Cation Diffusion and Conductivity in Solid Electrolytes. II. Mathematical Analyses
This paper constitutes Paper II of the series and presents theoretical analysis and supplements the results shown in Paper I. Equilibrium properties of the layer in which Na ions exist in - and -alumi...
This paper constitutes Paper II of the series and presents theoretical analysis and supplements the results shown in Paper I. Equilibrium properties of the layer in which Na ions exist in - and -alumi...
Exciton Superexchange, Resonance Pairs, and Complete Exciton Band Structure of 1B2u Naphthalene
A method for the determination of complete exciton band structures in molecular crystals is given. Pairwise exciton interactions are derived from resonance-pair data using an exciton “superexcha...
A method for the determination of complete exciton band structures in molecular crystals is given. Pairwise exciton interactions are derived from resonance-pair data using an exciton “superexcha...
Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First-Row Atoms
J. Chem. Phys. 55, 716 (1971); doi:10.1063/1.1676139
Issue Date: 15 July 1971
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Contracted [5s3p] and [5s4p] Gaussian basis sets for the first-row atoms are derived from the (10s6p) primitive basis sets of Huzinaga. Contracted [2s] and [3s] sets for the hydrogen atom obtained from primitive sets ranging in size from (4s) to (6s) are also examined. Calculations on the water and nitrogen molecules indicate that such basis sets when augmented with suitable polarization functions should yield wavefunctions near the Hartree–Fock limit.
©1971 American Institute of Physics
| History: | Received 1 March 1971 |
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REFERENCES (15)
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- T. H. Dunning, Jr., J. Chem. Phys. 53, 2823 (1970).
- T. H. Dunning, Jr., “Gaussian Basis Functions for Use in Molecular Calculations. IV. The Representation of Polarization Functions for the First-Row Atoms and Hydrogen,” J. Chem. Phys. (to be published).
- S. Huzinaga, J. Chem. Phys. 42, 1293 (1965).
- J. W. Moskowitz, D. B. Neumann, and M. C. Harrison, in Quantum Theory of Atoms, Molecules and the Solid State, edited by P.-O. Löwdin (Academic, New York, 1966);
- See also T. H. Dunning, Jr.,
Chem. Phys. Letters 7, 423 (1970) . - In the contraction splitting m(P/Q/
![[centered ellipsis]](http://scitation.aip.org/stockgif3/cellip.gif)
) indicates that for the m functions the first P primitives are contracted together, the next Q together, etc. Unless otherwise noted the functions are arranged in order of decreasing orbital exponents. The contraction coefficients are taken directly from the atomic calculations. - Cnm is the coefficient of the primitive function n in the atomic m orbital. Primitive functions are ordered according to decreasing orbital exponent.
- Following the established convention, primitive sets will be denoted by parentheses while brackets indicate that the set has been contracted.
- Even for the second-row atoms, where there are two parameters and three conditions to be satisfied (because of the 3s orbital), it has been found that obtaining x and y from Eq. (1) leads to quite satisfactory results, e.g., for the chlorine atom the resulting increase in the energy is only 3×10−6 a.u.
- S. Huzinaga and C. Arnau, J. Chem. Phys. 52, 2224 (1970).
- H. Basch (private communication).
- The primitive sets were obtained from Ref. 3.
- Note, however, that the difference in the energy for water obtained with the [5s3p/2s] and [5s3p/3s] sets of Ref. 1 is nearly as large, 0.0012 a.u.
- W. S. Benedict, N. Gailar, and E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
- For example, with a [6s5p/3s] set derived from an (11s7p/5s) primitive set we obtain for the water molecule (all in atomic units): EHF = −76.0242, µ = 1.0697,
zz = −0.1427, Ez(0) = −0.1348, and qxx(0) = −1.8755.
