Prediction of conformationally dependent atomic multipole moments in carbohydrates

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an “atom in a molecule,” thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol^?1 for open chains and just over 90% an error of maximum 4 kJ mol^?1 for rings. © 2015 Wiley Periodicals, Inc.     

Analysis of the transferability of atomic multipoles for amino acids in modeling macromolecular charge distribution from fragments

Cumulative Atomic Multipole Moments were calculated for all natural amino acids and symmetric cyclic hexapeptides within Self‐Consisted Field (SCF) and Density Functional Theory (DFT) approaches using a standard 6‐31G(d,p) basis set. These data were used to analyze in detail the quality and the conformational and the intermolecular transferability of molecular charge distributions expressed in the atomic multipole form. Intermolecular interaction energies were reproduced reasonably by CAMM transformed from other conformations. Good transferability of CAMM based model was also achieved between similar molecular environments, which opens a route to modeling electrostatic effects in highly symmetric (e.g., crystalline) systems. Transferability deficiencies of various charge distribution models were analyzed and attributed to different levels of multipole expansion. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1082–1097, 2001     

Atomic multipoles: Electrostatic potential fit,local reference axis systems,and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges. © 2012 Wiley Periodicals, Inc.     

Atomic forces for geometry‐dependent point multipole and Gaussian multipole models

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry‐dependent multipole models. In this study, atomic force expressions for geometry‐dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives . The force equations can be applied to electrostatic models based on atomic point multipoles or Gaussian multipole charge density. Hydrogen‐bonded dimers are used to test the intermolecular electrostatic energies and atomic forces calculated by geometry‐dependent multipoles fit to the ab initio electrostatic potential. The electrostatic energies and forces are compared with their reference ab initio values. It is shown that both static and geometry‐dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, whereas geometry‐dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry‐dependent multipole models. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank

A finite field method for calculating spherical tensor molecular polarizability tensors α_lm;l′m′ = ?Δ_lm/??_l′m′* by numerical derivatives of induced molecular multipole Δ_lm with respect to gradients of electrostatic potential ?_l′m′* is described for arbitrary multipole ranks l and l′. Interconversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole–hexadecapole level are calculated for water using the following ab initio methods: Hartree–Fock (HF), Becke three‐parameter Lee‐Yang‐Parr exchange‐correlation functional (B3LYP), Møller–Plesset perturbation theory up to second order (MP2), and Coupled Cluster theory with single and double excitations (CCSD). In addition, intermolecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared with ab initio reference values calculated by the Reduced Variation Space method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

An analysis of the electrostatic interaction between nucleic acid bases

Results from several commonly used approximate methods of evaluating electrostatic interactions have been compared to the rigorous, nonexpanded electrostatic energies at both uncorrelated and correlated levels of theory. We examined a number of energy profiles for both hydrogen bonded and stacked configurations of the nucleic acid base pairs. We found that the penetration effects play an extremely important role and the expanded electrostatic energies are significantly underestimated with respect to the ab initio values. Apart from the inability to reproduce the magnitudes of the ab initio electrostatic energy, there are other problems with the available approximate electrostatic models. For example, the distributed multipole analysis, one of the most advanced methods, is extremely sensitive to the basis set and level of theory used to evaluate the multipole moments. Detailed ab initio results are provided that other researchers could use to test their approximate models.     

Near ab initio quality molecular electrostatic potential maps using hybridization displacement charges at PM3 level and effects of geometrical changes in amino groups

Charge distributions, dipole moments, and molecular electrostatic potentials (MEP) around several molecules consisting of carbon, nitrogen, oxygen, fluorine, sulfur, and chlorine atoms were studied using the PM3 semiempirical method and the results compared with those obtained using ab initio calculations at the RHF/6‐31G** level. Thus it is shown that relative MEP values near different atoms can be obtained using hybridization displacement charges (HDC) obtained by employing PM3 density matrices that usually agree quite satisfactorily with the ab initio ones. Further, positions of ab initio MEP minima are correctly located and the corresponding relative MEP values usually correctly predicted using the PM3(HDC) charges distributed continuously in three dimensions according to the forms of squares of valence s atomic orbitals. The necessary parameters for HDC calculations using the PM3 method were optimized. It is shown how within the frameworks of both PM3 and AM1 methods the π electrons or lone pairs associated with amino group nitrogen atoms and ring atoms can be satisfactorily treated in different situations. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 299–312, 2001     

