Modeling of the mutual molecular polarization with an electronegativity equalization approach

A model for the mutual polarization of two approaching molecules is proposed, exploiting the principle of electronegativity equalization. The deformation of the electronic density of one molecule is the response to the perturbation of its chemical potential due to the electrostatic potential of the other molecule. The electronic densities, the density deformations, and the electrostatic potentials of both molecules are described with a previously developed asymptotic density model (ADM ). The ADM model allows a partitioning of all relevant properties in terms of atomic quantities. The perturbation of the chemical potential is given in atomic resolution, and the change of the electronic density is represented in terms of atomic charges. A hardness tensor, which determines the changes of the atomic chemical potentials due to the changes of the atomic charges, is modeled consistently with the ADM and earlier approaches. The results of the model, the changes of atomic charges within the molecules due to their mutual interaction, are compared with the changes of atomic charges obtained from population analysis of ab initio calculations. © 1995 John Wiley & Sons, Inc.     

Progress in the understanding of drug-receptor interactions, part 2: experimental and theoretical electrostatic moments and interaction energies of an angiotensin II receptor antagonist (C30H30N6(O)3S)

A combined experimental and theoretical charge density study of an angiotensin II receptor antagonist (1) is presented focusing on electrostatic properties such as atomic charges, molecular electric moments up to the fourth rank and energies of the intermolecular interactions, to gain an insight into the physical nature of the drug-receptor interaction. Electrostatic properties were derived from both the experimental electron density (multipole refinement of X-ray data collected at T=17 K) and the ab initio wavefunction (single molecule and fully periodic calculations at the DFT level). The relevance of SO and SN intramolecular interactions on the activity of 1 is highlighted by using both the crystal and gas-phase geometries and their electrostatic nature is documented by means of QTAIM atomic charges. The derived electrostatic properties are consistent with a nearly spherical electron density distribution, characterised by an intermingling of electropositive and -negative zones rather than by a unique electrophilic region opposed to a nucleophilic area. This makes the first molecular moment scarcely significant and ill-determined, whereas the second moment is large, significant and highly reliable. A comparison between experimental and theoretical components of the third electric moment shows a few discrepancies, whereas the agreement for the fourth electric moment is excellent. The most favourable intermolecular bond is show to be an NHN hydrogen bond with an energy of about 50 kJ mol(-1). Key pharmacophoric features responsible for attractive electrostatic interactions include CHX hydrogen bonds. It is shown that methyl and methylene groups, known to be essential for the biological activity of the drug, provide a significant energetic contribution to the total binding energy. Dispersive interactions are important at the thiophene and at both the phenyl fragments. The experimental estimates of the electrostatic contribution to the intermolecular interaction energies of six molecular pairs, obtained by a new model proposed by Spackman, predict the correct relative electrostatic energies with no exceptions.     

Tailoring approach for exploring electron densities and electrostatic potentials of molecular crystals

Experimental and theoretical studies of electron densities and the corresponding derived entities such as electrostatic potentials have been the primary means of understanding the chemical nature and electronic properties of crystalline substances. Conventional crystal calculation methods such as the embedded cluster models are capable of performing calculations on small and medium-sized molecules, while periodic ab initio methods can treat crystals with up to 200 atoms per unit cell. A linear scaling method, viz. the molecular tailoring approach, has recently been developed for obtaining ab initio quality one-electron properties. In the present study, the molecular tailoring approach is employed to generate electron density, electrostatic potential and interaction density maps with the ibuprofen crystal as a test case. The interaction density and electrostatic potential maps produced in the present work succinctly bring out the actual crystalline environment around a given reference molecule by including the interactions with atoms in its neighborhood. The results obtained from the molecular tailoring approach may thus be expected to enhance our understanding of the environment in the crystalline material with reasonably small computational effort.Contribution to the Jacopo Tomasi Honorary Issue     

Electronic properties of 3,3'-dimethyl-5,5'-bis(1,2,4-triazine): towards design of supramolecular arrangements of N-heterocyclic Cu(I) complexes

