Relativistic and nonrelativistic finite nucleus optimized double zeta basis sets for the 4p, 5p and 6p elements (Theor Chem Acc (1998) 99:366-371): addendum

 The coefficients of the atomic Foldy-Wout-huysen transformed large component, which can be used in scalar relativistic calculations, are provided in an internet archive for the relativistic double zeta basis sets for the 4p, 5p and 6p elements previously published by the author. Published online: 14 November 2002 Correspondence to: K.G. Dyall e-mail: dyall@schrodinger.com     

Valence 4p functions for the first-row transition metal atoms

For the valence 4p orbitals of the first-row transition metal atoms Sc through Zn, Gaussian-type basis functions are developed referring to excited 3d ^m 4s ¹4p ¹ electronic configurations. Molecular tests of the present work 4p sets are performed for the Cu atom, the diatomic Cu₂ molecule, and Cu₉ and Cu₁₃ clusters, and the results are compared with those from two literature sets. Received: 17 January 2000 / Accepted: 30 May 2000 / Published Online: 11 September 2000     

Reliability of atomic natural orbital basis sets in calculations involving pseudopotentials

The performance of Atomic Natural Orbital (ANO) basis sets for calculations involving nonempirical core pseudopotentials has been studied by comparing the results for atomic and molecular nitrogen obtained using contracted ANO basis sets with those obtained using both the primitive set and a segmented one. The primitive set has been optimized at the SCF level for atomic N treated as a five-electron pseudo-atom, and consists of 7s and 7p primitive GTOs supplemented by 2d and 1f GTOs optimized at the CI level. From this primitive set three contracted [3s 3p 2d 1f] sets have been obtained. The first one has been derived from the ANOs of the neutral atom, the second has been obtained from an averaged density matrix and the third one is a segmented set. For the atom, the segmented set gives a zero contraction error at the SCF level as it must be in valence-only calculations. The ANO basis sets show some small contraction error at the SCF level but perform better in CI calculations. However, for the diatomic N₂ molecule the ANO basis sets exhibit a rather large contraction error in the calculated SCF energy. A detailed analysis of the origin of this error is reported, which shows that the conventional strategy used to derive ANO basis sets does not work very well when pseudopotentials are involved.     

Contracted Gaussian-type basis functions revisited. IV. Atoms Rb to Xe

We report minimal-type contracted Gaussian-type function (GTF) sets, #n=(n3333/n33/n3) with n=5 and 6, #7= (74333/743/74), and #8= (84333/843/75), for the fourth-row atoms from Rb to Xe. Test calculations are performed on the Ag₂ molecule. Spectroscopic constants given by split valence sets derived from #5 and #6 are a little contaminated by basis set superposition error. However, we find that the fully valence split #8 set, (8433111/84111/711111), yields essentially the same results as a large GTF set, (22s15p12d), with a general contraction, when p-, d-, and f-type polarization functions are augmented. The present #7 and #8 CGTF sets are recommended for ab initio molecular calculations including fourth-row atoms. Received: 15 January 2002 / Accepted: 16 April 2002 / Published online: 24 June 2002     

Comments on relativistic basis sets

 Adding the tight and diffuse Gaussian-type functions (GTFs), Faegri's variationally determined double-zeta-quality basis sets for molecular relativistic calculations are examined. An example atom is Cm. When the tight s-type GTF is added the total energy increases, whereas when diffuse GTFs are added the total energy decreases. The reasons for these findings are clarified. It is also pointed out that not only the Faegri's sets but also other variationally determined basis sets would show similar behavior so far as the expansion terms are not sufficient. Received: 22 July 2002 / Accepted: 21 October 2002 / Published online: 31 January 2003 Correspondence to: H. Tatewaki e-mail: htatewaki@nsc.nagoya.cu.ac.jp     

Contracted Gaussian-type basis functions revisited. III. Atoms K through Kr

Six minimal basis sets of contracted Gaussian-type functions (GTFs) are developed for the third-row atoms K through Kr. The smallest and largest sets for transition metal atoms are (3333/33/3) and (8433/84/8), respectively, where a slash distinguishes the s, p, and d symmetries and single-digit figures in the parentheses denote the numbers of primitive GTFs. The two largest sets, (7433/74/7) and (8433/84/8), surpass the (62111111/33111/311) set of Schaefer et al. in the associated total energies. Our (8433/84/8) set is also superior to their (842111/631/411) set. The quality of the present basis sets is tested by self-consistent field (SCF) and configuration interaction (CI) calculations on the Cu₂ molecule. As the accuracy of the basis set increases, SCF calculations show a decrease in the dissociation energy and an increase in the equilibrium internuclear distance. The same tendencies are found in the results of CI calculations with and without a Davidson correction. All the present basis sets are freely available at the internet address: http://202.35.198.41/∼htatewak/. Received: 17 June 1998 / Accepted: 4 August 1998 / Published online: 23 November 1998     

Energy-adjusted pseudopotentials for the rare earth elements

Nonrelativistic and quasirelativistic energy-adjusted pseudopotentials and optimized (7s6p5d)/[5s4p3d]-GTO valence basis sets for use in molecular calculations for fixed f-subconfigurations of the rare earth elements, La through Lu, have been generated. Atomic excitation and ionization energies from numerical HF, as well as SCF pseudopotential calculations using the derived basis sets, differ by less than 0.1 eV from numerical HF all-electron results. Corresponding values obtained from CI(SD), CEPA-1, as well as density functional calculations using the quasirelativistic pseudopotentials, are in reasonable agreement with experimental data.     

