A half-century record of coral skeletal P/Ca reveals late 20th century nutrient pollution in Port Dickson, Malaysia.

Anthropogenic nutrient pollution has been identified as one of the key stressors of coastal ecosystems. However, the paucity of long-term nutrient records limits our understanding of both the extent of nutrient pollution as well as of the ecological impacts. Here, using coral skeletal phosphorus (P/Ca), we reconstructed a half-a-century record of seawater phosphate at Port Dickson, Malaysia. The P/Ca in the coral revealed an up to 8-fold increase in coral P/Ca from the late 1970s to 2000s, likely linked to increases in fertilizer use (R2 = 0.47) and variabilities in rainfall (R2 = 0.17). The rise in coral P/Ca in coincided with a contemporaneous 18 % decrease in coral skeletal density, suggesting phosphate enrichment may impact the growth and structural integrity of reef-building corals. Given the importance of both agriculture and heavy reliance on coral reefs by populations in Southeast Asia, our study highlights continue the need to develop environmental management upstream of coastal zones.

Modelling potential energy surfaces for small clusters using Shepard interpolation with Gaussian-form nodal functions.

The potential energy surface (PES) of a chemical system is an analytical function that outputs the potential energy of the system when a nuclear configuration is given as input. The PESs of small atmospheric clusters have theoretical as well as environmental significance. A common method used to generate analytical PESs is the Shepard interpolation, where the PES is a weighed sum of Taylor series expansions (nodal functions) at ab initio sample points. Based on this, in this study we present a new method based on the Shepard interpolation, where the nodal functions are composed of a symmetric Gaussian term and an asymmetric exponential term in each dimension. Corresponding sampling methods were also developed. We tested the method on several atmospheric bimolecular clusters and achieved root mean square errors (RMSE) below 0.13 kJ mol-1 in 150 samples for Ar-rigid H2O and Ne-rigid CO2, and below 0.39 kJ mol-1 in 1800 samples for rigid N2-rigid CO2.

When are Many-Body Effects Significant?

Many-body effects are required for an accurate description of both structure and dynamics of large chemical systems. However, there are numerous such interactions to consider, and it is not obvious which ones are significant. We provide a general and fast method for establishing which small set of three- and four-body interactions are important. This is achieved by estimating the maximum many-body effects, ϵmax, that can arise in a given arrangement of bodies. Through careful analysis of ϵmax, we find two overall causes for significant many-body interactions. First, many-body induction propagates in nonbranching paths, that is, in a chain-like manner. Second, linear arrangements of bodies promote the alignment of the dipoles to reinforce the many-body interaction. Consequently, compact and extended linear arrangements are favored. The latter result is not intuitive as these linear arrangements can lead to significant many-body effects extending over large distances. For the first time, this study provides a rigorous explanation as to how cooperative effects provide enhanced stability in helices making them one of the most common structures in biomolecules. Not only do these helices promote linear dipole alignment, but their chain-like structure is consistent with the way many-body induction propagates. Finally, using ϵmax to screen for significant many-body interactions, we are able to reproduce the total three- and four-body interaction energies using a small number of individual many-body interactions.

Comparing Vibrationally Averaged Nuclear Shielding Constants by Quantum Diffusion Monte Carlo and Second-Order Perturbation Theory.

Using the method of modified Shepard's interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second-order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard's interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations.

Many-Body Basis Set Superposition Effect.

The basis set superposition effect (BSSE) arises in electronic structure calculations of molecular clusters when questions relating to interactions between monomers within the larger cluster are asked. The binding energy, or total energy, of the cluster may be broken down into many smaller subcluster calculations and the energies of these subsystems linearly combined to, hopefully, produce the desired quantity of interest. Unfortunately, BSSE can plague these smaller fragment calculations. In this work, we carefully examine the major sources of error associated with reproducing the binding energy and total energy of a molecular cluster. In order to do so, we decompose these energies in terms of a many-body expansion (MBE), where a "body" here refers to the monomers that make up the cluster. In our analysis, we found it necessary to introduce something we designate here as a many-ghost many-body expansion (MGMBE). The work presented here produces some surprising results, but perhaps the most significant of all is that BSSE effects up to the order of truncation in a MBE of the total energy cancel exactly. In the case of the binding energy, the only BSSE correction terms remaining arise from the removal of the one-body monomer total energies. Nevertheless, our earlier work indicated that BSSE effects continued to remain in the total energy of the cluster up to very high truncation order in the MBE. We show in this work that the vast majority of these high-order many-body effects arise from BSSE associated with the one-body monomer total energies. Also, we found that, remarkably, the complete basis set limit values for the three-body and four-body interactions differed very little from that at the MP2/aug-cc-pVDZ level for the respective subclusters embedded within a larger cluster.

