT) functionals. In this study, we investigate whether hybrid DFT functionals can enhance the EFG calculation accuracy and the associated geometry optimization. Using the many-body expansion method, we focus on nitrogen EFGs in amino acids with complex H-bonding, which are often poorly described with GGA functionals. Our results show that both functionals provide highly accurate calculations that surpass current studies and approach experimental precision. The accuracies are also almost three times higher than available GIPAW/GGA calculations in the literature. However, we show that this difference is not due to the GGA functional but rather due to the improper selection of the nitrogen quadrupole moment.

Accelerating Density Matrix Embedding with Stochastic Density Fitting Theory: An Application to Hydrogen Bonded Clusters

In this work, we demonstrate how using semistochastic density fitting (ss-DF) can accelerate self-consistent density matrix embedding theory (DMET) calculations by reducing the number of auxiliary orbitals in the three-indexed DF integrals. This reduction results in significant time savings when building the Hartree-Fock (HF) Coulomb and Exchange Matrices and in transforming integrals from the atomic orbital (AO) basis to the embedding orbital (EO) basis. We apply ss-DF to a range of hydrogen-bonded clusters to showcase its effectiveness. First, we examine how the amount of deterministic space impacts the quality of the calculation in a (H2O)10 cluster. Next, we test the computational efficiency of ss-DF compared to deterministic DF (d-DF) in water clusters containing 6-30 water molecules using a triple-ζ basis set. Finally, we perform numerical structural optimizations on water and hydrogen fluoride clusters, revealing that DMET can recover weak interactions using a back-transformed energy formula. This work demonstrates the potential of using stochastic resolution of identity in quantum embedding theories and highlights its capability to recover weak interactions effectively.

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.

Toward Accurate Prediction of Ion Mobility in Organic Semiconductors by Atomistic Simulation

A multiscale scheme (MLMS: Multi-Level Multi-Scale) to predict the ion mobility (μ) of amorphous organic semiconductors is proposed, which was successfully applied to the hole mobility predictions of 14 organic systems. An inverse relationship between μ and reorganization energy is observed due to local polaronic distortions. Another moderate inverse correlation between μ and distribution of site energy change exists, representing the effects of geometric flexibility. The former and the latter represent the intramolecular and intermolecular geometric effects, respectively. In addition, a linear correlation between transfer coupling and μ is observed, showing the importance of orbital overlaps between monomers. Especially, the highest hole mobility of C6-2TTN is due to its large transfer coupling. On the other hand, another high hole mobility of CBP turned out to come from the high first neighbor density (ρ_FND) of its first self-solvation, emphasizing the proper description of amorphous structural configurations with a sufficiently large number of monomers. In general, systems with either unusually high transfer coupling or high first neighbor density can potentially have high μ regardless of geometric effects. Especially, the newly suggested design parameter, ρ_FND, is pointing to a new direction as opposed to the traditional π-conjugation strategy.

Analytic Gradient for Time-Dependent Density Functional Theory Combined with the Fragment Molecular Orbital Method

The analytic energy gradient of energy with respect to nuclear coordinates is derived for the fragment molecular orbital (FMO) method combined with time-dependent density functional theory (TDDFT). The response terms arising from the use of a polarizable embedding are derived. The obtained analytic FMO-TDDFT gradient is shown to be accurate in comparison to both numerical FMO-TDDFT and unfragmented TDDFT gradients, at the level of two- and three-body expansions. The gradients are used for geometry optimizations, molecular dynamics, vibrational calculations, and simulations of IR and Raman spectra of excited states. The developed method is used to optimize the geometry of the ground and excited electronic states of the photoactive yellow protein (PDB: 2PHY).

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

Recent developments in the general atomic and molecular electronic structure system

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

Geometry Optimization, Transition State Search, and Reaction Path Mapping Accomplished with the Fragment Molecular Orbital Method

Recent development of the fragment molecular orbital (FMO) method related to energy gradients, geometry optimization, transition state search, and chemical reaction mapping is summarized. The frozen domain formulation of FMO is introduced in detail, and the structure of related GAMESS input files for FMO is described.

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.

Simulations of infrared and Raman spectra in solution using the fragment molecular orbital method

Calculation of IR and Raman spectra in solution for large molecular systems made possible with analytic FMO/PCM Hessians.

