Application of the Electrostatically Embedded Many-Body Expansion to Microsolvation of Ammonia in Water Clusters

The structure of water-ammonia mixtures from classical and ab initio molecular dynamics

The structure of aqueous ammonia solutions is investigated through classical molecular dynamics (MD) and ab initio molecular dynamics (AIMD) simulations. We have preliminarily compared three well-known classical force fields for liquid water (SPC, SPC/E, and TIP4P) in order to identify the most accurate one in reproducing AIMD results obtained at the Generalized Gradient Approximation (GGA) and meta-GGA levels of theory. Liquid ammonia has been simulated by implementing an optimized force field recently developed by Chettiyankandy et al. [Fluid Phase Equilib. 511, 112507 (2020)]. Analysis of the radial distribution functions for different ammonia concentrations reveals that the three water force fields provide comparable estimates of the mixture structure, with the SPC/E performing slightly better. Although a fairly good agreement between MD and AIMD is observed for conditions close to the equimolarity, at lower ammonia concentrations, important discrepancies arise, with classical force fields underestimating the number and strength of H-bonds between water molecules and between water and ammonia moieties. Here, we prove that these drawbacks are rooted in a poor sampling of the configurational space spanned by the hydrogen atoms lying in the H-bonds of H2O⋯H2O and, more critically, H2O⋯NH3 neighbors due to the lack of polarization and charge transfer terms. This way, non-polarizable classical force fields underestimate the proton affinity of the nitrogen atom of ammonia in aqueous solutions, which plays a key role under realistic dilute ammonia conditions. Our results witness the need for developing more suited polarizable models that are able to take into account these effects properly.

A Tug of War between the Self- and Cross-associating Hydrogen Bonds in Neutral Ammonia-Water Clusters: Energetic Insights by Molecular Tailoring Approach

In the present work, the energies of various types of individual HBs observed in neutral (NH₃ )_m (H₂ O)_n , (m+n=2 to 7) clusters were estimated using the molecular tailoring approach (MTA)-based method. The calculated individual HB energies suggest that the O-H…N HBs are the strongest (1.21 to 12.49 kcal mol^-1 ). The next ones are the O-H…O (3.97 to 9.30 kcal mol^-1 ) HBs. The strengths of N-H…N (1.09 to 5.29 kcal mol^-1 ) and N-H…O (2.85 to 5.56 kcal mol^-1 ) HBs are the weakest. The HB energies in dimers also follow this rank ordering. However, the HB energies in dimers are much smaller than those obtained by the MTA-based method due to the loss in cooperativity contribution in the dimers. Thus, the calculated cooperativity contributions, for different types of HBs, fall in the range 0.64 to 5.73 kcal mol^-1 . We wish to emphasize based on the energetic rank ordering obtained by the MTA-based method that the O-H of water is a better HB donor than the N-H of ammonia. The reasons for the observed energetic rank ordering are two folds: (i) intrinsically stronger O-H…N HBs than the O-H…O ones as revealed by dimer energies and (ii) the higher cooperativity contribution in the former than the later ones. Indeed, the MTA-based method is useful in providing the missing energetic rank ordering of various type of HBs in neutral (NH₃ )_m (H₂ O)_n clusters, in the literature.

Hydrogen-Bond Topology Is More Important Than Acid/Base Strength in Atmospheric Prenucleation Clusters

We explored the hypothesis that on the nanoscale level, acids and bases might exhibit different behavior than in bulk solution. Our study system consisted of sulfuric acid, formic acid, ammonia, and water. We calculated highly accurate Domain-based Local pair-Natural Orbital- Coupled-Cluster/Complete Basis Set (DLPNO-CCSD(T)/CBS) energies on DFT geometries and used the resulting Gibbs free energies for cluster formation to compute the overall equilibrium constants for every possible cluster. The equilibrium constants combined with the initial monomer concentrations were used to predict the formation of clusters at the top and the bottom of the troposphere. Our results show that formic acid is as effective as ammonia at forming clusters with sulfuric acid and water. The structure of formic acid is uniquely suited to form hydrogen bonds with sulfuric acid. Additionally, it can partner with water to form bridges from one side of sulfuric acid to the other, hence demonstrating that hydrogen bonding topology is more important than acid/base strength in these atmospheric prenucleation clusters.