A new efficient and safe synthesis of 3,3'-dimethyl-5,5'-bis-(1,2,4-triazine) is presented. The electron-density distribution and electrostatic properties (charge, electrostatic potential) of this molecule were analyzed. These properties were derived from a high-resolution single-crystal X-ray diffraction experiment at 100 K and compared to the results obtained from ab initio DFT quantum-mechanical calculations. Comparisons of its electrostatic potential features and integrated atomic charges (quantum theory of atoms in molecules, QTAIM) have been made with those of related molecules such as bipyrimidine ligands. Two methods were used to derive integrated charges: one is based on the conventional analytical procedure and the second uses a steepest-ascent numerical algorithm. Excellent agreement was obtained between these two methods. Charges and electrostatic potential were used as predictive indices of metal chelation and discussed in the light of complexation abilities of the title compound and related molecules. The crystal structure of a Cu(I) complex of 3,3'-dimethyl-5,5'-bis(1,2,4-triazine) is reported here. In the solid state, this complex forms a three-dimensional multibranch network with open channels in which counterions and solvent molecules are located. This architecture involves both cis and trans isomers of the title compound.     

Fast assignment of accurate partial atomic charges: an electronegativity equalization method that accounts for alternate resonance forms

A fast, accurate method of assigning partial atomic charges is described. The method is based upon the concept of electronegativity equalization and is parametrized to fit electrostatic potentials obtained from ab initio quantum calculations. A novel algorithm for identifying alternate resonance forms is used to ensure that chemically equivalent atoms are assigned equal charges. The resulting charges are independent of conformation, yield good agreement with ab initio electrostatic potentials, and are similar to standard force field charges for common biochemical components. The method is broadly parametrized and generates charges for a drug-like compound in about 0.45 s on a 2.26 GHz Pentium 4 PC. It should thus be useful in a range of applications, such as molecular design and QSAR. The resonance algorithm is expected to have additional applications, such as in atom-typing and detection of molecular symmetry.     

Graphene actuators: quantum-mechanical and electrostatic double-layer effects

The electrochemical actuation of covalent carbon materials, such as graphene, immersed in liquid electrolytes has shown immense promise for a myriad of applications. To realize this potential, an intimate understanding of the physics behind the actuation is essential. With the use of ab initio density functional calculations, it is shown that the strain induced in monolayer graphene by the formation of an electrostatic double-layer (DL) is the dominant actuation mechanism. The DL-induced strain (~1%) is found to exceed the quantum-mechanical strain (~0.2%) due to charge injection only, for charges and electric potentials of greater than -0.08 e/C-atom and 1 V, respectively. Various methods of calculating the graphene atomic charges based on first principle charge densities are compared and contrasted. The electrochemical charge-strain and potential-strain relationships for monolayer graphene are shown to be parabolic in nature. This study proves that the origin of the high electrochemical strains in covalent carbon materials is the electrostatic DL potential, and demonstrates the true viability of using monolayer graphene for nanoelectromechanical systems (NEMS) actuators.     

Reassessment of large dipole moment enhancements in crystals: a detailed experimental and theoretical charge density analysis of 2-methyl-4-nitroaniline

The molecular dipole moment of MNA in the crystal has been critically reexamined, to test the conclusion from an earlier experimental charge density analysis that it was substantially enhanced due to a combination of strong intermolecular interactions and crystal field effects. X-ray and neutron diffraction data have been carefully measured at 100 K and supplemented with ab initio crystal Hartree-Fock calculations. Considerable care taken in the measurement and reduction of the experimental data excluded most systematic errors, and sources of error and their effects on the experimental electron density have been carefully investigated. The electron density derived from a fit to theoretical structure factors assisted in the determination of the scale and thermal motion model. The dipole moment enhancement for MNA in the crystal is much less than that reported previously and only on the order of 30-40% (approximately 2.5 D). In addition to the dipole moment, experimental deformation electron density maps, bond critical point data, electric field gradients at hydrogen nuclei, and atomic and group charges all agree well with theoretical results and trends. Anisotropic modeling of the motion of hydrogen atoms, integral use of periodic ab initio calculations, and improved data quality are all aspects of this study that represent a considerable advance over previous work.     

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.     

Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

Molecular simulation of guanidinium-based ionic liquids

A new systematic all-atom force field was developed for cyclic guanidinium-based ionic liquids (ILs) based on the AMBER force field. Optimized molecular geometries and equilibrium bond lengths and angles were obtained by ab initio calculations, and charges were allocated to each atom center by fitting the ab initio electrostatic potential. Molecular dynamics simulations were performed for eleven kinds of ILs that are comprised of NO3(-) anions and cyclic guanidinium-based cations. Validation was carried out by comparing our simulated densities with experimental and calculated data from the literature. Transport properties such as self-diffusion coefficients, viscosities, and conductivities were calculated by molecular dynamic simulation, and their dependence on the length of the alkyl chains of cyclic guanidinium-based cations are discussed. Radial distribution functions and spatial distribution functions were investigated to depict the microscopic structures of the ILs, and the relationship between their properties and microstructures is also discussed.     

