Relativistic pseudopotentional incorporating core/valence polarization and nonlocal effects

A relativistic pseudopotentional (RPP) for use in ab initio molecular electronic structure calculations is derived in the context of the relativistic effective core potential (REP) method of Lee et al. The resulting atom-specific RPP has salient features of the REP imbedded within it while retaining the form of a functional that is dynamically defined at runtime when used in calculations on molecules. The RPP is determined from Dirac-Fock wave functions for the isolated atom. Outer core two-electron interactions are incorporated into the RPP by means of variable coefficients that are defined in the context of the final molecular wave function. This form permits polarization of the outer core shells analogous to that occurring in all-electron molecular Hartree-Fock calculations while retaining these shells as part of the atomic pseudopotentional. Use of the RPP in post-Hartree-Fock molecular calculations permits the incorporation of core/valence correlation effects.     

AB initio effective core potentials including relativistic effects. A procedure for the inclusion of spin-orbit coupling in molecular wavefunctions

The first ab initio procedure for the treatment of spin-orbit coupling in molecules based on the use of relativistic effective potentials derived from Dirac-Fock atomic wavefunctions is presented. A rigorous definition for the spin-orbit operator is given and its use in molecular calculations discussed.     

Electronic structure of UH,UF, and their ions

A relativistic effective core potential (REP) has been generated for the uranium atom and used in self-consistent-field calculations of the A states of UH, UF, and their ions. Energy curves were calculated at the base configuration level which ensures the dissociating atoms are described by Hartree–Fock wavefunctions. The electronic bonding of these molecules is found to be similar to that of comparable alkaline–earth hydrides and fluorides. The uranium 6p, 6d, and 5f orbitals retain their atomic character but the orbitals extend into the bonding region and are distorted by overlap repulsion and electrostatic effects. Nonetheless, the atomic energetic coupling determines that low energy states will have the maximum spin multiplicity and maximum orbital angular momentum projection consonant with the charge-transfer bonding.     

Ab-initio calculations on large molecules and solids by desirable computational procedures

Desirable computational procedures developed here recently for ab-initio calculations on large molecules are outlined. Effective core model potentials (MODPOT) permit calculations of valence electrons only explicitly, yet accurately; a charge-conserving integral prescreening evaluation to decide whether a block of integrals will be larger than a preset threshold and thus be calculated explicitly is effective for spatially extended systems; an efficient MERGE technique to save and reuse common invariant skeletal integrals is useful for geometry variations and for adding basis fcuntions, substituent groups and molecules; and an effective configuration interaction (CI) Hamiltonian into which are folded the effects of the occupied molecular orbitals from which no excitations are allowed is useful for molecular decompositions and intermolecular reactions. These techniques have been extended for CI calculations on breaking a chemical bond in a molecule in a crystal or solid; atom-class/atomic-class potential functions and dispersion calculations have been added. In a new program, POLY-CRYST, all the integral strategies for large molecules are meshed.     

The solvation of Li and Na in acetonitrile from ab initio-derived many-body ion–solvent potentials

Several Li⁺- and Na⁺-acetonitrile models were derived from ab initio calculations at the counterpoise-corrected MP2/TZV++(d,p) level for distorted ion-(MeCN)_n clusters with n=1, 4 and 6. Two different many-body ion-acetonitrile models were constructed: an effective three-body potential for use with the six-site effective pair model of Böhm et al., and an effective polarizable many-body model. The polarizable acetonitrile model used in the latter model is a new empirical model which was also derived in the present paper. Mainly for comparative purposes, two ion-acetonitrile pair potentials were also constructed from the ab initio cluster calculations: one pure pair potential and one effective pair potential. Using all these potential models, MD simulations in the NPT ensemble were performed for the pure acetonitrile liquid and for Li⁺(MeCN) and Na⁺(MeCN) solutions with 1 ion in 512 solvent molecules and with a simulation time of at least 120 ps per system. Thermodynamic properties, solvation-shell structure and the self-diffusion coefficient of the ions and of the solvent molecules were calculated and compared between the different models and with experimental data, where available. The Li⁺ ion is found to be four-coordinated when the new many-body potentials are used, in contrast to the six-coordinated structure obtained for the pure pair and effective pair potentials. The coordination number of Na⁺ is close to six for all the models derived here, although the coordination number becomes slightly smaller with the many-body potentials. For both ions, the solvent molecules in the first shell point their nitrogen ends towards the cation, while in the second shell the opposite orientation is the most common.     

