Showing papers in "Theoretical Chemistry Accounts in 2005"

Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals

Abstract: Pseudopotential parameter sets for the elements from H to Kr using the relativistic, norm-conserving, separable, dual-space Gaussian-type pseudopotentials of Goedecker, Teter, and Hutter (GTH) are presented as optimized for the gradient-corrected exchange-correlation functionals of Becke, Lee, Yang, and Parr (BLYP), Becke and Perdew (BP), and Perdew, Burke, and Ernzerhof (PBE). The accuracy and reliability of the GTH pseudopotentials is shown by calculations for a series of small molecules.

Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements

Abstract: Sequences of basis sets that systematically converge towards the complete basis set (CBS) limit have been developed for the coinage metals (Cu, Ag, Au) and group 12 elements (Zn, Cd, Hg). These basis sets are based on recently published small-core relativistic pseudopotentials [Figgen D, Rauhut G, Dolg M, Stoll H (2005) Chem Phys 311:227] and range in size from double- through quintuple-ζ. Series of basis sets designed for valence-only and outer-core electron correlation are presented, as well as these sets augmented by additional diffuse functions for the accurate description of negative ions and weak interactions. Selected benchmark calculations at the coupled cluster level of theory are presented for both atomic and molecular properties. The latter include the calculation of both spectroscopic and thermochemical properties of the homonuclear dimers Cu2, Ag2, and Au2, as well as the van der Waals species Zn2, Cd2, and Hg2. The CBS limit results, including the effects of core-valence correlation and spin-orbit coupling, represent some of the most accurate carried out to date and result in new recommendations for the equilibrium bond lengths of the group 12 dimers. Comparisons are also made to a limited number of all-electron Douglas–Kroll–Hess (DKH) calculations (second and third order) carried out using new correlation consistent basis sets of triple-ζ quality.

Estimating the Hartree—Fock limit from finite basis set calculations

Abstract: It is demonstrated that the polarization-consistent basis sets, which are optimized for density functional methods, are also suitable for Hartree–Fock calculations, and can be used for estimating the Hartree–Fock basis set limit to within a few micro-hartree accuracy. Various two- and three-point extrapolation schemes are tested and exponential functions are found to be superior compared to functions depending on the inverse power of the highest angular momentum function in the basis set. Total energies can be improved by roughly an order of magnitude, but atomization energies are only marginally improved by extrapolation.

Variation of electrophilicity during molecular vibrations and internal rotations

Abstract: The interrelationships between global reactivity descriptors such as chemical hardness, chemical potential, polarizability and electrophilicity and associated electronic structure principles were investigated in detail by considering distortion along the normal coordinates from the equilibrium structure and internal rotation. The necessary conditions on the extremum of electrophilicity were probed along with other electronic structure principles associated with the global reactivity descriptors. It was observed that an extremum in electrophilicity is obtained where both chemical potential and chemical hardness attain their respective exiremal values in course of the molecular vibrations as well as internal rotations.

Theory and range of modern semiempirical molecular orbital methods

Abstract: Semiempirical molecular orbital methods have a long history. They serve to tackle large systems and complicated processes beyond the reach of ab initio or density functional methods. Although their setup is derived from Hartree–Fock theory, the design of approximate energy expressions and the empirical parameters are used to achieve higher accuracy than the underlying ab initio theory. In this way the effect of larger basis sets or correlation can be partially simulated. All widely used semiempirical methods establish their accuracy by error statistics for molecular properties with experimental and high-level ab initio or density functional theory calculations as a reference. Their computational efficiency makes them suitable for the study of biochemical systems and solid materials. The present review presents a variety of applications which demonstrate the need for and success of semiempirical methods.