Enthalpies of Sublimation and Crystal Lattice Energies of 9-Acridinamine and its Derivatives

Enthalpies of sublimation of acridine, 9-acridinamine, N-methyl-9-acridinamine, 10-methyl-9-acridinimine, N,N-dimethyl-9-acridinamine and N-methyl-10-methyl-9-acridinimine were determined by fitting to thermogravimetric curves with the Clausius-Clapeyron relationship. These values compare well with crystal lattice energies predicted theoretically as the sum of electrostatic, dispersive and repulsive interactions. Partial charges for these calculations were obtained on an ab initio level, while atomic parameters were taken from literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electric field-derived point charges to mimic the electrostatics in molecular crystals

Because of the way the electrostatic potential is defined in a crystal, it is not possible to determine potential-derived charges for atoms in a crystal. To overcome this limitation, we present a novel method for determining atomic charges for a molecule in a crystal based on a fit to the electric field at points on a surface around the molecule. Examples of fits to the electric field at points on a Hirshfeld surface, using crystal Hartree-Fock electron densities computed with a DZP basis set are presented for several organic molecular crystals. The field-derived charges for common functional groups are transferable, and reflect chemical functionality as well as the subtle effects of intermolecular interactions. The charges also yield an excellent approximation to the electric field surrounding a molecule in a crystal for use in cluster calculations on molecules in solids.     

Theoretical calculation of electrode potentials: Electron-withdrawing compounds

The electrode potential of 2,3-dicyanobenzoquinone in aqueous solution has been calculated relative to parabenzoquinone using a thermodynamic cycle approach that includes accurate gasphase ab initio calculations and calculation of differences in free energies of hydration using the free-energy perturbation method. The discrepancy between the calculated and experimental electrode potential is disappointingly large (99 mV) compared to previous studies using this approach. This, along with the experimental evidence, suggests that the experimental value itself is too large and that theoretical approaches may indeed be as reliable as experimental ones for determining redox properties of molecules such as 2,3-dicyanobenzoquinone. In the light of this discrepancy we have examined the variation of the results with the basis set, inclusion of electron correlation and changes in the parameters used in the molecular dynamics free-energy simulations. The results are shown to be dependent upon the torsional parameters and especially dependent upon the basis set or semiempirical method used to obtain the electrostatic potential-derived charges. The best charge set was determined using the ab initio criteria of completeness—as far as it can be applied to large molecules—and also by studying the effect of hydration on these charges. This was done by allowing the solvent to perturb the wave function prior to the electrostatic potential determination. Thus, 3-21G and 6-31G * basis sets were found to give satisfactory results. Similar results were obtained using semiempirical and ab initio geometries.     

Atomic charges for molecular dynamics calculations

Atomic charges obtained with the fit of the ab initio electrostatic potential suffers of several defects, for instance, chemical meaning is not insured. We have employed a method recently put forward for deriving atomic charges which addresses the issue of chemical meaning and conformational transferability to N,N-dibutylacetamide and ethylenediaminetetraacetate. The charges have been used in molecular dynamics calculations where the interaction with a metallic cation is considered. We found structural parameters for the complexes in good agreement with the available experimental results.     

On the use of AM1 and MNDO wave functions to compute accurate electrostatic charges

A new strategy to evaluate accurate electrostatic charges from semiempirical wave functions is reported. The rigorous quantum mechanical molecular electrostatic potentials computed from both MNDO and AM1 wave functions are fitted to the point-charge molecular electrostatic potential to obtain the electrostatic charges. The reliability of this strategy is tested by comparing the semiempirical electrostatic charges for 21 molecules with the semiempirical Mulliken charges and with the ab initio STO-3G and 6-31G* electrostatic charges. The ability of the dipoles derived from the semiempirical electrostatic and Mulliken charges as well as from the SCF charge distributions to reproduce the ab initio 6-31G* electrostatic dipoles and the gas phase experimental values is determined. The statistical analysis clearly point out the goodness of the semiempirical electrostatic charges, specially when the MNDO method is used. The excellent relationships found between the MNDO and 6-31G* electrostatic charges permit to define a scaling factor which allows to accurately reproduce the 6-31G* electrostatic charge distribution as well as the experimental dipoles from the semiempirical electrostatic charges.     

