Bonding study in all-metal clusters containing Al4 units

The nature of the bonding of a series of gas-phase all-metal clusters containing the Al4 unit attached to an alkaline, alkaline earth, or transition metal is investigated at the DFT level using Mulliken, quantum theory of atoms in molecules (QTAIM), and Hirshfeld iterative (Hirshfeld-I) atomic partitionings. The characterization of ionic, covalent, and metallic bonds is done by means of charge polarization and multicenter electron delocalization. This Article uses for the first time Hirshfeld-I multicenter indices as well as Hirshfeld-I based atomic energy calculations. The QTAIM charges are in line with the electronegativity scale, whereas Hirshfeld-I calculations display deviations for transition metal clusters. The Mulliken charges fail to represent the charge polarization in alkaline metal clusters. The large ionic character of Li-Al and Na-Al bonds results in weak covalent bonds. On the contrary, scarcely ionic bonds (Be-Al, Cu-Al and Zn-Al) display stronger covalent bonds. These findings are in line with the topology of the electron density. The metallic character of these clusters is reflected in large 3-, 4- and 5-center electron delocalization, which is found for all the molecular fragments using the three atomic definitions. The previously reported magnetic inactivity (based on means of magnetic ring currents) of the pi system in the Al42- cluster contrasts with its large pi electron delocalization. However, it is shown that the different results not necessary contradict each other.     

ChelpG and QTAIM atomic charge and dipole models for the infrared fundamental intensities of the fluorochloromethanes

ChelpG atomic charges and dipoles and the charge–charge flux–dipole flux (CCFDF) model have been used to quantitatively estimate the fundamental infrared intensities of the fluorochloromethanes. Since the ChelpG calculational procedure includes the constraint that the atomic charges and dipoles reproduce the equilibrium dipole moments the model results in accurate intensity values that have a root mean square error of 0.7 km mol^?1 compared to those determined directly from the MP2/6-311G++(3d,3p) electronic density and 23.1 km mol^?1 relative to the experimental intensities. Although these ChelpG results for total dipole moment derivatives are almost the same as those obtained previously using QTAIM (Quantum Theory of Atoms in Molecules) atomic charges and dipoles in the CCFDF model, their charge, charge flux and dipole flux contributions are completely different. Whereas the contributions calculated using the QTAIM parameters have values following expectations based on electronegativity concepts this is not true for those obtained from the ChelpG parameters. Mean dipole moment derivatives determined from experimental fundamental infrared intensities are compared with the ChelpG and QTAIM atomic charges. Furthermore, Generalized Atomic Polar Tensor Charges (GAPT) are found to need correction for their dynamic contributions if they are to be used as static atomic charges.     

On the applicability of QTAIM, Hirshfeld and Mulliken delocalisation indices as a measure of proton spin–spin coupling in aromatic compounds

A correlation between delocalization indices (DIs) and proton spin–spin coupling constants, previously observed for DIs calculated within the QTAIM scheme, is examined using Hirshfeld and Mulliken schemes. The original set of molecules has been extended with a number of five- and six-membered heteroaromatics containing nitrogen, oxygen, sulfur and selenium. QTAIM DIs are found to correlate well with the experimental values, even those containing the electronegative nitrogen and oxygen atoms. In contrast, an acceptable correlation with the Hirshfeld DIs is found only for polybenzenoids, whereas no correlation is found for the Mulliken DIs with any of the systems.     

Quantum theory of atoms in molecules charge-charge flux-dipole flux models for the infrared intensities of X(2)CY (X = H, F, Cl; Y = O, S) molecules

