Contracted polarization functions for the atoms helium through neon

Contracted Gaussian-type function sets are proposed for polarization functions of the atoms helium through neon, with the exception of lithium. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and orbital exponents are fully optimized to minimize the difference from accurate atomic natural orbitals. The present polarization functions yield more than 99% of atomic correlation energies predicted by accurate natural orbitals of the same size. Received: 16 April 1997 / Accepted: 26 June 1997     

Relativistic segmented contraction basis sets with core-valence correlation effects for atoms 57La through 71Lu: Sapporo-DK-nZP sets (n?=?D, T, Q)

For the 15 lanthanide atoms ₅₇La through ₇₁Lu, we report Sapporo-DK-nZP sets (n?=?D, T, Q), which are natural extensions of the Sapporo-(DK)-nZP sets for lighter atoms and efficiently incorporate the correlation among electrons in the N through P shells as well as the relativistic effect. The present sets well describe the correlation among the 4s and 4p electrons, which are important in the excitation of 4f electrons. Atomic test calculations of ₅₇La, ₅₈Ce, ₅₉Pr, and ₆₀Nd at configuration interaction with the Davidson correction level of theory confirm high performance of the present basis sets. Molecular test calculations are carried out for ₅₇LaF and ₇₀YbF diatomics at the coupled-cluster level of theory. The calculated spectroscopic constants approach smoothly to the experimental values as the quality of the basis set increases.     

Compact and efficient basis sets of s- and p-block elements for model core potential method

We propose compact and efficient valence-function sets for s- and p-block elements from Li to Rn to appropriately describe valence correlation in model core potential (MCP) calculations. The basis sets are generated by a combination of split MCP valence orbitals and correlating contracted Gaussian-type functions in a segmented form. We provide three types of basis sets. They are referred to as MCP-dzp, MCP-tzp, and MCP-qzp, since they have the quality comparable with all-electron correlation consistent basis sets, cc-pVDZ, cc-pVTZ, and cc-pVQZ, respectively, for lighter atoms. MCP calculations with the present basis sets give atomic correlation energies in good agreement with all-electron calculations. The present MCP basis sets systematically improve physical properties in atomic and molecular systems in a series of MCP-dzp, MCP-tzp, and MCP-qzp. Ionization potentials and electron affinities of halogen atoms as well as molecular spectroscopic constants calculated by the best MCP set are in good agreement with experimental values.     

Electronic correlation and effective interactions in small alkali clusters

The crucial importance of correlation effects versus delocalization, and their nature in small Alkali clusters is analysed from an ab-initio point of view through a detailed investigation of the Li₂ dimer. The role of the external correlation (provided by extended basis sets and large Configuration Interaction calculations) is shown to lower the energy of ionic configurations and to increase their weight in the electronic wavefunction, increasing simultaneously the importance of delocalization versus internal correlation within thes-band. Effective interactions are determined from accurate diabatic calculations on dimers and transfered to clusters via an effective hamiltonian spanned bys orthogonal orbitals. Although not including explicitely thep-band, this model provides results in good agreement with abinitio calculations on Lithium clusters.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

The basis set polarization method is used to generate the first-order polarized basis sets for Sn, Sb, Te, and I. The standard (spd) and extended (spdf) versions of those basis sets are derived for the purpose of calculations of dipole moments and dipole polarizabilities for molecules involving the fourth-row atoms. The verification of the performance of the generated polarized basis sets is achieved mainly by a cross-examination of different atomic and molecular results calculated in this paper. The role of the core-polarization and relativistic effects is investigated. It is shown that the relativistic contribution to dipole moments of the fourth-row hydrides is commensurate with the contribution due to electron correlation and must be explicitly considered in accurate calculations. The detailed basis set data for Sn through I are presented in the Appendix.     

