Solid-state energetics and electrostatics: Madelung constants and Madelung energies

The Madelung constants of ionic solids relate to their geometry and electrostatic interactions. Furthermore, because of issues in their evaluation, they are also of considerable mathematical interest. The corresponding Madelung (electrostatic, coulomb) energy is the principal contributor to the lattice energies of ionic systems, and these energies largely influence many of their physical properties. The Madelung constants are here defined and their properties considered. A difficulty with their application is that they may be defined relative to various lattice distances, and with various conventions for inclusion of the charges, leading to possible confusion in their use. Instead, the unambiguous Madelung energy, E(M), is to be preferred in chemistry. An extensive list of Madelung energies is presented. From this data set, it is observed that there is a strong linear correlation between the lattice energies of ionic solids, U(POT), and their Madelung energies: U(POT)/kJ mol(-1) = 0.8519E(M) + 293.9. This correlation establishes that the lattice energy, U(POT), for ionic solids is about 15% smaller than the attractive Madelung energy, the difference arising from the repulsions unaccounted for by the solely coulombic Madelung energy calculation. Correlations of U(POT) against E(M) for alkali metal hydrides and transition metal compounds, each having considerable covalency, show much reduced Madelung contributions to the lattice energy. These correlations permit ready estimation of lattice energies, and are the first to be based on actual data rather than a broad analysis. The independent volume-based thermodynamic (VBT) method, which relies on a separate correlation with the formula unit volume of the ionic material, complements these correlations.     

Dissolution thermochemistry of alkali metal dianion salts (M2X1, M = Li+, Na+, and K+ with X = CO3(2-), SO4(2-), C8H8(2-), and B12H12(2-))

The dissolution Gibbs free energies (ΔG°(diss)) of salts (M(2)X(1)) have been calculated by density functional theory (DFT) with Conductor-like Polarizable Continuum Model (CPCM) solvation modeling. The absolute solvation free energies of the alkali metal cations (ΔG(solv)(M(+))) come from the literature, which coincide well with half reduction potential versus SHE data. For solvation free energies of dianions (ΔG(solv)(X(2-))), four different DFT functionals (B3LYP, PBE, BVP86, and M05-2X) were applied with three different sets of atomic radii (UFF, UAKS, and Pauling). Lattice free energies (ΔG(latt)) of salts were determined by three different approaches: (1) volumetric, (2) a cohesive Gibbs free energy (ΔG(coh)) plus gaseous dissociation free energy (ΔG(gas)), and (3) the Born-Haber cycle. The G4 level of theory, electron propagator theory, and stabilization by dielectric medium were used to calculate the second electron affinity to form the dianions CO(3)(2-) and SO(4)(2-). Only the M05-2X/Pauling combination with the three different methods for estimating ΔG(latt) yields the expected negative dissolution free energies (ΔG°(diss)) of M(2)SO(4). Salts with large dianions like M(2)C(8)H(8) and M(2)B(12)H(12) reveal the limitation of using static radii in the volumetric estimation of lattice energies. The value of ΔE(coh) was very dependent on the DFT functional used.     

A Novel Charge Distribution Method for the Numerical Solution of the Poisson-Boltzmann Equation

A charge distribution method to solve the linearized Poisson-Boltzmann equation numerically through use of the finite difference method is proposed, The molecules are mapped by 1 and 0.25 Å grid systems. Each atom is modeled as a point charge and a weighted sum of point charge of every atom that is within its van der Waals radius with a grid point is assigned to the grid point. Depending on a charge distribution factor determined, the charge/grid (q/g) ratio calculated for every grid point inside a molecule can be fixed to a certain value. A grid size of the I Å grid is often fixed for mapping a small or large molecular system. Solvation energies for a group of small molecules calculated by the method arc comparable with those calculated by other methods and the grid energy calculated by the method is also reduced.     