A local density functional—LCAO method with effective potentials for obtaining the electronic structure of molecules and clusters

The introduction of effective core potentials into the Xα LCAO method can greatly expand the size of the molecular system which may be feasibly treated. Therefore, we have incorporated norm-conserving effective potentials into this framework, using a gaussian basis set, for calculations of the electronic structure of molecules and cluster models of solids and surfaces. This combined methodology makes possible the determination of equilibrium geometries and certain aspects of potential surfaces required for a large class of electronic structure problems.     

Application of potential constants: Electronic chemical potentials of polyatomic molecules—VIII

A new approach for the calculation of electronic chemical potentials of polyatomic systems is developed by applying the quadratic potential (force) constants which are available from normal coordinate analyses using spectroscopic data. The approach is constructed within the framework of density-functional theory into which the simple bond-charge model is incorporated. To evaluate the utility of such an approach, we have calculated electronic chemical potentials for various kinds of polyatomic molecules, and the calculated results have been compared favorably with experimental values as well as those obtained from ab initio SCF calculations. It seems that this approach offers the possibility of chemical potential calculations for polyatomic molecules whose quadratic stretching force constants are obtained by normal coordinate analyses.     

Ab initio relativistic calculation of the RbCs molecule

We apply the relativistic configuration-interaction valence-bond method to calculate various characteristics of the alkali-metal RbCs dimer. These include the electronic potentials and transition dipole moments between the ground and first excited states and permanent dipole moments of the X 1sigma+ and a 3sigma+ states of the ground configuration. In addition, we estimate the lifetime of the rovibrational levels of the X state due to blackbody radiation. These data can help experimentalists to optimize photoassociative formation of ultracold RbCs molecules and their longevity in a trap or in an optical lattice. Extended basis sets, constructed from Dirac-Fock and Sturm's orbitals, have been used to ensure convergence of our calculations. We compare our data with other theoretical and experimental results when they were available.     

On the use of common effective core potentials in density functional calculations. I. Test calculations on transition-metal carbonyls

The performance of effective core potentials adjusted at the Hartree-Fock level but applied in density functional calculations has been tested in a set of calculations using various basis sets and/or core potentials. Test molecules have been the first-row transition-metal carbonyls Cr(CO)₆, Fe(CO)₅, and Ni(CO)₄ and the second-row carbonyls Mo(CO)₆, Ru(CO)₅, and Pd(CO)₄. Only “small-core” potentials have been used, and these are able to reproduce molecular structures and bond energies from all-electron calculations. Relativistic effects have been estimated for the second-row carbonyls by using quasi-relativistic core potentials. © 1996 John Wiley & Sons, Inc.     

Computer simulation of colloidal dispersions

This paper discusses recent applications of statistical mechanics to dispersions with particular emphasis on the computer simulation of the dynamic properties.Fundamental to any computation on a colloidal dispersion is the knowledge of the potential of mean force for at least a pair of suspended particles. At low-to-moderate particle concentrations for stable dispersions, statistical mechanical calculations based on the normal DLVO pair potential produce reasonable agreement with experiment for a number of equilibrium properties of simple latex dispersions. This phenomenon indicates that under these conditions the DLVO pair potential is a reasonable effective pair potential. However, recent Monte Carlo simulations and experimental measurements with liquids of spherical molecules suggest that the force between a pair of dispersed particles at very small separation may differ significantly from that predicted by DLVO theory.The computation of dynamic properties of dispersions involves problems not encountered in the above equilibrium calculations. In particular, one must include the effects of indirect hydrodynamic as well as direct interactions among the particles. This computation may be easily accomplished at moderately low particle concentrations and the results of such calculations are able to give a very detailed analysis of the results of Photon Correlation Spectroscopy measurements on ion exchanged polystyrene latex suspensions at low concentration. These computations also, once again, emphasize the usefulness of DLVO pair potentials as effective pair potentials for systems of strongly interacting particles.     