Theoretical reference values for the AE6 and BH6 test sets from explicitly correlated coupled-cluster theory

We propose a new computational protocol to obtain highly accurate theoretical reference data. This protocol employs the explicitly correlated coupled-cluster method with iterative single and double excitations as well as perturbative triple excitations, CCSD(T)(F12), using quadruple-z\zeta basis sets. Higher excitations are accounted for by conventional CCSDT(Q) calculations using double-z\zeta basis sets, while core/core-valence correlation effects are estimated by conventional CCSD(T) calculations using quadruple-z\zeta basis sets. Finally, scalar-relativistic effects are accounted for by conventional CCSD(T) calculations using triple-z\zeta basis sets. In the present article, this protocol is applied to the popular test sets AE6 and BH6. An error analysis shows that the new reference values obtained by our computational protocol have an uncertainty of less than 1 kcal/mol (chemical accuracy). Furthermore, concerning the atomization energies, a cancellation of the basis set incompleteness error in the CCSD(T)(F12) perturbative triples contribution with the corresponding error in the contribution from higher excitations is observed. This error cancellation is diminished by the CCSD(T*)(F12) method. Thus, we recommend the use of the CCSD(T*)(F12) method only for small- and medium-sized basis sets, while the CCSD(T)(F12) approach is preferred for high-accuracy calculations in large basis sets.     

Relativistic atomic natural orbital type basis sets for the alkaline and alkaline-earth atoms applied to the ground-state potentials for the corresponding dimers

New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be₂).Acknowledgments.ensp;B.O.R. would like to express his gratitude to Prof. Jacopo Tomasi for all the inspiration that his scientific work has given him through the years and continues to do in particular through the work on solvent effects on molecular properties. This work has been supported by a grant from the Swedish Science Research Council, VR.Contribution to the Jacopo Tomasi Honorary Issue     

A critical study of basis set effects and the use of approximate natural orbitals in SCF-CI calculations of molecular geometries and heats of reaction

SCF-CI calculations have been performed on a number of chemical reactions between closed shell molecules in order to determine the heats of reaction. Contracted Gaussian type atomic basis sets of three different qualities were used and the CI calculations were performed in a truncated approximate natural orbital space. The conclusions to be drawn from these calculations are rather pessimistic. For heats of reaction, errors up to 6 kcal/mole are obtained on the SCF-level with a double zeta plus polarization atomic basis. A further improvement is only possible if extended basis sets are used. Correlation effects on heats of reaction are of the same size and CI calculations are therefore only meaningful with large atomic basis sets.For the CI calculations a one-electron space of approximate natural orbitals, obtained from second order RS perturbation theory, was used. Different truncations, using the occupation number as criterion, were tested. The general conclusion is that errors in energy differences obtained with a truncated basis set are of the same magnitude as the error in the total correlation energy. In practice this means that not more than 20–30% of the approximate natural orbitals can be deleted if the error is to be kept less than a few kcal/mole.Finally the truncation error in calculations of bond distances was tested for a few cases. Errors of around 10% of the total change due to correlation were found when 30% of the lowest occupied natural orbitals were deleted.     

Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets: applications to atoms and diatomics

We have implemented the use of mixed basis sets of Gaussian one- and two-electron (geminal) functions for the calculation of second-order M?ller-Plesset (MP2) correlation energies. In this paper, we describe some aspects of this implementation, including different forms chosen for the pair functions. Computational results are presented for some closed-shell atoms and diatomics. Our calculations indicate that the method presented is capable of yielding highly accurate second-order correlation energies with rather modest Gaussian orbital basis sets, providing an alternative route to highly accurate wave functions. For the neon atom, the hydrogen molecule, and the hydrogen fluoride molecule, our calculations yield the most accurate MP2 energies published so far. A critical comparison is made with established MP2-R12 methods, revealing an erratic behaviour of some of these methods, even in large basis sets.     

Contracted polarization functions for the atoms Ca, Ga–Kr, Sr, and In–Xe

 Contracted Gaussian-type function sets are proposed for polarization functions of the atoms Ga–Kr and In–Xe. We also report polarization functions for Ca and Sr. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and orbital exponents are fully optimized to minimize the deviation from accurate atomic natural orbitals. The present polarization functions yield more than 99% of atomic correlation energies predicted by accurate natural orbitals of the same size. Received: 23 February 2001 / Accepted: 19 April 2001 / Published online: 13 June 2001     

Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree-Fock and density functional theory

An efficient and accurate analytic gradient method is presented for Hartree-Fock and density functional calculations using multiresolution analysis in multiwavelet bases. The derivative is efficiently computed as an inner product between compressed forms of the density and the differentiated nuclear potential through the Hellmann-Feynman theorem. A smoothed nuclear potential is directly differentiated, and the smoothing parameter required for a given accuracy is empirically determined from calculations on six homonuclear diatomic molecules. The derivatives of N2 molecule are shown using multiresolution calculation for various accuracies with comparison to correlation consistent Gaussian-type basis sets. The optimized geometries of several molecules are presented using Hartree-Fock and density functional theory. A highly precise Hartree-Fock optimization for the H2O molecule produced six digits for the geometric parameters.     

