J. Stephen Binkley

Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets

Standard sets of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions (f functions) are defined for use with the 6‐31G and 6‐311G basis sets. Preliminary applications of the modified basis sets to the calculation of the bond energy and hydrogenation energy of N2 illustrate that these functions can be very important in the accurate computation of reaction energies.

Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements

The 6‐31G* and 6‐31G** basis sets previously introduced for first‐row atoms have been extended through the second‐row of the periodic table. Equilibrium geometries for one‐heavy‐atom hydrides calculated for the two‐basis sets and using Hartree–Fock wave functions are in good agreement both with each other and with the experimental data. HF/6‐31G* structures, obtained for two‐heavy‐atom hydrides and for a variety of hypervalent second‐row molecules, are also in excellent accord with experimental equilibrium geometries. No large deviations between calculated and experimental single bond lengths have been noted, in contrast to previous work on analogous first‐row compounds, where limiting Hartree–Fock distances were in error by up to a tenth of an angstrom. Equilibrium geometries calculated at the HF/6‐31G level are consistently in better agreement with the experimental data than are those previously obtained using the simple split‐valance 3‐21G basis set for both normal‐ and hypervalent compounds. Normal‐mode vibrational frequencies derived from 6‐31G* level calculations are consistently larger than the corresponding experimental values, typically by 10%–15%; they are of much more uniform quality than those obtained from the 3‐21G basis set. Hydrogenation energies calculated for normal‐ and hypervalent compounds are in moderate accord with experimental data, although in some instances large errors appear. Calculated energies relating to the stabilities of single and multiple bonds are in much better accord with the experimental energy differences.

Extensive theoretical studies of the hydrogen‐bonded complexes (H2O)2, (H2O)2H+, (HF)2, (HF)2H+, F2H−, and (NH3)2

The structures and binding energies of the complexes (H2O)2, (H2O)2H+, (HF)2, (HF)2H+, F2H−, and (NH3)2 have been examined using much higher levels of theory than has been previously applied to these systems. These methods including large basis sets and full optimization of structures with the effects of electron correlation included, are known to give single bond energies to an accuracy of about 2 kcal mol−1 and are found in this study to give excellent agreement with the extensive experimental data available for the hydrogen fluoride and water dimers. The Cs openform of ammonia dimer remains a very shallow minimum energy structure at these levels, in agreement with previous theoretical results but seemingly in disagreement with experiment. The theoretical enthalpy of association of H5O+2 is found to be −35.0 kcal mol−1, in slight disagreement with the most recent experimental results, but in accord with earlier ones, which suggests that these experiments should be reexamined. The enthalpy of association...

Self‐consistent molecular orbital methods. XVII. Geometries and binding energies of second‐row molecules. A comparison of three basis sets

Three basis sets (minimal s–p, extended s–p, and minimal s–p with d functions on second row atoms) are used to calculate geometries and binding energies of 24 molecules containing second row atoms. d functions are found to be essential in the description of both properties for hypervalent molecules and to be important in the calculations of two‐heavy‐atom bond lengths even for molecules of normal valence.

Analytic Raman intensities from molecular electronic wave functions

An analytic method for the evaluation of Ramanintensities from closed−shell self‐consistent‐field wave functions is presented. Predictioinsf or ethylenemolecule are also reported. (AIP)

Analytic evaluation and basis set dependence of intensities of infrared spectra

Equations are presented for the analytic determination of dipole moment derivatives with respect to nuclear coordinates for closed‐shell, open‐shell unrestricted, and open‐shell restricted Hartree–Fock wave functions. The efficient evaluation of these derivatives and the resulting infrared intensities simultaneously with determination of the vibrational frequencies is discussed. Intensities are presented for a selection of test molecules with a wide variety of basis sets. It is concluded that basis sets of double‐zeta polarized or higher quality usually give correct qualitative information about the ordering of the intensities, while smaller basis sets may not even predict the most intense mode correctly. Quantitative accuracy using the larger basis sets seems to be limited primarily by the use of the double harmonic approximation.

The malonaldehyde equilibrium geometry: A major structural shift due to the effects of electron correlation

Complete theoretical optimizations of the equilibrium geometry of malonaldehyde have been carried out within the framework of the self‐consistent‐field (SCF) approximation. Both Huzinaga–Dunning double zeta plus polarization (DZ+P) and Pople 6–31G** basis sets have been used, resulting in very similar results. The predicted O ⋅ ⋅ ⋅ H hydrogen bond distance is 1.88 A, in poor agreement with the value 1.68 A deduced from experiment. It appears that the Hartree–Fock approximation is incapable of describing the equilibrium geometry of malonaldehyde in a qualitatively correct manner. However, second‐order perturbation theory yields a structure (O ⋅ ⋅ ⋅ H distance 1.69 A) in good agreement with experiment. The structures of the keto tautomer and the transition state for symmetric intramolecular hydrogen transfer have also been determined, as have harmonic vibrational frequencies for all stationary points.

First and second derivatives of two electron integrals over Cartesian Gaussians using Rys polynomials

Formulas are developed for the first and second derivatives of two electron integrals over Cartesian Gaussians. Integrals and integral derivatives are evaluated by the Rys polynomial method. Higher angular momentum functions are not used to calculate the integral derivatives; instead the integral formulas are differentiated directly to produce compact and efficient expressions for the integral derivatives. The use of this algorithm in the ab initio molecular orbital programs gaussian 80 and gaussian 82 is discussed. Representative timings for some small molecules with several basis sets are presented. This method is compared with previously published algorithms and its computational merits are discussed.

Abinitio calculation of reaction energies. III. Basis set dependence of relative energies on the FH2 and H2CO potential energy surfaces

The relative energies of the stationary points on the FH2 and H2CO nuclear potential energy surfaces relevant to the hydrogen atom abstraction, H2 elimination and 1,2‐hydrogen shift reactions have been examined using fourth‐order Mo/ller–Plesset perturbation theory and a variety of basis sets. The theoretical absolute zero activation energy for the F+H2→FH+H reaction is in better agreement with experiment than previous theoretical studies, and part of the disagreement between earlier theoretical calculations and experiment is found to result from the use of assumed rather than calculated zero‐point vibrational energies. The fourth‐order reaction energy for the elimination of hydrogen from formaldehyde is within 2 kcal mol−1 of the experimental value using the largest basis set considered. The qualitative features of the H2CO surface are unchanged by expansion of the basis set beyond the polarized triple‐zeta level, but diffuse functions and several sets of polarization functions are found to be necessary ...

The quantum mechanical calculation of rotational spectra. A comparison of methods for C2H2, HCN, HNC, HCO+, N2H+, CO and N2. Predictions for HCNH+, COH+, HBO, HBNH, and HBF+.

Rotational frequencies determined with ab initio molecular orbital theory can play an important role in guiding spectroscopic searches for new molecules and in corroborating the assignment of unidentified lines, from the laboratory and from space. In a systematic study of 22 levels of molecular orbital theory, CISD/6-311G** gave rotational frequencies to an accuracy of +/- 0.4 GHz when an empirical correction is applied to the results for C2H2,HCN, HNC, HCO+, N2H+, CO, and N2. Larger errors can be expected when there are large vibrational effects on the rotational constants, as exemplified by COH+. Predicted J = 0--> 1 rotational frequencies using these methods are 73.9 +/- 0.4 GHz for HCNH+, 78.6 +/- 0.4 GHz for HBO, 65.8 +/- 0.4 GHz for HBNH, and 72.1 +/- 0.4 GHz for HBF+.