Bernard R. Brooks

A computational investigation of the nitrogen-boron interaction in o-(N,N-dialkylaminomethyl)arylboronate systems.

o-(N,N-Dialkylaminomethyl)arylboronate systems are an important class of compounds in diol-sensor development. We report results from a computational investigation of fourteen o-(N,N-dialkylaminomethyl)arylboronates using second-order Møller-Plesset (MP2) perturbation theory. Geometry optimizations were performed at the MP2/cc-pVDZ level and followed by single-point calculations at the MP2/aug-cc-pVDZ(cc-pVTZ) levels. These results are compared to those from density functional theory (DFT) at the PBE1PBE(PBE1PBE-D)/6-311++G(d,p)(aug-cc-pVDZ) levels, as well as to experiment. Results from continuum PCM and CPCM solvation models were employed to assess the effects of a bulk aqueous environment. Although the behavior of o-(N,N-dialkylaminomethyl) free acid and ester proved to be complicated, we were able to extract some important trends from our calculations: (1) for the free acids the intramolecular hydrogen-bonded B-O-H···N seven-membered ring conformers 12 and 16 are found to be slightly lower in energy than the dative-bonded N→B five-membered ring conformers 10 and 14 while conformers 13 and 17, with no direct boron-nitrogen interaction, are significantly higher in energy than 12 and 16; (2) for the esters where no intramolecular B-O-H···N bonded form is possible, the N→B conformers 18 and 21 are significantly lower in energy than the no-interaction forms 20 and 23; (3) H(2)O insertion reactions into the N→B structures 10, 14, 18, and 21 leading to the seven-membered intermolecular hydrogen-bonded B···OH(2)···N ring structures 11, 15, 19, and 22 are all energetically favorable.

Comparative Study of Various Normal Mode Analysis Techniques Based on Partial Hessians

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine‐stretch, the spectrum of quinine and a bis‐cinchona derivative, and the low frequency modes of the LAO binding protein.

Vibrational subsystem analysis: A method for probing free energies and correlations in the harmonic limit

A new vibrational subsystem analysis (VSA) method is presented for coupling global motion to a local subsystem while including the inertial effects of the environment. The premise of the VSA method is a partitioning of a system into a smaller region of interest and a usually larger part referred to as environment. This method allows the investigation of local-global coupling, a more accurate estimation of vibrational free energy contribution for parts of a large system, and the elimination of the tip effect in elastic network model calculations. Additionally, the VSA method can be used as a probe of specific degrees of freedom that may contribute to free energy differences. The VSA approach can be employed in many ways, but it will likely be most useful for estimating activation free energies in QM/MM reaction path calculations. Four examples are presented to demonstrate the utility of this method.

Mobile Block Hessian Approach with Adjoined Blocks: An Efficient Approach for the Calculation of Frequencies in Macromolecules.

In an earlier work, the authors developed a new method, the mobile block Hessian (MBH) approach, to accurately calculate vibrational modes for partially optimized molecular structures [ J. Chem. Phys. 2007 , 126 ( 22 ), 224102. ]. It is based on the introduction of blocks, consisting of groups of atoms, that can move as rigid bodies. The internal geometry of the blocks need not correspond to an overall optimization state of the total molecular structure. The standard MBH approach considers free blocks with six degrees of freedom. In the extended MBH approach introduced herein, the blocks can be connected by one or two adjoining atoms, which further reduces the number of degrees of freedom. The new approach paves the way for the normal-mode analysis of biomolecules such as proteins. It rests on the hypothesis that low-frequency modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino acid residues. The method is validated for a series of small molecules and further applied to alanine dipeptide as a prototype to describe vibrational interactions between two peptide units; to crambin, a small protein with 46 amino acid residues; and to ICE/caspase-1, which contains 518 amino acid residues.