二卤卡宾和苯甲醛反应机理的理论研究 ─ ylide 中间体的结构及反应特性

本文以SCF-MNDO方法进行计算, 获得了二氯卡宾与苯甲醛反应所形成的二卤羰基ylide中间体各异构体的构型、能量、电荷分布及其它有关数据, 并根据计算结果研究了ylide各异构体的不同化学行为, 进一步探讨了二卤卡宾与苯甲醛的反应机理。     

Energy of charged states in the acetanilide crystal: trapping of charge-transfer states at vacancies as a possible mechanism for optical damage

Calculations for the acetanilide crystal yield the effective polarizability (16.6 A(3)), local electric field tensor, effective dipole moment (5.41 D), and dipole-dipole energy (-12.8 kJ/mol). Fourier-transform techniques are used to calculate the polarization energy P for a single charge in the perfect crystal (-1.16 eV); the charge-dipole energy W(D) is zero if the crystal carries no bulk dipole moment. Polarization energies for charge-transfer (CT) pairs combine with the Coulomb energy E(C) to give the screened Coulomb energy E(scr); screening is nearly isotropic, with E(scr) approximately E(C)/2.7. For CT pairs W(D) reduces to a term deltaW(D) arising from the interaction of the charge on each ion with the change in dipole moment on the other ion relative to the neutral molecule. The dipole moments calculated by density-functional theory methods with the B3LYP functional at the 6-311++G(**) level are 3.62 D for the neutral molecule, changing to 7.13 D and 4.38 D for the anion and cation, relative to the center of mass. Because of the large change in the anion, deltaW(D) reaches -0.9 eV and modifies the sequence of CT energies markedly from that of E(scr), giving the lowest two CT pairs at -1.98 eV and -1.41 eV. The changes in P and W(D) near a vacancy are calculated; W(D) changes for the individual charges because the vacancy removes a dipole moment and modifies the crystal dielectric response, but deltaW(D) and E(C) do not change. A vacancy yields a positive change DeltaP that scatters a charge or CT pair, but the change DeltaW(D) can be negative and large enough to outweigh DeltaP, yielding traps with depths that can exceed 150 meV for single charges and for CT pairs. Divacancies yield traps with depths nearly equal to the sum of those produced by the separate vacancies and so they can exceed 300 meV. These results are consistent with a mechanism of optical damage in which vacancies trap optically generated CT pairs that recombine and release energy; this can disrupt the lattice around the vacancy, thereby favoring trapping and recombination of CT pairs generated by subsequent photon absorption, leading to further lattice disruption. Revisions to previous calculations on trapping of CT pairs in anthracene are reported.     

Electrostatic Energies in the 1,4‐Dichlorobenzene Polymorph Crystals: the Role of Charge Density Overlap Effects in Crystal Packing Analysis

Electrostatic and polarization energies for the three known polymorphic crystal structures of 1,4‐dichlorobenzene, as well as for one particularly stable virtual crystal structure generated by computer search, were calculated by a new accurate numerical integration method over static molecular charge densities obtained from high level ab initio molecular‐orbital calculations. Results are compared with those from standard empirical atom‐atom force fields. The new electrostatic energies, which include charge density overlap (penetration) effects, are seen to be much larger than and sometimes of opposite sign to those derived from point‐charge models. None of the four polymorphs is substantially more stable than the others on electrostatic‐energy grounds. Molecule‐molecule electrostatic energies have been calculated for the more important molecular pairs in each of the four structures; trends are found to be very different from those indicated by point‐charge energies or by total energies estimated with a parametric atom‐atom force field. Conclusions based exclusively on analysis of intermolecular atom contacts and point‐charge electrostatics may need to be modified in the light of the new kind of calculation.     

Electrostatic potentials,fields and field gradients from a general crystalline charge density

Explicit expressions for the electrostatic potential, the electric field and the electric field gradient at the nuclear positions of a crystalline lattice are presented. They are derived for a charge density given as an expansion in terms of spherical harmonics around the nuclear sites and as a Fourier series in the interstitial. These expressions can be decomposed into contributions from the spherical region centered around the lattice site of interest, from spherical regions surrounding all the other lattice sites and a contribution from the interstitital region.     

