Electron Correlation Corrections Research Articles

Ab initio pseudopotential study of M2As and M2Br (M = Cu, Ag, Au)

The equilibrium geometries and the vibration frequencies of M 2As - and M 2Br +(M=Cu,Ag,Au)are calculated at the HF and the MP2 levels with pseudopotentials. The calculated results indicate that the species have a bent structure(C 2v ). The electron correlation corrections on the geometrical structure are investigated at the MP2 level, the bond angles are reduced by 10°～20° for considered species. The electron correlation effects on the geometry of the Au 2As - are studied particularly at MP2, MP3, MP4, CCSD and CCSD(T) levels. Comparing the species containing Ag and Au, the relativistic effects slightly short the bond lengths of the species. The bonding possibility of the Au 2As - is predicted.

Calculations of Perovskite Surface Relaxation

AbstractThe (100) and (110) surface relaxations are calculated for SrTiO3 and BaTiO3 perovskite thin films by means of a semi-empirical shell model (SM) for different surface terminations. Our SM results for the (100) surface structure are in good agreement with our present ab initio Hartree-Fock calculations with electron correlation corrections, previous ab initio pseudopotential calculationsand LEED experiments. The surface energy for the Ba-, Sr-, TiO- terminated (110) surfaces is found much larger than that for the (100) one. In contrast, the surface energy for the asymmetric O-termination, where outermost O atoms are strongly on-plane displaced, is the lowest for all (110) terminations and thus the most stable.

Ab initio pseudopotential study of M2As? and M2Br+ (M = Cu, Ag, Au)

The equilibrium geometries and the vibration frequencies of M2As− and M2Br+ (M = Cu, Ag, Au) are calculated at the Hartree–Fock (HF) and the second-order Moller–Plesset (MP2) levels with pseudopotentials. The calculated results indicate that the species have a bent structure (C2v). The electron correlation corrections on the geometrical structure are investigated at the MP2 level, the bond angles are reduced by 10°–20° for considered species. The electron correlation effects on the geometry of the Au2As− are studied particularly at MP2, MP3, MP4, CCSD and CCSD(T) levels. Comparing the species containing Ag and Au, the relativistic effects slightly short the bond lengths of the species. The bonding possibility of the Au2As− is predicted. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 38–43, 2000

Modelling of silver adhesion on MgO(100) surface with defects

We show how surface defects (especially Fs0 and Vs0 centres) can play a major role in the adhesion of Ag (at 1:4 and 1:1 coverages) on the MgO(100) surface. Our calculations use a periodic (slab) model and an ab initio Hartree-Fock approach with a posteriori electron correlation corrections. We are able to analyse the interatomic bond populations, effective charges and multipole moments of ions, in combination with the interface binding energy and the equilibrium distances. Both surface defects cause strong redistributions of the electron density which increase the binding energy of metal atoms by more than an order of magnitude. This implies radiation-induced strengthening of metal adhesion on oxide substrates and clarifies defect mechanisms in nucleating film growth. We compare our atomistic predictions with those from simpler methods which might be used for complex technologically interesting systems. There is good general agreement with the image interaction model; differences arise partly from different treatments of dispersion and partly from subtle but significant charge redistribution in the Ag. Further, a simple Born-Haber analysis of charge transfer is consistent with the several cases predicted in the atomistic calculations.

Calculations of the indirect nuclear spin-spin coupling constants of PbH 4

We report ab initio calculations of the indirect nuclear spin–spin coupling constants of PbH4 using a basis set which was specially optimized for correlated calculations of spin–spin coupling constants. All nonrelativistic contributions and the most important part of the spin–orbit correction were evaluated at the level of the random phase approximation. Electron correlation corrections to the coupling constants were calculated with the multiconfigurational linear-response method using extended complete and restricted active space wavefunctions as well as with the second-order polarization propagator approximation and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes. The effects of nuclear motion were investigated by calculating the coupling constants as a function of the totally symmetric stretching coordinate. We find that the Fermi contact term dominates the Pb‐H coupling, whereas for the H‐H coupling it is not more important than the orbital paramagnetic and diamagnetic contributions. Correlation affects mainly the Fermi contact term. Its contribution to the one-bond coupling constant is reduced by correlation, independent of the method used; however, the different correlated methods give ambiguous results for the Fermi contact contribution to the H‐H couplings. The dependence of both coupling constants on the Pb‐H bond length is dominated by the change in the Fermi contact term. The geometry dependence is, however, overestimated in the random phase approximation.

