Order Electron Correlation Research Articles

Beyond chemical accuracy in the heavy p-block: The first ionization potentials and electron affinities of Ga-Kr, In-Xe, and Tl-Rn.

A relativistic coupled-cluster version of the Feller-Peterson-Dixon composite method has been used to accurately calculate the first ionization potentials (IPs) and electron affinities (EAs) of the post-d, p-block elements Ga-Rn. Complete basis set extrapolations including outer-core correlation at the CCSD(T) level of theory were combined with contributions from higher order electron correlation up to CCSDTQ, quantum electrodynamic effects (Lamb shift), and spin-orbit (SO) coupling including the Gaunt contribution. Several methods for including SO were investigated, in which all involved the four-component (4c) Dirac-Coulomb (DC) Hamiltonian. The treatment of SO coupling was the contribution that limited the final accuracy of the present results. In the cases where 4c-DC-CCSD(T) could be reliably used for the SO contributions, the final composite IPs and EAs agreed with the available experimental values to within an unsigned average error of just 0.16 and 0.20 kcal/mol, respectively. In all cases, the final IPs and EAs were within 1 kcal/mol of the available experimental values, except for the EAs of the group 13 elements (Ga, In, and Tl), where the currently accepted experimental values appear to be too large by as much as 4 kcal/mol. The values predicted in this work, which have estimated uncertainties of ±0.5 kcal/mol, are 5.25 (Ga), 7.69 (In), and 7.39 (Tl) kcal/mol. For the EAs of Po and At, which do not have experimental values, the current calculations predict values of 34.2 and 55.8 kcal/mol with estimated uncertainties of ±0.6 and ±0.3 kcal/mol, respectively.

Static second hyperpolarizability of inverse sandwich compounds (M1-C5H5-M2) of alkali (M1 = Li, Na, K) and alkaline earth metals (M2 = Be, Mg, Ca).

In the investigated inverse sandwich complexes, charge transfer from alkali metal (M1) led to aromatically stabilized Cp ring, which prevented further charge transfer from the alkaline earth metal (M2). This electron push effect resulted in diffusion of electron density from the outermost "ns" subshell of alkaline earth metal. The alkaline earth metal is weakly bound to the alkali metal-C5H5 complex. The vertical ionization energy of the chosen M1-Cp-M2 complexes was smaller than that of the corresponding alkaline earth metals. Large second hyperpolarizability (106-108 a.u.) was obtained for the studied molecules. The correction due to the basis set superposition error (BSSE) in the calculated second hyperpolarizability was found to be small for larger systems, while it was rather significant for small systems. The MP4SDQ and CCSD results were in fair agreement, which indicates the necessity of higher order electron correlation treatment in the accurate description of second hyperpolarizability. Calculated dynamic second hyperpolarizabilities at 1064 nm were found to increase considerably for most of the chosen metal complexes.

Thermochemical data of the oleic acid esterification reaction: A quantum mechanics approach

Biodiesel is an important renewable fuel that can be obtained from low cost oils once the esterification reaction of free fatty acids is carried out as a pretreatment. Scarcity of reliable thermochemical properties motivated the use of computational calculations to accurately predict these data for biodiesel compounds. The purpose of this study is to calculate thermochemical data of oleic acid esterification reactions with methanol, ethanol and propanol at several temperatures using the B3LYP hybrid functional with the standard 6-311+G(d,p) basis set. Calculated values of enthalpy of formation were corrected by applying a linear regression correction specifically developed for fatty acids and esters in order to decrease systematic errors related to the negligence of high order electron correlation energies in the B3LYP functional. Results showed that, although the esterification reactions are favoured by the temperature increase, these reactions are not spontaneous within the considered temperature range (from 273.15 to 373.15K), which indicates that additional energy is necessary to accomplish them. Methanol is the most reactive alcohol due its higher partial charge values and chemical equilibrium constants. All these values can be useful to supply missing experimental data in the literature and to better understand the thermodynamics of the oleic acid esterification reaction for biodiesel production purpose.

