Communication: variational many-body expansion: accounting for exchange repulsion, charge delocalization, and dispersion in the fragment-based explicit polarization method

A fragment-based variational many-body (VMB) expansion method is described to directly account for exchange repulsion, charge delocalization (charge transfer) and dispersion interactions in the explicit polarization (X-Pol) method. The present VMB/X-Pol approach differs from other fragment molecular orbital (FMO) techniques in two major aspects. First, the wave function for the monomeric system is variationally optimized using standard X-Pol method, as opposed to the iterative update procedure adopted in FMO. Second, the mutual polarizations in the dimeric terms are also variationally determined, whereas single-point energy calculations of the individual dimers embedded in a static monomer field are used in FMO. The second-order (two-body) VMB (VMB2) expansion method is illustrated on a series of water hexamer complexes and one decamer cluster, making use of Hartree-Fock theory, MP2, and the PBE1 and M06 density functionals to represent the monomer and dimer fragments. The computed binding energies are within 2 kcal/mol of the corresponding results from fully delocalized calculations. Energy decomposition analyses reveal specific dimeric contributions to exchange repulsion, charge delocalization, and dispersion. Since the wave functions for one-body and all two-body terms are variationally optimized in VMB2 and X-Pol, it is straightforward to obtain analytic gradient without the additional coupled-perturbed Hartree-Fock step. Thus, the method can be useful for molecular dynamics simulations.     

Topological analysis of the molecular charge density and impact sensitivy models of energetic molecules

Important explosives of practical use are composed of nitroaromatic molecules. In this work, we optimized geometries and calculated the electron density of 17 nitroaromatic molecules using the Density Functional Theory (DFT) method. From the DFT one-electron density matrix, we computed the molecular charge densities, thus the electron densities, which were then decomposed into electric multipoles located at the atomic sites of the molecules using the distributed multipole analysis (DMA). The multipoles, which have a direct chemical interpretation, were then used to analyze in details the ground state charge structure of the molecules and to seek for correlations between charge properties and sensitivity of the corresponding energetic material. The DMA multipole moments do not present large variations when the size of the Gaussian basis set is changed; the largest variations occurred in the range 10-15% for the dipole and quadrupole moments of oxygen atoms. The charges on the carbon atoms of the aromatic ring of each molecule become more positive when the number of nitro groups increases and saturate when there are five and six nitro groups. The magnitude and the direction of the dipole moments of the carbon atoms, indicators of site polarization, also depend on the nature of adjacent groups, with the largest dipole value being for C-H bonds. The total magnitude of the quadrupole moment of the aromatic ring carbon atoms indicates a decrease in the delocalized electron density due to an electron-withdrawing effect. Three models for sensitivity of the materials based on the DMA multipoles were proposed. Explosives with large delocalized electron densities in the aromatic ring of the component molecule, expressed by large quadrupole values on the ring carbon atoms, correspond to more insensitive materials. Furthermore, the charges on the nitro groups also influence the impact sensitivity.     

High Resolution Synchrotron Diffraction Study on Charge Density Distribution of Ampicillin Trihydrate

Charge density distribution in ampicillin trihydrate was investigated experimentally. Results were compared with the quantum calculations using density functional theory. The charge derived properties including Mulliken atomic charges, dipole moment, and molecular electrostatic potential were calculated. The multipole analysis was done for the refinement of experimental population parameters. The structure factors obtained from multipole treatment were used for the construction of Fourier maps. Topological properties of the charge distribution were discussed and the characteristics of (3,-1) critical points were analyzed.     

On the representation of electrostatic fields around ab initio charge distributions

Summary We compare two methods (Mulliken charges and a distributed multipole analysis, DMA) of representing an ab initio charge distribution for calculating the electrostatic field and potential outside the molecule, using pyrimidine and the RNA base uracil as examples. This is done using a 3-D graphical display of the electrostatic fields, which, when used with real-time rotation, zooming and clipping, has many advantages for qualitatively assessing the electrostatic interactions of a molecule. The errors involved in using Mulliken point charges may be of similar magnitude to the total electrostatic field in regions which are important in recognition processes. The DMA representation automatically includes the anisotropic electrostatic effects of non-spherical features in the charge distribution of each atom, and yet the displayed electrostatic fields around the atoms which have lone-pair density do not show marked anisotropy.     

Incorporation of a QM/MM buffer zone in the variational double self-consistent field method

The explicit polarization (X-Pol) potential is an electronic-structure-based polarization force field, designed for molecular dynamics simulations and modeling of biopolymers. In this approach, molecular polarization and charge transfer effects are explicitly treated by a combined quantum mechanical and molecular mechanical (QM/MM) scheme, and the wave function of the entire system is variationally optimized by a double self-consistent field (DSCF) method. In the present article, we introduce a QM buffer zone for a smooth transition from a QM region to an MM region. Instead of using the Mulliken charge approximation for all QM/MM interactions, the Coulombic interactions between the adjacent fragments are determined directly by electronic structure theory. The present method is designed to accelerate the speed of convergence of the total energy and charge density of the system.     