Efficient Calculation of QM/MM Frequencies with the Mobile Block Hessian

The calculation of the analytical second derivative matrix (Hessian) is the bottleneck for vibrational analysis in QM/MM systems when an electrostatic embedding scheme is employed. Even with a small number of QM atoms in the system, the presence of MM atoms increases the computational cost dramatically: the long-range Coulomb interactions require that additional coupled perturbed self-consistent field (CPSCF) equations need to be solved for each MM atom displacement. This paper presents an extension to the Mobile Block Hessian (MBH) formalism for QM/MM calculations with blocks in the MM region and its implementation in a parallel version of the Q-Chem/CHARMM interface. MBH reduces both the CPU time and the memory requirements compared to the standard full Hessian QM/MM analysis, without the need to use a cutoff distance for the electrostatic interactions. Special attention is given to the treatment of link atoms which are usually present when the QM/MM border cuts through a covalent bond. Computational efficiency improvements are highlighted using a reduced chorismate mutase enzyme system, consisting of 24 QM atoms and 306 MM atoms, as a test example. In addition, the drug bortezomib, used for cancer treatment of myeloma, has been studied as a test case with multiple MBH block choices and both a QM and QM/MM description. The accuracy of the calculated Hessians is quantified by imposing Eckart constraints, which allows for the assessment of numerical errors in second derivative procedures. The results show that MBH within the QM/MM description not only is a computationally attractive method but also produces accurate results.

Normal modes for large molecules with arbitrary link constraints in the mobile block Hessian approach.

In a previous paper [Ghysels et al., J. Chem. Phys. 126, 224102 (2007)] the mobile block Hessian (MBH) approach was presented. The method was designed to accurately compute vibrational modes of partially optimized molecular structures. The key concept was the introduction of several blocks of atoms, which can move as rigid bodies with respect to a local, fully optimized subsystem. The choice of the blocks was restricted in the sense that none of them could be connected, and also linear blocks were not taken into consideration. In this paper an extended version of the MBH method is presented that is generally applicable and allows blocks to be adjoined by one or two common atoms. This extension to all possible block partitions of the molecule provides a structural flexibility varying from very rigid to extremely relaxed. The general MBH method is very well suited to study selected normal modes of large macromolecules (such as proteins and polymers) because the number of degrees of freedom can be greatly reduced while still keeping the essential motions of the molecular system. The reduction in the number of degrees of freedom due to the block linkages is imposed here directly using a constraint method, in contrast to restraint methods where stiff harmonic couplings are introduced to restrain the relative motion of the blocks. The computational cost of this constraint method is less than that of an implementation using a restraint method. This is illustrated for the alpha-helix conformation of an alanine-20-polypeptide.

Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining †

Dimension reduction is often necessary when attempting to reach longer length and time scales in molecular simulations. It is realized by constraining degrees of freedom or by coarse‐graining the system. When evaluating the accuracy of a dimensional reduction, there is a practical challenge: the models yield vectors with different lengths, making a comparison by calculating their dot product impossible. This article investigates mapping procedures for normal mode analysis. We first review a horizontal mapping procedure for the reduced Hessian techniques, which projects out degrees of freedom. We then design a vertical mapping procedure for the “implosion” of the all‐atom (AA) Hessian to a coarse‐grained scale that is based upon vibrational subsystem analysis. This latter method derives both effective force constants and an effective kinetic tensor. Next, a series of metrics is presented for comparison across different scales, where special attention is given to proper mass‐weighting. The dimension‐dependent metrics, which require prior mapping for proper evaluation, are frequencies, overlap of normal mode vectors, probability similarity, Hessian similarity, collectivity of modes, and thermal fluctuations. The dimension‐independent metrics are shape derivatives, elastic modulus, vibrational free energy differences, heat capacity, and projection on a predefined basis set. The power of these metrics to distinguish between reasonable and unreasonable models is tested on a toy alpha helix system and a globular protein; both are represented at several scales: the AA scale, a Gō‐like model, a canonical elastic network model, and a network model with intentionally unphysical force constants. Published 2012 Wiley Periodicals, Inc.

A Computational Characterization of Boron−Oxygen Multiple Bonding in HN═CH−CH═CH−NH−BO

Structures, relative energies, and bonding characteristics for various conformers of 3-imino-N-(oxoboryl)prop-1-en-1-amine, HN=CH-CH=CH-NH-BO, and the corresponding borocycle (-HN=CH-CH=CH-NH-B-)O are discussed using results from second-order Møller-Plesset (MP2) perturbation theory with the Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets. These MP2 results are compared to those from computationally efficient density functional theory (DFT) calculations using the LDA, PBE, TPSS, BLYP, B3LYP, BVP86, OLYP, O3LYP, and PBE1PBE functionals in conjunction with the economical Pople-type 6-311++G(d,p) basis set to evaluate the suitability of these DFT/6-311++G(d,p) levels for use with larger boron-containing systems. The effects of an aqueous environment were incorporated into the calculations using COSMO methodology. The calculated boron-oxygen bond lengths, orbital compositions, and bond orders in all the (acyclic) HN=CH-CH=CH-NH-BO conformers were consistent with the presence of a boron-oxygen triple bond, similar to that found in H-BO and H2N-BO. The (-HN=CH-CH=CH-NH-B-)O borocycle is predicted to be planar (C2v symmetry), and it is approximately 30 kcal/mol lower in energy than any of the (acyclic) HN=CH-CH=CH-NH-BO conformers; the boron-oxygen bond in this borocycle has significant double bond character, a bonding scheme for which there has been only one experimental structure reported in the literature (Vidovic, D. ; et al. J. Am. Chem. Soc. 2005, 127, 4566- 4569).