Modelling Water: A Lifetime Enigma.

The first attempt to describe water dates back to 1933 with the Bernal-Fowler model and it would take another forty years before the first computer simulation of liquid water by Barker and Watts in 1969. Since then, over a hundred different water models have been proposed. Despite being widely studied, water remains poorly understood. Examining the evolution of water models, we identified three distinct philosophies in water modelling, namely the employment of effective point charges in pioneering empirical models, the incorporation of polarization to describe many-body inductive effects and the extensive use of ab initio calculations to describe short-range effects. In doing so, we can appraise the current understanding of water and identify attributes that a water model should possess to capture the intricate interactions between water molecules.

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.

Trouble with the Many-Body Expansion.

Longstanding conventional wisdom dictates that the widely used Many-Body Expansion (MBE) converges rapidly by the four-body term when applied to large chemical systems. We have found, however, that this is not true for calculations using many common, moderate-sized basis sets such as 6-311++G** and aug-cc-pVDZ. Energy calculations performed on water clusters using these basis sets showed a deceptively small error when the MBE was truncated at the three-body level, while inclusion of four- and five-body contributions drastically increased the error. Moreover, the error per monomer increases with system size, showing that the MBE is unsuitable to apply to large chemical systems when using these basis sets. Through a systematic study, we identified the cause of the poor MBE convergence to be a many-body basis set superposition effect exacerbated by diffuse functions. This was verified by analysis of MO coefficients and the behavior of the MBE with increasing monomer-monomer separation. We also found poor convergence of the MBE when applied to valence-bonded systems, which has implications for molecular fragmentation methods. The findings in this work suggest that calculations involving the MBE must be performed using the full-cluster basis set, using basis sets without diffuse functions, or using a basis set of at least aug-cc-pVTZ quality.

Ab initio NMR chemical-shift calculations based on the combined fragmentation method.

NMR chemical shift is a molecular property that can be computed from first principles. In this work we show that by utilizing our combined fragmentation method (CFM), one is able to accurately compute this property for small proteins. Without nonbonded interactions, the root mean square errors (RMSEs) compared to the full calculations for (1)H, (13)C, (15)N, (17)O and (33)S were 0.340, 0.649, 3.052, 6.928 and 0.122 ppm respectively, while with the inclusion of nonbonded interactions the RMSEs for (1)H, (13)C, (15)N, (17)O and (33)S were 0.038, 0.253, 0.681, 3.480 and 0.052 ppm respectively.

Combined Fragmentation Method: A Simple Method for Fragmentation of Large Molecules.

Here we present a new energy-based fragmentation method that is based on our previous work and combines the best elements of other energy-based fragmentation methods. Our new approach, termed "combined fragmentation method", is foremost simple to implement, robust, accurate, and produces small fragments, which are independent of conformation and size of the target molecule. Essentially small collections of bonded atoms in the target molecule are assigned to groups. Fragment molecules are formed by taking all bonded pairs of these groups. These fragments are then interacted with one another, and the interaction energy is simply added to the initial fragmentation energy. The method has been tested on numerous molecules of biological interest both in vacuum and in a continuum solvent.

Distributed Multipoles and Energies of Flexible Molecules.

In this work we show that energies and distributed multipoles, up to and including rank two, can be accurately determined via a modified Shepard interpolation of ab initio data for small molecules. The molecules considered here are the amino aldehydes, Gly and Ala, which may be typical smaller fragment molecules in certain molecular energy-based fragmentation schemes. The method is general and should be suitable for applications also involving crystal structure prediction, modeling molecular clusters, and Monte Carlo or molecular/reaction dynamics simulations. The configuration space covered by the interpolation includes that sampled by the Gly and Ala peptides in protein crystal structures, i.e., 12 dimensions for Gly: 3 torsion angles (φ, ψ, ω), 5 bond lengths, and 4 bond angles and 15 dimensions for Ala: 4 torsion angles, 6 bond lengths, and 5 bond angles. In this work we also describe a new method of importance, sampling the relevant configuration spaces, and show that it is possible to interpolate "axis free" multipoles.

Accurately reproducing ab initio electrostatic potentials with multipoles and fragmentation.

In this work, we show that our energy based fragmentation method (Bettens, R. P. A.; Lee, A. M. J. Phys. Chem. A 2006, 110, 8777) accurately reproduces the electrostatic potential for a selection of peptides, both charged and uncharged, and other molecules of biological interest at the solvent accessible surface and beyond when compared with the full ab initio or density functional theory electrostatic potential. We also consider the ability of various point charge models to reproduce the full electrostatic potential and compare the results to our fragmentation electrostatic potentials with the latter being significantly superior. We demonstrate that our fragmentation approach can be readily applied to very large systems and provide the fragmentation electrostatic potential for the neuraminidase tetramer (ca. 24,000 atom system) at the MP2/6-311(+)G(2d,p) level. We also show that by using at least distributed monopoles, dipoles, and quadrupoles at atomic sites in the fragment molecules an essentially identical electrostatic potential to that given by the fragmentation electrostatic potential at and beyond the solvent accessible surface can be obtained.