The molecular dipole moments, their derivatives, and the fundamental IR intensities of the X2CY (X = H, F, Cl; Y = O, S) molecules are determined from QTAIM atomic charges and dipoles and their fluxes at the MP2/6-311++G(3d,3p) level. Root-mean-square errors of +/-0.03 D and +/-1.4 km mol(-1) are found for the molecular dipole moments and fundamental IR intensities calculated using quantum theory of atoms in molecules (QTAIM) parameters when compared with those obtained directly from the MP2/6-311++G(3d,3p) calculations and +/-0.05 D and 51.2 km mol(-1) when compared with the experimental values. Charge (C), charge flux (CF), and dipole flux (DF) contributions are reported for all the normal vibrations of these molecules. A large negative correlation coefficient of -0.83 is calculated between the charge flux and dipole flux contributions and indicates that electronic charge transfer from one side of the molecule to the other during vibrations is accompanied by a relaxation effect with electron density polarization in the opposite direction. The characteristic substituent effect that has been observed for experimental infrared intensity parameters and core electron ionization energies has been applied to the CCFDF/QTAIM parameters of F2CO, Cl2CO, F2CS, and Cl2CS. The individual atomic charge, atomic charge flux, and atomic dipole flux contributions are seen to obey the characteristic substituent effect equation just as accurately as the total dipole moment derivative. The CH, CF, and CCl stretching normal modes of these molecules are shown to have characteristic sets of charge, charge flux, and dipole flux contributions.     

An atomic charge-charge flux-dipole flux atom-in-molecule decomposition for molecular dipole-moment derivatives and infrared fundamental intensities

The molecular dipole moment and its derivatives are determined from atomic charges, atomic dipoles, and their fluxes obtained from AIM formalism and calculated at the MP2(FC)/6-311++G(3d,3p) level for 16 molecules: 6 diatomic hydrides, CO, HCN, OCS, CO2, CS2, C2H2, C2N2, H2O, H2CO, and CH4. Root-mean-square (rms) errors of 0.052 D and 0.019 e are found for the dipole moments and their derivatives calculated using AIM parameters when compared with those obtained directly from the MP2(FC)/6-311++G(3d,3p) calculations and 0.097 D and 0.049 e when compared to the experimental values. The major deviations occur for the NaH, HF, and H2O molecules. Parallel polar tensor elements for the diatomic and linear polyatomic molecules, except H2, HF, LiH, and NaH, have values resulting from cancellations of substantial contributions from atomic charge fluxes and atomic dipole fluxes. These fluxes have a large negative correlation coefficient, -0.97. IR fundamental intensity sums for CO, HCN, OCS, CO2, CS2, C2H2, C2N2, H2CO, and CH4 calculated using AIM charges, charge fluxes, and atomic dipole fluxes have rms errors of 14.9 km mol(-1) when compared with sums calculated directly from the molecular wave function and 36.2 km mol(-1) relative to experimental values. The classical model proposed here to calculate dipole-moment derivatives is compared with the charge-charge flux-overlap model long used by spectroscopists for interpreting IR vibrational intensities. The utility of the AIM atomic charges and dipoles was illustrated by calculating the forces exerted on molecules by a charged particle. AIM quantities were able to reproduce forces due to a +0.1 e particle over a 3-8-A separation range for the CO and HF molecules in collinear and perpendicular arrangements. These results show that IR intensities do contain information relevant to the study of intermolecular interactions.     

Correlation effects in EOM-CCSD for the excited states: evaluated by AIM localization index (LI) and delocalization index (DI)

We have extended the evaluation and interpretation of QTAIM (quantum theory of atoms in molecules) localization and delocalization indices lambda (LI) and delta (DI) to electronic excited states by studying ground states (at HF and CCSD levels) and excited states (at CIS and EOM-CCSD) of H2C=CH2, HCCH, H2C=O, H2C=S, CO2, CS2, and SO2. These molecules undergo extensive geometrical changes upon the excitation to the valence adiabatic excited singlet state. The importance of Coulomb correlation effects was demonstrated by comparing the LIs and DIs at none-correlated levels (HF and CIS) and those at correlated levels (CCSD and EOM-CCSD). In interpreting the changes in the magnitudes of the LIs and DIs, we made use of simple molecular orbital and Walsh-diagram analyses. Coulomb correlation is important in determining the magnitude of the LIs and DIs and obtaining geometries that are close to experiment.     

