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.     

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.     

Halogen bonding: a theoretical study based on atomic multipoles derived from quantum theory of atoms in molecules

Atomic multipole moments derived from quantum theory of atoms in molecules are used to study halogen bonds in dihalogens (with general formula YX, in which X refers to the halogen directly interacted with the Lewis base) and some molecules containing C–X group. Multipole expansion is used to calculate the electrostatic potential in a vicinity of halogen atom (which is involved in halogen bonding) in terms of atomic monopole, dipole, and quadrupole moments. In all the cases, the zz component of atomic traceless quadrupole moments (where z axis taken along Y–X or C–X bonds) of the halogens plays a stabilizing role in halogen bond formation. The effects of atomic monopole and dipole moments on the formation of a halogen bond in YX molecules depend on Y and X atoms. In Br₂ and Cl₂, the monopole moment of halogens is zero and has no contribution in electrostatic potential and hence in halogen bonding, while in ClBr, FBr, and FCl it is positive and therefore stabilize the halogen bonds. On the other hand, the negative sign of dipole moment of X in all the YX molecules weakens the corresponding halogen bonds. In the C–X-containing molecules, monopole and dipole moments of X atom are negative and consequently destabilize the halogen bonds. So, in these molecules the quadrupole moment of X atom is the only electrostatic term which strengthens the halogen bonds. In addition, we found good linear correlations between halogen bonds strength and electrostatic potentials calculated from multipole expansion.     

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.     

Electrostatic model calculations on multiple adsorption at NaCl surfaces

A previously proposed electrostatic model for physisorption at ionic solids is extended to multiple adsorption of small molecules. A new algorithm is developed to avoid interpenetration of the interacting systems. The geometry optimization procedure is described. Ab initio calculations are used for the application of the method to the adsorption of CO and CO₂ at NaCl(100) surfaces simulated by Na₂₅Cl₂₅ clusters. The orientation of the adsorbate molecules in dependence on the cumulative atomic multipole moments (CAMMs) of the cluster atoms is discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 685–693, 1997     

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.     

Point charge representation of multicenter multipole moments in calculation of electrostatic properties

Summary Distributed Point Charge Models (PCM) for CO, (H₂O)₂, and HS-SH molecules have been computed from analytical expressions using multicenter multipole moments. The point charges (set of charges including both atomic and non-atomic positions) exactly reproduce both molecular and segmental multipole moments, thus constituting an accurate representation of the local anisotropy of electrostatic properties. In contrast to other known point charge models, PCM can be used to calculate not only intermolecular, but also intramolecular interactions. Comparison of these results with more accurate calculations demonstrated that PCM can correctly represent both weak and strong (intramolecular) interactions, thus indicating the merit of extending PCM to obtain improved potentials for molecular mechanics and molecular dynamics computational methods.Dedicated to Prof. Alberte PullmanPacific Northwest Laboratory is operated for the US Department of Energy by Battelle Memorial Institute under contract DE-ACO6-76RLO 1830     

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.     

Invariance properties of the multipole expansion with respect to the choice of the coordinate system

The physical interpretation of intermolecular interactions is usually based on the well-known multipole expansion of the inverse of the interparticle distance. The interaction energy is then interpreted as a sum of terms arising from the interaction of various multipole moments of both systems. It is supposed that the interaction energy calculated via the truncated multipole expansion generally depends on the choice of local coordinate systems through the coordinate dependence of the multipole moments. In this paper we prove that each term of the multipole expansion given in the form ∑_{k = 1} C_k/R^k is invariant with respect to identical translations and arbitrary rotations of the local coordinate systems. The invariant form of the convergence criterion of the multipole expansion is given and discussed.     

Accuracy and tractability of a kriging model of intramolecular polarizable multipolar electrostatics and its application to histidine

We propose a generic method to model polarization in the context of high‐rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc‐1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds (“1, 4 and higher” interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom–atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol^?1. © 2013 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.     

