Medium basis sets based upon contractions of Gaussian primitives are developed for the third-row elements Ga through Kr. The basis functions generalize the 6-31G and 6-31G* sets commonly used for atoms up to Ar. A reexamination of the 6-31G* basis set for K and Ca developed earlier leads to the inclusion of 3d orbitals into the valence space for these atoms. Now the 6-31G basis for the whole third-row K through Kr has six primitive Gaussians for 1s, 2s, 2p, 3s, and 3p orbitals, and a split-valence pair of three and one primitives for valence orbitals, which are 4s, 4p, and 3d. The nature of the polarization functions for third-row atoms is reexamined as well. The polarization functions for K, Ca, and Ga through Kr are single set of Cartesian d-type primitives. The polarization functions for transition metals are defined to be a single 7f set of uncontracted primitives. Comparison with experimental data shows good agreement with bond lengths and angles for representative vapor-phase metal complexes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 976–984, 2001

6-31G* basis set for third-row atoms

Kraitchman has shown that a single isotopic substitution on an atom is sufficient to determine directly the coordinates of that atom with respect to the principal axes of the original molecule. Kraitchman's formulas represent exact solutions of the equations for the equilibrium moments of inertia. However, the effects of the zero‐point vibrations are such that the coordinates obtained by substitution from the ground state moments of inertia I0 are systematically less than r0. These coordinates have here been called r (substitution) or rs, and it is found that rs≃(r0+re)/2, and Is= ∑ imirsi2≃(I0+Ie)/2.In the usual method of solution, the coordinate of one atom is determined from the equation for I0, and therefore the difference I0—Is must be made up by this one coordinate. This introduces a large error in the structures normally determined from ground state constants, and results in variations of 0.01 A in structures determined from different sets of isotopic species. If instead, we obtain the structure on...

A new criterion for the determination of molecular structures from ground state rotational constants

Basis sets have been developed for carrying out G2 calculations on bromine‐ and iodine‐containing molecules using all‐electron (AE) calculations and quasirelativistic energy‐adjusted spin–orbit‐averaged seven‐valence–electron effective core potentials (ECPs). Our recommended procedure for calculating G2[ECP] energies for such systems involves the standard G2 steps introduced by Pople and co‐workers, together with the following modifications: (i) second‐order Mo/ller–Plesset (MP2) geometry optimizations use polarized split‐valence [31,31,1] basis sets for bromine and iodine together with 6‐31G(d) for first‐ and second‐row atoms; (ii) single‐point higher‐level energies are calculated for these geometries using our new supplemented bromine and iodine valence basis sets along with supplemented 6‐311G and McLean–Chandler 6‐311G bases for first‐ and second‐row atoms, respectively; and (iii) first‐order spin–orbit corrections are explicitly taken into account. An assessment of the results obtained using such a procedure is presented. The results are also compared with corresponding all‐electron calculations. We find that the G2[ECP] calculations give results which are generally comparable in accuracy to those of the G2[AE] calculations but which involve considerably lower computational cost. They are therefore potentially useful for larger bromine‐ and iodine‐containing molecules for which G2[AE] calculations would not be feasible.

Extension of Gaussian‐2 (G2) theory to bromine‐ and iodine‐containing molecules: Use of effective core potentials

We present a new relativistic formulation for the calculation of nuclear magnetic resonance (NMR) shielding tensors. The formulation makes use of gauge-including atomic orbitals and is based on density functional theory. The relativistic effects are included by making use of the zeroth-order regular approximation. This formulation has been implemented and the 199Hg NMR shifts of HgMe2, HgMeCN, Hg(CN)2, HgMeCl, HgMeBr, HgMeI, HgCl2, HgBr2, and HgI2 have been calculated using both experimental and optimized geometries. For experimental geometries, good qualitative agreement with experiment is obtained. Quantitatively, the calculated results deviate from experiment on average by 163 ppm, which is approximately 3% of the range of 199Hg NMR. The experimental effects of an electron donating solvent on the mercury shifts have been reproduced with calculations on HgCl2(NH3)2, HgBr2(NH3)2, and HgI2(NH3)2. In addition, it is shown that the mercury NMR shieldings are sensitive to geometry with changes for HgCl2 of a...

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Density functional calculations of nuclear magnetic shieldings using the zeroth-order regular approximation (ZORA) for relativistic effects: ZORA nuclear magnetic resonance

The anharmonic force field of methane has been refined to fit spectroscopic data from the isotopic species 12CH4, 13CH4, 12CH4, 12CH3D, 12CHD3 and 12CH2D2. Six of the thirteen cubic force constants have been determined experimentally, the remaining cubic constants being fixed at values derived from ab initio calculations. The quartic force field is very crude, in that only frrrr has been refined. It is concluded however that the cubic and quartic force fields, even though they are subject to limitations, provide a considerable improvement in the experimental determination of the r e structure and the quadratic force field. The equilibrium bond length is found to be r e(CH) = 1·0858 ± 0·001 A.

The anharmonic force field and equilibrium structure of methane

The methyl bromide molecule: A critical consideration of perturbations in spectra

Accurate ground state rotational constants and reliable vibration-rotation interaction constants are available for CO2 and its isotopomers. Therefore CO2 has been used as a test case to study the various internuclear distances. We found that the r 0 distances appear, for a given carbon isotope, as a linear function of the inverse of the reduced mass. The r 3 distances obtained, even from purely ‘theoretical’ parameters, still show a small isotopic dependence. Finally Watson's method seems to yield, in the present case, r m distances differing from r e by only 5 × 10-5 A.

The carbon dioxide molecule

Simultaneous analysis of the ν1, ν4, 2ν2, ν2 + ν5, and 2ν5 infrared bands of 12CH3F

Simultaneous analysis of the 2ν2, 2ν5, and ν2 + ν5 vibration-rotation bands of CH3Br

The direct determination of the ground-state rotational constants A 0 and D 0 K of methyl fluoride has been accomplished through ground-state combination differences including perturbation-allowed transitions. The values found are A 0 = 5·182009 ± 0·000012 and D 0 K = (70·33 ± 0·25) × 10-6 cm-1. The ‘ normal ’ GSCD have also been used, in conjunction with microwave transitions, to yield improved values for the other rotational constants, including values for H 0 J K and H 0 KJ .

G. Graner

Papers

The methyl bromide molecule: A critical consideration of perturbations in spectra

The carbon dioxide molecule

Simultaneous analysis of the ν1, ν4, 2ν2, ν2 + ν5, and 2ν5 infrared bands of 12CH3F

Simultaneous analysis of the 2ν2, 2ν5, and ν2 + ν5 vibration-rotation bands of CH3Br

Determination of A 0 for CH3F from ground-state combination differences