SCF Deformation densities and electrostatic potentials of purines and pyrimidines

4-31G wave functions have been computed for five purines and pyrimidines. The calculated deformation densities have been partitioned into atomic fragments, which were integrated to yield atomic multipole moments. The transferability of atomic fragments between related molecules was verified by constructing model maps for uracil and guanine from appropriate fragments of cytosine and adenine. Model electrostatic potentials calculated from the moments of model atoms are similar to the corresponding 4-31G potentials. Comparison of 4-31G and 4-31G** deformation densities of cytosine provides simple rules for estimating the effects of polarization functions on the atomic multipole moments of most atom types occurring in the purines and pyrimidines. These rules were applied to the other molecules and yielded reasonable approximations for their molecular dipole moments. Substituting CH₃ for H has little effect on the deformation density beyond the substitution center.     

Cumulative potential-derived atomic multipoles

A method to derive the atomic multipole moments cumulatively up to quadrupole moments was developed. The multipole moments are obtained by least-square simulating the molecular electrostatic potentials. Only the components of the term of highest order in the atomic multipole expansion are optimized while the lower terms remain fixed. The calculations on HF, H₂O and NH₃ show that the cumulative method can give reasonable qualitative and fairly good quantitative results.     

Transferable atom equivalent multicentered multipole expansion method

The transferability of atomic and functional group properties is an implicit concept in chemistry. The work presented here describes the use of Transferable Atom Equivalents (TAE) to represent molecular electrostatic potential fields through the use of integrated atomic multipole moments that are associated with each TAE atom type used in the reconstruction. TAE molecular surface distributions of electrostatic potentials are compared with analytical ab initio and empirical (Gasteiger) partial charge reference models for several conformations of test peptides. Surface electrostatic potential distributions computed using TAE multipole representations were found to converge at the octopole level, with incremental improvement observed when hexadecapoles were included. Molecular electrostatic potential fields that were produced using the TAE method were observed to be responsive to conformational changes and to compare well with ab initio reference distributions. Generation of TAE atom types and their associated multipoles does not involve fitting to sample electrostatic potential fields, but rather utilizes integrated AIM atomic electron density distributions within representative chemical environments. The RECON program was used for TAE reconstruction. RECON is capable of processing 5,000 drug-sized molecules or 25 proteins per minute per 1.7 GHz P4 Linux processor.     

Polarisable multipolar electrostatics from the machine learning method Kriging: an application to alanine

We present a polarisable multipolar interatomic electrostatic potential energy function for force fields and describe its application to the pilot molecule MeNH-Ala-COMe (AlaD). The total electrostatic energy associated with 1, 4 and higher interactions is partitioned into atomic contributions by application of quantum chemical topology (QCT). The exact atom–atom interaction is expressed in terms of atomic multipole moments. The machine learning method Kriging is used to model the dependence of these multipole moments on the conformation of the entire molecule. The resulting models are able to predict the QCT-partitioned multipole moments for arbitrary chemically relevant molecular geometries. The interaction energies between atoms are predicted for these geometries and compared to their true values. The computational expense of the procedure is compared to that of the point charge formalism.     

Multipole moments for embedding potentials: Exploring different atomic allocation algorithms

Polarizable quantum mechanical (QM)/molecular mechanics (MM)‐embedding methods are currently among the most promising methods for computationally feasible, yet reliable, production calculations of localized excitations and molecular response properties of large molecular complexes, such as proteins and RNA/DNA, and of molecules in solution. Our aim is to develop a computational methodology for distributed multipole moments and their associated multipole polarizabilities which is accurate, computationally efficient, and with smooth convergence with respect to multipole order. As the first step toward this goal, we herein investigate different ways of obtaining distributed atom‐centered multipole moments that are used in the construction of the electrostatic part of the embedding potential. Our objective is methods that not only are accurate and computationally efficient, but which can be consistently extended with site polarizabilities including internal charge transfer terms. We present a new way of dealing with well‐known problems in relation to the use of basis sets with diffuse functions in conventional atomic allocation algorithms, avoiding numerical integration schemes. Using this approach, we show that the classical embedding potential can be systematically improved, also when using basis sets with diffuse functions, and that very accurate embedding potentials suitable for QM/MM embedding calculations can be acquired. © 2016 Wiley Periodicals, Inc.     

