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1.  Refinement of macromolecular structures against neutron data with SHELXL2013  
Journal of Applied Crystallography  2013;47(Pt 1):462-466.
SHELXL2013 contains improvements over the previous versions that facilitate the refinement of macromolecular structures against neutron data. This article highlights several features of particular interest for this purpose and includes a list of restraints for H-atom refinement.
Some of the improvements in SHELX2013 make SHELXL convenient to use for refinement of macromolecular structures against neutron data without the support of X-ray data. The new NEUT instruction adjusts the behaviour of the SFAC instruction as well as the default bond lengths of the AFIX instructions. This work presents a protocol on how to use SHELXL for refinement of protein structures against neutron data. It includes restraints extending the Engh & Huber [Acta Cryst. (1991), A47, 392–400] restraints to H atoms and discusses several of the features of SHELXL that make the program particularly useful for the investigation of H atoms with neutron diffraction. SHELXL2013 is already adequate for the refinement of small molecules against neutron data, but there is still room for improvement, like the introduction of chain IDs for the refinement of macromolecular structures.
PMCID: PMC3937812  PMID: 24587788
single-crystal neutron diffraction; macromolecular structure refinement; hydrogen restraints; SHELXL2013
2.  JLigand: a graphical tool for the CCP4 template-restraint library 
The CCP4 template-restraint library defines restraints for biopolymers, their modifications and ligands that are used in macromolecular structure refinement. JLigand is a graphical editor for generating descriptions of new ligands and covalent linkages.
Biological macromolecules are polymers and therefore the restraints for macromolecular refinement can be subdivided into two sets: restraints that are applied to atoms that all belong to the same monomer and restraints that are associated with the covalent bonds between monomers. The CCP4 template-restraint library contains three types of data entries defining template restraints: descriptions of monomers and their modifications, both used for intramonomer restraints, and descriptions of links for intermonomer restraints. The library provides generic descriptions of modifications and links for protein, DNA and RNA chains, and for some post-translational modifications including glycosylation. Structure-specific template restraints can be defined in a user’s additional restraint library. Here, JLigand, a new CCP4 graphical interface to LibCheck and REFMAC that has been developed to manage the user’s library and generate new monomer entries is described, as well as new entries for links and associated modifications.
PMCID: PMC3322602  PMID: 22505263
macromolecular refinement; restraint library; molecular graphics
3.  An introduction to stereochemical restraints 
A brief summary of the types of restraint defined in refinement dictionaries.
At the resolution available from most macromolecular crystals, the X-ray data alone are insufficient to lead to a chemically reasonable structure, so stereochemical restraints are essential. These usually restrain bond lengths, bond angles, planes and chiral volumes. The definition of these restraints and where the values come from are described. A dictionary entry contains information about the atom types, their connectivity and all the appropriate restraints. Torsion angles are not usually restrained, but they do have optimum values. In the special case of flexible five- and six-membered rings, including pentose and hexose sugars, the ring pucker is defined by combinations of torsion angles and the pucker affects the position of substituents.
PMCID: PMC2483478  PMID: 17164527
stereochemistry; restraints; bond lengths; bond angles; protein structure; crystallographic refinement
4.  A restraint molecular dynamics and simulated annealing approach for protein homology modeling utilizing mean angles 
BMC Bioinformatics  2005;6:91.
We have developed the program PERMOL for semi-automated homology modeling of proteins. It is based on restrained molecular dynamics using a simulated annealing protocol in torsion angle space. As main restraints defining the optimal local geometry of the structure weighted mean dihedral angles and their standard deviations are used which are calculated with an algorithm described earlier by Döker et al. (1999, BBRC, 257, 348–350). The overall long-range contacts are established via a small number of distance restraints between atoms involved in hydrogen bonds and backbone atoms of conserved residues. Employing the restraints generated by PERMOL three-dimensional structures are obtained using standard molecular dynamics programs such as DYANA or CNS.
To test this modeling approach it has been used for predicting the structure of the histidine-containing phosphocarrier protein HPr from E. coli and the structure of the human peroxisome proliferator activated receptor γ (Ppar γ). The divergence between the modeled HPr and the previously determined X-ray structure was comparable to the divergence between the X-ray structure and the published NMR structure. The modeled structure of Ppar γ was also very close to the previously solved X-ray structure with an RMSD of 0.262 nm for the backbone atoms.
