A systematic preparation of new contracted Gaussian-type orbital sets. V. From Na through Ca

Minimal compact contracted Gaussian basis sets are constructed for the atoms from Na to Ca. They give satisfactory valence shell orbital energies, although they are minimal-type basis sets. Split-type basis sets are also derived from the minimal Gaussian basis sets in order to enhance the flexibility of the basis sets for molecular calculations.     

A systematic preparation of new contracted Gaussian-type orbital sets. VIII. MINI-1 and MIDI-1 sets for Ga through Cd

Minimal contracted Gaussian basis sets are presented for Ga through Cd. Characteristically these Gaussian-based minimal sets give far better d orbital energies than those by minimal STO basis sets. These new basis sets were tested on Br₂ for which a new benchmark calculation was also performed. The test result is satisfactory in that these basis sets produce good general agreement with the near Hartree–Fock calculation with respect to the molecular spectroscopic constants.     

Ab initio calculations on large molecules using molecular fragments. Generalization of the molecular fragment basis at the minimum basis set level

By determining basis set parameters in molecular environments using other criteria than total energy, it is shown that a generalization of the molecular fragment basis can be obtained in which calculated geometric and electronic structural properties are predicted substantially better than with other basis sets of similar size. As a first step in the development of a series of basis sets having successively greater flexibility and accuracy, several single-zeta basis sets are created, using a two-Gaussian contraction for each basis orbital. The best of these basis sets produced calculated geometric and electronic properties for a series of molecules that model a wide variety of organic molecules that are of better accuracy than the corresponding STO -2G basis, and similar in most cases to STO -3G. In addition, the basis set is shown to be applicable in either a Cartesian Gaussian basis or a floating spherical Gaussian basis.     

Ab initio relativistic effective potentials with spin-orbit operators. VI. Fr through Pu

Ab initio averaged relativistic effective core potentials (AREP ), spin-orbit (SO ) operators, and valence basis sets are reported for the elements Fr through Pu in the form of expansions in Gaussian-type functions. Gaussian basis sets with expansion coefficients for the low-energy states of each atom are given. Atomic orbital energies calculated under the j–j coupling scheme within the self-consistent field approximation and employing the AREP 'S in their unaveraged form (REP 'S) agree to within 10% of orbital energies due to numerical all-electron Dirac–Fock calculations. The accuracy of the AREP 'S and so operators is also shown to be good through comparisons of calculated so splitting energies with all-electron Dirac–Fock results.     

Numerically stable optimized effective potential method with balanced Gaussian basis sets

A solution to the long-standing problem of developing numerically stable optimized effective potential (OEP) methods based on Gaussian basis sets is presented by introducing an approach consisting of an exact exchange OEP method with an accompanying construction and balancing scheme for the involved auxiliary and orbital Gaussian basis sets that is numerically stable and that properly represents an exact exchange Kohn-Sham method. The method is a purely analytical method that does not require any numerical grid, scales like Hartree-Fock or B3LYP procedures, is straightforward to implement, and is easily generalized to take into account orbital-dependent density functionals other than the exact exchange considered in this work. Thus, the presented OEP approach opens the way to the development and application of novel orbital-dependent exchange-correlation functionals. It is shown that adequately taking into account the continuum part of the Kohn-Sham orbital spectrum is crucial for numerically stable Gaussian basis set OEP methods. Moreover, it is mandatory to employ orbital basis sets that are converged with respect to the used auxiliary basis representing the exchange potential. OEP calculations in the past often did not meet the latter requirement and therefore may have led to erroneously low total energies.     