Comparative theoretical study of the Ag–MgO (100) and (110) interfaces

We have calculated the atomic and electronic structures of Ag–MgO(100) and (110) interfaces using a periodic (slab) model and an ab initio Hartree–Fock approach with a posteriori electron correlation corrections. The electronic structure information includes interatomic bond populations, effective charges, and multipole moments of ions. This information is analyzed in conjunction with the interface binding energy and the equilibrium distances for both interfaces for various coverages. There are significant differences between partly covered surfaces and surfaces with several layers of metal, and these can be understood in terms of electrostatics and the electron density changes.For complete monolayer (1:1) coverage of the perfect MgO(100) surface, the most favorable adsorption site energetically for the Ag atom is above the surface oxygen. However, for partial (1:4) coverage of the same surface, the binding energies are very close for all the three likely adsorption positions (Ag over O, Ag over Mg, Ag over a gap position).For a complete (1:1) Ag monolayer coverage of the perfect MgO(110) interface, the preferable Ag adsorption site is over the interatomic gap position, whereas for an Ag bilayer coverage the preferred Ag site is above the subsurface Mg2+ ion (the bridge site between two nearest surface O2− ions). In the case of 1:2 layer coverage, both sites are energetically equivalent. These two adhesion energies for the (110) substrate are by a factor of two to three larger than over other possible adsorption sites on perfect (110) or (100) surfaces.We compare our atomistic calculations for one to three Ag planes with those obtained by the shell model for 10 Ag planes and the Image Interaction Model addressing the case of thick metal layers. Qualitatively, our ab initio results agree well with many features of these models. The main charge redistributions are well in line with those expected from the Image Model. There is also broad agreement in regard to orders of magnitude of energies.

On the accurate theoretical determination of the static hyperpolarizability of trans-butadiene

Finite-field many-body perturbation theory and coupled cluster calculations are reported for the static second dipole hyperpolarizability γαβγδ of trans-butadiene. A very large basis set of [9s6p4d1f/6s3p1d] size (336 contracted Gaussian-type functions) should lead to self-consistent field (SCF) values of near-Hartree–Fock quality. We report γxxxx=6.19, γxxxz=−0.44, γxxyy=3.42, γzzxx=2.07, γxyyz=−0.50, γxzzz=1.73, γyyyy=14.72, γyyzz=8.46, γzzzz=24.10 and γ̄=14.58 for 10−3×γαβγδ/e4a04Eh−3 at the experimental geometry (molecule on the xz plane with z as the main axis). γ̄=(14.6±0.4)×103e4a04Eh−3 should be a very reliable estimate of the Hartree–Fock limit of the mean hyperpolarizability. Keeping all other molecular geometry parameters constant, we find that near the Hartree–Fock limit the mean hyperpolarizability varies with the C=C bond length as 10−3×γ̄(RC=C)/e4a04Eh−3=14.93+31.78ΔR+30.88ΔR2−2.96ΔR3 and with the C–C bond length as 10−3×γ̄(RC–C)/e4a04Eh−3=14.93−7.20ΔR+3.04ΔR2, where ΔR/a0 is the displacement from the respective experimental value. The dependence of the components of γαβγδ on the molecular geometry parameters is not uniform. Electron correlation corrections have been calculated at various molecular geometries at the coupled-cluster single, double and perturbatively linked triple excitations level of theory for all independent components of γαβγδ. In absolute terms, electron correlation affects strongly the γzzzz, less strongly the γxxxx, and even less strongly the out-of-plane component γyyyy. The present analysis suggests a conservative estimate of (3.0±0.6)×103e4a04Eh−3 for the electron correlation correction to γ̄ at the experimental molecular geometry. Most of this value is appropriate to γzzzz. A static limit of γ̄=(17.6±1.0)×103e4a04Eh−3 is advanced (neglecting vibrational averaging). Even if a crude theoretical estimate of the dispersion of γ̄ at 1064 nm is added to this value, the result sets up an unambiguous claim to accord with the experimental value of (20.18±0.11)×103e4a04Eh−3 [D. P. Shelton, Phys. Rev. A 42, 2578 (1990)].

