Contracted Basis Sets Research Articles

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

Generally contracted Basis sets for the atoms H-Kr have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANO's are constructed by averaging over the most significant electronic states, the ground state of the cation, the ground state of the anion for some atoms and the homonuclear diatomic molecule at equilibrium distance for some atoms. The contracted basis sets yield excellent results for properties of molecules such as bond-strengths and-lengths, vibrational frequencies, and good results for valence spectra, ionization potentials and electron affinities of the atoms, considering the small size of these sets. The basis sets presented in this article constitute a balanced sequence of basis sets suitable for larger systems, where economy in basis set size is of importance.

Kinetic balance in contracted basis sets for relativistic calculations

A demonstration of kinetic balance failure in heavily contracted basis sets is given. Other possible methods of constructing small component basis sets for 4-component relativistic calculations are discussed. The position of the additional negative energy levels in extended balance calculations in some recent many-electron calculations is examined.

Hartree-fock ab initio study of relaxation and electronic structure of lithium oxide slabs

Slabs from one to six layers thick were studied with the CRYSTAL ab initio program in order to test their suitability for simulating the (111) and (110) surfaces of a semi-infinite Li 2O crystal. The use of a contracted basis set was first tested by comparing several crystalline properties to those previously obtained with an extended basis set. Relaxed geometric structures and the surface formation energy were then determined and their electronic properties, band structure, density of states and orbital populations were established.

Compact contracted basis sets for third‐row atoms: Ga–Kr

AbstractThe (14s11p5d) primitive basis set of Dunning for the third‐row main group atoms Ga‐Kr has been contracted [6s4p1d]. The core functions have been relatively highly contracted while those which represent the valence region have been left uncontracted to maintain flexibility. Calculations with the [6s4p1d] contraction are reported for a variety of molecules involving third‐row atoms. This basis set is found to satisfactorily reproduce experimental properties such as geometric configurations, dipole moments, and vibrational frequencies for a range of molecules. Comparisons are made with the performance of the uncontracted basis set. Polarization functions for the contracted basis set are reported and performance of the basis set with and without polarization functions is examined. A relaxation of the [6s4p1d] contraction to [9s6p2d] for higher level evergy calculations is also presented.

Quasi-adiabatic basis functions for the S-matrix Kohn variational approach to quantum reactive scattering

A basis set contraction scheme is described for carrying out reactive scattering calculations within the S-matrix version of the Kohn variational principle. The new basis functions are distributed Gaussians for the radial (translational) degrees of freedom, as used before, but with quasi-adiabatic internal eigenfunctions for the internal degrees of freedom; i.e., each translational Gaussian has a different internal function, the adiabatic internal eigenfunction for that translational coordinate at which the Gaussian is centered. A very efficient and easy-to-use criterion is given for selecting which of these L{sup 2} functions to include in the basis. Application to the three-dimensional H + H{sub 2} reaction for various values of total angular momentum shows that accurate results can be obtained with half (or fewer) the number of basis functions that are necessary when asymptotic channel eigenfunctions are used for the internal degrees of freedom. The basis function selection criterion allows one to obtain moderately accurate results with very few basis functions and then to improve the accuracy systematically by increasing the basis in a determined fashion.

Efficient computation of two-electron - repulsion integrals and their nth-order derivatives using contracted Gaussian basis sets

We present an general algorithm for the evaluation of the nth derivatives (with respect to the nuclear Cartesian coordinates) of two-electron-repulsion integrals (ERIs) over Gaussian basis functions. The algorithm is a generalization of our recent synthesis of the McMurchie/Davidson and Head-Gordon/Pople methodologies for ERI generation. Any ERI nth derivative may be viewed as an inner product between a function (which we term a bra) of electron 1 and a function (which we term a key) of electron 2. After defining bras and kets appropriately, we derive five recurrence relations that enable any bra to be constructed recursively from very simple bras which we call p-bras

Translational basis set contraction in variational reactive scattering

A new translational basis set is introduced for quantum reactive scattering calculations that use the log derivative version of the Kohn variational principle. This basis set, which is similar in many respects to that used in electron–atom scattering calculations by Burke and Robb, is obtained by contracting a primitive basis of Lobatto shape functions to the box eigenfunctions of a one-dimensional reference Hamiltonian H0. In addition, a single energy-dependent scattering function is included in the variational expansion to ensure completeness at the boundary of the box. One fairly obvious choice for the reference Hamiltonian in an atom–diatom reaction is suggested, and all of the equations which are actually needed to implement the method in this context are carefully described. Example applications to the three-dimensional F+H2 reaction are then chosen to illustrate the practical potential of the approach.