On the impact of intermolecular interactions between the quaternary ammonium ions on interlayer spacing of quat-intercalated montmorillonite: A molecular mechanics and ab-initio study

The work comprises the nature of intermolecular interactions in the organoclays modified with quaternary ammonium ions, the SOMASIF ME100 organofilized with N-octadecyltrimethylammonium ions and the commercially available Cloisite 15A. The potential energy scan was carried out for two large organoclay models with consistent-valence force field and a few others for comparison. Then, the two-body model of the interacting ions in their most and less preferable orientations was build for both systems and the more detailed, electrically neutral model of the two ions adsorbed on montmorillonite was constructed in order to investigate the non-additive interactions. The most of the work was devoted to study ab-initio calculations performed on the Unrestricted Hartree–Fock level of theory, but the electron correlation effects were also considered. The calculated interaction energy was partitioned into exchange, delocalization and electrostatic terms and the latter was distributed into its multipolar expansion. The specific intermolecular order occurring for the most and the least energetically preferred arrangements was discussed in detail with respect to the intermolecular interactions with the special emphasis on the structures underlying the occurrence of three distinctive phases in organoclay samples, for which the X-ray data was present in the literature. The basis-set dependency of the variational-perturbation scheme adopted to decompose the calculated Hartree–Fock interaction energies was examined with the use of cc-pVDZ and 6-31G basis sets. The comparison proved high reliability of the method used, even for the less extended 3-21G basis. The results revealed the presence of the relationship between the sum of two- and three-body delocalization energy terms and the inverse induced dipole moment, calculated for three body system as well as the independent functional relations between the second order electron correlation correction and Hartree–Fock delocalization and inverse Heitler–London exchange energy terms for the system of two N-octadecyltrimethylammonium cations. The equations proposed may help to predict the values of the electron correlation correction and the stabilizing delocalization energy term from the calculations at Hartree–Fock level of theory as well as from the measured module of the induced dipole moment for molecules.

Potential energy curves for Mo2: multi-component symmetry-projected Hartree–Fock and beyond

The molybdenum dimer is an example of a transition metal system with a formal sextuple bond that constitutes a challenging case for ab initio quantum chemistry methods. In particular, the complex binding pattern in the Mo2 molecule requires a high-quality description of non-dynamic and dynamic electron correlation in order to yield the correct shape of the potential energy curve. The present study examines the performance of a recently implemented multi-component symmetry projected Hartree–Fock (HF) approach. In this work, the spin and spatial symmetries of a trial wavefunction written in terms of non-orthogonal Slater determinants are deliberately broken and then restored in a variation-after-projection framework. The resulting symmetry-projected HF wavefunctions, which possess well-defined quantum numbers, can account for static and some dynamic correlations. A single symmetry-projected configuration in a D∞hS-UHF or a D∞hKS-UHF framework offers a reasonable description of the potential energy curve of Mo2, though the binding energy is too small for the former. Our multi-component strategy offers a way to improve on the single configuration result in a systematic way towards the exact wavefunction: in the def2-TZVP basis set considered in this study, a 7-determinant multi-component D∞hS-UHF approach yields a bond length of 2.01 Å, in good agreement with experimental results, while the predicted binding energy is 39.2 mhartree. The results of this exploratory study suggest that a multi-component symmetry-projected HF stategy is a promising alternative in a high-accuracy description of the electronic structure of challenging systems. We also present and discuss some benchmark calculations based on the CEEIS-FCI (correlation energy extrapolation by intrinsic scaling – full configuration interaction) method for selected geometries.

Ab initio ro-vibrational spectroscopy of the group 11 cyanides: CuCN, AgCN, and AuCN

Accurate near-equilibrium potential energy and dipole moment functions have been calculated for the linear coinage-metal cyanides CuCN, AgCN, and AuCN using coupled cluster methods and sequences of correlation consistent basis sets. The explicitly correlated CCSD(T)-F12b method is used for the potential energy surfaces (PESs) with inclusion of core correlation, and is combined with contributions from molecular spin-orbit coupling, scalar relativity, and effects due to higher order electron correlation. The resulting composite PESs are used in both perturbative and variational calculations of the ro-vibrational spectra. In addition to accurate equilibrium geometries, the ro-vibrational spectra are predicted, which are found to be relatively intense in the 200-600 cm(-1) range due to the bending and metal-carbon stretching modes. The CN stretch near 2165 cm(-1) is also predicted to carry enough intensity to allow its observation by experiment. A strong Fermi-resonance is predicted between the first overtone of the bend and the fundamental of the metal-carbon stretch for both CuCN and AgCN. The heats of formation at 0 K are predicted from their calculated atomization energies to be 89.8, 88.6, and 104.5 kcal mol(-1) for CuCN, AgCN, and AuCN, respectively.

