Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2

Ab initio accurate all-electron relativistic molecular orbital Dirac–Fock self-consistent field calculations are reported for the linear symmetric XeF₂ molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₂ at various internuclear distances. The relativistic correction to the electronic energy of XeF₂ was calculated as ～ ?215 hartrees (?5850 eV) by using the Dirac–Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac–Fock–Breit self-consistent field and perturbation methods. The calculated Breit correction is ～6.5 hartrees (177 eV) for XeF₂. The relativistic Dirac–Fock as well as the nonrelativistic HF wave functions predict XeF₂ to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF₂ by using various ab initio post Hartree–Fock methods. The calculated dissociation energy obtained using the MP 2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ～ ?2 hartrees (?54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe—F distance of 1.979 Å in XeF₂. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (D_e) close to experimental value for XeF₂. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF₂. © 1995 John Wiley & Sons, Inc.     

Electron correlation and relativistic effects in xenon tetrafluoride

Ab initio all-electron fully relativistic Dirac–Fock self-consistent field and Dirac–Fock–Breit calculations are reported for the XeF₄ molecule at various internuclear distances assuming the experimental D_4h geometry with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₄ at various internuclear distances. The calculated relativistic correction to the total energy of molecule at the Dirac–Fock level is ～ ?5856 eV, whereas the magnetic part of the Breit correction to the electron-electron interaction is calculated as ～ 177 eV. The electron correlation effects were included in the nonrelativistic Hartree–Fock calculations using the second-order Møller-Plesset (MP 2) theory, and the calculated correlation energy for XeF₄ is ?71 eV. The basis-set superposition error (BSSE ) was estimated by using the counterpoise method for Xe and F. The inclusion of both the relativistic and electron correlation effects in the calculated total energies of F, Xe, and XeF₄ predicts the Xe—F bond length and dissociation energy of XeF₄ as 1.952 Å and 5.59 eV, respectively, which are in excellent agreement with the experimental values of 1.953 Å and 5.69 eV, respectively, for XeF₄. The contribution of the electron correlation and relativistic effects to the dissociation energy of XeF₄ is 8.11 and 0.05 eV, respectively. The Breit interaction, however, contributes only 0.02 eV to the dissociation energy of XeF₄. Electron correlation is most significant for the prediction of an accurate value of dissociation energy, whereas relativistic effects are very important for the prediction of spin-orbital splitting as well as the energies of the orbitals, especially the inner orbitals of XeF₄. © 1995 John Wiley & Sons, Inc.     

Comparative study on formamide–water complex

The hydrogen bonding of 1:1 complexes formed between formamide and water molecule have been investigated systematically using Hartree–Fock (HF), hybrid density functional theory (B3LYP), and post‐Hartree–Fock (MP2 and CCSD(T)) methods with range of basis sets 6‐31G(d), cc‐pVXZ (X = D, T, Q) and aug‐cc‐pVYZ (Y = D, T). Three stable structures are considered on the potential energy surface of formamide and water system. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The IR frequencies, intensities, and frequency shifts are reported. This study shows that B3LYP/aug‐cc‐pVDZ method gives better performance for formamide‐water complexes. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010.     

Binary (e,2e) spectroscopic study of carbonyl sulfide and the momentum-space chemistry of CO2, CS2 and OCS

The valence-shell binding energy spectra (8–44 eV) and molecular orbital momentum distributions of OCS have been studied by non-coplanar symmetric binary (e,2e) spectroscopy. Existing theoretical binding energy spectra calculated using the many-body 2ph-TDA Green's function (GF) method and using the symmetry-adapted cluster (SAC) on method are compared with the experiment. Intense many-body structure in the measured and calculated binding energy spectra indicates the general breakdown of the independent particle ionization picture. Experimental momentum distributions are compared with those calculated using ab initio SCF wavefunctions of minimal basis set quality and of near Hartree—Fock quality. Excellent agreement between the experimental momentum distributions and those calculated by the near Hartree—Fock wavefunction is obtained for the three innermost valence orbitals: 8σ, 7σ and 6σ. The correct order of the close lying outer-valence 2π and 9σ orbitals is unambiguously identified from the shapes of the measured momentum distributions. Momentum and position contour density maps computed from theoretical wavefunctions of near Hartree—Fock quality are used to interpret the shapes and atomic characters of the observed momentum distributions. The momentum densities of the outermost-valence antibonding π orbitals and of the outermost-valence bonding σ orbitals of the linear triatomic group: CO₂, CS₂ and OCS are compared respectively with each other. The associated chemical trends are discussed within the existing framework of momentum-space chemical principles.     