Computational Investigation of the Oxidative Deboronation of Boroglycine, H2N−CH2−B(OH)2, Using H2O and H2O2

We report results from a computational investigation of the oxidative deboronation of boroglycine, H2N-CH2-B(OH)2, using H2O and H2O2 as the reactive oxygen species (ROS) to yield aminomethanol, H2N-CH2-OH; these results complement our study on the protodeboronation of boroglycine to produce methylamine, H2N-CH3 (Larkin et al. J. Phys. Chem. A 2007, 111, 6489-6500). Second-order Møller-Plesset (MP2) perturbation theory with Dunning-Woon correlation-consistent (cc) basis sets were used for the calculations with comparisons made to results from density functional theory (DFT) at the PBE1PBE/6-311++G(d,p)(cc-pVDZ) levels. The effects of a bulk aqueous environment were also incorporated into the calculations employing PCM and CPCM methodology. Using H2O as the ROS, the reaction H2O + H2N-CH2-B(OH)2 --> H2N-CH2-OH + H-B(OH)2 was calculated to be endothermic; the value of DeltaH(298)(0) was +12.0 kcal/mol at the MP2(FC)/cc-pVTZ computational level in vacuo and +13.7 kcal/mol in PCM aqueous media; the corresponding value for the activation barrier, DeltaH(double dagger), was +94.3 kcal/mol relative to the separated reactants in vacuo and +89.9 kcal/mol in PCM aqueous media. In contrast, the reaction H2O2 + H2N-CH2-B(OH)2 --> H2N-CH2-OH + B(OH)3 was calculated to be highly exothermic with an DeltaH(298)(0) value of -100.9 kcal/mol at the MP2(FC)/cc-pVTZ computational level in vacuo and -99.6 kcal/mol in CPCM aqueous media; the highest-energy transition state for the multistep process associated with this reaction involved the rearrangement of H2N-CH2-B(OH)(OOH) to H2N-CH2-O-B(OH)2 with a DeltaH(double dagger) value of +23.2 kcal/mol in vacuo relative to the separated reactants. These computational results for boroglycine are in accord with the experimental observations for the deboronation of the FDA approved anticancer drug bortezomib (Velcade, PS-341), where it was found to be the principle deactivation pathway (Labutti et al. Chem. Res. Toxicol. 2006, 19, 539-546).

Comparison of Additive and Polarizable Models with Explicit Treatment of Long-Range Lennard-Jones Interactions Using Alkane Simulations

Long-range Lennard-Jones (LJ) interactions have a significant impact on the structural and thermodynamic properties of nonpolar systems. While several methods have been introduced for the treatment of long-range LJ interactions in molecular dynamics (MD) simulations, increased accuracy and extended applicability is required for anisotropic systems such as lipid bilayers. The recently refined Lennard-Jones particle-mesh Ewald (LJ-PME) method extends the particle-mesh Ewald (PME) method to long-range LJ interactions and is suitable for use with anisotropic systems. Implementation of LJ-PME with the CHARMM36 (C36) additive and CHARMM Drude polarizable force fields improves agreement with experiment for density, isothermal compressibility, surface tension, viscosity, translational diffusion, and 13C T1 relaxation times of pure alkanes. Trends in the temperature dependence of the density and isothermal compressibility of hexadecane are also improved. While the C36 additive force field with LJ-PME remains a useful model for liquid alkanes, the Drude polarizable force field with LJ-PME is more accurate for nearly all quantities considered. LJ-PME is also preferable to the isotropic long-range correction for hexadecane because the molecular order extends to nearly 20 Å, well beyond the usual 10-12 Å cutoffs used in most simulations.