J. A. Pople

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

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. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules

Two extended basis sets (termed 5–31G and 6–31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine. These basis functions are similar to the 4–31G set [J. Chem. Phys. 54, 724 (1971)] in that each valence shell is split into inner and outer parts described by three and one Gaussian function, respectively. Inner shells are represented by a single basis function taken as a sum of five (5–31G) or six (6–31G) Gaussians. Studies with a number of polyatomic molecules indicate a substantial lowering of calculated total energies over the 4–31G set. Calculated relative energies and equilibrium geometries do not appear to be altered significantly.

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

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. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals

Least‐squares representations of Slater‐type atomic orbitals as a sum of Gaussian‐type orbitals are presented. These have the special feature that common Gaussian exponents are shared between Slater‐type 2s and 2p functions. Use of these atomic orbitals in self‐consistent molecular‐orbital calculations is shown to lead to values of atomization energies, atomic populations, and electric dipole moments which converge rapidly (with increasing size of Gaussian expansion) to the values appropriate for pure Slater‐type orbitals. The ζ exponents (or scale factors) for the atomic orbitals which are optimized for a number of molecules are also shown to be nearly independent of the number of Gaussian functions. A standard set of ζ values for use in molecular calculations is suggested on the basis of this study and is shown to be adequate for the calculation of total and atomization energies, but less appropriate for studies of charge distribution.

Molecular orbital theory of the electronic structure of organic compounds. I. Substituent effects and dipole moments.

A recent approximate self-consistent molecular orbital theory (complete neglect of differential overlap or CNDO) is used to calculate charge distributions and electronic dipole moments of a series of simple organic molecules. The nuclear coordinates are chosen to correspond to a standard geometrical model. The calculated dipole moments are in reasonable agreement with experimental values in most cases and reproduce many of the observed trends. The associated charge distributions of dipolar molecules show widespread alternation of polarity in both saturated and unsaturated systems. These results suggest that charge alternation may be an intrinsic property of all inductive and mesomeric electronic displacements. ne of the long-term aims of quantum chemistry 0 is to provide a critical quantitative background for simple theories of electron distribution in large molecules. Most theoretical discussions of the role of electronic structure in organic chemistry are at present based either on qualitative arguments (such as the study of resonance structures) with no clear foundation in quantum mechanics, or on postulated relationships between charge distribution and various physical and chemical properties (reactivities, acidities, nmr chemical shifts, etc.), few of which can be subjected to direct test. If quantum mechanical calculations are to lead to independent methods of studying such phenomena, they ought to satisfy the following general conditions. (1) The methods must be simple enough to permit application to moderately large molecules without excessive computational effort. Quite accurate wave functions now exist for many diatomic and small polyatomic molecules, but it is unlikely that comparable functions will be readily available in the near future for the molecules of everyday interest to the organic chemist. To be accessible, a quantum mechanical theory has to be approximate. (2) Even though approximations have to be introduced, these should not be so severe that they eliminate any of the primary physical forces determining structure. For example, the relative stabilities of electrons in different energy levels, the directional character of the bonding capacity of atomic orbitals, and the electrostatic repulsion between electrons are all gross features with major chemical consequences and they should all be retained in a realistic treatment. (3) In order to be useful as an independent study, the approximate wave functions should be formulated in an unbiased manner, so that no preconceived ideas derived from conventional qualitative discussions are built in implicitly. For example, a critical theoretical study of the localization of a two-electron bond orbital ought to be based on a quantum mechanical theory which makes no reference to electron-pair bonds in its basis. Molecular orbital theories satisfy this type of condition insofar as each electron is treated as being free to move anywhere in the molecular framework. (4) The theory should be developed in such a way that the results can be interpreted in detail and used to support or discount qualitative hypotheses. For example, it is useful if the electronic charge distribution calculated from a wave function can be easily and realistically divided into contributions on individual atoms

The effect of d-functions on molecular orbital energies for hydrocarbons

Abstract Ab initio molecular orbital studies including d-functions in the basis set have been made on methane, acetylene, ethylene, ethane, propyne, allene, cyclopropene, propene and cyclopropane. It is shown that the strained cyclic molecules cyclopropene and cyclopropane are preferentially stabilized by the addition of d functions. If such functions are included, relative energies are given to an accuracy of 3 kcal/mole or better.

Self‐Consistent Molecular Orbital Methods. IV. Use of Gaussian Expansions of Slater‐Type Orbitals. Extension to Second‐Row Molecules

Least‐squares representations of the 3s and 3p Slater‐type atomic orbitals by a small number of Gaussian functions are presented. The use of these Gaussian representations in self‐consistent molecular orbital calculations extends our previous study to molecules containing second row elements. Calculated atomization energies, electric dipole moments, and atomic charges are shown to rapidly converge (with increasing number of Gaussians) to their Slater limits. Results of valence shell optimization studies on a series of second‐row compounds are nearly independent of the level of the Gaussian approximation, and they allow a set of standard molecular ξ exponents to be proposed.

Self‐Consistent Perturbation Theory. I. Finite Perturbation Methods

A general method is proposed for quantum‐mechanical study of physical properties of molecules involving polarization or distortion of the electronic structure. This consists of the calculation of self‐consistent molecular orbital wavefunctions (single determinants) in the presence of small but finite perturbations. The general theory of such methods is presented together with a preliminary discussion of numerical error.

Theory of Molecular Interactions. I. Molecular Orbital Studies of Water Polymers Using a Minimal Slater‐Type Basis

Ab initio minimal basis LCAOSCF molecular orbital calculations have been performed to determine the energies and configurations of small groups of water molecules, with particular emphasis on those aspects which are relevant to the structure of liquid water. An intermolecular potential which spans the complete range of possible relative orientations for the dimer is presented. The predicted equilibrium form of the dimer is found, together with estimates of some of the intermolecular force constants. Results of calculations on both open and cyclic polymeric water structures containing up to six molecules are included. It is found that polymers having OH···OH···OH··· chains are preferred, and that hydrogen‐bond energies deviate considerably from additivity. Cyclic structures are predicted to be most stable for the trimer and higher polymers.

Self‐Consistent Perturbation Theory. II. Nuclear‐Spin Coupling Constants

The finite pertubation method developed in the first paper of this series is applied to isotropic nuclear‐spin coupling constants, assuming that only a Fermi contact mechanism couples the electron and nuclear spins. Results for some simple systems are calculated using self‐consistent molecular orbital methods involving the neglect of differential overlap, and on the basis of these results, certain points regarding the mechanisms of spin coupling are discussed. A detailed discussion of the sources and magnitudes of the errors is also presented.