Low cost prediction of relative stabilities of hydrogen bonded complexes from atomic multipole moments for overly short intermolecular distances

The relative stability of biologically relevant, hydrogen bonded complexes with shortened distances can be assessed at low cost by the electrostatic multipole term alone more successfully than by ab initio methods. These results imply that atomic multipole moments may help improve ligand–receptor ranking predictions, particularly in cases where accurate structural data are not available. © 2013 Wiley Periodicals, Inc.     

A polarizable electrostatic model of the N‐methylacetamide dimer

Our previously developed polarizable electrostatic model is applied to isolated N‐methylacetamide (NMA) and to three hydrogen‐bonded configurations of the NMA dimer. Two versions of the model are studied. In the first one (POL1), polarizability along the valence bonds is described by induced bond charge increments, and polarizability perpendicular to the bonds is described by cylindrically isotropic induced atomic dipoles. In the other version (POL2), the induced bond charge increments are replaced by induced atomic dipoles along the bonds. The parameterization is done by fitting to ab initio MP2/6‐31++G(d,p) electric potentials. The polarizability parameters are determined by subjecting the NMA molecule to various external electric fields. POL1 turns out to be easier to optimize than POL2. Both models reproduce well the ab initio electric potentials, molecular dipole moments, and molecular polarizability tensors of the monomer and the dimers. Nonpolarizable models are also investigated. The results show that polarization is very important for reproducing the electric potentials of the studied dimers, indicating that this is also the case in hydrogen bonding between peptide groups in proteins. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1933–1943, 2001     

Fully polarizable QM/MM calculations: An application to the nonbonded iodine–oxygen interaction in dimethyl‐2‐iodobenzoylphosphonate

The compound dimethyl‐2‐iodobenzoylphosphonate is unusual in that it forms well‐ordered crystals that clearly show short iodine‐oxygen interactions in which both the iodine and the oxygen are in their normal oxidation states. These interactions were studied using a new hybrid quantum mechanical–molecular mechanical approach that employs a polarizable molecular mechanics component. The electric field at the molecular mechanics atoms was calculated from a distributed multipole expansion of the wave function; this induced dipoles on the molecular mechanics atoms. The electrostatic potential in a spherical shell around the induced dipoles was reproduced through induced charges on the atomic center and those bonded to it using an analytical (rather than numerical) procedure. The new atomic charges (induced charges plus permanent charges) were then able to interact with the quantum mechanical entity and polarize the wave function. The procedure was iterated to convergence. The calculations show that the iodine atom becomes more positive in the crystal environment (modeled by a chain of three molecules of dimethyl‐2‐iodobenzoylphosphonate). Thus, while the cooperative effects of the crystal environment may not be the only feature stabilizing this unusual interaction, they do play a significant role in reducing the otherwise unfavourable iodine–oxygen monopole–monopole interaction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 478–482, 2000     

The effects of atomic multipole moments obtained by the potential-derived method on hydrogen bonding

A potential-derived atomic multipole method called the cumulative potential-derived atomic multipole method is developed, with which electrostatic atomic multipole moments are derived by fitting the molecular electric potential in a cumulative way. It is applied to the hydrides of N , O , F , S , Cl , and methanol and the hydrogen-bonded dimers formed between them. The relationship between atomic multipole moments and molecular charge distributions is found. The structures calculated with Buckingham's electrostatic model are in good agreement with experiments. The phenomena of nonlinear structures of most H -bonded complexes—the deviations of symmetry axes of electron donors from H bonds—and correct distinguishing between two alternative structures are attributed to atomic dipole and quadrupole moments. Compared with other methods, this method has a quantitative and qualitative advantage and simple algorithm. The main conclusion is that the atomic multipole moments play a substantial role, although a potential-derived charge model was deemed sufficient previously. © 1993 John Wiley & Sons, Inc.