Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions (original) (raw)
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Theoretical Chemistry Accounts, 2005
Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).
An efficient basis set representation for calculating electrons in molecules
Molecular Physics, 2016
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one-and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N )) multiplication operations, not O(N 4 ), where N is the number of basis functions; N = n 3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one-(He + , H + 2 ), two-(H2, He), ten-(CH4) and 56-electron (C8H8) systems.
Journal of the Chemical Society, 1975
A new procedure for closely approximating the results of complete ab initio molecular orbital calculations is presented, evaluated, and applied to a few molecules. This simulated ab initio molecular orbital (SAMO) method consists in transferring ab initio Hartree-Fock matrix elements from calculations on pattern molecules, thereby avoiding repeated lengthy calculations of two-electron repulsion integrals. The matrix elements involve conventional hybridized and unhybridized atomic orbitals and are ultimately basis independent. The SAMO applications yield MO eigenspectra and eigenfunctions which reproduce complete results with unprecedented accuracy.
Newly developed basis sets for density functional calculations
Journal of Computational Chemistry, 2005
Optimized contracted Gaussian basis sets of double-zeta valence polarized (DZVP) quality for first-row transition metals are presented. The DZVP functions were optimized using the PWP86 generalized gradient approximation (GGA) functional and the B3LYP hybrid functional. For a careful analysis of the basis sets performance the transition metal atoms and cations excitation energies were calculated and compared with the experimental ones. The calculated values were also compared with those obtained using the previously available DZVP basis sets developed at the local-density functional level. Because the new basis sets work better than the previous ones, possible reasons of this behavior are analyzed. The newly developed basis sets also provide a good estimation of other atomic properties such as ionization energies.
Wiley Interdisciplinary Reviews: Computational Molecular Science, 2012
Electronic structure methods for molecular systems rely heavily on using basis sets composed of Gaussian functions for representing the molecular orbitals. A number of hierarchical basis sets have been proposed over the last two decades, and they have enabled systematic approaches to assessing and controlling the errors due to incomplete basis sets. We outline some of the principles for constructing basis sets, and compare the compositions of eight families of basis sets that are available in several different qualities and for a reasonable number of elements in the periodic table.
Physical Review A, 1998
The now well-established L2 techniques applied to the description of the electronic continuum of small molecules and generally implemented with suitable oscillating basis sets are here adapted and used in connection with Gaussian type orbital (GTO) functions. As a test, a K-matrix approach associated with extended sets of GTOs is employed to compute with satisfactory accuracy partial wave phase shifts and both the integral and differential photoionization cross sections of the hydrogen molecule. It is apparently possible to greatly extend the range of applicability of the usual L2 techniques beyond the limited set of molecular systems amenable to the one center expansion approximation.
Theoretica Chimica Acta, 1992
The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of Bill 3 (-0. 4 9 9 a.u.), Poll 2 (-0. 2 0 7 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to-0.230a.u.,-0.177a.u., and-0. 0 9 7 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.