Ionization energies in solution with the QM:QM approach

We discuss a fragment-based QM:QM scheme as a practical way to access the energetics of vertical electronic processes in the condensed phase. In the QM:QM scheme, we decompose the large molecular system into small fragments, which interact solely electrostatically. The energies of the fragments are calculated in a self-consistent field generated by the other fragments and the total energy of the system is calculated as a sum of the fragment energies. We show on two test cases (cytosine and a sodium cation) that the method allows one to accurately simulate the shift of vertical ionization energies (VIE) while going from the gas phase to the bulk. For both examples, the predicted solvent shifts and peak widths estimated at the DFT level agree well with the experimental observations. We argue that the QM:QM approach is more suitable than either an electrostatic embedding based QM/MM approach, a full quantum description at the DFT level with a generally used functional or a combination of both. We also discuss the potential scope of the applicability for other electronic processes such as Auger decay.

Molecular Hydration of Carbonic Acid: Ab Initio Quantum Chemical and Density Functional Theory Investigation

Molecular hydration of carbonic acid (H₂CO₃) is investigated in terms of bonding patterns in H₂CO₃···(H₂O) _n [ n = 1-4] hydrogen-bonded clusters within ab initio quantum chemical and density functional theory (DFT) frameworks. Successive addition of water molecules to H₂CO₃···H₂O entails elongation of O-H (hydroxyl) bond as well as contraction of specific intermolecular hydrogen bonds signifying hydration of carbonic acid; these structural features get markedly enhanced under the continuum solvation framework. A comparison between the structurally similar clusters H₂CO₃···(H₂O) _n and HCOOH···(H₂O) _n [ n = 1-3] brings out the structural stability of the former. The present investigation in conjunction with the binding energy behavior of approaching water molecule(s) should serve as a precursor for pathways exploring aqueous dissociation of H₂CO₃ for larger clusters, as well as development of force-field potentials for acid dissociation process.

First UHF Implementation of the Incremental Scheme for Open-Shell Systems

The incremental scheme makes it possible to compute CCSD(T) correlation energies to high accuracy for large systems. We present the first extension of this fully automated black-box approach to open-shell systems using an Unrestricted Hartree-Fock (UHF) wave function, extending the efficient domain-specific basis set approach to handle open-shell references. We test our approach on a set of organic and metal organic structures and molecular clusters and demonstrate standard deviations from canonical CCSD(T) values of only 1.35 kJ/mol using a triple ζ basis set. We find that the incremental scheme is significantly more cost-effective than the canonical implementation even for relatively small systems and that the ease of parallelization makes it possible to perform high-level calculations on large systems in a few hours on inexpensive computers. We show that the approximations that make our approach widely applicable are significantly smaller than both the basis set incompleteness error and the intrinsic error of the CCSD(T) method, and we further demonstrate that incremental energies can be reliably used in extrapolation schemes to obtain near complete basis set limit CCSD(T) reaction energies for large systems.

Quantum mechanical fragment methods based on partitioning atoms or partitioning coordinates

Conspectus The development of more efficient and more accurate ways to represent reactive potential energy surfaces is a requirement for extending the simulation of large systems to more complex systems, longer-time dynamical processes, and more complete statistical mechanical sampling. One way to treat large systems is by direct dynamics fragment methods. Another way is by fitting system-specific analytic potential energy functions with methods adapted to large systems. Here we consider both approaches. First we consider three fragment methods that allow a given monomer to appear in more than one fragment. The first two approaches are the electrostatically embedded many-body (EE-MB) expansion and the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), which we have shown to yield quite accurate results even when one restricts the calculations to include only electrostatically embedded dimers. The third fragment method is the electrostatically embedded molecular tailoring approach (EE-MTA), which is more flexible than EE-MB and EE-MB-CE. We show that electrostatic embedding greatly improves the accuracy of these approaches compared with the original unembedded approaches. Quantum mechanical fragment methods share with combined quantum mechanical/molecular mechanical (QM/MM) methods the need to treat a quantum mechanical fragment in the presence of the rest of the system, which is especially challenging for those parts of the rest of the system that are close to the boundary of the quantum mechanical fragment. This is a delicate matter even for fragments that are not covalently bonded to the rest of the system, but it becomes even more difficult when the boundary of the quantum mechanical fragment cuts a bond. We have developed a suite of methods for more realistically treating interactions across such boundaries. These methods include redistributing and balancing the external partial atomic charges and the use of tuned fluorine atoms for capping dangling bonds, and we have shown that they can greatly improve the accuracy. Finally we present a new approach that goes beyond QM/MM by combining the convenience of molecular mechanics with the accuracy of fitting a potential function to electronic structure calculations on a specific system. To make the latter practical for systems with a large number of degrees of freedom, we developed a method to interpolate between local internal-coordinate fits to the potential energy. A key issue for the application to large systems is that rather than assigning the atoms or monomers to fragments, we assign the internal coordinates to reaction, secondary, and tertiary sets. Thus, we make a partition in coordinate space rather than atom space. Fits to the local dependence of the potential energy on tertiary coordinates are arrayed along a preselected reaction coordinate at a sequence of geometries called anchor points; the potential energy function is called an anchor points reactive potential. Electrostatically embedded fragment methods and the anchor points reactive potential, because they are based on treating an entire system by quantum mechanical electronic structure methods but are affordable for large and complex systems, have the potential to open new areas for accurate simulations where combined QM/MM methods are inadequate.