A systematic preparation of new contracted Gaussian-type orbital sets. III. Second-row atoms from Li through ne

Four minimal Gaussian basis sets are generated for the second-row atoms Li through Ne. The first one, MINI-1, consists of a 3-term contraction of primitive Gaussian-type orbitals for 1s, 2s, and 2p atomic orbitals. The convenient shorthand notation would be (3,3) for Li? Be and (3,3/3) for B? Ne. The second one, MINI-2, can be represented by (3,3/4) for B? Ne. In the same way, MINI-3 is described as (4,3) for Li? Be, and MINI-3 and MINI-4 are represented by (4,3/3) and (4,3/4) for B? Ne, respectively. Although the four basis sets are the minimal type, they give the valence shell orbital energies which are close to those of DZ. These four and other sets derived from them are tested for the hetero- and homodiatomic molecules and some organic molecules. They are found to give the orbital energies that agree well with those given by extended calculations. Atomization energies and other spectroscopic constants are also calculated and compared with those of extended calculations. The results clearly indicate that the present basis sets can be used very effectively in the molecular calculations.     

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.     

The ellipsoidal Gaussian basis in molecular orbital theory

The ellipsoidal Gaussian basis function used in a minimal valence atomic orbital representation is compared with the double-zeta spherical Gaussian basis orbital representation for some seventeen molecules made up of first row atoms and hydrogen. Except for acetylene the double-zeta basis gives consistently better total electronic energies and generally better property values than the optimized ellipsoidal single zeta basis. Difference molecular density contour maps comparing the two basis sets, as well as other one-electron property values, indicate that the ellipsoidal basis exaggerates the transfer of charge from the atomic regions to the interatomic and lone pair regions of molecules. Apparently, the forced complete elliptization of the valence atomic orbital in the single-zeta representation does not allow the basis set sufficient flexibility to simultaneously represent both the basically spherical atomic part of these orbitals and the non-spherical molecular bond formation. Other properties and aspects of the ellipsoidal Gaussian basis are also discussed.     

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.     

Density functional theory investigation of the polarizability and second hyperpolarizability of polydiacetylene and polybutatriene chains: treatment of exact exchange and role of correlation

The static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEP-EXX) method developed by Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the Kohn-Sham orbitals [molecular orbital (MO) basis]. Our results were compared to coupled-perturbed Hartree-Fock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using 6-311++G** for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEP-EXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finite-basis-set Hartree-Fock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.     

Gaussian basis sets for calculation of spin densities in first-row atoms

Summary The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region.     

An ab initio comparison of dichalcogen hydrides

A theoretical study of HSH, HSeH, HTeH, HSSH, HSeSH, HSeSeH, HTeSH, HTeSeH, and HTeTeH was carried out by ab initio molecular orbital methods employing minimal Gaussian basis sets MINI-1 and MINI-1* of Huzinaga and his group. Both basis sets yield accurate estimates on the equilibrium geometries of monochalcogen hydrides. In the case of dichalcogen hydrides, however, the inclusion of d-polarization functions for sulfur, selenium, and tellurium greatly improve the accuracy of the geometry prediction. The unpolarized MINI-1 basis sets yield essentially correct orbital energies and therefore suffice for the comparative study on the electronic structures in similar molecules. The results with both basis sets imply close similarities in the electronic structures of SS, SeS, and SeSe bonds with more marked differences in bonds containing tellurium as a consequence of notably smaller orbital energy of the 5s- orbital of tellurium as compared to the corresponding orbitals in sulfur and selenium. The barriers to internal rotation about the chalcogen—chalcogen bond in all dichalcogen hydrides are similar. The cis- and trans-barrier heights are ca. 23 and 14 kJ mol⁻¹, respectively. The relative stabilities of different hydrides are discussed.     

On the relative importance of core and valence shell representations in the calculation of conformational energies using small Gaussian basis sets

Several “core-deficient” small Gaussian basis sets were constructed and analyzed in terms of the balance requirements of functions that contribute predominantly to the core. Variations in the conformational energy barriers and geometrical parameters for ammonia and ethane, calculated with these basis sets, were analyzed with a gradient technique. A scheme for the reduction of the size of molecular basis sets is proposed.     

Study of the quality of Gaussian basis sets for carbon and silicon: Calculations on methane and silane

A number of Gaussian basis sets for carbon and silicon have been examined in terms of the one-electron properties of methane and silane. The convergence of the properties to their limiting values is not monotonic but, in general, a representation that involves five Gaussian functions per occupied atomic orbital on the heavy atom is sufficient to closely approach the limits. A relationship between the sizes and partitioned electronic energies is shown to hold to a good approximation for the Boys spatially localized molecular orbitals employed in this study.     