The generator coordinate Dirac-Fock method applied to helium-like atomic species

The closed-shell Generator Coordinate Dirac-Fock method is applied to perform Dirac-Fock-Coulomb and Dirac-Fock-Breit calculations for the He atom and the helium-like ionic species Ne⁺⁸, Ar⁺¹⁶, and Sn⁺⁴⁸. With the Generator Coordinate Dirac-Fock method, the integral Dirac-Fock equations are integrated numerically so as to generate Gaussian basis sets for the atomic species under study. The Dirac-Fock-Coulomb and Dirac-Fock-Breit energies obtained here for He and He-like ionic species with the Generator Coordinate Dirac-Fock formalism are better than the corresponding energies obtained with variational calculations using even-tempered Gaussian-type functions. The Dirac-Fock-Coulomb energies obtained for Ne⁺⁸ and Ar⁺¹⁶ with the Generator Coordinate Dirac-Fock method are in excellent agreement with Desclaux’s numerical calculations, and for He and Sn⁺⁴⁸ our Dirac-Fock-coulomb energy results are lower than the corresponding energies obtained with Desclaux’s numerical-finite-difference program.     

Calculations of electronic structure of the UF<Subscript>6</Subscript> molecule and the UO<Subscript>2</Subscript> crystal with a relativistic pseudopotential

The influence of relativistic effects on the properties of uranium hexafluoride was considered. Detailed comparison of the spectrum of one-electron energies obtained in the nonrelativistic (by the Hartree-Fock method), relativistic (by the Dirac-Fock method), and scalar-relativistic (using a relativistic potential of the uranium atom core) calculations was carried out. The methods of optimization of atomic basis in the LCAO calculations of molecules and crystals are discussed which make it possible to consider distortion of atomic orbitals upon the formation chemical bonds. The influence of the atomic basis optimization on the results of scalar-relativistic calculations of the molecule UF₆ properties is analyzed. Calculations of the electronic structure and properties of UO₂ crystals with relativistic and nonrelativistic pseudopotentials are fulfilled.     

Electronic structure and prediction of atomization energy of naked homoleptic uranium hexacarbonyl U(CO)6

Our ab initio all-electron fully relativistic Dirac-Fock and nonrelativistic Hartree-Fock self-consistent field (SCF) calculations predict the octahedral (Oh) uranium hexacarbonyl U(CO)6 to be bound with the calculated atomization energy of 49.84 and 48.76 eV at the predicted U-C bond lengths (assuming the C-O bond distance fixed at 1.17 A) of 2.53 and 2.63 A, respectively. Moreover, our all-electron fully relativistic Dirac-Fock SCF calculations predict U(CO)6 to be lower in energy by 3.90 eV with respect to dissociation into U plus six CO ligands. We predict U(CO)6 (Oh) to be very stable in view of our predicted large atomization energy (approximately 49 eV) and stability (approximately 4 eV) with respect to dissociation into U plus six CO molecules. Innovative techniques should be devised for the synthesis of uranium hexacarbonyl since the usual synthetic methods have failed so far for this naked actinide hexacarbonyl.     