Accurate ab initio ro-vibronic spectroscopy of the $\tilde X^2 \Pi$X̃2Π CCN radical using explicitly correlated methods

Explicitly correlated CCSD(T)-F12b calculations have been carried out with systematic sequences of correlation consistent basis sets to determine accurate near-equilibrium potential energy surfaces for the X(2)Π and a(4)Σ(-) electronic states of the CCN radical. After including contributions due to core correlation, scalar relativity, and higher order electron correlation effects, the latter utilizing large-scale multireference configuration interaction calculations, the resulting surfaces were employed in variational calculations of the ro-vibronic spectra. These calculations also included the use of accurate spin-orbit and dipole moment matrix elements. The resulting ro-vibronic transition energies, including the Renner-Teller sub-bands involving the bending mode, agree with the available experimental data to within 3 cm(-1) in all cases. Full sets of spectroscopic constants are reported using the usual second-order perturbation theory expressions. Integrated absorption intensities are given for a number of selected vibronic band origins. A computational procedure similar to that used in the determination of the potential energy functions was also utilized to predict the formation enthalpy of CCN, ΔH(f)(0K) = 161.7 ± 0.5 kcal/mol.

On the Ionization Energy of HfO

Using a newly developed relativistic pseudopotential and a series of correlation consistent basis sets for Hf, the ionization energy of HfO and the spectroscopic properties of the HfO(+) cation have been determined in coupled cluster calculations. After accounting for basis set incompleteness, outer-core correlation, the pseudopotential approximation, and higher order electron correlation effects, excellent agreement with recent experimental measurements is obtained.

The structure and binding energies of the van der Waals complexes of Ar and N2 with phenol and its cation, studied by high level ab initio and density functional theory calculations

We have investigated, using both ab initio and density functional theory methods, the minimum energy structures and corresponding binding energies of the van der Waals complexes between phenol and argon or the nitrogen molecule, and the corresponding complexes involving the phenol cation. Structures were obtained at the MP2 level using a large basis, and the corresponding energies were corrected for basis set superposition error (BSSE), higher order electron correlation effects, and for basis set size. The structures of the global minima were further refined for the effects of BSSE and the corresponding binding energies were evaluated. For each neutral species, we find only a single true minimum, pi bonded for argon and OH bonded for nitrogen. For both cationic species, we find that the OH-bonded complex is preferred over other minima which we have identified as having Ar or N(2) between exogeneous atoms. The ab initio calculations are generally in excellent agreement with experimental binding energies and rotational constants. We find that the B3LYP functional is particularly poor at describing these complexes, while a density functional theory (DFT) method with an empirical correction for dispersive interactions (DFT-D) is very successful, as are some of the new functionals proposed by Zhao and Truhlar [J. Phys. Chem. A 109, 5656 (2005); J. Chem. Theory Comput. 2, 1009 (2006); Phys. Chem. Chem. Phys. 7, 2701 (2005); J. Phys. Chem. A 108, 6908 (2004)]. Both the ab initio and DFT-D methods accurately predict the intermolecular vibrational modes.

Vibrational spectrum, ab initio calculations, conformational stabilities and assignment of fundamentals of the C i conformer of 1,4-dichlorobutane

The infrared and Raman spectrum of 1,4-dichlorobutane is reported in solid, liquid and gas. Ab initio calculations for the nine stable or metastable conformers of 1,4-dichlorobutane are reported for Moller–Ploessett second order electron correlation and B3LYP density functionals with a variety of basis sets, using approximations as high as 6–311 + g(2d, 2p). Normal coordinate calculations were conducted for the nine conformers and the results used to provide assignments for some of the observed infrared and Raman bands. An attempt to use the assignments together with the ab initio intensities or Raman activities to investigate the composition of the liquid at room temperature proved modestly successful, and suggested that the populations are altered from those expected in the gas phase by interactions of the permanent electric dipole moments with the dipolar plasma in which the conformers are immersed in the liquid. A substantial disagreement between the Moeller–Ploessett and density functional results is reported, and the calculation of intensities and activities is insufficiently accurate to allow detailed interpretation of the spectrum of the room temperature liquid. A complete assignment of fundamentals is given for the conformer of C i symmetry, and one Raman and one infrared band is identified with the C 2h conformer. All the other infrared and Raman bands in the liquid or the gas are composites of several contributors.