Electronic structure of GaN nanotubes

Nanotube properties are strongly dependent on their structures. In this study, gallium nitride nanotubes (GaNNTs) are analyzed in armchair and zigzag conformations. The wurtzite GaN (0001) surface is used to model the nanotubes. Geometry optimization is performed at the PM7 semiempirical level, and subsequent single-point energy calculations are carried out via Hartree–Fock and B3LYP methods, using the 6-311G basis set. Semiempirical and ab initio methods are used to obtain strain energy, charge distribution, dipole moment, |HOMO-LUMO| gap energy, density of states and orbital contribution. The gap energy of the armchair structure is 3.82 eV, whereas that of the zigzag structure is 3.92 eV, in agreement with experimental data.     

A comparison of Hartree—Fock,MP2, and DFT results for the HCN dimer and crystal

A number of hydrogen-bond related quantities—geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies—were calculated at the Hartree—Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree—Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree—Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree—Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree—Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree—Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)₂ dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.     

Electronic correlation contribution to the three-body potentials for water trimers

A number of trimers of water molecules have been computed with an extended basis set in the Hartree–Fock and in the direct CI approximations. It has been verified that the three-body interaction energy can be calculated within the Hartree–Fock method. Therefore, the correlation corrections to the Hartree–Fock level are essentially additive and do not contribute significantly to three-body effects.     

Highly correlated particle densities and idempotent one-densities

The problem of determining idempotent one-densities which integrate to the exact or to a highly correlated particle density is considered. A method for obtaining the minimum energy idempotent one-density integrating to a given correlated particle density within a finite basis is described. The implications of this are twofold. First, Hartree–Fock accuracy can be exceeded in describing the electron density with an idempotent one-density; this is particularly relevant to the problem of constructing orbitals from experimental x-ray scattering data. Second, electron densities from analytic CI or MCSCF wave functions can be made available in a form as compact as the Hartree–Fock density by reporting the orbitals which define the correlated density via an idempotent one-density. A numerical example of the new method is given in which an accurate correlated density for He is “fitted” by an idempotent one-density represented in a finite (near Hartree–Fock) basis. Considering the deficiencies of the basis for this purpose, a technique is suggested for constructing basis sets optimized for prediction of one-electron properties rather than for energy.     

A correlation study of Li ground state by the MCHF procedure

Results are reported for multiconfiguration Hartree–Fock studies of correlation in the lithium ground state, which maintain orthogonality of orbitals within a configuration. It is shown that when the 1s- and 2s-orbitals are fixed at their Hartree–Fock value, configurations for which Brillouin's theorem holds may be important, particularly for atomic properties other than energy. The Fermi contact term is considered as an example.     

Coulomb-Hole–Hartree–Fock functional

We have extended to molecules a density functional previously parametrized for atomic computations. The Coulomb-hole–Hartree–Fock functional, introduced by Clementi in 1963, estimates the dynamical correlation energy by the computations of a Hartree–Fock-type single-determinant wave function, where the Hartree–Fock potential was augmented with an effective potential term, related to a hard Coulomb hole enclosing each electron. The method was later revisited by S. Chakravorty and E. Clementi [Phys. Rev. A 39 , 2290 (1989)], where a Yukawa-type soft Coulomb hole replaced the previous hard hole; atomic correlation energies, computed for atoms with Z = 2 to Z = 54 as well as for a number of excited states, validated the method. In this article, we parametrized a function, which controls the width of the soft Coulomb hole, by fitting the first and second atomic ionization potentials of the atoms with 1 ? Z ? 18. The parametrization has been preliminarily validated by computing the dissociation energy for a number of molecules. A few-determinant version of the Coulomb-hole–Hartree–Fock method, necessary to account for the nondynamic correlation corrections, is briefly discussed. © 1994 John Wiley & Sons, Inc.     