Effects of basis set and electron correlation on the calculated interaction energies of hydrogen bonding complexes: MP2/cc-pV5Z calculations of H2O–MeOH, H2O–Me2O, H2O–H2CO, MeOH–MeOH, and HCOOH–HCOOH complexes

The MP2 intermolecular interaction energies of the title complexes were calculated with the Dunning’s correlation consistent basis sets (cc-pVXZ, X=D, T, Q, and 5) and the interaction energies at the basis set limit were estimated. The second-order Mo/ller–Plesset (MP2) interaction energies greatly depend on the basis sets used, while the Hartree–Fock (HF) energies do not. Small basis sets considerably underestimate the attractive interaction. The coupled cluster single double triple [CCSD(T)] interaction energies are close to the MP2 ones. The expected CCSD(T) interaction energies of the H2O–MeOH, H2O–Me2O, H2O–H2CO, MeOH–MeOH, and HCOOH–HCOOH complexes at the basis set limit are −4.90, −5.51, −5.17, −5.45, and −13.93 kcal/mol, respectively, while the HF/cc-pV5Z energies are −3.15, −2.58, −3.60, −2.69, and −11.29 kcal/mol, respectively. The HF calculations greatly underestimate the attractive energies and fail to predict the order of the bonding energies in these complexes. These results show that a large basis set and the consideration of an appropriate electron correlation correction are essential to study interactions of hydrogen bonding complexes by ab initio molecular orbital calculation.

Torsional potential of biphenyl: Ab initio calculations with the Dunning correlation consisted basis sets

The internal rotational barrier heights of biphenyl were calculated with the Dunning correlation consisted basis sets (up to cc-pVQZ, 960 basis functions) and the electron correlation correction by the second order Mo/ller-Plesset method (MP2). Although previous Hartree–Fock (HF) and MP2 calculations showed that the internal rotational barrier height at 0° (ΔE0) was substantially larger than that at 90° (ΔE90), our MP2/cc-pVQZ//MP2/6-31G* calculations showed that ΔE0 (2.28 kcal/mol) was close to ΔE90 (2.13 kcal/mol), which agreed with the estimation from experimental measurements. The calculations of benzene dimers suggested that the dispersion interaction increased the relative stability of the coplanar conformer. The basis sets employed in the previous calculations were not large enough to evaluate the attractive dispersion interaction. The underestimation of the stabilization of the coplanar conformer by the dispersion interaction would be one of the reasons for the overestimation of ΔE0 in the previous calculations.

Molecular relativistic calculations of the electric field gradients at the nuclei in the hydrogen halides

Electric field gradients at the position of the nuclei in the hydrogen halides are calculated using four-component relativistic methods. Benchmark values at the Dirac–Hartree–Fock level of theory are obtained by using large uncontracted basis sets. Electron correlation corrections are obtained by means of finite field MP2, CCSD, and CCSD(T) calculations in smaller basis sets. The importance of spin–orbit coupling and the so-called picture change effect are discussed.