Variational calculations for helium-like ions using generalized Kinoshita-type expansions

 Variational calculations are reported for the ground states of the helium atom and its isoelectronic ions H⁻, Li⁺, …, Ne⁸⁺. The calculations use generalized Kinoshita expansions with freely optimized, noninteger powers of the Hylleraas coordinates s and u. One hundred-term expansions of this type lead to better energies than any other expansions in the literature with comparable numbers of terms. Received: 4 September 2002 / Accepted: 14 October 2002 / Published online: 21 January 2003 Correspondence to: T. Koga e-mail: koga@mmm.muroran−it.ac.jp Acknowledgements. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. The final 100-term computations with real powers were performed at the Advanced Computational Research Laboratory of the University of New Brunswick.     

High-quality Gaussian basis sets for fourth-row atoms

Summary Energy-optimized Gaussian basis sets of triple-zeta quality for the atoms Rb-Xe have been derived. Two series of basis sets are developed; (24s 16p 10d) and (26s 16p 10d) sets which we expand to 13d and 19p functions as the 4d and 5p shells become occupied. For the atoms lighter than Cd, the (24s 16p 10d) sets with triple-zeta valence distributions are higher in energy than the corresponding double-zeta distribution. To ensure a triple-zeta distribution and a global energy minimum the (26s 16p 10d) sets were derived. Total atomic energies from the largest basis sets are between 198 and 284E _H above the numerical Hartree-Fock energies.     

Systematic Sequences of Geometric Relativistic Basis Sets. I:s- and p-Block Elements up to Xe

In this work a scheme for constructing systematic sequences of relativistic SCF basis sets at a reasonable computational cost is presented and applied to atoms of the s- and p-block up to Xe. This scheme, which couples simplex optimization and the use of geometric series given by four-term polynomial expressions for the logarithm of the exponents, allows for the construction of basis sets that exhibit very regular patterns of convergence to the numerical reference values of atomic total energies, spinor energies and radial expectation values. This regularity, together with the broad range of basis set sizes presented, enables these sets to be used as building blocks for basis sets applicable in both routine and benchmark relativistic calculations on atomic and molecular systems.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd ⁿ ,d ^n–1 s, andd ^n–2 s ² for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.     

Combined bond-polarization basis sets for accurate determination of dissociation energies. II. Basis set superposition error as a function of the parent basis set

The effect of the parent basis set on the basis set superposition error caused by bond functions is investigated systematically. An important difference between BSSE at the SCF and correlated levels is pointed out. Three new basis sets are defined, denoted 6-311 + G(d,p)B, 6-311 + G(2d,p)B, and 6-311 + G(2df,p)B. BSSE for the first-row hydrides seems to increase uniformly with increasing atomic number of the central atom. Expansion of the valence part of the basis set from 6-31G to 6-311G, as well as adding f functions, has a significant effect on the BSSE. Additional BSSEs incurred by bond functions are less than or equal to 1 kcal/mol for the 6-311 + G(2df,p)B basis set. For the dissociation energies of the first-row hydride species, agreement with experiment within only a few kcal/mol can be obtained even without resorting to isogyric reaction cycles. For high-quality calculations, adding bond functions seems to have definite advantages over expanding the polarization space beyond the [2d1f] level.     

The effect of basis set superposition error on the convergence of interaction energies

 For the intermolecular interaction energies of ion-water clusters [OH⁻(H₂O) _n (n=1,2), F⁻(H₂O), Cl⁻(H₂O), H₃O⁺(H₂O) _n (n=1,2), and NH₄ ⁺(H₂O) _n (n=1,2)] calculated with correlation-consistent basis sets at MP2, MP4, QCISD(T), and CCSD(T) levels, the basis set superposition error is nearly zero in the complete basis set (CBS) limit. That is, the counterpoise-uncorrected intermolecular interaction energies are nearly equal to the counterpoise-corrected intermolecular interaction energies in the CBS limit. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are more reliable than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies evaluated using the MP2/aug-cc-pVDZ level is reliable. Received: 14 March 2001 / Accepted: 25 April 2001 / Published online: 9 August 2001     

NMR chemical shifts in the low–pH form of a-chymotrypsin. A QM/MM and ONIOM–NMR study

 The relationship between hydrogen bonding and NMR chemical shifts in the catalytic triad of low-pH α-chymotrypsin is investigated by combined use of the effective fragment potential [(2001) J Phys Chem A 105:293] and ONIOM–NMR [(2000) Chem Phys Lett 317:589] methods. Our study shows that while the His57 N^δ1−H bond is stretched by a relatively modest amount (to about 1.060 ?) this lengthening, combined with the polarization due to the molecular environment, is sufficient to explain the experimentally observed chemical shifts of 18.2 ppm. Furthermore, the unusual down-field shift of H^ɛ1 (9.2 ppm) observed experimentally is reproduced and shown to be induced by interactions with the C=O group of Ser214 as previously postulated. The free-energy cost of moving H^δ1 from His57 to Asp102 is predicted to be 5.5 kcal/mol. Received: 26 September 2001 / Accepted: 6 September 2002 / Published online: 21 January 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: J. H. Jensen e-mail: jan-jensen@uiowa.edu Acknowledgements. This work was supported by a Research Innovation Award from the Research Corporation and a type G starter grant from the Petroleum Research Fund. The calculations were performed on IBM RS/6000 workstations obtained through a CRIF grant from the NSF (CHE-9974502) and on supercomputers at the National Center for Supercomputer Applications at Urbana-Champaign. The authors are indebted to Visvaldas Kairys for help with the CHARMM program, and to Daniel Quinn for many helpful discussions.