Valence basis sets for lanthanide 4f-in-core pseudopotentials adapted for crystal orbital ab initio calculations

Abstract: Crystal orbital adapted Gaussian (4s4p3d), (5s5p4d) and (6s6p5d) valence primitive basis sets have been derived for calculating periodic bulk materials containing trivalent lanthanide ions modeled with relativistic energy-consistent 4f-in-core lanthanide pseudopotentials of the Stuttgart-Koeln variety. The calibration calculations of crystalline A-type Pm2O3 using different segmented contraction schemes (4s4p3d)/[2s2p2d], (4s4p3d)/[3s3p2d], (5s5p4d)/[2s2p2d], (5s5p4d)/[3s3p3d], (5s5p4d)/[4s4p3d], (6s6p5d)/[2s2p2d], (6s6p5d)/[3s3p3d] and (6s6p5d)/[4s4p4d] are discussed at both Hartree–Fock (HF) and density functional theory (DFT) levels for the investigation of basis set size effects. Applications to the geometry optimization of A-type Ln2O3 (Ln = La-Pm) show a satisfactory agreement with experimental data using the lanthanide valence basis sets (6s6p5d)/[4s4p4d] and the standard set 6-311G* for oxygen. The corresponding augmented sets (8s7p6d)/[6s5p5d] with additional diffuse functions for describing neutral lanthanide atoms were applied to calculate atomic energies of free lanthanide atoms for the evaluation of cohesive energies for A-Ln2O3 within both conventional Kohn-Sham DFT and the a posteriori-HF correlation DFT schemes.

About the Mulliken electronegativity in DFT

Abstract: In the framework of density functional theory, a new formulation of electronegativity that recovers the Mulliken definition is proposed and its reliability is checked by computing electronegativity values for a large number of elements It is found that the obtained values, which are compared with previously proposed electronegativity scales, fulfill the main periodic criteria

Basis set effects on relative energies and HOMO–LUMO energy gaps of fullerene C36

Abstract: Fifteen C36 isomers were examined to determine the influence that the quality of basis sets has on the geometry parameters, the relative stability and HOMO–LUMO energy gaps of fullerene isomers calculated with density functional theory. It is worthwhile to note that the geometry parameters of all C36 isomers are insensitive to basis sets. On the other hand, one set of d-type polarization functions plays an important role in evaluating relative stability and HOMO–LUMO energy gaps, while diffuse functions are not effective. To obtain reliable energies, at least a double-zeta plus polarization basis set is required, and a triple-zeta plus polarization basis set is suggested to lead to accurate energies at a reasonable computational cost.

Ab initio study of the O2 binding in dicopper complexes

Abstract: The structures and stabilities of [Cu2(μ-η2:η2- peroxo)]2+ (A) and [Cu2(μ-oxo)]2+ (B) complexes with three NH3 ligands per copper are investigated using DFT and high-level ab initio methods. These are model systems for active centers in enzymes like hemocyanine and tyrosinase. Previous studies have shown that at the DFT/B3LYP level the peroxo form A is more stable than the μ-oxo form B, while the opposite was found using CASPT2 (Flock M, Pierloot K (1999) J Phys Chem 103:95). At the two computational levels, the energy difference of the isomers differed by more than 30 kcal/mol. In this work this problem is reinvestigated using a localized orbital description and multireference configuration interaction (MRCI) methods. It is found that CASPT2 strongly over-corrects the correlation effect and MRCI predicts structure A to be energetically lower than B, in qualitative agreement with B3LYP and experiment. However, B3LYP seems to stabilize the biradicalic structure A too much, and this effect depends approximately linearly on the amount of exact exchange in the B3LYP density functional. Reducing the amount of exact exchange to 10–15% yields good agreement between MRCI and B3LYP.

Multi-level vibrational SCF calculations and FTIR measurements on furazan

Abstract: The structure and infrared spectrum of furazan (1,2,5-oxadiazole) were studied by vibrational SCF (VSCF) and configuration interaction (VCI) calculations based on a high quality potential derived from electronic structure calculations up to the CCSD(T)/aug-cc-pCVQZ level. In addition gas-phase FTIR measurements were performed, which allowed for several corrections in the spectrum of the first vibrational overtones. Excellent agreement was found between the computed and the experimental results.

The effects of solvation in the theoretical spectra of cationic dyes

Abstract: We present a quantum-mechanical study on the solvent effects in the structure and electronic spectra of some cationic dyes: acridine orange, proflavine, safranine, neutral red, thionine and methylene blue. The geometry optimizations were carried out with the AM1 and DFT (with B3LYP functional) methods and the theoretical spectra of the dyes under study were obtained with Zindo time-dependent methods (TD–DFT and TD–HF). The solvation methodology adopted was the integral equation formulation (IEF) version of the polarizable continuum model (PCM).