Applications of effective core potentials and density functional theory to the spin states of iron porphyrin

We investigated the performance of the B3LYP density functional in combination with ab initio effective core potentials (ECPs) that are derived from either Hartree-Fock or Dirac-Fock calculations. The transferability of ab initio ECPs is assessed on the basis of comparison with all-electron density functional calculations. For iron(II) porphyrin in particular, our assessment focused on the relative energetic ordering of five low-lying spin states, 1A1G, 3A1G, 3B2G, 5A2G, and 5B1G, and their properties, including optimized structures, charge distribution, spin density, and vibrational frequencies. Our results show that core electron correlation and core-valence electron correlation do not have significant effects on the relative energetics of the spin states of iron porphyrin. Our calculations suggest that effects of replacing the core electrons with ECPs are less significant than the choice of basis functions. We conclude that ab initio ECPs such as LANL2, RCEP, and MEFIT-R may be combined with the B3LYP density functional theory to provide consistent and accurate results.     

Density-functional theory with effective potential expressed as a direct mapping of the external potential: applications to atomization energies and ionization potentials

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Moller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods.     

Accuracy and limitations of the pseudopotential method

Molecular model potential calculations have been performed within the SCF approximation on nine di- and triatomic molecules from the first row of the periodic table. We compare the molecular constants with ab initio SCF values and with model potential results obtained by other authors. Our results are accurate to a few per cent. The three most significant approximations in molecular model potential theory are: 1) The molecular model potential is the sum of atomic model potentials; 2) The atomic model potential is energy-independent; 3) The electron interaction model operator is l/r ₁₂. We arrive at the following general conclusions concerning these approximations: 1) The first approximation does not hold for strongly ionic molecules and for some highly excited molecular states. 2) Approximations 2 and 3 cancel to a large extent in molecules as they do in atoms, except in the case where approximation 1 breaks down. 3) Although various model- and pseudo-potentials yield reasonable results for atoms, not all of them are suitable for molecular calculations.     

氯代苯阳离子的密度泛函理论研究

采用B3LYP方法及6-311G(d,p)和6-311+G(d,p)基组,对12种氯代苯阳离子进行了理论研究,优化其电子基态的结构,计算了对应分子的垂直电离势(VIP)和绝热电离势(AIP).依据Jahn-Teller理论,确定了1,3,5-C6H3Cl3+和C6Cl6+离子分别具有C2v(2B1)和D2h(2B2g)结构(对应分子分别为D3h和D6h结构).其余10个离子的构型的对称点群与对应分子相同,但构型参数值有明显差别.用B3LYP方法计算的各氯代苯分子的垂直电离势和绝热电离势与实验值符合得很好.     

Relativistic calculations of dissociation energies and related properties

Methods of calculation of potential energy curves or surfaces, including dissociation energies, bond distances, and vibration frequencies, are discussed as well as recently obtained results for several molecules. The ab initio relativistic methods involve the derivation of “shape-consistent” effective potentials from Dirac–Fock atomic calculations. These effective potentials are averaged and differenced with respect to spin with the differences, p_3/2 – p_1/2, etc., yielding spin-orbit operators. The molecular calculations are then set up in a familiar manner through the SCF stage using spin-averaged effective potentials. The final stage is a configuration-interaction calculation including the spin-orbit terms as well as the electron repulsion terms. Calculations that have been made for several low-lying excited states as well as the ground state for Au₂, TlH, Tl₂, Sn₂, and Pb₂ are reviewed. Good agreement is obtained with spectroscopic data and a number of interesting predictions are made.     

Inclusion of relativistic effects into ZDO methods. IV. Relativistic CNDO/1

A relativistic, four-component version of the CNDO (complete neglect of differential overlap) method is introduced. This method spans the class of zero-differential-overlap approximation and it utilizes a nonempirical parametrization based on results of atomic Dirac-Fock calculations. The spin-orbit splitting is included implicitly using the relativistic basis set which distinguishes Slater-type functions of the lower and higher component spinors. The method is applicable to closed-shell as well as to open-shell systems. The actual version used is the R -CNDO /1_χ with a variable scaling approach. Applications to molecular geometries, ionization potentials, and energies of spin-orbit splitting are demonstrated for AH, AH₂, AH₃, MH, InX, and HgI₂ molecules at the self-consistent-field level as well as in the second order of the many-body perturbation theory.