Spatially restricted Double Z-Simplified Box Orbital basis sets: Optimization and comparison with some standard basis sets

As part of previous studies, we introduced a new type of basis function named Simplified Box Orbitals (SBOs) that belong to a class of spatially restricted functions which allow the zero differential overlap (ZDO) approximation to be applied with complete accuracy. The original SBOs and their Gaussian expansions SBO-3G form a minimal basis set, which was compared to the standard Slater-type orbital basis set (STO-3G). In the present paper, we have developed the SBO basis functions at double-zeta (DZ) level, and we have assessed the option of expanding the SBO-DZ as a combination of Gaussian functions. Finally, we have determined the quality of the new basis set by comparing the molecular properties calculated with SBO-nG with those achieved with some standard basis sets.     

Expansion of linear combinations of slater-type orbitals in eigenfunctions of the three-dimensional isotropic harmonic oscillator

Several classes of functions related to the Gaussian have been used with success as basis sets for the representation of atomic and molecular orbitals. We have compared the representation of a hydrogen 1s orbital by a sum of Gaussian lobe functions with its expansion in eigenfunctions of the three-dimensional isotropic harmonic oscillator. The lobe functions are shown to achieve better expectation values of the energy, with fewer terms. The lobe functions have the further computational advantage of not containing high powers of the radius. It is concluded that the lobe functions are a superior basis set for use in calculations of the electronic structure of atoms and molecules.     

Efficiency of numerical basis sets for predicting the binding energies of hydrogen bonded complexes: evidence of small basis set superposition error compared to Gaussian basis sets

Binding energies of selected hydrogen bonded complexes have been calculated within the framework of density functional theory (DFT) method to discuss the efficiency of numerical basis sets implemented in the DFT code DMol3 in comparison with Gaussian basis sets. The corrections of basis set superposition error (BSSE) are evaluated by means of counterpoise method. Two kinds of different numerical basis sets in size are examined; the size of the one is comparable to Gaussian double zeta plus polarization function basis set (DNP), and that of the other is comparable to triple zeta plus double polarization functions basis set (TNDP). We have confirmed that the magnitudes of BSSE in these numerical basis sets are comparative to or smaller than those in Gaussian basis sets whose sizes are much larger than the corresponding numerical basis sets; the BSSE corrections in DNP are less than those in the Gaussian 6-311+G(3df,2pd) basis set, and those in TNDP are comparable to those in the substantially large scale Gaussian basis set aug-cc-pVTZ. The differences in counterpoise corrected binding energies between calculated using DNP and calculated using aug-cc-pVTZ are less than 9 kJ/mol for all of the complexes studied in the present work. The present results have shown that the cost effectiveness in the numerical basis sets in DMol3 is superior to that in Gaussian basis sets in terms of accuracy per computational cost.     

A systematic preparation of new contracted Gaussian- type orbital sets. VII. MINI-3, MINI-4, MIDI-3, and MIDI-4 sets for transition metal atoms

Two minimal contracted Gaussian-type orbital (CGTO ) sets are developed for the transition metal atoms. The expansion terms for the first set, MINI -3, are 4, 3, 3, and 3 for s-type CGTO s and others are all three. The abbreviation would be (4333/33/3) where the slash divides symmetry. The expansion terms for the other set, MINI -4, is (4333/43/4). The split-type basis sets, MIDI -3 and MIDI -4, are derived directly from MINI -3 and MINI -4, MINI -3 and MIDI -3 provide the outer-shell orbital energies which are far better than those by single-zeta (SZ ) STO s. MINI -4 and MIDI -4 provide the outer-shell orbital energies which are almost as good as those by double-zeta (DZ ) STO s. The total energies given by the present sets are better than those of SZ except for MINI -3 for Sc and Ti: the energies by MINI -4 and MIDI -4 are only 0.8–1.7 a.u. higher than DZ . The basis sets were tested on the Cu₂ molecule, where a large basis set was also used.