A short-range correlation energy density functional with multi-determinantal reference

Abstract: We introduce a short-range correlation density functional defined with respect to a multi-determinantal ref- erence which is meant to be used in a multi-determinantal extension of the Kohn-Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron-electron interaction. We construct the local density approximation for this functional and discuss its performance on the He atom.

Graphs to chemical structures 1. Sphericity indices of cycles for stereochemical extension of Pólya’s theorem

Abstract: Polya’s theorem has been concluded to be concerned with graphs, but not with chemical structures, where it is incapable of treating chiral ligands properly. In order to take account of chiral ligands along with achiral ones, coset representations (CRs) for cyclic subgroups have been examined to classify permutations of the CRs into proper and improper elements. As a result, a k-cycle contained in each permutation has been classified into an enantiospheric, homospheric, or hemispheric one. Thereby, sphericity indices of k-cycles have been defined according to the enantiospheric, homospheric, or hemispheric nature of each k-cycle. On the basis of the sphericity indices, cycle indices with chirality fittingness (CIs-CF) have been defined in place of Polya’s cycle indices. The CIs-CF have been proved to be capable of enumerating of stereoisomers with chiral and achiral ligands. Their capabilities have been confirmed by using allene derivatives as examples.

Reduced communication channels of molecular fragments and their entropy/information bond indices

Abstract: A reduction of the molecular “communication channel” in atomic resolution, which generates the entropy/information indices of the system chemical bonds, is performed by combining several atomic inputs and/or outputs into a single unit representing a collection of bonded atoms. The implications of such fragment-reduced communication channels for gaining both the internal (intra-subsystem) and external (inter-subsystem) bond-indices are examined. The entropy/information quantities of the reduced channels of molecular subsystems are proposed as descriptors of their information bond “order” and its covalent/ionic composition. These predictions are compared with the bond indices resulting from the molecular orbital (MO) theory. The rules for combining the subsystem entropy/information data into the corresponding global quantities describing the system as a whole are derived and tested. The so-called complementary reductions are used to formulate the exact combination rules for the molecular entropy/information bond indices. Applications to the three-orbital model and π-bond systems (butadiene and benzene) in the Huckel theory approximation are reported and used to illustrate the proposed concepts and techniques. The subsystem bond-order conservation and a competition between its ionic and covalent contributions are discussed. In contrast to the familiar MO bond indices, the entropic descriptors of molecular fragments are shown to exhibit a remarkable degree of equalization, thus emphasizing the information equilibrium of the ground-state distributions of electrons.

Graphs to chemical structures 2. Extended sphericity indices of cycles for stereochemical extension of Pólya’s coronas

Abstract: In order to enumerate nonrigid isomers, we have proposed the proligand approach, where extended sphericity indices of k-cycles have been defined according to the enantiospheric, homospheric, or hemispheric nature of each k-cycle. Then, cycle indices with chirality fittingness have been defined so as to enumerate nonrigid stereoisomers with chiral and achiral ligands. Results of the proligand approach using tetramethylmethane as an example have been compared with those based on Polya’s corona. Thereby, Polya’s corona is concluded to be concerned with graphs, but not with chemical structures, where it is incapable of treating chiral ligands properly.

Stationary points on the energy hypersurface of the reaction O3 + H•→ [•O3H]* ⇆ O2 + •OH and thermodynamic functions of •O3H at G3MP2B3, CCSD(T)-CBS (W1U) and MR-ACPF-CBS levels of theory

