Revised model core potentials for second-row transition metal atoms from Y to Cd

We have produced new relativistic model core potentials (spdsMCPs) for the second-row transition-metal atoms from Y to Cd treating explicitly 4s and 4p electrons in addition to 4d and 5s electrons in the same manner as for the first-row transition-metal atoms given in [Y. Osanai, M.S. Mon, T. Noro, H. Mori, H. Nakashima, M. Klobukowski, E. Miyoshi, Chem. Phys. Lett. 452 (2008) 210]. Using suitable correlating functions together with the split valence MCP functions, we demonstrate that the present MCP basis sets show reasonable performance in predicting the electronic structures of atoms and molecules, bringing about accurate excitation energies for atoms and reasonable spectroscopic constants for AgH.     

Molecular core-valence correlation effects involving the post-d elements Ga-Rn: benchmarks and new pseudopotential-based correlation consistent basis sets

Correlation consistent basis sets that are suitable for the correlation of the outer-core (n-1)spd electrons of the post-d elements Ga-Rn have been developed. These new sets, denoted by cc-pwCVXZ-PP (X=D,T,Q,5), are based on the previously reported cc-pVXZ-PP sets that were built in conjunction with accurate small-core relativistic pseudopotentials (PPs) and designed only for valence nsp correlation. These new basis sets have been utilized in benchmark coupled cluster calculations of the core-valence correlation effects on the dissociation energies and spectroscopic properties of several small molecules. As expected, the most important contribution is the correlation of the (n-1)d electrons. For example, in the case of the group 13 homonuclear diatomics (Ga(2),In(2),Tl(2)), this leads to a dissociation energy increase compared to a valence-only treatment from 1.5 to 3.2 kcal/mol, bond length shortenings from -0.076 to -0.125 A?, and harmonic frequency increases of 7-8?cm(-1). Even in the group 15 cases (As(2),Sb(2),Bi(2)), the analogous effects of (n-1)d electron correlation are certainly not insignificant, the largest values being +4.4?kcal/mol, -0.049 A?, and +9.6?cm(-1) for the effects on D(e), r(e), and ω(e), respectively. In general, the effects increase in magnitude down a group from 4p to 6p. Correlation of the outer-core (n-1)p electrons is about an order of magnitude less important than (n-1)d but larger than that of the (n-1)s. The effect of additional tight functions for Hartree-Fock and valence sp correlation was found to be surprisingly large, especially for the post-4d and post-5d elements. The pseudopotential results for the molecules containing post-3d elements are also compared to the analogous all-electron calculations employing the Douglas-Kroll-Hess Hamiltonian. The errors attributed to the PP approximation are found to be very small.     

Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials

We present auxilliary basis sets for the atoms H to At – excluding the Lanthanides – optimized for an efficient treatment of molecular electronic Coulomb interactions. For atoms beyond Kr our approach is based on effective core potentials to describe core electrons. The approximate representation of the electron density in terms of the auxilliary basis has virtually no effect on computed structures and affects the energy by less than 10⁻⁴ a.u. per atom. Efficiency is demonstrated in applications for molecules with up to 300 atoms and 2500 basis functions. Received: 17 December 1996 / Accepted: 8 May 1997     

van der Waals interactions and dipole polarizabilities of lanthanides: Tm(2F)-He and Yb(1S)-He potentials

Anisotropic dipole polarizabilities of Tm(2F), Tm+2(2F), and Yb(1S) are calculated using the finite-field multireference averaged quadratic coupled cluster (MR-AQCC) (Tm and Tm+2) and RCCSD(T) (Yb) methods with small-core relativistic pseudopotentials ECP28MWB combined with the augmented ANO basis sets. The lanthanide atoms are strongly polarizable with the scalar part originating from the 6s electrons and the tensorial part from the open 4f shells. The adiabatic interaction potentials 2Sigma+, 2Pi, 2Delta, and 2Phi of Tm(2F)-He and Tm+2(2F)-He were examined by the multireference approaches, multireference configuration interaction and MR-AQCC, using the basis sets designed in the polarizability calculations. A closed-shell lanthanide system Yb(1S)-He was included for comparison. The Tm-He 2Sigma+, 2Pi, 2Delta, and 2Phi interaction potentials are very shallow and nearly degenerate (within 0.01 cm(-1)), with the well depths in the range of 2.35-2.36 cm(-1) at R=6.17 A. The basis-set saturated well depths are expected to be larger by ca. 25%, as estimated using the bond-function augmented basis set. The interactions of lanthanide atoms with He are one order of magnitude less anisotropic than those involving first-row transition metal atoms. The suppression of anisotropy is chiefly attributed to the screening effected by the 6s shell. When these electrons are removed as in the di-cation complex Tm+2(2F)-He, the potentials deepen to a thousand wave number range and their anisotropy is enhanced 500-fold.     