Conformational constraint in ferroelectric liquid crystals incorporating a pyrrolidine‐type ring: FLC materials comprising parallel dipolar moments

Ferroelectric liquid crystals bearing a chiral pyrrolidine‐type ring were prepared using (–)‐(S)‐malic acid as a building block. The compounds were characterized using the thermal analysis techniques of DSC and POM, electrical measurements and temperature‐dependent XRD. Samples showed moderate spontaneous polarization values (P S) with helical pitches of about 2.997 µm and an average tilt angle of 16.2° for the SmC* planes. Conformational analysis of the chiral pyrrolidinol subunit and of all of the mesogenic targets was performed using several quantum methods including large basis sets and different treatments of electron correlation in order to correlate experimental results and theoretical predictions. For the most stable conformations, a very small dipole moment component perpendicular to the tilt plane was found which, according to the Boulder model, may be responsible for the moderate PS values obtained.

Analysis of Susceptibility in CeCoIn5Based on Fermi Liquid Theory

We propose a possible strategy of calculating physical quantities in normal states of Ce compounds, in the presence of a crystalline electric field (CEF). In particular, we show the specific heat γ and magnetic susceptibility χ cannot be estimated without correctly treating the CEF splitting and renormalization effect due to electron correlation. In the study, we discuss CeCoIn 5 as a typical example, and estimate γ and χ on the basis of the tight binding model which is suitable for CeCoIn 5 . Throughout the paper, we show how to treat electron correlation in order to construct a renormalized electronic structure. Using the renormalized electronic structure, we obtain reasonable values for physical quantities.

Ab initio Thermochemistry Involving Heavy Atoms: An Investigation of the Reactions Hg + IX (X: I, Br, Cl, O)

AbstractFor Abstract see ChemInform Abstract in Full Text.

Ab Initio Thermochemistry Involving Heavy Atoms: An Investigation of the Reactions Hg + IX (X = I, Br, Cl, O)

Accurate 0 K enthalpies have been calculated for reactions of mercury with a series of small iodine-containing molecules (I2, IBr, ICl, and IO). The calculations have been carried out with the coupled cluster singles and doubles method with a perturbative correction for connected triple excitations [CCSD(T)] using sequences of correlation consistent basis sets and accurate relativistic pseudopotentials. Corrections have been included to account for core-valence correlation, spin-orbit coupling, scalar relativity, and the Lamb shift. In a few cases coupled cluster calculations with iterative triple (CCSDT) and quadruple (CCSDTQ) excitations have been carried out to estimate the effects of higher order electron correlation. The pseudopotential calculations have also been compared to all electron calculations using second- and third-order Douglas-Kroll-Hess Hamiltonians. In addition to the reaction enthalpies, heats of formation, bond lengths, and harmonic vibrational frequencies have been calculated for the stable triatomic products HgI2, HgIBr, HgICl, and HgIO. Accurate dissociation energies, equilibrium bond lengths, and harmonic vibrational frequencies have also been calculated for each of the diatomic molecules involved in this study (HgI, HgBr, HgCl, HgO, I2, IBr, ICl, and IO). The reported enthalpies are expected to have accuracies of 1 kcal/mol or better.

An investigation of the HOMO frontier orbital electron density distributions of NH 3, the methylamines and NF 3 using DFT and electron momentum spectroscopy

Density functional theory (DFT: B3LYP and B3PW91) and Hartree–Fock (HF) calculations using large, saturated and diffuse basis sets are compared with earlier reported highest occupied molecular orbital (HOMO) electron momentum density distributions for NH 3, CH 3NH 2, (CH 3) 2NH, (CH 3) 3N and NF 3 [Chem. Phys. Lett. 137 (1987) 573; Chem. Phys. 123 (1988) 51], measured using electron momentum spectroscopy. Very good quantitative agreement is obtained between the DFT calculations and experiment, in contrast to the rather poor modeling provided by the simpler basis set HF calculations reported in the original studies. The present work demonstrates the need to include dynamic electron correlation in order to correctly model these frontier orbital (HOMO) electron densities.