Molecular modeling of the pendant chain in Nafion®

Ion transport through perfluorosulfonic acid ionomers such as Nafion® is controlled by both the microstructure of the polymer and the charge and water distribution in the hydrated polymer. We present here the results of theoretical calculations on the side chain of Nafion®, establishing microscopic information for the modeling of water and proton transport in the membrane. Optimized geometries for the trifluoromethane sulfonic acid fragment (CF 3SO 3H), the di-trifluoromethane ether fragment (CF 3OCF 3), and the side chain (CF 3-OCF 2CF(CF 3)OCF 2CF 2SO 3H) were determined by means of both ab initio Hartree Fock theory with second order Møller–Plesset electron correlation corrections, and density functional theory with Becke's three parameter hybrid method. Several rotational potential energy surfaces were calculated to assess chain flexibility and proton accessibility. A probe water molecule was added to each of the fragments to characterize hydrophilic sites. These calculations confirmed that the sulfonic acid group is hydrophilic and the ethers are hydrophobic. Molecular dynamics simulations were then performed on the side chain to check the conditions required to stretch the pendant chain. Thermal averages of several structural parameters assessing the flexibility and stretch of the chain were computed from selected conformations produced in the simulation and these results indicate that although the sulfonate group is free to rotate, the chain stretches little. The construction of a potential energy surface for rotation about the second ether group suggests that the side chain exists in a folded or curled up conformation. A physical continuum dielectric solvent model was used to obtain free energies of electrostatic interaction of the fragments and the full chain with the solvent.

Intermolecular interaction potential of the carbon dioxide dimer

The energy profile of the lowest energy path connecting the slipped parallel (C2h) and T-shaped (C2v) dimers of carbon dioxide was investigated using a reasonably large 6-311+G(2df) basis set with the MP2 level electron correlation correction and with the counterpoise correction. There was no inversion barrier and the T-shaped dimer was a transition state connecting the two slipped parallel dimers. The calculated interaction energies of the two dimers (−1.290 and −1.072 kcal/mol) were larger than those reported previously. The calculated energy difference of the two dimers (0.218 kcal/mol) was also larger than the previous values (less than 0.1 kcal/mol). The effects of basis set, electron correlation, and basis set superposition error were studied in detail. The second-order Mo/ller–Plesset (MP2) interaction energies of the two dimers were close to the coupled cluster calculations using single and double substitutions including noniteratively triple excitations [CCSD(T)] ones. The choice of the basis set greatly affected the calculated interaction energies. Small basis sets underestimated the attractive interaction energies. Diffuse polarization functions were essential to evaluate the attractive interaction. The calculated MP2 interaction energies of the two dimers with the counterpoise correction increased by the augmentation of the diffuse polarization functions to the 6-311G* basis set. These values were close to the estimated MP2 interaction energies at the complete basis set (−1.362 and −1.140 kcal/mol). The 6-311+G(2df) basis set was reasonably large to evaluate the attractive interactions. Although the basis set augmented with diffuse polarization functions had large basis set superposition error (BSSE), the calculated interaction energies with the counterpoise correction were close to those calculated with the nearly BSSE free cc-pV5Z and aug-cc-pVQZ basis sets and to the expected values at the complete basis set.

Relativistic, quantum electrodynamic and many-body effects in the water molecule

Ab initio calculations are reported of the electronic structure of the water molecule, based on the Dirac theory of the electron using correlation consistent basis sets. We calculate electron correlation corrections by second-order many-body perturbation theory, NMR shielding constants in the four-component relativistic interaction Hamiltonian formulation of QED, and report the first calculation of the electronic structure of a molecular system in which the Breit interaction is included both perturbatively and variationally in the calculation of the total energy.

Hyperpolarizability of H 2O revisited: accurate estimate of the basis set limit and the size of electron correlation effects