In summary, we present a new method for homology modeling capable of producing high-quality structure models. An advantage of the method is that it can be used in combination with incomplete NMR data to obtain reasonable structure models in accordance with the experimental data.
PMCID: PMC1127110  PMID: 15819976
5.  Integration of small angle X-ray scattering data into structural modeling of proteins and their assemblies 
Journal of molecular biology  2008;382(4):1089-1106.
A major challenge in structural biology is to determine the configuration of domains and proteins in multi-domain proteins and assemblies, respectively. To maximize the accuracy and precision of these models, all available data should be considered. Small angle x-ray scattering (SAXS) efficiently provides low-resolution experimental data about the shapes of proteins and their assemblies. Thus, we integrated SAXS profiles into our software for modeling proteins and their assemblies by satisfaction of spatial restraints. Specifically, we model the quaternary structures of multidomain proteins with structurally defined rigid domains as well as quaternary structures of binary complexes of structurally defined rigid proteins. In addition to SAXS profiles and the component structures, we employ stereochemical restraints and an atomic distance-dependent statistical potential. The scoring function is optimized by a biased Monte Carlo protocol, including quasi-Newton and simulated annealing schemes. The final prediction corresponds to the best scoring solution in the largest cluster of many independently calculated solutions. To quantify how well the quaternary structures are determined based on their SAXS profiles, we used a benchmark of 12 simulated examples as well as an experimental SAXS profile of the homo-tetramer D-xylose isomerase. Optimization of the SAXS-dependent scoring function generally results in accurate models, if sufficiently precise approximations for the constituent rigid bodies are available; otherwise, the best scoring models can have significant errors. Thus, SAXS profiles can play a useful role in the structural characterization of proteins and assemblies, if they are combined with additional data and used judiciously. Our integration of a SAXS profile into modeling by satisfaction of spatial restraints will facilitate further integration of different kinds of data for structure determination of proteins and their assemblies.
PMCID: PMC2745287  PMID: 18694757
small-angle X-ray scattering; quaternary structure; macromolecular assembly modeling; statistical potentials; protein structure prediction
6.  Disparate Behavior of Carbonyl and Thiocarbonyl Compounds: Acyl Chlorides vs Thiocarbonyl Chlorides and Isocyanates vs Isothiocyanates 
The Journal of organic chemistry  2009;74(10):3659-3664.
The reaction of benzoyl chloride with methanol catalyzed by pyridine is 9 times more rapid than is the same reaction with thiobenzoyl chloride. The difference in reactivity, as well as the dealkylation reactions that occur when the reaction of thiobenzoyl chloride is catalyzed by bases such as Et3N, can be understood in terms of the charge distributions in the intermediate acylammonium ions. The reaction of PhNCO with ethanol occurs at a much higher rate (4.8 × 104) than that of PhNCS, corresponding to a difference in activation free energies for the additions of 6 kcal/mol. Transition states for each of these reactions were located, and each involves two alcohol molecules in a hydrogen bonded six-membered ring arrangement. Information concerning differences in reactivity was derived from analysis of Hirshfeld atomic charge distributions and calculated hydrogenolysis reaction energies.
PMCID: PMC2754232  PMID: 19371054
7.  Atomistic insights into rhodopsin activation from a dynamic model 
Journal of the American Chemical Society  2008;130(31):10141-10149.
Rhodopsin, the light sensitive receptor responsible for blue-green vision, serves as a prototypical G protein-coupled receptor (GPCR). Upon light absorption, it undergoes a series of conformational changes that lead to the active form, metarhodopsin II (META II), initiating a signaling cascade through binding to the G protein transducin (Gt). Here, we first develop a structural model of META II by applying experimental distance restraints to the structure of lumi-rhodopsin (LUMI), an earlier intermediate. The restraints are imposed by using a combination of biased molecular dynamics simulations and perturbations to an elastic network model. We characterize the motions of the transmembrane helices in the LUMI-to-META II transition, and the rearrangement of interhelical hydrogen bonds. We then simulate rhodopsin activation in a dynamic model to study the path leading from LUMI to our META II model for wild-type rhodopsin and a series of mutants. Those simulations show a strong correlation between the transition dynamics and the pharmacological phenotypes of the mutants. These results help identify the molecular mechanisms of activation in both wild type and mutant rhodopsin. While static models can provide insights into the mechanisms of ligand recognition and predict ligand affinity, a dynamic model of activation could be applicable to study the pharmacology of other GPCRs and their ligands, offering a key to predictions of basal activity and ligand efficacy.