Effect of surrounding point charges on the density functional calculations of NixOx clusters (x = 4-12)

Embedded Ni(x)O(x) clusters (x = 4-12) have been studied by the density-functional method using compensating point charges of variable magnitude to calculate the ionic charge, bulk modulus, and lattice binding energy. The computations were found to be strongly dependent on the value of the surrounding point charge array and an optimum value could be found by choosing the point charge to reproduce the experimentally observed Ni--O lattice parameter. This simple, empirical method yields a good match between computed and experimental data, and even small variation from the optimum point charge value produces significant deviation between computed and measured bulk physical parameters. The optimum point charge value depends on the cluster size, but in all cases is significantly less than +/-2.0, the formal oxidation state typically employed in cluster modeling of NiO bulk and surface properties. The electronic structure calculated with the optimized point charge magnitude is in general agreement with literature photoemission and XPS data and agrees with the presently accepted picture of the valence band as containing charge-transfer insulator characteristics. The orbital population near the Fermi level does not depend on the cluster size and is characterized by hybridized Ni 3d and O 2p orbitals with relative oxygen contribution of about 70%.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.     

Grid positioning independence and the reduction of self-energy in the solution of the Poisson—Boltzmann equation

A common problem in the solution of the Poisson–Boltzmann equation using finite difference methods is the self-energy of the system, also known as the grid energy. Because atoms are typically modeled as a point charge, the infinite self-energy of a point charge is likewise modeled. In this article, a simple, alternate treatment of atomic charge is described where each atom is represented as a sphere of uniform charge. Unlike the point charge model, this method converges as the grid spacing is reduced. The uniform charge model generates the same electrostatic field outside the atoms. In addition, the use of fine grids reduces the variations in the potential due to variations in the position of atoms relative to the grid. Calculations of Born ion solvation energies, small-molecule solvation energies, and the electrostatic field of superoxide dismutase are used to demonstrate that this method yields the same results as the point charge model. © John Wiley & Sons, Inc.     

Why are ionic liquids liquid? A simple explanation based on lattice and solvation energies

We have developed a simple and quantitative explanation for the relatively low melting temperatures of ionic liquids (ILs). The basic concept was to assess the Gibbs free energy of fusion (Delta(fus)G) for the process IL(s) --> IL(l), which relates to the melting point of the IL. This was done using a suitable Born-Fajans-Haber cycle that was closed by the lattice (i.e., IL(s) --> IL(g)) Gibbs energy and the solvation (i.e., IL(g) --> IL(l)) Gibbs energies of the constituent ions in the molten salt. As part of this project we synthesized and determined accurate melting points (by DSC) and dielectric constants (by dielectric spectroscopy) for 14 ionic liquids based on four common anions and nine common cations. Lattice free energies (Delta(latt)G) were estimated using a combination of Volume Based Thermodynamics (VBT) and quantum chemical calculations. Free energies of solvation (Delta(solv)G) of each ion in the bulk molten salt were calculated using the COSMO solvation model and the experimental dielectric constants. Under standard ambient conditions (298.15 K and 10(5) Pa) Delta(fus)G degrees was found to be negative for all the ILs studied, as expected for liquid samples. Thus, these ILs are liquid under standard ambient conditions because the liquid state is thermodynamically favorable, due to the large size and conformational flexibility of the ions involved, which leads to small lattice enthalpies and large entropy changes that favor melting. This model can be used to predict the melting temperatures and dielectric constants of ILs with good accuracy. A comparison of the predicted vs experimental melting points for nine of the ILs (excluding those where no melting transition was observed and two outliers that were not well described by the model) gave a standard error of the estimate (s(est)) of 8 degrees C. A similar comparison for dielectric constant predictions gave s(est) as 2.5 units. Thus, from very little experimental and computational data it is possible to predict fundamental properties such as melting points and dielectric constants of ionic liquids.     

Finite difference Poisson-Boltzmann electrostatic calculations: Increased accuracy achieved by harmonic dielectric smoothing and charge antialiasing

A common problem in the calculation of electrostatic potentials with the Poisson-Boltzmann equation using finite difference methods is the effect of molecular position relative to the grid. Previously a uniform charging method was shown to reduce the grid dependence substantially over the point charge model used in commercially available codes. In this article we demonstrate that smoothing the charge and dielectric values on the grid can improve the grid independence, as measured by the spread of calculated values, by another order of magnitude. Calculations of Born ion solvation energies, small molecule solvation energies, the electrostatic field of superoxide dismutase, and protein-protein binding energies are used to demonstrate that this method yields the same results as the point charge model while reducing the positional errors by several orders of magnitude. © 1997 by John Wiley & Sons, Inc.     