On the Volume Chemistry of Solid Compounds: the Legacy of Wilhelm Biltz

For the calculation of the atomic or ionic volumes the Quantum Theory of Atoms In Molecules method was applied. The regions (basins) around the nuclei confined by the zero‐flux surfaces in the electron density gradient are called QTAIM atoms. They are non‐overlapping and completely fill the space. The volume of the basins gives volumes of atoms or ions. The integration of the electron density within the volumina yields effective charges, defining neutral or ionic character of the given QTAIM species. Present investigations refer to metal hydrides, metal nitrides and to intermetallic compounds of the system Al‐Pt. A linear relation between the ionic volumina of hydrogen or nitrogen established according to QTAIM and after Biltz has been found with (homodesmic) binary metal hydrides and binary metal nitrides, but has been observed merely as a trend with stronger deviations for heterodesmic compounds, such as ternary hydrido‐ and nitridometallates A_a[M_mX_x] (A – alkali or alkaline earth metal, M – transition metal and X – H or N). The deviation from linearity for heterodesmic compounds is caused by the different kinds of chemical bonds being present within the [M_mX_x] anions on the one hand and between the anions and the cations on the other hand reflected by the calculated volumes and the QTAIM charges of M and X components. Concerning the intermetallic compounds of the system Al‐Pt, the quantum chemical calculations reveal negative charges for the platinum atoms and positive ones for the aluminium atoms in accordance with their electronegativities. Introducing the variation of the atomic volume with the composition extends the Vegard's approach and gives a non‐linear slope for the concentration dependence of mean atomic volume which explains qualitatively the experimental results.     

QTAIM charge-charge flux-dipole flux interpretation of electronegativity and potential models of the fluorochloromethane mean dipole moment derivatives

Infrared fundamental vibrational intensities and quantum theory atoms in molecules (QTAIM) charge-charge flux-dipole flux (CCFDF) contributions to the polar tensors of the fluorochloromethanes have been calculated at the QCISD/cc-pVTZ level. A root-mean-square error of 20.0 km mol(-1) has been found compared to an experimental error estimate of 14.4 and 21.1 km mol(-1) for MP2/6-311++G(3d,3p) results. The errors in the QCISD polar tensor elements and mean dipole moment derivatives are 0.059 e when compared with the experimental values. Both theoretical levels provide results showing that the dynamical charge and dipole fluxes provide significant contributions to the mean dipole moment derivatives and tend to be of opposite signs canceling one another. Although the experimental mean dipole moment derivative values suggest that all the fluorochloromethane molecules have electronic structures consistent with a simple electronegativity model with transferable atomic charges for their terminal atoms, the QTAIM/CCFDF models confirm this only for the fluoromethanes. Whereas the fluorine atom does not suffer a saturation effect in its capacity to drain electronic charge from carbon atoms that are attached to other fluorine and chlorine atoms, the zero flux electronic charge of the chlorine atom depends on the number and kind of the other substituent atoms. Both the QTAIM carbon charges (r = 0.990) and mean dipole moment derivatives (r = 0.996) are found to obey Siegbahn's potential model for carbon 1s electron ionization energies at the QCISD/cc-pVTZ level. The latter is a consequence of the carbon mean derivatives obeying the electronegativity model and not necessarily to their similarities with atomic charges. Atomic dipole contributions to the neighboring atom electrostatic potentials of the fluorochloromethanes are found to be of comparable size to the atomic charge contributions and increase the accuracy of Siegbahn's model for the QTAIM charge model results. Substitution effects of the hydrogen, fluorine, and chlorine atoms on the charge and dipole flux QTAIM contributions are found to be additive for the mean dipole derivatives of the fluorochloromethanes.     

pi-H...O hydrogen bonds: multicenter covalent pi-H interaction acts as the proton-donating system

The MP2 method and the Pople-style basis sets 6-311++G(d,p), 6-311++G(2df,2pd), and 6-311++G(3df,3pd) were used to perform calculations on H3O+...C2H2 and C2H3+...C2H2 complexes and related species. Hydrogen bonds existing for the analyzed complexes were investigated as well as related pi-H...O --> pi...H-O and pi-H...pi --> pi...H-pi proton-transfer processes. For some of the complexes analyzed the multicenter pi-H interaction possessing the properties of a covalent bond acts as a proton donor; more generally it is classified as the Lewis acid. The quantum theory of "atoms in molecules" (QTAIM) was also applied to deepen the nature of these interactions in terms of characteristics of bond critical points. The pi-H...O, O-H...pi, and pi-H...pi interactions analyzed here may be classified as hydrogen bonds since their characteristics are the same as or at least similar to those of typical hydrogen bonds. H...pi interactions are common in crystal structures of organic and organometallic compounds. The analyses performed here show a continuum of such interactions since there are H...pi contacts possessing the characteristics of weak intermolecular interactions on the one hand and pi-H multicenter covalent bonds on the other. Ab initio and QTAIM results support the latter statements.     