Point atomic multipole moments for simulation of electrostatic potential and field in all-siliceous zeolites

Calibration method of atomic multipole moments (AMMs) is presented with respect to geometries of all-siliceous zeolite models obtained with X-ray diffraction (XRD) methods. Mulliken atomic charges and AMMs are calculated for all-siliceous types possessing small size elementary unit cells at the hybrid density functional theory (DFT) (B3LYP) and general gradient approximation (GGA) Perdew-Burke-Ernzerhof (PBE) levels and then used to fit the dependences versus geometry variables for the Mulliken charges and versus special coordinate for the AMMs. Fitted and exact charges and AMMs are used to compute electrostatic potential (EP) and electric field (EF) for all-siliceous zeolites with CRYSTAL. A possibility of application of the point AMMs to quantum mechanical/molecular mechanics computations or classic simulation of physical adsorption is evaluated. The considered models expand over wide range of structural parameters and could be applied even to amorphous all-siliceous systems.     

Partial charges by multipole constraint. Application to the amino acids

Atom-centered partial charges which exactly reproduce the lowest several multipoles of a molecule's charge distribution can be obtained in a straightforward and convenient manner from the output of existing electronic structure calculations. The multipole constraint method is demonstrated by a computation of partial charges for the twenty common amino acids. The electron density employed here, derived from a semiempirical MNDO calculation, incorporates Slater-type orbitals which imbue it with the exponential fall-off vital to electronic tunneling calculations. In addition, a procedure based on these charges is described which divides the original electron density into two components, a large component with a simple electrostatic potential, and a much smaller residual whose several lowest multipoles vanish.     

A finite expansion method for the calculation and interpretation of molecular electrostatic potentials

Because it is useful to have the molecular electrostatic potential as an element in a complex scheme to assess the toxicity of large molecules, efficient and reliable methods are needed for the calculation and characterization of these potentials. A multicenter multipole expansion of the molecular electron charge density calculated with a limited Gaussian basis set is shown here to have only a finite number of nonzero terms from which the molecular electrostatic potential can be calculated. The discrete contributions to the electrostatic potentials from the terms of this expansion provide a physically meaningful decomposition of the potential and a means for its characterization. With pyrrole as an example, the electrostatic potential calculated from this finite expansion of the electron density is compared to that obtained from exact calculations from the same wave function. Good agreement is obtained at distances greater than 1.5 A from any atom in the molecule. In contrast, rearrangement of the terms into an expansion corresponding only to Mulliken atomic charges and dipoles yields a decomposition that produces electrostatic potentials which agree less well with the exact potential. This discrepancy is attributable to the neglect of terms due to higher moments.     

Topological features of both electron density and electrostatic potential in the bis(thiosemicarbazide)zinc(II) dinitrate complex

The experimental electron density of the bis(thiosemicarbazide)zinc(II) dinitrate complex, [Zn(CH5N3S)2](NO3)2,was studied. The Hansen-Coppens multipole model was used to extract the electron density from high-resolution X-ray diffraction data collected at 100 K. Careful strategies were designed for the electron density refinements regarding the charge transfer between the anionic and the cationic parts of the complex. Particular attention was also paid to the treatment of the electron density of the zinc atom interacting with two thiosemicarbazide ligands in a tetrahedral coordination. Nevertheless, the filled 3d valence shell of Zn was found unperturbed, and only the 4s shell was engaged in the metal-ligand interaction. Topological properties of both electron density and electrostatic potential, including kinetic and potential energy densities, and atomic charges were reported to quantify a metal-ligand complex with particular Zn-S and Zn-N bonds and hydrogen-bonding features. Chemical activities were screened through the molecular surface on which the three-dimensional electrostatic potential function was projected. The experimental results were compared to those obtained from gas-phase quantum calculations, and a good agreement was reached between these two approaches. Finally, among other electrostatic potential critical points, the values at the maxima corresponding to the nuclear sites were used as indices of the hydrogen-bonding capacity of the thiosemicarbazide ligand.     

Electronic structure,Compton profiles and cohesive properties of Cs-halides

We have reported energy bands, density of states, valence electron charge densities and Compton profiles of CsCl, CsBr and CsI using linear combination of atomic orbitals with Hartree–Fock and density functional theories. We have also computed these properties, except the momentum densities, using full potential linearized augmented plane wave method. The general features of the energy bands and the density of states in these halides are found to be almost similar. To interpret the theoretical data on Compton line shapes, we have also measured the Compton profiles using our 20 Ci ¹³⁷Cs spectrometer. It is seen that the Hartree–Fock calculations give relatively a better agreement with the experimental momentum densities. On the basis of equal-valence-electron-density profiles, a comparison of relative nature of bonding is made which is in agreement with the valence charge densities and atomic charges by means of Mulliken analysis. Using our experimental and theoretical Compton profiles, we have also computed the cohesive energy of the halides.     