Ab initio Study on the Intermolecular Interaction and Thermodynamic Properties of Methyl Nitrate Dimer

Three stable dimers of methyl nitrate have been obtained and their geometries have been fully optimized at the HF/6‐31G,. level. Binding energies have been calculated with correction for the basis set superposition error (BSSE) and zero point energy (ZPE). The cyclic overlap‐type structure, the binding energy of which is 11.97 kJ/mol at the MP4SDTQ/6‐31G. / HF/6‐31G. level, is the most stable. No intermolecular hydrogen bond was found, and the charge transfer between two subsystems is minute. The thermodynamic properties of methyl nitrate and its dimers have been calculated based on the vibrational analysis and statistical thermodynamics.     

The effect of metal cations on the nature of the first electronic transition of liquid water as studied by attenuated total reflection far-ultraviolet spectroscopy

The first electronic transition (?←X?) of liquid water was studied from the perspective of the hydration of cations by analyzing the attenuated total reflection far-ultraviolet (ATR-FUV) spectra of the Group I, II, and XIII metal nitrate electrolyte solutions. The ?←X? transition energies of 1 M electrolyte solutions are higher (Li(+): 8.024 eV and Cs(+): 8.013 eV) than that of pure water (8.010 eV) and linearly correlate with the Gibbs energies of hydration of the cations. The increases in the ?←X? transition energies are mostly attributable to the hydrogen bond formation energies of water molecules in the ground state induced by the presence of the cations. The deviation from the linear relation was observed for the high charge density cations, H(+), Li(+), and Be(2+), which reflects that the electronic energies in the excited states are also perturbed. Quantum chemical calculations show that the ?←X? transition energies of the water-cation complexes depend on the hydration structures of the cations. The calculated ?←X? transition energies of the water molecules hydrating high charge density cations spread more widely than those of the low charge density cations. The calculated transition energy spreads of the water-cation complexes directly correlate with the widths of the ?←X? transition bands measured by ATR-FUV spectroscopy.     

硝酸甲酯分子间相互作用的DFT和ab initio比较

用密度泛函理论(DFT)和从头算(ab initio)方法,分别在B3LYP/6 31G和HF/6 31G水平上求得硝酸甲酯三种二聚体的全优化几何构型和电子结构,并用6 311G和6 311＋＋G基组进行总能量计算.对HF/6 31G计算结果进行MP4SDTQ电子相关校正.在各基组下均进行基组叠加误差(BSSE)和零点能(ZPE)校正求得结合能.对6 31G优化构型作振动分析并基于统计热力学求得200～600 K温度下单体和二聚体的热力学性质.详细比较两种方法的相应计算结果,发现DFT求得的分子间距离较短,分子内键长较长,所得结合能均小于相应ab initio计算值.     

蛋白质分子的HNP格点模型

从 6 0种球形蛋白质的结构出发 ,采用Miyazawa Jernigan相互作用矩阵 ,计算了蛋白质分子中氨基酸之间的相互作用能 .发现构成蛋白质分子的 2 0种氨基酸可分成疏水 (Hydrophobic ,H)、中性 (Neutral,N)、亲水(Hydrophilic ,P)基团 .在计算它们之间相互作用能的基础上 ,建立了蛋白质分子的HNP格点模型 .用这个模型计算了二维蛋白质分子在自然态 (Nativestate)时的构象性质 .同时研究了氨基酸序列为HHNHNPNHPP HPNPPHPHPPHHPHNH的折叠过程 ,得到其基态能量为 - 6 4 89RT .这能为研究球形蛋白质的构象性质及折叠过程提供一种更合理的格点模型     

A highly distorted hexacoordinated silver(I) complex: synthesis,crystal structure,and DFT studies

A new highly distorted hexacoordinated silver(I) complex [AgL₂NO₃] with 2-(bis(methylthio)methylene)-1-phenylbutane-1,3-dione (L) as ligand is synthesized and characterized using elemental analysis, FTIR, NMR, and X-ray single-crystal structure analysis. The ligand (L) and the nitrate group act as bidentate ligands. The geometry around the silver ion has an intermediate configuration between a trigonal prism (TP) and an octahedron (OCT). Continuous shape measure (CShM) analysis indicated a closer configuration to TP than OCT. Experimentally and theoretically, the Ag–S bonds are shorter than any of the Ag–O bonds, indicating a stronger interaction between Ag⁺ (soft metal) and S-atom as a softer site than oxygen. Natural bond orbital (NBO) analyses showed higher interaction energies between the S-atom lone pairs and the Ag–antibonding NBO (8.61–31.39 kcal/mol) than LP(O)→Ag (3.48–11.46 kcal/mol). The acceptor antibonding NBO of the Ag atom has mainly s-orbital character. The Ag atom has a natural charge of +0.7579 e at the experimental structure, suggesting that negative charge was transferred from the ligand (0.0666 e) and nitrate (0.1090 e) to the Ag ion. Using Hirshfeld surface analysis, the important intermolecular interactions between molecular units within the crystal lattice of the ligand and its Ag-complex were analyzed and compared.     