Infrared intensities of some SiH-containing compounds in the gas-phase

Infrared intensities measured in the gas-phase are reported for CH3SiH3, CH3SiD3, (CH3)2SiH2, (CH3)2SiD2, (SiH3)2CH2, (SiD3)2CH2, Si2H6, SiH2Cl2 and (SiH3)2O. These are compared with theoretical estimates from HF, MP2 and B3LYP calculations with the 6-311G** basis set. Literature values of nuCH intensities per bond from 18 compounds correlate linearly with the values calculated at MP2 and B3LYP levels: the corresponding HF plot is slightly curved. The new HC(Si) data fit these correlations adequately. In similar plots for SiH stretching intensity, the point for SiH2Cl2 is displaced, especially at the HF level. The lack of relation of nuCH or nuSiH intensity to Mulliken atomic charge points to the effect of varying atomic charge flux in the parameter thetamu/thetar. Anomalies associated with nuSiH intensities influenced by chlorine or OR substitution and previously explained by d(pi)-p(pi) bonding are attributed instead to charge flux variation. For silyl groups, deformation band intensities are roughly additive according to the number of such groups. However, this is not the case for the methyl symmetric deformation bands in methyl and dimethyl silanes.     

某些含氧酸中原子净电荷与pK_a的关系

在量子化学从头算 (分别采用HF/STO 3G ,HF/STO 3G ,HF/ 3 2 1G和MP2 /STO 3G)水平下 ,对 11种含氧酸分子 (H2 O ,H2 O2 ,HNO2 ,HNO3 ,HClO ,HClO2 ,HClO3 ,HCO2 H ,CH3 CO2 H ,HBrO和HIO)进行几何构型全优化和电子结构计算 ,将获得的电子结构数据与 pKa 实验值进行逐步回归分析 ,结果发现含氧酸中羟基氢原子净电荷、含氧酸中与羟基氧相连非氢原子净电荷两项与 pKa 呈良好的二元线性关系 ,表明含氧酸中羟基氧所连原子的净电荷在决定含氧酸的酸性上起重要作用     

QTAIM N-center delocalization indices as descriptors of aromaticity in mono and poly heterocycles

The implementation of the n-center electron delocalization indices, n-DIs, and n-order electron localization indices, n-LIs, within the framework of the quantum theory of atoms in molecules, QTAIM, is performed. n-DIs are shown to be very useful to study the local aromaticity in monocyclic and polycyclic compounds. Total and pi n-DIs from n=4 to 7 were computed for a series of typical 4, 5, 6, and 7-center aromatic and antiaromatic rings. For n>or=5 the pi n-DI accounts for the 95% of the total n-DI and can be employed alone to measure the aromaticity. A scaling factor on the n-DIs is required in order to compare the aromaticity of [5c-6e] and [6c-6e] rings, the same correction allows to estimate the relative aromatic stabilization of polycyclic compounds using the sum of its values for individual rings. This is called Effective Scaled Electron Delocalization, ESED. The comparison with other aromaticity indices reflects a good correlation between ESED and both resonance energies, and HOMA indices. The most important differences between scaled pi n-DIs and NICS(0) indices are found for compounds that contain rings with different number of centers or pi electrons.     

An atomic charge study of highly ionic diatomic molecular systems

Four atomic charge formalisms are compared using highly ionic diatomic molecules, such as LiF, NaF, KF, LiCl, NaCl, KCl, BF, AlF, GaF, BeO, and MgO. All calculations were done at the QCISD/6‐311G(2df) level. The only formalism consistent with the characteristics of all these systems is Quantum theory of atoms in molecules (QTAIM). Absolute Mulliken charge values are small. ChelpG charges are not reliable for systems in which the atoms are largely anisotropic. Generalized atomic polar tensor values are contaminated with charge fluxes and atomic dipole fluxes and fail when these contributions are important and do not cancel each other. Finally, the charge–charge flux–dipole flux model was applied to dipole moment derivatives with QTAIM. This analysis shows that charge flux and atomic dipole flux contributions during bond stretching are almost null, except for oxides. There are also evidences that the lone electron pair at Group 13 elements in fluorides becomes less localized as the bond is stretched. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Covalence and Ionicity in MgAgAs‐Type Compounds