Polarized basis sets for accurate calculations of static and dynamic electric properties of molecules

We report on the development and testing of large polarized basis sets (LPolX, where X is the element symbol) for accurate calculations of linear and nonlinear electric properties of molecules. The method used to generate LPolX sets is based on our studies of the analytic dependence of Gaussian functions on external time‐independent and time‐dependent electric fields. At variance with the earlier investigations of small, highly compact (ZPolX) basis sets for moderately accurate calculations of electric properties of large molecules, the present goal is to obtain basis sets that are nearly saturated with respect to the selected class of electric properties and can be used for accurate studies of interaction‐induced properties. This saturation makes the LPolX sets also useful in calculations of optical properties for chiral molecules. In this article, the LPolX sets are generated for X = H, C, N, O, and F, and examined in calculations of linear and nonlinear electric properties of four standard test systems: HF, N₂, CO, and HCN. The study of the performance of LPolX basis sets has been carried out at different levels of approximation ranging from the SCF HF method to highly correlated CCSD(T) approach. The results obtained in this study compare favorably with accurate reference data and show a high level of saturation of LPolX basis sets with respect to the polarization effect due to external electric fields. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Accurate ab initio ro-vibronic spectroscopy of the 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.     

Analysis of the errors in explicitly correlated electronic structure theory

The explicitly correlated second order M?ller-Plesset (MP2-R12) methods perform well in reproducing the last detail of the correlation cusp, allowing higher accuracy than can be accessed through conventional means. Nevertheless in basis sets that are practical for calculations on larger systems (i.e., around triple- or perhaps quadruple-zeta) MP2-R12 fails to bridge the divide between conventional MP2 and the MP2 basis set limit. In this contribution we analyse the sources of error in MP2-R12 calculations in such basis sets. We conclude that the main source of error is the choice of the correlation factor r12. Sources of error that must be avoided for accurate quantum chemistry include the neglect of exchange commutators and the extended Brillouin condition. The generalized Brillouin condition is found not to lead to significant errors.     

Finite-field many-body perturbation theory IV. Basis set optimization in MBPT calculations of molecular properties. Molecular quadrupole moments

The choice of truncated basis sets and their optimization for MBPT calculations of molecular properties are discussed. It is pointed out that computing the correlation corrections to some kth order property by using the MBPT approach requires the knowledge of accurate perturbed orbitals through the kth order. Hence, it is argued that the basis set functions can be optimized with respect to the perturbed energies calculated within the coupled Hartree-Fock method. The proposed procedure is illustrated by MBPT calculations of quadrupole moments of H₂ and FH. Additionally, also some estimates of the quadrupole polarizability tensor components for these molecules are obtained.     

Accurate theoretical near-equilibrium potential energy and dipole moment surfaces of HgClO and HgBrO

The complexes HgBrO and HgClO have been previously determined by ab initio methods to be strongly bound and were suggested to be important intermediates during mercury depletions events observed in the polar troposphere. In the present work accurate near-equilibrium potential energy surfaces (PESs) of these species are reported. The PESs are determined using accurate coupled cluster methods and a series of correlation consistent basis sets with subsequent extrapolation to the complete basis set limit. Additive corrections for both core-valence correlation energy and relativistic effects are also included. The anharmonic ro-vibrational spectra of HgBrO and HgClO have been calculated in variational calculations. Strong infrared band strengths are predicted for all fundamentals in these species. The spin-orbit splitting dominates over the vibronic coupling effect in both HgClO and HgBrO. The Renner-Teller vibronic energy levels corresponding to the bending mode of these molecules are calculated via perturbation theory.