A large (18s 13p 8d 5f / 12s 7p 3d 2f) basis set consisting of 256 uncontracted gaussian-type functions is expected to yield values near the Hartree–Fock limit for the static hyperpolarizability of H 2O: β zxx =−9.40, β zyy =−1.35, β zzz =−7.71 and β ̄ =−11.07 for β α β γ ( e 3 a 0 3 E h −2) and γ xxxx =569, γ yyyy =1422, γ zzzz =907, γ xxyy =338, γ yyzz =389, γ zzxx =287 and γ ̄ =985 for γ α β γ δ ( e 4 a 0 4 E h −3) at the experimental equilibrium geometry (with z as the C 2 axis, molecule on the xz plane). The respective electron correlation corrections obtained with the single, double and perturbatively linked triple excitations coupled-cluster method and a [9s 6p 6d 3f / 6s 4p 2d 1f] basis set are β zxx =−0.45, β zyy =−4.19, β zzz =−6.09, β ̄ =−6.44 and γ xxxx =267, γ yyyy =1228, γ zzzz =574, γ xxyy =295, γ yyzz =322, γ zzxx =152, γ ̄ =721 . For the static limit we propose β ̄ =−17.5±0.3 e 3 a 0 3 E h −2 and γ ̄ =(171±6)×10 1 e 4 a 0 4 E h −3, in near agreement with the experimental findings of β ̄ =−19.2±0.9 e 3 a 0 3 E h −2 and γ ̄ =1800±150 e 4 a 0 4 E h −3 deduced from EFISH measurements at 1064 nm by Kaatz et al. [P. Kaatz, E.A. Donley, D.P. Shelton, J. Chem. Phys. 108 (1998) 849].

Electronic Structure of Dipole-Bound Anions

Dipole-bound anionic states of HCN, (HF)2, CH3CN, C3H2, C4H2, C5H2, and stretched CH3F are studied using extended one-electron basis sets at the coupled cluster level of theory with single, double, and noniterative triple excitations (CCSD(T)). Orbital relaxation and electron correlation corrections to the Koopmans' theorem prediction of electron binding energy are analyzed, and a physical interpretation of low-order corrections is proposed. It is demonstrated that the second-order dispersion interaction between the loosely bound electron and the electrons of the neutral host should be included into physical models of dipole-bound anions. Higher-order electron correlation corrections are also found to be important, and a slow convergence of the Moller−Plesset series for electron binding energies is documented. Modifications of the potential energy surfaces of the above polar molecules upon electron attachment are studied at the second-order Moller−Plesset level, and Franck−Condon factors for the anion/neu...

Static first hyperpolarizability of small all-trans polymethincimine oligomers. Basis set and electron correlation effects

Ab initio calculations, which include the electronic correlation effects, of the static longitudinal first hyperpolarizability, β L , of small all-trans polymethineimine (PMI) chains (from monomer to trimer) have been performed with a large panel of basis sets. The electron correlation corrections were included via the Møller-Plesset partitioning and the Coupled-Cluster method. We show that the basis set effects are smaller when using correlated techniques than at the Hartree-Fock level. Moreover, the Hartree-Fock approximation does not reproduce the correct sign of β L even for the dimer and the trimer. Addition of d functions on carbon and nitrogen atoms is important in order to obtain a quantitative evaluation of β L , while the use of supplementary p functions on hydrogen atoms does not lead to significant variations. When polarization functions are added, the amplitude of β L decreases by going from a double-ζ to a triple-ζ basis set. Within the Møller-Plesset scheme, the second-order correction is by far the largest and is responsible for the sign change. However, contrary to the third-order correction, the fourth-order correction considerably changes the β L amplitude due to important single and triple contributions. In the Coupled-Cluster approaches, the inclusion of the singles strongly damps the correction due to the doubles, the inclusion of the triples within the CCSD(T) approach modulating it. Comparisons with other works demonstrate that the correlation effects are large in PMI oligomers. We conclude that the 6–31G basis set with d polarization functions on the carbon and nitrogen atoms, used in the Møller-Plesset partitioning consistent with electron-electron interactions through the fourth order, is suitable for the investigation of small PMI chains and would deserve to be considered in the study of longer chains.

Comparison of density functional and MP2 geometry optimizations of Na(H 2O) n ( n = 1–3) clusters

Geometry optimizations have been carried out for clusters of sodium with as many as three water molecules. Potential energy surfaces were generated both conventionally, via Hartree-Fock calculations with electron correlation correction by secondorder Møller-Plesset (MP2) perturbation theory, and by three methods based on density functional theory (DFT). The DFT methods have proven to be able to reproduce the most stable geometric configurations of the hydrogen-bonded clusters predicted by MP2. Some discrepancies occurred with the DFT methods, including erroneous energy ordering of local minimum structures and location of false minima on some potential surfaces.