MgAgAs‐type “half‐Heusler” compounds are known to realize two out of three possible atomic arrangements of this structure type. The number of transition metal components typically determines which of the alternatives is favored. On the basis of DFT calculations for all three variants of 20 eight‐ and eighteen‐valence‐electron compounds, the experimentally observed structural variant was found to be determined by basically two different bonding patterns. They are quantified by employing two complementary position‐space bonding measures. The Madelung energy ${E_{\rm{M}}^{{\rm{QTAIM}}} }$ calculated with the QTAIM effective charges reflects contributions of the ionic interactions to the total energy. The sum of nearest‐neighbor delocalization indices ?_nn characterizes the covalent interactions through electron sharing. With the aid of these quantities, the energetic sequence of the three atomic arrangements for each compound is rationalized. The resulting systematic is used to predict a scenario in which an untypical atomic arrangement becomes most favorable.     

An ab initio study of crystal field effects,part 3: Solid- and gas-phase geometry of formamide,modeling the changes in a peptide group due to hydrogen bonds

A model of the solid state of formamide is constructed by optimizing a central molecule in an electrostatic field of the proper symmetry. Attention is paid to the way the electrostatic charges are obtained. Point charges obtained from a Mulliken population analysis yield a final set of atomic charges in the central molecule that agree reasonably well with those obtained experimentally after ak-refinement of formamide. Point charges from a so-called stockholder partitioning agree slightly less. Furthermore, the simple crystal field adaptation of standard ab initio methods reproduces within experimental limits the differences in C=O and C-N lengths, observed between the gas-phase and the solid state geometry. Again, a Mulliken field agrees slightly better than a stockholder field, but the difference in performance is statistically insignificant. In a survey of 221 high-quality single-crystal x-ray determinations of compounds containing the peptide group N-C=O, we found evidence supporting quantitatively the conclusion that the increase of C=O and the decrease of C-N bond length in the gas-to-solid transition is dominated by the effects of hydrogen bonding. It was shown that the C=O bond lengthens by about 0.011 å per H-bond it accepts, while the N-C bond diminishes by about 0.015 å per H-bond it donates.Part 2, see Ref. [5].     

CH4和CO2合成乙酸中CO2与·H及·CH3相互作用的理论计算

采用量子化学密度泛函方法,对CO2与H及CH3自由基反应进行了理论计算,给出了CO2与H及CH3自由基相互作用的反应机理,提出了CO2与H及CH3自由基作用的4条反应路径.其中以H和CH3自由基进攻CO2的C原子反应为优先路径,主要产物为乙酸,而甲酸甲酯为动力学禁阻产物.计算结果与实验结果相当吻合.为CH4和CO2两步反应合成含氧化合物提供了理论解释和指导.     

Hydrogen–hydrogen interaction in planar biphenyl: A theoretical study based on the interacting quantum atoms and Hirshfeld atomic energy partitioning methods

The nature of H‐H interaction between ortho‐hydrogen atoms in planar biphenyl is investigated by two different atomic energy partitioning methods, namely fractional occupation iterative Hirshfeld (FOHI) and interacting quantum atoms (IQA), and compared with the traditional virial‐based approach of quantum theory of atoms in molecules (QTAIM). In agreement with Bader's hypothesis of H? H bonding, partitioning the atomic energy into intra‐atomic and interatomic terms reveals that there is a net attractive interaction between the ortho‐hydrogens in the planar biphenyl. This falsifies the classical view of steric repulsion between the hydrogens. In addition, in contrast to the traditional QTAIM energy analysis, both FOHI and IQA show that the total atomic energy of the ortho‐hydrogens remains almost constant when they participate in the H‐H interaction. Although, the interatomic part of atomic energy of the hydrogens plays a stabilizing role during the formation of the H? H bond, it is almost compensated by the destabilizing effects of the intra‐atomic parts and consequently, the total energy of the hydrogens remains constant. The trends in the changes of intra‐atomic and interatomic energy terms of ortho‐hydrogens during H? H bond formation are very similar to those observed for the H₂ molecule. © 2014 Wiley Periodicals, Inc.     