Electronic energy levels with the help of trajectory-guided random grid of coupled wave packets. I. Six-dimensional simulation of H2

As a preliminary to future work on the behavior of atoms and molecules in strong time-dependent fields, we apply the coupled coherent-states (CCS) technique of multidimensional phase-space quantum dynamics to obtain Born-Oppenheimer energy levels of electrons in molecules. Unlike traditional approaches based on atomic and molecular-orbital basis sets and time-independent Schrodinger equation the CCS method exploits the solution of the time-dependent Schrodinger equation in the basis of Monte Carlo-selected trajectory-guided coherent states, which treat classical electron correlations exactly. In addition the CCS trajectories move over averaged potentials, which remove the Coulombic singularities.     

Optimized Gaussian basis sets for use with relativistic effective (core) potentials: K,Ca, Ga—Kr

Correlation-consistent valence basis sets were developed for the third-row main block elements (K, Ca, Ga—Kr) for use with relativistic effective core potentials. These basis sets are somewhat larger than double-zeta in size, with polarization functions, and are balanced for use in both Hartree–Fock and correlation calculations. Spin–orbit splittings for atoms and molecules are calculated and compared to experiment. These calculations use the approximate spin–orbit operator from the relativistic effective core potentials. The use of these results in the calculation of accurate thermochemical data is discussed. © 1997 John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Inner-shell single and double ionization potentials of aminophenol isomers

A comprehensive study of single and double core ionization potentials of the aminophenol molecule is reported. The role of relaxation, correlation, relativistic, and basis set effects in these potentials is clarified. Special attention is paid to the isomer dependence of the single and double core ionization potentials. Some of them are also compared with the respective values of the phenol and aniline molecules. It is shown that the core level single ionization potentials of the para-, meta-, and ortho-aminophenol molecules differ only slightly from each other, rendering these structural isomers challenging to distinguish for conventional x-ray photoelectron spectroscopy. In contrast, the energy needed to remove two core electrons from different atoms depends noticeably on the mutual arrangement and even on the relative orientations of the hydroxyl and amine groups. Together with the electrostatic repulsion between the two core holes, relaxation effects accompanying double core ionization play a crucial role here. The pronounced sensitivity of the double ionization potentials, therefore, enables a spectroscopic characterization of the electronic structure of aminophenol isomers by means of x-ray two-photon photoelectron spectroscopy.     

Development and testing of a compact basis set for use in effective core potential calculations on rhodium complexes

We present a set of effective core potential (ECP) basis sets for rhodium atoms which are of reasonable size for use in electronic structure calculations. In these ECP basis sets, the Los Alamos ECP is used to simulate the effect of the core electrons while an optimized set of Gaussian functions, which includes polarization and diffuse functions, is used to describe the valence electrons. These basis sets were optimized to reproduce the ionization energy and electron affinity of atomic rhodium. They were also tested by computing the electronic ground state geometry and harmonic frequencies of [Rh(CO)₂μ‐Cl]₂, Rh(CO)₂ClPy, and RhCO (neutral and its positive, and negative ions) as well as the enthalpy of the reaction of [Rh(CO)₂μ‐Cl]₂ with pyridine (Py) to give Rh(CO)₂ClPy, at different levels of theory. Good agreement with experimental values was obtained. Although the number of basis functions used in our ECP basis sets is smaller than those of other ECP basis sets of comparable quality, we show that the newly developed ECP basis sets provide the flexibility and precision required to reproduce a wide range of chemical and physical properties of rhodium compounds. Therefore, we recommend the use of these compact yet accurate ECP basis sets for electronic structure calculations on molecules involving rhodium atoms. © 2012 Wiley Periodicals, Inc.     

An augmented effective core potential basis set for the calculation of molecular polarizabilities

Calculations of molecular polarizabilities require basis sets capable of accurately describing the responses of the electrons to an external perturbation. Unfortunately, basis sets that yield suitable quantitative results have traditionally been all-electron sets with large numbers of primitives, making their use computationally intractable even for moderately sized systems. We present a systematic augmentation of the effective core potential basis set of Stevens et al. [J Chem Phys 81, 12 (1984), Can J Chem 70, 612 (1992)] for 39 main group elements based on the procedure used to construct diffuse and polarization functions in the well-known Sadlej basis sets [Collec Czech Chem Comm 53, 1995 (1988)]. Representative calculations have been performed and we have shown that results to within 1% of all-electron calculations using the Sadlej basis set can be obtained for <1-35% of the computational cost using this new basis set.     

Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar

Correlation consistent basis sets have been optimized for use with explicitly correlated F12 methods. The new sets, denoted cc-pVnZ-F12 (n=D,T,Q), are similar in size and construction to the standard aug-cc-pVnZ and aug-cc-pV(n+d)Z basis sets, but the new sets are shown in the present work to yield much improved convergence toward the complete basis set limit in MP2-F12/3C calculations on several small molecules involving elements of both the first and second row. For molecules containing only first row atoms, the smallest cc-pVDZ-F12 basis set consistently recovers nearly 99% of the MP2 valence correlation energy when combined with the MP2-F12/3C method. The convergence with basis set for molecules containing second row atoms is slower, but the new DZ basis set still recovers 97%-99% of the frozen core MP2 correlation energy. The accuracy of the new basis sets for relative energetics is demonstrated in benchmark calculations on a set of 15 chemical reactions.     

Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn

The introduction of the resolution-of-the-identity (RI) approximation for electron repulsion integrals in quantum chemical calculations requires in addition to the orbital basis so-called auxiliary or fitting basis sets. We report here such auxiliary basis sets optimized for second-order Møller–Plesset perturbation theory for the recently published (Weigend and Ahlrichs Phys Chem Chem Phys, 2005, 7, 3297–3305) segmented contracted Gaussian basis sets of split, triple-ζ and quadruple-ζ valence quality for the atoms Rb–Rn (except lanthanides). These basis sets are designed for use in connection with small-core effective core potentials including scalar relativistic corrections. Hereby accurate resolution-of-the-identity calculations with second-order Møller–Plesset perturbation theory (MP2) and related methods can now be performed for molecules containing elements from H to Rn. The error of the RI approximation has been evaluated for a test set of 385 small and medium sized molecules, which represent the common oxidation states of each element, and is compared with the one-electron basis set error, estimated based on highly accurate explicitly correlated MP2–R12 calculations. With the reported auxiliary basis sets the RI error for MP2 correlation energies is typically two orders of magnitude smaller than the one-electron basis set error, independent on the position of the atoms in the periodic table.     

Approximate STO functions for the first-row transition metal atoms

Slater type orbital (STO) basis sets for the atoms Sc-Zn have been derived using a technique based on the distance between subspaces. The accuracy for several properties of these basis sets has been tested. Basis sets studied are of both single- and double-zeta sizes, although this technique can be generalized for any size. Uniform quality criteria through the series of atoms Sc-Zn are difficulty to establish due to the varying number of d electrons. A comparative study at the atomic level of the quality of STO basis sets (both the two new basis sets and Clementi's basis sets) for the first-row transition elements has been carried out. Results show that the new basis sets provide better simulation for several properties. Molecular calculations on compounds with these atoms using a Gaussian expansion fitted according to the new values of optimized STOs are also included. The results obtained are similar to those reported when STO-3G basis set is used.     

A generalized any-particle propagator theory: Calculations of nucleon's binding energies

Generalized one-particle propagator calculations were performed for fermions in atoms: neutrons, protons, and electrons. For this purpose, multicomponent Hartree-Fock equations were implemented using Gaussian basis sets where, for nucleons, we consider a non-Coulombic interaction, through a two-term Yukawa scalar potential and the interaction between electrons and the electrons with positive charge (protons) through a Coulombic potential. The strategy for evaluating the required interaction integrals follows Obara-Saika and Head-Gordon recurrence relations combined with the generalized Boys function suggested by Ten-no. Calculations on the isotopes ²H, ³H, ³He, ⁴He, ⁶Li, ⁶Be, ⁷Li, and ⁸Be were realized to test the accuracy of Koopmans' approximation and a second-order generalized one-particle propagator. Yukawa potentials were parametrized to reproduce nuclear properties as kinetic energies and radial distributions of density. These potentials produced the reference nuclear Hartree-Fock calculations on which fully ab initio propagator calculations were performed for these non-Coulombic potentials. This allowed us to explore the electronic structure of isotopes in an extended nucleus context.     

Complex absorbing potentials for stark resonances

In this work, we study the problem in calculation of Stark resonances by using complex absorbing potentials (CAPs), and its solutions. The motivation of using CAPs for calculating Stark resonances stems from the fact that CAPs can be easily inserted to a large variety of available codes for calculating the electronic structure of molecules and atoms. Our conclusion is that the appropriate CAPs for studying ac/dc Stark resonances are those that are associated with smooth-exterior-scaling (SES) transformations, which rotate the spatial contour of integration into the complex plane. The performance of SES-CAPs vs standard commonly used CAPs in different types of basis sets is investigated.     

When does the non-variational nature of second-order Møller-Plesset energies manifest itself? All-electron correlation energies for open-shell atoms from K to Br

All-electron correlation energies E(c) are not very well known for open-shell atoms with more than 18 electrons. The complete basis-set (CBS) limits of second-order M?ller-Plesset (MP2) perturbation theory energies are obtained for open-shell atoms by computations in large basis sets combined with a knowledge of the MP2/CBS limit for the next larger closed-shell atom with the same valence shell structure. Then higher-order correlation corrections are found by coupled-cluster calculations using basis sets that are not quite as large. The method is validated for the open-shell atoms from Al to Cl for which E(c) is reasonably well established. Then, the method is used to obtain non-relativistic E(c) values, probably accurate to 3%, for the open-shell atoms of the fourth period: K, Sc-Cu, and Ga-Br. These energies are compared with the predictions of 19 density functionals and may be useful for the parameterization of new ones. The results show that MP2 overestimates |E(c)| for atoms heavier than Fe.     