The conformers of hydroxyacetaldehyde.

Both two and eighteen dimensional quantum diffusion Monte Carlo (DMC) calculations were used to study the isomers of hydroxyacetaldehyde. A total of four unique minima, and the transition states connecting them, were located. Both two and eighteen dimensional potential energy surfaces were generated and used in the DMC runs. The rotational constants for the global minimum were predicted for all experimentally identified isotopomers and an approximate equilibrium structure obtained by combining our theoretical results with the experimentally observed rotational constants. The results obtained for the remaining isomers indicate that not all of them can be isolated in the gas phase.

First principles NMR calculations by fragmentation.

The nuclear magnetic shielding tensor is a molecular property that can be computed from first principles. In this work we show that by utilizing the fragmentation approach, one is able to accurately compute this property for a large class of molecules. This is of great significance because the computational expense required in the evaluation of the shielding tensor for all nuclei in a large molecule is now subject to near linear scaling. On the basis of previous studies and this work, it is also very likely that all molecular properties that can be expressed as derivatives of the total energy of the system are also amenable to accurate evaluation via fragmentation. If only the chemical shifts for nuclei in a small part of a large molecule are of interest, then only those molecular fragments containing those nuclei need to have their shielding tensors evaluated. Further, the fragmentation approach allows one to construct a database of molecular fragments that could, in principle, be used in the NMR characterization of molecules and at the same time provide possible three-dimensional representations of these molecules.

A new algorithm for molecular fragmentation in quantum chemical calculations.

In this study, we present a "black-box" method for fragmenting a molecule with a well-defined Kekulé or valence-bond structure into a significant number of smaller fragment molecules that are more amenable to high level quantum chemical calculations. By taking an appropriate linear combination of the fragment energies, we show that it is possible in many cases to obtain highly accurate total energies when compared to the total energy of the full molecule. Our method is derived from the approach reported by Deev and Collins, but it contains significant unique elements, including an isodesmic approach to the fragmentation process. Using a method such as that described in this work it is in principle possible to obtain very accurate total energies of systems containing hundreds, if not thousands, of atoms as the approach is subject to massive parallelization.

Approximating coupled cluster level vibrational frequencies with composite methods.

An extensive study of the harmonic frequencies of a large set of small polyatomic closed-shell molecules computed at both single level ab initio and composite approximations is presented here. Using various combinations of basis sets, composite methods are capable of predicting single level ab initio CCSD(T) harmonic frequencies to within 5 cm(-1) on average, which suggests a computationally affordable means of obtaining highly accurate vibrational frequencies compared to the CCSD(T) level. A general approach for calculating the composite level equilibrium geometries and harmonic frequencies for polyatomic systems that uses the Collin's method of interpolating potential energy surfaces is also described here. This approach is further tested on tetrafluoromethane, and an estimation of the potential CPU time savings that may be obtained is also presented. It is envisaged that the findings here will enable theoretical studies of fundamental frequencies and energetics of significantly larger molecular systems.

Bound state potential energy surface construction: ab initio zero-point energies and vibrationally averaged rotational constants.

Collins' method of interpolating a potential energy surface (PES) from quantum chemical calculations for reactive systems (Jordan, M. J. T.; Thompson, K. C.; Collins, M. A. J. Chem. Phys. 1995, 102, 5647. Thompson, K. C.; Jordan, M. J. T.; Collins, M. A. J. Chem. Phys. 1998, 108, 8302. Bettens, R. P. A.; Collins, M. A. J. Chem. Phys. 1999, 111, 816) has been applied to a bound state problem. The interpolation method has been combined for the first time with quantum diffusion Monte Carlo calculations to obtain an accurate ground state zero-point energy, the vibrationally average rotational constants, and the vibrationally averaged internal coordinates. In particular, the system studied was fluoromethane using a composite method approximating the QCISD(T)/6-311++G(2df,2p) level of theory. The approach adopted in this work (a) is fully automated, (b) is fully ab initio, (c) includes all nine nuclear degrees of freedom, (d) requires no assumption of the functional form of the PES, (e) possesses the full symmetry of the system, (f) does not involve fitting any parameters of any kind, and (g) is generally applicable to any system amenable to quantum chemical calculations and Collins' interpolation method. The calculated zero-point energy agrees to within 0.2% of its current best estimate. A0 and B0 are within 0.9 and 0.3%, respectively, of experiment.