Abstract: The relative enthalpies, ΔHo (0) and ΔHo (298.15), of stationary points (four minimum and three transition structures) on the •O3H potential energy surface were calculated with the aid of the G3MP2B3 as well as the CCSD(T)–CBS (W1U) procedures from which we earlier found mean absolute deviations (MAD) of 3.9 kJ mol−1 and 2.3 kJ mol−1, respectively, between experimental and calculated standard enthalpies of the formation of a set of 32 free radicals. For CCSD(T)-CBS (W1U) the well depth from O3 + H• to trans-•O3H, ΔHowell(298.15) = −339.1 kJ mol−1, as well as the reaction enthalpy of the overall reaction O3 + H•→O2 + •OH, ΔrHo(298.15) = −333.7 kJ mol−1, and the barrier of bond dissociation of trans-•O3H → O2 + •OH, ΔHo(298.15) = 22.3 kJ mol−1, affirm the stable short-lived intermediate •O3H. In addition, for radicals cis-•O3H and trans-•O3H, the thermodynamic functions heat capacity Cop(T), entropy So (T), and thermal energy content Ho(T) − Ho(0) are tabulated in the range of 100 − 3000 K. The much debated calculated standard enthalpy of the formation of the trans-•O3H resulted to be ΔfHo(298.15) = 31.1 kJ mol −1 and 32.9 kJ mol −1, at the G3MP2B3 and CCSD(T)-CBS (W1U) levels of theory, respectively. In addition, MR-ACPF-CBS calculations were applied to consider possible multiconfiguration effects and yield ΔfHo(298.15) = 21.2 kJ mol −1. The discrepancy between calculated values and the experimental value of −4.2 ± 21 kJ mol−1 is still unresolved.

Reduced–size polarized basis sets for calculations of molecular electric properties. III. Second–row atoms

Abstract: Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.

Spectroscopic identification of adsorption properties of Zn2+ ions at cationic positions of high-silica zeolites with distant placing of aluminium ions.

Abstract: For Zn2+ cations in ZnZSM-5 zeolite unusual type of cationic positions, formed by two distantly placed framework aluminium atoms, is considered. Some extent of structural destabilization of cations in these cationic positions in comparison with traditional localization should result in promoted Lewis activity and adsorption activity of these sites. The last ones are manifested in the significantly increased IR low frequency shifts for adsorbed molecules and in their ability for heterolytic dissociation at elevating temperature. DFT cluster quantum chemical modeling of light alkane adsorption on Zn2+ in ZnZSM-5 zeolites confirms these conjectures in full agreement with recent experiments. Similar to the previously considered dihydrogen and methane molecule adsorption, we present here the calculations of ethane molecular and dissociative adsorption on these sites. It is shown that the unusually large ethane IR frequency shift recently observed in ZnZSM-5 zeolite can result from adsorptive interaction of C2H6 with Zn2+ stabilized in a cationic position with distantly placed aluminium ions. The dissociative adsorption of ethane molecules with the formation of bridged hydroxyl group and Zn–C2H5 structure is considered and an activation energy of ethylene formation from the alkyl fragment is evaluated.

Density-functional theory and hybrid density-functional theory continuum solvation models for aqueous and organic solvents: universal SM5.43 and SM5.43R solvation models for any fraction of Hartree-Fock exchange

Abstract: Hybrid density functional theory, which is a combined Hartree–Fock and density functional method, provides a simple but effective way to incorporate nonlocal exchange effects and static and dynamical correlation energy into an orbital-based theory with affordable computational cost for many important problems of gas-phase chemistry. The inclusion of a reaction field representing an implicit solvent in a self-consistent hybrid density functional calculation provides an effective and efficient way to extend this approach to problems of liquid-phase chemistry. In previous work, we have parameterized several models based on this approach, and in the present article, we present several new parameterizations based on implicit solvation models SM5.43 and SM5.43R. In particular, we extend the applicability of these solvation models to several combinations of the MPWX hybrid-density functional with various one-electron basis sets, where MPWX denotes a combination of Barone and Adamo’s modified version of Perdew and Wang’s exchange functional, Perdew and Wang’s correlation functional, and a percentage X of exact Hartree–Fock exchange. SM5.43R parameter optimizations are presented for the MPWX/MIDI!, MPWX/MIDI!6D, and MPWX/6-31+G(d,p) combinations with X=0 (i.e., pure density functional theory), 25, 42.8, and 60.6, and for MPWX/6-31G(d) and MPWX/6-31+G(d), with X=0, 42.8, and 60.6; this constitutes a total of 18 new parameter sets. [Note that parameter optimizations using MPW25/6-31G(d) and MPW25/6-31+G(d) were carried out in a previous SM5.43R parameterization.] For each of the five basis sets, we found no significant loss in the accuracy of the model when parameters averaged over the four values of X are used instead of the parameters optimized for a specific value of X. Therefore for each of the five basis sets used here, the SM5.43R and SM5.43 models are defined to have a single parameter set that can be used for any value of X between 0 and 60.6. The new models yield accurate free energies of solvation for a broad range of solutes in both water and organic solvents. On the average, the mean-unsigned errors, as compared with those from experiment, of the free energies of solvation of neutral solutes range from 0.50 to 0.55 kcal/mol and those for ions range from 4.5 to 4.9 kcal/mol. Since the SM5.43R model computes the free energy of solvation as a sum of bulk-electrostatic and non-bulk-electrostatic contributions, it may be used for detailed analysis of the physical effects underlying a calculation of the free energy of solvation. Several calculations illustrating the partitioning of these contributions for a variety of solutes in n-hexadecane, 1-octanol, and water are presented.

