Ryan P. A. Bettens

Learning to interpolate molecular potential energy surfaces with confidence: A Bayesian approach

A modified form of Shepard interpolation of ab initio molecular potential energy surfaces is presented. This approach yields significant improvement in accuracy over previous related schemes. Here each Taylor expansion used in the interpolation formula is assigned a confidence volume which controls the relative weight assigned to that expansion. The parameters determining this confidence volume are derived automatically from a simple Bayesian analysis of the interpolation data. As the iterative scheme expands the data set, the confidence volumes are also iteratively refined. The potential energy surfaces for nine reactions are used to illustrate the accuracy obtained.

Temperature and Solvent Effects on Radical Scavenging Ability of Phenols

In this work we have demonstrated the free radical scavenging ability of two-hydroxy (catechol, hydroquinone, resorcinol) and three-hydroxy (phloroglucinol, pyrogallol, 1,2,4-benzenetriol) phenols against the diphenylpicrylhydrazyl radical at various temperatures (15-40 degrees C) and in different solvent media. Kinetic measurements, made by the stopped-flow method, showed that the phenols with OH groups in the ortho positions have the largest rate coefficients compared to those with OH groups in the meta and para positions at all temperatures and in all solvent media. Among the ortho-structured phenols catechol, pyrogallol, and 1,2,4-benzenetriol, pyrogallol (three OH groups ortho to each other) had the greatest radical scavenging ability. This suggested that intramolecular hydrogen bonding in phenols controlled the rate of radical scavenging ability. The radical scavenging ability of phenols was fastest in methanol and slowest in THF, which emphasized the importance of the interactive behavior of the phenolic OH with the solvent. We concluded from our kinetic data together with our theoretically calculated OH bond dissociation enthalpies of phenols that the OH position played a crucial role in addition to the temperature and nature of the medium in determining the rate of the radical scavenging ability of polyphenols.

Ab initio potential energy surface for the reactions between H2O and H

Zhang acknowledges partial support from the Academic Research nGrant No. RP3991603, The National University of nSingapore.

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.

Potential energy surfaces and dynamics for the reactions between C(3P) and H3+(1A1′)

Ab initio MCSCF/6−31G** u2002adiabatic potential energy surfaces have been determined for both the ground and first excited states of triplet CH3+. Classical trajectory studies of the collision of C(3P) with H3+(1A1′) on both surfaces yield an overall rate coefficient of 2.1×10−9u2009cm3u2009s−1 for the formation of CH+ (3Π)+H2 at 10 K, in good agreement with earlier work. A rate coefficient of 4.9×10−11u2009cm3u2009s−1 at 10 K has been determined for the previously unknown reaction which produces CH2+(2A1)+H. The properties of the reaction products are examined and the accuracy of the potential energy surfaces is investigated.

Interpolated potential energy surface and dynamics for the reactions between N(4S) and H3+(1A1′)

An ab initio potential energy surface for the quartet electronic state of NH3+ has been constructed at the MP2/6-31G(d,p) level of theory. The accuracy of this surface has been verified by comparison with high levels of theory. Classical simulations of the collision of N(4S) and H3+(1A1′) showed no reaction to form NH2++H at thermal energies. The possibility of reaction via surface hopping to the doublet electronic state has been investigated by calculation of the quartet–doublet energy gap at the MRCI/6-311+G(2df,p) level of theory. No evidence of surface crossing could be found for configurations accessible at thermal energies.

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.

Interpolated potential energy surface and reaction dynamics for O(3P)+H3+(1A1′) and OH+(3Σ−)+H2(1Σg+)

An ab initio potential energy surface for the triplet state of OH3+ has been constructed at the MP2/6-311G(2d,p) level of theory. Classical simulations of the title collisions have been carried out to evaluate the rate coefficients for three reactions, including H3++O→H2O++H. Examination of the singlet-triplet energy gap across the triplet surface has shown no evidence for significant surface crossing effects on the dynamics.

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.