PMCID: PMC2556288  PMID: 18620390
8.  Specific Non-Local Interactions Are Not Necessary for Recovering Native Protein Dynamics 
PLoS ONE  2014;9(3):e91347.
The elastic network model (ENM) is a widely used method to study native protein dynamics by normal mode analysis (NMA). In ENM we need information about all pairwise distances, and the distance between contacting atoms is restrained to the native value. Therefore ENM requires O(N2) information to realize its dynamics for a protein consisting of N amino acid residues. To see if (or to what extent) such a large amount of specific structural information is required to realize native protein dynamics, here we introduce a novel model based on only O(N) restraints. This model, named the ‘contact number diffusion’ model (CND), includes specific distance restraints for only local (along the amino acid sequence) atom pairs, and semi-specific non-local restraints imposed on each atom, rather than atom pairs. The semi-specific non-local restraints are defined in terms of the non-local contact numbers of atoms. The CND model exhibits the dynamic characteristics comparable to ENM and more correlated with the explicit-solvent molecular dynamics simulation than ENM. Moreover, unrealistic surface fluctuations often observed in ENM were suppressed in CND. On the other hand, in some ligand-bound structures CND showed larger fluctuations of buried protein atoms interacting with the ligand compared to ENM. In addition, fluctuations from CND and ENM show comparable correlations with the experimental B-factor. Although there are some indications of the importance of some specific non-local interactions, the semi-specific non-local interactions are mostly sufficient for reproducing the native protein dynamics.
PMCID: PMC3953337  PMID: 24625758
9.  Bis{tris­[3-(2-pyrid­yl)-1H-pyrazole]cadmium(II)} dodeca­molybdo(V,VI)phosphate hexa­hydrate 
The hydro­thermally prepared title compound, [Cd(C8H7N3)3]2[PMo12O40]·6H2O, is isotypic with its MnII analogue [Hao et al. (2010 ▶). Acta Cryst. E66, m231–m232]. The CdII cation is in a distorted octa­hedral environment, coordinated by six N atoms from three chelating 3-(2-pyrid­yl)-1H-pyrazole ligands. In the reduced heteropolyanion, two O atoms of the central PO4 group ( symmetry) are equally disordered about an inversion centre. N—H⋯O and O—H⋯O hydrogen bonds contribute to the crystal packing. Compared with the MnII analogue, the Cd—N bond lengths are longer at 2.316 (7)–2.334 (6) Å, versus 2.224 (6)–2.283 (5) Å for Mn—N, whereas all other bond lengths and angles and the hydrogen-bonding motifs are very similar in the two structures.
PMCID: PMC2983543  PMID: 21580219
10.  Refinement of docked protein–ligand and protein–DNA structures using low frequency normal mode amplitude optimization 
Nucleic Acids Research  2005;33(14):4496-4506.
Prediction of structural changes resulting from complex formation, both in ligands and receptors, is an important and unsolved problem in structural biology. In this work, we use all-atom normal modes calculated with the Elastic Network Model as a basis set to model structural flexibility during formation of macromolecular complexes and refine the non-bonded intermolecular energy between the two partners (protein–ligand or protein–DNA) along 5–10 of the lowest frequency normal mode directions. The method handles motions unrelated to the docking transparently by first applying the modes that improve non-bonded energy most and optionally restraining amplitudes; in addition, the method can correct small errors in the ligand position when the first six rigid-body modes are switched on. For a test set of six protein receptors that show an open-to-close transition when binding small ligands, our refinement scheme reduces the protein coordinate cRMS by 0.3–3.2 Å. For two test cases of DNA structures interacting with proteins, the program correctly refines the docked B-DNA starting form into the expected bent DNA, reducing the DNA cRMS from 8.4 to 4.8 Å and from 8.7 to 5.4 Å, respectively. A public web server implementation of the refinement method is available at .
PMCID: PMC1183489  PMID: 16087736
11.  Low-resolution refinement tools in REFMAC5 
Low-resolution refinement tools implemented in REFMAC5 are described, including the use of external structural restraints, helical restraints and regularized anisotropic map sharpening.
Two aspects of low-resolution macromolecular crystal structure analysis are considered: (i) the use of reference structures and structural units for provision of structural prior information and (ii) map sharpening in the presence of noise and the effects of Fourier series termination. The generation of interatomic distance restraints by ProSMART and their subsequent application in REFMAC5 is described. It is shown that the use of such external structural information can enhance the reliability of derived atomic models and stabilize refinement. The problem of map sharpening is considered as an inverse deblurring problem and is solved using Tikhonov regularizers. It is demonstrated that this type of map sharpening can automatically produce a map with more structural features whilst maintaining connectivity. Tests show that both of these directions are promising, although more work needs to be performed in order to further exploit structural information and to address the problem of reliable electron-density calculation.