Accurate basis set truncation for wavefunction embedding

Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)] to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.

Extrapolation to the Gold-Standard in Quantum Chemistry: Computationally Efficient and Accurate CCSD(T) Energies for Large Molecules Using an Automated Thermochemical Hierarchy

The CCSD(T) method is known as the gold-standard in quantum chemistry and has been the method of choice in quantum chemistry for over 20 years to obtain accurate bond energies and molecular properties. Its computational cost formally scales as the seventh power of the size of the system and can be prohibitive for large molecules. As part of our efforts to reduce the computational cost of the CCSD(T) method yet retain its accuracy, we present a simple, efficient, and user-friendly protocol to extrapolate to CCSD(T) energies in conjunction with MP2 energies. The method is based on the automated error-canceling thermochemical hierarchy previously developed by us called the Connectivity-Based Hierarchy (CBH). For a test set containing 30 diverse nonaromatic organic molecules and biomonomers, we obtain highly accurate extrapolated CCSD(T) energies (with a mean absolute error of only 0.2-0.3 kcal/mol with different basis-set). Additionally, the work also features the successful extrapolation to CCSD energies using a similar protocol.

Analysis of the Errors in the Electrostatically Embedded Many-Body Expansion of the Energy and the Correlation Energy for Zn and Cd Coordination Complexes with Five and Six Ligands and Use of the Analysis to Develop a Generally Successful Fragmentation Strategy

In the present paper, we apply the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE) to the calculation of zinc-ligand and cadmium-ligand bond dissociation energies, and we analyze the errors due to various fragmentation schemes in a variety of neutral, positively charged, and negatively charged Zn²⁺ and Cd²⁺ coordination complexes. As a result of the analysis, we are able to present a new, simple, and unambiguous fragmentation strategy. Following this strategy, we show that both methods perform well for zinc-ligand and cadmium-ligand bond dissociation energies for all systems studied in the paper, including a model of the catalytic site of the zinc-bearing anthrax toxin lethal factor (LF), which has garnered substantial attention as a target for drug development. To draw general conclusions we consider ten pentacoordinate and hexacoordinate zinc and cadmium containing coordination complexes, each with 10 or 15 different fragmentation schemes. By analyzing errors, we developed a prescription for the optimal fragmentation strategy. With this scheme, and using MP2 correlation energies as a test, we find that the electrostatically embedded three-body expansion of the correlation energy (EE-3B-CE) method is able to reproduce all 53 conventionally calculated bond energies with an average absolute error of only 0.59 kcal/mol. The paper also presents EE-MB-CE calculations using the CCSD(T) level of theory on an LF model system. With CCSD(T), EE-3B-CE has an average error of 0.30 kcal/mol.

Electrostatically Embedded Many-Body Expansion for Neutral and Charged Metalloenzyme Model Systems

The electrostatically embedded many-body (EE-MB) method has proven accurate for calculating cohesive and conformational energies in clusters, and it has recently been extended to obtain bond dissociation energies for metal-ligand bonds in positively charged inorganic coordination complexes. In the present paper, we present four key guidelines that maximize the accuracy and efficiency of EE-MB calculations for metal centers. Then, following these guidelines, we show that the EE-MB method can also perform well for bond dissociation energies in a variety of neutral and negatively charged inorganic coordination systems representing metalloenzyme active sites, including a model of the catalytic site of the zinc-bearing anthrax toxin lethal factor, a popular target for drug development. In particular, we find that the electrostatically embedded three-body (EE-3B) method is able to reproduce conventionally calculated bond-breaking energies in a series of pentacoordinate and hexacoordinate zinc-containing systems with an average absolute error (averaged over 25 cases) of only 0.98 kcal/mol.