A theoretical MO ab initio approach to the conformational properties and homolytic bond cleavage in aryl disulphides

The structural and conformational properties of disulphides R 1S-SR 2, with R 1 = phenil ring ( Ph) and R 2 = H, Me and Ph and, for a comparison, those of the disulphides with R 1, R 2 = H, Me were determined with MO ab initio calculations. The level of theory chosen was the 3–21G ∗ with full geometry relaxation and electron correlation corrections at a second order Møller-Plesset perturbation scheme (MP2/3-21G ∗//MP2/3-21G ∗). This choice allowed a comparison of the properties calculated for the molecules containing alkyl and phenyl groups at the same level of theory. All the disulphides examined showed patterns of the potential energy for internal rotation with a minimum conformation of skew type and two maxima, one of cis and one of trans type, with the former representing the higher transition state for internal rotation. The effect of the R group is higher on the cis barrier and the effect of Me and Ph is respectively to increase and decrease the barrier, with respect to RH. The bond energy required for homolitically breaking the bonds (BDE) in these molecules and in the radicals RSS was estimated both from calculated total molecular energies, and from heats of formation of the species involved in the dissociation processes. The BDE's from the ab initio energies were found to have been largely underestimated, which applies to a different extent to the SS, SH and CS bonds. For the SS bond, the BDE's calculated at the level of theory adopted here are proportional to values from experiments or from higher levels of theoretical approaches. For the disulphides with R 1, R 2 = H, Me, calculations were performed with the sophisticated Gaussian-2 (G2) scheme and the BDE's obtained are very close to the most accurate determinations, showing that a high level of theory is necessary to obtain these quantities at a convenient level of confidence. The origin of the barriers for internal rotation and of the different bond strengths in the molecules and radicals containing the SS bond was analyzed within the natural bond orbital (NBO) description of donor-acceptor interactions.

Single-Bond Torsional Potentials in Conjugated Systems: A Comparison of ab Initio and Density Functional Results

The fully relaxed single-bond torsional potentials in typical conjugated systems were evaluated with the aid of ab initio self-consistent-field and Moller−Plesset second-order calculations and, additionally, with several recently developed variants of the density functional theory. For this systematic investigation, 1,3-butadiene, styrene, biphenyl, 2,2‘-bithiophene, 2,2‘-bipyrrole and 2,2‘-bifuran have been selected as model molecules. As representative examples for nonconjugated systems, the molecules n-butane and 1-butene have been treated at the very same calculational levels. For all conjugated molecules, the electron correlation corrections to the self-consistent-field torsional potentials, as obtained with the density functional methods, are dramatically different from those resulting from the more conventional Moller−Plesset second-order approximation. For those cases where experimental data for torsional barriers are available, the self-consistent-field and the Moller−Plesset second-order results...

Atomic ionization potentials and electron affinities with relativistic and mass corrections

Relativistic corrections to ionization potentials (IPs) and electron affinities (EAs) of atoms with an atomic number Z≤54 are examined based on the first-order perturbation theory with an approximate Schrodinger form of the Dirac-Coulomb-Breit Hamiltonian. Using a Hartree-Fock (HF) wave function from the numerical HF method as the unperturbed function, both the LS-non-splitting and fine-structure corrections are evaluated together with the normal and specific mass corrections. The LS-non-splitting corrections are found to be important for IPs and EAs of transition metal atoms. The fine-structure corrections are generally larger in magnitude than the LS-non-splitting corrections for the atoms of groups 13–18 with Z≥31, and can never be neglected. Comparison of the IPs and EAs presented here and experimental IPs and EAs gives an estimation of the electron correlation correction for these properties. For some light atoms, the estimated values agree with the results directly obtained from correlated calculations.