Ab initio study of organic mixed valency

A series of six radical cations of the type (D L D)⁺ was investigated at the ab initio unrestricted Hartree–Fock level. One localized and one delocalized conformation were systematically searched by full geometry optimization. At both nuclear arrangements, mostly found as being minima in the symmetry‐restrained Hartree–Fock framework, excitation energies were calculated through the expansion of the wave function on single electronic excitations of the Hartree–Fock fundamental determinant and at the unrestricted Hartree–Fock or at the multiconfigurational self consistent field levels. Few calculations were also performed by taking into account some part of the electronic correlation. Except for N,N,N′,N′‐tetramethyl p‐phenylenediamine, all the studied compounds are localized stable cations, at the symmetry‐restrained Hartree–Fock level. However, the reoptimization of their wave function changes this observation since only three of them seem to conserve a localized stable conformation. Most of the studied systems are characterized by one or two excited electronic states very close to the fundamental one and should thus present an unresolved broadened first absorption band in the near‐infrared region. These features are in agreement with the available experimental data. Strong Hartree–Fock instabilities are found for the delocalized structure and put in relation with the existence of the large nonadiabatic coupling in this conformational region. The solvent influence is discussed in the Onsager dipolar reaction field framework. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 552–573, 2000     

Ab initio studies on hydrogen bonded chains. I. Equilibrium geometry of the infinite,linear chain of hydrogen fluoride molecules

The idealized case of an infinite, linear chain of hydrogen fluoride molecules is studied at the Hartree—Fock level with the aid of the crystal orbital method. Extended gaussian basis sets have been used to compute the equilibrium structure and the stabilization energy (hydrogen bond energy) per HF molecule. It is demonstrated that near Hartree—Fock limit results for this model system account for a large part of the observed differences between isolated dimers in the gas phase and the infinite periodic crystal. For the infinite chain the following results were obtained: r_HF = 1.721 bohr, r_FF = 5.049 bohr and ΔE (hydrogen bond energy per HF) = 5.9 kcal/mole.     

Adapted Gaussian basis sets for atoms Cs to Lr based on the generator coordinate Hartree–Fock method

We have applied a discretized version of the generator coordinate Hartree–Fock method to generate adapted Gaussian basis sets for atoms Cs (Z=55) to Lr (Z=103). Our Hartree–Fock total energy results, for all atoms studied, are better than the corresponding Hartree–Fock energy results attained with previous Gaussian basis sets. For the atoms Cs to Lr we have obtained an energy value within the accuracy of 10⁻⁴ to 10⁻³ hartree when compared with the corresponding numerical Hartree–Fock total energy results. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 858–865, 1998     

The two-dimensional band structure of (polyphthalocyaninato)Ni(II)

The two-dimensional (2D) band structure of (polyphthalocyaninato)Ni(II), Ni(ppc), has been analyzed by a self-consistent field (SCF ) Hartree–Fock (HF ) crystal orbital (CO ) formalism based on an INDO (intermediate neglect of differential overlap) type Hamiltonian. The calculated HF band gap of Ni(ppc) amounts to 0.24 eV. The highest filled band is a ringlike a_1u combination (D_4h symmetry label) localized at the carbon sites of the organic fragment. Remarkable hybridization in the valence band leads to the considerable band width Δ?_v of 2.92 eV. This value is close to the Δ?_v numbers which are conventionally encountered in one-dimensional metallomacrocycles. The effective width of the states in Ni(ppc) is 13.8 eV. In graphite a net π interval of 13.0 eV is predicted by the present CO formalism; i.e., the energetic distribution of the π electrons is roughly comparable in both 2D solids. The Ni 3d states in Ni(ppc) are far below the Fermi level which is calculated at ?4.9 eV; they are predicted between ?12.2 and ?16.4 eV in the mean-field approximation. Quasi-particle corrections lead to a significant shift of these strongly metal-centered states. Important electronic structure properties of Ni(ppc) are compared with those of 1D metallomacrocycles with similar molecular stoichiometry. The total density of states distribution of Ni(ppc) has been fragmented into projected (ligand π and σ, Ni 3d) contributions in order to allow for a transparent interpretation of the 2D band structure.     