Quantum-chemical study of the silver trifluoroacetate dimer

The results of quantum-chemical calculations of the formation energy, equilibrium structure, and potential surface sections along the nonrigid degrees of freedom of the silver trifluoroacetate dimer are presented. Calculations were performed by the B3LYP method with the cc-pVTZ correlation-coherent basis for C, O, and F atoms using the basis and relativistic effective core potentials Stuttgart 1997 RSC for Ag atoms, and, for comparison, by the HF method in the 6-31G(d) basis and MP2 method in the 6-311G(df) basis for C, O, and F atoms using the basis and relativistic effective core potentials SBKJC for Ag atoms. The eight-membered ring is a rigid planar fragment with a bond order of 0.2 between the silver nuclei. The nearly free internal rotation of the CF₃ group affects the geometrical parameters of the ring. It was substantiated that in electron diffraction experiments, the difficulties of interpretation could be explained not only by the presence of decomposition products in the sample, but also by possible oligomerization of silver trifluoroacetate.     

Accurate extrapolation of electron correlation energies from small basis sets

A new two-point scheme is proposed for the extrapolation of electron correlation energies obtained with small basis sets. Using the series of correlation-consistent polarized valence basis sets, cc-pVXZ, the basis set truncation error is expressed as deltaE(X) proportional, variant(X + xi(i))(-gamma). The angular momentum offset xi(i) captures differences in effective rates of convergence previously observed for first-row molecules. It is based on simple electron counts and tends to values close to 0 for hydrogen-rich compounds and values closer to 1 for pure first-row compounds containing several electronegative atoms. The formula is motivated theoretically by the structure of correlation-consistent basis sets which include basis functions up to angular momentum L = X-1 for hydrogen and helium and up to L = X for first-row atoms. It contains three parameters which are calibrated against a large set of 105 reference molecules (H, C, N, O, F) for extrapolations of MP2 and CCSD valence-shell correlation energies from double- and triple-zeta (DT) and triple- and quadruple-zeta (TQ) basis sets. The new model is shown to be three to five times more accurate than previous two-point schemes using a single parameter, and (TQ) extrapolations are found to reproduce a small set of available R12 reference data better than even (56) extrapolations using the conventional asymptotic limit formula deltaE(X) proportional, variantX(-3). Applications to a small selection of boron compounds and to neon show very satisfactory results as well. Limitations of the model are discussed.     

A new method for modelling spectator chemical groups in ab initio calculations: effective group potentials

 A new method for an increased numerical efficiency of ab initio calculations is proposed. It is based on the assumption that in most cases chemical properties of functional groups in molecules are mainly controlled by a few electrons. This statement allows one to distinguish between two classes of nuclei and electrons: active and inactive ones. The effective group potential (EGP) method presupposes that the effect of inactive electrons in a functional chemical group can be described by a pseudopotential, in the same way that core electrons are replaced by effective core potentials in atoms. It is shown that EGPs are able to predict chemical and structural features of the active part of a molecule and at a fraction of the ordinary computational cost. The preliminary results reported here concern the determination of EGPs for ammonia, the methyl radical and the cyclopendadienyl ligand, which represent different types of bonding. Received: 15 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Ab-initio and approximately rigorous calculations on small,medium, and large systems

We have explored two areas of approximately rigorous calculations for computing nonempirical wave functions for heavy and/or large molecules orders of magnitude faster than with conventional ab-initio methods but with the same chemical accuracy. First, we have developed and used a series of programs (starting from our new fast sets of ab-initio Gaussian SCF and SCF -CI programs) incorporating ab-initio effective core model potentials (MOD -POT ) which allow one to treat only the valence electrons explicitly, plus a charge conserving integral prescreening, which cuts down significantly on the number of integrals that have to be calculated, stored, or processed for a large molecule. We have named this latter procedure VRDDO (variable retention of diatomic differential overlap). With these MODPOT and MODPOT /VRDDO methods we have explored a variety of small, medium, and large systems ranging from electron affinities of atoms through to molecules of biological interest and large boron hydrides. The results compared to ab-initio SCF or SCF /CI calcuations are very good, usually within 0.001 to 0.002 a.u. for orbital energies and gross atomic populations (GAPS ) and even better along potential energy curves. Secondly, we have explored the use of the MS -Xα method for less conventional molecules and properties than those for which it is customarily employed.