Improved relativistic energy-consistent pseudopotentials for 3d-transition metals

Abstract: Energy-consistent relativistic pseudopotentials for 3d-transition metals Sc to Ni based on modified valence energies are proposed. The pseudopotentials are adjusted at the finite difference level within the intermediate coupling scheme with respect to multi-configuration Dirac–Hartree–Fock data based on the Dirac–Coulomb Hamiltonian with an estimate of the Breit contributions in quasidegenerate perturbation theory. Typically a few hundred to thousand J levels arising from about 35 to 40 configurations ranging from the anion down to the highly charged cation are considered as references. It is shown that introducing a small common energetic shift of all valence energies reduces the errors in the parameter adjustment considerably. Results of highly correlated atomic and molecular test calculations using large basis sets and basis set extrapolation techniques are presented.

Accurate partial atomic charges for high-energy molecules using class IV charge models with the MIDI! basis set

Abstract: We have recently developed a new class IV charge model for calculating partial atomic charges in molecules. The new model, called charge model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree–Fock theory and by hybrid density functional theory (HDFT) based on the modified Perdew–Wang density functional with several basis sets. In the present article, we extend CM3 for calculating partial atomic charges by Hartree–Fock theory with the economical but well balanced MIDI! basis set. Then, using a test set of accurate dipole moments for molecules containing nitramine functional groups (which include many high-energy materials), we demonstrate the utility of several parameters designed to improve the charges in molecules containing both N and O atoms. We also show that one of our most recently developed CM3 models that is designed for use with wave functions calculated at the mPWXPW91/MIDI! level of theory (where X denotes a variable percentage of Hartree–Fock exchange) gives accurate charge distributions in nitramines without additional parameters for N and O. To demonstrate the reliability of partial atomic charges calculated with CM3, we use these atomic charges to calculate polarization free energies for several nitramines, including the commonly used explosives 1,3,5-trinitro-s-triazine (RDX) and 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW), in nitromethane. These polarization energies are large and negative, indicating that electrostatic interactions between the charge distribution of the molecule and the solvent make a large contribution to the free energy of solvation of nitramines. By extension, the same conclusion should apply to solid-state condensation. Also, in contrast to some other charge models, CM3 yields atomic charges that are relatively insensitive to the presence of buried atoms and small conformational changes in the molecule, as well as to the level of treatment of electron correlation. This type of charge model should be useful in the future development of solvation models and force fields designed to estimate intramolecular interactions of nitramines in the condensed phase.

Interpolated potential energy surface for abstraction and exchange reactions of NH 3 + H and deuterated analogues

Abstract: An ab initio interpolated potential energy surface for the hydrogen abstraction and exchange reactions between ammonia and a hydrogen atom is reported. The interpolation is constructed over a set of data points calculated at the unrestricted coupled cluster approximation, using single and double excitations, and including the triple excitations non-iteratively. New data point selection methods were used to improve the convergence and accuracy of the interpolated surface.

On the accuracy of numerical Hartree–Fock energies

Abstract: It is demonstrated that numerical Hartree–Fock (HF) energies reported in the literature in some cases have errors in the milliHartree range. The main cause of these errors is due to the use of too small a value for the ‘practical infinity’ parameter in the finite difference method for generating the results. By systematically investigating the convergence with respect to the computational parameters, HF energies accurate to at least 1 microHartree are generated for 42 diatomic systems containing first and second row elements, encompassing both cationic, neutral and anionic systems.