A Comparison of the Interacting Quantum Atoms (IQA) Analysis of the Two-Particle Density-Matrices of MP4SDQ and CCSD

Within the quantum topological energy partitioning method called Interacting Quantum Atoms (IQA) we transition from Møller-Plesset (MP4SDQ) to CCSD in calculating intra- and interatomic electron correlation energies for a set of hydrides, diatomics, a few simple molecules and non-covalently bonded complexes, using the uncontracted basis set 6-31++G(2d,2p). CCSD-IQA allows a more rigorous analysis of atomic electron correlation than that offered by Møller-Plesset, which returns IQA contributions that are identical to Hartree–Fock counterparts except for two-electron terms. The CCSD-IQA analysis returns bond and other interatomic correlation energies that are typically much larger in magnitude than the MP4SDQ values. Crisp patterns of energy transferability are detected in water clusters, both for intra-atomic and interatomic correlation energies. CCSD determines that the intra-atomic correlation energy of an oxygen drops by 15 kJ · mol^–1 for donating a hydrogen and by 25 kJ · mol^–1 for accepting a hydrogen.     

The structure of naphthalene

The structure of naphthalene has been determined by ab initio gradient computation at the Hartree—Fock level using the 4–21 basis set. Special attention is paid to the small differences between the nearly equal C-C distances and to evaluation of the ability of electron diffraction experiments to distinguish among them. The computed orbital energies are used to assign the photoelectron spectrum.     

Hartree–Fock wave functions with a modified GTO basis for atoms

We have solved the atomic Hartree–Fock equations by using the algebraic approach, expanding the single-particle radial wave function in terms of a modified Gaussian type orbitals (GTOs) basis. Several atomic properties such as Kato's cusp condition for the electron density or the correct asymptotic behavior of the electron momentum density distribution are accurately verified. Additionally the energy of the atomic ground state can be obtained by using a smaller number of basis functions than in standard GTO expansions. This study has been performed for several atoms of the first three rows. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 59–64, 1997     

An interative scheme for electronic systems using one-electron green's functions

In this paper an iterative generalization of the minimum principle proposed for electronic systems by Hall, Hyslop, and Rees is investigated. It is shown that this generalization still retains the advantage of using members of a larger class of trial wave-functions, for example those with discontinuities, as initial approximations to the wave-functions. This scheme has the advantage that, at each stage of iteration, an upper bound is obtained which is at least as good as that obtained previously. The theory is first applied to the hydrogen atom. It is then adapted to estimate the Hartree–Fock energy of the helium atom, the Hartree–Fock limit being obtained after a relatively small number of iterations.     

Dyson-corrected orbital energies for the perturbative treatment of electron correlation

The effect of replacing the Hartree–Fock one-particle energies with ionization potentials obtained from inverse Dyson equation when calculating electron correlation energies perturbatively is investigated. Though the energy shifts vary from system to system, the slight decrease of the resulting excitation energies at around equilibrium geometries leads to a slight increase of the correlation energies in most cases. In the dissociation limit the inverse Dyson equation opens the gap, thus nondiverging potential curves emerge even at the restricted Hartree–Fock (RHF)+RS2 level. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 713–719, 1998     

Interacting stereo-irregular chains: A model for conducting polymers

Interacting stereo-irregular chains of hydrogen atoms, which simulate the topological structure of many conducting polymers, are generated by a computer and solved numerically with the unrestricted Hartree–Fock method with a modified spin polarized potential. The electron localization is investigated, and a mechanism for the interchain tunneling is discovered. Local antiferromagnetic ordering is derived which may explain the AF behavior observed in some conducting polymers.