Infrared and Raman spectra and theoretical study of methyl trifluoromethyl sulfone, CF 3SO 2CH 3

The infrared and Raman spectra were obtained for liquid CF 3SO 2CH 3, as well as the infrared spectrum of the gaseous substance. The molecular geometry was optimized by means of the Hartree–Fock (HF), second order electron correlation (MP2) and density functional theory (DFT) procedures of quantum chemistry, resulting in a structure with C s symmetry. The wavenumbers corresponding to the normal modes of vibration were calculated using the DFT (B3LYP/6-31G**) approximation and their agreement with the measured values improved after scaling of the associated force field. An assignment of bands is proposed on the basis of such calculations and the comparison with related molecules.

Kinetics of the hydrogen abstraction reactions of 1,1‐ and 1,2‐difluoroethane with hydroxyl radical: an ab initio study

The hydrogen abstraction reactions of 1,1- and 1,2-difluoroethane with the OH radical have been investigated by the ab initio molecular orbital theory. The geometries of the reactants, products, and transition states have been optimized at the (U)MP2=full level of theory in conjunction with 6-311G(d,p) basis functions. Single-point (U)MP2=full with larger basis set, such as 6-311G(3d,2p), and QCISD(T)=full/6-311G(d,p) calculations have also been carried out to observe the effects of basis sets utilized and higher order electron correlation. Three and four reaction channels have been identified for 1,1- and 1,2-difluoroethane, respectively. In the case of 1,1-difluoroethane, hydrogen abstraction from the α-carbon has been found to be easier than that from the β-carbon. The barriers of the four reaction channels for 1,2-difluoroethane are close to each other. Weak hydrogen bonding interactions have been observed between hydroxyl hydrogen and a fluorine atom in the transition states. Rate constants for the reactions of 1,1- and 1,2-difluoroethane with the OH radical have been calculated using the standard transition state theory and found to be in good agreement with the experimental results. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1305–1318, 2000

The expectation value of the spin operator [formula omitted] as a diagnostic tool in coupled cluster theory : The advantages of using UHF-CCSD theory for the description of homolytic dissociation

Coupled cluster (CC) theory carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function suffers less from spin contamination because infinite order electron correlation effects covered by the CC method in question reduce spin contamination. For example, UHF-CCSD, contrary to UHF, is not contaminated by a S+1 state. However, the value of 〈 S ̂ 2〉 CCSD , is strongly influenced by the response of the UHF-CCSD wave function on the spin contamination present at UHF and, therefore, adopts a relatively large value. A reliable diagnostic tool correctly reflecting the influence of spin contamination on the UHF-CCSD energy is obtained by just considering the energy related part of 〈 S ̂ 2〉 CCSD .

Calculation of molecular response properties with the second-order coupled perturbed electron propagator

We present the theory of the electron propagator perturbed by an external electric field and show how it can be used to calculate a variety of one-electron linear response properties that are accurate through second order in electron correlation. Some illustrative calculations are discussed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 625–640, 2000

An ab Initio Investigation of the Reactions of 1,1- and 1,2-Dichloroethane with Hydroxyl Radical

The hydrogen abstraction reactions by OH radical from 1,1-dichloroethane and 1,2-dichloroethane have been investigated by ab initio molecular orbital theory. Optimized geometries and harmonic vibrational frequencies have been calculated for all reactants, transition structures, and products at the (U)HF/6-311G(d,p) and (U)MP2=full/6-311G(d,p) levels of theory. Single point QCISD(T)/6-311G(d,p)//(U)MP2=full/6-311G(d,p) calculations have also been carried out for the inclusion of higher order electron correlation. Three distinct transition structures have been located for the H3C−CHCl2 + OH reaction (one for α-abstraction and two for β-abstraction). Four transition structures have been located for the reaction ClH2C-CH2Cl + OH. The calculated barrier heights, reaction enthalpies, and change in entropy are found to be in good agreement with available experimental values. In addition, the rate constants calculated by using the transition state theory are found to be in good agreement with the experimental results. Non-Arrhenius behavior of the rate constants arises from the tunneling effects and availability of multiple reaction channels.