Torque and atomic forces for Cartesian tensor atomic multipoles with an application to crystal unit cell optimization

New equations for torque and atomic force are derived for use in flexible molecule force fields with atomic multipoles. The expressions are based on Cartesian tensors with arbitrary multipole rank. The standard method for rotating Cartesian tensor multipoles and calculating torque is to first represent the tensor with n indexes and 3ⁿ redundant components. In this work, new expressions for directly rotating the unique (n + 1)(n + 2)/2 Cartesian tensor multipole components Θ_pqr are given by introducing Cartesian tensor rotation matrix elements X( R ). A polynomial expression and a recursion relation for X( R ) are derived. For comparison, the analogous rotation matrix for spherical tensor multipoles are the Wigner functions D( R ). The expressions for X( R ) are used to derive simple equations for torque and atomic force. The torque and atomic force equations are applied to the geometry optimization of small molecule crystal unit cells. In addition, a discussion of computational efficiency as a function of increasing multipole rank is given for Cartesian tensors. © 2016 Wiley Periodicals, Inc.     

Point charges and atomic multipole moments of Si and O in amorphous SiO2 for the estimation of the electrostatic field and potential

In order to estimate atomic multipole moments (AMMs) and charges in the model of amorphous SiO₂ a hybrid B3LYP functional with 30% of the Hartree-Fock Hamiltonian in the exchange part with the 88-31G*(Si)/8-411G*(O) basis set and the CRYSTAL06 package are used. A 192-atomic unit cell of amorphous SiO₂ is chosen as a model, the calculations with which agree well with the experimental static factor of neutron scattering. The second optimized model of amorphous SiO₂ (a-SiO₂) with a smaller number of defects is prepared with the use of the VASP package and full optimization of the initial a-SiO₂ model. For both models the atomic charges and AMMs are calculated (up to the fourth order included) and their approximation is performed. The approximation quality is compared for these models and with a model for crystalline systems whose AMMs were previously calculated. The conclusions are drawn about the applicability of charge and AMM estimates within the approaches such as the embedded cluster.     

Cumulative coordinates for approximations of high‐order atomic multipole moments in aluminosilicate and aluminophosphate sieves*

A scheme to obtain approximate analytical functions for the atomic distributed multipole moments of the crystallographically different atoms within aluminosilicate and aluminophosphate sieves is discussed. Respective atomic multipole moments are derived within the CRYSTAL95 ab initio periodic Hartree–Fock code with different basis sets, from minimal STO‐3G to 6‐21G*. In order to illustrate the possible applications, distributed analyses are carried out for various structural models from all‐siliceous zeolites and aluminophosphates with ratio Al/P=1 to hydrogen forms of aluminosilicates. Simple approximate forms based on charge and geometry coordinates are proposed for the high‐order moments of each atom, which are further required for the calculation of the electrostatic field within the structures. The possibility to use this analytical approach to evaluate the electrostatic field within embedded cluster models is also shortly discussed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 70–85, 2001     

SCF dipole moment derivatives,harmonic frequencies and infrared intensities for C2H2 and C2H4

Analytical derivative techniques are used to obtain the dipole moment derivatives and harmonic frequencies of C₂H₂ and C₂H₄ using SCF wavefunctions and large basis sets. The infrared intensities within the harmonic approximation are obtained. The multipole moments and polarizabilities are also calculated.     

Electric and magnetic multipole integrals in STO basis sets: an analytical approach

A new method for the evaluation of one- and two-centre magnetic and electric multipole integrals for Slater-type functions is presented. The method is strictly analytical in that no approximations of any kind are involved. Two simple functions, ℐ₁ ^aug and ℐ₂ ^aug, are introduced, which employ only functions that are well known in electronic structure theory. With the use of augmentation exponents these functions apply to multipole integrals as well as other one-electron integrals, such as nuclear attraction integrals. The proposed method includes the analytic determination of derivatives of the integrals with respect to atomic displacements. Some illustrative test calculations are presented and compared to results from the literature. Received: 20 April 1998 / Accepted: 13 October 1998 / Published online: 1 February 1999     

Nonempirical Atom-Atom Potentials for Main Components of Intermolecular Interaction Energy

Atom-atom potentials representing separate contributions to the nonempirical interaction energy have been derived in the SCF decomposition scheme corrected for basis set superposition error by the counterpoise method. The nontransferable long-range electrostatic multipole and classical induction terms have been evaluated directly from cumulative atomic multipole expansions, whereas the short-range exchange, charge-transfer, and electrostatic penetration contributions have been represented by simplified potentials of the form (β + δR^?1) exp(?δR) fitted to the corresponding ab initio results for 336 dimer configurations formed by HF, H₂O, NH₃, CH₄, CO, and CO₂. The dominant anisotropic character of electrostatic multipole atom-atom potentials and much more isotropic nature of the potentials representing short-range terms is illustrated in the Appendix for head-on interactions in CO ‥ OC and HF ‥ FH dimers.