A contracted Gaussian basis set (6‐311G**) is developed by optimizing exponents and coefficients at the Mo/ller–Plesset (MP) second‐order level for the ground states of first‐row atoms. This has a triple split in the valence s and p shells together with a single set of uncontracted polarization functions on each atom. The basis is tested by computing structures and energies for some simple molecules at various levels of MP theory and comparing with experiment.

Self‐consistent molecular orbital methods. XX. A basis set for correlated wave functions

An extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first‐row atoms carbon to fluorine. In this set, described as 4–31 G, each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively. The expansion coefficients and Gaussian exponents are determined by minimizing the total calculated energy of the atomic ground state. This basis set is then used in single‐determinant molecular‐orbital studies of a group of small polyatomic molecules. Optimization of valence‐shell scaling factors shows that considerable rescaling of atomic functions occurs in molecules, the largest effects being observed for hydrogen and carbon. However, the range of optimum scale factors for each atom is small enough to allow the selection of a standard molecular set. The use of this standard basis gives theoretical equilibrium geometries in reasonable agreement with experiment.

Self‐Consistent Molecular‐Orbital Methods. IX. An Extended Gaussian‐Type Basis for Molecular‐Orbital Studies of Organic Molecules

A method of ‘‘natural population analysis’’ has been developed to calculate atomic charges and orbital populations of molecular wave functions in general atomic orbital basis sets. The natural analysis is an alternative to conventional Mulliken population analysis, and seems to exhibit improved numerical stability and to better describe the electron distribution in compounds of high ionic character, such as those containing metal atoms. We calculated ab initio SCF‐MO wave functions for compounds of type CH3X and LiX (X=F, OH, NH2, CH3, BH2, BeH, Li, H) in a variety of basis sets to illustrate the generality of the method, and to compare the natural populations with results of Mulliken analysis, density integration, and empirical measures of ionic character. Natural populations are found to give a satisfactory description of these molecules, providing a unified treatment of covalent and extreme ionic limits at modest computational cost.

Natural population analysis

Describes and discusses the use of theoretical models as an alternative to experiment in making accurate predictions of chemical phenomena. Addresses the formulation of theoretical molecular orbital models starting from quantum mechanics, and compares them to experimental results. Draws on a series of models that have already received widespread application and are available for new applications. A new and powerful research tool for the practicing experimental chemist.

AB INITIO Molecular Orbital Theory

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 25. Supplementary functions for Gaussian basis sets

The polarized absorption spectra for single crystals of 1-methylthymine and 9-methyladenine and hydrogen-bonded complex of the two have been determined. A 
microspectro-photometer was constructed to carry out these measurements. A technique for preparing thin sections of the single crystals with thicknesses down to 10^(-5) cm has been developed. Special attention has been given to intensity determinations for the several ultraviolet absorption spectra.

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Polarized absorption spectra of purines and pyrimidines

Expansions of Clementi STO SCF AO's for some first‐row atoms with GTO's have been obtained by the method of least squares. Expansion lengths vary from two to five Gaussians for each AO. In addition, Gaussian sets with constraints that the exponential parameters be shared for 1s and 2s and 2s and 2p orbital expansions are reported. For all cases a full matrix least‐squares procedure was employed whereby the expansion coefficients and exponential parameters were simultaneously varied. All orbital expansions were constrained to a normalization condition. These expansions are useful for computing x‐ray scattering factors and can be used in quantum‐chemical studies.

Small Gaussian Expansions of Atomic Orbitals

Experimental Charge-Density Study of Methylammonium Hydrogen Succinate Monohydrate - A Salt with a Very Short O-H-O Hydrogen-Bond

Extensive and precise X-ray diffraction data for xylitol have been used to test different approaches to estimate nuclear parameters for H atoms in charge-density studies. The parameters from a neutron diffraction study of the same compound were taken as a reference. The resulting static charge densities obtained for the different approaches based on a multipole model were subjected to a topological analysis. The comparative analysis led to the following results. The procedure of extending the X-H bond to match bond lengths from neutron diffraction studies provides the best agreement with the neutron positional parameters. An isotropic model for the atomic displacements of H atoms is highly unsatisfactory and leads to significant deviations for the properties of the bond critical points including those that only involve non-H atoms. Anisotropic displacement parameters for H atoms can be derived from the X-ray data that are in agreement with the values from the neutron study, and the resulting charge-density models are in good agreement with the reference model. The anisotropic displacement parameters for H atoms are derived from the X-ray data as a sum of the external (rigid-body) and internal vibrations. The external vibrations are obtained from a TLS analysis of the ADPs of the non-H atoms and the internal vibrations from analysis of neutron diffraction studies of related compounds. The results from the analysis of positional and thermal parameters were combined to devise a 'best anisotropic' model, which was employed for three other systems where X-ray and neutron data were available. The results from the topological analysis of these systems confirm the success of the 'best anisotropic' model in providing parameters for the H atoms that give charge densities in agreement with the reference models based on H-atom parameters derived from neutron diffraction.

Modeling of the nuclear parameters for H atoms in X-ray charge-density studies.

Generalized x‐ray scattering factors for atoms (pseudoatoms) in diatomic molecules are determined from a finite multipole expansion of the charge density about each nucleus. The Fourier–Bessel coefficients of the pseudoatom radial density functions are determined by a least squares fit to the molecular form factor. All molecular one‐center averages of the form 〈g (ra) Pj(cosϑa) 〉 are correctly given by the pseudoatom superposition whenever j?J, where J is the highest order multipole included in the a pseudoatom, regardless of the highest multipole order K for the b pseudoatom. To illustrate this property, a number of relationships between moments of the molecular charge distribution and of the pseudoatom are given. In addition, a sum rule relating the molecular form factor to the expectation values 〈ra−(j+1)Pj(cosϑa) 〉 and 〈rb−(k+1)Pk(cosϑb) 〉 is derived. For H2 the theoretical, coherent x‐ray scattering intensity is reproduced to about 1% for J=K=1 and to about 0.1% for J=K=2.

Robert F. Stewart

Papers

Polarized absorption spectra of purines and pyrimidines

Small Gaussian Expansions of Atomic Orbitals

Experimental Charge-Density Study of Methylammonium Hydrogen Succinate Monohydrate - A Salt with a Very Short O-H-O Hydrogen-Bond

Modeling of the nuclear parameters for H atoms in X-ray charge-density studies.

Generalized x‐ray scattering factors in diatomic molecules