Geometry optimizations with the incremental molecular fragmentation method

Nuclear energy gradients for the incremental molecular fragmentation (IMF) method presented in our previous work [Meitei OR, Heßelmann A, Molecular energies from an incremental fragmentation method, J Chem Phys 144(8):084109, 2016] have been derived. Using the second-order Møller–Plesset perturbation theory method to describe the bonded and nonbonded energy and gradient contributions and the uncorrelated Hartree–Fock method to describe the correction increment, it is shown that the IMF gradient can be easily computed by a sum of the underlying individual derivatives of the energy contributions. The performance of the method has been compared against the supermolecular method by optimizing the structures of a range of polyglycine molecules with up to 36 glycine residues in the chain. It is shown that with a sensible set of parameters used in the fragmentation the supermolecular structures can be fairly well reproduced. In a few cases the optimization with the IMF method leads to structures that differ from the supermolecular ones. It was found, however, that these are more stable geometries also on the supermolecular potential energy surface.

Subsystem Analysis for the Fragment Molecular Orbital Method and Its Application to Protein-Ligand Binding in Solution

A subsystem analysis is derived incorporating interfragment interactions into the fragment properties, such as energies or charges. The relative stabilities of three alanine isomers, the α-helix, the β-turn, and the extended form are studied and the differences in fragment properties are elucidated. The analysis is further elaborated for studies of binding energies. The binding of the Trp-cage protein (PDB: 1L2Y ) to two ligands is studied in detail. Binding energies defined for each fragment can be used as a convenient descriptor for analyzing contributions to binding in solution.

The fragment molecular orbital method combined with density-functional tight-binding and the polarizable continuum model

The electronic gap in proteins is analyzed in detail, and it is shown that FMO-DFTB/PCM is efficient and accurate in describing the molecular structure of proteins in solution.

Large-Scale Quantum-Mechanical Molecular Dynamics Simulations Using Density-Functional Tight-Binding Combined with the Fragment Molecular Orbital Method

The fully analytic gradient is developed for density-functional tight-binding (DFTB) combined with the fragment molecular orbital (FMO) method (FMO-DFTB). The response terms arising from the coupling of the electronic state to the embedding potential are derived, and the gradient accuracy is demonstrated on water clusters and a polypeptide. The radial distribution functions (RDFs) obtained with FMO-DFTB are found to be similar to those from conventional DFTB, while the computational cost is greatly reduced; for 256 water molecules one molecular dynamics (MD) step takes 73.26 and 0.68 s with full DFTB and FMO-DFTB, respectively, showing a speed-up factor of 108. FMO-DFTB/MD is applied to 100 ps MD simulations of liquid hydrogen halides and is found to reproduce experimental RDFs reasonably well.

Quantum Fragment Based ab Initio Molecular Dynamics for Proteins

Developing ab initio molecular dynamics (AIMD) methods for practical application in protein dynamics is of significant interest. Due to the large size of biomolecules, applying standard quantum chemical methods to compute energies for dynamic simulation is computationally prohibitive. In this work, a fragment based ab initio molecular dynamics approach is presented for practical application in protein dynamics study. In this approach, the energy and forces of the protein are calculated by a recently developed electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method. For simulation in explicit solvent, mechanical embedding is introduced to treat protein interaction with explicit water molecules. This AIMD approach has been applied to MD simulations of a small benchmark protein Trpcage (with 20 residues and 304 atoms) in both the gas phase and in solution. Comparison to the simulation result using the AMBER force field shows that the AIMD gives a more stable protein structure in the simulation, indicating that quantum chemical energy is more reliable. Importantly, the present fragment-based AIMD simulation captures quantum effects including electrostatic polarization and charge transfer that are missing in standard classical MD simulations. The current approach is linear-scaling, trivially parallel, and applicable to performing the AIMD simulation of proteins with a large size.

Ab initio molecular dynamics of liquid water using embedded-fragment second-order many-body perturbation theory towards its accurate property prediction

A direct, simultaneous calculation of properties of a liquid using an ab initio electron-correlated theory has long been unthinkable. Here we present structural, dynamical, and response properties of liquid water calculated by ab initio molecular dynamics using the embedded-fragment spin-component-scaled second-order many-body perturbation method with the aug-cc-pVDZ basis set. This level of theory is chosen as it accurately and inexpensively reproduces the water dimer potential energy surface from the coupled-cluster singles, doubles, and noniterative triples with the aug-cc-pVQZ basis set, which is nearly exact. The calculated radial distribution function, self-diffusion coefficient, coordinate number, and dipole moment, as well as the infrared and Raman spectra are in excellent agreement with experimental results. The shapes and widths of the OH stretching bands in the infrared and Raman spectra and their isotropic-anisotropic Raman noncoincidence, which reflect the diverse local hydrogen-bond environment, are also reproduced computationally. The simulation also reveals intriguing dynamic features of the environment, which are difficult to probe experimentally, such as a surprisingly large fluctuation in the coordination number and the detailed mechanism by which the hydrogen donating water molecules move across the first and second shells, thereby causing this fluctuation.