PMCID: PMC3322599  PMID: 22505260
low-resolution refinement; REFMAC5
12.  Redetermination of catena-poly[[chlorido­(thio­urea-κS)copper(I)]-μ-thio­urea-κ2 S:S] at 100 K 
The structure of the polymeric title compound, [CuCl(CH4N2S)2]n, has been redetermined to modern standards of precision with anisotropic refinement and location of the H atoms. The previous structure report [Spofford & Amma (1970 ▶). Acta Cryst. B26, 1474–1483] is generally confirmed to higher precision [typical Cu—S bond length s.u. values = 0.005 (old) and 0.001 Å (new)]. The asymmetric unit contains two formula units, with both CuI atoms coordinated by one terminal S atom and two bridging S atoms of thio­urea ligands. This connectivity leads to polymeric [100] chains in the crystal. If very long contacts to nearby chloride ions [2.8687 (9) and 3.1394 (12) Å] are considered to be bonding, then very distorted CuS3Cl tetra­hedral coordination polyhedra arise. The crystal structure is consolidated by weak intra- and inter-chain N—H⋯S and N—H⋯Cl hydrogen bonds.
PMCID: PMC3297225  PMID: 22412415
13.  Low-temperature redetermination of benzofurazan 1-oxide 
In the six-membered ring of the low-temperature crystal structure of benzofurazan 1-oxide, C6H4N2O2, the two C atoms adjacent to the N atoms are linked by a delocalized aromatic bond [1.402 (2) Å]; each is connected to its neighbour by a longer, more localized, bond [1.420 (2), 1.430 (2) Å]. However, the next two bonds in the ring approximate double bonds [1.357 (2), 1.366 (2) Å]. As such, the six-membered ring is better described as a cyclo­hexa­diene system, in contrast to the description in the room-temperature structure reported by Britton & Olson (1979 ▶) [Acta Cryst. B35, 3076–3078].
PMCID: PMC2969705  PMID: 21583137
14.  Redetermination of (NH4)2HAsO4  
In comparison with the original determination based on Weissenberg film data [Khan et al. (1970 ▶). Acta Cryst. B26, 1889–1892], the current redetermination of diammonium hydrogenarsenate(V) reveals all atoms with anisotropic displacement parameters and all H atoms localized. This allowed an unambiguous assignment of the hydrogen-bonding pattern, which is similar to that of the isotypic phosphate analogue (NH4)2HPO4. The structure of the title compound consists of slightly distorted AsO3(OH) and NH4 tetra­hedra, linked into a three-dimensional structure by an extensive network of O—H⋯O and N—H⋯O hydrogen bonds.
PMCID: PMC3515085  PMID: 23284312
15.  Diaquabis­[3-(hydroxy­imino­)butanoato]nickel(II): a triclinic polymorph 
The title centrosymmetric mononuclear complex, [Ni(C4H6NO3)2(H2O)2], is a polymorph of the previously reported complex [Dudarenko et al. (2010 ▶). Acta Cryst. E66, m277–m278]. The NiII atom, lying on an inversion center, is six-coordinated by two carboxyl­ate O atoms and two oxime N atoms from two trans-disposed chelating 3-hydroxy­imino­butanoate ligands and two axial water mol­ecules in a distorted octa­hedral geometry. The hydr­oxy group forms an intra­molecular hydrogen bond with the coordinated carboxyl­ate O atom. The complex mol­ecules are linked in stacks along [010] by a hydrogen bond between the water O atom and the carboxyl­ate O atom of a neighboring mol­ecule. The stacks are further linked by O—H⋯O hydrogen bonds into a layer parallel to (001).
PMCID: PMC2983669  PMID: 21580256
16.  Hexa­kis­(thio­urea-κS)nickel(II) nitrate: a redetermination 
A preliminary X-ray study of the title mol­ecular salt, [Ni(CH4N2S)6](NO3)2, has been reported twice previously, by Maďar [Acta Cryst. (1961), 14, 894] and Rodriguez, Cubero, Vega, Morente & Vazquez [Acta Cryst. (1961), 14, 1101], using film methods. We confirm the previous studies, but to modern standards of precision and with all H atoms located. The central Ni atom (site symmetry ) of the dication is octa­hedrally coordinated by six S-bound thio­urea mol­ecules. The crystal structure is stabilized by intra- and inter­molecular N—H⋯S and N—H⋯O hydrogen bonds.