An ab initio and density functional study of microsolvation of carbon dioxide in water clusters and formation of carbonic acid

Abstract: Geometry of the CO2–H2O complex and reaction barriers leading to the formation of H2CO3were studied at the RHF/6-311++G**, MP2/6-311++G**, B3LYP/AUG-cc-pVDZ, B3LYP/AUG-cc-pVTZ, MP2/AUG-cc-pVDZ and CCD/AUG-cc-pVDZ levels of theory. The rotational barrier of the CO2–H2O complex and the reaction barrier leading to the formation of H2CO3–H2O from CO2–(H2O)2 were studied using the first three of the above-mentioned methods. Microsolvation of CO2 in water clusters having upto eight water molecules was studied using the B3LYP/AUG-cc-pVDZ method. Various methods except MP2/AUG-cc-pVDZ predict the equilibrium structure of the CO2–H2O complex to be symmetric while the MP2/AUG-cc-pVDZ method predicts it to be unsymmetric. Formation of H2CO3 from CO2–H2O is strongly catalyzed by the presence of a second water molecule. Atomic orbitals are strongly rehybridized in going from the equilibrium structures of the CO2–H2O and CO2–(H2O)2 complexes to the transition states involved in the formation of H2CO3 and H2CO3–H2O, respectively, as shown by hybridization displacement charges.

A DFT study on the hydrated V2O5-TiO2-anatase catalyst: stability of monomeric species

Abstract: A combined cluster and periodic study has been carried out to elucidate the stability of hydrated species on the vanadia/titania catalyst. First, the hydration of a V2O5 cluster was analyzed for the successive adsorption of one to four water molecules. The dimeric skeleton is found to be preserved at a low water concentration. However, after the adsorption of four water molecules on the dimer, it is found to break to generate stable monomeric OV(OH)3 units. The two moieties are related by the equation: Such OV(OH)3 units have been taken as a monomer model for the periodic representation of the vanadia/titania catalyst. On the (100) surface, the OV(OH)3 moieties are anchored by three V–O–Ti bonds to the support surface in a pyramidal arrangement. The vanadyl V=O bond is found to be very stable.

Generic implementation of semi-analytical CI gradients for NDDO-type methods

Abstract: Generic semi-analytical energy gradients are derived and implemented for NDDO-type methods, by using numerical integral and Fock matrix derivatives in the context of an otherwise analytical approach for configuration interaction (CI) and other non-variational treatments. The correctness, numerical precision, and performance of this hybrid approach are established through comparisons with fully numerical and fully analytical calculations. The semi-analytical evaluation of the CI gradient is generally much faster than the fully numerical computation, but somewhat slower than a fully analytical calculation, which however shows the same scaling behavior. It is the method of choice whenever a fully analytical CI gradient is not available due to the lack of analytical integral derivatives. The implementation is generic in the sense that it can easily be extended to any new NDDO-type Hamiltonian. The present development of a semi-analytical CI gradient will facilitate studies of electronically excited states with recently proposed NDDO methods that include orthogonalization corrections.

A new proposal for the reason of magic numbers in alkali cation microhydration clusters

Abstract: Alkali cation microhydration clusters M+(H2O) n , n≤24, M = Na, K, Cs, have been globally optimised, using a specialised version of genetic algorithms and the common TIP4P/OPLS model potential. The results constitute a first unbiased and systematic overview on structures of alkali cation microhydration clusters. Simple reasons for differing structural trends could be provided. Dodecahedral cages occur, but do not play as prominent a role as frequently believed. In particular, they do not seem to determine the occurrence of magic numbers. A structural pattern all magic number cluster structures do have in common is that only three and/or four-coordinated water molecules can be observed. Molecular dynamics simulations were run in the canonical ensemble, and free energy differences of dissociating clusters were obtained, with dodecahedral cages again showing no special feature. Structures containing only three and/or four-coordinated water molecules, however, are more stable than others thus arriving at a possible explanation for magic numbers.