A multipole approximation of the electrostatic potential of molecules

The problem of approximating three-dimensional spatial distributions of quantum-mechanical electrostatic potentials of molecules by analytic potentials on the basis of atomic charges, real dipoles, and atomic multipoles up to quadrupoles inclusive was considered. Real dipole potentials are created by pairs of point charges of opposite signs, and the search for their arrangement in the volume of a molecule is part of the approximation problem. A FitMEP program was developed for the optimization of the parameters of models of the types specified taking into account molecular symmetry. It was shown for the example of several molecules (HF, CO, H₂O, NH₃, CH₄, formaldehyde, methanol, formamide, ethane, cyclopropane, cyclobutane, cyclohexane, tetrahedrane, cubane, adamantane, ethylene, and benzene) that the real dipole and atomic multipole models gave errors in approximated quantum-mechanical electrostatic potential values smaller by one or two orders of magnitude compared with the atomic charge model. The atomic charge model was shown to be virtually inoperative as applied to saturated hydrocarbons. Real dipole models were slightly inferior to atomic multipole models in quality but had all the advantages of the potential of point charges as concerned simplicity and compactness, and their use in potential energy calculations did not require changes in the existing program codes.     

Ab Initio Calculation of structures and properties of halogenated general anesthetics: halothane and sevoflurane

To correctly analyze the effects of general anesthetics on their potential targets by large‐scale molecular simulation, the structural parameters and partial atomic charges of the anesthetics are of determinant importance. Geometric optimizations using the Hartree–Fock and the B3LYP density functional theory methods with the large 6‐311+G(2d,p) basis set were performed to determine the structures and charge distributions of two halogenated anesthetics, 2‐bromo‐2‐chloro‐1,1,1‐trifluoroethane (halothane) and fluoromethyl‐2,2,2,‐trifluoro‐1‐(trifluoromethyl) ethyl ether (sevoflurane). The calculated bond lengths and angles are within 3% of the corresponding experimental values reported for the similar molecular groups. Charges are assigned using the Mulliken population analysis and the electrostatic potential (ESP) based on the Merz–Kollman–Singh scheme. The atoms‐in‐molecules (AIM) theory is also used to assign the charges in halothane. The dipole moments calculated with the Mulliken population analysis and ESP for the structures optimized by B3LYP/6‐311+(2d,p) were respectively 1.355 and 1.430 D for halothane and 2.255 and 2.315 D for sevoflurane. These are in excellent agreement with the experimental values of 1.41 and 2.33 D for halothane and sevoflurane, respectively. The calculated structures and partial charge distributions can be readily parameterized for molecular mechanics and molecular dynamics simulations involving these halogenated agents. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 436–444, 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.     

A relativistic study of the electronic and magnetic properties of cerocene and thorocene and its anions

In this study, we evaluated the importance of the relativistic effects on the optical and magnetic properties of cerocene and thorocene and its corresponding anions. The optimized molecular structures show D(8h) symmetry for all systems, in good agreement with the experimental data. Atomic charges were analyzed using different approaches (Mulliken, AIM, multipole, and NBO), and the results suggest that the net charge on the thorium is greater than on the cerium atom; however, none of the methodologies were able to predict the expected net charge Ce(III) and Th(IV) atoms. However, by an energy decomposition analysis, a significant electrostatic, ionic, interaction, ~58% and ~61%, was found between the metal and the COT(2-) rings, respectively. The calculated electronic excitations are underestimated in comparison with the experimental data, while the calculated EPR g-tensors are in agreement with previous theoretical and experimental data. Besides, the NICS analysis shows an increased ring electron delocalization due to the lanthanide and actinide metals.     

Theoretical study of 3d‐metal mononitrides using DFT method

3d‐Metal mononitrides are studied using the density functional theory method. The lowest spin state for these dimers is obtained using the B3LYP hybrid functional with the 6‐311+G* basis set. The equilibrium geometries, vibrational frequencies, binding energies, Mulliken, and natural orbital population analysis charges, natural orbital electronic configuration, electron affinity, and ionization potential are obtained. Mulliken as well as natural orbital population analysis charges indicate that for all dimers, in cations most of the positive charge localized on the transition metal atom where in anions most of the negative charge localized on nitrogen atom. The binding energies for 3d‐metal mononitrides are higher than those for monocarbides and monoxides. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Voronoi deformation density (VDD) charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD methods for charge analysis

We present the Voronoi Deformation Density (VDD) method for computing atomic charges. The VDD method does not explicitly use the basis functions but calculates the amount of electronic density that flows to or from a certain atom due to bond formation by spatial integration of the deformation density over the atomic Voronoi cell. We compare our method to the well-known Mulliken, Hirshfeld, Bader, and Weinhold [Natural Population Analysis (NPA)] charges for a variety of biological, organic, and inorganic molecules. The Mulliken charges are (again) shown to be useless due to heavy basis set dependency, and the Bader charges (and often also the NPA charges) are not realistic, yielding too extreme values that suggest much ionic character even in the case of covalent bonds. The Hirshfeld and VDD charges, which prove to be numerically very similar, are to be recommended because they yield chemically meaningful charges. We stress the need to use spatial integration over an atomic domain to get rid of basis set dependency, and the need to integrate the deformation density in order to obtain a realistic picture of the charge rearrangement upon bonding. An asset of the VDD charges is the transparency of the approach owing to the simple geometric partitioning of space. The deformation density based charges prove to conform to chemical experience.