State-selective preparation of NO2+ and the effects of NO2+ vibrational mode on charge transfer with NO

Two color resonance-enhanced multiphoton ionization (REMPI) scheme of NO(2) through the E (2)Sigma(u)(+) (3psigma) Rydberg state was used to prepare NO(2)(+) in its ground and (100), (010), (02(0)0), (02(2)0), and (001) vibrational states. Photoelectron spectroscopy was used to verify >96% state selection purity, in good agreement with results of Bell et al. for a similar REMPI scheme. The effects of NO(2)(+) vibrational excitation on charge transfer with NO have been studied over the center-of-mass collision energy (E(col)) range from 0.07 to 2.15 eV. Charge transfer is strongly suppressed by collision energy at E(col) < approximately 0.25 eV but is independent of E(col) at higher energies. Mode-specific vibrational effects are observed for both the integral and differential cross-sections. The NO(2)(+) bending vibration strongly enhances charge transfer, with enhancement proportional to the bending quantum number, and is not dependent on the bending angular momentum. The enhancement results from increased charge transfer probability in large impact parameter collisions that lead to small deflection angles. The symmetric stretch also enhances reaction at low collision energies, albeit less efficiently than the bend. The asymmetric stretch has virtually no effect, despite being the highest-energy mode. A model is proposed to account for both the collision energy and the vibrational state dependence.     

Charge and energy dynamics in photo-excited poly(para-phenylenevinylene) systems

We report results from simulations of charge and energy dynamics in poly(para-phenylenevinylene) (PPV) and PPV interacting with C60. The simulations were performed by solving the time-dependent Schrodinger equation and the lattice equation of motion simultaneously and nonadiabatically. The electronic system and the coupling of the electrons to the lattice were described by an extended three-dimensional version of the Su-Schrieffer-Heeger model, which also included an external electric field. Electron and lattice dynamics following electronic excitations at different energies have been simulated. The effect of additional lattice energy was also included in the simulations. Our results show that both exciton diffusion and transitions from high to lower lying excitations are stimulated by increasing the lattice energy. Also field induced charge separation occurs faster if the lattice energy is increased. This separation process is highly nonadiabatic and involves a significant rearrangement of the electron distribution. In the case of PPV coupled to C60, we observe a spontaneous charge separation. The separation time is in this case limited by the local concentration of C60 molecules close to the PPV chain.     

A nonempirical anisotropic atom-atom model potential for chlorobenzene crystals

A nearly nonempirical, transferable model potential is developed for the chlorobenzene molecules (C6ClnH6-n, n = 1 to 6) with anisotropy in the atom-atom form of both electrostatic and repulsion interactions. The potential is largely derived from the charge densities of the molecules, using a distributed multipole electrostatic model and a transferable dispersion model derived from the molecular polarizabilities. A nonempirical transferable repulsion model is obtained by analyzing the overlap of the charge densities in dimers as a function of orientation and separation and then calibrating this anisotropic atom-atom model against a limited number of intermolecular perturbation theory calculations of the short-range energies. The resulting model potential is a significant improvement over empirical model potentials in reproducing the twelve chlorobenzene crystal structures. Further validation calculations of the lattice energies and rigid-body k = 0 phonon frequencies provide satisfactory agreement with experiment, with the discrepancies being primarily due to approximations in the theoretical methods rather than the model intermolecular potential. The potential is able to give a good account of the three polymorphs of p-dichlorobenzene in a detailed crystal structure prediction study. Thus, by introducing repulsion anisotropy into a transferable potential scheme, it is possible to produce a set of potentials for the chlorobenzenes that can account for their crystal properties in an unprecedentedly realistic fashion.