PMCID: PMC3007420  PMID: 21588080
17.  Di-n-butyl­ammonium 2-[(3,5-di-tert-butyl-4-hy­droxy­benz­yl)sulfan­yl]benzoate 
The title salt, C8H20N+·C22H27O3S−, is a proton-transfer compound derived from the recently reported parent carb­oxy­lic acid [Alhadi et al. (2010). Acta Cryst. E66, o1787] by the addition of a second equivalent of di-n-butyl­amine, yielding the di-n-butyl­ammonium carboxyl­ate salt. The structure of the carboxyl­ate anion resembles that of the parent carb­oxy­lic acid. The main difference lies in the position of the H atom in the 4-hy­droxy group. In the anion the O—H bond is perpendicular, rather than parallel, to the benzyl ring. This position appears to facilitate hydrogen bonding to an O atom of the carboxyl­ate group of a symmetry-related anion. In addition, there are three N—H⋯O hydrogen bonds. In contrast, the neutral species hydrogen bonds via a carboxylic acid dimer. The dihedral angle between the benzene rings in the anion is 79.19 (7)°.
PMCID: PMC3007956  PMID: 21588774
18.  Redetermination of tetra­kis(N,N-diethyl­dithio­carbamato)tin(IV) 
The crystal structure of the title compound, [Sn(C5H10NS2)4], was originally determined by Harreld & Schlemper [Acta Cryst. (1971), B27, 1964–1969] using intensity data estimated from Weissenberg films. In comparison with the previous refinement, the current redetermination reveals anisotropic displacement parameters for all non-H atoms, localization of the H atoms, and higher precision of lattice parameters and inter­atomic distances. The complex features a distorted S6 octa­hedral coordination geometry for tin and a cis disposition of the monodentate dithio­carbamate ligands.
PMCID: PMC2969649  PMID: 21583036
19.  Tetra­chlorido(1,10-phenanthroline-κ2 N,N′)platinum(IV) monohydrate 
In the title complex, [PtCl4(C12H8N2)]·H2O, the Pt4+ ion is six-coordinated in a distorted octa­hedral environment by two N atoms of a 1,10-phenanthroline ligand and by four Cl atoms. As a result of the different trans effects of the N and Cl atoms, the Pt—Cl bonds trans to the N atom are slightly shorter than those trans to the Cl atom. The compound displays inter­molecular π–π inter­actions between the six-membered rings, with a centroid–centroid distance of 3.834 Å. There are also weak intra­molecular C—H⋯Cl hydrogen bonds. According to the IR spectrum, solvent water was present in the crystal, but owing to the high thermal motion of the uncoordinated O atom, the H atoms could not be detected.
PMCID: PMC2968294  PMID: 21581820
20.  (E)-3-Hy­droxy-5,5-dimethyl-2-(3-phenyl­prop-2-en-1-yl)cyclo­hex-2-en-1-one 
Five of the atoms of the six-membered cyclo­hexene ring of the title compound, C17H20O2, are essentially coplanar (r.m.s. deviation = 0.006 Å), with the sixth (the dimethyl­methyl C atom) deviating from the mean plane of the five atoms by 0.610 (2) Å. This plane is nearly perpendicular to the cinnamyl portion, the two planes being aligned at 85.1 (1)°. Two mol­ecules are linked by an O—H⋯O hydrogen bond about a center of inversion. The cyclo­hexene ring is disordered over two directly overlapping positions. As a result, the hy­droxy group and the keto O atom cannot be distinguished from one another.
PMCID: PMC3200708  PMID: 22058958
21.  1-Decyl-6-nitro-1H-benzimidazol-2(3H)-one 
The title mol­ecule, C17H25N3O3, is built up from fused six- and five-membered rings linked to a –C10H21 chain. The fused-ring system is essentially planar, the largest deviation from the mean plane being 0.009 (2) Å. The chain is roughly perpendic­ular to this plane, making a dihedral angle of 79.5 (2)°. In the crystal, N—H⋯O hydrogen bonds build infinite chains along [010]. There are channels in the structure containing disordered hexane. The contribution of this solvent to the scattering power was suppressed using the SQUEEZE option in PLATON [Spek (2009 ▶). Acta Cryst. D65, 148–155].