Gas-phase acidities of disubstituted methanes and of enols of carboxamides substituted by electron-withdrawing groups

The gas-phase acidities DeltaG degrees (acid) of some 20 amides/enols of amides RNHCOCHYY'/RNHC(OH)=CYY' [R = Ph, i-Pr; Y, Y' = CO(2)R', CO(2)R' ', or CN, CO(2)R', R', R' ' = Me, CH(2)CF(3), CH(CF(3))(2)], the N-Ph and N-Pr-i amides of Meldrum's acid, 1,3-cyclopentanedione, dimedone, and 1,3-indanedione, and some N-p-BrC(6)H(4) derivatives and of nine CH(2)YY' (Y, Y' = CN, CO(2)R', CO(2)R' '), including the cyclic carbon acids listed above, were determined by ICR. The acidities were calculated at the B3LYP/6-31+G//B3LYP/6-31+G level for both the enol and the amide species or for the carbon acid and the enol on the CO in the CH(2)YY' series. For 12 of the compounds, calculations were also conducted with the larger base sets 6-311+G and G-311+G. The DeltaG degrees (acid) values changed from 341.3 kcal/mol for CH(2)(CO(2)Me)(2) to 301.0 kcal/mol for PhNHC(OH)=C(CN)CH(CF(3))(2). The acidities increased for combinations of Y and Y' based on the order CO(2)Me < CO(2)CH(2)CF(3) < CN, CO(2)CH(CF(3))(2) for a single group and reflect the increased electron-withdrawal ability of Y,Y' coupled with the ability to achieve planarity of the crowded anion. The acidities of corresponding YY'-substituted systems follow the order N-Ph enols > N-Pr-i enols > CH(2)YY'. Better linear relationships between DeltaG degrees (acid) values calculated for the enols and the observed values than those for the values calculated for the amides suggest that the ionization site is the enolic O-H of most of the noncyclic trisubstituted methanes. The experimental DeltaG degrees (acid) value for Meldrum's acid matches the recently reported calculated value. The calculated structures and natural charges of all species are given, and the changes occurring in them on ionization are discussed. Correlations between the DeltaG degrees (acid) values and the pK(enol) values, which are linear for the trisubstituted methanes, excluding YY' = (CN)(2) and nonlinear for the CH(2)YY' systems, are discussed.     

Theoretical study of the electronic gas-phase spectrum of glycine, alanine, and related amines and carboxylic acids

A theoretical study on the origin of the common electronic excitations in amino acids is presented, focusing on the excited states of glycine, alanine and the related substructures formic acid, acetic acid, propionic acid, ammonia, methylamine, and ethylamine. Special attention is given to the valence excitation from the nonbonding lone-pair on the carboxylic oxygen atom to the antibonding pi-orbital (n(O) --> pi*(CO)) and the first Rydberg excitation from the nonbonding lone-pair on the nitrogen atom (n(N) --> 3s). From extensive calculations on formic acid and methylamine, different basis sets and electron correlation treatments are benchmarked using a hierarchy of coupled cluster (CC) methods, consisting of CCS, CC2, CCSD, CCSDR(3), and CC3, in combination with augmented correlation consistent basis sets. The dependence of the excitation energies on the size of the backbone structure in the two groups of molecules is investigated, and 0-0 transition energies for the n(O) --> pi*(CO) and n(N) --> 3s transitions are calculated for the smallest molecules. Excellent agreement with experimental values is found where secure experimental assignments are available. A few outstanding problems in the experimental assignments found in the literature are described for both the carboxylic acids and the amines. Final predictions for vertical excitation energies are given for all molecules, including glycine and alanine where no gas-phase experimental results are available. Finally, calculations on protonated amino acids are presented showing an isolation of the n(O) --> pi*(CO) from higher lying states by as much as 1.9 eV for alanine.     

Estimation of pKa for organic oxyacids using calculated atomic charges

A method for the estimation of pK_a from empirically calculated atomic charges has been developed and tested on a diverse set of organic oxyacids. The approach involves a comparison of the atomic charges calculated for both the acid and the negative ion that is formed after loss of the acidic proton. These charges have been used in conjunction with the familiar concepts of induction and resonance to develop an accurate formula to predict pK_a. Results for a set of 135 compounds, including alcohols, phenols, and carboxylic acids, yielded a fit of pK_a with r = 0.993 and an rms error of 0.455. © John Wiley & Sons, Inc.