Accurate ab intio determination of binding energies for rare-gas dimers by basis set extrapolation

Abstract: To investigate the electron correlation effect on the binding energies of very weakly bound complexes at highly correlated levels, an extrapolation scheme exploiting the convergent behavior of the binding energy differences between two correlation levels with the correlation-consistent basis set aug-cc-pVXZ was explored. The scheme is based on extrapolating the binding energy differences between the lower and higher correlation levels (such as second-order Moller–Plesset perturbation theory and the single and double coupled-cluster method with perturbative triple correction level), CCSD(T), by X−3 for relatively small basis set calculations to estimate the corresponding basis set limit, which is then added to the complete basis set(CBS) limit binding energy at the lower correlation level to derive the CBS limit binding energy at the higher level. Test results on rare-gas dimers Rg2 (Rg is He, Ne, Ar) show that the CCSD(T) CBS limit binding energies estimated by this scheme with aug-cc-pVXZ and aug-cc-pV(X+1)Z basis sets are more accurate than the CBS limit estimated by direct extrapolation of correlation energies by X−3 with aug-cc-pV(X+1)Z and aug-cc-pV(X+2)Z basis sets in most cases, which signifies the utility of the proposed extrapolation scheme as the level of electron correlation treatment increases. The nonnegligible discrepancy in the well depth near equilibrium between the experimental and the full connected single, double, and triple coupled-cluster method CBS limit estimate obtained by this procedure in the case of Ar2 suggests that the previous semiempirical potential may be too attractive near equilibrium compared with the actual one.

Density functional theory analysis of some triple-decker sandwich complexes of iron containing cyclo-P5 and cyclo-As5 ligands

Abstract: Structure and bonding in triple-decker cationic complexes [(η5-Cp)Fe(μ,η:η5-E5) Fe(η5-Cp)]+ (1: E = CH, 2: E = P, 3: E = As) and [(η5-Cp)Fe(μ,η:η5-Cp)Fe(η5-E5)]+ (E = P, As) are examined by density functional theory (DFT) calculations at the B3LYP/6-31+G* level. These species exhibit the lowest energy when all the three ligands are eclipsed. In the complexes with bifacially coordinated cyclo-E5, the perfectly eclipsed D5h sandwich structure a is found to be a potential minimum. The energy difference between the fully eclipsed and the staggered conformations b and c are within 1.0, 2.1, and 6.3 kcal/mol, respectively, for E = CH, P, and As. The isomeric species with monofacially coordinated cyclo-E5 (E =P, As), [(η5 -Cp)Fe(μ,η :η5-Cp)Fe(η5-E5)]+ are predicted to be about 30 and 60 kcal/mol higher in energy , respectively, for E = P and As. The calculations predict that the bifacially coordinated cyclo-E5 (E =P, As) undergoes significant ring expansion leading to ``loosening of bonds'' as observed experimentally. The consequent loss of aromaticity in the central cyclo-E5 indicates that significant π-electron density from the ring can be directed towards bonding with the iron centers on both sides. The diffuse nature of the π-orbitals of cyclo-P5 and cyclo-As5 can lead to better overlap with the iron d-orbitals and result in stronger bonding. This is reflected in the bond order values of 0.377 and 0.372 for the Fe-P and Fe-As bonds in 2a and 3a, respectively. The natural population analysis reveals that the Fe atom that is coordinated to a cyclo-E5 (E = P, As) possesses a negative charge of −0.23 to −0.38 units due to transfer of electron density from the inorganic ring to the metal center.

Multipole electrostatic model for MNDO-like techniques with minimal valence spd-basis sets

Abstract: We report an implementation of an atomic multipole model (up to quadrupole) for calculating the electrostatic properties of molecules based on electron densities derived from MNDO-like NDDO-based semiempirical MO calculations with minimal s,p,d valence basis sets. The results were validated by a comparison of the calculated values of the molecular electrostatic potential with those obtained from fine grain numerical integrations (both with AM1*), B3LYP/6–31G(d) and MP2/6–31G(d). The DFT and ab initio potentials can be reproduced remarkably well (mean unsigned error <2 kcal mol−1 e−1) using simple linear regression equations to correct the AM1* (multipole) results.