A comparative molecular field analysis (CoMFA) study using semiempirical, density functional, ab initio methods and pharmacophore derivation using DISCOtech on sigma 1 ligands

The Comparative Molecular Field Analysis (CoMFA) was developed to investigate a three-dimensional quantitative structure activity relationship (3D-QSAR) model of ligands for the sigma 1 receptor. The starting geometry of sigma-1 receptor ligands was obtained from the Tripos force field minimizations and conformations were decided from DISCOtech using the SYBYL 6.8. program. The structures of 48 molecules were fully optimized at the ab initio HF/3-21G* and semiempirical AM1 calculations using GAUSSIAN 98. The electrostatic charges were calculated using several methods such as semiempirical AM1, density functional B3LYP/3-21G*, and ab initio HF/3-21G*, MP2/3-21G* calculations within GAUSSIAN 98. Using the optimized geometries, the CoMFA results derived from the HF/3-21G method were better than those from AM1. The best CoMFA was obtained from HF/3-21G* optimized geometry and charges (R2 = 0.977). Using the optimized geometries, the CoMFA results derived from the HF/3-21G methods were better than those from AM1 calculations. The training set of 43 molecules gave higher R2 (0.989-0.977) from HF/3-21G* optimized geometries than R2 (0.966-0.911) values from AM1 optimized geometries. The test set of five molecules also suggested that HF/3-21G* optimized geometries produced good CoMFA models to predict bioactivity of sigma 1 receptor ligands but AM1 optimized geometries failed to predict reasonable bioactivity of sigma 1 receptor ligands using different calculations for atomic charges.     

Quantum chemical study on the interaction of some bisphosphonates and Ca2+: The role of molecular electrostatic potentials in the prediction of binding geometry

Summary Molecular electrostatic potentials have been used to model the calcium binding properties of some bisphosphonate drugs, which are used to treat various bone diseases. The mechanism of action involves the binding of bisphosphonates to the bone surface, where calcium plays an important role. Electrostatic potential maps derived from ab initio partial charges have been compared with both the crystal structure and the fully optimized ab initio structure of (dichloro)methylenebisphosphonate-calcium ion complex. Molecular electrostatic potentials can correctly predict the calcium binding geometry of bisphosphonate-type compounds and this type of information can be used in the practical drug design work.     

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     

Conformational preferences for hydroxyl groups in substituted tetrahydropyrans

Quantum mechanical (ab initio and semiempirical) and force field calculations are reported for representative torsion potentials in several tetrahydropyran derivatives. The overall agreement between the various methods is quite good except that the AMBER torsion profiles are sensitive to the choice of atomic point charges. Using electrostatic potential (ESP) derived atomic point charges determined with the STO-3G basis set we find that AMBER is able to match the best quantum mechanical results quite well. However, when the point charges are derived using the 6-31G* basis set we find that scaling the intramolecular electrostatic nonbond interactions is necessary. AM1 does not work very well for these compounds when compared to the ab initio methods and, therefore, should only be used in cases when ab initio calculations would be prohibitive. Based upon our results we feel that any force field that makes use of 6-31G* ESP derived atomic point charges will need to scale intramolecular interactions. Implications of scaling intramolecular interactions to the development of force fields based on 6-31G* ESP derived atomic point charges are discussed. © 1992 by John Wiley & Sons, Inc.     

Minimal set of molecule-adapted atomic orbitals from maximum overlap criterion

The criterion of maximum overlap with the canonical free-atom orbitals is used to construct a minimal set of molecule-intrinsic orthogonal atomic orbitals that resemble the most their promolecular origins. Partial atomic charges derived from population analysis within representation of such molecule-adopted atomic orbitals are examined on example of first-row hydrides and compared with charges from other methods. The maximum overlap criterion is also utilized to approximate the exact free-atom orbitals obtained from ab initio calculations in any arbitrary basis set and the influence of the resulting fitted canonical atomic orbitals on properties of molecule-adopted atomic orbitals is briefly discussed.