Molecular geometry and frequencies of vibration of the molecule Li 2CO 3

Molecular orbital calculations are reported for different structures of the molecule Li 2CO 3. The calculations were carried out at the RHF-SCF level employing contracted Gaussian basis sets 3-21G and 3-21G*. Configurations of C 2v and C 3v symmetry were examined and were found to be stationary points. The bidentate structure is the stable equilibrium form of Li 2CO 3 while the monodentate one is a saddle point for lithium atom migration around the group CO 2− 3. The non-planar C 3v structure is the highest energy point on the hypersurface explored. Harmonic frequencies of vibration were computed for CO 2− 3 and bidentate C 2v symmetry Li 2CO 3.

A program system for ab initio mo calculations on vector and parallel processing machines I. Evaluation of integrals

We present a program system for ab initio molecular orbital calculations on vector and parallel computers. The present article is devoted to the computation of one- and two-electron integrals over contracted Gaussian basis sets involving s-, p-, d- and f-type functions. The McMurchie and Davidson (MMD) algorithm has been implemented and parallelized by distributing over a limited number of logical tasks the calculation of the 55 relavant classes of integrals. All sections of the MMD algorithm have been efficiently vectorized, leading to a scalar/vector ratio of 5.8. Different algorithms are proposed and compared for an optimal vectorization of the contraction of the “intermediate integrals” generated by the MMD formalism. Advantage is taken of the dynamic storage allocation for tunning the lenght of the vector loops (i.e. the size of the vectorization buffer) as a function of (i) the total memory available for the job, (ii) the number of logical tasks defined by the user (≤13), and (iii) the storage requested by each specific class of integrals. Test calculations carried out on a CRAY-2 computer show that the average number of finite integrals computed over a (s,p,d,f) CGTO basis set is about 118000 per second and per processor. The combination of vectorization and parallelism on this 4-processor machine reduces the CPU time by a factor larger than 20 with respect to the scalar and sequential performance.

Effects of basis set contraction in relativistic calculations on neon, argon, and germanium

Calculations on neon, argon, and germanium have been performed with basis sets of contracted and uncontracted Gaussian-type functions. Both relativistic and non-relativistic Hartree—Fock and many-body perturbation theory calculations have been performed with the intent of observing to what extent basis set contraction affects calculated relativistic and correlation contributions to total atomic energy. It is found that even severe contraction has relatively little effect on calculated relativistic effects.

General contraction of Gaussian basis sets. II. Atomic natural orbitals and the calculation of atomic and molecular properties

Our recently proposed scheme for using natural orbitals from atomic configuration interaction wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outermost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital sets.

Contracted well-tempered Gaussian basis sets in SCF calculations on the ground and excited electronic states of neutral and ionized diatomic molecules containing first-row atoms

Calculations were done on ground and excited states of C2, C2+, C2−, N2, N2+, O2, O2+, O2−, CO, CO+, CO2+, and CO− using contracted well-tempered basis sets. The (14s 10p) basis sets were augmented with threed, one or twof, and oneg functions. Total energies, orbital energies, and spectroscopic constants were compared with the best available computational data.

An adapted form of the collocation method for calculating energy levels of rotating atom–diatom complexes

A method is presented for calculating energy levels of atom–rigid-diatom systems for various values of the total angular momentum (J) of the complex. The technique is based upon the collocation method for the vibrational motions of the system and the Galerkin approach for the total rotation. Unlike the Rayleigh–Ritz variational principle, the method does not require the evaluation of integrals over the Hamiltonian and so is very simple to implement. An important feature of the method is that the wave function is obtained in an analytic form and so it is a simple matter to calculate many quantities of spectroscopic interest such as rotational constants and spectral intensities. It is also shown that contracted basis sets can be used in conjunction with the collocation method to enhance the efficiency of the calculation. The method is demonstrated by calculating rovibrational levels of the van der Waals complex Ar–HCl for J up to 10.