PMCID: PMC3247349  PMID: 22219967
22.  Bis[glycinium(0.5+)] perrhenate 
All the residues of the title compound, (C2H5.5NO2)2[ReO4], are located in general crystallographic positions. The glycine mol­ecules have usual conformations [Rodrigues Matos Beja et al. (2006 ▶). Acta Cryst. C62, o71–o72] with the H atom of the carboxylate group half-occupied, thus bearing a formal half-positive charge per molecule. The perrhenate anion has nearly ideal tetra­hedral geometry. A large number of strong hydrogen bonds give rise to the overall three-dimensional network. A two-dimensional network, parallel to (100), is made up of strong O—H⋯O hydrogen bonds with a donor acceptor distance of 2.445 (2) Å. A large number of weaker O—H⋯O and N—H⋯O hydrogen bonds consolidates the structure into an overall three-dimensional network.
PMCID: PMC2967868  PMID: 21581493
23.  Redetermined structure of diphenyl­phospho­nimidotriphenyl­phospho­rane: location of the hydrogen atoms and analysis of the inter­molecular inter­actions 
The title compound, C30H25NOP2, is a bulky phosphazene derivative. Its previous crystal structure [Cameron et al. (1979 ▶). Acta Cryst. B35, 1373–1377] is confirmed and its H atoms have been located in the present study. The formal P=N double bond is about 0.05 Å shorter than the P—N single bond and the large P=N—P bond angle reflects the steric strain in the mol­ecule. An intra­molecular C—H⋯O inter­action occurs. In the crystal, short C—H⋯O contacts connect the mol­ecules into chains propagating in [011], which are cross-linked via C—H⋯π inter­actions, generating a three-dimensional network. Aromatic π–π stacking also occurs [shortest centroid–centroid separation = 3.6012 (11) Å].
PMCID: PMC3089147  PMID: 21754359
24.  Protein fold determined by paramagnetic magic-angle spinning solid-state NMR spectroscopy 
Nature chemistry  2012;4(5):410-417.
Biomacromolecules that are challenging for the usual structural techniques can be studied with atomic resolution by solid-state nuclear magnetic resonance. However, the paucity of >5 Å distance restraints, traditionally derived from measurements of magnetic dipole-dipole couplings between protein nuclei, is a major bottleneck that hampers such structure elucidation efforts. Here we describe a general approach that enables the rapid determination of global protein fold in the solid phase via measurements of nuclear paramagnetic relaxation enhancements (PREs) in several analogs of the protein of interest containing covalently-attached paramagnetic tags, without the use of conventional internuclear distance restraints. The method is demonstrated using six cysteine-EDTA-Cu2+ mutants of the 56-residue B1 immunoglobulin-binding domain of protein G, for which ~230 longitudinal backbone 15N PREs corresponding to ~10-20 Å distances were obtained. The mean protein fold determined in this manner agrees with the X-ray structure with a backbone atom root-mean-square deviation of 1.8 Å.
PMCID: PMC3335742  PMID: 22522262
25.  HPAM: Hirshfeld Partitioned Atomic Multipoles 
Computer physics communications  2012;183(2):390-397.
An implementation of the Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge density partitioning schemes is described. Atomic charges and atomic multipoles are calculated from the HD and HD-I atomic charge densities for arbitrary atomic multipole rank lmax on molecules of arbitrary shape and size. The HD and HD-I atomic charges/multipoles are tested by comparing molecular multipole moments and the electrostatic potential (ESP) surrounding a molecule with their reference ab initio values. In general, the HD-I atomic charges/multipoles are found to better reproduce ab initio electrostatic properties over HD atomic charges/multipoles. A systematic increase in precision for reproducing ab initio electrostatic properties is demonstrated by increasing the atomic multipole rank from lmax = 0 (atomic charges) to lmax = 4 (atomic hexadecapoles). Both HD and HD-I atomic multipoles up to rank lmax are shown to exactly reproduce ab initio molecular multipole moments of rank L for L ≤ lmax. In addition, molecular dipole moments calculated by HD, HD-I, and ChelpG atomic charges only (lmax = 0) are compared with reference ab initio values. Significant errors in reproducing ab initio molecular dipole moments are found if only HD or HD-I atomic charges used.
PMCID: PMC3225920  PMID: 22140274
Atomic multipoles; Hirshfeld charges; dipole; quadrupole

Results 1-25 (318445)