Calculation of spin densities in diatomic first-row hydrides

Fermi contact spin densities have been theoretically determined for the ground-state diatomic first-row hydrides CH, OH, and NH having open shell π electrons. Multiconfiguration self-consistent-field wave functions include the dominant configuration and single excitations from it describing the most important spin and orbital polarization effects. Optimization of the orbitals by precise numerical grid methods shows that this simple wave function model is capable of providing spin densities in satisfactory agreement with experiment. Gaussian basis sets suitable for use with this wave function model are determined by comparing to the precise numerical spin density results. Huzinaga’s popular (9s5p‖4s) primitive Gaussian basis provides a good starting point if augmented with diffuse and polarization functions and with a tight (high exponent) s function at hydrogen. Only the innermost few primitive functions may be contracted. Contraction coefficients may be determined on the basis of free atom Hartree–Fock calculations. These studies lead to economical contracted Gaussian basis sets that should be useful for spin density calculations on larger polyatomic radicals.

Contraction of the well‐tempered Gaussian basis sets: The first‐row diatomic molecules

AbstractThe well‐tempered Gaussian basis sets (14s 10p) for atoms from lithium to neon were contracted and used in restricted Hartree–Fock calculations on 13 systems: Li2(Σ), B2(Σ), C2(Σ), N2(Σ), O2(Σ), F2(Σ), Ne2(Σ), LiF(Σ), BeO(Σ), BF(Σ), CN−(Σ), CO(Σ), and NO+(Σ). Spectroscopic constants (Re, ωe, ωexe, Be, αe, and ke) and one‐electron properties (dipole, quadrupole, and octupole moments at the center of mass and electric field, electric field gradient, potential, and electron density at the nuclei) were evaluated and compared with the Hartree–Fock results. The largest contracted basis set (7s6p3d) gives results very close to the Hartree–Fock values; the remaining differences are attributed to the absence of the f functions in the present basis sets. For Ne2, the interaction energy was calculated; the magnitude of the basis‐set superposition error was found to be very small (less than 3 μEh at 2.8 a0 and less than 2 μEh at 5.0 a0).

Quantum chemical applications of the theory of the distance between subspaces

The theory for the characterization of pairs of subspaces, previously developed by Jankowski, is rederived from the concept of distance between vectors and generalized. Moreover, several new applications of the theory are proposed. In particular, it is shown that the theory is useful for introducing quality criteria on the wave functions, for solving the basis set reduction or contraction problems and for obtaining trial orbitals in variational calculations. These applications are clarified in several examples.

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

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.

Ab initio mo calculation of nuclear quadrupole coupling constants of 2H, 7Li and 35Cl in LiCl and HCl molecules

Nuclear quadrupole coupling constants (nqcc) of 2H, 7Li and 35Cl in ionic LiCl and polar HCl are calculated at ab initio level, employing contracted Gaussian basis sets augmented with bond functions (BF) and BF + negative ion function. Results obtained with polarisation function (PF) along with BF are also reported and compared with other calculated values. It is found that the quadrupole coupling obtained with basis sets employing BF are in fair agreement with experiment. The negative ion function on the other hand, is found to be necessary on Cl atom in both LiCl and HCl.

Effects of contraction and reduction of basis set size on the He2 interaction energy components

AbstractThe effect of basis set contraction and elimination of primitive Gaussian orbitals on the He2 interaction energy components have been studied within the SCF counterpoise corrected approach supplemented by a dispersion term calculated within the variation‐perturbation scheme. Despite elimination of almost half of the primitive Gaussian functions from the saturated sp basis set and complete contraction of the remaining ones, the components of interaction energy in He2 suffer a remarkably small loss of accuracy except for the short range charge transfer contribution.

Localized representations for large amplitude molecular vibrations

Two novel, closely related variational quantum approaches for efficient and accurate calculation of highly excited vibrational levels of triatomic molecules are presented. The two approaches employ, in slightly different ways, the discrete variable representation (DVR) and the distributed Gaussian basis (DGB) for representation of the internal degrees of freedom. The scope of their applicability is broad; they are particularly suitable for molecules having one or more large amplitude vibrations, on potential surfaces with several local minima. Although formulated in Jacobi and hyperspherical coordinates, respectively, both approaches can be implemented in any coordinate system for which suitable DVRs can be defined. The DVR allows us to define sequentially problems of lower dimensionality, whose truncated sets of eigenvectors serve as very compact, contracted basis sets for the higher dimensional problem. Other important advantages of the DVR-DGB approaches, as well as applications to molecules like LiCN/LiNC, HCN/HNC and H 2O, are discussed.